Patent Publication Number: US-6983438-B1

Title: Design tool for integrated circuit design

Description:
FIELD OF THE INVENTION 
     The present invention relates to designing integrated circuits, and in particular, to determining whether a particular die fits into a particular package. 
     DESCRIPTION OF RELATED ART 
     Integrated circuits are used to carry out a wide variety of tasks in many different electrical and electronic components. For these reasons, integrated circuit designs vary according to the function and environment that an integrated circuit is designed to operate in. Integrated circuits typically comprise a die attached to a package, often utilizing aluminized bond pads around the edge of the die and electroplated, e.g., gold over nickel over copper, post pads on the package.  FIG. 3   a  depicts a die  354  on a package  350 . Post pads  352  are part of the package  350 , and provide electrical contacts on the upper surface  360  ( FIG. 3   b ), for example via electrical connection to pins  358  ( FIG. 3   b ) through the package  350 , communicating to electrical components of which the package becomes a part. Bond pads  356  are part of the die  354 , and provide electrical contact points for the electronics embedded in the die. Connecting the bond pads  356  to the post pads  352 , for example using a wire (not shown), allows the electronics embedded in the die to communicate with the electrical components of which the package becomes a part. 
     Electrical connections are made between the bond pads and the post pads by a thin wire, usually of gold or aluminum, to connect the input/output regions of the die to the package, and to connect the die to the power and ground connections of the package. In a package design, the term “post pad pitch” refers to the distance from the center of one post pad to the center of a neighboring post pad, and the term “bond pad pitch” refers to the distance from the center of one bond pad to the center of a neighboring bond pad. 
     The wide variety of tasks that integrated circuits perform require new integrated circuit designs to constantly be made in order to create new and faster electronics. A challenging aspect of designing an integrated circuit is determining whether a die with a particular bond pad pitch fits into a particular package with a specified post pad pitch. Because of a need for electrical isolation, and because of physical design constraints, the bond pads on a die are limited as to how close they can be placed to one another. Correspondingly, the post pads on the package are also limited as to how close they may be placed to one another. The features and functions that a die performs dictate the number of input/output connections, power connections, and ground connections (collectively wire bond connections) that a die is going to make with a package. According to the number of wire bond connections required between the die and the package, a certain number of bond pads are formed along the edge of the die and a number of post pads, at least equal to the number of bond pads on the die that will be bonded, are placed on the package. 
     In order to determine whether a particular die fits into a particular package, several assumptions are made. A designer assumes aspects of the geometry of the die; for example, the length of one of the die&#39;s edges, the number of bond pads that can be placed on the die, and the pitch between the bond pads on the die. A designer must also assume a post pad pitch for the bonding pads that are part of the package. In order to determine whether a particular package fits into a particular die, a designer generates a computer drawing of the package and the die. Depending on the skill of the designer, several drawings of a package and die combination are made before a fit is found between a die and a package having the required number of bonded wire bonds. This process often requires three to four days to complete, and is therefore very time and resource consuming. 
     SUMMARY OF THE INVENTION 
     There is a need for reducing the time required to design a die and a package that fit with one another, and contain sufficient bonding and post pads to form the required number of wire bonds needed for the package and die to operate correctly. This need, and others, are addressed by the present invention, which evaluates whether a particular die fits into a particular package based on an input design parameter, without needing to generate any drawings. In one embodiment, a computer program, for example implemented on a spreadsheet, is configured to store a set of rules pertaining to packages and dies. The program is also configured to perform calculations that determine whether a die and package combination fits together after receiving inputs regarding the die and/or the package. Accordingly, one aspect of the invention relates to a method for determining whether a square die fits into a particular package. A design parameter for the square die is received as input, and is used to calculate characteristics of the die. The calculated die characteristics are then compared to characteristics of the package to determine whether a die with the calculated characteristics fits into the package. 
     Another aspect of the invention relates to a method for determining whether a particular square die fits into a particular ball grid array (BGA) package. An input for a die pad pitch is received, and is used to calculate die characteristics. Then, a maximum number of die pads allowed and a required package post pad pitch are calculated. Finally, whether a die with the input die pad pitch fits into a particular BGA package is determined by comparing the calculated required package post pad pitch, and a minimum pre-defined package post pad pitch for the BGA package. 
     In certain embodiments, the calculated die characteristics comprise a maximum number of wire bond connections per side of the die, a maximum number of wire bond connections for the die, and a minimum die edge length. In certain embodiments, the package post pads are staggered and arranged along an arc. In other embodiments, the package post pads are in-line and arranged along an arc. In other embodiments, the package post pads are staggered and arranged linearly. In yet other embodiments, the package post pads are in-line and arranged linearly. 
     Another aspect of the invention relates to determining whether a particular square die fits into a particular BGA package. A total number of wire bond connections is received as input, and used to calculate die characteristics. Then a maximum number of die pads allowed and a required package pad pitch are calculated using the calculated die characteristics. Finally, whether a die with the input total number of wire bond connections fits into a particular BGA package is determined by comparing a calculated required package pad pitch with a minimum pre-defined package pad pitch for the BGA package. 
     In certain embodiments, the calculated die characteristics comprise a minimum die pad pitch, and a minimum die edge length. In certain embodiments, determining whether a particular square die fits into a particular BGA package is performed for package post pads that are staggered and arranged along an arc. In other embodiments, determining whether a particular square die fits into a particular BGA package is performed for package post pads that are in-line and arranged along an arc. In still other embodiments, determining whether a particular square die fits into a particular BGA package is performed for package post pads that are staggered and arranged linearly. In yet other embodiments, determining whether a particular square die fits into a particular BGA package is performed for package post pads that are in-line and arranged linearly. 
     Another aspect of the invention relates to determining whether a particular square die fits into a particular plastic quad flat pack (PQFP) package. A die pad pitch is received as input, and is used to calculate die characteristics. Then, a maximum number of die pads allowed and a required package pad pitch are calculated. Finally, whether a die with the input die pad pitch fits into the particular PQFP package is determined by comparing the calculated required package pad pitch with a minimum pre-defined package pad pitch for the PQFP package. 
     In certain embodiments, the calculated die characteristics comprise a maximum number of wire bond connections per side of the die, and a maximum number of wire bond connections for the die. In certain embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are in-line and arranged circularly. In other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are staggered and arranged circularly. In other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are staggered and arranged conventionally. In yet other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are in-line and arranged conventionally. 
     Yet another aspect of the present invention relates to whether a particular square die fits into a particular PQFP package. A total number of wire bond connections is received as input, and is used to calculate die characteristics. Then, a maximum number of die pads allowed and a required package pad pitch are calculated. Finally, whether a die with the input total number of wire bond connections fits into the particular PQFP package is determined by comparing the calculated required package pad pitch with a minimum pre-defined package pad pitch for the PQFP package. In certain embodiments, the calculated die characteristics comprise a minimum die pad pitch. In certain embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are in-line and arranged circularly. In other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are staggered and arranged circularly. In other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are staggered and arranged conventionally. In yet other embodiments, determining whether a particular square die fits into a particular package is performed for package post pads that are in-line and arranged conventionally. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a flowchart of the processing performed by an embodiment of the present invention. 
         FIG. 1   a  depicts an embodiment of a spreadsheet programmed to carry out the present invention. 
         FIG. 2  depicts a second embodiment of a spreadsheet programmed to carry out the present invention. 
         FIG. 3  is a diagram that illustrates various package parameters used with the present invention. 
         FIG. 3   a  is a diagram illustrating package post pads and die bond pads. 
         FIG. 3   b  is a diagram illustrating a side view of a die attached to a package having pins. 
         FIG. 4  is a diagram that illustrates various die parameters used with the present invention. 
         FIG. 5  depicts a BGA package having staggered package bonding pads arranged linearly. 
         FIG. 6  depicts a BGA package having in line package post pads arranged in an arc. 
         FIG. 7  depicts a conventional PQFP package having in line package post pads. 
         FIG. 8  depicts a circular PQFP package having in line package post pads. 
         FIG. 9  depicts a computer system capable of implementing the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A methodology for determining whether a particular square die fits into a particular package is described. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art, that the present invention may be practiced without these specific details. In other instances, well-know structures and devices are shown in blocked-diagram form in order to avoid unnecessarily obscuring the present invention. 
     Present practices for designing new integrated circuits typically occupy three to four days, and involve generating seven or eight drawings to determine whether a particular die fits into a particular package. The present invention reduces preliminary design time to several minutes, and can be easily implemented as a spreadsheet tool. 
       FIG. 1  depicts the processing flow of an embodiment of the present invention. In step  10 , a design parameter for a square die is received as input. In step  12 , the input design parameter is utilized to calculate characteristics of the die. In step  14 , the calculated characteristics of the die are compared to pre-determined characteristics of the package in order to make a determination whether a die with the calculated characteristics fits into the package. Preferably, a spreadsheet is programmed to receive the input parameter and calculate whether a die fits into a particular package. The spreadsheet can also be used to match a package to a die, or for designing a package and a die. 
     BGA Design Parameters 
     In one embodiment, for step  10 , several design parameters are input, using spreadsheet  100 , depicted in  FIG. 1   a . The top portion  102  of the spreadsheet  100  contains parameters that define the package and die characteristics. These parameters are typically supplied by the manufacturer of the packages and dies, and are entered by the user into the spreadsheet. “In-line or staggered”  110  refers to the positioning of the package post pads. An example of in-line package post pads is illustrated in  FIG. 6  where the post pads  600  have their centers substantially along a line for each group  602  of post pads  600 . An example of staggered post pads is illustrated in  FIG. 5  where each post pad  500  has its center off-set from the center of adjacent post pads  500  for each group  502  of post pads  500 . 
     “Post in arc or straight line”  112  also refers to the positioning of the package post pads. In  FIG. 5 , the staggered package post pads  500  are arranged along a straight line. This straight line arrangement means that the center of each post pad  500  in the further row  504  from edge  508  of die  510  lies on a common line, and that the center of each post pad  500  in the closer row  506  to edge  508  of die  510  lies on a common line. If the post pads  500  were not staggered, but were in-line, then one common line would pass through the center of each post pad arranged along the edge  508  of die  510 . The line or lines passing through the centers of the post pads  500  are substantially parallel to the edge  508  of die  510 . In  FIG. 6 , the in-line package post pads  600  are arranged along an arc. This arc arrangement means that while the center of post pads  600  in a group  602  are substantially along a line, the centers of post pads  600  arranged off an edge of the die  610  all lie along a common arc. Although not shown, the in-line package post pads  600  of  FIG. 6  could be staggered, as are the post pads  500  in  FIG. 5 , and still be arranged along the same arc as well as along a second arc concentric with the first arc. 
     “Post-tip radius (if arc)”  114  refers to the radius from the center of the bond cavity, which is the center of the die-attach area, i.e., the inner-most rectangle in  FIGS. 3 and 4 , to the tip of the package post pads, if the package post pads are arranged along an arc, as depicted in  FIG. 6 . 
     “Max wire angle”  116  refers to the maximum angle that is permitted for a wire between a bond pad and a post pad. Referring to  FIG. 3 , the max wire angle  308  is depicted as angle θ. Generally, if θ exceeds 45 degrees then wires are likely to cross causing electrical shorts and other problems inhibiting the die  302  from operating properly with the package  300 . 
     “Max wire length”  118  refers to the maximum length of a wire between a bond pad and a post pad that is permitted. The max wire length  310  is also depicted in  FIG. 3 , and is determined as the distance between a corner bond pad and a corner post pad. The maximum wire length is typically specified by the manufacturer of a package, and gives a wire length above which sagging of the wire may occur, causing a short circuit of something within the integrated circuit, or possible problems with carrying an electrical current. 
     “Min substrate post pitch”  120  refers to the minimum post pitch allowable for the post pads on a package. Min substrate post pitch is depicted in  FIG. 3  as the center-point-to-center-point distance  312  between two post pads  318  on the package. This minimum distance is also specified by the package manufacturer. 
     “Gap between bonding points on rings”  122  refers to the distance of the bonding points on the ground and power rings on a package. Referring to  FIG. 3 , the gap between bonding points on the power and ground rings,  304  and  306  respectively, is depicted as the center point-to-center point distance between bonding points  318  on the power ring. Although not shown, the same gap between bonding points applies to bonding points on the ground ring and to adjacent bonding points where one is on the power ring  304  and the other is on the ground ring  306 . 
     “Percent power and ground connections”  124  refers to the number of wire bond connections, for example,  322  on  FIG. 3 , from the die that are connected to the power and ground rings. This percentage varies depending upon the intended design of the integrated circuit. The remaining percentage of wire bond connections that are not connected to power and ground are for input/output connections, for example,  310 ,  320  on  FIG. 3 . 
     “Die pad width”  126  refers to the width of one of the bonding pads on the die. Referring to  FIG. 4 , the die pad width is depicted as the edge-to-edge distance  400  of one of the bond pads  410  on the die  302 . 
     “Min die corner clearance”  128  refers to the minimum clearance between a bond pad on the die and the corner of the die itself. Referring to  FIG. 4 , the minimum die corner clearance  404  is depicted as the distance from the edge  412  of the die  302  to the closest edge  414  of the closest bonding pad  1 . 
     “Number of corner pads with different pitch (in each corner, per side)”  130  refers to the number of bond pads on the die that have a pitch different from the standard pitch of the bond pads on the die. Referring to  FIG. 4 , it is seen that bond pads  1 ,  2 ,  3  and  4  have a different pitch than the other bond pads  410  depicted. In the example of  FIG. 4 , the number of corner pads with a different pitch is 4, and this number 4 is entered into the spreadsheet  100 . 
     “Corner pad pitch”  132  refers to the pad pitch between the bond pads at the corner of the die. Referring to  FIG. 4 , corner pad pitch is the center-to-center distance  406  of the bonding pads  2  and  3  on the corner. The pitch between bonding pads  1 ,  2 ,  3  and  4  is the same, i.e.,  406 , whereas the pitch between bonding pads  4 ,  410  and between each bonding pad  410  is the same, i.e.,  408 . 
     “Min bond pad overlap”  134 , “post width”  136 , and “wire diameter”  138 , are all optional parameters that may be provided. Bond pad overlap is depicted in  FIG. 4  as the edge-to-edge distance  402  between a bond pad  416  and the aluminized bonding surface on which it sits. Post width is depicted in  FIG. 3 , and is the width  314  of one of the post pads  318  on the package  300 . Wire diameter refers to the diameter of the wires that connect the bond pads with the post pads. 
     Calculating Die Characteristics for a BGA Package 
     The spreadsheet embodiment depicted in  FIG. 1   a  is capable of three separate and independent sets of calculations,  104 ,  106 , and  108 . Depending upon what the designer is designing, any or all of the three sets of calculations are used to determine whether a square die fits into a package. Additionally, modifications to the package parameters defined in section  102  are modified to change the characteristics of the package itself. 
     A designer desiring to determine a maximum number of wire bond connections and a minimum die edge size utilizes the calculations performed in section  104 . Inputting a pad pitch  140  (for the die) results in calculations of a maximum number of wire bond connections  144  and a minimum die edge size  146  for a die with the input pad pitch. 
     A designer desiring to determine a minimum die pad pitch and a minimum die edge size utilizes the calculations performed in section  106 . Inputting a total number of wire bond connections  160  (for the die) results in calculations of a minimum die pad pitch  162  and a minimum die edge size  164  for a die with the input total number of wire bond connections  160 . 
     If the designer further desires to determine whether a die with either the input pad pitch  140  or the input total number of wire bond connections  160  fits into a package as defined in section  102 , the calculations in section  108  are utilized. If a die with an input pad pitch is considered, then the input pad pitch  140  is entered along with the calculated maximum total number of wire bond connections  144  and the calculated minimum die edge size  146  into section  108 . Section  108  then calculates a maximum total number of die pads allowed  190 , a required bond finger pitch  192  (which is the package post pad pitch), and determines 194 whether the die currently fits into the package defined by section  102 . However, if a die with an input total number of wire bond connections is considered, then the input total number of wire bond connections  160  is entered along with the calculated minimum die pad pitch  162  and the calculated minimum die edge size  164  into section  108 . Section  108  then calculates a maximum total number of die pads allowed  190 , a required bond finger pitch  192  (which is the package post pad pitch), and determines 194 whether the die currently fits into the package defined by section  102 . 
     In the set of calculations  104 , when a die pad pitch is input  140 , the spreadsheet  100  uses the input die pad pitch, as well as the package parameters from section  102 , to calculate a maximum number of wire bond connections per side of the die  142 , a maximum total number of wire bond connections for the die  144 , and a minimum die edge length  146 . These calculations are performed utilizing respective equations depending upon the arrangement of the post pads on the package. 
     For clarity, determining whether a square die fits into a particular package when package bond fingers, i.e., post pads, are arranged linearly and in-line is described in detail. The calculations utilized for different bond finger arrangements are then given later. 
     When the package post pads are in-line and arranged linearly an equation used to calculate the maximum number of connections for a side of the die  142  is: 
       2   ×     [               2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   IBPP   -     IBPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   IBPP       ]         
 
where:
 
MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with different pitch  130 ; CPP is the corner pad pitch  132  (μm); IBPP is the input die bond pad pitch  140  (μm); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on power and ground rings  122  (μm); and CTPG is the percentage of connections from the die to the power and ground rings  124 . Truncating the result from this equation gives the maximum number of connections for a side of the die.
 
     The maximum total number of wire bond connections for the die is calculated by multiplying the truncated result of the above equation by 4. 
     Calculating the minimum die edge size  146  for in-line package post pads is performed utilizing an equation: 
                 2   ×   MDCC     +   DPW   +       (     CPWDP   -   1     )     ×   2   ×   CPP     +                 (     MNC   -       (     CPWDP   -   1     )     ×   2     -   1     )     ×   IBPP           1000       
 
where:
         MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); MNC is the maximum number of connections per side of the die  142 ; and IBPP is the input die bond pad pitch  140  (μm).       

     If a designer wishes to determine whether a die with the input pad pitch fits into a package as defined by the parameters in section  102 , the third set of calculations  108  is used. Section  108  receives as inputs the calculated minimum die edge size  146 , the previously input die pad pitch  140 , and the calculated total number of wire bond pads on the die  144 , all of which are bonded with a wire. Using these inputs and the package parameters in section  102 , a maximum total number of die pads allowed  190 , and the required bond finger pitch  192 , i.e., the post pad pitch, are calculated. These calculations are performed utilizing different equations depending upon the arrangement of the post pads on the package. 
     When the package post pads are in-line and either arranged along an arc or linearly, an equation used to calculate the maximum total number of die pads allowed  190  is: 
       4   ×     [                 100   ×   DEL     -     2   ×   MDCC     -   DPW   -                 (     CPWDP   -   1     )     ×   2   ×   CPP           DPP     +       (     CPWDP   -   1     )     ×   2     +   1     ]         
 
where:
         DEL is the die edge size  180  (mm); MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); and DPP is the die pad pitch  182  (μm). The portion in the square bracket is rounded to the nearest integer before being multiplied by 4.       

     When the package post pads are in-line and arranged linearly, an equation used to calculate the required bond finger pitch  192  is: 
           [     DPP   +               2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -               DPP   -     Dpp   ×     (     CPWDP   -   1     )     ×   2               WBP   4         ]     -     CTPG   ×   GBDP         1   -   CTPG         
 
where:
         DPP is the die pad pitch  182  (μm); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; GBDP is the gap between bonding points on the power and ground rings  122  (μm); and WBP is the total number of bonded wire bond pads  184 .       

     A determination is then made whether it is currently possible to manufacture a die with the input pad pitch  140  to fit within a package, as defined by the parameters in section  102 . The determination is made by comparing the calculated, required post pad pitch from section  108  to the “Min Substrate Post Pitch”  120  in section  102 . The calculated, required bond finger, i.e., post pad, pitch  192  is rounded up to the nearest integer, e.g., if the calculated, required bond finger pitch  192  is 23.2 then it would be rounded to 24, before being compared to the “Min Substrate Post Pitch”  120 . If the required bond finger pitch  192  is smaller than the “Min Substrate Post Pitch”  120  then an indication that it is not possible to manufacture a square die with the input pad pitch  140  so that it fits into the package described by the parameters in section  102  is made. 
     In the above manner, the calculations in section  104  are combined with the calculations in section  108  to discover the design parameters of a square die, and to determine whether the square die fits into a package as defined in section  102 . In the second set of calculations  106 , a total number of wire bond connections  160  is input. The spreadsheet  100  uses the input total number of wire bond connections  160 , as well as the package parameters from section  102 , to calculate a minimum die pad pitch  162  and a minimum die edge size  164 . These calculations are performed utilizing different equations depending upon the arrangement of the post pads, i.e., bond fingers, on the package. Again, for clarity, only when the post pads are arranged linearly and in-line is described, with the calculations for other arrangements given later. 
     When the package post pads are in-line and arranged linearly, an equation used to calculate the minimum die pad pitch  162  is: 
                   WBC   4     ×     (     MPP   -     CTPG   ×     (     MPP   -   GBDP     )         )       -       (     CPWDP   -   1     )     ×   2   ×   CPP     -               2   ×   MWL   ×   25.4   ×   Sin   ⁢           ⁢     ⅇ   ⁡     (       π   ×   MWA     180     )                   WBC   4     -       (     CPWDP   -   1     )     ×   2     -   1         
 
where:
         WBC is the total number of wire bond connections  160 ; MPP is the minimum post pitch  120  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; GBDP is the gap between bonding points on the power and ground rings  122  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (em); MWL is the maximum wire length  118  (mils); and MWA is the maximum wire angle  116  (degrees).       

     When the package post pads are in-line, an equation used to calculate the minimum die edge size  164  is: 
                 2   ×   MDCC     +   DPW   +       (     CPWDP   -   1     )     ×   2   ×   CPP     +                 (       WBC   4     -       (     CPWDP   -   1     )     ×   2     -   1     )     ×   MDPP           1000       
 
where:
         MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); WBC is the total number of wire bond connections  160 ; and MDPP is the minimum die pad pitch  162  (μm).       

     A determination is then made whether it is currently possible to manufacture a die with the input total number of wire bond connections  160  to fit within a package, as defined by the parameters in section  102 . The determination is made by comparing the calculated, required post pad pitch from section  108  to the “Min Substrate Post Pitch”  120  in section  102 . The calculated, required bond finger, i.e., post pad, pitch  192  is rounded up to the nearest integer, e.g., if the calculated, required bond finger pitch  192  is 23.2 then it would be rounded to 24, before being compared to the “Min Substrate Post Pitch”  120 . If the required bond finger pitch  192  is smaller than the “Min Substrate Post Pitch”  120  then an indication that it is not possible to manufacture a square die with the input total number of wire bond connections  160  so that it fits into the package described by the parameters in section  102  is made. 
     In the above manner, the calculations in section  106  are combined with the calculations in section  108  to discover the design parameters of a square die, and to determine whether the square die fits into a package as defined in section  102 . 
     Calculations for Alternative BGA Arrangements 
     As previously mentioned, other calculations may be employed depending on different BGA arrangements in section  104 . These calculations are as follows: 
     When the package post pads are staggered and arranged along an arc an equation used to calculate the maximum number of connections for a side of the die  142  is: 
         2   ×     (     2   ×   PTR   ×   Arc   ⁢           ⁢     Sin   [                 2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   IBPP   -     IBPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   IBPP       ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         ]       )         MPP   -       (     MPP   -   GBDP     )     ×   CTPG           
 
where:
 
PTR is the post tip radius relating to the pads on the package  114  (μm); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with different pitch  130 ; CPP is the corner pad pitch  132  (μm); IBPP is the input die bond pad pitch  140  (em); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on power and ground rings  122  (μm); and CTPG is the percentage of connections from the die to the power and ground rings  124 . Truncating the result from this equation gives the maximum number of connections for a side of the die.
 
     When the package post pads are staggered and arranged linearly an equation used to calculate the maximum number of connections for a side of the die  142  is: 
       2   ×     [               2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   IBPP   -     IBPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   IBPP       ]         
 
where:
         MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with different pitch  130 ; CPP is the corner pad pitch  132  (μm); IBPP is the input die bond pad pitch  140  (μm); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on power and ground rings  122  (μm); and CTPG is the percentage of connections from the die to the power and ground rings  124 . Truncating the result from this equation gives the maximum number of connections for a side of the die.       

     Calculating the minimum die edge size  146  for staggered package post pads is performed utilizing an equation: 
                 2   ×   MDCC     +   DPW   +       (     CPWD   -   1     )     ×   2   ×   CPP     +               IBPP   ×       MNC   -     2   ×   CPWDP       2             1000       
 
where:
         MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); IBPP is the input die bond pad pitch  140  (μm); and MNC is the maximum number of connections per side of the die  142 .       

     When the package post pads are in-line and arranged along an arc an equation used to calculate the maximum number of connections for a side of the die  142  is: 
         (     2   ×   PTR   ×   Arc   ⁢           ⁢     Sin   ⁡     [                 2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   IBPP   -     IBPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   IBPP       ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         ]         )       MPP   -       (     MPP   -   GBDP     )     ×   CTPG           
 
where:
         PTR is the post tip radius relating to the pads on the package  114  (μm); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with different pitch  130 ; and CPP is the corner pad pitch  132  (μm); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on power and ground rings  122  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; and IBPP is the input die bond pad pitch  140  (μm). Truncating the result from this equation gives the maximum number of connections for a side of the die.       

     Other calculations performed in section  106  are as follows: 
     When the package post pads are staggered and arranged along an arc, an equation used to calculate the minimum die pad pitch  162  is: 
           2   ×   PTR   ×     Sin   ⁡     (         0.5   ×   WBC     4     ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         )         -       (     CPWDP   -   1     )     ×   2   ×   CPP     -     2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )                   (       (       0.5   ×     WBC   4       -       (     CPWDP   -   1     )     ×   2     -   1     )     +     0.4185   ×                     exp   (     0.0258   ×               2   ×   PTR   ×   Sin   ⁢           ⁢     ⅇ   ⁡     (     0.5   ×     WBC   4     ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         )         -                   (     CPWDP   -   1     )     ×   2   ×   CPP     -     2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )                     0.5   ×     WBC   4       -           ⁢       (     CPWDP   -   1     )     ×   2     -   1         )     )               
 
     PTR is the post tip radius  114  (μm); WBC is the total number of wire bond connections  160 ; MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on the power and ground rings  122  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (em); MWL is the maximum wire length  118  (mils); and MWA is the maximum wire angle  116  (degrees). 
     When the package post pads are staggered and arranged linearly, an equation used to calculate the minimum die pad pitch  162  is: 
                 0.5   ×     WBC   4     ×     (     MPP   -     CTPG   ×     (     MPP   -   GBDP     )         )       -                   (     CPWDP   -   1     )     ×   2   ×   CPP     -     2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )                     0.5   ×     WBC   4       -       (     CPWDP   -   1     )     ×   2     -   1         
 
where:
         WBC is the total number of wire bond connections  160 ; MPP is the minimum post pitch  120  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; GBDP is the gap between bonding points on the power and ground rings  122  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); MWL is the maximum wire length  118  (mils); and MWA is the maximum wire angle  116  (degrees).       

     When the package post pads are staggered, an equation used to calculate the minimum die edge size  164  is: 
                 2   ×   MDCC     +   DPW   +       (     CPWDP   -   1     )     ×   2   ×   CPP     +               IBPP   ×       MNC   -     2   ×   CPWDP       2             1000       
 
where:
         MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); IBPP is the input die bond pad pitch  140  (μm); and MNC is the maximum number of connections per side of the die  142 .       

     When the package post pads are in-line and arranged along an arc, an equation used to calculate the minimum die pad pitch  162  is: 
           2   ×   PTR   ×     Sin   ⁡     (       WBC   4     ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         )         -       (     CPWDP   -   1     )     ×   2   ×   CPP     -     2   ×   MWL   ×   25.4   ×   Sin   ⁢           ⁢     ⅇ   ⁡     (       π   ×   MWA     180     )                   (       (       WBC   4     -       (     CPWDP   -   1     )     ×   2     -   1     )     +     0.4185   ×                     exp   ⁢     (     0.0258   ×               2   ×   PTR   ×     Sin   ⁡     (       WBC   4     ×       MPP   -       (     MPP   -   GBDP     )     ×   CTPG         2   ×   PTR         )         -                   (     CPWDP   -   1     )     ×   2   ×   CPP     -     2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )                     WBC   4     ⁢           -       (     CPWDP   -   1     )     ×   2     -   1         )       )               
 
where:
         PTR is the post tip radius  114  (μm); WBC is the total number of wire bond connections  160 ; MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on the power and ground rings  122  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); MWL is the maximum wire length  118  (mils); and MWA is the maximum wire angle  116  (degrees).       

     Other calculations performed in section  108  are as follows: 
     When the package post pads are staggered and either arranged along an arc or linearly, an equation used to calculate the maximum total number of die pads allowed  190  is: 
         4   ×     [               100   ×   DEL     -     2   ×   MDCC     -   DPW   -                 (     CPWDP   -   1     )     ×   2   ×   CPP           DPP     ]     ×   2     +     2   ×     (     CPWDP   -   1     )       +   1       
 
where:
         DEL is the die edge size  146  (mm); MDCC is the minimum die corner clearance  128  (μm); DPW is the die pad width  126  (μm); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); and DPP is the die pad pitch  182  (μm). The portion in the square bracket is rounded to the nearest integer before being multiplied by 4.       

     When the package post pads are staggered and arranged along an arc, an equation used to calculate the required bond finger pitch  192  is: 
           2   ×     (       2   ×   PTR   ×   Arc   ⁢           ⁢     Sin   [                 2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )         +       (     CPWDP   -   1     )     ×   2   ×                 CPP   -   DPP   -     DPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   DPP       ×             MPP   -     (     MPP   -                     GBDP   )     ×   CTPG             2   ×   PTR         ]         WBP   4       )       -     GPDP   ×   CTPG         1   -   CTPG         
 
where:
         PTR is the post tip radius  114  (em); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); DPP is the die pad pitch  182  (μm); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on the power and ground rings  122  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; and WBP is the total number of bonded wire bond pads  184 .       

     When the package post pads are in-line and arranged along an arc, an equation used to calculate the required bond finger pitch  192  is: 
           (       2   ×   PTR   ×   Arc   ⁢           ⁢     Sin   [                 2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )         +       (     CPWDP   -   1     )     ×   2   ×                 CPP   -   DPP   -     DPP   ×     (     CPWDP   -   1     )     ×   2                 (     MPP   -       (     MPP   -   GBDP     )     ×   CTPG       )     -   DPP       ×             MPP   -     (     MPP   -                     GBDP   )     ×   CTPG             2   ×   PTR         ]         WBP   4       )     -     GPDP   ×   CTPG         1   -   CTPG         
 
where:
         PTR is the post tip radius  1114  (μm); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); DPP is the die pad pitch  182  (μm); MPP is the minimum post pitch  120  (μm); GBDP is the gap between bonding points on the power and ground rings  122  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; and WBP is the total number of bonded wire bond pads  184 .       

     When the package post pads are staggered and arranged linearly, an equation used to calculate the required bond finger pitch  192  is: 
           [     DPP   +               2   ×   MWL   ×   25.4   ×     Sin   ⁡     (       π   ×   MWA     180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   DPP   -     DPP   ×     (     CPWDP   -   1     )     ×   2               WBP   6         ]     -     CTPG   ×   GBDP         1   -   CTPG         
 
where:
         DPP is the die pad pitch  182  (μm); MWL is the maximum wire length  118  (mils); MWA is the maximum wire angle  116  (degrees); CPWDP is the number of corner pads with a different pitch  130 ; CPP is the corner pad pitch  132  (μm); CTPG is the percentage of connections from the die to the power and ground rings  124 ; GBDP is the gap between bonding points on the power and ground rings  122  (μm); and WBP is the total number of bonded wire bond pads  184 .
 
PQFP Design Parameters
       

       FIG. 2  depicts an embodiment of a spreadsheet  200  for carrying out the present invention to determine whether a square die fits into a particular PQFP package. “In line or Staggered”  210 , refers to the same design choice arrangement for the package post pads, as presented in  FIG. 1   a . “Conventional or circular frame”  212  refers to the type of PQFP frame that is used. A conventional PQFP frame is depicted in  FIG. 7 . A circular PQFP frame is depicted in  FIG. 8 , note that the leads from the die to the package post pads are not shown. “Min die edge size”  214  refers to the minimum length for an edge of the die. “Max wire angle”  216  is the same as max wire angle described in relation to  FIG. 1   a , as is “max wire length”  218 . “Min bond finger pitch”  220  corresponds to min substrate post pitch, and is the distance between the center points of the post pads on the package. “Tie bar width”  222  refers to the width of the metal support structure in the four corners of the die attach pad and must be taken into account when calculating an arc of leads. “Bond finger gap width”  224  refers to the distance between edges of the post pads on the package, for example 324 between post pads  318  ( FIG. 3 ). “Die pad width”  226 , “min die corner clearance”  228 , “number of corner pads with different pitch”  230 , and “corner pad pitch”  232 , all correspond to the same items related to  FIG. 1   a , and as depicted in  FIG. 4 . As related to  FIG. 1   a , “min bond pad overlap”  234 , “bond finger width”  236 , and “wire diameter”  238 , are optional, and may be ignored in various embodiments. 
     Calculating Die Characteristics for a PQFP Package 
     As in  FIG. 1   a , three separate and independent sets of calculations are performed in the embodiment depicted in  FIG. 2 . In a similar fashion, the calculations may be utilized independently of one another, or either section  204  or section  206  may be combined with section  208  to calculate die parameters and determine whether a square die with the calculated parameters fits into a package as defined in section  202 . 
     In the top set of calculations  204 , a pad pitch  240  for the die is received as input. The input pad pitch  240 , and the package parameters defined in section  202 , are used to calculate a maximum number of wire bond connections per side of the die  242 , and a maximum total number of wire bond connections for the die  244 . Depending upon the arrangement of the package post pads different equations are used to calculate the maximum number of wire bond connections per side of the die and the maximum total number of wire bond connections for the die. Utilizing the spreadsheet embodiment in  FIG. 2  is described relating to bond fingers arranged conventionally and in-line. 
     Calculations utilized for other bond finger arrangements are given later. 
     When the package post pads are in-line, an equation for calculating the maximum number of wire bond connections per side of the die  242  is: 
         [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP       IDPP     ]     +     2   ×     (     CPWDP   -   1     )       +   1       
 
where:
         MDEL is the minimum die edge size  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and IDPP is the input die pad pitch  240  (μm). The square bracket portion is truncated before being multiplied by 2.       

     The maximum number of wire bond connections for the die is calculated by multiplying the result from the preceding equation by 4. 
     As described above, the third set of calculations  208  is utilized to complete the design inquiry. The die pad pitch  240 , as well as the calculated total number of wire bond connections  244  are input into the third set of calculations  208  in order to determine whether a square die with the input pad pitch  240  and the calculated total number of wire bond connections  244  fits into a package as defined in section  202 . The third set of calculations  208  uses these two inputs, and the package parameters in section  202 , to calculate a maximum total number of die pads allowed  290 , a required bond finger (pad) pitch  292 , and whether it is currently possible to manufacture a die  294  with the input pad pitch  240  into a package, as defined by the parameters in section  202 . 
     When the package post pads are in-line, an equation for calculating the maximum number of die pads allowed  290  is: 
       4   ×     (       [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP       IDPP     ]     +     2   ×     (     CPWDP   -   1     )       +   1     )         
 
and wherein the result from the equation in square brackets is truncated; and
         MDEL is the minimum die edge size  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and IDPP is the input die pad pitch  280  (μm).       

     When the package post pads are in-line and arranged conventionally, an equation for calculating the required bond finger (pad) pitch  292  is: 
       IDPP   +     (         2   ×   MWL   ×   25.4   ×     Sine   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +       (     CPWDP   -   1     )     ×   2   ×   CPP     -   IDPP   -     IDPP   ×     (     CPWDP   -     1   ×   2               (     TNWBP   ÷   4     )       )         
 
and where:
         IDPP is the input die pad pitch  280  (μm); MWL is the maximum wire length  218  (mils); MWA is the maximum wire angle  216  (degrees); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and TNWBP is the total number of wire bond pads  282 .       

     The determination whether a die with the input pad pitch  240  fits into the package described by section  202  is made in the same manner as described in relation to  FIG. 1   a  by comparing the required bond finger (i.e., the package post pad) pitch  292  to the “Min Bond Finger Pitch”  220  given in section  202 . 
     The set of calculations  206  are also used to calculate a die parameter, however a total number of wire bond connections is input instead of a bond pad pitch. The input total number of wire bond connections  260 , and the package parameters in section  202 , are used to calculate a minimum die pad pitch  262 . Depending upon the arrangement of the package post pads two different equations are utilized to calculate the minimum die pad pitch. 
     When the package post pads are in-line, an equation used to calculate the minimum die pad pitch  262  is: 
       [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP           (     TNWBC   ÷   4     )     -   1   -     2   ×     (     CPWDP   -   1     )           ]       
 
where:
         MDEL is the minimum die edge size  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and TNWBC is the total number of wire bond connections  260 .       

     The calculated die pad pitch  262  and the total number of wire bond connections  260  are then input into the third set of calculations  208 , as described supra, to calculate a maximum total number of die pads allowed  290 , a required bond finger pitch  292 , and whether it is currently possible to manufacture  294  a die having the total number of wire bond connections  260  and the calculated minimum die pad pitch  262  within an existing package, is made. 
     Calculations for Alternative PQFP Arrangements 
     As previously mentioned, other calculations may be employed depending on different PQFP arrangements in section  204 . These calculations are as follows: 
     When the package post pads are staggered, an equation for calculating the maximum number of wire bond connections per side of the die  242  is: 
           [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP       IDPP     ]     ×   2     +     2   ×     (     CPWDP   -   1     )       +   1       
 
where:
         MDEL is the minimum die edge size  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and IDPP is the input die pad pitch  240  (μm). The square bracket portion is truncated before being multiplied by 2.       

     The maximum number of wire bond connections for the die is calculated by multiplying the result from the preceding equation by 4. 
     Other calculations utilized in section  206  are as follows: 
     When the package post pads are staggered, an equation used to calculate the minimum die pad pitch  262  is: 
       2   ⁡     [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP           (     TNWBC   ÷   4     )     -   1   -     2   ×     (     CPWDP   -   1     )           ]         
 
where:
         MDEL is the minimum die edge length  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and TNWBC is the total number of wire bond connections  260 .       

     Other calculations utilized in section  208  are as follows: 
     When the package post pads are staggered, an equation for calculating the maximum number of die pads allowed  290  is: 
       4   ×     (       2   ×     [         MDEL   ×   1000     -     2   ×   MDCC     -   DPW   -     2   ×     (     CPWDP   -   1     )     ×   CPP       IDPP     ]       +     2   ×     (     CPWDP   -   1     )       +   1     )         
 
and wherein the result from the equation in square brackets is truncated; and
         MDEL is the minimum die edge length  214  (mm); MDCC is the minimum die corner clearance  228  (μm); DPW is the die pad width  226  (μm); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and IDPP is the input die pad pitch (μm)  280 .       

     When the package post pads are in-line and arranged circularly, an equation for calculating the required bond finger (pad) pitch  292  is: 
       (         2   ⁢     π   ⁡     (       MDEL   ×   500     +     MWL   ×   25.4       )         -     4   ⁢     (       TBW   ×   25.4     +     3   ×   BFGW             TNWBP     )       
 
and where:
         MDEL is the minimum die edge length  214  (mm); MWL is the maximum wire length  218  (mils); TBW is the tie bar width  222  (mils); BFGW is the bond finger gap width  224  (mils); and TNWBP is the total number of wire bond pads  282 .       

     When the package post pads are staggered and arranged circularly, an equation for calculating the required bond finger (pad) pitch  292  is: 
       (         2   ⁢     π   ⁡     (       MDEL   ×   500     +     MWL   ×   25.4       )         -     4   ⁢     (       TBW   ×   25.4     +     3   ×   BFGW               (     TNWBP   ÷   2     )       )       
 
and where:
         MDEL is the minimum die edge length  214  (mm); MWL is the maximum wire length  218  (mils); TBW is the tie bar width  222  (mils); BFGW is the bond finger gap width  224  (mils); and TNWBP is the total number of wire bond pads  282 .       

     When the package post pads are staggered and arranged conventionally, an equation for calculating the required bond finger (pad) pitch  292  is: 
       IDPP   +     (               2   ×   MWL   ×   25.4   ×     Sine   ⁡     (       (     π   ×   MWA     )     ÷   180     )         +                   (     CPWDP   -   1     )     ×   2   ×   CPP     -   IDPP   -     IDPP   ×     (     CPWDP   -   1     )     ×   2               (     TNWBP   ÷   8     )       )         
 
and where:
         IDPP is the input die pad pitch  280  (μm); MWL is the maximum wire length  218  (mils); MWA is the maximum wire angle  216  (degrees); CPWDP is the number of corner pads with a different pitch  230 ; CPP is the corner pad pitch  232  (μm); and TNWBP is the total number of wire bond pads  282 .
 
Computer Hardware Overview
       

       FIG. 9  is a block diagram that illustrates a computer system  1300  upon which an embodiment of the invention may be implemented. Computer system  1300  includes a bus  1302  or other communication mechanism for communicating information, and a processor  1304  coupled with bus  1302  for processing information. Computer system  1300  also includes a main memory  1306 , such as a random access memory (RAM) or other dynamic storage device, coupled to bus  1302  for storing information and instructions to be executed by processor  1304 . Main memory  1306  also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor  1304 . Computer system  1300  further includes a read only memory (ROM)  1308  or other static storage device coupled to bus  1302  for storing static information and instructions for processor  1304 . A storage device  1310 , such as a magnetic disk or optical disk, is provided and coupled to bus  1302  for storing information and instructions. 
     Computer system  1300  may be coupled via bus  1302  to a display  1312 , such as a cathode ray tube (CRT), for displaying information to a computer user. An input device  1314 , including alphanumeric and other keys, is coupled to bus  1302  for communicating information and command selections to processor  1304 . Another type of user input device is cursor control  1316 , such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor  1304  and for controlling cursor movement on display  1312 . This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. 
     The invention is related to the use of computer system  1300  for determining whether a particular square die fits into a particular package. According to certain embodiments of the invention, determination whether a particular square die fits into a particular package is provided by computer system  1300  in response to processor  1304  executing one or more sequences of one or more instructions contained in main memory  1306 . Such instructions may be read into main memory  1306  from another computer-readable medium, such as storage device  1310 . Execution of the sequences of instructions contained in main memory  1306  causes processor  1304  to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequences of instructions contained in main memory  1306 . In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions to implement the invention. Thus, embodiments of the invention are not limited to any specific combination of hardware circuitry and software. 
     The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to processor  1304  for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device  1310 . Volatile media include dynamic memory, such as main memory  1306 . Transmission media include coaxial cables, copper wire and fiber optics, including the wires that comprise bus  1302 . Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read. 
     Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor  1304  for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system  1300  can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus  1302  can receive the data carried in the infrared signal and place the data on bus  1302 . Bus  1302  carries the data to main memory  1306 , from which processor  1304  retrieves and executes the instructions. The instructions received by main memory  1306  may optionally be stored on storage device  1310  either before or after execution by processor  1304 . 
     Computer system  1300  also includes a communication interface  1318  coupled to bus  1302 . Communication interface  1318  provides a two-way data communication coupling to a network link  1320  that is connected to a local network  1322 . For example, communication interface  1318  may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface  1318  may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface  1318  sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information. Network link  1320  typically provides data communication through one or more networks to other data devices. For example, network link  1320  may provide a connection through local network  1322  to a host computer  1324  or to data equipment operated by an Internet Service Provider (ISP)  1326 . ISP  1326  in turn provides data communication services through the worldwide packet data communication network, now commonly referred to as the “Internet”  1328 . Local network  1322  and Internet  1328  both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link  1320  and through communication interface  1318 , which carry the digital data to and from computer system  1300 , are exemplary forms of carrier waves transporting the information. 
     Computer system  1300  can send messages and receive data, including program code, through the network(s), network link  1320 , and communication interface  1318 . In the Internet example, a server  1330  might transmit a requested code for an application program through Internet  1328 , ISP  1326 , local network  1322  and communication interface  1318 . In accordance with the invention, one such downloaded application provides for automatically creating lot numbers and product identification numbers for a residual lot as described herein. 
     The received code may be executed by processor  1304  as it is received, and/or stored in storage device  1310 , or other non-volatile storage for later execution. In this manner, computer system  1300  may obtain application code in the form of a carrier wave. 
     The present invention may be embodied in a computer system as described above, or it may be a program designed to operate on any configuration for a computer system. 
     Embodiments of the present invention can therefore greatly decrease the amount of time required to design new integrated circuits and requires fewer and less expensive computing resources than currently employed, replacing the trial and error method of guessing package and corresponding die parameters, and generating a drawing based upon these guesses, with calculating die and/or package parameters and determining whether a die and package combination fit together. Thus, a die may be designed to fit a particular package, a package may be designed to fit a particular die, and simultaneous design of both a die and a package that fit one another may be accomplished. The number of drawings that must be generated is significantly reduced, and the total time to design a new integrated circuit is correspondingly reduced from several days. 
     While this invention has been described in connection with what is presently considered to the most practical and preferred embodiments, the invention is not limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.