CN120317199B - Sequencing method for accelerating analysis of yield of integrated circuit under complex constraint condition - Google Patents

Abstract

The invention belongs to the field of integrated circuit yield analysis, and particularly relates to a sequencing method for accelerating the analysis of the integrated circuit yield under complex constraint conditions. A sequencing method for accelerating the analysis of the yield of integrated circuit under complex constraint condition includes such steps as comparing the judging parameters with the reference parametersThe evaluation indexes of the system are respectively represented by the branch judging functions, the total judging function is a logic combination of the branch judging functions, normalization is carried out on data so as to facilitate calculation, failure areas of a sample space are divided according to logic relations among linear inequality constraint conditions of all the branch judging functions of the total judging function, effective probability distances d between each sample data and failure boundaries are calculated, and simulation is carried out after the effective probability distances d are arranged according to the value of the effective probability distances d. The sorting method for the yield analysis effectively solves the problem that the HSMC method cannot be suitable for the limitation of the yield judgment under the complex multi-constraint condition.

Description

Sequencing method for accelerating analysis of yield of integrated circuit under complex constraint condition

Technical Field

The invention belongs to the field of integrated circuit yield analysis, and particularly relates to a sequencing method for accelerating the analysis of the integrated circuit yield under complex constraint conditions.

Background

With the continued advancement of integrated circuit fabrication processes, the feature sizes of chips have entered the nanometer scale, which places higher demands on the performance and yield of the chips. However, at the nanoscale, small fluctuations in process parameters can have a significant impact on the electrical performance of the transistor, resulting in a decrease in chip yield. Therefore, the electric Lu Liang rate is accurately estimated in the chip design stage, and the method has important significance for improving the overall efficiency of chip production and reducing the cost.

Currently, integrated circuit yield analysis at the design stage mainly depends on a Monte Carlo simulation method. The Monte Carlo simulation method is characterized in that the Monte Carlo simulation method randomly samples in a parameter space, utilizes circuit simulation tools such as SPICE to simulate a sample point, judges whether a circuit fails or not based on simulation results, and then estimates the electric Lu Liang rate by calculating the proportion of the number of failed sample points to the total number of samples. However, with the increase of chip integration, the simulation times required by the method based on Monte Carlo sampling increase exponentially, which results in huge consumption of computing resources and low efficiency. To solve this problem, various methods for accelerating monte carlo, such as a method based on a surrogate model, a method based on a classifier, and a method for sampling importance, have been proposed in researchers, but these theoretical research results are either questioned in terms of accuracy and reliability (such as surrogate model and classification method), or rely on a large-scale circuit (such as an importance adoption method) which is not suitable for high-dimensional parameters or can be truly applied to actual chip design, and there are few methods.

The rapid Monte Carlo method (HSMC) is a sequencing simulation method based on a substitution model, can maintain the same precision as a classical Monte Carlo method while accelerating simulation, and has the advantages of high precision, suitability for large-scale circuits and easiness in implementation. However, the biggest problem is that the method is only suitable for carrying out yield analysis on simple linear constraint conditions of single variables, and cannot be used for yield analysis on complex nonlinear constraint conditions of multiple variables. The yield constraint condition in the real chip design is often a multi-variable nonlinear composite function, for example, parameters for judging failure are circuit delay, gain, power consumption and the like, and particularly, the judging function of the parameters is nonlinear constraint. The existing HSMC method cannot effectively process the requirements, and can only perform classical Monte Carlo simulation (simulate all samples), or split complex constraint conditions, and then perform HSMC simulation individually for each constraint condition one by one, so that the time of overall yield simulation analysis is increased, the efficiency of chip design optimization is reduced, and the comprehensive design optimization goal of PPA equalization cannot be realized.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides a sequencing method for accelerating the analysis of the yield of the integrated circuit under the complex constraint condition, which carries out logic equivalent deformation and normalization processing through a complex yield judgment function to divide a failure area, and then creatively introducing a directional probability distance to calculate the effective distance from the sample point to each failure area, and finally taking the directional probability distance value as the characteristic weight of sample sequencing, thereby effectively solving the limitation problem that the HSMC method cannot be suitable for the yield judgment of complex multi-constraint conditions.

In order to solve the technical problems, the invention adopts the following technical scheme that the sequencing method for accelerating the analysis of the yield of the integrated circuit under the complex constraint condition comprises the following steps:

s1, total judging function Equivalent variation of (a) for the decision parameterRespectively according to the evaluation index of (2)、......Wherein the expression of each partial decision function is the inequality of the parameter decision index, then the total decision functionLogical combinations of decision functions are determined for each partition. When a certain decision parameterIf the criterion of (2) is a nonlinear relation of a plurality of parameters, it divides the criterion into a decision functionFor the nonlinear inequality constraint, an equivalent variable S is defined and is equal to the partial decision functionIs a non-linear constraint expression of (2), then the score-decision functionEqual to the equivalent variable S, so that the partial decision functionThe transition is to a linear inequality constraint on the equivalent variable S. The total decision function is thenWhich translates into a logical combination of linear inequality constraints expressed by a number of fractional decision functions.

S2, data normalization processing, namely firstly calculating the value of the equivalent variable S, updating the value into a new sample data set D, and carrying out total judgment function on all sample data and all sample data in the sample data set DNormalizing the constant judgment values to obtain judgment parametersDimensionless values and normalized sample data values.

S3, dividing the failure area according to the total judging functionThe rule is that two constraint conditions connected by an AND operator are used and combined to form a failure area, two constraint conditions connected by an OR operator are used and respectively form an independent failure area, then the failure area A ₁、A₂......A_k can be obtained, and corresponding failure boundaries a ₁、a_2......a_k are respectively obtained according to the determined failure areas, wherein k is less than or equal to n.

S4, calculating the effective probability distance d from each sample data to the failure boundary, wherein the increasing direction of the failure probability is taken as the positive direction, and the effective probability distance d from each sample data to each failure region boundary is respectively d ₁、d₂ D _k, wherein the calculation rule of the directed distance d at the boundary of each failure area is that the failure area is formed by combining two constraint conditions, the directed distance d is the minimum value of the directed distances from the sample data point to the two failure boundaries, the failure area is formed by juxtaposing two constraint conditions, the directed distance d is the maximum value of the directed distances from the sample data point to the two failure boundaries, and the unique effective directed probability distance d corresponding to each sample data is calculated according to the priority relation of ' and ' or '.

S5, after the effective directional distances d are arranged according to the algebraic value, simulating, namely, after the effective directional probability distances d of the sample data obtained in the S4 are arranged according to the descending order of the algebraic value, the sample data with larger directional probability distances are sent to a Monte Carlo simulation algorithm module for simulation, the probability of failure is larger, and all failure samples are obtained according to the required precision condition.

Preferably, the normalization formula in step S2 is: (1) Wherein As the mean value of the sample,Is the sample bias.

Preferably, the direction of the increase of the failure probability in the failure area is taken as a positive direction, and the linear inequality of the corresponding partial judgment function is taken as a basis.

Preferably, in step S4, the sample data is located at a distance d from the failure boundary in each failure region ₁、d₂ D _k is the position of the point and the failure boundary a ₁、a₂ A _k.

Preferably, in step S4, the directional distance d of the sample data _Di in each failure area ₁、d₂ D _k, merging step by step according to the priority relation of 'and' then 'or', until an effective directed distance d is formed.

The method has the advantages that 1, a plurality of complex yield constraint conditions are subjected to equivalent simplified deformation, the complex yield constraint conditions are converted into a plurality of linear constraint conditions, complex high-dimensional curved surface distance calculation is successfully converted into one-dimensional data calculation, a problem processing mode is greatly simplified, mass calculation operations are saved, 2, directional probability distances are creatively introduced to serve as characteristic weights of sample ordering in an HSMC (high speed Monte Carlo) simulation algorithm module, the vector direction points to the increasing direction of the sample failure probability in space, and the method has the characteristic that the larger the value of a code is, the higher the failure probability is represented. Then, by calculating the directional probability distances between the sample points and the boundaries of a plurality of failure areas and selecting the effective distances as sample sorting weights according to the logic relations among the failure areas, the limitation that the traditional HSMC method cannot simultaneously perform sample simulation of multi-target complex yield constraint conditions is overcome; and 3, when the yield constraint condition is a simple single-target open interval, the method is degraded into a traditional method for sorting according to the size of the single-target predicted value, and the traditional method has compatibility and equivalence.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram of a three-dimensional quadric constraint boundary when the constraint condition is three-dimensional;

FIG. 3 is a schematic representation of the transformation of FIG. 1 into a one-dimensional linear constraint boundary in accordance with the present invention;

FIG. 4 is a schematic illustration of a failure zone A1 formed in accordance with the present invention;

FIG. 5 is a schematic illustration of a failure zone A2 formed in accordance with the present invention;

FIG. 6 is a schematic illustration of the calculation of directional distances according to the present invention;

FIG. 7 is a schematic representation of the calculated effective distance of the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings. The following examples are only for the purpose of more clearly illustrating the structure of the present invention.

For a sense amplifier circuit commonly used in the design of a memory chip, we will usually examine its delay #) Minimum resolution voltage%) Gain [ ]) And dynamic power consumption (P). The failure determination criterion is defined as that the circuit is determined to be failed when the circuit delay is greater than 55ps and the gain is less than 65dB, and that the circuit is determined to be failed regardless of other indexes if the dynamic power consumption of the circuit is greater than 3 mW. Since the dynamic power consumption of the sense amplifier is expressed as: (2) Wherein P _S is the static power consumption, K is the constant related to the circuit structure, and the yield determination function is a composite function containing a plurality of constraint conditions and nonlinear constraint. At this time, the yield analysis cannot be accelerated by using a certain variable predictive value sequence through the existing HSMC algorithm, because the larger the predictive value of the delay is, the smaller the gain value is not necessarily, and vice versa, and the smaller the value of the gain value is, the smaller the dynamic power consumption is, and the more dissatisfied Is the failure condition of (2).

Therefore, as shown in FIG. 1, the method for ordering the yield analysis of the integrated circuit under the acceleration complex constraint condition comprises the following steps of a first step of an overall judging functionEquivalent variation of (a) for the decision parameterRespectively according to the evaluation index of (2)、......Wherein the expression of each partial decision function is the inequality of the parameter decision index, then the total decision functionFor each score determining function、......Is a logical combination of (a) and (b). When a certain decision parameterIf the criterion of (2) is a nonlinear relation of a plurality of parameters, it divides the criterion into a decision functionFor the nonlinear inequality constraint, an equivalent variable S is defined and is equal to the partial decision functionIs a non-linear constraint expression of (2), then the score-decision functionEqual to the equivalent variable S, so that the partial decision functionTransitioning to a linear inequality constraint on the equivalent variable S, the overall decision function is thenWhich translates into a logical combination of linear inequality constraints expressed by a number of fractional decision functions.

Still taking the failure determination standard of the sense amplifier as an example, when the circuit delay is larger than a and the gain is smaller than b, if the dynamic power consumption of the circuit is larger than c, the circuit is determined to be failed regardless of other indexes, and X _1,X₂ and X ₃ are used for representing index delay, gain and static power consumption parameters respectively, the total yield determination function is expressed as a formula (3):

(3)

Wherein the method comprises the steps of For a given constant according to design specifications, e.g.K is a constant related to a circuit design structure and takes different values according to different process nodes, for example, in an SRAM circuit of a 90nm process, K generally takes 0.01-0.05, and in a 7nm process, K takes smaller value and generally takes 0.0005-0.002.

In the first step we need to determine the function for the totalEquivalent deformation was performed, expressed as formula (4):

(4)

Wherein the method comprises the steps of AndAre simple linear inequality constraints, whileIs a complex quadric constraint, in which we define an equivalent variable S and make it satisfy(5) ThenThe equivalent variation of (2) is converted from equation (4) to equation (6):

(6),

Then, the total decision function The logical combination of the constraint that translates into the linear inequality constraint expressed by the 3 partial decision functions can be expressed as equation (7):

(7)。

The second step of data normalization processing, namely firstly calculating the value of the equivalent variable S, updating the value into a new sample data set D, and carrying out total judgment function on all sample data and all sample data in the sample data set D Normalizing the constant judgment values to obtain judgment parametersDimensionless values and normalized sample data values.

Specifically into this embodiment, each sample point in the raw sample dataset is found in the sample dataset using equation (5)Substituting the corresponding values under the parameters to obtain the S value of each sample point, and obtaining the updated sample data set D. As shown in FIG. 2, the original complex constraintThe failure area boundary of (2) is a quadric surface, and the failure probability of the quadric surface cannot be compared simply according to the magnitude of a certain predicted sample value. However, by the equivalent processing in the first step and introducing a new sample variable S, this quadric boundary is linearized to obtain fig. 3, so that the failure probability can be compared according to the magnitude of the newly calculated predicted sample value S _i.

In fig. 2, let k=1 for 2 prediction sample dataAndAlthoughBut is provided withBut is smaller thanAnd thus cannot simply pass the prediction samplesOr alternativelyTo compare the failure probabilities.

In FIG. 3, after linearization, forFrom probability of failureThe samples may thus be ordered according to the size of the sample data S value.

Because the units of different indexes are different and cannot be compared directly, normalization processing is also needed for all sample data and constant judgment values in constraint conditions to obtain comparable dimensionless values. For example, if the circuit structure is unknown, and the data distribution of the simulation sample is also unknown, the data may be normalized using the Z-Score method, where the normalization formula is:

(1)

Wherein the method comprises the steps of As the mean value of the sample,Is the sample bias. It should be noted that not only the sample values but also the determination values in the respective constraints in the yield determination function are normalized, for example, for (3)The dimensionless value obtained by normalization processing according to the corresponding sample data set is。

Because ordering is only concerned with the relative size of the results, such processing does not change the ordering and accuracy of the final calculated results.

Dividing the failure area according to the total judging functionThe rule is that two constraint conditions connected by an AND operator are used and combined to form a failure area, two constraint conditions connected by an OR operator are used and respectively form an independent failure area, then the failure area A _1、A₂......A_k can be obtained, and failure boundaries a _1、a_2......a_k corresponding to the failure area A _1、A₂......A_k are respectively obtained according to the determined failure areas, wherein k is less than or equal to n.

In this embodiment, the total decision function is according to equation (7)Can be divided into two failure zones A ₁ and A ₂, where A ₁ isA ₂ isIf the boundary condition a ₁ of a ₁ needs to satisfy both a and b, the failure area A1 is shown as a blue part in fig. 4 of the specification, and the boundary condition of the failure area a ₂ is a ₂ and satisfies a ₂ > c, specifically shown as a pink part in fig. 5 of the specification.

Assuming a complex failure discriminant functionAccording to the priority order of ' NOT ' and ' NOT ' or ', the method can be divided into 3 failure areas, and according to the constraint condition of each failure area, three failure areas are obtained:

。

Calculating effective direction probability distance d from each sample data to failure boundary by taking the increasing direction of failure probability as positive direction, and for each sample data, the direction distance d1 and d2 at each failure region boundary is respectively The calculation rule of the effective directional distance d at the boundary of each failure area is that the effective directional distance d of the failure area formed by combining two constraint conditions is the minimum value of the directional distances from the sample data point to the two failure boundaries, the effective directional distance d of the failure area formed by juxtaposing two constraint conditions is the maximum value of the directional distances from the sample data point to the two failure boundaries, and the unique effective directional probability distance d corresponding to each sample data is calculated according to the priority relation of first and then or.

The directional probability distance is called because the direction of failure probability increase is regulated to be positive when the distance is calculated, and the coordinates of the sample data point in A1 are shown as [ ] as shown in figure 6) Whereas the failure area A1 in FIG. 6 is defined by two boundary conditionsA and< B combination composition, whereinA is represented by the blue region, and< B is represented by the orange region, two constraints need to be met simultaneously, i.e. blue and orange overlap in fig. 6. For the first conditionA, the direction in which the x ₁ axis increases in the coordinate system is the positive direction, so the directional distance d of the sample data point in the x ₁ axis direction _x1= -A. As can be seen from the figures of the drawing,Since d _x1 is a number greater than 0, the absolute value is greater, and the failure probability is higher as the direction is the same as the direction in which the failure probability increases. While the second failure condition in FIG. 6 is x ₂＜b_, in the coordinate systemThe direction in which the axis decreases is the direction in which the failure probability increases is the positive direction, so the sample data point isDirectional distance in axial direction d _x2 =b-As can be seen from FIG. 6, b < >Therefore, d _x2 is a value smaller than 0, which means that the direction is opposite to the increasing direction of the failure probability, and the larger the absolute value is, the smaller the failure probability is.

As shown in fig. 6 of the specification, the failure area A1 is formed byA and< B combined, the directed distance is the minimum of the directed distances of the sample data points to the two failure boundaries, i.e., d ₁=min(d_x1,d_x2).

For the failure area formed by logical OR, the effective directed distance is the maximum value of the directed distances from the sample data point to the two failure boundaries as long as the effective directed distance falls within any constraint condition. As shown in fig. 7 of the specification, the failure area A2 is formed by S > c, and the sample data point is (S _i), the directional distance d ₂=d_si of the sample data point in the S-axis direction. As is clear from the formula (7), A1 shown in fig. 6 and A2 shown in fig. 7 are in parallel relation, so that the effective probability distance d=max (d ₁,d₂) of the sample data point.

When the system consists of a plurality of logic relations, according to the priority relation of ' AND ' and ' then ' OR ', the unique effective probability distance d corresponding to each sample data is calculated by utilizing the rule of calculating the effective probability distance of two failure areas step by step

E.g. failure discrimination functionThe failure boundaries of the three failure zones are:

The sample data is obtained by obtaining the directional distances d _1、d₂ and d _3, in the failure areas of A1, A2, and A3, and the relation among A1, A2, and A3 is logical or, and the effective probability distance d=max (d _1,d₂,d₃). In this way, a unique one of the effective probability distances d for each sample data point is calculated.

In this step, the precondition that each failure region can be plotted under the same coordinate system is that normalization processing is performed.

And fifthly, after the effective directional distances d are arranged according to the algebraic value, simulating, namely, after the effective directional probability distances d of the sample data obtained in the fourth step are arranged according to the descending order of the algebraic value, sending the sample data into a Monte Carlo simulation algorithm module for simulation, wherein the larger the directional probability distance algebraic value is, the larger the failure probability is, and all failure samples are obtained according to the required precision condition.

Because the larger the effective direction probability distance d is, the larger the failure probability of the samples is, so that the samples with large failure probability can be preferentially simulated after sequencing, the simulation process is quickened, and all failure samples can be found more quickly.

The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.

Claims (5)

1. A sequencing method for accelerating analysis of yield of integrated circuits under complex constraint conditions is characterized by comprising the following steps:

s1, total judging function Equivalent variation of (a) for the decision parameterRespectively according to the evaluation index of (2)、......Wherein the expression of each partial decision function is the inequality of the parameter decision index, then the total decision functionLogic combinations for each of the score determination functions;

When a certain decision parameter If the criterion of (2) is a nonlinear relation of a plurality of parameters, it divides the criterion into a decision functionFor the nonlinear inequality constraint, an equivalent variable S is defined and is equal to the partial decision functionIs a non-linear constraint expression of (2), then the score-decision functionEqual to the equivalent variable S, so that the partial decision functionConverting to a linear inequality constraint on the equivalent variable S;

the total decision function is then Conversion into a number of partial decision functions、......Logical combinations of expressed linear inequality constraints;

s2, data normalization processing, namely firstly calculating the value of an equivalent variable S and updating the value into a new sample data set D;

For all sample data in sample data set D and the total decision function Normalizing the constant judgment values to obtain judgment parametersDimensionless values and normalized sample data values;

s3, dividing the failure area according to the total judging function The logical relationship between the linear inequality constraints of all the score decision functions of (a) divides the failure area of the sample space, the rule is:

Two constraint conditions connected with an AND operator are used, and the two constraint conditions are combined to form a failure area;

two constraints connected by an OR operator, wherein each constraint forms an independent failure area;

Obtaining a plurality of failure areas A ₁、A₂......A_k, and respectively obtaining corresponding failure boundaries a ₁、a_2......a_k according to the determined failure areas, wherein k is less than or equal to n;

S4, calculating the effective probability distance d from each sample data to the failure boundary, wherein the increasing direction of the failure probability is taken as the positive direction, and the effective probability distance d at each failure area boundary is respectively calculated for each normalized sample data ₁、d₂ D _k, and the calculation rule of the directed distance at each failure area boundary is as follows:

The failure area consists of two constraint conditions in a merging way, and the directed distance of the failure area is the minimum value of the directed distances from the sample data point to two failure boundaries;

the failure area consists of two constraint conditions in parallel, and the directed distance of the failure area is the maximum value of the directed distances from the sample data point to two failure boundaries;

According to the priority relation of 'and' then 'or', calculating a unique effective probability distance d corresponding to each sample data;

s5, after the effective probability distances d of the sample data obtained in the S4 are arranged in descending order of the values of the codes, the effective probability distances d are sent to a Monte Carlo simulation algorithm module for simulation, the larger the value of the effective probability distances is, the larger the failure probability is, and all failure samples are obtained according to the required precision conditions.

2. The method for accelerating the sequencing of the yield analysis of the complex constraint integrated circuit according to claim 1, wherein the normalization formula in the step S2 is: (1) Wherein As the mean value of the sample,Is the sample bias.

3. The method for accelerating the sequencing of the yield analysis of the complex constraint integrated circuit according to claim 1, wherein the failure area is based on a linear inequality of a corresponding score judgment function by taking a direction of increase of the failure probability as a positive direction.

4. The method for accelerating the sequencing of the yield analysis of the complex constraint integrated circuit of claim 3, wherein the sample data in step S4 is located at a distance d from the failure boundary in each failure area ₁、d₂ D _k is the position of the point and the failure boundary a ₁、a₂ A _k.

5. The method for accelerating the ordering of the yield analysis of the complex constraint integrated circuit according to claim 1, wherein the step S4 is characterized in that the directional distance d of the sample data in each failure area ₁、d₂ D _k, merging step by step according to the priority relation of 'and' then 'or', until an effective directed distance d is formed.