A method and system for extracting characteristic parameters of performance fluctuations of integrated circuits

Abstract

The application discloses a method and system for extracting characteristic parameters of performance fluctuation of an integrated circuit, and the method comprises the following steps: constructing a substitute model of circuit simulation according to a functional relationship between each component parameter and performance parameter; performing Monte Carlo sampling in a component parameter space; simulating samples obtained through the Monte Carlo sampling by using the substitute model, and calculating the mean value and variance of the performance fluctuation characteristic parameters of this sampling; and calculating the total mean value and variance of the performance fluctuation characteristic parameters according to the mean value and variance of multiple groups of samples. The technical scheme of the application can efficiently extract the characteristic parameters of performance fluctuation of the integrated circuit.

Description

Technical Field

[0001] This invention relates to the field of integrated circuit technology, and in particular to a method and system for extracting characteristic parameters of integrated circuit performance fluctuations based on sensitivity analysis. Background Technology

[0002] In the integrated circuit design and manufacturing process, parameter fluctuations are unavoidable. These fluctuations are statistical in nature, and the circuit function and system design rely heavily on the validity of the law of large numbers and statistical analysis assumptions. However, with further improvements in process technology, many parameters fluctuate around their nominal values, and the correlation between these fluctuations becomes increasingly strong. For example, at the nanoscale, changes related to photolithography can affect geometric parameters such as the effective width and length of transistors, exacerbating the parameter fluctuation problem. In semiconductor devices, as process dimensions shrink to the nanometer scale, the impact of these parameter fluctuations on design performance becomes increasingly significant, and their proportion in total chip delay is also increasing compared to gate delay. Therefore, analyzing chip performance fluctuations through parameter fluctuations and extracting characteristic parameters of these fluctuations is crucial for accurately determining chip yield and performance.

[0003] Monte Carlo simulation is a commonly used method in the industry for extracting fluctuation characteristic parameters. The Monte Carlo method assumes that process fluctuation parameters follow a Gaussian distribution and are independent of each other. Sample points are randomly generated according to this distribution, and delay values ​​are obtained through circuit simulation. This process is repeated multiple times to obtain the circuit delay distribution. The Monte Carlo method is widely used due to its simplicity and effectiveness; fluctuation characteristic parameters estimated by a large number of Monte Carlo simulations are considered the "gold standard" in the industry. However, obtaining an accurate result through Monte Carlo simulation requires simulating a large number of samples. Furthermore, with advancements in manufacturing processes, the number of transistors in each circuit has increased dramatically, reaching hundreds of thousands or even millions, making the Monte Carlo algorithm extremely inefficient and time-consuming when handling such fluctuation characteristic extraction problems.

[0004] Another method for extracting fluctuation characteristic parameters is the discrete numerical method. The discrete numerical method represents the random variable of unit delay as a polynomial function of various process fluctuation parameters and uses discrete numerical calculations to solve for their corresponding relationships. This method has high accuracy but high computational complexity. First-order polynomials are used under normal voltage conditions, while second-order polynomials are used under low voltage conditions due to the nonlinear relationship between delay and process parameters. To further reduce computational load and consider the correlation coefficients between units, non-Gaussian distributions, such as inverse Gaussian, Weibull, skewed, and log-skewed distributions, will replace the default Gaussian distribution for process parameters when solving practical problems. The disadvantage of the discrete numerical method is that although it reduces time overhead compared to the Monte Carlo method, the higher the required accuracy, the greater the computational time overhead. In the worst case, its computational time overhead is exponentially related to the number of discrete points required for calculation. Summary of the Invention

[0005] The purpose of this invention is to address the technical shortcomings of existing integrated circuit fluctuation characteristic parameter extraction methods, which are inefficient and time-consuming under high-dimensional problems in advanced process technology, by providing a method and system for extracting integrated circuit performance fluctuation characteristic parameters based on sensitivity analysis.

[0006] In this embodiment of the invention, a method for extracting characteristic parameters of integrated circuit performance fluctuations is provided, comprising:

[0007] Step S1: Construct a parameter sample space, determine the dimension N of the circuit parameter space, and perform 4N+1 samplings in the parameter space;

[0008] Step S2: Construct a simulation performance parameter space, perform circuit simulation on the collected sample points, and obtain the corresponding performance parameters;

[0009] Step S3: Calculate the sensitivity of the performance parameters to each component parameter, and construct the relationship function between the component parameters and the performance parameters;

[0010] Step S4: Based on the functional relationship between the parameters and performance parameters of each component, construct an alternative model for circuit simulation;

[0011] Step S5: Perform Monte Carlo sampling in the component parameter space;

[0012] Step S6: Use the alternative model to simulate the samples obtained from Monte Carlo sampling, and calculate the mean and variance of the performance fluctuation characteristic parameters of this sampling.

[0013] Step S7: Calculate the quality factor and determine whether the quality factor is less than the set convergence threshold. If yes, proceed to step S8; otherwise, return to step S5.

[0014] Step S8: Calculate the total mean and variance of the performance fluctuation characteristic parameters by combining the mean and variance of multiple samples.

[0015] In this embodiment of the invention, step S1 specifically includes:

[0016] Step S11: Define the parameter x for each component i nominal value μ i and standard deviation σ i ;

[0017] Step S12: The point X0 = (μ1, μ2, μ3, ..., μ...) where all component parameters are at their nominal values. N-1 μ N Sampling was performed;

[0018] Step S13: All other parameters are set to nominal values, and the value of the i-th component parameter is μ. i -3σ i μ i -1.5σ i μ i +1.5σ i μ i +3σ i The sampling points obtained by point sampling are:

[0019] x i1 =(μ1,μ2,μ3,...,μ i -3σ i , ..., μ N -1, μ N )

[0020] x i2 =(μ1,μ2,μ3,…,μ i -1.5σ i , ..., μ N-1 μ N )

[0021] x i3 =(μ1,μ2,μ3,...,μ i +1.5σ i , ..., μ N-1 μ N )

[0022] x i4 =(μ1,μ2,μ3,…,μ i +3σ i , ..., μ N-1 μ N ).

[0023] In this embodiment of the invention, step S3, constructing the relationship function between component parameters and performance parameters, includes:

[0024] For each component parameter x, a piecewise linear interpolation function f is constructed using the four points sampled for that parameter. i (x), we get:

[0025]

[0026] In this embodiment of the invention, step S4, constructing an alternative model for circuit simulation, includes:

[0027] Step S41: Obtain the performance value f0 at the nominal value point X0 during circuit simulation;

[0028] Step S42: Obtain the alternative model for circuit simulation using the following formula:

[0029]

[0030] In this embodiment of the invention, the Monte Carlo sampling method in the component parameter space in step S5 is as follows:

[0031] Extract N from the parameter space j A random number x ij i = 1, ..., N j , making x ij ~N(μ) j , σ j ).

[0032] In this embodiment of the invention, the mean value E of the characteristic parameter of the performance fluctuation in this sampling is calculated. j S and variance j The formulas are as follows:

[0033]

[0034]

[0035] In this embodiment of the invention, the formula for calculating the quality factor fp in step S7 is as follows:

[0036]

[0037] In this embodiment of the invention, the formulas for calculating the overall mean E and variance S in step S8 are as follows:

[0038]

[0039]

[0040] Where k is the number of sample groups.

[0041] In this embodiment of the invention, there is also a system for extracting characteristic parameters of integrated circuit performance fluctuation, which uses the above-described method for extracting characteristic parameters of integrated circuit performance fluctuation.

[0042] Compared with existing technologies, the method and system for extracting integrated circuit performance fluctuation characteristic parameters of this invention utilizes the relationship between fluctuation parameters and circuit performance to construct a functional relationship between the parameters and circuit performance. This allows for accurate simulation of circuit performance with a small number of samplings, improving the efficiency of fluctuation characteristic parameter extraction. It is applicable to fluctuation characteristic parameter extraction problems in high-dimensional parameter spaces and multiple failure domains. The number of samplings and parameter dimensions are linearly related, ensuring stable sampling numbers even in high-dimensional problems. The number of samplings is far less than that of the traditional Monte Carlo method, greatly reducing unnecessary circuit simulations and further improving the efficiency of fluctuation characteristic parameter extraction. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the process for extracting characteristic parameters of integrated circuit performance fluctuations according to an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram illustrating the construction of a piecewise linear interpolation function for a parameter and the corresponding distribution of the parameter and performance space in an embodiment of the present invention. Detailed Implementation

[0045] like Figure 1 As shown in the embodiment of the present invention, a method for extracting characteristic parameters of integrated circuit performance fluctuation is provided, which includes steps S1-S8.

[0046] Step S1: Construct a parameter sample space, determine the dimension N of the circuit parameter space, and perform 4N+1 samplings in the parameter space.

[0047] In this embodiment of the invention, step S1 specifically includes:

[0048] Step S11: Determine the parameter x for each component i nominal value μ i and standard deviation σ i ;

[0049] Step S12: The point X0 = (μ1, μ2, μ3, ..., μ...) where all component parameters are at their nominal values. N-1 μ N Sampling was performed;

[0050] Step S13: All other parameters are set to nominal values, and the parameter of the i-th component is set to μ. i -3σ i μi -1.5σ i μ i +1.5σ i μ i +3σ i The sampling points obtained by point sampling are:

[0051] x i1 =(μ1,μ2,μ3,…,μ i -3σ i , ..., μ N-1 μ N )

[0052] x i2 =(μ1,μ2,μ3,...,μ i -1.5σ i , ..., μ N-1 μ N )

[0053] x i3 =(μ1,μ2,μ3,…,μ i +1.5σ i , ..., μ N-1 (μN)

[0054] x i4 =(μ1,μ2,μ3,…,μ i +3σ i , ..., μ N -1, μ N ).

[0055] A total of 4N+1 sample points were collected through steps S12 and S13.

[0056] Step S2: Construct a simulation performance parameter space, perform circuit simulation on the collected sample points, and obtain the performance parameters corresponding to each sample point.

[0057] Step S3: Calculate the sensitivity of the performance parameters to each component parameter, and construct the relationship function between the component parameters and the performance parameters.

[0058] Specifically, in this embodiment of the invention, constructing the relationship function between component parameters and performance parameters includes:

[0059] like Figure 2 As shown, for each component parameter x, a piecewise linear interpolation function f is constructed using four points sampled for that parameter. i (x), we get:

[0060]

[0061] Step S4: constructing a surrogate model for circuit simulation according to the functional relationship between each component parameter and the performance parameter.

[0062] In the embodiment of the present invention, constructing the surrogate model for circuit simulation comprises:

[0063] Step S41: obtaining a performance value f0 at a point x0 of a nominal value during circuit simulation;

[0064] Step S42: obtaining the surrogate model for circuit simulation by the following formula:

[0065]

[0066] Step S5: performing Monte Carlo sampling in a component parameter space.

[0067] In the embodiment of the present invention, the method for performing Monte Carlo sampling in the component parameter space is as follows:

[0068] Drawing N j random numbers x ij , i=1,…,N j , such that x ij ~N(μ j , σ j ).

[0069] Step S6: simulating the samples obtained by Monte Carlo sampling using the surrogate model, and calculating the mean and variance of the performance fluctuation characteristic parameter of the current sampling.

[0070] In the embodiment of the present invention, the formulas for calculating the mean E j and the variance S j of the performance fluctuation characteristic parameter of the current sampling are respectively as follows:

[0071]

[0072]

[0073] Step S7: calculating a figure of merit, and determining whether the figure of merit is less than a set convergence threshold, if yes, exiting iteration and proceeding to step S8, otherwise returning to step S5 to continue iteration.

[0074] In the embodiment of the present invention, in step S7, the calculation formula of the figure of merit fp is as follows:

[0075]

[0076] If fp<Fp, exiting iteration and proceeding to step S8; if fp≥Fp, jumping to step S5, wherein Fp is the set convergence threshold.

[0077] Step S8: Calculate the total mean and variance of the performance fluctuation characteristic parameters by combining the mean and variance of multiple samples.

[0078] In this embodiment of the invention, the formulas for calculating the overall mean E and variance S in step S8 are as follows:

[0079]

[0080]

[0081] Where k is the number of sample groups.

[0082] It should be noted that during the iteration process from step S7 to step S5, a set of samples is obtained each time, and the mean and variance are calculated each time. When calculating the total mean and variance, the mean and variance of each set of samples are averaged to obtain the total mean and variance.

[0083] Furthermore, in this embodiment of the invention, there is also a system for extracting integrated circuit performance fluctuation characteristic parameters, which uses the above-described method for extracting integrated circuit performance fluctuation characteristic parameters.

[0084] In summary, the method and system for extracting integrated circuit performance fluctuation characteristic parameters of this invention utilize the relationship between fluctuation parameters and circuit performance to construct a functional relationship between the parameters and circuit performance. This allows for accurate simulation of circuit performance with a small number of samplings, improving the efficiency of fluctuation characteristic parameter extraction. It is applicable to fluctuation characteristic parameter extraction problems in high-dimensional parameter spaces and multiple failure domains. The linear relationship between the number of samplings and the parameter dimension ensures stable sampling numbers even in high-dimensional problems. The number of samplings is far less than that of the traditional Monte Carlo method, significantly reducing unnecessary circuit simulations and further improving the efficiency of fluctuation characteristic parameter extraction.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extracting characteristic parameters of integrated circuit performance fluctuations, characterized in that, include: Step S1: Construct a parameter sample space, determine the dimension N of the integrated circuit's component parameter space, and perform 4N+1 samplings in the parameter space; Step S2: Construct a simulation performance parameter space, perform circuit simulation on the collected sample points, and obtain the corresponding performance parameters; Step S3: Calculate the sensitivity of the performance parameters to each component parameter, and construct the relationship function between the component parameters and the performance parameters; Step S4: Based on the functional relationship between the parameters and performance parameters of each component, construct an alternative model for circuit simulation; Step S5: Perform Monte Carlo sampling in the component parameter space; Step S6: Use the alternative model to simulate the samples obtained from Monte Carlo sampling, and calculate the mean and variance of the performance fluctuation characteristic parameters of this sampling. Step S7: Calculate the quality factor and determine whether the quality factor is less than the set convergence threshold. If yes, proceed to step S8; otherwise, return to step S5. Step S8: Calculate the total mean and variance of the performance fluctuation characteristic parameters by combining the means and variances of multiple samples; Step S1 specifically includes: Step S11: Determine the parameters of each component nominal value and standard deviation ; Step S12: Point where all component parameters are set to nominal values Perform sampling; Step S13: All other parameters are set to nominal values, and the values ​​of the i-th component parameters are respectively... The sampling points obtained by point sampling are: ， ， ， ； In step S3, the relationship function between component parameters and performance parameters is constructed, including: For each component parameter x, a piecewise linear interpolation function f is constructed using the four points sampled for that parameter. i (x), we get: ； In step S4, an alternative model for circuit simulation is constructed, including: Step S41: Obtain the point at the nominal value during circuit simulation. performance values ; Step S42: Obtain the alternative model for circuit simulation using the following formula: 。 2. The method for extracting characteristic parameters of integrated circuit performance fluctuation as described in claim 1, characterized in that, In step S5, the Monte Carlo sampling method in the component parameter space is as follows: Extract N from the parameter space j A random number x ij i=1,…,N j , making .

3. The method for extracting characteristic parameters of integrated circuit performance fluctuation as described in claim 2, characterized in that, Calculate the mean value E of the characteristic parameter of performance fluctuation in this sampling. j S and variance j The formulas are as follows: , 。 4. The method for extracting characteristic parameters of integrated circuit performance fluctuation as described in claim 3, characterized in that, In step S7, the formula for calculating the quality factor fp is as follows: 。 5. The method for extracting characteristic parameters of integrated circuit performance fluctuation as described in claim 4, characterized in that... In step S8, the formulas for calculating the overall mean E and variance S are as follows: ， ； Where k is the number of sample groups.

6. A system for extracting characteristic parameters of integrated circuit performance fluctuations, characterized in that, When extracting characteristic parameters of integrated circuit performance fluctuation, the method for extracting characteristic parameters of integrated circuit performance fluctuation as described in any one of claims 1-5 is adopted.

Images