Abstract:
An approach is provided that computes electrical delay ranges that correspond to a number of shapes included in a hardware design layout. The electrical delay ranges are converted to shape tolerances for each of the shapes. A lithography mask of the hardware design layout is generated using the shape tolerances so that the images of the shapes in the mask produced lie within the shape tolerances that correspond to the respective shape.

Description:
TECHNICAL FIELD 
     The present disclosure relates to an approach for understanding design tolerances in a semiconductor design. More specifically, the present disclosure relates to an approach that propagates these design tolerances to shape tolerances used in the lithographic process. 
     BACKGROUND 
     Lithography, such as photolithography, is a method used to structure material on a precise scale and is often used in the manufacture of semiconductors (e.g., microchips). Lithography employed to create semiconductors uses a photomask as a master from which a final pattern is created. Current methodologies of lithography treat the target layout (pattern) as a fixed requirement. Having fixed requirements in lithography is increasingly challenging due to modern semiconductor designs that pack more and more design elements in a smaller package. In order to fit the increased number of design elements on a small package, tolerances of the mask must often be extremely tight. These tight tolerances result various challenges, such as increased time to create a mask, which result in increased cost to manufacture the semiconductors. 
     SUMMARY 
     An approach is provided that computes electrical delay ranges that correspond to a number of shapes included in a hardware design layout. The electrical delay ranges are converted to a shape tolerances for each of the shapes. A lithography mask of the hardware design layout is generated using the shape tolerances so that the shapes in the lithography mask are masked within the shape tolerances that correspond to the respective shape. 
     The foregoing is a summary and thus contains, by necessity, simplifications, generalizations, and omissions of detail; consequently, those skilled in the art will appreciate that the summary is illustrative only and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the present disclosure, as defined solely by the claims, will become apparent in the non-limiting detailed description set forth below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings, wherein: 
         FIG. 1  is a block diagram example of a data processing system in which the methods described herein can be implemented; 
         FIG. 2  provides an extension example of the information handling system environment shown in  FIG. 1  to illustrate that the methods described herein can be performed on a wide variety of information handling systems which operate in a networked environment; 
         FIG. 3  is a flow diagram showing the steps taken to generate shape slack information and lithography tolerance bands; 
         FIG. 4  is a flowchart showing the steps taken to pre-characterize library cells that are stored in a shape library; 
         FIG. 5  is a flowchart showing the steps taken to convert electrical slack in the hardware design to physical shape slack; 
         FIG. 6  is a flowchart of a first phase in converting the electrical slack in the design to physical shape slack by analyzing the electrical slack distribution in the design; and 
         FIG. 7  is a flowchart of a second phase in converting the electrical slack in the design to physical shape slack by converting the delay slack to shape slack. 
     
    
    
     DETAILED DESCRIPTION 
     Certain specific details are set forth in the following description and figures to provide a thorough understanding of various embodiments of the disclosure. Certain well-known details often associated with computing and software technology are not set forth in the following disclosure, however, to avoid unnecessarily obscuring the various embodiments of the disclosure. Further, those of ordinary skill in the relevant art will understand that they can practice other embodiments of the disclosure without one or more of the details described below. Finally, while various methods are described with reference to steps and sequences in the following disclosure, the description as such is for providing a clear implementation of embodiments of the disclosure, and the steps and sequences of steps should not be taken as required to practice this disclosure. Instead, the following is intended to provide a detailed description of an example of the disclosure and should not be taken to be limiting of the disclosure itself. Rather, any number of variations may fall within the scope of the disclosure, which is defined by the claims that follow the description. 
     As will be appreciated by one skilled in the art, aspects of the present disclosure may be embodied as a system, method or computer program product. Accordingly, aspects of the present disclosure may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present disclosure may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Aspects of the present disclosure are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The following detailed description will generally follow the summary of the disclosure, as set forth above, further explaining and expanding the definitions of the various aspects and embodiments of the disclosure as necessary. To this end, this detailed description first sets forth a computing environment in  FIG. 1  that is suitable to implement the software and/or hardware techniques associated with the disclosure. A networked environment is illustrated in  FIG. 2  as an extension of the basic computing environment, to emphasize that modern computing techniques can be performed across multiple discrete devices. 
       FIG. 1  illustrates information handling system  100 , which is a simplified example of a computer system capable of performing the computing operations described herein. Information handling system  100  includes one or more processors  110  coupled to processor interface bus  112 . Processor interface bus  112  connects processors  110  to Northbridge  115 , which is also known as the Memory Controller Hub (MCH). Northbridge  115  connects to system memory  120  and provides a means for processor(s)  110  to access the system memory. Set of instructions  113  are stored in system memory  120  for execution by the one or more processors  110 . Graphics controller  125  also connects to Northbridge  115 . In one embodiment, PCI Express bus  118  connects Northbridge  115  to graphics controller  125 . Graphics controller  125  connects to display device  130 , such as a computer monitor. 
     Northbridge  115  and Southbridge  135  connect to each other using bus  119 . In one embodiment, the bus is a Direct Media Interface (DMI) bus that transfers data at high speeds in each direction between Northbridge  115  and Southbridge  135 . In another embodiment, a Peripheral Component Interconnect (PCI) bus connects the Northbridge and the Southbridge. Southbridge  135 , also known as the I/O Controller Hub (ICH) is a chip that generally implements capabilities that operate at slower speeds than the capabilities provided by the Northbridge. Southbridge  135  typically provides various busses used to connect various components. These busses include, for example, PCI and PCI Express busses, an ISA bus, a System Management Bus (SMBus or SMB), and/or a Low Pin Count (LPC) bus. The LPC bus often connects low-bandwidth devices, such as boot ROM  196  and “legacy” I/O devices (using a “super I/O” chip). The “legacy” I/O devices ( 198 ) can include, for example, serial and parallel ports, keyboard, mouse, and/or a floppy disk controller. The LPC bus also connects Southbridge  135  to Trusted Platform Module (TPM)  195 . Other components often included in Southbridge  135  include a Direct Memory Access (DMA) controller, a Programmable Interrupt Controller (PIC), and a storage device controller, which connects Southbridge  135  to nonvolatile storage device  185 , such as a hard disk drive, using bus  184 . 
     ExpressCard  155  is a slot that connects hot-pluggable devices to the information handling system. ExpressCard  155  supports both PCI Express and USB connectivity as it connects to Southbridge  135  using both the Universal Serial Bus (USB) the PCI Express bus. Southbridge  135  includes USB Controller  140  that provides USB connectivity to devices that connect to the USB. These devices include webcam (camera)  150 , infrared (IR) receiver  148 , keyboard and trackpad  144 , and Bluetooth device  146 , which provides for wireless personal area networks (PANs). USB Controller  140  also provides USB connectivity to other miscellaneous USB connected devices  142 , such as a mouse, removable nonvolatile storage device  145 , modems, network cards, ISDN connectors, fax, printers, USB hubs, and many other types of USB connected devices. While removable nonvolatile storage device  145  is shown as a USB-connected device, removable nonvolatile storage device  145  could be connected using a different interface, such as a Firewire interface, etcetera. 
     Wireless Local Area Network (LAN) device  175  connects to Southbridge  135  via the PCI or PCI Express bus  172 . LAN device  175  typically implements one of the IEEE 802.11 standards of over-the-air modulation techniques that all use the same protocol to wireless communicate between information handling system  100  and another computer system or device. Optical storage device  190  connects to Southbridge  135  using Serial ATA (SATA) bus  188 . Serial ATA adapters and devices communicate over a high-speed serial link. The Serial ATA bus also connects Southbridge  135  to other forms of storage devices, such as hard disk drives. Audio circuitry  160 , such as a sound card, connects to Southbridge  135  via bus  158 . Audio circuitry  160  also provides functionality such as audio line-in and optical digital audio in port  162 , optical digital output and headphone jack  164 , internal speakers  166 , and internal microphone  168 . Ethernet controller  170  connects to Southbridge  135  using a bus, such as the PCI or PCI Express bus. Ethernet controller  170  connects information handling system  100  to a computer network, such as a Local Area Network (LAN), the Internet, and other public and private computer networks. 
     While  FIG. 1  shows one information handling system, an information handling system may take many forms. For example, an information handling system may take the form of a desktop, server, portable, laptop, notebook, or other form factor computer or data processing system. In addition, an information handling system may take other form factors such as a personal digital assistant (PDA), a gaming device, ATM machine, a portable telephone device, a communication device or other devices that include a processor and memory. 
     The Trusted Platform Module (TPM  195 ) shown in  FIG. 1  and described herein to provide security functions is but one example of a hardware security module (HSM). Therefore, the TPM described and claimed herein includes any type of HSM including, but not limited to, hardware security devices that conform to the Trusted Computing Groups (TCG) standard, and entitled “Trusted Platform Module (TPM) Specification Version 1.2.” The TPM is a hardware security subsystem that may be incorporated into any number of information handling systems, such as those outlined in  FIG. 2 . 
       FIG. 2  provides an extension example of the information handling system environment shown in  FIG. 1  to illustrate that the methods described herein can be performed on a wide variety of information handling systems that operate in a networked environment. Types of information handling systems range from small handheld devices, such as handheld computer/mobile telephone  210  to large mainframe systems, such as mainframe computer  270 . Examples of handheld computer  210  include personal digital assistants (PDAs), personal entertainment devices, such as MP3 players, portable televisions, and compact disc players. Other examples of information handling systems include pen, or tablet, computer  220 , laptop, or notebook, computer  230 , workstation  240 , personal computer system  250 , and server  260 . Other types of information handling systems that are not individually shown in  FIG. 2  are represented by information handling system  280 . As shown, the various information handling systems can be networked together using computer network  200 . Types of computer network that can be used to interconnect the various information handling systems include Local Area Networks (LANs), Wireless Local Area Networks (WLANs), the Internet, the Public Switched Telephone Network (PSTN), other wireless networks, and any other network topology that can be used to interconnect the information handling systems. Many of the information handling systems include nonvolatile data stores, such as hard drives and/or nonvolatile memory. Some of the information handling systems shown in  FIG. 2  depicts separate nonvolatile data stores (server  260  utilizes nonvolatile data store  265 , mainframe computer  270  utilizes nonvolatile data store  275 , and information handling system  280  utilizes nonvolatile data store  285 ). The nonvolatile data store can be a component that is external to the various information handling systems or can be internal to one of the information handling systems. In addition, removable nonvolatile storage device  145  can be shared among two or more information handling systems using various techniques, such as connecting the removable nonvolatile storage device  145  to a USB port or other connector of the information handling systems. 
       FIG. 3  is a flow diagram showing the steps taken to generate shape slack information and lithography tolerance bands. Three types of information are extracted from hardware design layout  300 . In the example shown, circuit sensitivity information is extracted using the process on the left hand side, lithography sensitivity is extracted using the process in the middle, and power and performance specifications are extracted along the right hand side. 
     In the process shown on the left side that extracts circuit sensitivity, at step  305 , the first shape is selected from hardware design layout  300 . At step  310 , the electrical characteristics are extracted from the selected shape At step  315 , an electrical analysis (e.g., analysis of power and performance) is performed on the selected shape. Steps  310  and  315  may be performed by using a standard circuit simulator to extract circuit parameters at different configurations of the shape in question. The circuit sensitivity data derived from the electrical analysis are stored in circuit sensitivity data store  340 . A determination is made as to whether there are more shapes in the design that need to be extracted and analyzed (decision  320 ). While there are more shapes to analyze, decision  320  loops back to step  305  to select and process the next shape. This looping continues until there are no further shapes to analyze, at which point decision  320  branches to “no” branch  330  whereupon circuit sensitivity extraction and analysis ends at  335 . 
     Lithography sensitivity process is extracted using the process shown in the middle of  FIG. 3 . Here, at step  350 , a lithography simulator is used to process an emulation of the hardware design layout. The lithography simulator uses models of the manufacturing process to generate the expected shape on the wafer from the given target shape. Results of the simulation point to the degree of difficulty in printing a given shape. This results in lithography sensitivity data that is stored in data store  360 . One possible metric for comparing lithography sensitivity is to compute the area of the process variability bands (PV Bands) for a given shape. The band comprises of wafer contours at different process conditions and is indicative of how the feature will behave under variability in the manufacturing process. A shape more difficult to print will have wider PV Bands and a shape that is more easily printed will have narrower PV Bands. 
     Power and performance specifications are extracted on the right side of  FIG. 3 . As shown, power and performance specifications data store  370  is used to store the power and performance specifications that pertain to hardware design layout  300 . 
     At step  375 , shape tolerance analysis and optimization is performed using circuit sensitivity data  340 , lithography sensitivity  360 , and power and performance specifications  370  as inputs. Step  340  is explained in greater detail in  FIG. 4 , while step  375  is explained in greater detail in  FIGS. 5 through 7 . The result of step  375  are tolerance bands for each shape which are stored in tolerance bands data store  380 . These tolerance bands are then used by mask generator  390  to generate the photolithographic mask. These tolerance bands provide a range of layouts that can provide electrical performance that are each within tolerance. In essence, tolerance bands are designer-approved tolerances for the lithography that aid manufacturing of the masks by allowing greater lithography flexibility without impacting the performance of the hardware design. 
       FIG. 4  is a flowchart showing the steps taken to pre-characterize library cells that are stored in a shape library. Processing commences at  400  whereupon, at step  410 , the first shape is selected from shape library  430 . In this example, shapes are the transistors representing by polysilicon overlapping active area. A determination is made as to whether there are more input slews to process (decision  450 ). If there are more input slews to process for the selected shape, then decision  450  branches to “yes” branch  452  which loops back to select the next input slew for the selected shape. This looping continues until all input slews for the selected shape have been selected and processed, at which time decision  450  branches to “no” branch  485 .Shape library  430  is a data store that is used to store data pertaining to shapes used in hardware designs. As the name of the flowchart indicates, the processing performed in  FIG. 3  can be performed before any hardware designs need to be analyzed so that the delay and slew data pertaining to the shapes will be available when hardware designs are ready for analysis. At step  420 , the first input slew is selected for the selected shape. Input slew is the time taken for the signal at the input of a gate to change from its initial value to its final value and is representative of the slope or how slow/fast the signal changes. A faster changing signal will result in lower delay and a slower changing signal will result in a faster delay. At step  425 , a linear delay model is built for the selected input slew. The mathematical formula relates the change in delay at the output of the gate to the change in the shape dimension (which is gate length in this case) using a linear function. The delay data resulting from this formula is stored in shape library  430 . At step  440  the linear output slew model is built. Output slew is the slew or slope at the output of a gate as opposed to the input of a gate. A determination is made as to whether there are more input slews to process (decision  450 ). If there are more input slews to process for the selected shape, then decision  450  branches to “yes” branch  452  which loops back to select the next input slew for the selected shape. This looping continues until all input slews for the selected shape have been selected and processed, at which time decision  450  branches to “no” branch  458 . 
     At step  460 , the first output load is selected for the selected shape. Output slew is the slope of the signal at the output of the gate, representing how fast or slow it changes. Output load is the capacitance on the output pin of the gate. The higher the capacitance, the slower the signal will change.] At step  470 , a linear model is built for the selected output slew. Once again, the delay model relates the output delay of the cell to the change in shape dimension (in this case, gate length) using a linear approximation. The delay data resulting from this formula is stored in shape library  430 . At step  475 , the linear slew model is built for the selected output slew. A determination is made as to whether there are more output slews to process (decision  480 ). If there are more output slews to process for the selected shape, then decision  480  branches to “yes” branch  485  which loops back to select the next output slew for the selected shape. This looping continues until all output slews for the selected shape have been selected and processed, at which time decision  480  branches to “no” branch  490  which loops back to step  410  which selects the next shape from shape library  430  and builds the delay and slew models as described above. This looping continues until all of the shapes in shape library  430  have been processed, at which the processing shown in  FIG. 4  ends. As new shapes are added to shape library  430  (e.g., because of a new hardware design, etc.), these new shapes are characterized using the steps shown in  FIG. 4  so that the delay and slew data is available in the shape library. 
       FIG. 5  is a flowchart showing the steps taken to convert electrical slack in the hardware design to physical shape slack. Processing commences at  500  whereupon, during a first phase, predefined process  510  is performed to determine the electrical slack distribution (see  FIG. 6  and corresponding text for processing details). Electrical slack is for the design as a whole.  FIG. 5  shows how to propagate this slack to shapes in the design in the form of shape slack. The delay range resulting from predefined process  510  is stored in delay range  520 . Delay range represents the maximum and minimum values of delay within which a gate can operate while still meeting design requirements. 
     During a second phase, predefined process  530  is performed to convert the delay slack into shape slack (see  FIG. 7  and corresponding text for processing details). Inputs to predefined process  530  include shape weightings  525  which is provided by lithography processes as well as delay range data  520  resulting from phase  1 . The data for  520  is obtained by the procedure described for  360  previously shown in  FIG. 3 . The result of predefined process  530  are tolerances data  540  which indicate the inner and outer bounds of a shape (e.g., shape  550 ). As shown in the example, shape  550  has inner bound (tolerance)  551  which is a smaller footprint than outer bound (tolerance)  552 . So long as the shape is generated within these inner and outer bounds it will be acceptable to the hardware design. Mask generator  570  generates mask  580  taking the hardware design layout  560  as input as well as tolerances data  540 . The mask generator has flexibility to generate the mask for the hardware design layout using the tolerances (inner/outer tolerances) provided for each shape. Some shapes might have tighter, or more precise, tolerances than other shapes in the design. 
       FIG. 6  is a flowchart of a first phase in converting the electrical slack in the design to physical shape slack by analyzing the electrical slack distribution in the design. Processing commences at  600  whereupon, at step  620  all of the gates in the hardware design are selected at the same time. The hardware design representation is netlist data store  610 . All of the gates in the netlist are selected simultaneously because the way in which the slack gets divided amongst the gates depends on how they are interconnected. For example, if there are five gates connected to each other on a path with some slack, the slack should be divided equally among the five gates as opposed to giving all the slack to just one of the gates. Each gate selected from hardware design  610  is processed by steps  630  to  690  in parallel (essentially, simultaneously with the other gates). At step  630 , the delay of each gate is computed as a function of the input slew and output load pertaining to each of the gates. This is a well-known computation that is done by all timing tools. It involves the use of lookup tables. At step  640 , slack variables are established for each gate (S i ) and assigned to each gate&#39;s late mode (which is constrained by setup time). The late mode of a gate determines the latest time at which the output of a gate will change. Early mode determines the opposite, i.e. what is the earliest at which the output of the gate will change. The latest arriving time is constrained by the setup time at a latch/flip-flop into which the output of the gate will be stored. Early mode is constrained by the hold time of the same latch/flip-flop. At step  650 , slack variables are established for each gate (H i ) and assigned to each gate&#39;s early mode which is constrained by hold time. At step  660 , the allowable delay range of each gate is computed to be in the range of the sum of the delay and the hold time to the sum of the delay and the late mode (in the range of (D i +H i ) to (D i +S i )). So long as the delay of each of the gates is between this range (established for each of the gates) the timing constraints of the hardware design will not be violated. At step  670 , the arrival time at each gate&#39;s output gate (a i ) is computed. 
     The delays, setup times, hold times, allowable ranges, and arrival times are fed into the equation shown in step  690  along with the list of primary input nodes ( 675 ) and the list of primary output nodes ( 680 ). Step  690  takes as input, the delays of each gate along with their connectivity as well as the design constraints in terms of setup times and hold times at each flop/latch. It then uses the optimization formulation outlined to generate the delay slack values (S i ,H i ) for each gate such that design constraints are satisfied. The optimization formulation for  690  may be solved as a linear program (LP) using a commercial LP solver. 
       FIG. 7  is a flowchart of a second phase in converting the electrical slack in the design to physical shape slack by converting the delay slack to shape slack. In  FIG. 7 , the delay ranges computed in  FIG. 6  are converted to allowable shape tolerances. Processing commences at  700  whereupon, at step  705 , the number of gates in hardware design  610  is identified (set in the example to variable N). The current gate that is being processed is set to the first gate (initializing variable i to 1). At step  710 , the first gate from netlist  610  is selected and each shape in the selected gate is assigned an identifier (1 to M with M being the number of shapes in the selected gate). At step  715 , all of the shapes (1 to M) in the selected gate are selected for simultaneous (or near-simultaneous) processing. At step  720 , the drawn dimension of each shape is assigned to the variable L (e.g., L 1  to L M ). At step  725 , an outer bound of each shape is assigned to the variable O (e.g., O 1  to O M ). Likewise, at step  730 , an inner bound of each shape is assigned to the variable I (e.g.,I 1  to I M ). When processing is completed, each of the shapes will have a computed inner and outer bound value assigned that specifies a physical range tolerance. So, for example, the first shape in the netlist will have a drawn dimension of L 1 , an inner bound dimension of I 1 , and an outer bound dimension of O 1 . When the mask generator is generating the mask for this first shape, the shape of the mask can be anywhere between these bounds and still create an acceptable mask for the hardware design. 
     At step  740 , the total shape slack (range) is maximized using the equations shown in  750  and is subject to timing constraints determined in Phase  1  (see  FIG. 6  and corresponding text for details regarding computation of timing constraints). Each gate has a delay range that was computed in Phase  1 . In addition, each of the shapes can have a weight applied. In one embodiment, the weight can be driven by lithography processes. Box  750  describes the optimization formulation for generating an inner (I j ) and outer (O j ) tolerance on each shape in a gate given the range of delay values (D i +H i ,D i +S i ) that the gate can take. The weights (wj) are obtained from the computations performed for litho sensitivity in  360 . The result of step  740  are tolerances stored in tolerances data store  755  that include inner and outer bounds (I j  and O j ) for each shape in the gate. These tolerances are used by the mask generator to create shapes (e.g. shape  550 ) within this physical range tolerance. 
     A determination is made as to whether there are more gates in the hardware design to process (decision  760 ). If there are more gates to process, decision  760  branches to “yes” branch  765  whereupon, at step  770 , the gate variable (i) is incremented to represent the next gate in the hardware design. Processing then loops to the beginning of the process (step  710 ) to select the next gate in the design, select all of the shapes in the next gate, and process the selected shapes as described above. This looping continues until there are no more gates in hardware design  610  to process, at which point decision  760  branches to “no” branch  775  and processing ends at  795 . 
     The flowchart and block diagrams in the FIGures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the FIGures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. 
     While particular embodiments of the present disclosure have been shown and described, it will be obvious to those skilled in the art that, based upon the teachings herein, that changes and modifications may be made without departing from this disclosure and its broader aspects. Therefore, the appended claims are to encompass within their scope all such changes and modifications as are within the true spirit and scope of this disclosure. Furthermore, it is to be understood that the disclosure is solely defined by the appended claims. It will be understood by those with skill in the art that if a specific number of an introduced claim element is intended, such intent will be explicitly recited in the claim, and in the absence of such recitation no such limitation is present. For non-limiting example, as an aid to understanding, the following appended claims contain usage of the introductory phrases “at least one” and “one or more” to introduce claim elements. However, the use of such phrases should not be construed to imply that the introduction of a claim element by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim element to disclosures containing only one such element, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an”; the same holds true for the use in the claims of definite articles.