The semiconductor integrated circuit (IC) industry has experienced rapid growth. In the course of IC evolution, functional density (i.e., the number of interconnected devices per chip area) has generally increased while geometry size (i.e., the smallest component (or line) that can be created using a fabrication process) has decreased. This scaling down process generally provides benefits by increasing production efficiency and lowering associated costs.
Another aspect of the IC evolution involves increased IC design complexity and shortened time-to-market. Designers generally face a demanding project schedule from IC conception to IC production. To meet these challenges, designers generally perform simulations on an IC design, and check the performance and functionality of the IC design as thorough as possible before taping it out. A realistic simulation takes into account of variations in device properties across an entire area of the IC. Such variations are commonly referred to as on-chip variation (OCV). OCV in a fabricated IC may be caused by factors such as channel length variations among transistors; hot spots in the IC; variations in interconnect lengths; and so on. A typical OCV modeling uses local variations, assuming a fixed percentage change of circuit property (e.g., propagation delay) for timing analysis. However, it has been found that local variations are not a fixed value across the entire area of an IC chip, and are in fact a function of distances among the devices (such as transistors). This phenomenon is called OCV spatial effects.
To obtain more realistic IC simulations, attempts have been made to model OCV spatial effects by creating spatially correlated random variations in device properties. Such random variations must simultaneously satisfy correlation constraints between all pairs of devices. As the number of devices on an IC increases, this task has become increasingly challenging.
Accordingly, what is needed is improvement in this area.
Aspects of the present disclosure are best understood from the following detailed description when read with the accompanying figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.
The following disclosure provides many different embodiments, or examples, for implementing different features of the provided subject matter. Specific examples of components and arrangements are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. For example, the formation of a first feature over or on a second feature in the description that follows may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed between the first and second features, such that the first and second features may not be in direct contact. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed.
Further, spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly.
The present disclosure is generally related to methods for IC design and manufacturing, and more particularly to methods for modeling OCV with spatial effects in order to provide realistic IC simulation during IC design.
The IC design flow 100 then proceeds to circuit design 106. In an example, the circuit design 106 uses a bottom-up hierarchical approach where a plurality of cells are built with elementary circuit components such as resistors, capacitor, and transistors, then more complex functional blocks are built with the plurality of cells as components. Various components within a cell are coupled to form desired functionality for the cell. One mechanism for the coupling is through interconnect, also called routing. Various Computer Aided Design (CAD) tools are available to capture the design of the cells, the design of the functional blocks, and the design of the IC into a computer readable file. In an embodiment, the IC design is described in Register Transfer Level (RTL) language such as Verilog or VHDL and then is synthesized into a netlist. In another embodiment, the IC design is described graphically in schematic using the aforementioned hierarchical approach.
Then, the IC design flow 100 proceeds to physical design 108 where an IC design layout is produced. The IC design layout includes various geometrical patterns designed for the IC 114. The geometrical patterns correspond to patterns of metal, oxide, or semiconductor layers that make up the various components of the IC device 114 to be fabricated. The various layers combine to form various IC features. For example, a portion of the IC design layout includes various IC features, such as active regions, gate electrodes, sources and drains, metal lines and vias of an interlayer interconnection, and openings for bonding pads, to be formed in or on a semiconductor substrate (such as a silicon wafer) and various material layers disposed on the semiconductor substrate. The IC design layout is presented in one or more data files having information of the geometrical patterns. For example, the IC design layout can be expressed in a GDSII file format (or DFII file format). The physical design 108 includes various operations which will be described in greater details later in the document.
Then, the IC design flow 100 proceeds to mask creation 110 to produce one or more masks to be used for fabricating the various layers of the IC 114 according to the IC design layout. The mask creation 110 includes various tasks such as mask data preparation, where the IC design layout is translated into a form that can be physically written by a mask writer, and mask fabrication, where the design layout prepared by the mask data preparation is modified to comply with a particular mask writer and/or mask manufacturer and is then fabricated. The mask data preparation may include optical proximity correction (OPC) and lithography process checking (LPC). The mask data preparation can include further resolution enhancement techniques (RET), such as off-axis illumination, sub-resolution assist features, phase-shifting masks, other suitable techniques, or combinations thereof.
The mask fabrication may use various technologies. For example, a mask may be formed using binary technology. A binary mask includes a transparent substrate (e.g., fused quartz) and an opaque material (e.g., chromium) coated in the opaque regions of the mask. In another example, a mask is formed using a phase shift technology. In a phase shift mask (PSM), various features on the mask are configured to have proper phase difference to enhance the resolution and imaging quality. A phase shift mask can be attenuated PSM, alternating PSM, or other types of PSM.
Then, the IC design flow 100 proceeds to IC fabrication 112. The IC fabrication 112 may be performed by a myriad of manufacturing facilities. For example, there may be a manufacturing facility for the front end fabrication of a plurality of IC products (i.e., front-end-of-line (FEOL) fabrication), while a second manufacturing facility may provide the back end fabrication for the interconnection and packaging of the IC products (i.e., back-end-of-line (BEOL) fabrication), and a third manufacturing facility may provide other services for the foundry business.
In an example, a semiconductor wafer is fabricated using the mask (or masks) to form the IC device 114. The semiconductor wafer includes a silicon substrate or other proper substrate having material layers formed thereon. Other proper substrate materials include another suitable elementary semiconductor, such as diamond or germanium; a suitable compound semiconductor, such as silicon carbide, indium arsenide, or indium phosphide; or a suitable alloy semiconductor, such as silicon germanium carbide, gallium arsenic phosphide, or gallium indium phosphide. The semiconductor wafer may further include various doped regions, dielectric features, and multilevel interconnects (formed at subsequent manufacturing steps).
After being fabricated, the IC devices 114 typically go through packaging and testing processes before being delivered to the market.
The physical design 108 also includes layout/GDS module 206 for performing layout and creating GDS file. After optimized placement and routing, the physical layout is created (in GDS format in one example) and finalized for further layout enhancement and sign-off verification. The physical design 108 also includes design rule check (DRC) and layout vs. schematic (LVS) module 208. DRC is performed on the physical layout to verify that the manufacturing process requirements have been satisfied. LVS is performed such that the devices and interconnects are extracted to generate a netlist for comparison with an original design netlist defined at circuit design 106. This step is sometimes referred to as sign-off verification as well.
The physical design 108 also includes a parasitic (such as resistance and capacitance) extraction module 210. Electrical parameter extraction of the physical layout is performed after the sign-off verification 208 has been accomplished. Parasitic resistance and capacitance of the interconnection and the devices are extracted based on the layout to reflect realistic electric characteristics of various circuit elements.
In the present embodiment, the physical design 108 also includes an on-chip variation (OCV) with spatial correlation module 212. The OCV module 212 takes into account OCV spatial effects and randomizes the parasitic values with certain probability distribution. As illustrated in
With the number of devices on an IC chip increases, it becomes increasingly challenging to efficiently model OCV with spatial effects. This is because the random distributions need to simultaneously satisfy spatial correlation constraints between all pairs of devices and the number of correlation constraints to be satisfied grows exponentially. One approach to OCV with spatial effects is to divide an IC chip into zones as illustrated in
Referring back to
When both the sign-off verification 208 and simulation 204 indicate that the design layout is satisfactory, the physical design 108 proceeds to tape-out 220, i.e., to generate the data files for mask creation 110.
Referring now to
At operation 302, the method 300 fabricates a plurality of devices 308 such as 308-1, 308-2, 308-3, 308-4, . . . and 308-x (x number of devices 308). The devices (or post-fabrication devices) 308 include test patterns in an embodiment, which are used for characterizing one or more manufacturing processes and for obtaining data points for parasitic extraction and modeling OCV with spatial effects. For example, the devices 308 may include one or more transistors, resistor, capacitors, inductors, metal interconnects, vias, contacts, and/or other IC features. To further this embodiment, operation 302 fabricates the devices 308 using one or more test wafers 304 which include a plurality of dies 306. Each of the dies 306 includes the devices 308. Each of the devices 308 is associated with a coordinate on the die 306, which is designated as (xi, yi) for the following discussion. Here, (xi, yi) represents the coordinates of the device 308-i in the “x” direction and in the “y” direction respectively. In the present embodiment, the “x” and “y” directions are perpendicular and define a plane that is parallel to the top surface of the wafer 304. In the example given in
At operation 312, the method 300 measures values of a device property of interest. The measurements are done on a large number of devices 308 in order to get enough statistical data points. The device property may be capacitance, resistance, propagation delay, signal rise time, signal fall time, transistor threshold voltage, other MOSFET electrical parameters such as saturation region current, linear region current, and so on. In the example shown in
At operation 314, the method 300 derives a spatial correlation matrix R of the selected device property from the measured values v1, v2, v3, v4, . . . and vx. In an embodiment, the spatial correlation matrix R is in the form:
In another embodiment, the spatial correlation matrix R is in the form:
In each of the equations (1) and (2),
In the present embodiment, the spatial correlation between any two devices 308 is a function of the Euclidean distance between the two devices. For example, for two arbitrary devices 308 at positions (x1, y1) and (x2, y2) respectively, the spatial correlation between the two, corr((x1, y1), (x2, y2)), is expressed as:
corr((x1,y1),(x2,y2))=Ra,b_c,d if (|x1−x2|,|y1−y2|)=(|xa−xc|,|yb−yd|) (3)
Each spatial correlation Ra,b_c,d is a real number and can be obtained through a statistics tool by inputting the values measured from the devices 308.
At operation 316, the method 300 uses the spatial correlation matrix R to derive a random number generation function g(x, y) such that random numbers for a device (in a new IC design) at coordinate (x, y) can be generated independently (independent of other devices in the new IC) by the function g(x, y), and all pairs of random numbers satisfy the spatial correlation matrix R.
Wherein:
represents partial correlation at coordinate (x, y) by the spatial frequencies u and v, and F(u, v) represents relative contribution of the partial correlation by the spatial frequencies u and v at coordinate (x, y) to the overall spatial correlation.
In the step 404, the operation 316 normalizes the partial correlations to derive a coordinate-independent factor Ai and a coordinate-dependent factor Ωi(x, y) as follows:
The product of (Ai·Ωi(x, y)) quantifies the relative contribution of the partial correlation by the spatial frequencies u and v at the coordinate (x, y). In equation (6), the sign “±” can be either “+” or “−.”
In the step 406, the operation 316 derives the random number generation function g(x, y) using the coordinate-independent factor Ai, the coordinate-dependent factor Ωi(x, y), and a Gaussian random function gaussuv (having values randomly distributed in a Gaussian distribution) as follows:
The equation (7) can be re-written into the following form:
Wherein S=(2M+1)(2N+1).
In the above equation (5), the relative contribution Ai at a spatial frequency (u, v) may be used to select the more important components for the random number generation function g(x, y). For example, if a relative contribution Ai at a particular spatial frequency (u, v) is insignificant, the term (Ai·Ωi(x, y)) may be pruned, thereby reducing the number of terms in the function g(x, y) and simplifying further calculations.
As can be seen from the equation (7) or (8), after a coordinate (x, y) is specified, the random number generation function becomes a weighted linear combination of Gaussian rand numbers gaussuv. As a result, the random numbers generated for a certain device also follows Gaussian distribution. Further, the number of variations to be generated by OCV module 212 becomes a linear function of the number of devices, instead of an exponential function of the number of devices like in traditional approaches. This greatly reduces the calculation complexity in the OCV module 212.
Where K=(M+1)(N+1).
In the step 504, the operation 316 normalizes the partial correlations to derive a coordinate-independent factor Ai and a coordinate-dependent factor Ωi(x, y) as follows:
Ai=√{square root over (λi)} (10)
Ωi(x,y)=vi(x,y) (11)
The product of (Ai·Ωi(x, y)) quantifies the relative contribution of every partial correlation at the coordinate (x, y).
In the step 506, the operation 316 derives the random number generation function g(x, y) using the coordinate-independent factor Ai, the coordinate-dependent factor Ωi(x, y), and a Gaussian random function gaussuv (having values randomly distributed in a Gaussian distribution) as follows:
In the above equation (10), the relative contribution Ai may be used to select the more important components for the random number generation function g(x, y). For example, if a relative contribution Ai is insignificant, the term (Ai·Ωi(x, y)) may be pruned, thereby reducing the number of terms in the function g(x, y) and simplifying further calculations. In an embodiment, the relative contribution Ai is insignificant when it is smaller than a threshold value.
The equations (7), (8), and (12) can be generalized into the following form:
As can be seen from the above equation (12) or (13), after a coordinate (x, y) is specified, the random number generation function becomes a weighted linear combination of Gaussian rand numbers gaussuv. As a result, the random numbers generated for a certain device also follows Gaussian distribution. Further, the number of variations to be generated by OCV module 212 becomes a linear function of the number of devices, instead of an exponential function of the number of devices like in traditional approaches. This greatly reduces the calculation complexity in the OCV module 212.
Referring to
At operation 324, the method 300 uses the random number generation function g(x, y) to produce a series of random numbers r1, r2, . . . , rn, one for each nominal values nv1, nv2, . . . nvn. In the present embodiment, operation 324 produces the random numbers by supplying each of the coordinates of the devices 322 into the function g(x, y) shown in equation (7), (8), or (12). For each device, the number of function calls to gaussi is a linear function of the number of devices in the die 306. Therefore, the total number of calculations in operation 324 is a linear function of the number of devices in the die 306 and the number of devices in the IC design layout 320.
At operation 328, the method 300 performs pair-wise multiplication of (1+ri) with nvi, wherein i=1, 2, . . . n. The product ((1+ri)·nvi) follows a Gaussian distribution such as shown in
As described above, the IC design layout 320 is processed according to the IC design flow 100 (
Referring now to
Computer system 600 includes a microprocessor 602, an input device 604, a storage device 606, a video controller 608, a system memory 610, a display 614, and a communication device 616 all interconnected by one or more buses 612.
The microprocessor 602 represents one or more general-purpose processing devices such as a microprocessor, central processing unit, or the like. More particularly, the microprocessor 602 may be a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, or a processor implementing other instruction sets or processors implementing a combination of instruction sets. The microprocessor 602 may also be one or more special-purpose processing devices such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. The microprocessor 602 is configured to execute instructions for performing the operations and steps discussed herein.
The storage device 606 is a non-transitory computer-readable storage media which comprises all computer-readable storage media except for a transitory, propagating signal. Some common forms of computer-readable media include, for example, floppy disk, flexible disk, hard disk, magnetic tape, any other magnetic medium, CD-ROM, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, RAM, PROM, EPROM, FLASH-EPROM, any other memory chip or cartridge, or any other medium from which a computer is adapted to read. For example, the storage device 606 may be a floppy disk, a magnetic hard disk drive (HDD), a solid-state drive (SSD), or an optical memory (e.g., CD-ROM, DVD, and Blu-Ray Disc). In addition, the storage device 606 may be capable of receiving a floppy disk, CD-ROM, DVD-ROM, or any other form of computer-readable medium that may contain computer-executable instructions.
Further, communication device 616 could be a modem, network card, or any other device to enable the computer system to communicate with other nodes. It is understood that any computer system could represent a plurality of interconnected (whether by intranet or Internet) computer systems, including without limitation, personal computers, mainframes, PDAs, and cell phones.
A computer system typically includes at least hardware capable of executing machine readable instructions, as well as the software for executing acts (typically machine-readable instructions) that produce a desired result. In addition, a computer system may include hybrids of hardware and software, as well as computer sub-systems.
Hardware generally includes at least processor-capable platforms, such as client-machines (also known as personal computers or servers), and hand-held processing devices (such as smart phones, personal digital assistants (PDAs), or personal computing devices (PCDs), for example). Further, hardware may include any physical device that is capable of storing machine-readable instructions, such as memory or other data storage devices. Other forms of hardware include hardware sub-systems, including transfer devices such as modems, modem cards, ports, and port cards, for example.
Software includes any machine code stored in any memory medium, such as RAM or ROM, and machine code stored on other devices (such as floppy disks, flash memory, or a CD ROM, for example). Software may include source or object code, for example. In addition, software encompasses any set of instructions capable of being executed in a client machine or server.
Combinations of software and hardware could also be used for providing enhanced functionality and performance for certain embodiments of the present disclosure. One example is to directly manufacture software functions into a silicon chip. Accordingly, it should be understood that combinations of hardware and software are also included within the definition of a computer system and are thus envisioned by the present disclosure as possible equivalent structures and equivalent methods.
The system may be designed to work on any specific architecture. For example, the system may be executed on a single computer, local area networks, client-server networks, wide area networks, internets, hand-held and other portable and wireless devices and networks.
Although not intended to be limiting, one or more embodiments of the present disclosure provide many benefits to IC design and manufacturing. For example, embodiments of the present disclosure provide a method for extracting OCV with spatial effects and applying such to a new IC design. Methods according to the present disclosure model OCV based on the coordinates of an individual device, therefore providing more accurate modeling than zone-based approaches. Further, calculation complexity of the OCV modeling methods according to the present disclosure is linear, rather than exponential, to the number of devices in an IC design layout. This greatly reduces the computing resources needed by the design tool.
In one exemplary aspect, the present disclosure is directed to a method for a computerized integrated circuit (IC) design tool. The method includes receiving a spatial correlation matrix, wherein each element in the spatial correlation matrix is a spatial correlation between values of a property of a set of post-fabrication IC devices having different coordinates. The method further includes deriving a random number generation function from the spatial correlation matrix, wherein the random number generation function has a coordinate-dependent factor and a coordinate-independent factor. The method further includes receiving an IC design layout having a set of pre-fabrication IC devices, each of the pre-fabrication IC devices having a coordinate and a first value of the property. The method further includes, for each of the pre-fabrication IC devices, generating a random number using the coordinate of the respective pre-fabrication IC device and the random number generation function. The method further includes, for each of the pre-fabrication IC devices, deriving a second value of the property by applying the random number to the first value. The method further includes running a simulation on the pre-fabrication IC devices with the second values of the property of the pre-fabrication IC devices, and modifying the IC design layout based on a result of the simulation. In this embodiment, at least one of the following operations is performed by a computer: the deriving of the random number generation function; the generating of the random number; the deriving of the second value of the property; and the running of the simulation.
In another exemplary aspect, the present disclosure is directed to a method for a computerized integrated circuit (IC) design tool. The method includes receiving a spatial correlation matrix, R, of values of a property of a set of IC devices that have been fabricated. Each element Ra,b_c,d in R is a correlation between the values of the property of the set of the post-fabrication IC devices at coordinates (xa, yb) and (xc, yd), wherein each of a and c ranges in [0, M] and each of b and d ranges in [0, N], and M and N are integers greater than 1. The method further includes performing a 2-dimensional Discrete Fourier Transformation (2-D DFT) to R, thereby deriving spatial frequencies u and v, such that
The method further includes constructing a random number generation function g(x, y), wherein:
wherein gaussuv is a random number having a Gaussian distribution. The method further includes receiving an IC design layout having a set of pre-fabrication IC devices, each of the pre-fabrication IC devices having a coordinate and a first value of the property. The method further includes, for each of the pre-fabrication IC devices, generating a random number using the coordinate of the respective pre-fabrication IC device and the random number generation function g(x, y). The method further includes storing the second values of the property of the pre-fabrication IC devices in a non-transitory memory for access by a computerized IC simulation tool. In this method, at least one of the following operations is performed by a computer: the performing of the 2-D DFT to R; the constructing of the random number generation function g(x, y); the generating of the random number using the coordinate of the respective pre-fabrication IC device and the function g(x, y); the deriving of the second value of the property; and the storing of the second values of the property of the pre-fabrication IC devices in the non-transitory memory.
In another exemplary aspect, the present disclosure is directed to a method for integrated circuit (IC) design. The method includes receiving a spatial correlation matrix, R, of values of a property of a set of post-fabrication IC devices. Each element Ra,b_c,d in R is a correlation between the values of the property of the set of the post-fabrication IC devices at coordinates (xa, yb) and (xc, yd), wherein each of a and c ranges in [0, M] and each of b and d ranges in [0, N], and M and N are integers greater than 1. The method further includes deriving eigenvalues, λ1 . . . λk, and eigenvectors, v1 . . . vk, of R, such that:
The method further includes constructing a random number generation function g(x, y), wherein:
wherein gaussi is a random number having a Gaussian distribution. The method further includes receiving an IC design layout having a set of pre-fabrication IC devices, each of the pre-fabrication IC devices having a coordinate and a first value of the property. The method further includes, for each of the pre-fabrication IC devices, generating a random number using the coordinate of the respective pre-fabrication IC device and the random number generation function g(x, y), and deriving a second value of the property by multiplying the first value with a sum of one and the random number. The method further includes storing the second values of the property of the pre-fabrication IC devices in a non-transitory memory for use by an IC simulation tool in a process of manufacturing the IC design layout onto wafers. In this method, at least one of the following operations is performed by a computer: the deriving of the eigenvalues and eigenvectors of R; the constructing of the random number generation function g(x, y); the generating of the random number using the coordinate of the respective pre-fabrication IC device and the function g(x, y); and the deriving of the second value of the property.
In yet another exemplary aspect, the present disclosure is directed to an integrated circuit (IC) design system. The system includes a non-transitory memory and one or more hardware processors coupled to the non-transitory memory, the one or more hardware processors to execute instructions to perform operations that include receiving a spatial correlation matrix, R, of values of a property of a set of post-fabrication IC devices, wherein each element Ra,b_c,d in R is a correlation between the values of the property of the set of the post-fabrication IC devices at coordinates (xa, yb) and (xc, yd), wherein each of a and c ranges in [0, M] and each of b and d ranges in [0, N], wherein M and N are integers greater than 1. The operations further include performing a 2-dimensional Discrete Fourier Transformation (2-D DFT) to R, thereby deriving spatial frequencies u and v, such that:
The operations further include constructing a random number generation function g(x, y), wherein:
wherein gaussuv is a random number having a Gaussian distribution.
The foregoing outlines features of several embodiments so that those skilled in the art may better understand the aspects of the present disclosure. Those skilled in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the embodiments introduced herein. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions, and alterations herein without departing from the spirit and scope of the present disclosure.
This application is a continuation of U.S. patent application Ser. No. 15/335,091, filed Oct. 26, 2016, which claims the benefits of U.S. Provisional Application Ser. No. 62/328,423, entitled “Method and System for Integrated Circuit Design with On-Chip Variation and Spatial Correlation,” filed Apr. 27, 2016, herein incorporated by reference in its entirety.
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Child | 16721255 | US |