Statistical timing analysis method and device based on improved adaptive random configuration method

Abstract

The invention relates to a statistical static timing analysis method. In the method, the MAX approximation problem in the statistical static timing analysis method is solved through an adaptive random configuration method (MASCM) based on an improved nested sparse grid integration method. In the MASCM, the MAX approximation is divided into two classes according to input end conditions, namely a linear input condition and a nonlinear input condition, wherein under the linear input condition, an input end with the maximum mean value is selected as output of the MAX; and under the nonlinear input condition, the orthogonal multinomial expansion coefficient is calculated by the improved nested sparse grid integration method. The improved nested sparse grid integration method improves the utilization rate of integration points in the random configuration method, guarantees the integration accuracy, reduces the number of configuration points and reduces the calculation time for statistical static timing analysis. Compared with the conventional methods, the provided MASCM has the equivalent calculation accuracy, while the needed number of integration points and calculation time are greatly reduced.

Description

Technical field:

[0001] The invention belongs to the field of integrated circuits, and in particular relates to a statistical static timing analysis method based on an improved self-adaptive random configuration method. Background technique

[0002] As the feature size of integrated circuits enters the nanometer level, the impact of process deviation on circuit performance is becoming more and more serious. In order to analyze the impact of process deviation on the timing of integrated circuits, Statistical Static Timing Analysis (SSTA) was introduced into timing analysis. "Statistical Time-Series Analysis: From Fundamentals to State-of-the-art", 27(4), pp. 589-607. In statistical static timing analysis, due to the influence of random process deviation, the delay of the circuit is no longer a definite value, but a random variable with a certain distribution. Statistical static timing analysis analyzes circuit timing by passing a random distribution of delays through the ci...

Examples

Embodiment Construction

[0028] The present invention is based on the statistical static timing analysis method of the improved adaptive random configuration method MASCM such as figure 1 shown, including the following steps:

[0029] step one : Establish the statistical delay model of gate unit and interconnection line based on random orthogonal polynomial. Firstly, the independent random vectors of d-dimensional normal distribution obtained after principal component analysis on the process parameter disturbance are as follows: ,here represents the number of random variables. The delays of gate units and interconnection lines can be expressed in the form of second-order random Hermite orthogonal polynomial expansion based on these random variables, namely

[0030] (1)

[0031] in express Dimensional Hermite random orthogonal polynomials. For the specific form of Hermite orthogonal polynomials, see the paper "Stochastic Analysis of Inner Link Performance in Existing Pro...

Technical field:

[0001] The invention belongs to the field of integrated circuits, and in particular relates to a statistical static timing analysis method based on an improved self-adaptive random configuration method. Background technique

[0002] As the feature size of integrated circuits enters the nanometer level, the impact of process deviation on circuit performance is becoming more and more serious. In order to analyze the impact of process deviation on the timing of integrated circuits, Statistical Static Timing Analysis (SSTA) was introduced into timing analysis. "Statistical Time-Series Analysis: From Fundamentals to State-of-the-art", 27(4), pp. 589-607. In statistical static timing analysis, due to the influence of random process deviation, the delay of the circuit is no longer a definite value, but a random variable with a certain distribution. Statistical static timing analysis analyzes circuit timing by passing a random distribution of delays through the ci...

Examples

Embodiment Construction

[0028] The present invention is based on the statistical static timing analysis method of the improved adaptive random configuration method MASCM such as figure 1 shown, including the following steps:

[0029] step one : Establish the statistical delay model of gate unit and interconnection line based on random orthogonal polynomial. Firstly, the independent random vectors of d-dimensional normal distribution obtained after principal component analysis on the process parameter disturbance are as follows: ,here represents the number of random variables. The delays of gate units and interconnection lines can be expressed in the form of second-order random Hermite orthogonal polynomial expansion based on these random variables, namely

[0030] (1)

[0031] in express Dimensional Hermite random orthogonal polynomials. For the specific form of Hermite orthogonal polynomials, see the paper "Stochastic Analysis of Inner Link Performance in Existing Pro...

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