CN116205182A - Yield estimation method and system based on important boundary sampling - Google Patents

Abstract

The invention discloses a yield estimation method and a system based on important boundary sampling, wherein the method comprises the following steps: step S1: exploring all possible failure regions in the integrated circuit process parameter space; step S2: establishing a boundary model for each failure area, and describing the boundary of each failure area; step S3: importance sampling is performed by using the generated boundary model, and yield estimation is performed according to the importance sampled samples. By adopting the technical scheme of the invention, the problem of high-dimensional yield estimation can be solved.

Description

Yield estimation method and system based on important boundary sampling

Technical Field

The invention relates to the technical field of integrated circuit yield estimation, in particular to a yield estimation method and a system based on important boundary sampling.

Background

As integrated circuits enter the nanoera, process parameter variations have become a major challenge for design and fabrication. Circuit performance parameters may not meet design specifications due to many uncertainties in the manufacturing process of photolithography, chemical Mechanical Polishing (CMP), etching, and the like. Algorithms that provide fast and accurate yield estimates are urgently sought, and circuits that are particularly important are large-scale, requiring expensive and high-precision simulations. Yield, defined as the percentage of a circuit that can operate at an acceptable performance level, is an important indicator for measuring the robustness of a circuit design. As feature sizes expand toward physical limits, variations due to uncertainty are becoming an increasing concern in integrated circuit design. This typically requires statistical methods, such as yield analysis of the monte carlo method, but is very time consuming. Worse still, highly repeatable unit devices, such as SRAM, generally require extremely low failure rates, i.e., higher yields, to ensure reasonably moderate yields of the entire chip. Of these circuits, SRAM yield analysis is most interesting. In each technology node, the design of SRAM is subject to the most stringent design rules to help meet increasingly stringent performance specifications and higher levels of integration. In order to evaluate the yield of the SRAM unit, the simple Monte Carlo method directly samples the parameter space, but the convergence rate is extremely poor. The reason is that most of the sampling points are in the feasible region, and only a very small part of the sampling points are in the failure region. Therefore, a more intelligent yield estimation method is urgently needed.

Existing SRAM yield analysis methods can be broadly divided into two categories: a Monte Carlo method based on important sampling and a non-Monte Carlo method based on boundary search. The key idea of important sampling is to sample the dead region with a warped Probability Density Function (PDF) rather than the original PDF of process variation. For these methods, a good distortion PDF passOften circuit specific, this presents challenges for versatility, particularly in the areas of multiple failures due to multiple performance specifications. At the same time, a sample is drawn in the deformed PDF (typically 10 ³ ～10 ⁴ Individual samples) is still expensive because each sample should be evaluated by SPICE simulation. It is desirable to further reduce the simulation cost of SPICE. This is particularly important if yield estimates need to be inserted into the yield optimization flow, as yield estimates need to be performed multiple times.

Compared with the important sampling method, the boundary searching method comprises the following steps: YNESS method and QuickYIeld method.

YENSS: a nonlinear surface local search method. It can handle nonlinear performance constraints and non-convex yield volumes. It starts from a nominal performance space and a tangential search along the surface boundary to find the surface boundary points provides good accuracy without using the monte carlo method. However, YENSS still requires multiple simulations to locate each point on the surface boundary due to the local search. Moreover, each step requires calculation sensitivity, and in a performance constraint equation containing a large number of parameters, calculation such as derivation and the like greatly increases calculation time cost, which is very unfavorable for solving high-dimensional yield estimation.

QuickYield: the rapid global searching method is an effective parameter yield calculating method. The QuickYield application Qu Miandian looks up and global searches to locate points on the surface boundaries. The performance constraints are first included into a Differential Algebraic Equation (DAE) describing the circuit and an augmented system of equations is built. By solving the augmentation system equation, points on the surface boundaries within the parametric domain can be determined. And then estimating the yield according to the obtained surface boundary. Fast returns can help simulate extremely expensive problems. The experimental results show that with the same accuracy, it is several times faster than YENSS.

The boundary search method attempts to search for the entire fault boundary. Once the boundaries are constructed, yield can be obtained by calculating the volume of the failure zone without the need for time-consuming SPICE simulations. However, these methods cannot address the high-dimensional problem of having multiple process variables because searching the entire fault boundary in the process parameter space is extremely complex. Therefore, a method capable of handling the high-dimensional estimated yield is urgently needed.

Disclosure of Invention

The invention aims to solve the technical problem that a yield estimation method in the prior art cannot process a plurality of process variables, and provides a yield estimation method and a yield estimation system based on important boundary sampling.

The embodiment of the invention provides a yield estimation method based on important boundary sampling, which comprises the following steps:

step S1: exploring all possible failure regions in the integrated circuit process parameter space;

step S2: establishing a boundary model for each failure area, and describing the boundary of each failure area;

step S3: importance sampling is performed by using the generated boundary model, and yield estimation is performed according to the importance sampled samples.

In the embodiment of the present invention, step S1 includes:

step S11: solving an optimal mean shift vector X by a solving formula (8) _r1 And solve for X according to equation (9) _r2 Thereby defining a basic area, wherein the basic area is the basic area explored by a failure area and is the area in two superballs, and the radius of the basic area is I X _r1 I to X _r2 ||，

Wherein X is ⁺ And X ^- Respectively the maximum value and the minimum value of X;

prob∈[e ^-4 ,e ^-2 ]

step S12: searching the centers of failure areas within the basic area one by one, wherein the failure areas are defined as hyper-spheres with the centers of Xi and the radius of R, namely

LFR _i :||X—X _i ||＜R，

Where i is the number of failure zones LFR and R represents the radius of the failure zone.

In the embodiment of the present invention, step S2 includes:

step S21: according to the influence of the function variable and the independent variable on the circuit performance, determining the variable and the independent variable which influence the circuit performance;

step S22: generating initial training samples satisfying constraint (11) and generating test samples,

f(X)—f _spec ＝0 (11)，

wherein f _spec Is a circuit specification, X is a variable and an independent variable affecting circuit performance;

step S23: adding a new training sample meeting the constraint condition (11) into the training sample set;

step S24: training a current boundary model;

step S25: testing the current boundary model if the accuracy is greater than a given threshold CC _BM Then go to step S26; otherwise, please go to step S22;

step S26: and obtaining a trained boundary model.

In embodiments of the present invention, for a given failure zone, the failure boundary may be described as a function of:

x _k ＝f _BM (x ₁ ，…，x _k-1 ，x _k+1 ，…x _D )＝f _BM (x _D-1 )

wherein x= [ X ] ₁ ,x ₂ ,…,x _D ] ^T Satisfying the constraint epsilon=1e-3||f _spec I and ε=1e-3 x i f _spec ||。

In the embodiment of the present invention, step S3 includes:

first, for each failure region, an optimal mean shift vector X within that region is determined by solving equation (8) based on the corresponding boundary model _opt,i ；

Then, a probability density function q (X) of the warp is defined as follows:

wherein t is the number of failure areas, alpha _i Is a weight coefficient;

finally, samples are generated from the warped probability density function q (X) to evaluate the failure rate.

Further, in the embodiment of the present invention, a yield estimation system based on important boundary sampling is provided, and when estimating the yield of the integrated circuit, the yield estimation method based on important boundary sampling is adopted.

Compared with the prior art, the yield estimation method and system based on important boundary sampling, provided by the invention, have the advantages of combining the prior important sampling method and boundary searching method, avoiding the problems existing in both the important sampling method and the boundary searching method, and compared with the prior important sampling method, the probability density function based on distortion is based on all possible failure areas (instead of the most possible failure areas), so that all potential failure conditions can be sampled; compared with the traditional boundary searching method, the method only explores possible failure boundaries (instead of the whole failure boundary), so the method has the potential of being applied to high-dimensional problems; at the same time, the present invention further accelerates the method using alternative models. Experimental results under the high-dimensional process parameter space and multi-performance application show that compared with the existing method, the method has stronger universality and is suitable for the yield analysis problem of a multi-failure area; meanwhile, the calculation speed of the method is much faster than that of the existing method, and the calculation time cost is saved.

Drawings

Fig. 1 (a), (b), and (c) are schematic diagrams of three methods of the prior art, namely, the monte carlo method, the importance sampling method, and the boundary search method, respectively.

Fig. 2 is a process schematic diagram of a yield estimation method based on importance boundary sampling according to an embodiment of the present invention.

Fig. 3 is a flowchart of a yield estimation method based on importance boundary sampling according to an embodiment of the present invention.

Fig. 4 is a schematic diagram of searching for the LFR according to an embodiment of the present invention, where fig. 4 (a) is a schematic diagram of a basic area, fig. 4 (b) is a schematic diagram of performing LFR search for the first time, fig. 4 (c) is a schematic diagram of performing LFR search for the second time, and fig. 4 (d) is a schematic diagram of deleting the first LFR.

FIG. 5 is a schematic diagram of a population-based optimization algorithm solving optimization formula (8) in an embodiment of the invention.

FIG. 6 is a flow chart of generating new training samples in an embodiment of the invention.

Fig. 7 is a schematic diagram of multi-mean shift vector sampling according to an embodiment of the present invention, wherein fig. 7 (a) is a three-dimensional schematic diagram and fig. 7 (b) is a two-dimensional schematic diagram.

Fig. 8 is a schematic diagram of two special conditions for setting the LFR range in the embodiment of the present invention, fig. 8 (a) is a schematic diagram of LFR not including the fault region completely, and fig. 8 (b) is a schematic diagram of LFR including a plurality of actual fault regions.

FIG. 9 is a schematic diagram of constructing a two-dimensional failure zone in an embodiment of the present invention.

Detailed Description

The performance parameters of SRAM vary with its process parameters including gate length, oxide thickness, and threshold voltage, among others.

Let x= [ X ] ₁ ,x ₂ ,…,x _D ] ^T Is a variation of the D-dimensional random variable modeling process, whose joint PDF (probability density function) can be defined as p (X), as shown in equation (1). These random variables include variations in gate length, oxide thickness, threshold voltage, and the like. Typically, X is a multivariate normal distribution. Without loss of generality, we further assume the random variable [ X ] in vector X ₁ ,x ₂ ,…,x _D ]Is a standard positive independent of each otherState variables (i.e. mean and unit variance are zero), then

The failure rate of an SRAM can be expressed mathematically as:

for ease of description, the failure rate in equation (2) is equivalently defined as:

wherein I (X) is an index function:

Ω denotes a failure zone.

The following three methods for estimating SRAM yield in the prior art: the monte carlo method, the importance sampling method, and the boundary searching method are described.

A. Monte Carlo method

Conventionally, failure rate P _f Can be estimated by the monte carlo method as shown in fig. 1 (a). The key idea of the monte carlo method is to extract N random samples { X) from p (X) ⁽¹⁾ ,X ⁽²⁾ ,…,X ^(N) Circuit performance was then obtained by SPICE simulations. From the results of SPICE simulation, an index function can be calculated

{I(X ⁽¹⁾ ),I(X ⁽²⁾ ),…,I(X ^(N) ) }. Finally, the failure rate formula of the Monte Carlo method is as follows:

B. importance sampling method

The importance sampling method is generally implemented in two steps:

first, a deformed PDF q (X) is generated as shown in formula (5):

second, M sampling points { X } are extracted from q (X) ⁽¹⁾ ,X ⁽²⁾ ,…,X ^(M) And by estimating the failure rate as follows:

the key to the important sampling method is how to generate the deformed PDF q (X). Theoretically, the optimal PDF q (X) with the greatest estimation accuracy (only one sample is required) is as follows:

in practical applications, it is not feasible to generate an optimal PDF, but we can note from equation (7) that the samples should be generated in the most likely failure region. The existing important sampling method is mainly based on the idea. For example, using the optimal mean shift vector x= [ X ₁ x ₂ ] ^T To determine the most likely failure area, and the deformed PDF q (X) is based on it, as shown in fig. 1 (b). Finally, from the samples generated from q (X), the failure rate can be calculated by equation (7). For the importance sampling method, a good deformed PDF is often circuit-specific, which is a general challenge, especially in the case of multiple fault areas. As shown in fig. 2 (b), the fault region also has a great influence on the reliability of the circuit. However, these regions are difficult to sample in the deformed PDF q (X).

Meanwhile, in the existing method, a sample required for the deformed PDF q (X)Is still expensive (typically 10 ³ ～10 ⁴ Samples), each sample should be generated by SPICE simulation. Since SPICE simulation times are the current bottleneck, the computational cost of SRAM yield estimation still needs to be reduced.

C. Boundary searching method

As shown in fig. 1 (c), another existing method attempts to search for the ratio of the entire fault boundary and the failed region of the calculated area (or volume) in the entire parameter space, which does not have time-consuming monte carlo simulation, greatly improving efficiency, as compared to the sample-based method.

As shown in fig. 2 and 3, the present invention combines the advantages of the prior art importance sampling method and the boundary searching method to provide a new importance boundary sampling method, which includes steps S1-S3, and is described below.

Step S1, finding possible fault regions Exploring Likely Failure Regions (LFRs), including basic region definition and LFRs exploration. The exploration process is shown in fig. 4. Specifically, step S1 includes steps S11 to S12, which are described below.

Step S11, defining a basic area.

The basic region is the region explored for LFRs, defined as the region within two superspheres, with radius of ||X _r1 I to X _r2 I. As shown in fig. 4 (a). X is shown as _r1 Is the optimal mean shift vector. As can be seen from the formula (1), the maximum failure probability density occurs when the distance from the failure area to the origin is minimum. Thus, by solving equation (8), the optimal mean shift vector X can be determined _r1 ：

/>

Wherein X is ⁺ And X ^- Respectively the maximum value and the minimum value of X;

optimizing boundary X ^± Should cover the entire variation space (e.g., X ^± = ±4 sigma). In determining X _r1 After that, the processing unit is configured to, X _r2 The base should be large enough to be a baseOther fault conditions are difficult to occur in this region. From equation (8), X _r2 The I can be determined as

prob∈[e ^-4 ,e ^-2 ]

I.e. ||X _r2 The sampling probability of the region beyond the value is Prob, which is smaller than the value X _r1 Sampling probability of regions other than. In practice, prob can be derived from 1e ^-4 To 1e ^-2 Is selected.

Since the present invention only seeks LFR (rather than to obtain an exact value of circuit performance), approximation of circuit performance is important for accelerating analysis. To speed up the Xr1 calculation process, a uniformly distributed latin-hypercube sampling method is used in the search space X to generate samples. Typically, the number of initial samples may be selected between 200 and 400. The circuit performance, i.e. I (X), can be obtained through SPICE simulation, and can be quickly calculated due to the fact that the sampling times are not large. Equation (1) is essentially a global optimization problem. The best class of algorithms to solve the global optimization is the overall-based optimization algorithm. In general, many population-based optimization methods, such as genetic algorithms and particle swarm algorithms, may be used. As shown in fig. 4. First, in each iteration t, a population [ X ] will be generated ₁ (t)，X ₂ (t)，...，X _N (t)]. Each individual will then pass SPICE simulations. Next, the population will be updated according to the algorithm, including mutation, crossover and selection, and then the next iteration is performed until the optimal individual meets the convergence criteria. The optimal solution can be obtained through a population optimization algorithm, and the optimal solution is Xr1.

The maximum failure probability density occurs when the distance from the failure area to the origin is minimum. Thus, by solving equation (8), the optimal mean shift vector Xr1 can be determined, and after Xr1 is determined, xr2 can be determined according to equation (9).

Step S12: the search for LFRs begins.

After defining the base region, LFRs may be generated therefrom. As shown in fig. 4 (b) - (d), the center Xi of each LFR is searched in turn by repeatedly solving the optimization formula (8). When an optimal solution is found, the surrounding fault area is removed and defined as the acceptance area. Then, by repeating the optimization, other centers of the LFR can be explored one by one within the base region. LFR is defined as a hyper-sphere centered at Xi and having a radius R, i.e

LFR _i :||X-X _i ||<R (10)

Where i is the number of LFRs. R represents the radius of the LFR.

Regarding the calculation of R, in order to increase efficiency, it should be ensured that R is large enough so that most of the samples in step S3 can be created within the corresponding LFR (i.e. the samples can be evaluated by a boundary model). Typically, as shown in fig. 4, one LFR will interpret one actual failure zone. However, since R is preset, in the embodiment of the present invention, two special conditions are set as shown in fig. 8. Condition 1: in fig. 8 (a), the actual failure area is large, so the LFR does not fully contain it. Condition 2: in fig. 8 (b), the actual fault areas are small and overlap, so the LFR contains multiple actual fault areas.

In the embodiment of the present invention, when the condition 1 occurs, the actual fault area is regarded as a plurality of fault areas, and the other parts will be discussed in step S1. Accordingly, when condition 2 occurs, the actual fault region will be considered as one fault region. Since the boundary can be precisely described in step S2, these two special conditions can be solved in the same manner as the conventional conditions.

Step S2: boundary modeling (Boundary Modeling), which specifically comprises the steps of:

step S21: according to the influence of the function variable and the independent variable on the circuit performance, determining the variable and the independent variable which influence the circuit performance;

step S22: generating initial training samples satisfying the constraint (12) and generating test samples,

f(X)—f _spec ＝0 (11)，

wherein f _spec Is a circuit standard, X is a shadowVariables and arguments that sound circuit performance;

step S23: adding a new training sample meeting the constraint condition (11) into the training sample set;

step S24: training a current boundary model;

step S25: testing the current boundary model if the accuracy is greater than a given threshold CC _BM Then go to step S26; otherwise, please go to step S22;

step S26: and obtaining a trained boundary model.

After step S1 explores LFRs, step S2 will describe the failure boundaries of each region more precisely. The boundaries of the partitioned acceptance area and the failure area may be described by a performance constraint (11). In practice, however, since the boundary points cannot be precisely obtained, the constraint is approximated using the following equation (12):

f(X)-f _spec ≤ε (12)

wherein ε=1e-3 _spec ||。

For a given LFR, the fault boundary may be described as a function of:

x _k ＝f _BM (x ₁ ，…，x _k-1 ，x _k+1 ，…x _D )＝f _BM (x _D-1 ) (13)

wherein x= [ X ] ₁ ,x ₂ ,…,x _D ] ^T The constraint condition (12) is satisfied. I.e. selecting a process variable x _k As a function, other process variables are arguments describing failure boundaries. The function variable x should be selected _k As the process parameter with the greatest influence on the circuit performance, to avoid the independent variable X _D-1 Is a multiple of (1). For example, when embodiments of the present invention solve the problem shown in FIG. 9, x should be selected separately ₂ And x ₁ As a function variable of the upper LFR and the right LFR to avoid multiple solutions. In an embodiment of the invention, a gaussian process (kriging) model is used as an alternative model to describe the function (13).

Model predictive function value x _k The mean μ and variance σ are random variables. Through several training samples

The constraint (12) is satisfied and by setting the derivative of the likelihood function to 0 and solving the equation, the optimal values of μ and σ are obtained as follows:

where N is the number of training samples, I is the N x 1 unit vector, and R is the gaussian correlation matrix between training samples.

Compared with the traditional modeling method taking circuit performance as a function variable, the boundary modeling of the embodiment of the invention adopts one of the process parameters as a function, and can well describe the boundary. However, the modeling method of the embodiment of the present invention brings two problems: 1) How to effectively generate training samples, so that the number of training samples can be minimized; 2) How each training sample satisfies the constraint (12).

To address these problems, embodiments of the present invention propose an adaptive training process. The key idea is that each new training sample is generated gradually during the training process. As long as the accuracy of the model meets the convergence condition, the training process is stopped, so that the training sample can be minimized.

First, some initial training samples need to be generated. Initial training samples are generated using a latin-hypercube sampling method that is uniformly distributed in the search space. In practice, the number of initial training samples may be chosen from between 20 and 50, since the following training samples will be generated step by step.

Next, for training space X _D-1 ＝[x ₁ ,x ₂ ,…,x _K-1 ,x _K+1 ,x _D ] ^T Each new training sample

Should be the same as the generated sample set +.>

In contrast, the generation is performed at the position with the longest distance. For this purpose, a flow chart as shown in FIG. 6 is created +.>

First, as shown in fig. 6 (b), the training space is adaptively meshed through the delaunay triangulation algorithm, and each generated sample is connected with its natural neighbors. The triangle with the largest area is selected as shown in fig. 6 (c). Then, the center of gravity of the selected triangle is calculated as +.>

As shown in fig. 6 (d). The iterations may generate the following training samples, as shown in fig. 6 (e) - (h). This method can be easily generalized to high-dimensional X _D-1 Is a kind of medium.

In order to meet the constraint condition (12) of each training sample, the embodiment of the invention provides a searching method based on spline interpolation. For each fixed argument X _D-1 Or by SPICE simulation search of function variable x _k Calculating circuit performance, and performing spline interpolation to find expected x meeting constraint _k . Finally, the iteration should stop under appropriate convergence conditions.

In addition to training samples, embodiments of the present invention generate a set of test samples near the boundary. Typically, the number of test samples may be selected from between 100 and 300. In each iteration, these test samples are used to verify the accuracy of the currently trained boundary model. When the percentage of test samples accurately predicted by the boundary model is greater than a given threshold CC _BM When the iteration stops.

In the embodiment of the invention, CC is adopted _BM As a convergence condition for boundary modeling. When the percentage of accurately predicted test samples is greater than CC _BM When the iteration stops. As to how to select CC _BM Different CCs from 90% to 100% may be used _BM Testing was performed. After obtaining the failure rate, the failure rate is obtained relative to the CC _BM Error in the value. Can be according to the actual needsDetermination of CC _BM . In general practice, CC _BM The value of (2) should be from 95% to 100%.

Compared with the traditional boundary modeling method, the modeling method provided by the embodiment of the invention has the advantages that the modeling method can be divided into two parts. First, embodiments of the present invention do not explore all of the boundaries of the entire region, but only those boundaries that are located in the LFR, which would significantly reduce the time cost. Second, each new training sample is at the longest distance compared to the sample set generated by the delaunay triangulation algorithm, avoiding wastage in characterizing the boundary, and thus improving efficiency.

Step S3: multiple mean shift vector importance sampling.

After a boundary model is established for each LFR, importance samples can be taken using these generated boundary models. To consider all LFRs, embodiments of the present invention propose the following multi-mean-shift vector importance sampling method. First, for each LFRI, an optimal mean shift vector X within the region is determined by solving equation (8) based on the corresponding boundary model _opt,i . Since each LFR is much smaller than the area explored in the first stage, the corresponding optimization problem is easier to solve than the optimization in step S1. The deformed PDF q (X) is defined as:

wherein t is the number of LFRs, alpha _i Is a weight coefficient.

As shown in fig. 7, equations (15) and (16). First alpha _i The sum of (2) is 1 to ensure that the total probability of q (X) is 1. Meanwhile, X is obtained from the formula (1) _opt,i The smaller the sample generated in this failure zone, the more samples. Next, samples may be generated from the deformed PDF q (X) to evaluate the failure rate. PDF q (X) due to distortionThe method can directly sample, and the embodiment of the invention adopts two steps to realize the sampling process. For each sample, first, one LFRi is randomly selected, and the probability of selection is proportional to the weight coefficient α. Then, according to PDF p (X-X _opt,i ) Samples are randomly generated from the region. Finally, for each sample, I (X) is calculated from the boundary model to which the sample belongs. To when the sample is within the boundary, I (X) =0; otherwise, I (X) =1. If there is no region to which the sample belongs, then SPICE simulation will be used to calculate I (X).

Failure rates can be obtained by sampling the importance of the multi-mean shift vector provided by the embodiment of the invention, and the sampling considers all possible failure areas.

Further, in the embodiment of the present invention, a yield estimation system based on important boundary sampling is provided, and when estimating the yield of the integrated circuit, the yield estimation method based on important boundary sampling is adopted.

In summary, the yield estimation method and system based on important boundary sampling, combined with the advantages of the existing important sampling method and boundary searching method, avoid the problems existing in both methods, and compared with the traditional important sampling method, the probability density function of distortion is based on all possible failure areas (instead of the most possible failure areas), so that all potential failure conditions can be sampled; compared with the traditional boundary searching method, the method only explores possible failure boundaries (instead of the whole failure boundary), so the method has the potential of being applied to high-dimensional problems; at the same time, the present invention further accelerates the method using alternative models. Experimental results under the high-dimensional process parameter space and multi-performance application show that compared with the existing method, the method has stronger universality and is suitable for the yield analysis problem of a multi-failure area; meanwhile, the calculation speed of the method is much faster than that of the existing method, and the calculation time cost is saved.

The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (6)

1. The utility model provides a yield estimation method based on important boundary sampling, which is characterized by comprising the following steps:

step S1: exploring all possible failure regions in the integrated circuit process parameter space;

step S2: establishing a boundary model for each failure area, and describing the boundary of each failure area;

step S3: importance sampling is performed by using the generated boundary model, and yield estimation is performed according to the importance sampled samples.

2. The method for estimating a yield based on important boundary sampling according to claim 1, wherein step S1 comprises:

step S11: solving an optimal mean shift vector X by a solving formula (8) _r1 And solve for X according to equation (9) _r2 Thereby defining a basic area, wherein the basic area is the basic area explored by a failure area and is the area in two superballs, and the radius of the basic area is I X _r1 I to X _r2 ||，

Wherein X is ⁺ And X ^- Respectively the maximum value and the minimum value of X;

prob∈[e ^-4 ,e ^-2 ]

step S12: searching the centers of failure areas within the basic area one by one, wherein the failure areas are defined as hyper-spheres with the centers of Xi and the radius of R, namely

LFR _i ：||X-X _i ||＜R，

Where i is the number of failure zones LFR and R represents the radius of the failure zone.

3. The method for estimating a yield based on important boundary sampling according to claim 2, wherein step S2 comprises:

step S21: according to the influence of the function variable and the independent variable on the circuit performance, determining the variable and the independent variable which influence the circuit performance;

step S22: generating initial training samples satisfying constraint (11) and generating test samples,

f(X)-f _spec ＝0 (11)，

wherein f _spec Is a circuit specification, X is a variable and an independent variable affecting circuit performance;

step S23: adding a new training sample meeting the constraint condition (11) into the training sample set;

step S24: training a current boundary model;

step S25: testing the current boundary model if the accuracy is greater than a given threshold CC _BM Then go to step S26; otherwise, please go to step S22;

step S26: and obtaining a trained boundary model.

4. The method for estimating a yield based on important boundary sampling as claimed in claim 3,

for a given failure zone, the failure boundary can be described as a function of:

x _k ＝f _BM (x ₁ ，…，x _k-1 ，x _k+1 ，…x _D ）＝f _BM （x _D-1 ）

wherein x= [ X ] ₁ ,x ₂ ,…,x _D ] ^T Satisfying the constraint epsilon=1e-3||f _spec I and ε=1e-3 x i f _spec ||。

5. The method for estimating a yield based on important boundary sampling according to claim 4, wherein step S3 comprises:

first, for each failure region, an optimal mean shift vector X within that region is determined by solving equation (8) based on the corresponding boundary model _opt,i ；

Then, a probability density function q (X) of the warp is defined as follows:

wherein t is the number of failure areas, alpha _i Is a weight coefficient;

finally, samples are generated from the warped probability density function q (X) to evaluate the failure rate.

6. A yield estimation system based on important boundary sampling, wherein the yield estimation method based on important boundary sampling according to any one of claims 1-5 is used for estimating the yield of an integrated circuit.

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