PATENT ABSTRACT
For a mulitlayer chip carrier module a computer program receives a large plurality of module design parameters and provides as output a graphical representation of the design together with text files that rate module wireability, including die pad position, attachment of each die pad to its BGA pad, and net cross-over; and quantifies the number of redistribution layers; summarizes input parameters; creates a truth table for rating wireability and thermal requirements; and provides cost sensitive parameters.

PATENT DESCRIPTION
CROSS-REFERENCE TO RELATED PATENT APPLICATION 
     This application is a continuation-in-part application of Ser. No. 09/429,990, filed on Oct. 29, 1999. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention pertains to the modeling and estimating of substrate characteristics in preferably multi-layer chip carrier designs. More particularly, the invention is directed to physical modeling of electronic modules, including the interconnection of chip and chip carriers, such as the count calculation of chip carrier layers in order to optimize chip carrier designs by employing surface laminar circuitry (SLC) or buildup technology; and quantifies the number of redistribution layers of the chip carriers. 
     2. Discussion of the Prior Art 
     In essence, several methods are available in the technology for modeling chip and chip carrier interconnection layouts. 
     One approach is to review a data base of all previously designed modules, and select the one with matching fundamental parameters, such as die size, carrier size, and the number of chip inputs/outputs. However, a problem existent with this approach resides in the difficulty of identifying and dealing with all of the above-mentioned parameters which are required to attain the intended goals. Another approach is to build the design from the start; this being a time consuming process that often results in the necessity for discarding the design as the parameters change due to new requirements and/or design objectives. 
     A further approach would be to initially prepare a layout or sketch of the die showing the die pad positions required by a customer and then to laminate manually. The problem with this approach again resides in the level of skill and experience required in effecting the foregoing, and the difficulty in identifying and dealing with all of the parameters required, and the difficulty in visually expressing and modifying the design as may be necessary in order to meet all conditions. 
     There is, consequently, a need in the technology for a method and system providing for a quick and visual representation of a complicated module design which takes into account all relevant parameters. This is needed for early modeling of a more complex process and essentially useful for the early design and quick modeling of chip carriers, such as plastic ball grid array (PBGA), flip chip, or wirebond chip carriers. 
     As disclosed in the parent application, Ser. No. 09/429,990, an object is to provide an improved system and method for simulating and graphically assessing the cost and feasibility of general and specific wiring design cases. Another purpose is to provide a system and method for simulating general and specific wiring design cases and quickly assess the simulated design graphically. Moreover, provision is made for a system and method for assessing a simulated wiring design with respect to crossing, choking, signal runs, wiring channels and input/output; and for transmitting simulated design graphical data to a wiring design tool. 
     In accordance with the foregoing, pursuant to the disclosure of the parent application, a system and method is provided for modeling and estimating substrate characteristics preliminary to preparing a detailed design. Input parameters include die size and substrate size and, optionally, a netlist of interconnections between the die and substrate. Responsive to these input parameters, a representation of an optimized estimated fanout of the interconnections is graphically presented together with a set of substrate parameters derived from the optimized estimated fanout. In that connection, a computer program product is configured to be operable to graphically model an optimized fanout of die to substrate interconnections. 
     SUMMARY OF THE INVENTION 
     In essence, as a further improvement over the parent application, which relates to a chip carrier design simulation, estimator, and an early design for providing a system for quickly modeling and estimating substrate characteristic including optimized single layer fanout, substrate parameters such as size, wiring rules and I/O layout, the present invention provides a tool which is a system or method for electrically estimating multilayer substrates for various chip carrier designs as set forth herein. 
     Basically, the problem which is solved by the present invention with regard to a chip carrier layer count calculation resides in that an accurate and fast estimate for various customer die designs is provided in that the customer provides a die showing die pad position, and a further request as to the physical size of the package, the package I/O, the design rules, the number of layers and ultimately the cost. 
     For that purpose, the inventive concept is grounded in providing a subroutine as part of the overall program generally referred to as buildup technology or SLC (surface laminar circuitry). Thus, given the specified input parameters, the invention provides a program determinative of the number of signal distribution layers required to access module I/O bumps (BGA&#39;s). 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other features and advantages of this invention will become apparent from the following detailed description of the preferred embodiment of the invention, taken in conjunction with the accompanying drawings; in which: 
     FIG. 1 is a high level flow diagram of the method in accordance with the parent application for early design and modeling of an electronic module; 
     FIGS. 2A-2C, arranged as shown in FIG. 2, represent an output display in accordance with the method of FIG. 1; 
     FIG. 3 is an enlarged view of the upper right corner of the display of FIG. 2B; 
     FIG. 4 is, in mirror image, an enlarged view of chip pads shown in FIG. 2B; 
     FIG. 5 is an enlarged view of a section of FIG. 2B illustrating cross over; 
     FIG. 6 is an enlarged view of a portion of FIG. 2B illustrating chip attach region labeling in accordance with the invention; 
     FIGS. 7 and 8 are two views of a ball grid array (BGA) connection system; 
     FIG. 9 illustrates a wire bond attachment system; 
     FIG. 10 illustrates a flip chip attachment system; 
     FIGS. 11A-11C, arranged as shown in FIG. 11, are a flow diagram of the method steps of the invention; and 
     FIGS. 12A-12D illustrate, respectively, output wiring displays in accordance with the inventive method. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     As detailed hereinbelow with reference to FIGS. 1 through 11C, the description is a reiteration of the method and system described and claimed in parent patent application Ser. No. 09/429,990. 
     Referring to FIG. 1, input parameters  100  are received and input to code module  102  running in a main frame or PC using REXX language and/or WINDOWS type interfaces. The output of code module  102  includes script file  118  and graphical file  106 , centroid file  108 , and wireability files  110 , including summary file  112 , crossing file  114 , wireable text file  116 , and (SLC) or buildup layer count file, as described hereinbelow in specific detail. 
     Graphical file  106  includes and when printed or displayed provides, as is illustrated in FIG. 2, an annotated graphical drawing of the module design, including graphical layout display  133  showing the point to point connections between die or chip pads  120  to ball grid array (BGA) pads  122 . The annotations include alpha numeric pad row and column identifiers  124 ,  126 , BGA pad designations  128 , chip pad designations  130 , chip input parameters  132 , and chip carrier, substrate or parameters  134 . These are shown enlarged in FIGS. 3 and 4. 
     Centroid file  108  includes die pad number, chip pad name, X-Y position of chip pad center, quadrant, BGA alpha-numeric designation (when applicable), X-Y position of BGA pad center, and chip pad to BGA pad line slope. (An example of centroid file  108  is shown in Table 2.) The slope column indicates the slope of the line described by the direct line from chip pad to BGA pad, and is tracked for closest slope routing. Also, in the north and south quadrants the slope is defined as x/y whereas in the east and west quadrants it is the traditional y/x. This is done inasmuch as direct north y/x explodes into the undefined value 1/0. The crossing column indicates how many lines cross a particular line. 
     FIGS. 9 and 10 illustrate the interconnect configuration for flip chip, and FIGS. 7 and 8 illustrate the interconnect configuration for wire bond. Flip chip interconnection includes chip attach pad  190 , wire  192 , top via land  194 , via  196 , bottom via land  198 , dogbone  200 , and bga pad  202 , on substrate  204 . 
     FIG. 8 illustrates a wiring configuration with wire bond fingers. Interconnection is from die pad  206 , to wirebond  208 , to wire bond finger  210 , to wire  212 , to top via land  194 . 
     Referring to FIG. 11 in connection with Table 1, the processes executed by code  102  are set forth pseudo code. 
     
       
         
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 CODE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 STEP 210: Set Analyses/Output/Chip and Package IO Basis 
               
             
          
           
               
                   
                 Graphical Script 
               
             
          
           
               
                   
                 Physical 
               
               
                   
                 Mechanical 
               
             
          
           
               
                   
                 Text Files 
               
             
          
           
               
                   
                 BGAXY 
               
               
                   
                 Drill Data 
               
               
                   
                 RFS 
               
               
                   
                 Quadrant Analysis 
               
               
                   
                 Quadrant Crossing 
               
               
                   
                 SLC Layer Count (described hereinbelow) 
               
               
                   
                 Specify # IO or Pitch 
               
               
                   
                 Chip 
               
               
                   
                 Package 
               
             
          
           
               
                 STEP 212: Set Variables 
               
             
          
           
               
                   
                 Case A,B,C 
               
             
          
           
               
                   
                 Case ‘A’ = Random Die, Random Netlist 
               
               
                   
                 Case ‘B’ = Specified Die, Random Netlist 
               
               
                   
                 Case ‘C’ = Specified Die, Specified Netlist 
               
             
          
           
               
                   
                 Set Technology 
               
             
          
           
               
                   
                 Flip Chip 
               
               
                   
                 Wirebond Laminate Technology =  SLC or STD 
               
             
          
           
               
                   
                 Define Chip Parameters 
               
               
                   
                 Define Package Parameters 
               
             
          
           
               
                   
                 Circuitization rules 
               
               
                   
                 Package General Parameters 
               
               
                   
                 Package Thermals 
               
             
          
           
               
                 STEP 214: Jedec Full Matrix Determination given Package 
               
               
                 Size/EGA pitch/Tight or Loose 
               
             
          
           
               
                   
                 Find Matrix Polarity 
               
               
                   
                 Quadrant Dividing Slope 
               
               
                   
                 Depopulation Determination 
               
               
                   
                 Per Module IO Set or Outer Row Set 
               
               
                   
                 Define Alphas for Row Number 
               
             
          
           
               
                 STEP 216: Create Die (Case A) 
               
             
          
           
               
                   
                 Flip Chip 
               
             
          
           
               
                   
                 Define Matrix Per IO or Chip Pitch 
               
               
                   
                 Determine Polarity of Matrix 
               
               
                   
                 Construct the Die Centroid String (#, X,Y, 
               
               
                   
                 Quadrant) 
               
               
                   
                 Assign Ground/Voltage and Signals Randomly per 
               
               
                   
                 Set PCT (#, Name, X, Y, Quadrant) 
               
               
                   
                 Calculate Composition Ratios (Signals and G/V&#39;s), 
               
               
                   
                 #Signals, #Grounds, #Vlt per side 
               
             
          
           
               
                   
                 Wirebond 
               
             
          
           
               
                   
                 Define Pads per Side or Chip Pitch 
               
               
                   
                 Construct the Die Centroid String (#, X,Y, 
               
               
                   
                 Quadrant) 
               
               
                   
                 Assign Ground/Voltage and Signals Randomly per 
               
               
                   
                 Set PCT (#,Name, X, Y, Quadrant) 
               
               
                   
                 Calculate Composition Ratios (Signals and G/V&#39;s), 
               
               
                   
                 #Signals, #Grounds, #Voltages side 
               
             
          
           
               
                 STEP 218: Create Centroid String for Die (Case B) 
               
             
          
           
               
                   
                 Input Die Centroid Data 
               
               
                   
                 Assign a Quadrant 
               
               
                   
                 Sort in Sequential Order/CCW Feed 
               
               
                   
                 Determine Minimum Chip Pitch and Kerf 
               
               
                   
                 Calculate Composition Ratios (Signals and G/V&#39;s), 
               
               
                   
                 #Signals, #Grounds, #Voltages on perside 
               
             
          
           
               
                 STEP 220: Create Centroid String for Die and BGA (Case C) 
               
             
          
           
               
                   
                 Input Die and Netlist 
               
             
          
           
               
                   
                 Assign a Quadrant 
               
               
                   
                 Calculate Composition Ratios (Signals and G/V&#39;s), 
               
               
                   
                 #Signals, #Grounds, #Voltages on perside 
               
             
          
           
               
                 STEP 222: Create BGA Matrix 
               
             
          
           
               
                   
                 Find X,Y, Slope, Side (Assign Border BGA&#39;s to 
               
               
                   
                 Quadrants Evenly) 
               
               
                   
                 Determine Alphanumeric per Matrix and Cavity/Dieup 
               
               
                   
                 Centroid BGA Dataset (X,Y, Slope from 0,0, Side, 
               
               
                   
                 Alphanumeric) 
               
               
                   
                 Punch Out Depops 
               
               
                   
                 Separate into separate matrices by Quadrant 
               
               
                   
                 Assign Type (Ground, Voltage, and Signals) for each 
               
             
          
           
               
                 BGA 
               
               
                 STEP 224: Chip to EGA Routing 
               
             
          
           
               
                   
                 Case A and Case B Routing 
               
             
          
           
               
                   
                 Separate Chip Centroid into matrices by Quadrant 
               
               
                   
                 Closest Slope Search Routine 
               
               
                   
                 Output String (#, Name, Chipx, Chipy, Side, 
               
               
                   
                 Alphanumeric, BGAx, BGAy, Slope) 
               
             
          
           
               
                   
                 Case C Routing 
               
             
          
           
               
                   
                 Calculate Row, Column Position from Alphanumeric 
               
               
                   
                 Add Slope to String 
               
             
          
           
               
                 STEP 226: Quadrant Analysis Routine 
               
             
          
           
               
                   
                 Calculate Runs 
               
               
                   
                 Calculate Power Levels and Quadrant Location 
               
               
                   
                 Calculate Number of WB Fingers Needed 
               
               
                   
                 Print to a File 
               
             
          
           
               
                 STEP 229: Buildup or SLC Layer Count Analysis (described 
               
               
                 hereinbelow) 
               
               
                 STEP 228: Crossing Factor Analysis 
               
             
          
           
               
                   
                 Take each Routing and count the number of times it is 
               
               
                   
                 crossed by another line within Quadrant 
               
               
                   
                 Use Cramer&#39;s Rule to solve two equation/two 
               
               
                   
                 unknowns. 
               
               
                   
                 Append Centroid String to include Crossing Count 
               
               
                   
                 Rank in Descending Order 
               
               
                   
                 Print to a File 
               
             
          
           
               
                 STEP 230: Summary (RFS) Analysis 
               
             
          
           
               
                   
                 Calculate Line Width/Space for 1 thru 8 LPC on BGA 
               
               
                   
                 side 
               
               
                   
                 Calculate Line Width/Space for 1 thru 8 LPC on Die Up 
               
               
                   
                 Side 
               
               
                   
                 Match Wiring Rules to above 
               
               
                   
                 Calculate Distance Left for Fingers plus Fanout for 
               
               
                   
                 Dieup and Cavity 
               
               
                   
                 Calculate Choke Factor which is fanout space/Wiring 
               
               
                   
                 Pitch(12) 
               
               
                   
                 Gold Area Calculation (10) 
               
             
          
           
               
                   
                 Set Goldcost, Nickel Cost, and thickness 
               
               
                   
                 Ground Ring Area + Voltage Ring Area + Finger Area 
               
               
                   
                 Full Gold Via Area on Cavity (Lands + Inner Walls); 
               
               
                   
                 estimate Via Count 
               
               
                   
                 Flower Pad Calculation 
               
               
                   
                 Selective Gold Via Area on Die UP (Lands + Inner 
               
               
                   
                 Walls); estimate Via Count 
               
               
                   
                 BGA Area 
               
               
                   
                 Stiffener Area 
               
               
                   
                 Cavity Wall 
               
               
                   
                 Wiring Area Front and Back 
               
               
                   
                 Gold Runner 
               
             
          
           
               
                   
                 Summation of Total Gold for Die Up 
               
               
                   
                 Summation of Total Gold for Cavity 
               
               
                   
                 Complexity Factor 
               
             
          
           
               
                   
                 Die Area/Signal Count . . . Die Escape Factor 
               
               
                   
                 Die Area/ChipIO . . . Chip Density Factor 
               
               
                   
                 Laminate Area/Signal Count . . . BGA Escape 
               
               
                   
                 Factor 
               
             
          
           
               
                   
                 Flatness Calculation 
               
             
          
           
               
                   
                 Drill Count Calculation 
               
             
          
           
               
                   
                 Print All to Summary File plus Key Input Parameters 
               
             
          
           
               
                 STEP 232: Autocad Scrip Generation 
               
             
          
           
               
                   
                 Construct All Layers 
               
               
                   
                 Define Laminate Coordinates for Top View and Side View 
               
               
                   
                 Define Die Coordinates for Top View and Side View 
               
               
                   
                 Draw Chamfer 
               
               
                   
                 If Mechanical Document Package 
               
             
          
           
               
                   
                 Side View of Laminate 
               
               
                   
                 Side View of Die 
               
               
                   
                 Top View of Lid 
               
               
                   
                 Side View of BGA Ball 
               
               
                   
                 Side View of C4 Balls 
               
               
                   
                 Spacing between Plan View and Side View 
               
               
                   
                 Draw Side View and Move it over 
               
               
                   
                 Draw Top View of Lid 
               
             
          
           
               
                   
                 If Physical 
               
             
          
           
               
                   
                 Draw Multi Vertice RATS(13) 
               
               
                   
                 Draw BGA, Procoat, Middle of Bone and Holes 
               
               
                   
                 (Print Holes to File too) 
               
               
                   
                 Set on a 45 Degree Angle According to 
               
               
                   
                 Octant 
               
               
                   
                 Draw Flower Pad Construction Circles 
               
               
                   
                 Draw Voltage and Ground Plane Outlines 
               
               
                   
                 Draw Ground Ring and Voltage Ring(s) 
               
             
          
           
               
                   
                 Draw Chip Pads and Chip Text 
               
               
                   
                 Draw BGA Alphanumerics on 4 sides 
               
               
                   
                 Draw Aphanumerics on BGA Balls Themselves. 
               
               
                   
                 Print Out Chip Parameters to the Left of 
               
               
                   
                 Drawing and Substrate Parameters to rt. 
               
               
                   
                 Print to an Autocad File 
               
             
          
           
               
                 STEP 234: Print out Drill Data 
               
               
                 STEP 326: Print out BGAXY Data 
               
               
                 STEP 238: Run Autocad Script File from Autocad. 
               
               
                   
               
             
          
         
       
     
     Referring to Tables 2 and 3, a “rat” is a colloquial term meaning an unedited straight line that emanates from the center of a die pad to a ball grid array (BGA) pad, or analogous connections on a mother board. It is then manipulated by moving within a layer and/or placing part of the path on other layers of the package. In the examples of Tables 2 and 3, the centroid data of a die has been created and routed out to the center of a BGA pad, either by a customer definition (case C) or by creation within the program (case A). 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 CENTROID FILE 
               
             
          
           
               
                 No. 
                 ID 
                 CHIPX 
                 CHIPY 
                 SIDE 
                 ALPHA 
                 BGAX 
                 BGAY 
               
               
                   
               
               
                 1 
                 VSS 
                 4890 
                 −4688 
                 East 
                   
                   
                   
               
               
                 2 
                 Signal 
                 4890 
                 −4563 
                 East P8 
                 4445 
                 −3175 
               
               
                 3 
                 VDD 
                 4890 
                 −4438 
                 East 
               
               
                 4 
                 Signal 
                 4890 
                 −4313 
                 East V3 
                 9525 
                 −9525 
               
               
                 5 
                 VDD 
                 4890 
                 −4188 
                 East 
               
               
                 6 
                 Signal 
                 4890 
                 −4068 
                 East Y1 
                 12065 
                 −12065 
               
               
                 7 
                 Signal 
                 4890 
                 −3938 
                 East 
                 W3 
                 10795 
                 −9525 
               
               
                 8 
                 Signal 
                 4890 
                 −3813 
                 East 
                 U5 
                 8255 
                 −6985 
               
               
                   
               
             
          
         
       
     
     In Tables 2 and 3, the numbering (No.) convention is counterclockwise. Identifier (ID) represents the name assigned. Typically, but not in the examples of Tables 1 and 2, signals are given unique names, such as Signal 1 , Signal 2 , etc. 
     CHIPX is the X dimension to the center of die with reference to the center of the package (0,0). CHIPY is the Y dimension to the center of die with reference to the center of the package (0,0). SIDE is the quadrant (north, south, east or west) to which the die belongs. ALPHA is the alphanumeric position of the ball grid array (BGA) pad as defined by the Jedec Standard. BGAX is the X dimension to the center of the BGA pad with reference to the center of the package (0,0). BGAY is the Y dimension to the center of the BGA pad with reference to the center of the package (0,0). 
     Table 3 is the centroid file  108  for the example illustrated in FIG.  2 A. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 CENTROID FILE 
               
             
          
           
               
                 # 
                 ID 
                 CHIPX 
                 CHIPY 
                 SIDE 
                 ALPHA 
                 BGAX 
                 BGAY 
                 SLOPE 
                 CROSS 
               
               
                   
               
             
          
           
               
                 1 
                 Signal 
                 3890 
                 −3688 
                 East 
                 E22 
                 10795 
                 −10795 
                 −1.029 
                 0 
               
               
                 2 
                 Signal 
                 3890 
                 −3563 
                 East 
                 C24 
                 13335 
                 −13335 
                 −1.035 
                 0 
               
               
                 3 
                 Signal 
                 3890 
                 −3438 
                 East 
                 A26 
                 15875 
                 −15875 
                 −1.038 
                 0 
               
               
                 4 
                 Signal 
                 3890 
                 −3313 
                 East 
                 B26 
                 15875 
                 −14605 
                 −0.942 
                 0 
               
               
                 5 
                 Signal 
                 3890 
                 −3188 
                 East 
                 D24 
                 13335 
                 −12065 
                 −0.940 
                 0 
               
               
                 6 
                 Signal 
                 3890 
                 −3063 
                 East 
                 F22 
                 10795 
                 −9525 
                 −0.936 
                 0 
               
               
                 7 
                 VDD 
                 3890 
                 −2938 
                 East 
               
               
                 8 
                 Signal 
                 3890 
                 −2813 
                 East 
                 E24 
                 13335 
                 −10795 
                 −0.845 
                 0 
               
               
                 9 
                 Signal 
                 3890 
                 −2688 
                 East 
                 F23 
                 12065 
                 −9525 
                 −0.836 
                 0 
               
               
                 10 
                 Signal 
                 3890 
                 −2563 
                 East 
                 E25 
                 14605 
                 −10795 
                 −0.768 
                 0 
               
               
                 11 
                 Signal 
                 3890 
                 −2438 
                 East 
                 H22 
                 10795 
                 −6985 
                 −0.659 
                 0 
               
               
                 12 
                 Signal 
                 3890 
                 −2313 
                 East 
                 F26 
                 15875 
                 −9525 
                 −0.602 
                 0 
               
               
                 13 
                 Signal 
                 3890 
                 −2188 
                 East 
                 G26 
                 15875 
                 −8255 
                 −0.506 
                 0 
               
               
                 14 
                 Signal 
                 3890 
                 −2063 
                 East 
                 H25 
                 14605 
                 −6985 
                 −0.459 
                 0 
               
               
                 15 
                 VSS 
                 3890 
                 −1938 
                 East 
               
               
                 16 
                 VSS 
                 3890 
                 −1813 
                 East 
               
               
                 17 
                 Signal 
                 3890 
                 −1688 
                 East 
                 J23 
                 12065 
                 −5715 
                 −0.493 
                 0 
               
               
                 18 
                 Signal 
                 3890 
                 −1563 
                 East 
                 H26 
                 15875 
                 −6985 
                 −0.452 
                 0 
               
               
                 19 
                 Signal 
                 3890 
                 −1438 
                 East 
                 J26 
                 15875 
                 −5715 
                 0.357 
                 0 
               
               
                 20 
                 Signal 
                 3890 
                 −1313 
                 East 
                 K25 
                 14605 
                 −4445 
                 −0.292 
                 0 
               
               
                 21 
                 Signal 
                 3890 
                 −1188 
                 East 
                 L22 
                 10795 
                 −3175 
                 −0.288 
                 0 
               
               
                 22 
                 Signal 
                 3890 
                 −1063 
                 East 
                 L25 
                 14605 
                 −3175 
                 −0.197 
                 0 
               
               
                 23 
                 Signal 
                 3890 
                 −938 
                 East 
                 M24 
                 13335 
                 −1905 
                 −0.102 
                 0 
               
               
                 24 
                 Signal 
                 3890 
                 −813 
                 East 
                 N24 
                 13335 
                 −635 
                 0.019 
                 0 
               
               
                 25 
                 Signal 
                 3890 
                 −688 
                 East 
                 N23 
                 12065 
                 −635 
                 0.006 
                 0 
               
               
                 26 
                 VSS 
                 3890 
                 −563 
                 East 
               
               
                 27 
                 Signal 
                 3890 
                 −438 
                 East 
                 P24 
                 13335 
                 635 
                 0.114 
                 0 
               
               
                 28 
                 Signal 
                 3890 
                 −313 
                 East 
                 P23 
                 12065 
                 635 
                 0.116 
                 0 
               
               
                 29 
                 Signal 
                 3890 
                 −188 
                 East 
                 P22 
                 10795 
                 635 
                 0.119 
                 0 
               
               
                 30 
                 Signal 
                 3890 
                 −63 
                 East 
                 R25 
                 14605 
                 1905 
                 0.184 
                 0 
               
               
                 31 
                 Signal 
                 3890 
                 63 
                 East 
                 R23 
                 12065 
                 1905 
                 0.225 
                 0 
               
               
                 32 
                 Signal 
                 3890 
                 188 
                 East 
                 T26 
                 15875 
                 3175 
                 0.249 
                 0 
               
               
                 33 
                 Signal 
                 3890 
                 313 
                 East 
                 T25 
                 14605 
                 3175 
                 0.267 
                 0 
               
               
                 34 
                 Signal 
                 3890 
                 438 
                 East 
                 T24 
                 13335 
                 3175 
                 0.290 
                 0 
               
               
                 35 
                 Signal 
                 3890 
                 563 
                 East 
                 U26 
                 15875 
                 4445 
                 0.324 
                 0 
               
               
                 36 
                 Signal 
                 3890 
                 688 
                 East 
                 T22 
                 10795 
                 3175 
                 0.360 
                 0 
               
               
                 37 
                 Signal 
                 3890 
                 813 
                 East 
                 V25 
                 14605 
                 5715 
                 0.457 
                 0 
               
               
                 38 
                 Signal 
                 3890 
                 938 
                 East 
                 W26 
                 15875 
                 6985 
                 0.505 
                 0 
               
               
                 39 
                 Signal 
                 3890 
                 1063 
                 East 
                 U22 
                 10795 
                 4445 
                 0.490 
                 0 
               
               
                 40 
                 Signal 
                 3890 
                 1188 
                 East 
                 W25 
                 14605 
                 6985 
                 0.541 
                 0 
               
               
                 41 
                 Signal 
                 3890 
                 1313 
                 East 
                 Y26 
                 15875 
                 8255 
                 0.579 
                 0 
               
               
                 42 
                 Signal 
                 3890 
                 1438 
                 East 
                 V22 
                 10795 
                 5715 
                 0.619 
                 0 
               
               
                 43 
                 Signal 
                 3890 
                 1563 
                 East 
                 W23 
                 12065 
                 6985 
                 0.663 
                 0 
               
               
                 44 
                 Signal 
                 3890 
                 1688 
                 East 
                 AA26 
                 15875 
                 9525 
                 0.654 
                 0 
               
               
                 45 
                 Signal 
                 3890 
                 1813 
                 East 
                 Y24 
                 13335 
                 8255 
                 0.682 
                 0 
               
               
                 46 
                 Signal 
                 3890 
                 1938 
                 East 
                 AA25 
                 14605 
                 9525 
                 0.708 
                 0 
               
               
                 47 
                 VSS 
                 3890 
                 2063 
                 East 
               
               
                 48 
                 Signal 
                 3890 
                 2188 
                 East 
                 W22 
                 10795 
                 6985 
                 0.695 
                 0 
               
               
                 49 
                 Signal 
                 3890 
                 2313 
                 East 
                 AB26 
                 15875 
                 10795 
                 0.708 
                 0 
               
               
                 50 
                 VSS 
                 3890 
                 2438 
                 East 
               
               
                 51 
                 VDD 
                 3890 
                 2563 
                 East 
               
               
                 52 
                 Signal 
                 3890 
                 2688 
                 East 
                 Y23 
                 12065 
                 8255 
                 0.681 
                 0 
               
               
                 53 
                 Signal 
                 3890 
                 2813 
                 East 
                 AB25 
                 14605 
                 10795 
                 0.745 
                 0 
               
               
                 54 
                 VSS 
                 3890 
                 2938 
                 East 
               
               
                 55 
                 Signal 
                 3890 
                 3063 
                 East 
                 AC26 
                 15875 
                 12065 
                 0.751 
                 0 
               
               
                 56 
                 Signal 
                 3890 
                 3188 
                 East 
                 AC25 
                 14605 
                 12065 
                 0.828 
                 0 
               
               
                 57 
                 Signal 
                 3890 
                 3313 
                 East 
                 AD26 
                 15875 
                 13335 
                 0.836 
                 0 
               
               
                 58 
                 Signal 
                 3890 
                 3438 
                 East 
                 AB23 
                 12065 
                 10795 
                 0.900 
                 0 
               
               
                 59 
                 Signal 
                 3890 
                 3563 
                 East 
                 AC24 
                 13335 
                 12065 
                 0.900 
                 0 
               
               
                 60 
                 Signal 
                 3890 
                 3688 
                 East 
                 AE26 
                 15875 
                 14605 
                 0.911 
                 0 
               
               
                 61 
                 Signal 
                 3688 
                 3890 
                 North 
                 AC20 
                 8255 
                 12065 
                 1.790 
                 1 
               
               
                 62 
                 Signal 
                 3563 
                 3890 
                 North 
                 AF22 
                 10795 
                 15875 
                 1.657 
                 1 
               
               
                 63 
                 Signal 
                 3438 
                 3890 
                 North 
                 AE22 
                 10795 
                 14605 
                 1.456 
                 1 
               
               
                 64 
                 Signal 
                 3313 
                 3890 
                 North 
                 AB20 
                 8255 
                 10795 
                 1.397 
                 1 
               
               
                 65 
                 VSS 
                 3188 
                 3890 
                 North 
               
               
                 66 
                 Signal 
                 3063 
                 3890 
                 North 
                 AF23 
                 12065 
                 15875 
                 1.331 
                 2 
               
               
                 67 
                 Signal 
                 2938 
                 3890 
                 North 
                 AE19 
                 6985 
                 14605 
                 2.648 
                 5 
               
               
                 68 
                 VDD 
                 2813 
                 3890 
                 North 
               
               
                 69 
                 Signal 
                 2688 
                 3890 
                 North 
                 AE23 
                 12065 
                 14605 
                 1.143 
                 1 
               
               
                 70 
                 Signal 
                 2563 
                 3890 
                 North 
                 AF24 
                 13335 
                 15875 
                 1.113 
                 1 
               
               
                 71 
                 Signal 
                 2438 
                 3890 
                 North 
                 AF2S 
                 14605 
                 15875 
                 0.985 
                 4 
               
               
                 72 
                 Signal 
                 2313 
                 3890 
                 North 
                 AB24 
                 13335 
                 14605 
                 0.972 
                 4 
               
               
                 73 
                 VDD 
                 2188 
                 3890 
                 North 
               
               
                 74 
                 VSS 
                 2063 
                 3890 
                 North 
               
               
                 75 
                 Signal 
                 1938 
                 3890 
                 North 
                 AD23 
                 12065 
                 13335 
                 0.933 
                 4 
               
               
                 76 
                 VDD 
                 1813 
                 3890 
                 North 
               
               
                 77 
                 Signal 
                 1688 
                 3890 
                 North 
                 AB21 
                 9525 
                 10795 
                 0.881 
                 4 
               
               
                 78 
                 Signal 
                 1563 
                 3890 
                 North 
                 AF26 
                 15875 
                 15875 
                 0.837 
                 4 
               
               
                 79 
                 Signal 
                 1438 
                 3890 
                 North 
                 AD17 
                 4445 
                 13335 
                 3.141 
                 8 
               
               
                 80 
                 Signal 
                 1313 
                 3890 
                 North 
                 AD24 
                 13335 
                 13335 
                 0.786 
                 4 
               
               
                 81 
                 VDD 
                 1188 
                 3890 
                 North 
               
               
                 82 
                 Signal 
                 1063 
                 3890 
                 North 
                 AB16 
                 3175 
                 10795 
                 3.269 
                 7 
               
               
                 83 
                 Signal 
                 938 
                 3890 
                 North 
                 AB22 
                 10795 
                 10795 
                 0.701 
                 3 
               
               
                 84 
                 Signal 
                 813 
                 3890 
                 North 
                 AC16 
                 3175 
                 12065 
                 3.461 
                 8 
               
               
                 85 
                 Signal 
                 688 
                 3890 
                 North 
                 AB7 
                 −8255 
                 10795 
                 −0.772 
                 5 
               
               
                 86 
                 Signal 
                 563 
                 3890 
                 North 
                 AF16 
                 3175 
                 15875 
                 4.588 
                 10 
               
               
                 87 
                 Signal 
                 438 
                 3890 
                 North 
                 AF2 
                 −14605 
                 15875 
                 −0.797 
                 4 
               
               
                 88 
                 Signal 
                 313 
                 3890 
                 North 
                 AD5 
                 −10795 
                 13335 
                 −0.850 
                 4 
               
               
                 89 
                 Signal 
                 188 
                 3890 
                 North 
                 AE4 
                 −12065 
                 14605 
                 −0.874 
                 4 
               
               
                 90 
                 Signal 
                 63 
                 3890 
                 North 
                 AF3 
                 −13335 
                 15875 
                 −0.895 
                 4 
               
               
                 91 
                 Signal 
                 63 
                 3890 
                 North 
                 AB8 
                 −6985 
                 10795 
                 −0.998 
                 4 
               
               
                 92 
                 Signal 
                 −188 
                 3890 
                 North 
                 AF4 
                 −12065 
                 15875 
                 −1.009 
                 4 
               
               
                 93 
                 Signal 
                 −313 
                 3890 
                 North 
                 AE5 
                 −10795 
                 14605 
                 −1.022 
                 4 
               
               
                 94 
                 Signal 
                 −438 
                 3890 
                 North 
                 AD6 
                 −9525 
                 13335 
                 −1.039 
                 5 
               
               
                 95 
                 Signal 
                 −563 
                 3890 
                 North 
                 AP15 
                 1905 
                 15875 
                 4.856 
                 11 
               
               
                 96 
                 Signal 
                 −688 
                 3890 
                 North 
                 AC7 
                 −8255 
                 12065 
                 −1.080 
                 4 
               
               
                 97 
                 Signal 
                 −813 
                 3890 
                 North 
                 AD7 
                 −8255 
                 13335 
                 −1.269 
                 4 
               
               
                 98 
                 VSS 
                 −938 
                 3890 
                 North 
               
               
                 99 
                 Signal 
                 −1063 
                 3890 
                 North 
                 AF6 
                 −9525 
                 15875 
                 −1.416 
                 4 
               
               
                 100 
                 Signal 
                 −1188 
                 3890 
                 North 
                 AD14 
                 635 
                 13335 
                 5.181 
                 12 
               
               
                 101 
                 Signal 
                 −1313 
                 3890 
                 North 
                 AE14 
                 635 
                 14605 
                 5.501 
                 12 
               
               
                 102 
                 Signal 
                 −1438 
                 3890 
                 North 
                 AE7 
                 −8255 
                 14605 
                 −1.572 
                 2 
               
               
                 103 
                 Signal 
                 −1563 
                 3890 
                 North 
                 AF14 
                 635 
                 15875 
                 5.453 
                 13 
               
               
                 104 
                 Signal 
                 −1688 
                 3890 
                 North 
                 AD8 
                 −6985 
                 13335 
                 −1.783 
                 3 
               
               
                 105 
                 Signal 
                 −1813 
                 3890 
                 North 
                 AF7 
                 −8255 
                 15875 
                 −1.860 
                 4 
               
               
                 106 
                 Signal 
                 −1938 
                 3890 
                 North 
                 AC9 
                 −5715 
                 12065 
                 −2.164 
                 4 
               
               
                 107 
                 Signal 
                 −2063 
                 3890 
                 North 
                 AC13 
                 635 
                 12065 
                 5.725 
                 8 
               
               
                 108 
                 Signal 
                 −2188 
                 3890 
                 North 
                 AB10 
                 −4445 
                 10795 
                 −3.059 
                 3 
               
               
                 109 
                 Signal 
                 −2313 
                 3890 
                 North 
                 AF9 
                 −5715 
                 15875 
                 −3.523 
                 3 
               
               
                 110 
                 Signal 
                 −2438 
                 3890 
                 North 
                 AC10 
                 −4445 
                 12065 
                 −4.073 
                 3 
               
               
                 111 
                 Signal 
                 −2563 
                 3890 
                 North 
                 AD10 
                 −4445 
                 13335 
                 −5.019 
                 3 
               
               
                 112 
                 Signal 
                 −2688 
                 3890 
                 North 
                 AB12 
                 −1905 
                 10795 
                 8.819 
                 6 
               
               
                 113 
                 Signal 
                 −2813 
                 3890 
                 North 
                 AE10 
                 −4445 
                 1460S 
                 −6.566 
                 2 
               
               
                 114 
                 VSS 
                 −2938 
                 3890 
                 North 
               
               
                 115 
                 Signal 
                 −3063 
                 3890 
                 North 
                 AE12 
                 −1905 
                 14605 
                 9.253 
                 8 
               
               
                 116 
                 Signal 
                 −3188 
                 3890 
                 North 
                 AF12 
                 −1905 
                 15875 
                 9.341 
                 8 
               
               
                 117 
                 Signal 
                 −3313 
                 3890 
                 North 
                 AF10 
                 −4445 
                 15875 
                 −10.587 
                 2 
               
               
                 118 
                 Signal 
                 −3438 
                 3890 
                 North 
                 AC11 
                 −3175 
                 12065 
                 31.084 
                 1 
               
               
                 119 
                 Signal 
                 −3563 
                 3890 
                 North 
                 AD11 
                 −3175 
                 13335 
                 24.343 
                 1 
               
               
                 120 
                 VSS 
                 −3688 
                 3890 
                 North 
               
               
                 121 
                 Signal 
                 −3890 
                 3688 
                 West 
                 AB5 
                 −10795 
                 10795 
                 −1.029 
                 0 
               
               
                 122 
                 Signal 
                 −3890 
                 3563 
                 West 
                 AE1 
                 −15875 
                 14605 
                 −0.921 
                 0 
               
               
                 123 
                 Signal 
                 −3890 
                 3438 
                 West 
                 AC3 
                 −13335 
                 12065 
                 −0.913 
                 0 
               
               
                 124 
                 Signal 
                 −3890 
                 3313 
                 West 
                 AB4 
                 −12065 
                 10795 
                 −0.915 
                 0 
               
               
                 125 
                 Signal 
                 −3890 
                 3188 
                 West 
                 AA5 
                 −10795 
                 9525 
                 −0.918 
                 0 
               
               
                 126 
                 Signal 
                 −3890 
                 3063 
                 West 
                 AC2 
                 −14605 
                 12065 
                 −0.840 
                 0 
               
               
                 127 
                 VSS 
                 −3890 
                 2938 
                 West 
               
               
                 128 
                 Signal 
                 −3890 
                 2813 
                 West 
                 AB3 
                 −13335 
                 10795 
                 −0.845 
                 0 
               
               
                 129 
                 Signal 
                 −3890 
                 2688 
                 West 
                 Y5 
                 −10795 
                 8255 
                 −0.806 
                 0 
               
               
                 130 
                 Signal 
                 −3890 
                 2563 
                 West 
                 AA3 
                 −13335 
                 9525 
                 −0.737 
                 0 
               
               
                 131 
                 VSS 
                 −3890 
                 2438 
                 West 
               
               
                 132 
                 Signal 
                 −3890 
                 2313 
                 West 
                 AE1 
                 −15875 
                 10795 
                 −0.708 
                 0 
               
               
                 133 
                 Signal 
                 −3890 
                 2188 
                 West 
                 W5 
                 −10795 
                 6985 
                 −0.695 
                 0 
               
               
                 134 
                 Signal 
                 −3890 
                 2063 
                 West 
                 V5 
                 −10795 
                 5715 
                 −0.529 
                 0 
               
               
                 135 
                 Signal 
                 −3890 
                 1938 
                 West 
                 Y1 
                 −15875 
                 8255 
                 −0.527 
                 0 
               
               
                 136 
                 VSS 
                 −3890 
                 1813 
                 West 
               
               
                 137 
                 VDD 
                 −3890 
                 1688 
                 West 
               
               
                 138 
                 Signal 
                 −3890 
                 1563 
                 West 
                 V4 
                 −12065 
                 5715 
                 −0.508 
                 0 
               
               
                 139 
                 VSS 
                 −3890 
                 1438 
                 West 
               
               
                 140 
                 Signal 
                 −3890 
                 1313 
                 West 
                 W2 
                 −14605 
                 6985 
                 −0.529 
                 0 
               
               
                 141 
                 Signal 
                 −3890 
                 1188 
                 West 
                 U5 
                 −10795 
                 4445 
                 −0.472 
                 0 
               
               
                 142 
                 Signal 
                 −3890 
                 1063 
                 West 
                 U3 
                 −13335 
                 4445 
                 −0.358 
                 0 
               
               
                 143 
                 Signal 
                 −3890 
                 938 
                 West 
                 U1 
                 −15875 
                 4445 
                 −0.293 
                 0 
               
               
                 144 
                 Signal 
                 −3890 
                 813 
                 West 
                 T3 
                 −13335 
                 3175 
                 −0.250 
                 0 
               
               
                 145 
                 Signal 
                 −3890 
                 688 
                 West 
                 T1 
                 −15875 
                 3175 
                 −0.208 
                 0 
               
               
                 146 
                 Signal 
                 −3890 
                 563 
                 West 
                 R4 
                 −12065 
                 1905 
                 −0.164 
                 0 
               
               
                 147 
                 Signal 
                 −3890 
                 438 
                 West 
                 R2 
                 −14605 
                 1905 
                 −0.137 
                 0 
               
               
                 148 
                 VSS 
                 −3890 
                 313 
                 West 
               
               
                 149 
                 Signal 
                 −3890 
                 188 
                 West 
                 R1 
                 −15875 
                 1905 
                 −0.143 
                 0 
               
               
                 150 
                 Signal 
                 −3890 
                 63 
                 West 
                 P2 
                 −14605 
                 635 
                 −0.053 
                 0 
               
               
                 151 
                 Signal 
                 −3890 
                 −63 
                 West 
                 N1 
                 −15875 
                 −635 
                 0.048 
                 0 
               
               
                 152 
                 Signal 
                 −3890 
                 −188 
                 West 
                 N5 
                 −10795 
                 −635 
                 0.065 
                 0 
               
               
                 153 
                 Signal 
                 −3890 
                 −313 
                 West 
                 M1 
                 −15875 
                 −1905 
                 0.133 
                 0 
               
               
                 154 
                 Signal 
                 −3890 
                 −438 
                 West 
                 M2 
                 −14605 
                 −1905 
                 0.137 
                 0 
               
               
                 155 
                 Signal 
                 −3890 
                 −563 
                 West 
                 M3 
                 −13335 
                 −1905 
                 0.142 
                 0 
               
               
                 1S6 
                 Signal 
                 −3890 
                 −688 
                 West 
                 M5 
                 −10795 
                 −1905 
                 0.176 
                 0 
               
               
                 157 
                 VDD 
                 −3890 
                 −813 
                 West 
               
               
                 158 
                 Signal 
                 −3890 
                 −938 
                 West 
                 L1 
                 −15875 
                 −3175 
                 0.187 
                 0 
               
               
                 159 
                 VDD 
                 −3890 
                 −1063 
                 West 
               
               
                 160 
                 Signal 
                 −3890 
                 −1188 
                 West 
                 L2 
                 −14605 
                 −3175 
                 0.185 
               
               
                 161 
                 Signal 
                 −3890 
                 −1313 
                 West 
                 L4 
                 −12065 
                 −3175 
                 0.228 
                 0 
               
               
                 162 
                 VDD 
                 −3890 
                 −1438 
                 West 
               
               
                 163 
                 Signal 
                 −3890 
                 −1563 
                 West 
                 L5 
                 −10795 
                 −3175 
                 0.233 
                 0 
               
               
                 164 
                 Signal 
                 −3890 
                 −1688 
                 West 
                 K1 
                 −15875 
                 −4445 
                 0.230 
                 0 
               
               
                 165 
                 Signal 
                 −3890 
                 −1813 
                 West 
                 K2 
                 −14605 
                 −4445 
                 0.246 
                 0 
               
               
                 166 
                 Signal 
                 −3890 
                 −1938 
                 West 
                 J1 
                 −15875 
                 −5715 
                 0.315 
                 0 
               
               
                 167 
                 Signal 
                 −3890 
                 −2063 
                 West 
                 J2 
                 −14605 
                 −5715 
                 0.341 
                 0 
               
               
                 168 
                 Signal 
                 −3890 
                 −2188 
                 West 
                 K5 
                 −10795 
                 −4445 
                 0.327 
                 0 
               
               
                 169 
                 Signal 
                 −3890 
                 −2313 
                 West 
                 J3 
                 −13335 
                 −5715 
                 0.360 
                 0 
               
               
                 170 
                 Signal 
                 −3890 
                 −2438 
                 West 
                 J4 
                 −12065 
                 −5715 
                 0.401 
                 0 
               
               
                 171 
                 VSS 
                 −3890 
                 −2563 
                 West 
               
               
                 172 
                 Signal 
                 −3890 
                 −2688 
                 West 
                 H3 
                 −13335 
                 −6985 
                 0.455 
                 0 
               
               
                 173 
                 Signal 
                 −3890 
                 −2813 
                 West 
                 F1 
                 −15875 
                 −9525 
                 0.560 
                 0 
               
               
                 174 
                 Signal 
                 −3890 
                 −2938 
                 West 
                 E2 
                 −14605 
                 −10795 
                 0.733 
                 0 
               
               
                 175 
                 Signal 
                 −3890 
                 −3063 
                 West 
                 G5 
                 −10795 
                 −8255 
                 0.752 
                 0 
               
               
                 176 
                 VDD 
                 −3890 
                 −3188 
                 West 
               
               
                 177 
                 VSS 
                 −3890 
                 −3313 
                 West 
               
               
                 178 
                 Signal 
                 −3890 
                 −3438 
                 West 
                 F4 
                 −12065 
                 −9525 
                 0.745 
                 0 
               
               
                 179 
                 Signal 
                 −3890 
                 −3563 
                 West 
                 F5 
                 −10795 
                 −9525 
                 0.863 
                 0 
               
               
                 180 
                 Signal 
                 −3890 
                 −3688 
                 West 
                 C2 
                 −14605 
                 −13335 
                 0.900 
                 0 
               
               
                 181 
                 Signal 
                 −3688 
                 −3890 
                 South 
                 D10 
                 −4445 
                 −12065 
                 10.799 
                 0 
               
               
                 182 
                 Signal 
                 −3563 
                 −3890 
                 South 
                 B10 
                 −4445 
                 −14605 
                 12.149 
                 0 
               
               
                 183 
                 Signal 
                 −3438 
                 −3890 
                 South 
                 A10 
                 −4445 
                 −15875 
                 11.902 
                 0 
               
               
                 184 
                 Signal 
                 −3313 
                 −3890 
                 South 
                 E10 
                 −4445 
                 −10795 
                 6.100 
                 0 
               
               
                 185 
                 Signal 
                 −3188 
                 −3890 
                 South 
                 C9 
                 −5715 
                 −13335 
                 3.738 
                 0 
               
               
                 186 
                 Signal 
                 −3063 
                 −3890 
                 South 
                 D9 
                 −5715 
                 −12065 
                 3.083 
                 1 
               
               
                 187 
                 Signal 
                 −2938 
                 −3890 
                 South 
                 A8 
                 −6985 
                 −15875 
                 2.961 
                 2 
               
               
                 188 
                 Signal 
                 −2813 
                 −3890 
                 South 
                 B8 
                 −6985 
                 −14605 
                 2.568 
                 2 
               
               
                 189 
                 Signal 
                 −2688 
                 −3890 
                 South 
                 E11 
                 −3175 
                 −10795 
                 14.179 
                 3 
               
               
                 190 
                 VSS 
                 −2563 
                 −3890 
                 South 
               
               
                 191 
                 Signal 
                 −2438 
                 −3890 
                 South 
                 D11 
                 −3175 
                 −12065 
                 11.092 
                 2 
               
               
                 192 
                 Signal 
                 −2313 
                 −3890 
                 South 
                 39 
                 −5715 
                 −10795 
                 2.030 
                 0 
               
               
                 193 
                 Signal 
                 −2188 
                 −3890 
                 South 
                 A7 
                 −8255 
                 −15875 
                 1.975 
                 0 
               
               
                 194 
                 VSS 
                 −2063 
                 −3890 
                 South 
               
               
                 195 
                 Signal 
                 −1938 
                 −3890 
                 South 
                 B7 
                 −8255 
                 −14605 
                 1.696 
                 0 
               
               
                 196 
                 Signal 
                 −1813 
                 −3890 
                 South 
                 D8 
                 −6985 
                 −12065 
                 1.581 
                 2 
               
               
                 197 
                 VSS 
                 −1688 
                 −3890 
                 South 
               
               
                 198 
                 Signal 
                 −1563 
                 −3890 
                 South 
                 C7 
                 −8255 
                 −13335 
                 1.411 
                 2 
               
               
                 199 
                 Signal 
                 −1438 
                 −3890 
                 South 
                 D12 
                 −1905 
                 −12065 
                 17.505 
                 2 
               
               
                 200 
                 Signal 
                 −1313 
                 −3890 
                 South 
                 B12 
                 −1905 
                 −14605 
                 18.100 
                 2 
               
               
                 201 
                 Signal 
                 −1188 
                 −3890 
                 South 
                 A5 
                 −10795 
                 −15875 
                 1.248 
                 0 
               
               
                 202 
                 Signal 
                 −1063 
                 −3890 
                 South 
                 C6 
                 −9525 
                 −13335 
                 1.116 
                 0 
               
               
                 203 
                 Signal 
                 −938 
                 −3890 
                 South 
                 B5 
                 −10795 
                 −14605 
                 1.087 
                 0 
               
               
                 204 
                 Signal 
                 −813 
                 −3890 
                 South 
                 A4 
                 −12065 
                 −15875 
                 1.065 
                 0 
               
               
                 205 
                 Signal 
                 − 688 
                 −3890 
                 South 
                 B4 
                 −12065 
                 −14605 
                 0.942 
                 0 
               
               
                 206 
                 Signal 
                 −S63 
                 −3890 
                 South 
                 A2 
                 −14605 
                 −15875 
                 0.854 
                 2 
               
               
                 207 
                 Signal 
                 −438 
                 −3890 
                 South 
                 D5 
                 −10795 
                 −12065 
                 0.789 
                 2 
               
               
                 208 
                 Signal 
                 −313 
                 −3890 
                 South 
                 E6 
                 −9525 
                 −10795 
                 0.750 
                 2 
               
               
                 209 
                 Signal 
                 −188 
                 −3890 
                 South 
                 C3 
                 −13335 
                 −13335 
                 0.718 
                 2 
               
               
                 210 
                 Signal 
                 −63 
                 −3890 
                 South 
                 C13 
                 −635 
                 −13335 
                 16.512 
                 4 
               
               
                 211 
                 Signal 
                 63 
                 −3890 
                 South 
                 B13 
                 −635 
                 −14605 
                 15.351 
                 4 
               
               
                 212 
                 Signal 
                 188 
                 −3890 
                 South 
                 D23 
                 12065 
                 −12065 
                 −0.688 
                 0 
               
               
                 213 
                 Signal 
                 313 
                 −3890 
                 South 
                 B25 
                 14605 
                 −14605 
                 −0.750 
                 0 
               
               
                 214 
                 Signal 
                 438 
                 −3890 
                 South 
                 D22 
                 10795 
                 −12065 
                 −0.789 
                 0 
               
               
                 215 
                 Signal 
                 563 
                 −3890 
                 South 
                 B24 
                 13335 
                 −14605 
                 −0.839 
                 0 
               
               
                 216 
                 Signal 
                 688 
                 −3890 
                 South 
                 A25 
                 14605 
                 −15875 
                 −0.861 
                 2 
               
               
                 217 
                 Signal 
                 813 
                 −3890 
                 South 
                 A24 
                 13335 
                 −15875 
                 −0.957 
                 2 
               
               
                 218 
                 Signal 
                 938 
                 −3890 
                 South 
                 D20 
                 8255 
                 −12065 
                 −1.117 
                 2 
               
               
                 219 
                 Signal 
                 1063 
                 −3890 
                 South 
                 E19 
                 6985 
                 −10795 
                 −1.166 
                 2 
               
               
                 220 
                 Signal 
                 1188 
                 −3890 
                 South 
                 B14 
                 635 
                 −14605 
                 19.376 
                 4 
               
               
                 221 
                 VSS 
                 1313 
                 −3890 
                 South 
               
               
                 222 
                 Signal 
                 1438 
                 −3890 
                 South 
                 A14 
                 635 
                 −15875 
                 14.925 
                 4 
               
               
                 223 
                 Signal 
                 1563 
                 −3890 
                 South 
                 C20 
                 8255 
                 −13335 
                 −1.411 
                 0 
               
               
                 224 
                 Signal 
                 1688 
                 −3890 
                 South 
                 D19 
                 6985 
                 −12065 
                 −1.543 
                 0 
               
               
                 22S 
                 Signal 
                 1813 
                 −3890 
                 South 
                 B20 
                 8255 
                 −14605 
                 −1.663 
                 0 
               
               
                 226 
                 Signal 
                 1938 
                 −3890 
                 South 
                 E18 
                 5715 
                 −10795 
                 −1.828 
                 4 
               
               
                 227 
                 Signal 
                 2063 
                 −3890 
                 South 
                 C19 
                 6985 
                 −13335 
                 −1.919 
                 4 
               
               
                 228 
                 Signal 
                 2188 
                 −3890 
                 South 
                 D18 
                 5715 
                 −12065 
                 −2.318 
                 4 
               
               
                 229 
                 Signal 
                 2313 
                 −3890 
                 South 
                 E15 
                 1905 
                 −10795 
                 16.924 
                 3 
               
               
                 230 
                 Signal 
                 2438 
                 −3890 
                 South 
                 D15 
                 1905 
                 −12065 
                 15.338 
                 3 
               
               
                 231 
                 Signal 
                 2563 
                 −3890 
                 South 
                 B15 
                 1905 
                 −14605 
                 16.284 
                 3 
               
               
                 232 
                 Signal 
                 2688 
                 −3890 
                 South 
                 A15 
                 1905 
                 −15875 
                 15.307 
                 3 
               
               
                 233 
                 VSS 
                 2813 
                 −3890 
                 South 
               
               
                 234 
                 VDD 
                 2938 
                 −3890 
                 South 
               
               
                 235 
                 Signal 
                 3063 
                 −3890 
                 South 
                 D17 
                 4445 
                 −12065 
                 −5.915 
                 0 
               
               
                 236 
                 Signal 
                 3188 
                 −3890 
                 South 
                 A17 
                 4445 
                 −15875 
                 −9.535 
                 3 
               
               
                 237 
                 Signal 
                 3313 
                 −3890 
                 South 
                 C16 
                 3175 
                 −13335 
                 68.442 
                 1 
               
               
                 238 
                 Signal 
                 3438 
                 −3890 
                 South 
                 B16 
                 3175 
                 −14605 
                 40.741 
                 1 
               
               
                 239 
                 Signal 
                 3563 
                 −3890 
                 South 
                 A16 
                 3175 
                 −15875 
                 30.889 
                 1 
               
               
                 240 
                 VDD 
                 3688 
                 −3890 
                 South 
               
               
                   
               
               
                 Summary file 112 includes six tables:  
               
             
          
         
       
     
     (1) Table 4: chip statistics (die size, die pitch, die pad size, and die matrix size), chip input/output total and per quadrant, number of signals total and per quadrant, ground and voltage pads on the chip total and per quadrant. 
     (2) Table 5: module statistics, including module input/output input parameter, number of signal pads, voltage and ground pads, percent number of signal BGA pads per total BGA pads, percent number of ground and voltage BGA pads per total ground and voltage BGA pads; module laminate size; BGA pad pitch; BGA matrix size (rows by columns); full matrix or depopulated matrix identifier; die facing parameter (whether die pads are facing toward or away from carrier); enumerate the number of voltage rings; wire bond length, space for fingers plus fan out wiring, space for fan out wiring; 
     (3) Table 6: truth table for testing that five required parameters (Table 7) evaluate true, as follows: 
     first, wiring distance between wire bond fingers and either (a) the edge of via lands on an upper facing die, or (b) either the procoat opening or copper diameter of BGA pads on a downward facing die; 
     second, enough BGA pads for number of chip signal pads; 
     third, enough wiring channel capacity to match total die signal count (Referring to FIG. 3, wiring channel  123  represents the spacing between adjacent procoat openings for downward facing die, and wiring channel  125  represents the spacing between via pad  136  and closest via pad  138 ) for, based on the amount of depopulation, the number of channels is calculated and multiplied by three lines per channel and four lines per channel; 
     forth, calculated wire line width compared with minimum manufacturing line width capability (which is an input requirement); 
     fifth, calculated wire line space compared with minimum manufacturing line space capability (which is an input requirement); 
     (4) Tables 8 and 9: calculated density factors, including 
     first, calculated choke factor (choke=channel space divided by (line space plus the line width)), back door vias (vias located in the space between the inner most edge of bond finger on the laminate and the outer most edge of the most outer voltage ring); 
     second, chip escape factor (die area divided by number of chip signal pads); 
     third, chip density factor (die area divided by number of chip I/O pads); and 
     fourth, BGA escape factor ((laminate area minus die area)/number of chip signals), for giving an estimate of density of wiring in the global area of the laminate for chip escape. 
     (5) Tables 10 and 11: gold area, including BOA pads, cavity wall (for wire bond), via areas, wiring surface front and back, wire bonding surfaces, gold stiffener (if included), including total area and cost, and minimum total thermal resistance required based on ambient temperature, chip power, and junction temperature. 
     (6) Tables 12 and 13: other miscellaneous statistics and parameters. 
     
       
         
               
             
               
             
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 CHIP STATISTICS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Die Size =  8.00 mm × 8.00 mm 
               
               
                 Die Pitch = 125 microns 
               
               
                 Die Pad Size = 70 microns 
               
               
                 The Die Matrix = 60 × 60 
               
             
          
           
               
                 Chip I/O (total/side) 
                 Chip Signals %/#Side 
                 Chip G&amp;V %/#Side 
               
               
                 240/60 
                 85.0%/51/204 
                 15.0%/9/36 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 MODULE STATISTICS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Module I/O 
                 Signal Ratio/Signal Count 
                 G/V Ratio/G/V 
               
               
                 Count 
                 48.6%/204 
                 51.4%/216 
               
               
                 420 
               
             
          
           
               
                 Module Size =  35 mm 
               
               
                 BGA Pitch = 1.27 mm 
               
               
                 Matrix Size = 26 × 26 
               
               
                 This is a 5 outer row configuration 
               
               
                 This is run is for a cavity part. 
               
               
                 This is run is for a 2S0P part. 
               
               
                 There are 1 voltage ring(s) in addition to the Ground Ring 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 TRUTH TABLE 
               
             
          
           
               
                 # Outer 
                 I/O 
                 Signals 
                 Signals 
                 Wiring 
                 Multiples 
                 Deficit 
                 Deficit 
                 Works 
                 Works 
               
             
          
           
               
                 Rows 
                 Count 
                 @3 
                 1 pc 
                 @4 
                 1 pc 
                 Fanout 
                 of Pitch 
                 @3 
                 @4 
                 @3 
                 @4 
               
               
                   
               
             
          
           
               
                 1 
                 100 
                 97/ 
                 388 
                 121/ 
                 484 
                 9.06 
                 77.251 
                 −44 
                 −68 
                 n.YNYYY 
                 n.YNYYY 
               
               
                 2 
                 192 
                 89/ 
                 356 
                 111/ 
                 444 
                 7.79 
                 66.424 
                 −36 
                 −58 
                 n.YNYYY 
                 n.YNYYY 
               
               
                 3 
                 276 
                 81/ 
                 324 
                 101/ 
                 404 
                 6.52 
                 55.597 
                 −28 
                 −48 
                 y.YYYYY 
                 y.YYYYY 
               
               
                 4 
                 352 
                 73/ 
                 292 
                 91/ 
                 364 
                 5.25 
                 44.770 
                 −20 
                 −38 
                 y.YYYYY 
                 y.YYYYY 
               
               
                 5 
                 420 
                 65/ 
                 260 
                 81/ 
                 324 
                 3.98 
                 33.943 
                 −12 
                 −28 
                 y.YYYYY 
                 y.YYYYY 
               
               
                 6 
                 480 
                 57/ 
                 228 
                 71/ 
                 284 
                 2.71 
                 23.116 
                 −4 
                 −18 
                 y.YYYYY 
                 y.YYYYY 
               
               
                 7 
                 532 
                 49/ 
                 196 
                 61/ 
                 244 
                 1.44 
                 12.289 
                 4 
                 −8 
                 n.YYNYY 
                 y.YYYYY 
               
               
                 8 
                 576 
                 41/ 
                 164 
                 51/ 
                 204 
                 0.17 
                 1.462 
                 12 
                 2 
                 n.NYNYY 
                 n.NYNYY 
               
               
                 9 
                 612 
                 33/ 
                 132 
                 41/ 
                 164 
                 −1.10 
                 −9.365 
                 20 
                 12 
                 n.NYNYY 
                 n.NYNYY 
               
               
                 10 
                 640 
                 25/ 
                 100 
                 31/ 
                 124 
                 −2.37 
                 −20.192 
                 28 
                 22 
                 n.NYNYY 
                 n.NYNYY 
               
               
                 11 
                 660 
                 17/ 
                 68 
                 21/ 
                 84 
                 −3.64 
                 −31.019 
                 36 
                 32 
                 n.NYNYY 
                 n.NYNYY 
               
               
                 12 
                 672 
                 9/ 
                 36 
                 11/ 
                 44 
                 −4.91 
                 −41.846 
                 44 
                 42 
                 n.NYNYY 
                 n.NYNYY 
               
               
                 13 
                 676 
                 1/ 
                 4 
                 1/ 
                 4 
                 −6.18 
                 −52.673 
                 52 
                 52 
                 n.NYNYY 
                 n.NYNYY 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 PARAMETERS TEST OUTPUT 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 First Position =  Enough Wiring Room after Fingers 
               
               
                 (non-Choked) 
               
               
                 Second Position =  Enough BGA Balls for Chip Signals 
               
               
                 Third Position =  Enough Channel Capacity to match Signal 
               
               
                 Count 
               
               
                 Fourth Position = Wire Width above Minimum 
               
               
                 Fifth Position =  Wire to Wire Space above Minimum 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 WIRE DIMENSION AND PITCH 
               
             
          
           
               
                 Nominal Wire Bond Length is 2.4 mm. 
               
               
                 Space for fingers plus fanout wiring 6.05 mm 
               
               
                 Space for fanout wiring is 3.98 mm 
               
               
                 Multiples of Pitch (Lower is more choked) 33.9 
               
               
                 Back Door Vias selected (per Quadrant) is 10 
               
               
                 Lines per Channel Selected is 4 
               
               
                 Corresponding Line Width, Space, and Pitch is 51.0, 
               
               
                 66.3,and 117.3 microns. 
               
               
                 Procoat Registration is 25 microns. 
               
             
          
           
               
                   
                 Lines/ 
                 Wire 
                 Wire 
                 Wire 
               
               
                   
                 Channel 
                 Width 
                 Space 
                 Pitch 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 148.6 
                 193.2 
                 341.8 
               
               
                   
                 2 
                 90.7 
                 117.9 
                 208.6 
               
               
                   
                 3 
                 65.2 
                 84.8 
                 150.0 
               
               
                   
                 4 
                 51.0 
                 66.3 
                 117.3 
               
               
                   
                 5 
                 41.8 
                 54.3 
                 96.1 
               
               
                   
                 6 
                 35.4 
                 46.0 
                 81.4 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 ESCAPE FACTORS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Chip Escape Factor (die area/chipsigs)is 
                 0.31 sq 
               
               
                   
                   
                 mm/chipsig 
               
               
                   
                 Chip Density Factor (die area/chipio)is 
                 0.27 sq 
               
               
                   
                   
                 mm/chipio 
               
               
                   
                 BGA Escape Factor (laminate area-die 
                 5.7 sq 
               
               
                   
                 shadow/chipsig) is 
                 mm/chipsig 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 DIE UP 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Total Gold Area on a die up 
                 0.36 sq. inches 
               
               
                   
                 Cost of Gold Area on a die up 
                 0.03 dollars 
               
               
                   
                 Flower Area is 
                 0.08 sq. inches 
               
               
                   
                 Bonding Surface (Fingers, 
               
               
                   
                 Voltage Ring, Ground Ring) 
                 0.055 
               
               
                   
                 Via Land Area on S2 side 
                 0.001 
               
               
                   
                 Ground Buss on S2 Side 
                 0.019 
               
               
                   
                 BGA Area is 
                 0.202 
               
               
                   
                 Gold Runner area is 
                 0.008 
               
               
                   
                 Wiring Gold on a Die Up Part 
               
               
                   
                 is assumed to be masked 
               
               
                   
                 Via Count for Die-Up Part is 
                 206 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 CAVITY PART 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Total Gold Area on a Cavity 
                   
               
               
                   
                 Part (minus Stiffener) 
                 1.00 sq. inches 
               
               
                   
                 Gold Stiffener Area is 
                 1.90 sq. inches 
               
               
                   
                 Total Gold Area Cost on a 
               
               
                   
                 Cavity Part (with Stiffener) 
                 0.28 dollars 
               
               
                   
                 Bonding Surface (Fingers, 
                 0.055 
               
               
                   
                 Voltage Ring, Ground Ring) 
               
               
                   
                 Wiring Front and Back (from 
                 0.668 
               
               
                   
                 fingers out) 
               
               
                   
                 BOA Pads 
                 0.202 
               
               
                   
                 Cavity Wall 
                 0.022 
               
               
                   
                 Via Area 
                 0.054 
               
               
                   
                 Via Count for Cavity Part is 
                 77 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
               
                 MISCELLANEOUS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Flatness per inch 
                 2.07 
               
               
                   
                 Cavity size is 
                 9.00 mm 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 THERMALS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Ambient Temperature is 
                 40 C. 
               
               
                   
                 Chip Power is 
                 10 watts. 
               
               
                   
                 Assumed Maximum Junction 
                 125 
               
               
                   
                 Temperature is 
               
               
                   
                 Minimum Total Resistance 
                 8.5 C./Watt 
               
               
                   
                 needed is 
               
               
                   
                   
               
             
          
         
       
     
     Crossing file  114  includes four columns, including: 
     (1) chip pad number (same as centroid data, supra); 
     (2) quadrant (north, west, east, or south); 
     (3) BGA pad; and 
     (4) number of lines that have crossed the die pad to BGA pad line. 
     Code  102  analyzes each connection line for the number of times any other connection line crosses it. The more crosses, the tougher the design. This file is sorted in descending order of number of crossings, so that the top of the file identifies the lines (or, nets) that are not well placed. Table 14 is an example of the top part of a crossing file  114 . 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
             
             
               
                   
               
               
                 CROSSINGS FILE 
               
             
          
           
               
                   
                 CHIP 
                   
                   
                 BGA 
                   
               
               
                   
                 PAD 
                   
                 QUADRANT 
                 PAD 
                 CROSSINGS 
               
               
                   
                   
               
             
          
           
               
                  1 
                 103 
                 Signal 
                 North 
                 AF14 
                 13  
               
               
                  2 
                 100 
                 Signal 
                 North 
                 AD14 
                 12  
               
               
                  3 
                 101 
                 Signal 
                 North 
                 AE14 
                 12  
               
               
                  4 
                  95 
                 Signal 
                 North 
                 AF15 
                 11  
               
               
                  5 
                  86 
                 Signal 
                 North 
                 AF16 
                 10  
               
               
                  6 
                  79 
                 Signal 
                 North 
                 AD17 
                 8 
               
               
                  7 
                  84 
                 Signal 
                 North 
                 AC16 
                 8 
               
               
                  8 
                 107 
                 Signal 
                 North 
                 AC13 
                 8 
               
               
                  9 
                 115 
                 Signal 
                 North 
                 AE12 
                 8 
               
               
                 10 
                 116 
                 Signal 
                 North 
                 AF12 
                 8 
               
               
                 11 
                  82 
                 Signal 
                 North 
                 AB16 
                 7 
               
               
                 12 
                 112 
                 Signal 
                 North 
                 AB12 
                 6 
               
               
                 13 
                  67 
                 Signal 
                 North 
                 AE19 
                 5 
               
               
                 14 
                  85 
                 Signal 
                 North 
                 AB7 
                 5 
               
               
                 15 
                  94 
                 Signal 
                 North 
                 AD6 
                 5 
               
               
                 16 
                  71 
                 Signal 
                 North 
                 AF25 
                 4 
               
               
                 17 
                  72 
                 Signal 
                 North 
                 AE24 
                 4 
               
               
                 18 
                  75 
                 Signal 
                 North 
                 AD23 
                 4 
               
               
                 19 
                  77 
                 Signal 
                 North 
                 AB21 
                 4 
               
               
                 20 
                  78 
                 Signal 
                 North 
                 AF26 
                 4 
               
               
                 21 
                  80 
                 Signal 
                 North 
                 AD24 
                 4 
               
               
                 22 
                  87 
                 Signal 
                 North 
                 AF2 
                 4 
               
               
                 23 
                  88 
                 Signal 
                 North 
                 AD5 
                 4 
               
               
                 24 
                  89 
                 Signal 
                 North 
                 AE4 
                 4 
               
               
                 25 
                  90 
                 Signal 
                 North 
                 AF3 
                 4 
               
               
                 26 
                  91 
                 Signal 
                 North 
                 AB8 
                 4 
               
               
                 27 
                  92 
                 Signal 
                 North 
                 AF4 
                 4 
               
               
                 28 
                  93 
                 Signal 
                 North 
                 AE5 
                 4 
               
               
                 29 
                  96 
                 Signal 
                 North 
                 AC7 
                 4 
               
               
                 30 
                  97 
                 Signal 
                 North 
                 AD7 
                 4 
               
               
                 31 
                  99 
                 Signal 
                 North 
                 AF6 
                 4 
               
               
                 32 
                 105 
                 Signal 
                 North 
                 AF7 
                 4 
               
               
                 33 
                 106 
                 Signal 
                 North 
                 AC9 
                 4 
               
               
                 34 
                 210 
                 Signal 
                 South 
                 C13 
                 4 
               
               
                 35 
                 211 
                 Signal 
                 South 
                 B13 
                 4 
               
               
                 36 
                 220 
                 Signal 
                 South 
                 B14 
                 4 
               
               
                 37 
                 222 
                 Signal 
                 South 
                 A14 
                 4 
               
               
                 38 
                 226 
                 Signal 
                 South 
                 E18 
                 4 
               
               
                 39 
                 227 
                 Signal 
                 South 
                 C19 
                 4 
               
               
                 40 
                 228 
                 Signal 
                 South 
                 D18 
                 4 
               
               
                 41 
                  83 
                 Signal 
                 North 
                 AB22 
                 3 
               
               
                 42 
                 104 
                 Signal 
                 North 
                 AD8 
                 3 
               
               
                 43 
                 108 
                 Signal 
                 North 
                 AB10 
                 3 
               
               
                 44 
                 109 
                 Signal 
                 North 
                 AF9 
                 3 
               
               
                 45 
                 110 
                 Signal 
                 North 
                 AC10 
                 3 
               
               
                 46 
                 111 
                 Signal 
                 North 
                 AD10 
                 3 
               
               
                 47 
                 189 
                 Signal 
                 South 
                 E11 
                 3 
               
               
                 48 
                 229 
                 Signal 
                 South 
                 E15 
                 3 
               
               
                 49 
                 230 
                 Signal 
                 South 
                 D15 
                 3 
               
               
                 50 
                 231 
                 Signal 
                 South 
                 B15 
                 3 
               
               
                 51 
                 232 
                 Signal 
                 South 
                 A15 
                 3 
               
               
                 52 
                 236 
                 Signal 
                 South 
                 A17 
                 3 
               
               
                 53 
                  66 
                 Signal 
                 North 
                 AF23 
                 2 
               
               
                 54 
                 102 
                 Signal 
                 North 
                 AE7 
                 2 
               
               
                 55 
                 113 
                 Signal 
                 North 
                 AE10 
                 2 
               
               
                 56 
                 117 
                 Signal 
                 North 
                 AF10 
                 2 
               
               
                 57 
                 187 
                 Signal 
                 South 
                 A8 
                 2 
               
               
                 58 
                 188 
                 Signal 
                 South 
                 B8 
                 2 
               
               
                 59 
                 191 
                 Signal 
                 South 
                 D11 
                 2 
               
               
                 60 
                 196 
                 Signal 
                 South 
                 D8 
                 2 
               
               
                 61 
                 198 
                 Signal 
                 South 
                 C7 
                 2 
               
               
                 62 
                 199 
                 Signal 
                 South 
                 D12 
                 2 
               
               
                 63 
                 200 
                 Signal 
                 South 
                 B12 
                 2 
               
               
                 64 
                 206 
                 Signal 
                 South 
                 A2 
                 2 
               
               
                 65 
                 207 
                 Signal 
                 South 
                 D5 
                 2 
               
               
                 66 
                 208 
                 Signal 
                 South 
                 E6 
                 2 
               
               
                 67 
                 209 
                 Signal 
                 South 
                 C3 
                 2 
               
               
                 68 
                 216 
                 Signal 
                 South 
                 A25 
                 2 
               
               
                 69 
                 217 
                 Signal 
                 South 
                 A24 
                 2 
               
               
                 70 
                 218 
                 Signal 
                 South 
                 D20 
                 2 
               
               
                 71 
                 219 
                 Signal 
                 South 
                 E19 
                 2 
               
               
                 72 
                  61 
                 Signal 
                 North 
                 AC20 
                 1 
               
               
                 73 
                  62 
                 Signal 
                 North 
                 AF22 
                 1 
               
               
                 74 
                  63 
                 Signal 
                 North 
                 AE22 
                 1 
               
               
                 75 
                  64 
                 Signal 
                 North 
                 AB20 
                 1 
               
               
                 76 
                  69 
                 Signal 
                 North 
                 AE23 
                 1 
               
               
                 77 
                  70 
                 Signal 
                 North 
                 AF24 
                 1 
               
               
                 78 
                 118 
                 Signal 
                 North 
                 AC11 
                 1 
               
               
                 79 
                 119 
                 Signal 
                 North 
                 AD11 
                 1 
               
               
                 80 
                 186 
                 Signal 
                 South 
                 D9 
                 1 
               
               
                 81 
                 237 
                 Signal 
                 South 
                 C16 
                 1 
               
               
                 82 
                 238 
                 Signal 
                 South 
                 B16 
                 1 
               
               
                 83 
                 239 
                 Signal 
                 South 
                 A16 
                 1 
               
               
                 84 
                  1 
                 Signal 
                 East 
                 E22 
                 0 
               
               
                 85 
                  2 
                 Signal 
                 East 
                 C24 
                 0 
               
               
                 86 
                  3 
                 Signal 
                 East 
                 A26 
                 0 
               
               
                   
               
             
          
         
       
     
     An optional output is illustrated, in part, in Table 15. Holes.txt is a file that gives the X, Y coordinates of where vias are positioned next to BGAs. These are calculated by code  102  from input parameters  100 . 
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 HOLES 
               
             
          
           
               
                   
                 X COORD 
                 Y COORD 
               
               
                   
                   
               
             
          
           
               
                   
                 11102.5885 
                 −11102.5885 
               
               
                   
                 11102.5885 
                 −9832.5885 
               
               
                   
                 11102.5885 
                 −8562.5885 
               
               
                   
                 11102.5885 
                 −7292.5885 
               
               
                   
                 11102.5885 
                 −6022.5885 
               
               
                   
                 11102.5885 
                 −4752.5885 
               
               
                   
                 11102.5885 
                 −3482.5885 
               
               
                   
                 11102.5885 
                 −2212.5885 
               
               
                   
                 11102.5885 
                 −942.5885 
               
               
                   
                 11102.5885 
                 942.5885 
               
               
                   
                 11102.5885 
                 2212.5885 
               
               
                   
                 11102.5885 
                 3482.5885 
               
               
                   
                 11102.5885 
                 4752.5885 
               
               
                   
                 11102.5885 
                 6022.5885 
               
               
                   
                 11102.5885 
                 7292.5885 
               
               
                   
                 11102.5885 
                 8562.5885 
               
               
                   
                 11102.5885 
                 9832.5885 
               
               
                   
                 12372.5885 
                 −11102.5885 
               
               
                   
                 9832.5885 
                 13642.5885 
               
               
                   
                 9832.5885 
                 14912.5885 
               
               
                   
                 9832.5885 
                 16182.5885 
               
               
                   
                 11102.5885 
                 11102.5885 
               
               
                   
                 11102.5885 
                 12372.5885 
               
               
                   
                 11102.5885 
                 13642.5885 
               
               
                   
                 11102.5885 
                 14912.5885 
               
               
                   
                 11102.5885 
                 16182.5885 
               
               
                   
                 12372.5885 
                 13642.5885 
               
               
                   
                 12372.5885 
                 14912.5885 
               
               
                   
                 12372.5885 
                 16182.5885 
               
               
                   
                 13642.5885 
                 13642.5885 
               
               
                   
                 13642.5885 
                 14912.5885 
               
               
                   
                 13642.5885 
                 16182.5885 
               
               
                   
                 14912.5885 
                 16182.5885 
               
               
                   
                 16182.5885 
                 16182.5885 
               
               
                   
                   
               
             
          
         
       
     
     Wireable text file  116  (Tables 16 and 17) is multi-purpose. It provides a code  102  generated count of consecutive (that is, runs) signals or grounds or voltages—the larger the run of signals, the more difficult it is to wire. Code  102  scans the netlist which has either been generated or received as input, identifies the power and ground names and quadrant, and determines the number of wirebond finger positions needed. 
     Wireable text file  116  has two parts: 
     (1) Table 16: runs analysis, in which for each of the four quadrants runs are defined by the number of consecutive signals or consecutive power and ground lines, number of wirebond fingers needed per side, and a total number of die pads, signal pads, and ground/voltage pads. 
     (2) Table 17: net list scan, whether fabricated by program or provided as input, that enumerates the different voltage levels per quadrant. 
     
       
         
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
           
               
                 TABLE 16 
               
             
             
               
                   
               
               
                 WIREABLE TEXT FILE - RUNS 
               
             
          
           
               
                   
                 Run 
                 Side 
                 Signal 
                 Ground 
               
               
                   
                   
               
               
                   
                 1 
                 East 
                 0 
                 4 
               
               
                   
                 2 
                 East 
                 2 
                 2 
               
               
                   
                 6 
                 East 
                 2 
                 0 
               
               
                   
                 7 
                 East 
                 1 
                 0 
               
               
                   
                 9 
                 East 
                 1 
                 0 
               
               
                   
                 20  
                 East 
                 1 
                 0 
               
             
          
           
               
                   
                 Total Fingers needed for this side is 54 
               
               
                   
                 Total Pads, Signal Pads, Gnd/Vlt Pads 60 52 8 
               
             
          
           
               
                   
                 1 
                 North 
                 1 
                 7 
               
               
                   
                 2 
                 North 
                 1 
                 1 
               
               
                   
                 4 
                 North 
                 3 
                 0 
               
               
                   
                 5 
                 North 
                 1 
                 0 
               
               
                   
                 15  
                 North 
                 1 
                 0 
               
               
                   
                 16  
                 North 
                 1 
                 0 
               
             
          
           
               
                   
                 Total Fingers needed for this side is 52 
               
               
                   
                 Total Pads, Signal Pads, Gnd/Vlt Pads 60 51 9 
               
             
          
           
               
                   
                 1 
                 West 
                 2 
                 8 
               
               
                   
                 2 
                 West 
                 1 
                 2 
               
               
                   
                 3 
                 West 
                 2 
                 0 
               
               
                   
                 4 
                 West 
                 2 
                 0 
               
               
                   
                 6 
                 West 
                 1 
                 0 
               
               
                   
                 8 
                 West 
                 3 
                 0 
               
             
          
           
               
                   
                 Total Fingers needed for this side is 50 
               
               
                   
                 Total Pads, Signal Pads, Gnd/Vlt Pads 60 48 12 
               
             
          
           
               
                   
                 1 
                 South 
                 0 
                 5 
               
               
                   
                 2 
                 South 
                 1 
                 1 
               
               
                   
                 3 
                 South 
                 1 
                 0 
               
               
                   
                 5 
                 South 
                 1 
                 0 
               
               
                   
                 9 
                 South 
                 1 
                 0 
               
               
                   
                 11  
                 South 
                 1 
                 0 
               
               
                   
                 23  
                 South 
                 1 
                 0 
               
             
          
           
               
                   
                 Total Fingers needed for this side is 54 
               
               
                   
                 Total Pads, Signal Pads, Gnd/Vlt Pads 60 53 7 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 17 
               
             
             
               
                   
               
               
                 NET LIST SCAN 
               
             
          
           
               
                 # 
                 Power/Ground 
                 Side 
               
               
                   
               
               
                 1 
                 VDD 
                 East 
               
               
                 2 
                 VSS 
                 East 
               
               
                 1 
                 VSS 
                 North 
               
               
                 2 
                 VDD 
                 North 
               
               
                 1 
                 VSS 
                 West 
               
               
                 2 
                 VDD 
                 West 
               
               
                 1 
                 VSS 
                 South 
               
               
                 2 
                 VDD 
                 South 
               
               
                   
               
             
          
         
       
     
     Code  102  also generates script file  118 . A session is opened in Autocad to run script file  118  to create therefrom graphical file  106 . 
     Table 17 is a pseudo code representation of the process implemented by code  102  for generating script file  118 . This is the script file that is “played” when in the Autocad environment to generate graphical representation  106 , a display of which is shown in FIG.  2 . In a preferred embodiment, script file  118  is an Autocad script file, but equivalent computer automated design (CAD) environments may also be used. This Table 17 sets forth editing friendly code within code  102  for the “RATS”. Rats is a term referring to a straight line that emanates from the center of a die pad  178  to a BGA ball  180 . It is then manipulated by moving within a layer and/or placing part of the path on other layers of the package  144 . In this case, the centroid data of the die has been created and routed out to the center of the BGA pad; either by customer definition (Case “C”) or by creation within the program  102  (Case “A”). 
     As is set forth in Table 17, code  102  creates a line or rat from (Chipx, Chipy) to (BGAx, BGAy). This line is multiverticed. Each rat has a width that is first zero and then increments to a final value with steps in the middle. It is stepped larger and larger as processing and graphical display moves counter clockwise (CCW) around the die. After code  102  creates the rats, Autocad displays graphical file  106  which shows where rats come from relative to the die sequence without having to window out and over to the die or having to select the wire to have a dialog box displayed. At the end of processing, all the wires are then converted to one width. Alternatively to using different line widths, the graphic display may use different colors. 
     
       
         
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
           
               
                 TABLE 17 
               
               
                   
               
               
                 SCRIPT FILE GENERATION 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 /* RATS 
                 */ 
               
               
                 if rats=1 then do 
                 /* Indicator in the program to have 
               
               
                   
                 RATS created*/ 
               
               
                   
                 /*ratsline is the name of the matrix 
               
               
                   
                 that is a line for line autocad script 
               
               
                   
                 text file. The variable index is 
               
               
                   
                 line1, line2......*/ 
               
             
          
           
               
                 ratsline.index=‘-layer set Rats’ 
                 /* Autocad command that 
               
               
                   
                 creates a layer with 
               
               
                   
                 Autocad that all RATS 
               
               
                   
                 are drawn in; this is a 
               
               
                   
                 drawing organization 
               
               
                   
                 technique* / 
               
             
          
           
               
                 index=index+1 
                 /* increment index to write to the 
               
               
                   
                 next line*/ 
               
               
                 do yy=1 to chipio 
                 /* start stepping through the centroid 
               
               
                   
                 file line for line by incrementing 
               
               
                   
                 line.yy matrix */ 
               
               
                   
                 /*# lab xc yc sd an xb yb s */ 
               
             
          
           
               
                 parse value line.yy with v1 v2 v3 v4 v5 v6 v7 v8 v9 
               
             
          
           
               
                   
                 /* Take the Centroid Data file; read 
               
               
                   
                 the line and parse the string by using 
               
               
                   
                 the blanks as demarcation*/ 
               
             
          
           
               
                 Select 
               
             
          
           
               
                 when v6=‘’then do 
                 /*V6 is the Alpha Numeric; when v6 
               
               
                   
                 is null, this is either a ground 
               
               
                   
                 or voltage, not a die to end BGA 
               
               
                   
                 signal connection*/ 
               
               
                 otherwise 
                 /* the line has to be a signal*/ 
               
               
                 xfrom=v3;yfrom=v4 
                 /* Start point is the die pad 
               
               
                   
                 centroid*/ 
               
             
          
           
               
                 xinc=(v7−v3)/linesegments;yinc=(v8−v4)/linesegments 
               
             
          
           
               
                   
                 /* take the distance in both the x 
               
               
                   
                 and y dimension from the die pad 
               
               
                   
                 to the BGA and divide it by the 
               
               
                   
                 number of segments selected in 
               
               
                   
                 code above in program; this will 
               
               
                   
                 give each vertex of the line.*/ 
               
             
          
           
               
                 rat=‘’ 
                 /* give the string rat an initial 
               
               
                   
                 value of null string*/ 
               
               
                   
                 /* note in REXX “∥” is the 
               
               
                   
                 concatenation operator; it joins 
               
               
                   
                 text that is with quote marks*/ 
               
             
          
           
               
                 do ratpoint=1 to (linesegments+1) 
                 /* start creating 
               
               
                   
                 each point defining 
               
               
                   
                 the vertices*/ 
               
               
                 Select 
               
             
          
           
               
                 when ratpoint=1 then do 
                 /* first point will be 
               
               
                   
                 the die pad centroid*/ 
               
               
                 rat=rat∥v3∥‘,’∥v4∥‘’ 
                 /* create the string 
               
               
                   
                 that will become part of 
               
               
                   
                 the autocad command 
               
               
                   
                 language*/ 
               
               
                 end 
               
             
          
           
               
                 when ratpoint=linesegments+1 then do 
               
             
          
           
               
                   
                 /* end point will be the BGA 
               
               
                   
                 pad centroid*/ 
               
             
          
           
               
                 rat=rat∥v7∥‘,’∥v8∥‘’ 
                 /* create the string 
               
               
                   
                 that will become part of 
               
               
                   
                 the autocad command 
               
               
                   
                 language*/ 
               
               
                 end 
               
               
                 otherwise 
                 /* defining a vertex point 
               
               
                   
                 other than the endpoints of 
               
               
                   
                 the RAT*/ 
               
             
          
           
               
                 xto=xfrom+xinc;yto=yfrom+yinc 
                   
               
               
                 rat=rat∥xto∥‘,’∥yto∥‘’ 
                 /*This keeps 
               
               
                   
                 accumulating the 
               
               
                   
                 string of vertices 
               
               
                   
                 into one string*/ 
               
             
          
           
               
                 xfrom=xto;yfrom=yto 
                 /* This makes the vertex that 
               
               
                   
                 was defined as “to”, as the 
               
               
                   
                 “from” so the next point can 
               
               
                   
                 be calculated*/ 
               
               
                 end 
                 /* the Select*/ 
               
               
                 end 
                 /* Do loop*/ 
               
             
          
           
               
                 ratsline.index=‘pline ’∥rat 
                 /* Autocad language command: 
               
               
                   
                 pline x1 y1 x2 y2 x3 y3, 
               
               
                   
                 etc*/ 
               
               
                 index=index+1 
                 /* next line of the Autocad Script 
               
               
                   
                 File ratsline.index*/ 
               
             
          
           
               
                 if ratwidth&gt;ratwidthmax then ratwidth=1 
               
             
          
           
               
                   
                 /* if Rat width (line width) 
               
               
                   
                 reaches a number greater than what 
               
               
                   
                 was set, then set back to 1 
               
               
                   
                 micron*/ 
               
             
          
           
               
                 ratsline.index=‘width ’∥ratwidth 
                 /* Create Autocad 
               
               
                   
                 command that specifies 
               
               
                   
                 the width of line by the 
               
               
                   
                 command followed by the 
               
               
                   
                 width as a numeric*/ 
               
             
          
           
               
                 index=index+1 
                 /* next line of the Autocad Script 
               
               
                   
                 File ratsline.index*/ 
               
               
                 ratsline.index=blankline 
                 /* Need a blankline to 
               
               
                   
                 toggle the Autocad Program to 
               
               
                   
                 go back to “Command:” 
               
               
                   
                 Prompt*/ 
               
               
                 index=index+1 
                 /* next line of the Autocad Script 
               
               
                   
                 File ratsline.index*/ 
               
             
          
           
               
                 ratwidth=ratwidth+ratwidthinc 
                 /*increment the width of the 
               
               
                   
                 line for the next Rat created 
               
               
                   
                 in the next loop*/ 
               
             
          
           
               
                 end 
                 /*Select*/ 
               
               
                 end 
                 /*Do Loop*/ 
               
               
                 end 
                 /*End the If statement on whether 
               
               
                   
                 Rats are part of the script*/ 
               
               
                   
               
             
          
         
       
     
     Depopulation refers to removal of a center most matrix of BGA balls to leave some number of outside rows. This is done to remove balls immediately under the chip site. 
     Referring to FIG. 2, an example output of graphical file  106  is illustrated for a wire bond constructed module. This shows an annotated plan view of a module  140  including chip  142 , laminate  144  which includes wires  146  interconnecting chip pads  142  with BGA site  150  and associated via. This is further illustrated in FIGS. 7 and 8 where BGA site  150  includes BGA  156 , procoat opening  154 , procoat layer  152 , substrate layers  164 , top side  160  of plated through via  158 , dogbone  162  (a dogbone is a connector between BGA pad  156  and via  160 ). 
     Voltage ring  166  is a continuous surface of constant width, generally, that is offset from and encompasses or surrounds chip  142  site. Some wires (the power and ground wires) from chip pads  148  connect to voltage rings  166 . The innermost voltage ring  166  is usually the ground level. (For a flip chip constructed module, voltage rings  166  are not required.) Wire bond fingers  210 , shown in FIG. 9, are not shown in FIG.  2 . These are oblong shaped copper features that are placed between rings  166  and BGA procoat opening  154  in a die down configuration or between rings  166  and via lands  160  in a die up configuration. 
     As shown in FIG. 2, and enlarged in FIG. 5, which is an enlargement of the north west corner of FIG. 2, on the west side there are circuit lines  172  which run between die pads  174  and BGA sites  176  (which only appear in FIG. 2) without crossover. On the north side, extensive cross over  170  occurs for lines interconnecting die pads  178  and BGA sites  180 . 
     FIG. 11 sets forth method steps executed within code module  102 , and these are further described in the pseudo code representation of Table 1. 
     Set analysis step  210  controls the files  106 - 116  to be output, and the run mode. The user may specify the pitch of the die or the number of die I/O desired. Also, the user may specify the number of outer rows (matrix size minus (the depopulation divided by 2)) or the number of BGA I/O pads desired. 
     Set variables step  212  defines cases A, B and C. For case A, the user tells the program  102  that the die and net list are to be calculated by code  102  (that is, the program creates its own). For case B, the user specifies the die in terms of a die centroid file input without defining the net list. A net list is a listing of die pad connections giving pad number and/or die pad names to BGA connections in terms of alpha numeric coordinate. For case C, the user defines both the die centroid file and the net list. The assembly technology is set as flip chip or wirebond. Chip parameters are received as input, including such parameters as chip size, chip width, chip length, chip pitch, chip I/O, die pad size, die pad shape, and percent ground and voltage (defined above). Package parameters are defined, including such parameters as die up or cavity configuration, substrate size, module I/O count, number of outer rows, BGA pitch, number of vertex points defined for a line, number of rings, width and spacing of voltage and ground rings, size of via features (pad, dogbone, vias), increment of variable width, wire bond length, and wiring rules (minimum wire space and width). 
     Full matrix determination step  214 , based on module size and pitch of BGA, calculates whether the number of columns is odd or even. Quadrant dividing slope is calculated, which is the slope of an imaginary line from the center of the package to the corner of the die, and an adjacent pair of these defines a quadrant. If the desired number of module I/O pads, or the number of outer rows, is provided by the user, the amount of depopulation is calculated. The Jedec alpha designation is entered for each row. 
     For case A, create die step  216  creates centroid data for flip chip or wire bond configuration. Table 17 sets forth the code  102  for step  216  generation of die. There are two cases of Generation of a Die: 1) Wirebond Single Row Peripheral, and 2) Flip Chip Area Array (which assumes square die). 
     For case B, create centroid data step  218 , responsive to user provided centroid data, assigns each pad to a quadrant. This list is reordered, if needed, to a clockwise order while calculating the minimum chip pitch for output to graphical file  106  (minimum spacing between wire pads on a wirebound) and the curve (distance between edge of die and center line of outermost wire bond pad). Code  102  then calculates composition ratios. 
     For case C, create centroid step  220 , assigns quadrants and calculates compositions (less work than case B). 
     
       
         
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
               
             
               
             
               
               
             
               
             
           
               
                 TABLE 18 
               
               
                   
               
               
                 CENTROID DIE DATA GENERATION 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 /* Flip PADS CALCULATION...Case A */ 
               
               
                 if case =‘a’ then closestpads=‘Any Orthogonal Adjacent’ 
               
             
          
           
               
                   
                 /* Print Ont in Graphical File 
               
               
                   
                 that keeps track of closest C4 to 
               
               
                   
                 C4 distance*/ 
               
             
          
           
               
                 Select 
                 /* This Select chooses between 
               
               
                   
                 Flip Chip Routine or Wirebond 
               
               
                   
                 Routine*/ 
               
             
          
           
               
                 when case=‘a’ &amp; tech=‘fc’ then do 
                 /* In the case of 
               
               
                   
                 Flip Chip*/ 
               
             
          
           
               
                 Select 
                 /* This Select chooses between 
               
               
                   
                 setting the minimum C4 pitch to a 
               
               
                   
                 minimum or setting the number of 
               
               
                   
                 chip IO*/ 
               
             
          
           
               
                 when setchipcp=‘1’ then do 
                 /* If the chip 
               
               
                   
                 pitch is specified, 
               
               
                   
                 then do the 
               
               
                   
                 following*/ 
               
             
          
           
               
                 indent=edge+.5*dp 
                 /* Figure out how far in the 
               
               
                   
                 centerline of the first pad 
               
               
                   
                 should be; edge (distance 
               
               
                   
                 defined by user representing 
               
               
                   
                 die edge to edge of die pad) 
               
               
                   
                 + half a die pad width*/ 
               
               
                 dist=cz*1000−2*indent 
                 /* Figure out the span, 
               
               
                   
                 in um when each 
               
               
                   
                 indentation is taken 
               
               
                   
                 out; cz=chip size in 
               
               
                   
                 mm*/ 
               
               
                 spaces=dist%cp 
                 /* Take distance and divide 
               
               
                   
                 by chip pitch; cp. The % 
               
               
                   
                 sign in REXX takes the 
               
               
                   
                 integer part only*/ 
               
               
                 pads=spaces+1 
                 /* The total numbers of pads 
               
               
                   
                 is 1 more than the total 
               
               
                   
                 number of spaces*/ 
               
               
                 chipio=pads*pads 
                 /* The total number pads is 
               
               
                   
                 the matrix of pad by pad*/ 
               
               
                 end 
               
             
          
           
               
                 when setchipio=‘1’ then do 
                 /* This is the case 
               
               
                   
                 when you have a total 
               
               
                   
                 number of chip IO in 
               
               
                   
                 mind*/ 
               
             
          
           
               
                 do n=1 to 1000 
                 /* Start stepping from a 1X1 
               
               
                   
                 array, 2x2 array, etc until 
               
               
                   
                 nXn is larger than the 
               
               
                   
                 requested IO*/ 
               
               
                 test=n*n-chipio 
               
               
                 if test n&gt;=0 then leave 
                 /* when test is larger 
               
               
                   
                 than 0, then this 
               
               
                   
                 defines the matrix; it 
               
               
                   
                 will give chipio &gt;=1 
               
               
                   
                 rowx1row greater*/ 
               
               
                 end 
               
               
                 pads=n 
               
               
                 indent=75+0.5*dp 
                 /* Figure out how far in the 
               
               
                   
                 centerline of the first pad 
               
               
                   
                 should be; 75 um + half a die 
               
               
                   
                 pad width*/ 
               
               
                 dist=cz*1000−2*indent 
                 /* Figure out the span, 
               
               
                   
                 in um when each 
               
               
                   
                 indentation is taken 
               
               
                   
                 out; cz=chip size in 
               
               
                   
                 mm*/ 
               
               
                 cp=dist/(pads−1) 
                 /* Figure out the chip pitch 
               
               
                   
                 by taking the number of space 
               
               
                   
                 (pads−1) and divide it into 
               
               
                   
                 the distance available*/ 
               
               
                 end 
               
               
                 otherwise; end 
               
               
                   
                 /*Calculate Actual Chip Pads that 
               
               
                   
                 are G/V or signals*/ 
               
             
          
           
               
                 chipgv=chiprat/100*chipio%1 
                 /*Take the 
               
               
                   
                 Ground/Voltage Ratio; 
               
               
                   
                 chiprat, which is an 
               
               
                   
                 input parameter, 
               
               
                   
                 multiply by chipio and 
               
               
                   
                 take integer part...this 
               
               
                   
                 gives the number of chip 
               
               
                   
                 ground and voltage 
               
               
                   
                 chipio*/ 
               
             
          
           
               
                 chipsig=chipio-chipgv 
                 /*Take the total Chipio, 
               
               
                   
                 subtract out the chip ground 
               
               
                   
                 and voltage and this gives 
               
               
                   
                 the number of signals*/ 
               
               
                   
                 /* Need the padssig variable for the 
               
               
                   
                 lines per channel calculation*/ 
               
               
                 padssig=chipio%4 
                 /*Padssig is the number of 
               
               
                   
                 signals per quadrant*/ 
               
             
          
           
               
                 if padssig//4&gt;0 then padssig=padssig+1 
               
             
          
           
               
                   
                 /* Add one per side if there is 1,2, or 
               
               
                   
                 3 signal pads required*/ 
               
               
                   
                 /*Polarity of C4 Matrix*/ 
               
               
                   
                 /* Polarity of matrix means simply if 
               
               
                   
                 there is an odd number of columns/rows 
               
               
                   
                 it is odd; even if there is an even 
               
               
                   
                 number of rows*/ 
               
             
          
           
               
                 c4Polarity=‘odd’ 
                 /*Assume the polarity is 
               
               
                   
                 always odd*/ 
               
             
          
           
               
                 if pads//2=0 then c4Polarity=‘even’ 
                 /* Test to see if 
               
               
                   
                 the number of pads 
               
               
                   
                 per side is evenly 
               
               
                   
                 divisible by 2; 
               
               
                   
                 remainder is set to 
               
               
                   
                 even if it passes 
               
               
                   
                 this test*/ 
               
             
          
           
               
                   
                 /* Build the Dataset*/ 
               
               
                   
                 /* Figure out where to start the pad 
               
               
                   
                 most extreme from the center of the die 
               
               
                   
                 (0,0) */ 
               
             
          
           
               
                 Select 
               
               
                 when c4polarity=‘odd’ then do 
               
             
          
           
               
                 xstart=−pads%2*cp 
                 /* Start in the third 
               
               
                   
                 quadrant and when odd, and it 
               
               
                   
                 is the integer part of a 
               
               
                   
                 division by two that gives 
               
               
                   
                 the number of pads on one 
               
               
                   
                 side of the y axis*/ 
               
               
                 ystart=xstart 
                 /* the y coordinate start 
               
               
                   
                 equals the x coordinate 
               
               
                   
                 start*/ 
               
               
                 end 
               
               
                 otherwise 
                 /* This is the even case*/ 
               
             
          
           
               
                 xstart=−(pads/2−1)*cp−0.5*cp 
                 /* There is a half 
               
               
                   
                 pitch step from the 
               
               
                   
                 y axis plus the 
               
               
                   
                 number of spaces 
               
               
                   
                 (pads/2−1)times the 
               
               
                   
                 pitch*/ 
               
             
          
           
               
                 ystart=xstart 
                 /* the y coordinate start 
               
               
                   
                 equals the x coordinate 
               
               
                   
                 start*/ 
               
               
                 end 
               
             
          
           
               
                 /* Create repeating column vector*/ 
               
             
          
           
               
                 b=0 
                 /* b is the pad number counter*/ 
               
               
                 do e=1 to pads 
                 /* Start stepping from pad index 
               
               
                   
                 number 1 to the number of pads in 
               
               
                   
                 one column*/ 
               
               
                 do t=1 to pads 
                 /* Start stepping from pad index 
               
               
                   
                 number 1 to the number of pads in 
               
               
                   
                 one row*/ 
               
               
                 b=b+1 
                 /* Set up the index number for the 
               
               
                   
                 die pad about to be defined in x 
               
               
                   
                 and y*/ 
               
               
                 xcoor=xstart+(e−1)*cp 
                 /* x coordinate as a 
               
               
                   
                 function of starting 
               
               
                   
                 position plus the number 
               
               
                   
                 pad within the row*/ 
               
               
                 ycoor=ystart+(t−1)*cp 
                 /* y coordinate as a 
               
               
                   
                 function of starting 
               
               
                   
                 position plus the number 
               
               
                   
                 pad within the column*/ 
               
               
                 padxy.b=xcoor∥‘ ’∥ycoor 
                 /* create a string that 
               
               
                   
                 has two components, the 
               
               
                   
                 x and y coordinate*/ 
               
               
                 end 
                 /*Do Loop*/ 
               
               
                 end 
                 /*Do Loop*/ 
               
             
          
           
               
                 /* Assign the Die Pad Coordinate to a north, west, south, 
               
               
                 east side*/ 
               
             
          
           
               
                 divider=chipwidth/chiplength 
                 /* This represents the 
               
               
                   
                 slope of an imaginary 
               
               
                   
                 line struck between the 
               
               
                   
                 origin and the corner of 
               
               
                   
                 the die*/ 
               
             
          
           
               
                 cnteast=0; cntnorth=0; cntwest=0; cntsouth=0;hit=0 
               
             
          
           
               
                   
                 /*cnteast is the number 
               
               
                   
                 of pads assigned to the 
               
               
                   
                 eastern quadrant*/ 
               
             
          
           
               
                 n=0;nn=0;nnn=0;nnnn=0 
               
               
                 do b=1 to chipio 
               
               
                 parse value padxy.b with chipx chipy 
               
             
          
           
               
                 chipxx=chipx 
                 /* need to call it something 
               
               
                   
                 else because next line 
               
               
                   
                 changes it just for one 
               
               
                   
                 calculation */ 
               
             
          
           
               
                 if chipx=0 then chipxx=.001 
                 /* Die Pad on the Y 
               
               
                   
                 axis is the Case of 
               
               
                   
                 infiniteslope; then 
               
               
                   
                 artificially set 
               
               
                   
                 just off y axis*/ 
               
               
                 chipslope=chipy/chipxx 
                 /* Strike a line from 
               
               
                   
                 the center of the die to 
               
               
                   
                 the center of the pad*/ 
               
               
                 Select 
               
             
          
           
               
                 when abs(chipslope)&lt;divider&amp;chipxx&gt;0 then do 
               
             
          
           
               
                   
                 /* when the slope of 
               
               
                   
                 line is less than the 
               
               
                   
                 slope to the corner of 
               
               
                   
                 the die and the 
               
               
                   
                 xcoordinate is greater 
               
               
                   
                 than zero, then you know 
               
               
                   
                 you are on the east 
               
               
                   
                 side*/ 
               
             
          
           
               
                 side=‘East’; cnteastcnteast+1; end 
               
               
                 when abs(chipslope)&lt;divider&amp;chipxx&lt;0 then do 
               
             
          
           
               
                   
                 /* when the slope of line is less 
               
               
                   
                 than the slope to the corner of 
               
               
                   
                 the die and the xcoordinate is 
               
               
                   
                 less than zero, then position is 
               
               
                   
                 on the west side*/ 
               
             
          
           
               
                 side=‘West’;cntwest=cntwest+1;end 
               
               
                 when abs (chipslope)&gt;divider&amp;chipy&gt;0 then do 
               
             
          
           
               
                   
                 /* when the slope of line is 
               
               
                   
                 greater than the slope to the 
               
               
                   
                 corner of the die and the y 
               
               
                   
                 coordinate is greater than zero, 
               
               
                   
                 then position is on the north 
               
               
                   
                 side */ 
               
             
          
           
               
                 side=‘North’; cntnorth=cntnorth+1; end 
               
               
                 when abs (chipslope)&gt;divider&amp;chipy&lt;0 then do 
               
             
          
           
               
                   
                 /* when the slope of line is 
               
               
                   
                 greater than the slope to the 
               
               
                   
                 corner of the die and the 
               
               
                   
                 ycoordinate is less than zero, 
               
               
                   
                 then position is on the south 
               
               
                   
                 side*/ 
               
             
          
           
               
                 side=‘South’; cntsouth=cntsouth+1;end 
               
             
          
           
               
                   
                 /* Next to represent those that 
               
               
                   
                 might be on the dividing line; 
               
               
                   
                 alternate by taking the odd/even 
               
               
                   
                 of a counter*/ 
               
             
          
           
               
                 when abs (chipslope)=divider&amp;chipy&gt;0&amp;chipx&gt;0 then do 
               
             
          
           
               
                   
                 /* On the Northeast dividing 
               
               
                   
                 line*/ 
               
             
          
           
               
                 n=n+1 
                 /*Index the counter*/ 
               
               
                 Select 
               
               
                 when n//2=0 then do 
                 /* when the counter is even, 
               
               
                   
                 assign to North side*/ 
               
               
                 side=‘North’ 
               
               
                 cntnorth=cntnorth+1 
               
               
                 end 
               
               
                 otherwise 
                 /* if the counter is not even, 
               
               
                   
                 then it must be odd, so assign to 
               
               
                   
                 East side*/ 
               
               
                 side=‘East’ 
               
               
                 cnteast=cnteast+1 
               
               
                 end 
               
               
                 end 
               
             
          
           
               
                 when abs(chipslope=divider &amp; chipy&lt;0 &amp; chipx&lt;0 then 
               
               
                 do 
               
             
          
           
               
                   
                 /* On the Southwest dividing 
               
               
                   
                 line*/ 
               
             
          
           
               
                 nn=nn+1 
                   
               
               
                 Select 
               
               
                 when nn//2=0 then do 
                 /* when the counter 
               
               
                   
                 is even, assign to 
               
               
                   
                 South side*/ 
               
               
                 side=‘South’ 
               
               
                 cntsouth=cntsouth+1 
               
               
                 end 
               
               
                 otherwise 
                 /* if the counter is not even, 
               
               
                   
                 then it must be odd, so assign to 
               
               
                   
                 West side*/ 
               
               
                 side=‘West’ 
               
               
                 cntwest=cntwest+1 
               
               
                 end 
               
               
                 end 
               
             
          
           
               
                 when abs(chipslope)=divider &amp; chipy&lt;0 &amp; chipx&gt;0 
               
               
                 then do 
               
             
          
           
               
                   
                 /* On the Southeast dividing 
               
               
                   
                 line*/ 
               
               
                 nnn=nnn+1 
               
               
                 Select 
               
               
                 when nnn//2=0 then do 
                 /* when the counter is 
               
               
                   
                 even, assign to East 
               
               
                   
                 side*/ 
               
               
                 side=‘East’ 
               
               
                 cnteast=cnteast+1 
               
               
                 end 
               
               
                 otherwise 
                 /* if the counter is not even, 
               
               
                   
                 then it must be odd, so assign to 
               
               
                   
                 South side*/ 
               
               
                 side=‘South’ 
               
               
                 cntsouth=cntsouth+1 
               
               
                 end 
               
               
                 end 
               
             
          
           
               
                 when abs (chipsiope)=divider &amp; chipy&gt;0 &amp; chipx&lt;0 then 
               
               
                 do 
               
             
          
           
               
                   
                 /* On the Northwest dividing 
               
               
                   
                 line* / 
               
               
                 nnnn=nnnn+1 
               
               
                 Select 
               
               
                 when nnnn//2=0 then do 
                 /* when the counter is even, 
               
               
                   
                 assign to West side*/ 
               
               
                 side=‘West’ 
               
               
                 cntwest=cntwest+1 
               
               
                 end 
               
               
                 otherwise 
                 /* if the counter is not even, 
               
               
                   
                 then it must be odd, so assign to 
               
               
                   
                 North side*/ 
               
               
                 side=‘North’ 
               
               
                 cntnorth=cntnorth+1 
               
               
                 end 
               
               
                 end 
               
               
                 otherwise; end 
               
               
                 padxy.b=padxy.b∥‘ ’∥side 
                 /* add on to the 
               
               
                   
                 centroid string that has 
               
               
                   
                 x and y coordinates with 
               
               
                   
                 the quadrant side*/ 
               
               
                 end 
               
             
          
           
               
                 /*RANDOMIZE THE CHIP LABELS*/ 
               
               
                 /*This section now takes the % Ground/Voltage to 
               
               
                 define the type of Chipio; either a signal, ground, or 
               
               
                 voltage*/ 
               
             
          
           
               
                 chipgv=0 
                 /* Set the Ground and Voltage 
               
               
                   
                 counter to Zero*/ 
               
               
                 clip=100−chiprat 
                 /* Find the percentage requested 
               
               
                   
                 that is signal io*/ 
               
               
                 Do b=1 to chipio 
                 /* Start stepping through each 
               
               
                   
                 chipio*/ 
               
             
          
           
               
                 generate1=random(1,100)%1 
                 /* Generate a random number 
               
               
                   
                 between 1 and 100; % gives 
               
               
                   
                 you the integer part only*/ 
               
               
                 Select 
               
               
                 when generate1&gt;clip then do 
                 /* When the number is 
               
               
                   
                 above the signal pct; it 
               
               
                   
                 will be either a voltage 
               
               
                   
                 or ground*/ 
               
               
                 chipgv=chipgv+1 
                 /* Add to the Ground and Voltage 
               
               
                   
                 Counter*/ 
               
               
                 generate2=random(1,2) 
                 /* Now figure out whether it 
               
               
                   
                 will be a voltage or ground 
               
               
                   
                 by generating a number 
               
               
                   
                 between 1 and 2*/ 
               
               
                 Select 
               
               
                 when generate2=1 then do 
                 /* if is 1 then it is a 
               
               
                   
                 voltage*/ 
               
               
                 label=‘VDD’ 
               
               
                 end 
               
               
                 otherwise 
               
             
          
           
               
                 label=‘VSS’ 
                 /* if it is not 1 then it is 
               
               
                   
                 a ground*/ 
               
               
                 end 
               
               
                 end 
               
               
                 otherwise 
                 /* when the number is below the 
               
               
                   
                 clip, assign the label as signal*/ 
               
               
                 label=‘Signal’ 
               
               
                 end 
               
             
          
           
               
                 padxy.b=format(b,5,0)∥‘ ’∥label∥padxy.b 
               
             
          
           
               
                   
                 /* add to the front of the 
               
               
                   
                 centroid string the number of pad 
               
               
                   
                 plus the S,G,V label*/ 
               
             
          
           
               
                 end 
                 /*Do Loop End*/ 
               
               
                 end 
                 /* End Select*/ 
               
             
          
           
               
                 when case=‘a’ &amp; tech=‘wb’ then do 
               
             
          
           
               
                   
                 /* Wire Bond CHIP PADS CALCULATION */ 
               
             
          
           
               
                 kerf=.5*dp+75 
                 /* Calculate the kerf, the distance 
               
               
                   
                 between the die edge and the center of 
               
               
                   
                 the first pad. It is a half a die pad 
               
               
                   
                 plus the distance “edge” (defined by 
               
               
                   
                 user to represent die edge to edge of 
               
               
                   
                 die pad*/ 
               
               
                 indent=1.25*dp+kerf 
                 /* Indent is going to be the 
               
               
                   
                 distance from the die pad to the 
               
               
                   
                 edge, in the direction parallel to 
               
               
                   
                 the succession of die pads; this 
               
               
                   
                 keeps the pads from overlapping 
               
               
                   
                 each other in the corners*/ 
               
               
                 dist=cz*1000−2*indent 
                 /* This calculates the total 
               
               
                   
                 distance, from extreme die pad 
               
               
                   
                 centroid to extreme die pad 
               
               
                   
                 centroid*/ 
               
               
                 spaces=dist%cp 
                 /* The integer part of the 
               
               
                   
                 distance divided by the chip 
               
               
                   
                 pitch; this gives you the number 
               
               
                   
                 of spaces available*/ 
               
               
                 pads=spaces+1 
                 /* The total number of pads is 
               
               
                   
                 the number of spaces plus 1*/ 
               
               
                 chipio=4*pads 
                 /* Total number of chipio is the 
               
               
                   
                 pads on one side multiplied by 4*/ 
               
             
          
           
               
                 /* CHIP I/O DATASET CREATION */ 
               
               
                 /* Repeating Vector*/ 
               
             
          
           
               
                   
                 /* This will start die formation on the 
               
               
                   
                 east side of the die; most southern 
               
               
                   
                 point*/ 
               
             
          
           
               
                 xstart=.5*cz*1000−kerf 
                 /* Figure the centroid of the 
               
               
                   
                 first die pad; it is half the 
               
               
                   
                 chip size (cz;in microns) 
               
               
                   
                 minus the kerf (calc. 
               
               
                   
                 above) */ 
               
               
                 ystart=.5*spaces*cp 
                 /* This calculates the y position 
               
               
                   
                 where the first pad will start*/ 
               
               
                 do e=1 to pads 
                 /* Create the repeating 
               
               
                   
                 coordinates */ 
               
               
                 a.e=−1*ystart+(e−1)*cp 
               
               
                 end 
               
             
          
           
               
                 /* COORDINATES FOR ALL PADS BUT IN 4 VECTOR SETS */ 
               
               
                 /* Create the centroid string for each side. 
               
               
                 Contents will include: Pad #, X, Y, and side of 
               
               
                 Die */ 
               
               
                 /*Start on the East side, then north, then west, 
               
               
                 then South (CCW)*/ 
               
             
          
           
               
                 do n=1 to pads 
                 /* Step thru pads on the east 
               
               
                   
                 side*/ 
               
               
                 id=n 
               
             
          
           
               
                 eastx.n=format(xstart,5,0) 
                 /* Create a matrix 
               
               
                   
                 called eastx, with an 
               
               
                   
                 index equal to the pad 
               
               
                   
                 number, the coordinate 
               
               
                   
                 will always equal 
               
               
                   
                 xstart*/ 
               
               
                 easty.n=format(a.n,5,0) 
                 /* Create a matrix 
               
               
                   
                 called easty, with an 
               
               
                   
                 index equal to the pad 
               
               
                   
                 number, the coordinate 
               
               
                   
                 will be a function of 
               
               
                   
                 the pad number, ystart 
               
               
                   
                 and, the chip pitch*/. 
               
             
          
           
               
                 padxy.id=eastx.n∥‘ ’∥easty.n∥‘East’ 
               
             
          
           
               
                   
                 /* Create the matrix 
               
               
                   
                 padxy, whose value is a 
               
               
                   
                 string and index is pad 
               
               
                   
                 number that */ 
               
             
          
           
               
                 /* Do the similar thing for the other 3 sides of the 
               
               
                 die, while giving each pad a successively higher pad 
               
               
                 number*/ 
               
               
                 end 
               
               
                 do n=1 to pads 
               
               
                 id=1*pads+n 
               
               
                 northx.n=−1*format(a.n,5,0) 
               
               
                 northy.n=format(xstart,5,0) 
               
               
                 padxy.id=northx.n∥‘ ’∥northy.n∥‘North’ 
               
               
                 end 
               
               
                 do n=1 to pads 
               
               
                 id=2*pads+n 
               
               
                 westx.n=−1*format(xstart,5,0) 
               
               
                 westy.n=−1*format(a.n,5,0) 
               
               
                 padxy.id=westx.n∥‘ ’∥westy.n∥‘West’ 
               
               
                 end 
               
               
                 do n=1 to pads 
               
               
                 id=3*pads+n 
               
               
                 southx.n=1*format(a.n,5,0) 
               
               
                 southy.n=−1*format(xstart,5,0) 
               
               
                 padxy.id=southx.n∥‘ ’∥southy.n∥‘South’ 
               
               
                 end 
               
               
                 /* RANDOMIZE THE CHIP LABELS*/ 
               
               
                 /* This is the same routine as was used in the area 
               
               
                 array pad generation; commenting therefore is 
               
               
                 similar/exact*/ 
               
               
                 chipgv=0 
               
               
                 Do b=1 to chipio 
               
               
                  clip=100−chiprat 
               
               
                  generate1=random(1,100)%1 
               
               
                 Select 
               
               
                  when generate1&gt;clip then do 
               
               
                   chipgv=chipgv+1 
               
               
                   generate2=random (1,2) 
               
               
                  Select 
               
               
                   when generate2=1 then do 
               
               
                   label=‘VDD’ 
               
               
                   end 
               
               
                   otherwise 
               
               
                   label=‘VSS’ 
               
               
                   end 
               
               
                  end 
               
               
                  otherwise 
               
               
                  label=‘Signal’ 
               
               
                  end 
               
               
                 padxy.b=format(b,5,0)∥‘ ’∥label∥‘ ’padxy.b 
               
               
                 end /*Do Loop End*/ 
               
               
                 end /* End When for Theoretical Die creation*/ 
               
               
                   
               
             
          
         
       
     
     Create BGA matrix step  222  for all cases A, B and C, starting with a full BGA matrix, creates a line of data with its x position, y position, slope from center of package, and quadrant. An alphanumeric matrix specifies the alpha/numeric location of the ball. Punch out depops data for balls that are not supposed to be there (from input). The resulting data set is separated into four separate quadrants. This step randomly assigns a type for each BGA pad in a quadrant to a signal, ground or voltage. 
     For case A and B, chip to BGA routing  224  separates chip centroid data into four matrices based on quadrant. The closest slope search routine starts on east side, takes the quadrant dividing slope (step  214 ) for this die pad position, determines the slope to all BGAs in the quadrant, and then finds the slope that is the closest to the quadrant dividing slope, and that slope defines the routing for this chip pad. Signal, but not ground and voltage, lines are thus routed. The selected BGA pad is then designated “used”, and not available for subsequent pad selection. This process is repeated for die pads in order in this quadrant. The new maximum slope is that defined by the routing of the previous pad. 
     Step  226  calculates the runs, the power levels, wire bond fingers needed, and outputs to a file. 
     Step  228  uses Cramer&#39;s rule to solve for the intersection of all possible line combinations within the quadrant to see if the intersection falls within the space between a die pad and its connected BGA pad. If so, the count of crossings is incremented. 
     Step  230  generates summary file  112 , and is more fully described in Tables 19-21. 
     
       
         
               
             
               
             
               
               
               
             
           
               
                 TABLE 19 
               
               
                   
               
               
                 GOLD AND NICKEL CONSTANTS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 /* GOLD AND NICKEL CONSTANTS */ 
               
             
          
           
               
                 gdens=19.3 
                 /* specific gravity of gold 
                 */ 
               
               
                 ndens=8.89 
                 /* specific gravity of nickel 
                 */ 
               
               
                 water=1/10000**3 
                 /* grams per cubic micron 
                 */ 
               
               
                   
                 /* of water 
                 */ 
               
               
                 goldcost=goldcost*16/454 
                 /* $ per gram of gold 
                 */ 
               
               
                 nickelcost=nickelcost*16/454 
               
               
                   
                 /* $ per gram of nickel 
                 */ 
               
               
                 numberrings=1 
                 /* number of bond rings in 
                 */ 
               
               
                   
                 /* addition to the ground 
                 */ 
               
               
                   
                 /* ring 
                 */ 
               
               
                 sqmicron2sqin=1/1000**2/25.4**2 
               
               
                   
                 /* conversion from sq microns 
                 */ 
               
               
                   
                 /* to sq inches 
                 */ 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 CALCULATION OF GOLD AREA 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 /* GOLD AREA FOR GROUND RING, VOLTAGE RING(S) AND 
                 */ 
               
               
                 /* BOND FINGERS 
                 */ 
               
               
                 /* unit of area used is in square microns 
                 */ 
               
               
                 /* set width to voltage ring width established at the 
                 */ 
               
               
                 /* beginning of the overall program 
                 */ 
               
               
                 width=voltagewidth 
               
               
                 /* ring area accumulator 
                 */ 
               
               
                 ringarea=0 
               
               
                 /* create a routine that sums up the ring areas 
                 */ 
               
               
                 /* starting at the inner ground area and working out 
                 */ 
               
               
                 /* j stands for the ring number; j=1 is the ground 
                 */ 
               
               
                 /* ring, j=2 is the first voltage ring, j=3 is the 
                 */ 
               
               
                 /* second voltage ring, etc. 
                 */ 
               
               
                 do j=1 to (numberrings +1) 
               
               
                  Select 
               
               
                  when j=1 then do 
               
               
                   width=groundwidth 
               
               
                  end 
               
               
                  otherwise 
               
               
                   width=voltagewidth 
               
               
                  end 
               
               
                  Select 
               
               
                  when j=2 then do 
               
               
                   voltageringpitch=groundwidth/2 
               
               
                    +ringspace+voltagewideth/2 
               
               
                  end 
               
               
                  otherwise 
               
               
                   voltageringpitch=voltagewidth+ringspace 
               
               
                  end 
               
               
                 ring1length=chiplength*1000+diespace+(j−1) *voltageringpitch 
               
               
                 ring2length=chipwidth*1000+diespace+(j−1) *voltageringpitch 
               
               
                 ringarea=(ring1length+ring2length) *width*2+ringarea 
               
               
                 end 
               
               
                 /* end of summation of ring areas 
                 */ 
               
               
                 /* Calculate the total area of all the wire 
                 */ 
               
               
                 /* bond fingers 
                 */ 
               
               
                 Finger=chipsig*wbfingerlgth*wbfingerwdth 
               
               
                 /* GOLD AREA FOR VIAS ON FULL GOLD FOR CAVITY 
                 */ 
               
               
                 /* Via area is the addition of the lands (top and 
                 */ 
               
               
                 /* bottom; which are disks) and the inner vertical 
                 */ 
               
               
                 /* surface 
                 */ 
               
               
                 finishedvia=viasize-2cuthk 
               
               
                 /* Estimate via count for cavity, 16 vias added in 
                 */ 
               
               
                 viacnc=.3*chipsig+4*4*numberrings 
               
               
                 /* Calculate lands 
                 */ 
               
               
                 vialandsc=2*3.1416*(viapadf**2-finishedvia**2)/4*viacnc 
               
               
                 /* Inside vertical surface of PTH 
                 */ 
               
               
                 viainnerc=finishedvia*3.1416*lamthick*viacnc 
               
               
                 /* Lands + Inner Surface 
                 */ 
               
               
                 viagdc=vialandsc+viainnerc 
               
               
                 /* FLOWER PAD 
                 */ 
               
               
                 /* Estimate the diameter of the solid part of the 
                 */ 
               
               
                 /* Flower Pad 
                 */ 
               
               
                 diaf=.5*cz*1000 
               
               
                 /* Add the Petals of the Flower plus the Circular 
                 */ 
               
               
                 /* Area 
                 */ 
               
               
                 flower=6*cz*1000*petalwidth+3.1416*diaf*diaf/4 
               
               
                 /* GOLD AREA OF VIAS FOR SELECTIVE DIE UP FLOWER 
                 */ 
               
               
                 /* AND RING REGIONS 
                 */ 
               
               
                 /* Estimate 2 vias per .25″× .25″ area FOR DIAUP 
                 */ 
               
               
                 /* FLOWER AREA 
                 */ 
               
               
                 Viacndflower=flower/(6.35**2*1000**2)*2 
               
               
                 /* Total number of drilled vias in a Diaup 
                 */ 
               
               
                 viacnd=viacndflower+ chipsig 
               
               
                 /* Total number of Backside(S2) Land Area 
                 */ 
               
               
                 viagdd=viacndflower*3.1416*(viapadb**2=finishedvia**2)/4 
               
               
                 /* Estimate of ground bussing typically found on 
                 */ 
               
               
                 /* S2 under the die 
                 */ 
               
               
                 groundbussd=3.1416*diaf*diaf/4 
               
               
                 /* Adjust flower area for vias and inner surface 
                 */ 
               
               
                 flower=flower-3.1416*(viasize-2*cuthk)**2/4*viacondflower 
               
               
                 +3.1416*(viasize=2*cuthk)*viacndflower 
               
               
                 /* GOLD AREA BGA PADS 
                 */ 
               
               
                 bgarea=)bgapadsize**2*3.1416/4) 
               
               
                 +dogwidth*(bgaprocoat=bgadia)/2 
               
               
                 /* Number of BGA pads on a cavity 
                 */ 
               
               
                 bgac=modio*bgarea 
               
               
                 /* Number of BGA pads on a dia up 
                 */ 
               
               
                 bgad=bgac+thermal*bgarea 
               
               
                 /* STIFFENER AREA 
                 */ 
               
               
                 /* Stiffener is a piece of copper, the size of the 
                 */ 
               
               
                 /* substrate, on cavity parts 
                 */ 
               
               
                 stiff=size*size*1000*1000 
               
               
                 /* CAVITY WALL AREA 
                 */ 
               
               
                 /* This is the area, on a cavity only, where the 
                 */ 
               
               
                 /* ground ring wraps around the corner and downward 
                 */ 
               
               
                 /* to the S2 
                 */ 
               
               
                 cav=((chipwidth*1000+diespace)*2 
               
               
                 +(chiplength*1000+diespace))*(lamthick+2*cuthk) 
               
               
                 /* CAVITY WIRING AREA FRONT AND BACK 
                 */ 
               
               
                 /* Figure out the area remaining that is available for 
                 */ 
               
               
                 /* wiring and then apply a percentage of that area 
                 */ 
               
               
                 /* that is wiring distance in one dimension 
                 */ 
               
               
                 /* encompassing the fingers, die, etc. 
                 */ 
               
               
                 innerside=(outeractual/1000-spacefnactual) 
               
               
                 /* Area of this innerside 
                 */ 
               
               
                 innerarea=innerside*innerside 
               
               
                 /* Area of part, minus inner area, lands, BGA 
                 */ 
               
               
                 wiringarea=stiff-innerarea-vialandsc-bgac 
               
               
                 /* Estimate wiring covers 30% front 10% back 
                 */ 
               
               
                 wdensc=(0.3+0.1)*wiring area 
               
               
                 /* CIRCUIT WIRING GOLD SUMMATION 
                 */ 
               
               
                 /* Add fingers and bonding rings; these are the 
                 */ 
               
               
                 /* surface that are bonded to 
                 */ 
               
               
                 bondinggold=finger+ringarea 
               
               
                 /* GOLD RUNNER 
                 */ 
               
               
                 /* Gold runner is a small area used during the molding 
                 */ 
               
               
                 /* process for die up 
                 */ 
               
               
                 goldrun=goldrunwdth*goldrunhgt 
               
               
                 /* TOTAL GOLD FOR CAVITY 
                 */ 
               
               
                 /* Add the bonding surfaces, vias, wiring, cavity 
                 */ 
               
               
                 /* wall, and BGA 
                 */ 
               
               
                 togold=bondinggold-+-viagdc+bgac+cav 
               
               
                 /* Multiply by gold thickness to get volume and 
                 */ 
               
               
                 /* multiply by density 
                 */ 
               
               
                 cost=goldcost*(tcgold+stiff)*goldthk*water*gdens 
               
               
                 /* TOTAL GOLD FOR DIE UP SELECTIVE 
                 */ 
               
               
                 /* Add the bonding surfaces, flower pads, vias, BGA, 
                 */ 
               
               
                 /* and ground buss 
                 */ 
               
               
                 tdgold=bondinggold+flower+viagdd+bgad+groundbussd 
               
               
                 /* Multiply by gold thickness to get volume and 
                 */ 
               
               
                 /* multiply by density 
                 */ 
               
               
                 dcst=goldcost*tdgold*goldthk*water*gdens 
               
               
                   
               
             
          
         
       
     
     Table 21 is a pseudo code representation of choke factor determination. Choke factor is a measure of the amount of room left between the bond fingers and either the array of via lands (in a die up) or BGA pads (in a cavity). It is not a linear dimension but is unitless. It is unitless because the linear space is divided by the wiring pitch. This by definition is then the number of wiring pitches that can fit into the allotted space. Lower numbers are more choked, higher numbers are less choked. Negative numbers mean that there is no fanout room. 
     Dividing by the pitch gives a relative measure of the distance verses the ‘fineness’ of the wiring technology. A choke clip level is used to determine whether the module can be wired. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE 21 
               
               
                   
               
               
                 CHOKE FACTOR DETERMINATION 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 /* DISTANCE LEFT FOR FINGERS AND FANOUT 
                 */ 
               
               
                   
                 /* Units are microns 
                 */ 
               
               
                   
                 /* Calculate the distance from the center of the 
                 */ 
               
               
                   
                 /* substrate to the furthest voltage ring 
                 */ 
               
               
                   
                 /* Width of ground ring + space between rings 
                 */ 
               
               
                   
                 /* + voltage ring width*number of rings 
                 */ 
               
               
                   
                 /* CZ is the die in mm 
                 */ 
               
               
                   
                 inner=cz/2*1000+rings 
               
               
                   
                 /* The following routine determines the square that 
                 */ 
               
               
                   
                 /* inscribes either the BGA pads (in a cavity), or 
                 */ 
               
               
                   
                 /* the via land (in a dieup). This square is 
                 */ 
               
               
                   
                 /* tangent to the 
                 */ 
               
               
                   
                 /* inside edge of either pad; and it is towards the 
                 */ 
               
               
                   
                 /* die. A matrix outer.k represents the size of 
                 */ 
               
               
                   
                 /* the spare for all possible depopulatons of BGA 
                 */ 
               
               
                   
                 /* balls. In reality, outer.k is half the length 
                 */ 
               
               
                   
                 /* of the square. 
                 */ 
               
               
                   
                 /* Depop.k is a matrix that existed higher up in the 
                 */ 
               
               
                   
                 /* overall program, and is an array whose value is 
                 */ 
               
               
                   
                 /* the number of positions in the depopulated BGA 
                 */ 
               
               
                   
                 /* matrix. 
                 */ 
               
               
                   
                 /* The index, k, represents the number of outer rows 
                 */ 
               
               
                   
                 /* in the depopulated BGA matrix. 
                 */ 
               
               
                   
                 /* Maxouterrow is calculated higher in the overall 
                 */ 
               
               
                   
                 /* program and is the largest number of outer 
                 */ 
               
               
                   
                 /* rows that a particular substrate size can 
                 */ 
               
               
                   
                 /* possibly have. 
                 */ 
               
               
                   
                 do k=1 to maxouterrow 
               
               
                   
                 Select 
               
               
                   
                 when style=‘cavity’ then do 
               
               
                   
                 /* This figures the distance from the center of the 
                 */ 
               
               
                   
                 /* module out to the linear edge of BGA precoat, 
                 */ 
               
               
                   
                 /* of the inner roll of balls. 
                 */ 
               
               
                   
                 outer.k=(depop.k-1)/2*bgapitch_bgapitch-bgaprocoat/2 
               
               
                   
                 end 
               
               
                   
                 when style=‘dieup’ then do 
               
               
                   
                 /* This figures the distance from the center of 
                 */ 
               
               
                   
                 /* the module out to the inner edge of the via 
                 */ 
               
               
                   
                 /* land on the inner rows of vias. 
                 */ 
               
               
                   
                 outer.k=(depop.k-1)2*bgapitch+bgapitch+doglength-viapadf/2 
               
               
                   
                 end 
               
               
                   
                 otherwise; end 
               
               
                   
                 /* This is the calculation of the distance between the 
                 */ 
               
               
                   
                 /* BGA or Vias and rings; this is left for fingers 
                 */ 
               
               
                   
                 /* and fanout 
                 */ 
               
               
                   
                 spaceff.k=(outer.k-inner)/;1000 
               
               
                   
                 /* These three equations calculate the space left 
                 */ 
               
               
                   
                 /* after subtracting out that needed for the wire 
                 */ 
               
               
                   
                 /* bond wire and its pad and its procoat. The three 
                 */ 
               
               
                   
                 /* equations are similar, except for a variance of 
                 */ 
               
               
                   
                 /* bondwire length, nominal, high, and low. 
                 */ 
               
               
                   
                 spacefn.k=(outer.k-((cz/2*1000)-indent)-wbnom 
               
               
                   
                 -wbfingerlgth/2-wbprocoat)/1000 
               
               
                   
                 spacefh.k=(outer.k-((cz/2*l000)-indent)-wbhi 
               
               
                   
                 wbfingerlgth/2-wbprocoat)/1000 
               
               
                   
                 spacefl.k=(outer.k-))cz/2*1000)-indent)-wblo 
               
               
                   
                 +wbfingerlgth/2-wbprocoat)/1000 
               
               
                   
                 /* Fanout length as a multiple of finest wiring pitch 
                 */ 
               
               
                   
                 /* This is the choke factor: fancha.k 
                 */ 
               
               
                   
                 /* fancha.k i the nominal space for fanout, converted 
                 */ 
               
               
                   
                 /* to microns and divided by the wiring pitch 
                 */ 
               
               
                   
                 /* The wiring pitch is a constant and it is defined 
                 */ 
               
               
                   
                 /* high up in the code as wire width+wire space 
                 */ 
               
               
                   
                 /* The index, k, represents the number of outer rows 
                 */ 
               
               
                   
                 /* of BGA 
                 */ 
               
               
                   
                 /* Choke Factor fancha.k 
                 */ 
               
               
                   
                 fancha. k=spacefn.k*1000/wirepitch 
               
               
                   
                 . . 
               
               
                   
                 end      /* End do loop 
                 */ 
               
               
                   
                   
               
             
          
         
       
     
     Basically, the buildup technology (SLC) which is employed in providing the chip carrier layer count calculating method and system comprises a subroutine as follows: 
     This program keys in one the number of signals required to be fanned out per quadrant and calculates the number of sequential layers that would be required. Layer count is a critical cost intensive parameter since each layer added to the laminate has a compounding effect on yield. 1 layer=80%, 1 layers=80%80%=64%, etc. 
     This routine is part of the foregoing described larger program. The inputs to this subroutine are from this program. The recommended subroutine below indicates these inputs. 
     Extracted and contracted commented aspects are derived from this program that serves as a general flow chart: 
     Begin SLC Sizing Section 
     cz was defined above; it is the size of the physical chip expressed in mm; 
     cp was defined above as minimum chip bump to chip bumppitch; it can be an input or calculated; 
     c4pad is an input; it is the size of the pad on the substrate that the chip bump sits on; 
     c4line this is an input; it is the minimum line width capable by mfg process; 
     c4space this is an input; it is the minimum space line to line capable by mfg process; 
     This defines a file named: Slc_customer 
     “Customer” is an input by the user, tags the file with the company name; 
     Figure out if the copper pad edge or procoat opening edge will define the wiring channel; 
     Calculate the maximum number of wiring pitches (spaces+width) that fit into the wiring channel; 
     Calculate the number of rows and corresponding number of chip pads on a quadrant basis; 
     Take a quadrant slide of the die along the diagonals Padsrow.o is a matrix that will define the number of pads that are left as you proceed towards the middle of the die, row by row, starting from edge and decremented by the two flanking diagonals. Pads A variable that has been calculated either by pitch/die size inputs or total chipio input. 
     This variable is the number of pads across one side of the chip. Calculates the number of wires per layer and stores in a matrix. Calculates the total number of pads rows until center is reached. 
     Calculate number of SLC Layers to handle required Chip Signal Count. This value is stored in a variable called max layers. 
     Output on a per layer basis and also summary. 
     The signal needs per quadrant, the layer number, the number of wires on this layer, the resulting un-wired of the total signals per quadrant, the number need divided by the wires per this layer . . . this is important on the last layer because it gives you an idea if you needed every bit of the last layer or you needed a very small pct. This either effects your confidence (the former), or (the latter) tells you might be able to go one layer less if you could just find a way to wire out just several. 
     Output a summary . . . See Output. 
     Pursuant to a more specific application, and wherein the particular layouts of the wiring lines or rats are illustrated in FIGS. 12A through 12D, the tabular representation of the foregoing is indicated in Table 22 referring to SLC output. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
           
               
                 TABLE 22 
               
             
             
               
                   
               
               
                 SLC OUTPUT 
               
             
          
           
               
                 Signals Needed 
                   
                   
                   
                   
               
               
                 in Layer 
                 Layer 
                 Number of Wires 
                   
                 Needed/ 
               
               
                 Per Quadrant 
                 Number 
                 per Layer 
                 Deficit 
                 WIres 
               
               
                   
               
             
          
           
               
                 125 
                 1 
                 65 
                 193 . 
                 3.97 
               
               
                 193 
                 2 
                 62 
                 131 . 
                 3.11 
               
               
                 131 
                 . 3 
                 59 
                 72 
                 2.22 
               
               
                 72 
                 . 4 
                 56 
                 16 
                 1.29 
               
               
                 16 
                 . 5 
                 53 
                 −37 
                 0.30 
               
             
          
           
               
                 This is a 5+5 SLC Structure (Does not Count FC1) 
               
               
                 Chipio is 2238 
               
               
                 Chip Pitch is 224.50 
               
               
                 Chip Size is 18 
               
               
                 Total Rows of the die is 22 
               
               
                 The Die Matrix = 65×65 
               
               
                 C4 Pad Diameter is 127 um 
               
               
                 C4 Procoat Diameter is 195 um 
               
               
                 Type of C4 Pad Site is nsmd 
               
               
                 Number of Lines through C4 Channels is 0 
               
               
                 Maximum Number of Layers given the total rows 22 
               
               
                 Setting is Chipio, Chip Pitch 0 1 
               
               
                   
               
             
          
         
       
     
     Pursuant to a further specific application, predicated on the code set forth below, the inputs needed are as follows: 
     1. c4 pad size 
     2. c4 procoat size 
     3. minimum c4 wiring space 
     4. minimum c4 wire width 
     5. chip C4 pitch 
     6. chip size 
     7. Chip kerf 
     8. % Chip IO that are ground or Voltage 
     
       
         
               
             
           
               
                   
               
             
             
               
                  * * * * * * * * * * * * * *Beginning of Code* * * * * * * * * * * * * * 
               
               
                   /*Begin SLC Sizing Section */ 
               
               
                   if c4pad&gt;c4procoat then c4definintion=‘smd’ 
               
               
                   if c4procoat&gt;c4pad then c4definition=‘nsmd’ 
               
               
                   Select 
               
               
                    when c4definition=‘smc’ then do 
               
               
                    c4wirespace=cp−c4pad 
               
               
                    end 
               
               
                    otherwise 
               
               
                    c4wirespace=cp−c4procoat 
               
               
                    end 
               
               
                 c4wiringpitches−c4wirespace/(c4line+c4space)- 
               
               
                 c4space/(c4line4+c4space) 
               
               
                 c41pc=c4wiringpitches%1 
               
               
                 spread_rule=c4wirespace/(2*crlpc+1)/*Optimized Spread*/ 
               
               
                 spread_rule=format(spread_rule,3,0) 
               
               
                 padsrow.1=pads 
               
               
                 do 0=2 to 1000 
               
               
                   p+0−1 
               
               
                   padsrow.0=padsrow.p−3/*Note it is not minus 2; have to 
               
               
                 account for quad neighbor*/if padsrow.0&lt;0 then do 
               
               
                 ttlrows=o−1 
               
               
                 leave 
               
               
                   end 
               
               
                 end 
               
               
                 start=1; finish=start+c41pc 
               
               
                 do layer=1 to 30 
               
               
                 wires=0 
               
               
                 do 0=start to finish 
               
               
                 wires=padsrow.0+wires 
               
               
                 if ttlrows=0 then leave 
               
               
                 end 
               
               
                 numberwires.layer=wires 
               
               
                 start=finish+1; finish=startn+c41pc 
               
               
                 if start&gt;ttlrows then keave 
               
               
                 end 
               
               
                 maxlayers=layer 
               
               
                 chipsigneed=chipsig/4 
               
               
                 out=‘Signals Needed” Layer” Number of Wires” Deficit” 
               
               
                 Needed/Wires in Layer’ 
               
               
                 out_file˜lineout (OUT) 
               
               
                 out=‘Per Quadrant” Number” per Layer’ 
               
               
                 out_file˜lijeout (OUT) 
               
               
                 Do layer=1 to maxlayers 
               
               
                 if numberwires.layer&lt;=0 then do 
               
               
                 leave 
               
               
                 end 
               
               
                 delta=chipsigneed-numberwires.layer 
               
               
                 pct=chipsigneed/numberwires.layer 
               
               
                 pct=format(pct,2,2) 
               
               
                 out=chipsigneed’ layer’ ‘numberwires.layer’ ‘delta’ ‘pct 
               
               
                 out_file˜lineout (OUT) 
               
               
                 chipsigneed=chipsigneed-numberwires.layer 
               
               
                 if chipsigneed&lt;=0 then leave 
               
               
                 end 
               
               
                 slccount=layer’ ‘pct’ 
               
               
                 ***************End of Code*************** 
               
               
                   
               
             
          
         
       
     
     Furthermore, there is provided a tabulation of two outputs as follows: 
     Outputted in tow Places: 
     Under Chart.txt.File: which is a routine that looks at all the possible combinations of a Chip Carrier given a set of input structure. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Portion 
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 Layer 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 LW/Space 
               
               
                 Case 
                 Size 
                 Rows 
                 IO 
                 Pitch 
                 Pwr/Gnd 
                 Size 
                 Pitch 
                 Sigs 
                 Pwr/Gnd 
                 Layers Used 
                 Full = 1 
                 C4LPC 
               
               
                   
               
             
             
               
                 1 
                 17 
                 3 
                 156 
                 1000 
                 40% 
                 5 
                 250 
                 94 
                 77% 
                 1 + 1 
                 0.64 
                 42 
               
               
                 2 
                 17 
                 4 
                 192 
                 1000 
                 51% 
                 5 
                 250 
                 94 
                 77% 
                 1 + 1 
                 0.64 
                 42 
               
               
                 3 
                 17 
                 5 
                 220 
                 1000 
                 57% 
                 5 
                 250 
                 94 
                 77% 
                 1 + 1 
                 0.64 
                 42 
               
               
                 4 
                 17 
                 6 
                 240 
                 1000 
                 61% 
                 5 
                 250 
                 94 
                 77% 
                 1 + 1 
                 0.64 
                 42 
               
               
                   
               
             
          
         
       
     
     Second Output: 
     Under SLC.txt File: This focuses in on one particular point and gives more detail on how the signals are being 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
               
               
                 Signals Needed 
                 Layer 
                 Number of Wires 
                   
                 Needed/ 
               
               
                 Per Quadrant 
                 Number 
                 per Layer 
                 Deficit 
                 Wires in Layer 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 112.25 
                 1 
                 45 
                 67.25 
                 2.49 
               
               
                 67.25 
                 2 
                 33 
                 3.25 
                 2.04 
               
               
                 34.25 
                 3 
                 21 
                 13.25 
                 1.63 
               
               
                 13.25 
                 4 
                 9 
                 4.25 
                 1.47 
               
               
                   
               
             
          
         
       
     
     This is a 5+5 SLC Structure (Does not Count FC1) 
     Chipio is 576 
     Chip Pitch is 250 
     Chip Size is 6 
     Total Rows of the die is 9 
     The Die Matrix=24×24 
     C4 Pad Diameter is 125 um 
     C4 Procoat Diameter is 110 um 
     Type of C4 Pad Site is smd 
     Number of Lines through C4 Channels is 1 
     Maximum Number of Layers given the total rows 5 
     The foregoing, by way of an example, is in connection with a 5+5 SLC structure, although other variations are readily implementable through intermediary of the present invention, which essentially is a further improvement on the parent patent application. 
     It will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without departing from the spirit and scope of the invention. In particular, it is within the scope of the invention to provide a computer program product or program element, or a program storage or memory device such as a solid or fluid transmission medium, magnetic or optical wire, tape or disc, or the like, for storing signals readable by a machine, for controlling the operation of a computer according to the method of the invention and/or to structure its components in accordance with the system of the invention. 
     Further, each step of the method may be executed on any general computer, such as an IBM System 390, AS/400, PC or the like and pursuant to one or more, or a part of one or more, program elements, modules or objects generated from any programming language, such as C++, JAVA, P1/1, FORTRAN or the like. And still further, each said step, or a file or object or the like implementing each said step, may be executed by special purpose hardware or a circuit module designed for that purpose. 
     While the invention has been particularly shown and described with respect to preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing and other changes in form and details may be made therein without departing from the spirit and scope of the invention.