Patent Publication Number: US-2018052951-A1

Title: Acceleration Of Voltage Propagation Based On Device Chain Reduction

Description:
FIELD OF THE DISCLOSED TECHNOLOGY 
     The present disclosed technology relates to integrated circuit design and process technologies. Various implementations of the disclosed technology may be particularly useful for reliability verification of a circuit design. 
     BACKGROUND OF THE DISCLOSED TECHNOLOGY 
     Many power-efficient circuit designs today have multiple voltage domains. Device electrical overstress occurs when a low-voltage device is driven by a high-voltage power rail, signal, or bulk connection with the potential to cause long-term or permanent damage (usually in the form of oxide breakdown). This damage results in circuit degradation or failure over time. Conversely, when insufficient voltage is applied to a high-voltage device and the device is driven by a low-voltage net, the device may not switch, or may switch slowly, again degrading circuit performance. 
     Thin-oxide transistors, used extensively at advanced nodes, are less robust against electrical failure and impose new electrical overstress verification challenges. Thinner oxide generally allows for the use of lower voltage and provides less power. When power domain design errors occur, effects such as negative bias temperature instability (NBTI) can lead to the threshold voltage of the PMOS transistors increasing over time, resulting in reduced switching speeds for logic gates, and hot carrier injection (HCI) issues, altering the threshold voltage of NMOS devices over time. Soft breakdown (SBD), as a time-dependent failure mechanism, also contributes to the degradation effects of gate oxide breakdown. 
     Electrical overstress is an important concern for both analog and digital designers, due to the variety of power conditions commonly used in all designs, such as multiple power domains, standby/wake-up/low power/power-down conditions (in which there is no bias current, but the battery is present), and the presence of high-voltage signals. Understanding device pin voltages in all modes of operation is thus critical for detecting potential electrical overstress issues. The ability to identify device breakdown, recognize reverse breakdown issues in high-voltage areas, and detect maximum voltage across gate oxides are all part of a robust electrical overstress detection strategy. However, verifying device operating voltage conditions in voltage-controlled designs is very complicated. 
     Many design teams employ SPICE simulations and user-generated marker layers or text points to check for electrical overstress, but this is an error-prone method because it requires the designer to manually determine how voltages propagate throughout the design, and manually mark the correct regions for high-voltage design rules. Markers are also extremely difficult to maintain as the design is changed. 
     With consumer expectations for longer device operation at sustained performance levels, designing for reliability is no longer an optional product feature, but a necessary and integral part of a product&#39;s specifications. Designers need verification tools and techniques that go beyond the traditional triumvirate of design rule checking (DRC), layout vs. schematic (LVS) comparison, and electrical rule checking (ERC) to provide thorough detection of and protection against electrical overstress conditions. 
     BRIEF SUMMARY OF THE DISCLOSED TECHNOLOGY 
     Aspects of the disclosed technology relate to techniques of voltage propagation-based reliability verification. In one aspect, there is a method comprising: analyzing a circuit design to identify circuit component chains; propagating voltage values across components of the circuit design based, at least in part, on treating the circuit component chains as virtual single components; analyzing the propagated voltage values to detect problems in the circuit design; and reporting the detected problems in the circuit design. 
     The circuit component chains may comprise chains of transistors, chains of resistors, or both. The analyzing a circuit design may be performed within subcircuits of the circuit design. The analyzing a circuit design may employ a circuit component tracing method. 
     The propagating may further be based on employing both global iterations and local iterations, wherein at least one of the global iterations comprises local iterations for a subcircuit of the circuit design. The local iterations suspend when voltage values on nets of the subcircuit are not changed from one local iteration to a next local iteration or one preset condition is met. 
     The detected problems in the circuit design may comprise electrical overstress. The reporting may comprise storing and/or displaying information of the detected problems. 
     In another aspect, there is one or more computer-readable media storing computer-executable instructions for causing one or more processors to perform the above method. 
     In still another aspect, there is a system, comprising: one or more processors, the one or more processors programmed to perform the above method. 
     Certain inventive aspects are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims. 
     Certain objects and advantages of various inventive aspects have been described herein above. Of course, it is to be understood that not necessarily all such objects or advantages may be achieved in accordance with any particular embodiment of the disclosed technology. Thus, for example, those skilled in the art will recognize that the disclosed technology may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other objects or advantages as may be taught or suggested herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an example of a computing system that may be used to implement various embodiments of the disclosed technology. 
         FIG. 2  illustrates an example of a multi-core processor unit that may be used to implement various embodiments of the disclosed technology. 
         FIG. 3  shows an example of a circuit design  300  for illustrating how voltage propagation operates according to some embodiments of the disclosed technology. 
         FIG. 4  illustrates an example of a reliability verification tool that may be implemented according to various embodiments of the disclosed technology. 
         FIG. 5  illustrates a flowchart showing a process of voltage propagation-based reliability verification that may be implemented according to various examples of the disclosed technology. 
         FIG. 6  illustrates an example of CMOS (complementary metal-oxide-semiconductor) transistor-level realization of a five-input OR gate 
         FIG. 7  illustrates an example of a shift register  700  and an example of a flip-flop  705 . 
         FIG. 8  illustrates an example of a hierarchical structure of a circuit design. 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSED TECHNOLOGY 
     Various aspects of the present disclosed technology relate to techniques of voltage propagation. In the following description, numerous details are set forth for the purpose of explanation. However, one of ordinary skill in the art will realize that the disclosed technology may be practiced without the use of these specific details. In other instances, well-known features have not been described in detail to avoid obscuring the present disclosed technology. 
     Although the operations of some of the disclosed methods, apparatus, and systems are described in a particular, sequential order for convenient presentation, it should be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth below. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed methods, apparatus, and systems can be used in conjunction with other methods, apparatus, and systems. Additionally, the description sometimes uses terms like “propagate”, “analyze”, and “report” to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms may vary depending on the particular implementation and are readily discernible by one of ordinary skill in the art. 
     Any of the disclosed techniques can be implemented in whole or in part by software comprising computer-executable instructions stored on computer-readable media. Such software can comprise, for example, an appropriate electronic design automation (“EDA”) software tool. Such software can be executed on a single computer or on a networked computer (e.g., via the Internet, a wide-area network, a local-area network, a client-server network, or other such network). For clarity, only certain selected aspects of the software-based implementations are described. Other details that are well known in the art are omitted. For example, it should be understood that the disclosed technology is not limited to any specific computer language, program, or computer. For example, the disclosed technology can be implemented using any commercially available computer executing a program written in any commercially available or otherwise suitable language. Any of the disclosed methods can alternatively be implemented (partially or completely) in hardware (e.g., an ASIC, PLD, or SoC). 
     Any data produced from any of the disclosed methods (e.g., intermediate or final test patterns, test patterns values, or control data) can be stored on computer-readable media (e.g., tangible computer-readable media, such as one or more CDs, volatile memory components (such as DRAM or SRAM), or nonvolatile memory components (such as hard drives)) using a variety of different data structures or formats. Such data can be created, updated, or stored using a local computer or over a network (e.g., by a server computer). 
     As used in this disclosure, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly dictates otherwise. Additionally, the term “includes” means “comprises.” Moreover, the term “design” is intended to encompass data describing an entire microdevice, such as an integrated circuit device or micro-electromechanical system (MEMS) device. This term also is intended to encompass a smaller group of data describing one or more components of an entire microdevice, however, such as a layer of an integrated circuit device, or even a portion of a layer of an integrated circuit device. 
     Still further, the term “design” also is intended to encompass data describing more than one microdevice, such as data to be used to create a mask or reticle for simultaneously forming multiple microdevices on a single wafer. The layout design data may be in any desired format, such as, for example, the Graphic Data System II (GDSII) data format or the Open Artwork System Interchange Standard (OASIS) data format proposed by Semiconductor Equipment and Materials International (SEMI). Other formats include an open source format named Open Access, Milkyway by Synopsys, Inc., and EDDM by Mentor Graphics, Inc. 
     Illustrative Operating Environment 
     The execution of various electronic design automation processes according to embodiments of the disclosed technology may be implemented using computer-executable software instructions executed by one or more programmable computing devices. Because these embodiments of the disclosed technology may be implemented using software instructions, the components and operation of a generic programmable computer system on which various embodiments of the disclosed technology may be employed will first be described. Further, because of the complexity of some electronic design automation processes and the large size of many circuit designs, various electronic design automation tools are configured to operate on a computing system capable of simultaneously running multiple processing threads. The components and operation of a computer network having a host or master computer and one or more remote or servant computers therefore will be described with reference to  FIG. 1 . This operating environment is only one example of a suitable operating environment, however, and is not intended to suggest any limitation as to the scope of use or functionality of the disclosed technology. 
     In  FIG. 1 , the computer network  101  includes a master computer  103 . In the illustrated example, the master computer  103  is a multi-processor computer that includes a plurality of input and output devices  105  and a memory  107 . The input and output devices  105  may include any device for receiving input data from or providing output data to a user. The input devices may include, for example, a keyboard, microphone, scanner or pointing device for receiving input from a user. The output devices may then include a display monitor, speaker, printer or tactile feedback device. These devices and their connections are well known in the art, and thus will not be discussed at length here. 
     The memory  107  may similarly be implemented using any combination of computer readable media that can be accessed by the master computer  103 . The computer readable media may include, for example, microcircuit memory devices such as read-write memory (RAM), read-only memory (ROM), electronically erasable and programmable read-only memory (EEPROM) or flash memory microcircuit devices, CD-ROM disks, digital video disks (DVD), or other optical storage devices. The computer readable media may also include magnetic cassettes, magnetic tapes, magnetic disks or other magnetic storage devices, punched media, holographic storage devices, or any other medium that can be used to store desired information. 
     As will be discussed in detail below, the master computer  103  runs a software application for performing one or more operations according to various examples of the disclosed technology. Accordingly, the memory  107  stores software instructions  109 A that, when executed, will implement a software application for performing one or more operations. The memory  107  also stores data  109 B to be used with the software application. In the illustrated embodiment, the data  109 B contains process data that the software application uses to perform the operations, at least some of which may be parallel. 
     The master computer  103  also includes a plurality of processor units  111  and an interface device  113 . The processor units  111  may be any type of processor device that can be programmed to execute the software instructions  109 A, but will conventionally be a microprocessor device. For example, one or more of the processor units  111  may be a commercially generic programmable microprocessor, such as Intel® Pentium® or Xeon™ microprocessors, Advanced Micro Devices Athlon™ microprocessors or Motorola 68K/Coldfire® microprocessors. Alternately or additionally, one or more of the processor units  111  may be a custom-manufactured processor, such as a microprocessor designed to optimally perform specific types of mathematical operations. The interface device  113 , the processor units  111 , the memory  107  and the input/output devices  105  are connected together by a bus  115 . 
     With some implementations of the disclosed technology, the master computing device  103  may employ one or more processing units  111  having more than one processor core. Accordingly,  FIG. 2  illustrates an example of a multi-core processor unit  111  that may be employed with various embodiments of the disclosed technology. As seen in this figure, the processor unit  111  includes a plurality of processor cores  201 . Each processor core  201  includes a computing engine  203  and a memory cache  205 . As known to those of ordinary skill in the art, a computing engine contains logic devices for performing various computing functions, such as fetching software instructions and then performing the actions specified in the fetched instructions. These actions may include, for example, adding, subtracting, multiplying, and comparing numbers, performing logical operations such as AND, OR, NOR and XOR, and retrieving data. Each computing engine  203  may then use its corresponding memory cache  205  to quickly store and retrieve data and/or instructions for execution. 
     Each processor core  201  is connected to an interconnect  207 . The particular construction of the interconnect  207  may vary depending upon the architecture of the processor unit  111 . With some processor cores  201 , such as the Cell microprocessor created by Sony Corporation, Toshiba Corporation and IBM Corporation, the interconnect  207  may be implemented as an interconnect bus. With other processor units  111 , however, such as the Opteron™ and Athlon™ dual-core processors available from Advanced Micro Devices of Sunnyvale, Calif., the interconnect  207  may be implemented as a system request interface device. In any case, the processor cores  201  communicate through the interconnect  207  with an input/output interface  209  and a memory controller  210 . The input/output interface  209  provides a communication interface between the processor unit  111  and the bus  115 . Similarly, the memory controller  210  controls the exchange of information between the processor unit  111  and the system memory  107 . With some implementations of the disclosed technology, the processor units  111  may include additional components, such as a high-level cache memory shared by the processor cores  201 . 
     While  FIG. 2  shows one illustration of a processor unit  111  that may be employed by some embodiments of the disclosed technology, it should be appreciated that this illustration is representative only, and is not intended to be limiting. Also, with some implementations, a multi-core processor unit  111  can be used in lieu of multiple, separate processor units  111 . For example, rather than employing six separate processor units  111 , an alternate implementation of the disclosed technology may employ a single processor unit  111  having six cores, two multi-core processor units each having three cores, a multi-core processor unit  111  with four cores together with two separate single-core processor units  111 , etc. 
     Returning now to  FIG. 1 , the interface device  113  allows the master computer  103  to communicate with the servant computers  117 A,  117 B,  117 C . . .  117   x  through a communication interface. The communication interface may be any suitable type of interface including, for example, a conventional wired network connection or an optically transmissive wired network connection. The communication interface may also be a wireless connection, such as a wireless optical connection, a radio frequency connection, an infrared connection, or even an acoustic connection. The interface device  113  translates data and control signals from the master computer  103  and each of the servant computers  117  into network messages according to one or more communication protocols, such as the transmission control protocol (TCP), the user datagram protocol (UDP), and the Internet protocol (IP). These and other conventional communication protocols are well known in the art, and thus will not be discussed here in more detail. 
     Each servant computer  117  may include a memory  119 , a processor unit  121 , an interface device  123 , and, optionally, one more input/output devices  125  connected together by a system bus  127 . As with the master computer  103 , the optional input/output devices  125  for the servant computers  117  may include any conventional input or output devices, such as keyboards, pointing devices, microphones, display monitors, speakers, and printers. Similarly, the processor units  121  may be any type of conventional or custom-manufactured programmable processor device. For example, one or more of the processor units  121  may be commercially generic programmable microprocessors, such as Intel® Pentium® or Xeon™ microprocessors, Advanced Micro Devices Athlon™ microprocessors or Motorola 68K/Coldfire® microprocessors. Alternately, one or more of the processor units  121  may be custom-manufactured processors, such as microprocessors designed to optimally perform specific types of mathematical operations. Still further, one or more of the processor units  121  may have more than one core, as described with reference to  FIG. 2  above. For example, with some implementations of the disclosed technology, one or more of the processor units  121  may be a Cell processor. The memory  119  then may be implemented using any combination of the computer readable media discussed above. Like the interface device  113 , the interface devices  123  allow the servant computers  117  to communicate with the master computer  103  over the communication interface. 
     In the illustrated example, the master computer  103  is a multi-processor unit computer with multiple processor units  111 , while each servant computer  117  has a single processor unit  121 . It should be noted, however, that alternate implementations of the disclosed technology may employ a master computer having single processor unit  111 . Further, one or more of the servant computers  117  may have multiple processor units  121 , depending upon their intended use, as previously discussed. Also, while only a single interface device  113  or  123  is illustrated for both the master computer  103  and the servant computers, it should be noted that, with alternate embodiments of the disclosed technology, either the computer  103 , one or more of the servant computers  117 , or some combination of both may use two or more different interface devices  113  or  123  for communicating over multiple communication interfaces. 
     With various examples of the disclosed technology, the master computer  103  may be connected to one or more external data storage devices. These external data storage devices may be implemented using any combination of computer readable media that can be accessed by the master computer  103 . The computer readable media may include, for example, microcircuit memory devices such as read-write memory (RAM), read-only memory (ROM), electronically erasable and programmable read-only memory (EEPROM) or flash memory microcircuit devices, CD-ROM disks, digital video disks (DVD), or other optical storage devices. The computer readable media may also include magnetic cassettes, magnetic tapes, magnetic disks or other magnetic storage devices, punched media, holographic storage devices, or any other medium that can be used to store desired information. According to some implementations of the disclosed technology, one or more of the servant computers  117  may alternately or additionally be connected to one or more external data storage devices. Typically, these external data storage devices will include data storage devices that also are connected to the master computer  103 , but they also may be different from any data storage devices accessible by the master computer  103 . 
     It also should be appreciated that the description of the computer network illustrated in  FIG. 1  and  FIG. 2  is provided as an example only, and it not intended to suggest any limitation as to the scope of use or functionality of alternate embodiments of the disclosed technology. 
     Design Flow and Reliability Verification 
     Electronic circuits, such as integrated microcircuits, are used in a variety of products, from automobiles to microwaves to personal computers. Designing and fabricating integrated circuit devices typically involves many steps, sometimes referred to as a “design flow.” The particular steps of a design flow often are dependent upon the type of integrated circuit, its complexity, the design team, and the integrated circuit fabricator or foundry that will manufacture the microcircuit. Typically, software and hardware “tools” verify the design at various stages of the design flow by running software simulators and/or hardware emulators. These steps aid in the discovery of errors in the design, and allow the designers and engineers to correct or otherwise improve the design. 
     Several steps are common to most design flows. Initially, the specification for a new circuit is transformed into a logical design, sometimes referred to as a register transfer level (RTL) description of the circuit. With this logical design, the circuit is described in terms of both the exchange of signals between hardware registers and the logical operations that are performed on those signals. The logical design typically employs a Hardware Design Language (HDL), such as the Very high speed integrated circuit Hardware Design Language (VHDL). The logic of the circuit is then analyzed, to confirm that it will accurately perform the functions desired for the circuit. This analysis is sometimes referred to as “functional verification.” 
     After the accuracy of the logical design is confirmed, it is converted into a device design by synthesis software. The device design, which is typically in the form of a schematic or netlist, describes the specific electronic devices (such as transistors, resistors, and capacitors) that will be used in the circuit, along with their interconnections. This device design generally corresponds to the level of representation displayed in conventional circuit diagrams. The relationships between the electronic devices are then analyzed, to confirm that the circuit described by the device design will correctly perform the desired functions. This analysis is sometimes referred to as “formal verification.” Additionally, preliminary timing estimates for portions of the circuit are often made at this stage, using an assumed characteristic speed for each device, and incorporated into the verification process. 
     Once the components and their interconnections are established, the design is again transformed, this time into a physical design that describes specific geometric elements. This type of design often is referred to as a “layout” design. The geometric elements, which typically are polygons, define the shapes that will be created in various layers of material to manufacture the circuit. Typically, a designer will select groups of geometric elements representing circuit device components (e.g., contacts, channels, gates, etc.) and place them in a design area. These groups of geometric elements may be custom designed, selected from a library of previously-created designs, or some combination of both. Lines are then routed between the geometric elements, which will form the wiring used to interconnect the electronic devices. Layout tools (often referred to as “place and route” tools), such as Mentor Graphics&#39; IC Station or Cadence&#39;s Virtuoso, are commonly used for both of these tasks. 
     Integrated circuit layout descriptions can be provided in many different formats. The Graphic Data System II (GDSII) format is a popular format for transferring and archiving two-dimensional graphical IC layout data. Among other features, it contains a hierarchy of structures, each structure containing layout elements (e.g., polygons, paths or poly-lines, circles and textboxes). Other formats include an open source format named Open Access, Milkyway by Synopsys, Inc., EDDM by Mentor Graphics, Inc., and the more recent Open Artwork System Interchange Standard (OASIS) proposed by Semiconductor Equipment and Materials International (SEMI). These various industry formats are used to define the geometrical information in IC layout designs that are employed to manufacture integrated circuits. Once the microcircuit device design is finalized, the layout portion of the design can be used by fabrication tools to manufacture the device using a photolithographic process. 
     Process variations and technical limitations of the photo-lithography techniques can make it difficult or even impossible to print some layout features. To achieve a high overall yield and reliability for the design, the layout is measured by a set of geometric constraints, or design rules, specific to a particular photolithographic process before tapeout. Design rule checking is thus a major step during physical verification signoff on the design. Still further, the layout design may be modified to include the use of redundant geometric elements or the addition of corrective features to various geometric elements, to counteract limitations in the manufacturing process, etc. For example, the design flow process may include one or more resolution enhancement technique (RET) processes (e.g., optical proximity correction), that modify the layout design data to improve the usable resolution of the reticle or mask created from the design in a photolithographic manufacturing process. 
     Circuit designs and layout designs are also reviewed for reliability issues caused by the electrical system. This is sometimes referred to as reliability verification. Reliability verification can include reviewing the design for protection from electrostatic discharge (ESD) events, detecting electrical overstress (EOS) situations, performing voltage-aware design rule checking (DRC), or the like. Tools that can detect electrical overstress situations and perform voltage-aware design rule checking, often do so in a two-stage process-performing voltage propagation through the design, for example, at the schematic-level, and then comparing particular circuits in the design and their corresponding propagated voltages to various electric rules or design rules. Since reliability verification is typically performed without design simulation, i.e., without an understanding of electrical performance of the devices in the design, the tools often propagate a common voltage throughout the design, perform rule checking based on that common voltage, and determine a presence of electrical violations. 
     Voltage propagation can be performed in a vectored mode (circuit input states provided), a vectorless mode (only power/ground rails provided), or a hybrid mode. In a vectorless mode, for example, transistors may be assumed to be turned on and voltage values are propagated directly across them. In some cases, voltage values can only be propagated across a transistor in one direction (e.g., only from one terminal connected directly to a power or ground rail). Nets connected to power supply or ground rails are an example of break nets (i.e., nets to which voltage values are not propagated). A net is a conductor interconnecting two or more terminals of components of the circuit design. Other components like inductors or resistors may be treated as short connections while diodes and capacitors may be considered as open circuits. These rules may be set as default rules for vectorless voltage propagation. Users may provide rules for particular components of the circuit design. For example, users may specify that certain transistors should be assumed to be in an “off” state during the voltage propagation process. 
     The voltage propagation typically needs to be performed for multiple iterations before voltage values on nets of the circuit design become stable. Here, stable means unchanged from one iteration to the next iteration or that one preset condition is met. One example of the one preset condition may be a maximum number of the iterations being reached.  FIG. 3  shows an example of a circuit design  300  for illustrating how the voltage propagation operates according to some embodiments of the disclosed technology. The circuit design  300  includes an inverter and two transmission gates. The inverter includes two transistors  305  and  315 ; the first transmission gate includes two transistors  325  and  335 ; and the second transmission gate includes two transistors  345  and  355 . Ports  310  and  340  are the input and output of the circuit design, respectively. Ports  370  and  380  are connected to the power supply and ground rails, respectively. Ports  350  and  360  are for control signal inputs of the two transmission gates, respectively. 
     If the transistors  305  and  315  connected to the power/ground rails are considered for voltage propagation first, voltage values on the net  320  will become known. If the transistors  325  and/or  335  are considered next, voltage values on the net  330  will become known. Finally, after the transistors  345  and/or  355  are considered, voltage values on the net  340  will become known. For this sequence, one iteration of voltage propagation is sufficient to assign voltage values to all of the nets, and the next iteration will not change any of the voltage values. It should be noted that at least two iterations are normally needed for a voltage propagation process because it will not terminate until voltage values on the nets become stable or a predefined condition is met. The former is decided by checking whether or not the voltage values change from one iteration to the next. The latter is usually satisfied after multiple iterations. 
     If either of the two transmission gates is considered first, however, at least two iterations of voltage propagation are needed to assign voltage values to all of the nets. For example, if the transistors  325  and  335  are considered first, voltage values on neither of the two nets  320  and  330  will be assigned. After all of the transistors are analyzed once, only voltage values on the net  320  become known. At least one more iteration is needed to propagate the voltage values on the net  320  to the nets  330  and  340 . Therefore, voltage values on the nets are said to be unstable after one iteration because voltage values on some of the nets are changed (here, from unknown to known) from the first iteration to the second iteration. 
     The number of iterations of voltage propagation required before voltage values on all nets of the circuit design  300  are stable thus depends, at least in part, upon the sequence of components of the circuit design  300  being considered. The circuit design  300  is a relatively simple circuit design. For a more complex circuit design, searching for a voltage propagation path such that one iteration is sufficient might be impractical for a voltage propagation tool. It is thus desirable to explore other approaches for accelerating voltage propagation. 
     Reliability Verification Tool 
       FIG. 4  illustrates an example of a reliability verification tool  400  that may be implemented according to various embodiments of the disclosed technology. As seen in this figure, the reliability verification tool  400  includes a chain identification unit  408 , a voltage propagation unit  410  and a voltage analysis unit  420 . Some implementations of the reliability verification tool  400  may cooperate with (or incorporate) one or more of a graph unit  430 , an input database  405  and an output database  455 . 
     As will be discussed in more detail below, the reliability verification tool  400  can receive a circuit design from the input database  405 . The chain identification unit  408  can analyze a circuit design to identify circuit component chains. The voltage propagation unit  410  can propagate voltage values across components of the circuit design based, at least in part, on treating the circuit component chains as virtual single components. The voltage analysis unit  420  can analyze the propagated voltage values to detect problems in the circuit design. The reliability verification tool  400  can report the detected problems in the circuit design. The reporting may comprise storing in the output database  455  and/or displaying by the graph unit  430 , information about the detected problems. 
     As previously noted, various examples of the disclosed technology may be implemented by one or more computing systems, such as the computing system illustrated in  FIGS. 1 and 2 . Accordingly, one or more of the chain identification unit  408 , the voltage propagation unit  410 , the voltage analysis unit  420  and the graph unit  430  may be implemented by executing programming instructions on one or more processors in one or more computing systems, such as the computing system illustrated in  FIGS. 1 and 2 . Correspondingly, some other embodiments of the disclosed technology may be implemented by software instructions, stored on a non-transitory computer-readable medium, for instructing one or more programmable computers/computer systems to perform the functions of one or more of the chain identification unit  408 , the voltage propagation unit  410 , the voltage analysis unit  420  and the graph unit  430 . As used herein, the term “non-transitory computer-readable medium” refers to computer-readable medium that are capable of storing data for future retrieval, and not propagating electro-magnetic waves. The non-transitory computer-readable medium may be, for example, a magnetic storage device, an optical storage device, or a solid state storage device. 
     It also should be appreciated that, while the chain identification unit  408 , the voltage propagation unit  410 , the voltage analysis unit  420  and the graph unit  430  are shown as separate units in  FIG. 4 , a single computer (or a single processor within a master computer) or a single computer system may be used to implement all of these units at different times, or components of these units at different times. 
     With various examples of the disclosed technology, the input database  405  and the output database  455  may be implemented using any suitable computer readable storage device. That is, either of the input database  405  and the output database  455  may be implemented using any combination of computer readable storage devices including, for example, microcircuit memory devices such as read-write memory (RAM), read-only memory (ROM), electronically erasable and programmable read-only memory (EEPROM) or flash memory microcircuit devices, CD-ROM disks, digital video disks (DVD), or other optical storage devices. The computer readable storage devices may also include magnetic cassettes, magnetic tapes, magnetic disks or other magnetic storage devices, holographic storage devices, or any other non-transitory storage medium that can be used to store desired information. While the input database  405  and the output database  455  are shown as separate units in  FIG. 4 , a single data storage medium may be used to implement some or all of these databases. 
     Voltage-Propagation-Based Reliability Verification 
       FIG. 5  illustrates a flowchart  500  showing a process of reliability verification that may be implemented according to various examples of the disclosed technology. For ease of understanding, methods of reliability verification that may be employed according to various embodiments of the disclosed technology will be described with reference to the reliability verification tool  400  in  FIG. 4  and the flow chart  500  illustrated in  FIG. 5 . It should be appreciated, however, that alternate implementations of a reliability verification tool  400  may be used to perform the methods of reliability verification illustrated by the flow chart  500  according to various embodiments of the disclosed technology. Likewise, the reliability verification tool  400  may be employed to perform other methods of reliability verification according to various embodiments of the disclosed technology. 
     In operation  520 , the chain identification unit  408  analyzes a circuit design to identify circuit component chains. The circuit design can describe components, such as resistors, transistors, or the like, and the connectivity of those components in an electronic device. The circuit design can model the electronic device at a schematic-level, for example, in a netlist coded with a Simulation Program with Integrated Circuit Emphasis (SPICE) language, an Electronic Design Interchange Format (EDIF) language, or the like. In some embodiments, the reliability verification tool  400  can receive the circuit design from a source external to the reliability verification tool  400 , such as a user interface of the computer network  101 , another tool implemented by the computer network  101 , or the reliability verification tool  400  may internally generate the circuit design. 
     A circuit component chain may be a chain of transistors, resistors, or other type of circuit components. With various implementations of the disclosed technology, the chain identification unit  408  can identify circuit component chains by tracing circuit components through the circuit design. In some embodiments, the circuit component tracing is confined within a subcircuit. For ease of understanding, the circuit component tracing is described with respect to an example of CMOS (complementary metal-oxide-semiconductor) transistor-level realization of a five-input OR gate as is illustrated in  FIG. 6 . In the figure, A 1 -A 5  represent five input terminals of the OR gate, Q is the output terminal of the OR gate, and Vdd/Vss are power supply/ground rails. Five transistors  600 - 640  are connected in series and another five transistors  650 - 690  are connected in parallel. A pair of transistors  692 - 693  forms an inverter, driving the output. The five transistors connected in parallel  650 - 690  will pull down the voltage of a net  695  to logic 0 if one or more of the five inputs A 1 -A 5  have a voltage of logic 1. The five transistors connected in series  600 - 640  will pull up the voltage of a net  695  to logic 1 if all of the five inputs A 1 -A 5  become logic 0. These five transistors  600 - 640  form a circuit component chain. 
     To identify this circuit component chain, the chain identification unit  408  may start from, for example, the transistor  610 . The chain identification unit  408  traces up from the source terminal of the transistor  610  and finds the transistor  600 . Further tracing up terminates at the source terminal of the transistor  600  because it is connected to the power supply rail V dd . The chain identification unit  408  traces down from the drain terminal of the transistor  610  and finds the transistors  620 - 640  in turn. Further tracing down terminates at the source terminal of the transistor  600  because it branches out to multiple devices. Accordingly, the transistors  600 - 640  are identified to form a circuit component chain. 
     A person of ordinary skill in the art will appreciate that the above example is just for illustration. Additional or alternative tracing rules may also be implemented. A person of ordinary skill in the art will also appreciate that circuit topology recognition methods other than the circuit component tracing may be applicable according to various embodiments of the disclosed technology. 
     In operation  540  of the flow chart  500 , the voltage propagation unit  410  propagates voltage values across components of the circuit based, at least in part, on treating the circuit component chains as virtual single components. As discussed previously, the voltage propagation typically needs to be performed for multiple iterations before voltage values on nets of the circuit design become stable. Collapsing the circuit component chains into virtual single components reduces the number of circuit components which require inspection and the number of nets on which voltage values need to be stabilized. As a result, the time spent on each iteration and the number of iterations may both be reduced. The voltage propagation unit  410  may also propagate voltage values along the circuit component chains once outside the iterations to determine voltage values on the nets within the circuit component chains. For the circuit design shown in  FIG. 6 , the transistors  600 - 640  will be treated by the voltage propagation unit  410  as a virtual single transistor during iterations. 
     To further speed up the voltage propagation, the voltage propagation unit  410  may combine global iterations with local iterations. The global iteration concerns the circuit design while the local iteration concerns a subcircuit of the circuit design. With various implementations of the disclosed technology, at least one of the global iterations comprises local iterations for a subcircuit of the circuit design, which suspends when voltage values on nets of the subcircuit are stable (i.e., voltage values on nets of the subcircuit are not changed from one local iteration to the next local iteration) or one preset condition is met. 
     Referring back to the circuit design  300  shown in  FIG. 3 , if the circuit design  300  is a subcircuit of a larger circuit design, voltage values will probably not be stable with respect to not only the larger circuit design but also the subcircuit  300  after one global iteration of voltage propagation without local iterations (all eligible components of the larger circuit design are considered once). With various implementations of the disclosed technology, the voltage propagation unit  410  will conduct iterations of voltage propagation for the subcircuit  300  (referred to as local iterations) within an iteration of voltage propagation for the larger circuit design (referred to as global iterations). The local iterations suspend when voltage values on nets of the subcircuit  300  become stable with respect to the present global iteration. In the next global iteration, the voltage propagation unit  410  may conduct the local iterations again. This is needed when, for example, one or more voltage values different from the ones derived from the previous local iterations appear at port  390  after the previous global iteration is completed. 
     While inserting local iterations into a global iteration may slow down the global iteration, the total number of the global iterations can be greatly reduced. As a result, the whole voltage propagation process will be accelerated. Some experiments have shown a reduction of processing time at least by half. In various embodiments, the reliability verification tool  400  may allow users to specify directly/indirectly on which subcircuits to conduct local iterations and/or in which global iterations to include local iterations. 
     The circuit design may be represented by a flat description or a hierarchical description. 
     In the hierarchical description, the circuit design is viewed as a collection of component aggregates that are further divided into sub-aggregates in a recursive and hierarchical manner. These hierarchical units are commonly referred to as cells (or modules, blocks, macros, and so on); the use of a cell at a given level of hierarchy is called a cell instance. The use of a cell at some point in a circuit implies that the entire content of the cell&#39;s definition is present at that point in the final circuit. Multiple uses of a cell indicate that the cell contents are to be repeated at each use. 
       FIG. 7  illustrates an example of a shift register  700  and an example of a flip-flop  705 . 
     The shift register  700  contains a plurality of flip-flops (cells)  710 - 740  for storing bits of data and a plurality of AND and OR gates for controlling the mode of inputs: serial or parallel inputs. Each flip-flop contains various logical gates (cells) such as AND gates, as shown by the flip-flop  705 . Each logical gate is formed mainly by transistors. Thus, multiple instances of the AND gate cell are present on two different levels of the hierarchy design of the shift register. The shift register may itself be a cell in a larger circuit design.  FIG. 8  illustrates an example of a hierarchical structure of a circuit design. In the figure, cell A is the root cell, cells C, E and G are leaf cells, and cell B, D and F are composition cells. 
     The circuit design processed in the operation  520  may use a hierarchical description. 
     The global iterations performed by the voltage propagation unit  410  may comprise propagating voltage values up and down the circuit hierarchy. The subcircuits for which the local iterations are performed by the voltage propagation unit  410  may comprise the root cell, one or more of the composition cells, one or more of the leaf cells, or any combination thereof. 
     One major reason for using a hierarchical description is to hide the vast amount of detail in a circuit design. By reducing the distracting detail to a single object that is lower in the hierarchy, one can greatly simplify many circuit design/verification operations. The voltage propagation unit  410  may propagate voltage values in a cell for one or more local iterations until voltage values on the nets of the cell become stable (i.e., voltage values on the nets of the cell are not changed from one iteration to the next iteration) or one preset condition is met and then apply the result to instances of the cell that have the same voltage values at the power supply and input ports. 
       FIG. 8  also illustrates how global and local iterations may be performed according to some embodiments of the disclosed technology. The curved dash lines with arrows represent local iterations while the straight dash lines with arrows represent global iterations. Each of the global iterations includes a propagation up the design hierarchy (illustrated by straight dash lines with arrows upwards) and a propagation down the design hierarchy (illustrated by straight dash lines with arrows downwards). In the propagation up the design hierarchy, the individual cells perform their own local iterations until voltage values on nets within the individual cells are stable. In the propagation down the design hierarchy, voltage values on nets in the cells that are connected to cell input ports are updated with voltage values at the cell input ports. 
     In operation  560  of the flow chart  500 , the voltage analysis unit  420  analyzes the propagated voltage values to detect problems in the circuit design. In some embodiments, the voltage analysis unit  420  compares the propagated voltages and the corresponding components against various electrical or design rules. For example, the voltage analysis unit  420  can determine whether a component, such as a thin-film transistor, receives a voltage in excess of its rating capacity, whether certain components are located within always-on voltage nets, determine whether the circuit design provides adequate spacing between components on different voltage nets, or the like. Additionally or alternatively, the voltage analysis unit  420  may determine whether the circuit design provides adequate spacing between components on different voltage nets by performing a latch-up check, a dielectric breakdown test, or the like. 
     The voltage analysis unit  420  may also utilize an indication of whether different voltages are synchronized when determining whether the circuit design includes any electrical violations based on the propagated voltages. For example, one type of electrical violation check can compare a minimum voltage of one net versus a maximum voltage of another net, and vice versa, to identify what layout spacing should be between the two nets. When the two nets have a synchronous voltage, however, the analysis by the voltage analysis unit  420  can correspond to a comparison of minimum voltages for the two different nets and a comparison of maximum voltages for the two different nets, which should reduce inaccurate identifications of electrical violations. 
     Besides finding problems in the layout design, the voltage analysis may help reduce layout spacing requirements for two neighboring features if the voltage differences are relatively low. 
     In operation  560  of the flowchart  500 , the reliability verification tool  400  reports the detected problems in the circuit design. The reporting may comprise storing and/or displaying information of the detected problems. The reliability verification tool  400  (or the graph unit  430 ) may annotate the graphical representation of the circuit design with indications of electrical violations, for example, which can identify a location of the electrical violations, the corresponding rule prompting the electrical violation, or the like. In some embodiments, the graph display unit  430  may display the annotated graphical representation of the circuit design on a display device. 
     Conclusion 
     Having illustrated and described the principles of the disclosed technology, it will be apparent to those skilled in the art that the disclosed embodiments can be modified in arrangement and detail without departing from such principles. In view of the many possible embodiments to which the principles of the disclosed technologies can be applied, it should be recognized that the illustrated embodiments are only preferred examples of the technologies and should not be taken as limiting the scope of the disclosed technology. Rather, the scope of the disclosed technology is defined by the following claims and their equivalents. We therefore claim as our disclosed technology all that comes within the scope and spirit of these claims.