JP2012155418A - Analysis support program, analysis support device, and analysis support method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately estimate a correlation distribution of delay values and leak current values of a circuit.SOLUTION: An analysis support device 100 sets a correction value for correcting a value featuring a delay distribution representing variance in delay value of a cell to a variance model for the delay value of the cell. The analysis support device 100 sets a correction value for correcting a value featuring a leak current distribution representing variance in leak current value of a cell to a variance model for the leak current value of the cell. The analysis support device 100 acquires a measured correlation distribution 110 of measured delay values and leak current values of a chip C after manufacture associated with a circuit to be analyzed. The analysis support device 100 calculates correction values set for the respective variance models so that an estimated correlation distribution 120 of delay values and leak current values of the circuit to be analyzed which are calculated using the variance models for the delay values and leak current values of the cell matches the acquired measured correlation distribution 110.

Description

  The present invention relates to an analysis support program, an analysis support apparatus, and an analysis support method for supporting circuit analysis.

  In recent years, with the miniaturization of semiconductor integrated circuits, delays due to process rules and variations in leak current (delay variations, leak current variations) are increasing. The process rule is a process condition such as the width and interval of the wiring expressed by using the minimum processing dimension (hereinafter simply referred to as “process”). The delay is the time required for input / output of a signal between elements in a circuit or between elements. A leak current is a current that flows out at a location that should not flow in an electronic circuit.

  As a method for estimating the delay and leakage current of the analysis target circuit in consideration of these variations, there are statistical delay analysis (SSTA: Statistical Static Timing Analyzer) and statistical leakage current analysis. SSTA is a technique for optimizing timing estimation by giving delay variation of each element in the analysis target circuit as a probability density distribution and statistically handling the delay of the entire circuit. Statistical leak current analysis is a method of calculating the distribution of the leak current of the entire circuit as the sum of the variations of the leak current of each element in the analysis target circuit.

  On the other hand, it is known that the delay variation and the leakage current variation are correlated with each other because they are caused by the process. For example, the delay and the leakage current have a trade-off relationship that the leakage current increases as the delay decreases. For this reason, in order to accurately analyze the yield of the analysis target circuit, a correlation analysis between the delay and the leakage current is performed.

JP 2010-128562 A

  However, it is difficult to create a variation model of delay and leakage current in consideration of all variations caused by the process. For this reason, in the conventional correlation analysis between delay and leakage current, there is a problem that an error may occur between the correlation distribution calculated using the variation model and the correlation distribution actually measured.

  The present invention provides an analysis support program, an analysis support apparatus, and an analysis support method capable of estimating a correlation distribution between a delay value of a circuit and a leakage current value in order to solve the above-described problems caused by the prior art. Objective.

  In order to solve the above-described problems and achieve the object, the disclosed analysis support program, analysis support apparatus, and analysis support method are measured with the variation of the leakage current value of the chip after manufacture related to the analysis target circuit. A set of chip delay values is acquired, and based on the acquired set of delay values of the chip, a value that characterizes a first delay distribution that represents variation in the delay values of the chip is calculated, and a value in the analysis target circuit is calculated. Based on a set of unique values for each of the elements that characterizes the delay distribution that represents the variation in the delay value of the element, a value that characterizes the second delay distribution that represents the variation in the delay value of the analysis target circuit is calculated. A value that characterizes the first delay distribution is divided by a value that characterizes the calculated second delay distribution to calculate a delay correction value that corrects a unique value for each element. And it outputs the the calculated result.

  In order to solve the above-described problems and achieve the object, the disclosed analysis support program, analysis support apparatus, and analysis support method were measured along with the variation of the delay value of the chip after manufacture related to the analysis target circuit. Obtaining a set of leakage current values of the chip, and calculating a value characterizing a first leakage current distribution representing variation in the leakage current values of the chip based on the acquired set of leakage current values of the chip; Based on a set of unique values for each of the elements that characterize the leakage current distribution, an unknown leak current correction value that corrects the value that characterizes the leakage current distribution that represents the variation in the leakage current value of the elements in the analysis target circuit, A second leakage current distribution value representing a variation in leakage current value of the analysis target circuit is calculated, and the calculated second leakage current distribution is characterized. And match the calculated value characterizing the first leakage current distribution calculating the leakage current correction value, and outputs the calculated calculation results.

  According to the analysis support program, the analysis support apparatus, and the analysis support method, there is an effect that the correlation distribution between the delay value of the circuit and the leakage current value can be estimated.

It is explanatory drawing which shows one Example of the analysis assistance process of the analysis assistance apparatus 100 concerning embodiment. It is explanatory drawing which shows an example of the hardware constitutions of the analysis assistance apparatus 100 concerning embodiment. It is a block diagram which shows the functional structure of the analysis assistance apparatus 100 concerning embodiment. It is explanatory drawing which shows an example of the memory content of the measurement correlation data table. 5 is an explanatory diagram illustrating an example of stored contents of a delay variation data table 500. FIG. 5 is an explanatory diagram illustrating an example of stored contents of a correction value table 600. 6 is an explanatory diagram showing an example of stored contents of a leakage current variation data table 700. FIG. FIG. 11 is an explanatory diagram showing an example of stored contents of a delay variation data table 800. 5 is an explanatory diagram illustrating an example of stored contents of a correlation distribution table 900. It is a flowchart (the 1) which shows an example of the analysis assistance process sequence of the analysis assistance apparatus 100 concerning embodiment. It is a flowchart (the 2) which shows an example of the analysis assistance processing procedure of the analysis assistance apparatus 100 concerning embodiment. It is a flowchart (the 1) which shows an example of the analysis process sequence of the analysis assistance apparatus 100 concerning embodiment. It is a flowchart (the 2) which shows an example of the analysis process sequence of the analysis assistance apparatus 100 concerning embodiment.

  Exemplary embodiments of an analysis support program, an analysis support apparatus, and an analysis support method according to the present invention will be explained below in detail with reference to the accompanying drawings.

(An example of this analysis support method)
This analysis support method improves the accuracy of the correlation analysis between the delay value of the analysis target circuit and the leakage current value. Here, the analysis target circuit is a semiconductor integrated circuit (for example, a processor) that is a target of correlation analysis between the delay value and the leakage current value. The analysis target circuit includes a plurality of paths that operate in parallel.

  A path is a partial circuit from a certain cell in the circuit to be analyzed to another cell. Specifically, for example, the path is a partial circuit including a pair of data path and clock path. The cell is an element such as an FF (flip-flop), a NOT gate, an AND gate, a wiring, a buffer, or an INV (inverter) in the analysis target circuit.

  That is, the path is, for example, a path from one FF in the analysis target circuit to another FF. The path may be a path from the data input terminal in the analysis target circuit to the FF, or may be a path from the FF to a certain data output terminal.

  Next, variation in delay values of cells in the analysis target circuit will be described. As the variation of the delay value of the cell, there are an independent variation in each cell in the analysis target circuit and a common variation in all cells in the analysis target circuit. Specifically, the variation in the delay value of the cell includes a first delay variation independent of each cell in the analysis target circuit and a second delay variation common to all cells in the analysis target circuit.

For this reason, the dispersion | variation in the delay value of a cell can be expressed like the following formula (1), for example. Here, d _C is a variation in the delay value of the cell, α is a parameter related to the first delay variation, and β is a parameter related to the second delay variation. M is the average of the first delay distributions of the cells representing the first delay variation, and s is the standard deviation of the first delay distribution. Further, ap and an are standard deviations of the second delay distribution of the cells representing the second delay variation.

d _C = m + s × α + f (β)
f (β) = ap × β (β ≧ 0), f (β) = an × β (β <0)
... (1)

  Variations in the delay values of the paths in the analysis target circuit and the entire circuit can be calculated by, for example, statistical delay analysis (SSTA) using the variation model of the above equation (1).

  Next, the variation in the leak current value of the cells in the analysis target circuit will be described. As a variation in the leak current value of the cell, there are an independent variation in each cell in the analysis target circuit and a common variation in all cells in the analysis target circuit. Specifically, the variation in the leak current value of the cell includes a first leak current variation independent of each cell in the analysis target circuit and a second leak current variation common to all cells in the analysis target circuit.

For this reason, the variation in the leak current value of the cell can be expressed as, for example, the following formula (2). Here, l _C is a variation in the leakage current value of the cell, α ′ is a parameter relating to the first leakage current variation, and β ′ is a parameter relating to the second leakage current variation. A, B, and C are model coefficients specific to each cell.

l _C = exp (A + B × α ′ + C × β ′) (2)

  The variation of the leakage current value of the entire circuit of the analysis target circuit can be calculated by, for example, statistical leakage current analysis using the variation model of the above formula (2).

  The parameters α, α ′, β, β ′ included in the above formulas (1) and (2) are, for example, standard normal distribution random variables having a mean “0” and a standard deviation “1”. The parameters α and α ′ have a correlation coefficient ρα. The correlation coefficient ρα is a value unique to each cell in the analysis target circuit. The parameters β and β ′ have a correlation coefficient ρ. The correlation coefficient ρ is a value common to all cells in the analysis target circuit.

Here, it is known that the influence of the first leakage current variation on the variation 1 _C of the leakage current value of the cell is smaller than the influence of the second leakage current variation. For this reason, the value of the parameter α ′ included in the equation (2) can be replaced as follows.

Specifically, 'for the parameter α' exp (Biarufa) "'by the above formula (2) Average value when swung the value of the random is" exp (B ^2/2) ". Therefore, 'the value of "exp (Bα' parameter alpha can be replaced by)" is the average value "exp (B ^2/2)" value when the "alpha '= B / 2". As a result, the variation 1 _C of the leak current value of the cell can be expressed as the following formula (3).

_{l C = exp (A + B} 2/2 + C × β ') ··· (3)

In this way, by expressing the cell leakage current value variation l _C using the above equation (3), the correlation between the parameter α related to the first delay variation and the parameter α ′ related to the first leakage current variation (phase The relation number ρα) can be ignored. As a result, the correlation distribution between the delay value and the leakage current value of the circuit to be analyzed is obtained by, for example, correlation analysis ρ of the parameters β and β ′ by correlation analysis using the variation model of the above formulas (1) and (3). It can be calculated considering only.

  Here, the average m, the standard deviation s, ap, and an included in the formula (1) are values unique to each cell, and are given as variation data unique to each cell. The model coefficients A, B, and C included in the above equation (3) are values unique to each cell, and are given as variation data unique to each cell.

  Specifically, for example, the average m, standard deviation s, ap, an and model coefficients A, B, and C of each cell are values empirically obtained from chips manufactured by various processes. A chip is an arbitrary IC (Integrated Circuit) chip cut out from a silicon wafer manufactured using circuit information of a circuit to be analyzed.

  Therefore, in a chip manufactured by a specific process, there is an error between the actual value and the average m, standard deviation s, ap, an and model coefficients A, B, C of each cell given as variation data. May occur. In addition, it is difficult to create a variation model of cell delay values and leakage current values in consideration of all variation factors resulting from the process.

  For this reason, when the correlation analysis between the delay value of the analysis target circuit and the leakage current value was performed, the correlation distribution between the calculated delay value and the leakage current value and the actual measurement using the chip after manufacture were performed. There may be an error between the correlation distribution between the delay value and the leakage current value.

  Therefore, in this analysis support method, the correlation distribution between the delay value and the leak value of the analysis target circuit calculated using the variation models of the cell delay value and the leak current value is measured using the chip. Modify each variation model to match the distribution. Hereinafter, an example of the analysis support process of the analysis support apparatus 100 according to the embodiment will be described.

FIG. 1 is an explanatory diagram of an example of the analysis support process of the analysis support apparatus 100 according to the embodiment. (I) The analysis support apparatus 100 sets a correction value for correcting a value characterizing the delay distribution representing the variation in the delay value of the cell with respect to the variation model of the delay value of the cell. Specifically, for example, analysis support apparatus 100, the above equation with respect to (1), a correction coefficient r _m for correcting the average of the delay distribution of the cell, the correction factor for correcting the standard deviation of the delay distribution of a cell r Set _s .

As a result, the above formula (1) is converted into, for example, the following formula (4). However, r _m is the correction coefficient for correcting an average delay distribution of cell. r _s is a correction coefficient for correcting the standard deviation of the cell delay distribution.

d _C = r _m × m + r _s × s × α + f (β)
f (β) = r _s × ap × β (β ≧ 0), f (β) = r _s × an × β (β <0)
... (4)

(Ii) The analysis support apparatus 100 sets a correction value for correcting a value characterizing the leakage current distribution representing the variation of the cell leakage current value, with respect to the variation model of the cell leakage current value. Specifically, for example, analysis support apparatus 100, the above equation with respect to (3), the correction coefficient m _L for correcting the average of the leak current distribution representing a second leak current variation of the cell, of the leakage current distribution A correction coefficient σ _L for correcting the standard deviation is set.

As a result, the above formula (3) is converted into, for example, the following formula (5). Here, m _L is a correction coefficient for correcting the average of the leakage current distribution representing the second leakage current variation of the cell. σ _L is a correction coefficient for correcting the standard deviation of the leakage current distribution representing the second leakage current variation of the cell.

_{l C = exp {A + B} 2/2 + C × (σ L × β '+ m L)} ··· (5)

  (Iii) The analysis support apparatus 100 acquires the measured correlation distribution 110 between the measured delay value and the leak current value of the manufactured chip C regarding the analysis target circuit. Here, the measured correlation distribution 110 is, for example, a set of pairs of the delay value and the leakage current value of the chip C measured along with the variation of the delay value (or the leakage current value) of the chip C.

(Iv) In the analysis support apparatus 100, the estimated correlation distribution 120 between the delay value and the leakage current value of the analysis target circuit calculated using the above formulas (4) and (5) matches the acquired actual correlation distribution 110. As described above, the values of the correction coefficients r _m , r _s , m _L , and σ _L included in the equations (4) and (5) are calculated. Further, the analysis support apparatus 100 calculates a correlation coefficient ρ between the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation so that the estimated correlation distribution 120 matches the measured correlation distribution 110.

(V) The analysis support apparatus 100 outputs the calculated correction coefficients r _m , r _s , m _L , σ _L and the correlation coefficient ρ. As a result, it is possible to obtain a variation model in which a value that characterizes the delay distribution representing the variation in the delay value of the cell is corrected, and a variation model in which the value characterizing the leak current distribution that represents the variation in the cell leakage current value is corrected. .

As a result, the correlation distribution between the delay value and the leakage current value of the circuit to be analyzed is calculated using each variation model and the correlation coefficient ρ corrected by the correction coefficients r _m , r _s , m _L , and σ _L in the following. It can be calculated with high accuracy. Further, since the values of the correction coefficients r _m , r _s , m _L , σ _L and the correlation coefficient ρ are values specific to the process, the corrected variation model and the correlation coefficient ρ are manufactured in the same process. It can also be applied to other analysis target circuits.

(Hardware configuration of analysis support apparatus 100)
FIG. 2 is an explanatory diagram illustrating an example of a hardware configuration of the analysis support apparatus 100 according to the embodiment. In FIG. 2, the analysis support apparatus 100 includes a CPU (Central Processing Unit) 201, a ROM (Read-Only Memory) 202, a RAM (Random Access Memory) 203, a magnetic disk drive 204, a magnetic disk 205, and an optical disk. A drive 206, an optical disk 207, a display 208, an I / F (Interface) 209, a keyboard 210, a mouse 211, a scanner 212, and a printer 213 are provided. Each component is connected by a bus 200.

  Here, the CPU 201 governs overall control of the analysis support apparatus 100. The ROM 202 stores a program such as a boot program. The RAM 203 is used as a work area for the CPU 201. The magnetic disk drive 204 controls reading / writing of data with respect to the magnetic disk 205 according to the control of the CPU 201. The magnetic disk 205 stores data written under the control of the magnetic disk drive 204.

  The optical disk drive 206 controls reading / writing of data with respect to the optical disk 207 according to the control of the CPU 201. The optical disk 207 stores data written under the control of the optical disk drive 206, or causes the computer to read data stored on the optical disk 207.

  The display 208 displays data such as a document, an image, and function information as well as a cursor, an icon, or a tool box. As the display 208, for example, a CRT, a TFT liquid crystal display, a plasma display, or the like can be adopted.

  The I / F 209 is connected to a network 214 such as a LAN (Local Area Network), a WAN (Wide Area Network), and the Internet through a communication line, and is connected to another computer via the network 214. The I / F 209 serves as an internal interface with the network 214 and controls data input / output from an external computer. For example, a modem or a LAN adapter may be employed as the I / F 209.

  The keyboard 210 includes keys for inputting characters, numbers, various instructions, and the like, and inputs data. Moreover, a touch panel type input pad or a numeric keypad may be used. The mouse 211 performs cursor movement, range selection, window movement, size change, and the like. A trackball or a joystick may be used as long as they have the same function as a pointing device.

  The scanner 212 optically reads an image and takes in the image data into the analysis support apparatus 100. The scanner 212 may have an OCR (Optical Character Reader) function. The printer 213 prints image data and document data. As the printer 213, for example, a laser printer or an ink jet printer can be adopted.

(Functional configuration of the analysis support apparatus 100)
FIG. 3 is a block diagram of a functional configuration of the analysis support apparatus 100 according to the embodiment. In FIG. 3, the analysis support apparatus 100 includes an acquisition unit 301, a first calculation unit 302, a second calculation unit 303, a third calculation unit 304, a creation unit 305, an analysis unit 306, and an output. Part 307. Specifically, each functional unit (acquisition unit 301 to output unit 307) causes the CPU 201 to execute a program stored in a storage device such as the ROM 202, the RAM 203, the magnetic disk 205, and the optical disk 207 illustrated in FIG. Or the I / F 209 realizes the function. Note that the processing results of the respective functional units are stored in a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example.

  The acquisition unit 301 acquires measured correlation data regarding the correlation distribution between the measured delay value of the manufactured chip related to the analysis target circuit and the leakage current value. Here, the actual correlation data is, for example, a set of pairs of the chip delay value and the leakage current value measured in accordance with the variation of the chip delay value (or leakage current value).

  As the delay value of the chip, for example, the delay value of an arbitrary path in the chip may be measured, or the maximum delay value among the delay values for each path in the chip may be measured. Further, the delay value of the ring oscillator embedded in the chip may be used as the chip delay value.

  The ring oscillator is an oscillation circuit that realizes an oscillation function by combining, for example, an odd number of inverters. The ring oscillator is embedded without being connected to any path in the chip, for example. The delay value of the ring oscillator can be calculated by obtaining the reciprocal of the frequency of the ring oscillator measured along with the fluctuation of the leak current value of the chip.

  Specifically, for example, the acquisition unit 301 acquires measured correlation data by a user operation input using the keyboard 210 and the mouse 211 illustrated in FIG. The acquisition unit 301 may acquire actual correlation data from an external computer via the network 214.

  The acquired actual correlation data is stored, for example, in the actual correlation data table 400 shown in FIG. The actual correlation data table 400 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207 shown in FIG. Here, a specific example of the actual measurement correlation data table 400 will be described.

  FIG. 4 is an explanatory diagram showing an example of the contents stored in the actual correlation data table 400. In FIG. 4, the actual correlation data table 400 has fields for the number of measurements, a leakage current value, and a frequency. By setting information in each field, the measured correlation data 400-1 to 400-K are stored as records.

  The number of measurements is the number of times the leakage current value of the chip and the frequency of the ring oscillator embedded in the chip are measured. The leakage current value is a leakage current value of the chip measured with a change in the frequency of the ring oscillator embedded in the chip. The frequency is the frequency of the ring oscillator measured along with the fluctuation of the leakage current value of the chip.

Taking the actual correlation data 400-k as an example, the leak current value I _k of the chip measured for the kth time and the frequency f _{k of the} ring oscillator are shown. The measured correlation data 400-k indicates that the frequency of the ring oscillator when the leakage current value of the chip is “I _k ” is “f _k ”.

Returning to the description of FIG. 3, the first calculation unit 302 calculates a value that characterizes the measured delay distribution representing the variation in the delay value of the chip based on the acquired measured correlation data. Here, the values that characterize the actually measured delay distribution are, for example, the average, standard deviation, and variance of the actually measured delay distribution. Specifically, for example, first, the first calculation unit 302 calculates the delay value d _k of the ring oscillator based on the frequency f _k of the ring oscillator embedded in the chip stored in the measured correlation data table 400. calculate.

More specifically, for example, the first calculation unit 302 can calculate the delay value d _k of the ring oscillator using the following equation (6). Here, f _k is the frequency of the ring oscillator measured at the k-th time (k = 1, 2,..., K). d _k is a delay value of the ring oscillator.

d _k = 1 / f _k (6)

Next, based on the calculated set of delay values of the ring oscillator (delay values d _{1 to} d _K ), the first calculation unit 302 calculates the average m _{d of the} actually measured delay distribution representing the variation of the delay values of the ring oscillator. The standard deviation σ _d is calculated. More specifically, for example, the first calculation unit 302 uses the following formulas (7) and (8) to calculate the average m _d and the standard deviation σ _{d of the} measured delay distribution representing the variation of the delay value of the ring oscillator. Can be calculated.

m _d = (d ₁ + d ₂ +... + d _K ) / K (7)

σ _d ² = {(d ₁ −m _d ) ² + (d ₂ −m _d ) ² +... + (d _K −m _d ) ² } / K (8)

  Further, the first calculation unit 302 calculates a value that characterizes the measured leakage current distribution that represents the variation in the leakage current value of the chip, based on the acquired measured correlation data. Here, the values characterizing the measured leakage current distribution are, for example, the average, standard deviation, and variance of the measured leakage current distribution.

Specifically, for example, the first calculation unit 302 uses the chip leakage current value set (leakage current values I _{1 to} I _K ) stored in the actual correlation data table 400 to measure the actual chip leakage. An average m _l and a standard deviation σ _l of the current distribution are calculated. More specifically, for example, a first calculation unit 302, using the following equation (9) and (10), the mean m _l of measured leakage current distribution representing the variation of the leakage current value of the chip, the standard deviation σ _l can be calculated.

m _l = (I ₁ + I ₂ +... + I _K ) / K (9)

σ _l ² = {(I ₁ −m _l ) ² + (I ₂ −m _l ) ² +... + (I _K −m _l ) ² } / K (10)

In addition, the first calculation unit 302 is a logarithm representing a variation in logarithmic leak current value obtained by taking a logarithm of the leak current value of the chip based on a set of leak current values of the chip (leak current values I _{1 to} I _K ). A value characterizing the leakage current distribution is calculated. Here, the values characterizing the logarithmic leak current distribution are, for example, the average, standard deviation, variance, etc. of the logarithmic leak current distribution.

Specifically, for example, the first calculation unit 302 first determines the chip current based on a set of chip leakage current values (leakage current values I _{1 to} I _K ) stored in the measured correlation data table 400. A logarithmic leak current value obtained by taking the logarithm of the leak current value is calculated. More specifically, for example, the second calculation unit 303 can calculate a logarithmic leakage current value X _{k obtained} by taking the logarithm of the leakage current value I _k of the chip using the following formula (11).

X _k = log (I _k ) (11)

Next, the first calculation unit 302 calculates the average m _X and the standard deviation σ _X of the log leakage current distribution of the chip based on the set of log leakage current values of the chip (log leakage current values X _{1 to} X _K ). calculate. More specifically, for example, the first calculation unit 302 uses the following formulas (12) and (13) to represent a logarithmic leakage current that represents the variation of the logarithmic leakage current value obtained by taking the logarithm of the leakage current value of the chip. The average m _{X of} the distribution and the standard deviation σ _X can be calculated.

m _X = (X ₁ + X ₂ +... + X _K ) / K (12)

σ _X ² = {(X ₁ -m _X ) ² + (X ₂ -m _X ) ² + ... + (X _K -m _X ) ² } / K (13)

  In addition, the acquisition unit 301 acquires a set of unique values for each cell that characterizes a delay distribution that represents variation in delay values of cells in the analysis target circuit. Here, the delay distribution representing the variation of the delay value of the cell is, for example, a first delay distribution representing the first delay variation of the cell or a second delay distribution representing the second delay variation.

  The first delay variation is a variation of an independent delay value in each cell in the analysis target circuit. The second delay variation is a variation of a delay value common to all cells in the analysis target circuit. That is, the unique value for each cell characterizing the delay distribution representing the variation of the delay value of the cell is, for example, the average m of the first delay distribution, the standard deviation s, or the standard deviation ap, an of the second delay distribution.

  In addition, when the delay value of the ring oscillator embedded in the chip is used as the delay value of the chip described above, the acquisition unit 301 is specific to each cell that characterizes the delay distribution representing the variation of the delay value of the cells in the ring oscillator. A set of values may be acquired. Hereinafter, a unique value for each cell that characterizes the delay distribution representing the variation in the delay value of the cell is referred to as “delay variation data”.

  Specifically, for example, the acquisition unit 301 acquires delay variation data unique to each cell by a user operation input using the keyboard 210 or the mouse 211. The acquisition unit 301 may acquire specific delay variation data for each cell by extraction from a library or from an external computer.

  The acquired delay variation data unique to each cell is stored, for example, in the delay variation data table 500 shown in FIG. The delay variation data table 500 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example. Here, a specific example of the delay variation data table 500 will be described.

  FIG. 5 is an explanatory diagram showing an example of the stored contents of the delay variation data table 500. In FIG. 5, the delay variation data table 500 includes fields of cell ID, m, s, ap, and an. By setting information in each field, delay variation data 500-1 to 500-n are stored as records.

  The cell ID is a cell identifier. Cells C (1) to C (n) shown in FIG. 5 are cells in a ring oscillator embedded in a chip. m is the average of the first delay distribution of the cells. s is the standard deviation of the first delay distribution of the cell. ap and an are standard deviations of the second delay distribution of the cell. Here, ap is a standard deviation when the parameter β related to the second delay variation is “β ≧ 0”, and an is a standard deviation when the parameter β related to the second delay variation is “β <0”.

Taking the delay variation data 500-i as an example, the average m _i of the first delay distribution of cell C (i), and the standard deviation s _i of the first delay distribution of cell C (i), cell C (i) The standard deviations ap _i and an _i of the second delay distribution are shown.

  Returning to the description of FIG. 3, the second calculation unit 303 characterizes the estimated delay distribution representing the variation of the delay value of the analysis target circuit based on the set of delay variation data unique to each cell in the analysis target circuit. Is calculated. Here, the values that characterize the estimated delay distribution are, for example, the average, standard deviation, and variance of the estimated delay distribution.

  Specifically, for example, the second calculation unit 303 estimates the delay that represents the variation of the delay value of the ring oscillator based on the delay variation data 500-1 to 500 -n stored in the delay variation data table 500. The average M of the distribution and the standard deviation S are calculated. More specifically, for example, the second calculation unit 303 calculates the average M and the standard deviation S of the estimated delay distribution representing the variation of the delay value of the ring oscillator using the following equations (14) and (15). can do.

M = m ₁ + m ₂ +... + M _n + (AP−AN) / 2π
AP = ap ₁ + ap ₂ +... + Ap _n
AN = an ₁ + an ₂ +… + an _n
(14)

Note that “(AP−AN) / 2π” included in the equation (14) is, for example, when the standard deviation ap _i and the standard deviation an _i of the second delay distribution of the cell C (i) are different (ap _i ≠ an _i ).

S ² = σ ₁ ² + σ ₂ ² +... + Σ _n ² + (AP ² + AN ² ) / 2− (AP−AN) ² / 2π
... (15)

The third calculation unit 304 divides the value characterizing the measured delay distribution representing the variation in the delay value of the chip by the value characterizing the estimated delay distribution representing the variation in the delay value of the analysis target circuit, and calculates the cell delay value. A delay correction value for correcting a value characterizing the delay distribution representing the variation is calculated. Here, the delay correction value is, for example, a correction coefficient r _m for correcting the average m of the first delay distribution of the cell, and a correction coefficient for correcting the standard deviations s, ap, an of the first and second delay distributions of the cell. r _s .

Specifically division, for example, the third calculating unit 304, an average m _d of the measured delay distribution representing the variation in the delay value of the ring oscillator, the average M estimates delay distribution representing the variation in the delay value of the ring oscillator and calculates a correction coefficient r _m. More specifically, for example, the third calculating unit 304, using the following equation (16) can calculate the correction coefficient r _m.

r _m = m _d / M (16)

Further, the third calculation unit 304 divides the standard deviation σ _d of the measured delay distribution representing the variation of the delay value of the ring oscillator by the standard deviation S of the estimated delay distribution representing the variation of the delay value of the ring oscillator, A correction coefficient r _s is calculated. More specifically, for example, the third calculation unit 304 can calculate the correction coefficient r _s using the following equation (17).

r _s = σ _d / S (17)

  The calculated delay correction value is stored in, for example, the correction value table 600 shown in FIG. The correction value table 600 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example. Here, a specific example of the correction value table 600 will be described.

FIG. 6 is an explanatory diagram showing an example of the stored contents of the correction value table 600. In FIG. 6, the correction value table 600 includes fields for delay distribution average, standard deviation, leak current distribution average, standard deviation, and correlation coefficient. Field "average of delay distribution" is a field for storing a correction coefficient r _m for correcting the average of the delay distribution of the cells. The “standard deviation of delay distribution” field stores a correction coefficient r _s for correcting the standard deviation of the delay distribution of the cell.

The “average of leakage current distribution” field is a field for storing a correction coefficient m _L for correcting the average of the leakage current distribution representing the second leakage current variation of the cells. The “standard deviation of leak current distribution” field is a field for storing a correction coefficient σ _L for correcting the standard deviation of the leak current distribution representing the second leak current variation of the cell. The “correlation coefficient” field stores a correlation coefficient ρ between the parameter β related to the second delay variation of the cell and the parameter β ′ related to the second leakage current variation of the cell.

Here, in (6-1) of FIG. 6, a correction coefficient r _m for correcting the average of the delay distribution of the cell, the correction coefficient r _s for correcting the standard deviation of the delay distribution of cells, the "average of delay distribution" Field and the “standard deviation of delay distribution” field.

  Returning to the description of FIG. 3, the acquisition unit 301 acquires a set of unique values for each cell that characterizes the leakage current distribution representing the variation in the leakage current value of the cells in the analysis target circuit. Here, the leakage current distribution representing the variation in the leakage current value of the cell is, for example, a leakage current distribution representing the first leakage current variation of the cell or a leakage current distribution representing the second leakage current variation.

  The first leakage current variation is a variation in an independent leakage current value in each cell in the analysis target circuit. The second leakage current variation is a variation in a leakage current value common to all cells in the analysis target circuit. That is, the values unique to each cell characterizing the leakage current distribution representing the variation in the leakage current value of the cells are, for example, model coefficients A, B, and C unique to each cell. Hereinafter, a unique value for each cell that characterizes the leakage current distribution representing the variation in the leakage current value of the cell is referred to as “leakage current variation data”.

  Specifically, for example, the acquisition unit 301 acquires leak current variation data unique to each cell by a user operation input using the keyboard 210 or the mouse 211. Further, the acquisition unit 301 may acquire specific leakage current variation data for each cell by extraction from a library or from an external computer.

  For example, the obtained leak current variation data for each cell is stored in the leak current variation data table 700 shown in FIG. The leakage current variation data table 700 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example. Here, a specific example of the leakage current variation data table 700 will be described.

  FIG. 7 is an explanatory diagram showing an example of the contents stored in the leakage current variation data table 700. In FIG. 7, the leakage current variation data table 700 has cell ID, A, B, and C fields. By setting information in each field, leakage current variation data 700-1 to 700-m are stored as records.

The cell ID is a cell identifier. Cells C1 to Cm shown in FIG. 7 are cells in the analysis target circuit. A, B, and C are model coefficients specific to each cell that characterize a leakage current distribution that represents variations in the leakage current value of each cell. Taking the leakage current variation data 700-j as an example, model coefficients A _j , B _j , C _j unique to the cell Cj are shown.

  Returning to the description of FIG. 3, the second calculation unit 303 calculates the estimated leakage current distribution that represents the variation in the leakage current value of the analysis target circuit based on the set of leakage current variation data unique to each cell in the analysis target circuit. A value that characterizes is calculated.

  Here, the values characterizing the estimated leakage current distribution are, for example, the average, standard deviation, variance, etc. of the estimated leakage current distribution. Further, as a value characterizing the estimated leakage current distribution, for example, an average or standard of the estimated leakage current distribution, such as a value obtained by adding the square of the average of the estimated leakage current distribution and the square of the standard deviation of the estimated leakage current distribution. You may decide to use the value calculated using a deviation, dispersion | distribution, etc.

Specifically, for example, the second calculation unit 303 uses the leakage current correction value for correcting the value characterizing the leakage current distribution indicating the variation in the leakage current value of the cells in the analysis target circuit as an unknown, and the estimated leakage current distribution A value that characterizes is calculated. Here, the leakage current correction value is, for example, a correction coefficient. A correction coefficient m _L for correcting the average of the leak current distribution representing the second leak current variation of the cell, and a correction coefficient σ _L for correcting the standard deviation of the leak current distribution.

More specifically, for example, the second calculation unit 303 uses the correction coefficients m _L and σ _L as unknowns and uses the following formula (18) to estimate the leakage current value representing the variation in the leakage current value of the analysis target circuit: The average X of the distribution is calculated.

Further, for example, the second calculation unit 303 uses the correction coefficients m _L and σ _L as unknowns and uses the following equation (19) to calculate the average of the estimated leakage current distribution representing the variation in the leakage current value of the analysis target circuit. A value Y is calculated by adding the square and the square of the standard deviation of the estimated leakage current distribution.

In addition, the third calculation unit 304 matches the value that characterizes the estimated leakage current distribution that represents the variation in the leakage current value of the analysis target circuit with the value that characterizes the actual leakage current distribution that represents the variation in the leakage current value of the chip. A current correction value is calculated. Here, the leakage current correction values are, for example, the above-described correction coefficients m _L and σ _L.

Specifically, for example, the third calculation unit 304 uses the correction coefficients m _L and σ _L as unknowns as shown in the following equation (20), and calculates the average X of the estimated leakage current distribution of the analysis target circuit and the chip creating a mean m _l and equals equation the measured leakage current distribution.

Further, for example, the third calculation unit 304 uses the correction coefficients m _L and σ _L as unknowns as shown in the following formula (21), and the average square of the estimated leakage current distribution of the analysis target circuit and the standard deviation of 2 equation ride Doo value Y obtained by adding the square and the square and the sum combined value of the standard deviation sigma _l of average m _l of measured leakage current distribution in the chip ^{_{(m l 2 + σ l 2}} ) and is equal Create

  The equations (20) and (21) are derived, for example, by moment matching between the estimated leakage current distribution of the analysis target circuit and the measured leakage current distribution of the chip.

In addition, the third calculation unit 304 calculates the correction coefficients m _L and σ _L by solving the equations (20) and (21). Specifically, for example, the third calculation unit 304 calculates the correction coefficients m _L and σ _L by numerically solving the equations (20) and (21) using the Newton method. be able to.

The calculated leakage current correction value is stored, for example, in the correction value table 600 shown in FIG. Here, in (6-2) of FIG. 6, the correction coefficient m _L for correcting the average of the leakage current distribution representing the second leakage current variation of the cell is stored in the “average of leakage current distribution” field. Further, a correction coefficient σ _L for correcting the standard deviation of the leakage current distribution representing the second leakage current variation of the cell is stored in the “standard deviation of leakage current distribution” field.

  Further, the third calculation unit 304 calculates the degree of correlation between the delay value of the cell and the leak current value based on the calculated value that characterizes the actually measured delay distribution of the chip and the value that characterizes the logarithmic leak current distribution of the chip. The correlation coefficient shown is calculated. Here, the correlation coefficient indicating the degree of correlation between the delay value of the cell and the leakage current value is, for example, the correlation coefficients ρα and ρ described above.

However, when the variation 1 _C of the leak current value of the cell is expressed using the above equation (3), the correlation coefficient ρα between the parameter α related to the first delay variation and the parameter α ′ related to the first leak current variation is ignored. be able to. For this reason, here, a correlation coefficient ρ between the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation is obtained.

  Here, a random variable representing a variation in delay value of the ring oscillator embedded in the chip is referred to as a “random variable D”. Further, it is assumed that the standard deviations ap and an of the second delay distribution of the cell included in the above formula (1) expressing the variation of the delay value of the cell are “ap = an”. In this case, the random variable D representing the variation of the delay value of the ring oscillator is expressed by the following equation (22).

D = m ₁ + m ₂ + ... + m _n + s ₁ α ₁ + s ₂ α ₂ + ... + s _n α _n + (ap ₁ + ap ₂ + ... +
ap _n ) β (22)

Further, a random variable representing the variation of the leakage current value of the ring oscillator embedded in the chip is set as “probability variable I”, and the variation of the leakage current value of the cell is expressed using the above equation (3). In this case, the random variable I representing the variation in the leakage current value of the ring oscillator is expressed by the following equation (23). However, A _(i) , B _(i) and C _(i) are model coefficients A, B and C specific to the cell C (i) in the ring oscillator.

_{I = exp (A (1)} + B (1) 2/2 + C (1) × β ') + exp (A (2) + B (2) 2/2
_{+ C (2) × β '} ) + ... + exp (A (n) + B (n) 2/2 + C (n) × β')
(23)

Further, the above equation (23) can be converted into the following equation (24) using Wilkinson approximation. U and V are constants obtained from A _{(1) to} A _(n) , B _{(1) to} B _(n) , C _{(1) to} C _(n) (i = 1, 2,...). , N).

    I≈exp (U + V × β ′) (24)

  Here, when the logarithm of the above equation (24) is taken, the following equation (25) is obtained.

    log I≈U + V × β ′ (25)

As a result, the above equations (22) and (25) are linear equations related to the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation. Therefore, from the definition of the correlation coefficient, the correlation coefficient between the “D” and the “log I” (hereinafter referred to as “correlation coefficient ρ ₀ ”) is the difference between the “β” and the “β ′”. Correlation coefficient ρ. That is, by obtaining the correlation coefficient ρ ₀ between the “D” and the “log I”, the correlation coefficient ρ between the “β” and the “β ′” can be obtained.

Specifically, for example, the third calculation unit 304 calculates the correlation coefficient ρ between the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation using the following equation (26). be able to. Here, X _{1 to} X _K are logarithmic leak current values of the chip. d _{1 to} d _K are ring oscillator delay values. m _d and σ _d are the average and standard deviation of the actually measured delay distribution representing the variation of the delay value of the ring oscillator. m _X and σ _X are the average and standard deviation of the logarithmic leak current distribution representing the variation of the logarithmic leak current value obtained by taking the logarithm of the leak current value of the chip.

ρ = ρ ₀ = {(X ₁ −m _X ) × (d ₁ −m _d ) + (X ₂ −m _X ) × (d ₂ −m _d ) +
... (X _K -m _X ) × (d _K -m _d )} / (K × σ _X × σ _d ) (26)

  The calculated correlation coefficient is stored, for example, in the correction value table 600 shown in FIG. Here, in (6-3) of FIG. 6, the correlation coefficient ρ between the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation is stored in the “correlation coefficient” field.

The creation unit 305 creates a first function including a random variable and a delay correction value related to the variation in the delay value of the cell as a function representing the variation in the delay value of the cell in the analysis target circuit. Specifically, for example, creating unit 305, by referring to the correction value table 600, a correction coefficient r _m and the correction coefficient r _s by substituting the above equation (4), the variation model of the delay value of the cell create.

  In addition, the creation unit 305 creates a first function including a random variable and a delay correction value related to the variation in the delay value of the path as a function representing the variation in the delay value of the path in the analysis target circuit. Good. Hereinafter, an arbitrary path in the analysis target circuit is expressed as “path Pi” (i = 1, 2,..., N).

Specifically, for example, creating unit 305, by referring to the correction value table 600, a correction coefficient r _m and the correction coefficient r _s by substituting the following equation (27), the variation model of the delay value of the path Pi Create Here, D _i is a variation in the delay value of the path Pi in the analysis target circuit, α is a parameter related to the first delay variation, and β is a parameter related to the second delay variation. M _i is the average of the first delay distribution of the path Pi representing the first delay variation, and S _i is the standard deviation of the first delay distribution. Ap _i and An _i are standard deviations of the second delay distribution of the path Pi representing the second delay variation.

D _i = r _m × M _i + r _s × S _i × α + f (β)
_{f (β) = r s ×} Ap i × β (β ≧ 0), f (β) = r s × An i × β (β <0)
... (27)

In addition, the creation unit 305 creates a second function including a random variable and a leakage current correction value related to the variation in the leakage current value of the cell as a function representing the variation in the leakage current value of the cell in the analysis target circuit. Specifically, for example, the creation unit 305 refers to the correction value table 600 and substitutes the correction coefficient m _L and the correction coefficient σ _L into the above equation (5), whereby the cell leakage current value variation model. Create

  The analysis unit 306 calculates the delay value of the analysis target circuit based on the generated first and second functions and the correlation coefficient indicating the degree of correlation between the calculated cell delay value and the leak current value. By performing a correlation analysis with the leakage current value, a correlation distribution representing the correlation between the delay value of the circuit to be analyzed and the leakage current value is acquired.

  Specifically, for example, the analysis unit 306 performs various types of information necessary for correlation analysis between the delay value of the analysis target circuit and the leakage current value to the simulator and executes the Monte Carlo simulation. The simulator may be provided in the analysis support apparatus 100 or may be provided in an external computer. Then, the analysis unit 306 acquires a correlation distribution representing a correlation between the delay value of the analysis target circuit and the leakage current value from the simulator.

  Here, various kinds of information necessary for the correlation analysis between the delay value of the analysis target circuit and the leakage current value are, for example, circuit information of the analysis target circuit, delay variation data unique to each cell Cj in the analysis target circuit, and leakage This is a variation model of each of the current variation data, the delay value of the cell Cj, and the leakage current value. The circuit information of the analysis target circuit is, for example, a net list that represents the connection relationship and the arrangement relationship between cells in the analysis target circuit.

  Further, as various kinds of information necessary for the correlation analysis between the delay value of the analysis target circuit and the leak current value, the delay variation data unique to each path Pi is used instead of the delay variation data unique to each cell Cj. May be. In this case, the various types of information given to the simulator include, for example, inherent delay variation data for each path Pi, inherent leakage current variation data for each cell Cj, delay value variation model for the path Pi, and leakage current value variation for the cell Cj. Become a model.

  The delay variation data unique to each path Pi may be acquired by the acquisition unit 301 by, for example, a user operation input using the keyboard 210 or the mouse 211, or may be acquired by extraction from a library or from an external computer. May be. The delay variation data of the path Pi is calculated from the delay variation data of each cell in the path Pi by, for example, a known technique of statistical delay analysis (SSTA).

  Delay variation data unique to each acquired path Pi is stored, for example, in a delay variation data table 800 shown in FIG. The delay variation data table 800 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example. Here, a specific example of the delay variation data table 800 will be described.

  FIG. 8 is an explanatory diagram showing an example of the stored contents of the delay variation data table 800. In FIG. 8, the delay variation data table 800 has fields of path ID, M, S, Ap, and An. By setting information in each field, delay variation data 800-1 to 800-n are stored as records.

  The path ID is an identifier of a path in the analysis target circuit. M is the average of the first delay distribution of the path. S is the standard deviation of the first delay distribution of the path. Ap and An are standard deviations of the second delay distribution of the path. However, Ap is a standard deviation when the parameter β related to the second delay variation is “β ≧ 0”, and An is a standard deviation when the parameter β related to the second delay variation is “β <0”.

Taking the delay variation data 800-i as an example, the average M _i of the first delay distribution of path Pi, and the standard deviation S _i of the first delay distribution of path Pi, standard deviation Ap of the second delay distribution of path Pi _i and An _i are shown.

  Further, the correlation distribution representing the correlation between the acquired delay value of the analysis target circuit and the leakage current value is stored in, for example, the correlation distribution table 900 shown in FIG. The correlation distribution table 900 is realized by a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207, for example. Here, a specific example of the correlation distribution table 900 will be described.

  FIG. 9 is an explanatory diagram showing an example of the contents stored in the correlation distribution table 900. In FIG. 9, a correlation distribution table 900 has fields for correlation ID, delay value, and leakage current value. By setting information in each field, correlation data 900-1 to 900-P are stored as records.

  The correlation ID is an identifier of an analysis result by the p-th Monte Carlo simulation (p = 1, 2,..., P). P is the number of iterations of Monte Carlo simulation. The delay value is an analysis value that represents the delay value of the analysis target circuit. The leak current value is an analysis value representing the leak current value of the analysis target circuit.

  Returning to the description of FIG. 3, the output unit 307 outputs a correlation distribution representing the correlation between the acquired delay value of the analysis target circuit and the leakage current value. Specifically, for example, the output unit 307 outputs the correlation data 900-1 to 900-P stored in the correlation distribution table 900 illustrated in FIG. Examples of the output format include display on the display 208, print output to the printer 213, and transmission to an external computer via the I / F 209. Alternatively, the data may be stored in a storage device such as the RAM 203, the magnetic disk 205, and the optical disk 207.

  The output unit 307 may output a delay correction value that corrects a value that characterizes the delay distribution that represents the variation of the calculated delay value of the cell. The output unit 307 may output a leakage current correction value that corrects a value that characterizes the leakage current distribution that represents the variation in the leakage current value of the cell. The output unit 307 may output a correlation coefficient indicating the degree of correlation between the cell delay value and the leakage current value.

Specifically, for example, the output unit 307 outputs the correction coefficients r _m , r _s , m _L , σ _L and the correlation coefficient ρ stored in the correction value table 600 shown in FIG. Also good. As a result, the correlation distribution between the delay value and the leakage current value of the circuit to be analyzed is calculated using each variation model and the correlation coefficient ρ corrected by the correction coefficients r _m , r _s , m _L , and σ _L in the following. It can be calculated with high accuracy.

(Analysis support processing procedure of the analysis support apparatus 100)
Next, an analysis support processing procedure of the analysis support apparatus 100 according to the embodiment will be described. The analysis support process is a process for calculating, for example, the correction coefficients r _m , r _s , m _L , σ _L and correlation coefficient ρ described above.

  10 and 11 are flowcharts illustrating an example of the analysis support processing procedure of the analysis support apparatus 100 according to the embodiment. In FIG. 10, it is determined whether or not the actual correlation data 400-1 to 400-K, the delay variation data 500-1 to 500-n, and the leakage current variation data 700-1 to 700-m are acquired by the acquisition unit 301. (Step S1001).

Here, the acquisition unit 301 waits to acquire the measured correlation data 400-1 to 400-K, the delay variation data 500-1 to 500-n, and the leakage current variation data 700-1 to 700-m (step S1001). : No). Then, when the various types of data are acquired by the acquisition unit 301 (step S1001: Yes), the delay of the ring oscillator is based on the actual correlation data 400-1 to 400-K acquired by the first calculation unit 302. Values d _{1 to} d _K are calculated (step S1002).

Thereafter, the first calculation unit 302 calculates the average m _d and the standard deviation σ _d of the actually measured delay distribution of the ring oscillator based on the calculated delay values d _{1 to} d _K of the ring oscillator (step S1003). . Next, the average m _l and standard deviation σ _l of the measured leakage current distribution of the chip are calculated by the first calculation unit 302 based on the acquired measured correlation data 400-1 to 400-K (step S1004). .

Thereafter, the first calculation unit 302 obtains logarithmic leak current values X ₁ to X which are logarithms of the leak current values I _{1 to} I _K of the chip based on the actual correlation data 400-1 to 400 -K acquired. X _K is calculated (step S1005). Then, the first calculation unit 302 calculates the average m _X and the standard deviation σ _X of the log leakage current distribution of the chip based on the calculated log leakage current values X _{1 to} X _K of the chip (step S1006). .

Next, the average M and the standard deviation S of the estimated delay distribution of the ring oscillator are calculated by the second calculation unit 303 based on the acquired delay variation data 500-1 to 500-n (step S1007). Then, by the third calculation unit 304, an average m _d of the measured delay distribution calculated in step S1003, by dividing the average M estimates delay distribution calculated in step S1007, calculates a correction coefficient r _m ( Step S1008).

Further, the third calculation unit 304 calculates the correction coefficient r _s by dividing the standard deviation σ _d of the actually measured delay distribution calculated in step S1003 by the standard deviation S of the estimated delay distribution calculated in step S1007. Then (step S1009), the process proceeds to step S1101 shown in FIG. The calculated correction coefficients r _m and r _s are stored, for example, in the correction value table 600 shown in FIG.

In the flowchart of FIG. 11, first, based on the leak current variation data 700-1 to 700 -m acquired by the second calculation unit 303, the correction coefficients m _L and σ _L are set as unknowns to estimate the analysis target circuit. An average X of the leakage current distribution is calculated (step S1101). Further, the second calculation unit 303 sets the correction coefficients m _L and σ _L as unknowns based on the leakage current variation data 700-1 to 700 -m, and the mean square of the estimated leakage current distribution of the analysis target circuit. A value Y is calculated by adding the square of the standard deviation (step S1102).

Subsequently, by the third calculation unit 304, the correction coefficient m _L, sigma _L as unknowns, and the average X of the estimated leak current distribution of the analysis target circuit, and the average m _l of measured leakage current distribution in the chip becomes equal equation Is created (step S1103).

Further, the third calculation unit 304 adds the correction coefficient m _L and σ _L as unknowns, the sum Y of the mean square of the estimated leakage current distribution of the analysis target circuit and the square of the standard deviation, and the chip. to create a measured leakage current average m 2 square and square and the sum combined value of the standard deviation ^{_{σ l (m l 2 + σ}} l 2) and is equal equations _l of distribution (step S1104).

Then, the third calculation unit 304 calculates the correction coefficients m _L and σ _L by solving the equations created in steps S1103 and S1104 (step S1105). The calculated correction coefficients m _L and σ _L are stored, for example, in the correction value table 600 shown in FIG.

Thereafter, the third calculation unit 304 calculates a correlation coefficient ρ between the parameter β related to the second delay variation and the parameter β ′ related to the second leakage current variation (step S1106). Specifically, the third calculation unit 304 calculates the phase of “log I” which is the logarithm of the random variable D representing the variation of the delay value of the ring oscillator and the random variable I representing the variation of the leakage current value of the ring oscillator. The correlation coefficient ρ is calculated by calculating the relation number ρ ₀ . The calculated correlation coefficient ρ is stored in the correction value table 600 shown in FIG.

Then, the output unit 307 outputs the correction coefficients r _m , r _s , m _L , σ _L and the correlation coefficient ρ stored in the calculated correction value table 600 (step S1107), and the series according to this flowchart. Terminate the process.

Thereby, the correction coefficients r _m and r _s for correcting the average m and the standard deviation s of the delay distribution of the cell Cj can be obtained. Further, correction coefficients m _L and σ _L for correcting the average and standard deviation of the leakage current distribution of the cell Cj can be obtained. Further, the correlation coefficient ρ between the delay value of the cell Cj and the leakage current value can be obtained in accordance with the actually measured value.

(Analysis processing procedure of the analysis support apparatus 100)
Next, the analysis processing procedure of the analysis support apparatus 100 will be described. The analysis processing is processing for performing a correlation analysis between the delay value of the analysis target circuit and the leakage current value. For example, the analysis processing includes delay variation data 800-i unique to each path Pi, leak current variation data 700-j unique to each cell Cj, and correction coefficients r _m , r _s , m in the correction value table 600. _This is executed by giving _L , σ _L and a correlation coefficient ρ to the simulator.

  12 and 13 are flowcharts illustrating an example of an analysis processing procedure of the analysis support apparatus 100 according to the embodiment. In FIG. 12, the analysis unit 306 sets the number of iterations P of the Monte Carlo simulation (step S1201). The number of repetitions P is set in advance and stored in a storage device such as the ROM 202, RAM 203, magnetic disk 205, and optical disk 207, for example.

  Next, the analysis unit 306 sets the number of iterations “p” to “p = 1” (step S1202). Then, the analysis unit 306 generates standard normal random numbers β and β ′ of the correlation coefficient ρ (step S1203). The correlation coefficient ρ is the correlation coefficient calculated in step S1106 shown in FIG.

Subsequently, the generating unit 305, a correction coefficient r _m and the correction coefficient r _s by substituting the above equation (27), to create a variation model of the delay value of the path Pi (step S1204). Correction coefficient r _m and the correction coefficient r _s is the correction coefficient calculated in step S1008 and step S1009 shown in FIG. 10.

Further, the creation unit 305 creates a variation model of the leakage current value of the cell Cj by substituting the correction coefficient m _L and the correction coefficient σ _L into the above equation (5) (step S1205). The correction coefficient m _L and the correction coefficient σ _L are correction coefficients calculated in step S1105 shown in FIG. Then, the analysis unit 306 sets “i” of the path Pi to “i = 1” (step S1206).

Next, the standard normal random number α is generated by the analysis unit 306 (step S1207). Then, the analysis unit 306 uses the created delay value variation model of the path Pi to calculate the delay value variation “D _i = r _m × M _i + r _s × S _i × α + f (β)” of the path Pi. Calculate (step S1208). _{However, f (β) = r s} × Ap i × β (β ≧ 0), is _{f (β) = r s ×} An i × β (β <0).

  Next, the analysis unit 306 increments “i” of the path Pi (step S1209), and determines whether “i” is greater than “n” (step S1210). Here, if “i ≦ n” (step S1210: No), the process returns to step S1207.

On the other hand, when “i> n” (step S1210: Yes), the analysis unit 306 calculates the delay value “D (p) = max {D ₁ , D ₂ ,..., D _n }” of the analysis target circuit. (Step S1211), the process proceeds to step S1301 shown in FIG. The calculated delay value D (1) of the circuit to be analyzed is stored in the correlation distribution table 900 shown in FIG.

  In the flowchart of FIG. 13, first, the analysis unit 306 sets the leakage current value I (p) of the analysis target circuit to “I (p) = 0” (step S1301), and “j” of the cell Cj in the analysis target circuit. Is set to “j = 1” (step S1302).

Then, the analysis unit 306, using the variation model of the leakage current value of the cell Cj created, the variation of the leakage current value of the cell Cj "I (p) = I (p ) + exp {A + B 2/2 + C × (σ _L × β ′ + m _L )} ”is calculated (step S1303).

  Next, the analysis unit 306 increments “j” of the cell Cj (step S1304), and determines whether “j” is greater than “m” (step S1305). If “j ≦ m” is satisfied (step S1305: NO), the process returns to step S1303.

  On the other hand, if “j> m” (step S1305: Yes), the analysis unit 306 increments the number of iterations “p” (step S1306) and determines whether “p” is greater than “P”. (Step S1307). If “p ≦ P” (step S1307: NO), the process returns to step S1203 shown in FIG.

  On the other hand, in the case of “p> P” (step S1307: Yes), the output unit 307 causes the output data 307 to generate correlation data 900-1 to 900- related to the correlation distribution between the delay value of the analysis target circuit and the leakage current value. P is output (step S1308), and a series of processing according to this flowchart is terminated.

  Thereby, the correlation distribution between the delay value of the analysis target circuit and the leakage current value can be calculated with high accuracy.

As described above, according to the analysis support apparatus 100 according to the embodiment, an average m _d of the measured delay distribution of the produced chips, by dividing by the average M of the estimated delay distribution of the analysis target circuit, the cell it can be obtained a correction coefficient r _m for correcting the average m of the delay distribution of cj. Further, according to the analysis support apparatus 100, the standard deviation σ _d of the actually measured delay distribution of the manufactured chip is divided by the standard deviation S of the estimated delay distribution of the analysis target circuit, so that the standard deviation of the delay distribution of the cell Cj is obtained. A correction coefficient r _s for correcting _s can be obtained.

Thereby, the variation of the delay value of each cell Cj estimated using the delay variation model can be corrected according to the actually measured value. Further, by calculating the average m _d and standard deviation σ _d of the actually measured delay distribution using the delay value of the ring oscillator embedded in the chip, the load on the calculation process of the correction coefficients r _m and r _s is reduced. be able to.

Further, according to the analysis support apparatus 100, the average and standard deviation of the estimated leakage current distribution of the analysis target circuit are used as the correction coefficients m _L and σ _L for correcting the average and standard deviation of the leakage current distribution of the cell Cj. average m _l of measured leakage current distribution, the correction coefficient m _L match the standard deviation sigma _l, can be determined sigma _L.

  Thereby, the variation of the leakage current value of each cell Cj estimated using the variation model of the leakage current can be corrected according to the actual measurement value.

Further, according to the analysis support apparatus 100, the correlation coefficient ρ ₀ between the random variable D representing the variation of the chip delay value and the log variable “log I” taking the logarithm of the random variable I representing the variation of the leakage current value of the chip is obtained. By calculating, the correlation coefficient ρ between the delay value of cell Cj and the leakage current value can be obtained.

  Thereby, the correlation coefficient ρ between the delay value of the cell Cj and the leakage current value can be corrected according to the actually measured value. Further, by calculating the random variable D using the delay value of the ring oscillator embedded in the chip, it is possible to reduce the load on the calculation process of the correlation coefficient ρ.

From these facts, according to the analysis support apparatus 100 according to the embodiment, the analysis target circuit is used by using each variation model and the correlation coefficient ρ corrected by the correction coefficients r _m , r _s , m _L , and σ _L. The correlation distribution between the delay value and the leakage current value can be accurately estimated. As a result, it is possible to accurately estimate the yield distribution of the chip and the like to prevent rework of the circuit design, reduce the work load on the designer, and shorten the design period. Further, since the values of the correction coefficients r _m , r _s , m _L , σ _L and the correlation coefficient ρ are values specific to the process, the corrected variation model and the correlation coefficient ρ are manufactured in the same process. It can also be applied to other analysis target circuits.

  The analysis support method described in this embodiment can be realized by executing a program prepared in advance on a computer such as a personal computer or a workstation. The analysis support program is recorded on a computer-readable recording medium such as a hard disk, a flexible disk, a CD-ROM, an MO, and a DVD, and is executed by being read from the recording medium by the computer. The analysis support program may be distributed via a network such as the Internet.

  In addition, the analysis support apparatus 100 described in the present embodiment is an application-specific IC (hereinafter simply referred to as “ASIC”) such as a standard cell or a structured ASIC (Application Specific Integrated Circuit), or a PLD (Programmable) such as an FPGA. It can also be realized by Logic Device). Specifically, for example, the functions of the above-described analysis support apparatus 100 (acquisition unit 301 to output unit 307) are defined by HDL description, and the HDL description is logically synthesized and given to the ASIC or PLD to support analysis. The device 100 can be manufactured.

  The following additional notes are disclosed with respect to the embodiment described above.

(Appendix 1) An acquisition step of acquiring a set of delay values of the chip measured in accordance with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation step of calculating a value characterizing a first delay distribution representing variation of the delay value of the chip based on a set of delay values of the chip acquired by the acquisition step;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculating step for calculating;
A value that characterizes the first delay distribution calculated by the first calculation step is divided by a value that characterizes the second delay distribution calculated by the second calculation step, and is a unique value for each element. A third calculation step of calculating a delay correction value for correcting
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support program characterized in that a computer is executed.

(Supplementary Note 2) The acquisition step further acquires a set of leakage current values of the chip measured along with a variation in the delay value of the chip,
The first calculation step further calculates a value characterizing the first leakage current distribution representing variation in the leakage current value of the chip based on the set of leakage current values of the chip,
In the second calculation step, the element that characterizes the leak current distribution is further defined by using a leak current correction value that corrects a value that characterizes a leak current distribution that represents a variation in leak current values of elements in the analysis target circuit as an unknown. Based on a set of unique values for each, a value characterizing the second leakage current distribution representing the variation in the leakage current value of the circuit to be analyzed is calculated,
The third calculation step further includes a value characterizing the second leakage current distribution calculated by the second calculation step, and a value characterizing the first leakage current distribution calculated by the first calculation step. The analysis support program according to appendix 1, wherein the leak current correction value to be matched with is calculated.

(Supplementary Note 3) The first calculation step further includes a logarithmic leakage current distribution representing a variation of a logarithmic leakage current value obtained by taking a logarithm of the leakage current value of the chip based on a set of leakage current values of the chip. Calculate the value to characterize,
The third calculation step further includes a correlation indicating a degree of correlation between the delay value of the element and the leak current value based on the value characterizing the first delay distribution and the value characterizing the logarithmic leak current distribution. The analysis support program according to attachment 2, wherein the number is calculated.

(Supplementary note 4)
A first creation step of creating a first function including a random variable related to the variation of the delay value of the element and the delay correction value as a function representing the variation of the delay value of the element;
A second creation step of creating a second function including a random variable related to the variation in the leakage current value of the element and the leakage current correction value as a function representing the variation in the leakage current value of the element;
Based on the first and second functions created by the first and second creation steps and the correlation coefficient calculated by the third calculation step, the delay value and leakage current of the circuit to be analyzed Executing a correlation analysis with a value, and performing an analysis step of obtaining a correlation distribution representing a correlation between a delay value of the analysis target circuit and a leakage current value,
The analysis support program according to appendix 3, wherein the output step outputs a correlation distribution representing a correlation between a delay value of the circuit to be analyzed and a leak current value acquired in the analysis step.

(Supplementary Note 5) The acquisition step acquires a set of delay values of ring oscillators embedded in the chip measured along with fluctuations in the leakage current value of the chip,
The first calculation step calculates a value that characterizes a first delay distribution that represents a variation in the delay value of the ring oscillator based on a set of delay values of the ring oscillator;
In the second calculation step, a second value representing a variation in the delay value of the ring oscillator based on a set of unique values for each of the elements characterizing a delay distribution representing a variation in the delay value of the elements in the ring oscillator. The analysis support program according to any one of appendices 1 to 4, wherein a value characterizing the delay distribution is calculated.

(Additional remark 6) The acquisition process which acquires the set of the leak current value of the above-mentioned chip measured with the change of the delay value of the chip after manufacture about the analysis object circuit,
A first calculation step for calculating a value characterizing a first leakage current distribution representing a variation in the leakage current value of the chip based on a set of leakage current values of the chip acquired by the acquisition step;
Based on a set of unique values for each of the elements that characterize the leakage current distribution, with an unknown leak current correction value that corrects the value that characterizes the leakage current distribution representing the variation in the leakage current value of the elements in the analysis target circuit A second calculation step of calculating a value characterizing the second leakage current distribution representing the variation in the leakage current value of the analysis target circuit;
The leak current correction value that matches the value characterizing the second leak current distribution calculated by the second calculation step with the value characterizing the first leak current distribution calculated by the first calculation step is calculated. A third calculation step,
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support program characterized in that a computer is executed.

(Supplementary Note 7) An acquisition unit that acquires a set of delay values of the chip measured along with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation unit that calculates a value characterizing a first delay distribution that represents a variation in the delay value of the chip based on a set of delay values of the chip acquired by the acquisition unit;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculation unit for calculating;
A value that characterizes the first delay distribution calculated by the first calculation unit is divided by a value that characterizes the second delay distribution calculated by the second calculation unit, and is a unique value for each element. A third calculation unit for calculating a delay correction value for correcting
An output unit for outputting a calculation result calculated by the third calculation unit;
An analysis support apparatus comprising:

(Supplementary Note 8) An acquisition unit that acquires a set of leakage current values of the chip measured along with a variation in a delay value of the chip after manufacture related to the analysis target circuit;
A first calculation unit that calculates a value that characterizes a first leakage current distribution that represents a variation in the leakage current value of the chip, based on a set of leakage current values of the chip acquired by the acquisition unit;
Based on a set of unique values for each of the elements that characterize the leakage current distribution, with an unknown leak current correction value that corrects the value that characterizes the leakage current distribution representing the variation in the leakage current value of the elements in the analysis target circuit A second calculation unit that calculates a value that characterizes a second leakage current distribution that represents a variation in a leakage current value of the analysis target circuit;
The leak current correction value that matches the value characterizing the second leak current distribution calculated by the second calculator with the value characterizing the first leak current distribution calculated by the first calculator is calculated. A third calculation unit that
An output unit for outputting a calculation result calculated by the third calculation unit;
An analysis support apparatus comprising:

(Supplementary note 9) An acquisition step of acquiring a set of delay values of the chip measured in accordance with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation step of calculating a value characterizing a first delay distribution representing variation of the delay value of the chip based on a set of delay values of the chip acquired by the acquisition step;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculating step for calculating;
A value that characterizes the first delay distribution calculated by the first calculation step is divided by a value that characterizes the second delay distribution calculated by the second calculation step, and is a unique value for each element. A third calculation step of calculating a delay correction value for correcting
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support method characterized in that a computer executes the above.

(Additional remark 10) The acquisition process which acquires the set of the leak current value of the above-mentioned chip measured with the change of the delay value of the chip after manufacture about the analysis object circuit,
A first calculation step for calculating a value characterizing a first leakage current distribution representing a variation in the leakage current value of the chip based on a set of leakage current values of the chip acquired by the acquisition step;
Based on a set of unique values for each of the elements that characterize the leakage current distribution, with an unknown leak current correction value that corrects the value that characterizes the leakage current distribution representing the variation in the leakage current value of the elements in the analysis target circuit A second calculation step of calculating a value characterizing the second leakage current distribution representing the variation in the leakage current value of the analysis target circuit;
The leak current correction value that matches the value characterizing the second leak current distribution calculated by the second calculation step with the value characterizing the first leak current distribution calculated by the first calculation step is calculated. A third calculation step,
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support method characterized in that a computer executes the above.

DESCRIPTION OF SYMBOLS 100 Analysis support apparatus 301 Acquisition part 302 1st calculation part 303 2nd calculation part 304 3rd calculation part 305 Creation part 306 Analysis part 307 Output part 400 Actual correlation data table 500,800 Delay variation data table 600 Correction value table 700 Leakage current variation data table 900 Correlation distribution table

Claims (8)

An acquisition step of acquiring a set of delay values of the chip measured along with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation step of calculating a value characterizing a first delay distribution representing variation of the delay value of the chip based on a set of delay values of the chip acquired by the acquisition step;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculating step for calculating;
A value that characterizes the first delay distribution calculated by the first calculation step is divided by a value that characterizes the second delay distribution calculated by the second calculation step, and is a unique value for each element. A third calculation step of calculating a delay correction value for correcting
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support program characterized in that a computer is executed. The acquisition step includes
Further, a set of leakage current values of the chip measured with the variation of the delay value of the chip is obtained,
The first calculation step includes:
Further, based on the set of leakage current values of the chip, a value characterizing the first leakage current distribution representing the variation in the leakage current value of the chip is calculated,
The second calculation step includes:
Further, the analysis is performed based on a set of unique values for each of the elements that characterize the leakage current distribution, with an unknown leak current correction value that corrects a value that characterizes the leakage current distribution representing variation in the leakage current value of the element. Calculate the value of the second leakage current distribution that represents the variation in the leakage current value of the target circuit,
The third calculation step includes:
Further, the leak current correction value for matching the value characterizing the second leak current distribution calculated by the second calculation step with the value characterizing the first leak current distribution calculated by the first calculation step. The analysis support program according to claim 1, wherein: The first calculation step includes:
Further, based on the set of leakage current values of the chip, a value that characterizes a logarithmic leakage current distribution that represents a variation of the logarithmic leakage current value that is a logarithm of the leakage current value of the chip is calculated,
The third calculation step includes:
Further, a correlation coefficient indicating a degree of correlation between the delay value of the element and the leak current value is calculated based on a value characterizing the first delay distribution and a value characterizing the logarithmic leak current distribution. The analysis support program according to claim 2. In the computer,
A first creation step of creating a first function including a random variable related to the variation of the delay value of the element and the delay correction value as a function representing the variation of the delay value of the element;
A second creation step of creating a second function including a random variable related to the variation in the leakage current value of the element and the leakage current correction value as a function representing the variation in the leakage current value of the element;
Based on the first and second functions created by the first and second creation steps and the correlation coefficient calculated by the third calculation step, the delay value and leakage current of the circuit to be analyzed Executing a correlation analysis with a value, and performing an analysis step of obtaining a correlation distribution representing a correlation between a delay value of the analysis target circuit and a leakage current value,
The output step includes
The analysis support program according to claim 3, wherein a correlation distribution representing a correlation between a delay value of the circuit to be analyzed and a leak current value acquired in the analysis step is output. The acquisition step includes
Obtaining a set of delay values of the ring oscillator embedded in the chip measured along with the fluctuation of the leakage current value of the chip;
The first calculation step includes:
Based on the set of delay values of the ring oscillator, calculate a value characterizing the first delay distribution representing the variation of the delay value of the ring oscillator;
The second calculation step includes:
Characterizing a delay distribution representing variation in delay values of elements in the ring oscillator Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values of the ring oscillator is calculated. The analysis support program according to any one of claims 1 to 4, wherein An acquisition step of acquiring a set of leakage current values of the chip measured in accordance with a variation in a delay value of the chip after manufacture related to the analysis target circuit;
A first calculation step for calculating a value characterizing a first leakage current distribution representing a variation in the leakage current value of the chip based on a set of leakage current values of the chip acquired by the acquisition step;
Based on a set of unique values for each of the elements that characterize the leakage current distribution, with an unknown leak current correction value that corrects the value that characterizes the leakage current distribution representing the variation in the leakage current value of the elements in the analysis target circuit A second calculation step of calculating a value of a second leakage current distribution representing variation in the leakage current value of the analysis target circuit;
The leak current correction value that matches the value characterizing the second leak current distribution calculated by the second calculation step with the value characterizing the first leak current distribution calculated by the first calculation step is calculated. A third calculation step,
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support program characterized in that a computer is executed. An acquisition unit for acquiring a set of delay values of the chip measured in accordance with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation unit that calculates a value characterizing a first delay distribution that represents a variation in the delay value of the chip based on a set of delay values of the chip acquired by the acquisition unit;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculation unit for calculating;
A value that characterizes the first delay distribution calculated by the first calculation unit is divided by a value that characterizes the second delay distribution calculated by the second calculation unit, and is a unique value for each element. A third calculation unit for calculating a delay correction value for correcting
An output unit for outputting a calculation result calculated by the third calculation unit;
An analysis support apparatus comprising: An acquisition step of acquiring a set of delay values of the chip measured along with a change in a leakage current value of the chip after manufacture related to the analysis target circuit;
A first calculation step of calculating a value characterizing a first delay distribution representing variation of the delay value of the chip based on a set of delay values of the chip acquired by the acquisition step;
Characterizing a delay distribution representing variation in delay values of elements in the circuit to be analyzed Based on a set of unique values for each element, a value characterizing a second delay distribution representing variation in delay values in the circuit to be analyzed A second calculating step for calculating;
A value that characterizes the first delay distribution calculated by the first calculation step is divided by a value that characterizes the second delay distribution calculated by the second calculation step, and is a unique value for each element. A third calculation step of calculating a delay correction value for correcting
An output step of outputting the calculation result calculated by the third calculation step;
An analysis support method characterized in that a computer executes the above.

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