A ranking method to accelerate yield analysis of integrated circuits with complex constraints

Abstract

The present invention belongs to the field of integrated circuit yield analysis, and specifically relates to a ranking method for accelerating integrated circuit yield analysis under complex constraints. The method comprises the following steps: representing the evaluation indicators of the judgment parameter #imgabs0# using sub-judgment functions, where the overall judgment function is a logical combination of the sub-judgment functions; normalizing the data for ease of calculation; dividing the failure region of the sample space according to the logical relationship between the linear inequality constraints of all sub-judgment functions of the overall judgment function; and calculating the effective directed probability distance of each sample data to the failure boundary. d , according to the effective directed distance d The algebraic values ​​of the HSMC are arranged and then simulated. This sorting method for yield analysis effectively solves the limitation of the HSMC method that it is not applicable to yield determination under complex multi-constraint conditions.

Description

Technical Field

[0001] The present invention belongs to the field of integrated circuit yield analysis, and in particular relates to a sorting method for accelerating integrated circuit yield analysis under complex constraints. Background Art

[0002] With the continuous advancement of integrated circuit manufacturing processes, chip feature sizes have entered the nanometer range, placing higher demands on chip performance and yield. However, at the nanometer scale, even slight fluctuations in process parameters can significantly affect the electrical performance of transistors, leading to a decrease in chip yield. Therefore, accurately estimating circuit yield during the chip design phase is crucial for improving overall chip production efficiency and reducing costs.

[0003] Currently, integrated circuit yield analysis during the design phase primarily relies on Monte Carlo simulation methods. Monte Carlo simulation methods randomly sample points in parameter space and simulate the circuit using circuit simulation tools such as SPICE. Based on the simulation results, circuit failure is determined. The yield is then estimated by calculating the proportion of failed points to the total number of samples. However, with increasing chip integration, the number of simulations required by Monte Carlo sampling methods has increased exponentially, resulting in significant computational resource consumption and low efficiency. To address this issue, researchers have proposed various accelerated Monte Carlo methods, such as those based on surrogate models, classifiers, and importance sampling. However, these theoretical research results have either been questioned in terms of accuracy and reliability (e.g., surrogate models and classification methods) or rely on circuit characteristics or are unsuitable for large-scale circuits with high-dimensional parameters (e.g., importance sampling methods). Consequently, few methods have been truly applicable to practical chip design.

[0004] Among existing technologies that have been widely accepted and applied in the industry, the High-Speed ​​Monte Carlo method (HSMC) is a ranking simulation method based on surrogate models. It accelerates simulation while maintaining the same accuracy as the classic Monte Carlo method. It boasts high accuracy, applicability to large-scale circuits, and ease of implementation. However, its primary drawback is that it is only suitable for yield analysis of simple, single-variable linear constraints and cannot be applied to yield analysis of multivariable, complex, nonlinear constraints. Yield constraints in real-world chip designs are often multivariable, nonlinear, composite functions. For example, failure criteria include circuit delay, gain, power consumption, and other parameters. In particular, some parameters have nonlinear constraint functions. Current HSMC methods cannot effectively address these requirements and can only perform classic Monte Carlo simulations (simulating all samples) or break down complex constraints and perform separate HSMC simulations for each constraint. This not only increases the overall yield simulation analysis time and reduces the efficiency of chip design optimization, but also fails to achieve the comprehensive design optimization goal of balanced performance per performance (PPA). Summary of the Invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a sorting method for accelerating the yield analysis of integrated circuits with complex constraints. This sorting method performs logical equivalent deformation and normalization processing on a complex yield determination function to divide the failure area. Then, it creatively introduces a directed probability distance to calculate the effective distance from the sample point to each failure area. Finally, the algebraic value of the directed probability distance is used as the feature weight for sample sorting, thereby effectively solving the limitation problem that the HSMC method is not applicable to yield determination with complex multi-constraint conditions.

[0006] To solve the above technical problems, the present invention adopts the following technical solution: a sorting method for accelerating yield analysis of integrated circuits with complex constraints, comprising the following steps:

[0007] S1: Total decision function Equivalent deformation: for the judgment parameters The evaluation indexes are respectively based on the judgment function 、 ...... The expression of each sub-determinant function is the inequality of the parameter determination index, then the total determination function It is the logical combination of each judgment function. The judgment index is a nonlinear relationship between multiple parameters, then its judgment function is For nonlinear inequality constraints, define an equivalent variable S And make it equal to the judgment function The nonlinear constraint expression of Equal to the equivalent variable S , so the judgment function Transformed into the equivalent variable S Linear inequality constraints. Then the total decision function Converted into a logical combination of linear inequality constraints expressed by several decision functions.

[0008] S2: Data normalization: First, the equivalent variables S The value of is calculated and updated to the new sample data set D; all sample data and the total decision function in the sample data set D are The constant judgment values ​​in are normalized to obtain the judgment parameters The dimensionless value and normalized sample data value of .

[0009] S3: Divide the failure area: according to the total judgment function The logical relationship between the linear inequality constraints of all the sub-determinant functions divides the failure area of ​​the sample space. The rule is: if two constraints are connected by the "and" operator, the two constraints are combined to form a failure area; if two constraints are connected by the "or" operator, the two constraints each form an independent failure area; the failure area can be obtained. A 1 、A 2 ...... A k ， According to the determined failure area, the corresponding failure boundaries are obtained respectively a 1 、a 2..... .a k ,in k≤n .

[0010] S4: Calculate the effective directed probability distance from each sample data to the failure boundary d : Taking the direction of failure probability growth as the positive direction, for each sample data ， The directed distances at the boundaries of each failure region are d 1 、d 2 d k ， And the directed distance at the boundary of each failure area d The calculation rule is: the failure area composed of two constraints is the directed distance dThe minimum value of the directed distance from the sample data point to the two failure boundaries; the failure area composed of two constraints in parallel, its directed distance d The maximum value of the directed distance between the sample data point and the two failure boundaries; according to the priority relationship of "and" first and "or", the unique effective directed probability distance corresponding to each sample data is calculated d .

[0011] S5: By effective directed distance d After arranging the algebraic values, simulation: the effective directional probability distance of each sample data obtained in S4 is d After being sorted in descending order by algebraic value, the samples are sent to the Monte Carlo simulation algorithm module for simulation. The sample data with a larger algebraic value of the directed probability distance has a greater probability of failure. According to the required accuracy conditions, all failed samples are obtained.

[0012] Preferably, the normalization formula in step S2 is: (1), where is the sample mean, is the sample bias.

[0013] Preferably, the direction of growth of the failure probability in the failure area is a positive direction, based on the linear inequality of the corresponding determination function.

[0014] Preferably, in step S4, the distance between the sample data in each failure region and the failure boundary is d 1 、d 2 d k The position of the point and the failure boundary a 1 、a 2 a k The directed difference between .

[0015] Preferably, the sample data in step S4 Di Directed distance within each failure area d 1 、d 2 d k , according to the priority relationship of "and" first and "or" later, merge step by step until a valid directed distance is formed d .

[0016] The beneficial effects of the present invention are: 1. Multiple complex yield constraints are equivalently simplified and transformed into multiple linear constraints, successfully transforming the complex high-dimensional surface distance calculation into one-dimensional data calculation, greatly simplifying the problem handling method and saving massive computing operations; 2. Creatively introducing directed probability distance as the feature weight for sample sorting in the HSMC fast Monte Carlo simulation algorithm module, its vector direction points to the direction of the growth of the sample failure probability in space, and has the characteristic that the larger the algebraic value, the higher the failure probability. Then, by calculating the directed probability distance of the sample point from the boundaries of multiple failure areas, and selecting the effective distance as the sample sorting weight based on the logical relationship between the failure areas, the limitation of the traditional HSMC method that cannot simultaneously perform sample simulation of multiple-target complex yield constraints is overcome; 3. When the yield constraint is a simple single-target open interval, the present invention will degenerate into the traditional method of sorting by the size of the single-target prediction value, which is compatible and equivalent to the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of the present invention;

[0018] Figure 2 Schematic diagram of the constraint boundary when the constraint condition is a three-dimensional quadratic surface;

[0019] Figure 3 This invention Figure 1 Schematic diagram of the transformation into a one-dimensional linear constraint boundary;

[0020] Figure 4 is a schematic diagram of the failure area A1 formed by the present invention;

[0021] Figure 5 is a schematic diagram of the failure area A2 formed by the present invention;

[0022] Figure 6 It is a schematic diagram of calculating directed distance in the present invention;

[0023] Figure 7 It is a schematic diagram of calculating effective directed distance in the present invention. DETAILED DESCRIPTION

[0024] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the structure of the present invention.

[0025] For a sense amplifier circuit commonly used in memory chip design, we usually examine its delay ( )、Minimum resolution voltage( ), Gain( ), dynamic power consumption (P), and other indicators. Assume that the failure judgment standard is defined as follows: if the circuit delay is greater than 55ps and the gain is less than 65dB, it is judged as a failure; if the circuit dynamic power consumption is greater than 3mW, it is also judged as a failure regardless of other indicators. Since the dynamic power consumption of the sense amplifier is expressed as: (2), where P S is the static power consumption, K is a constant related to the circuit structure, and the yield determination function is a composite function that includes multiple constraints and nonlinear constraints. In this case, it is impossible to use the existing HSMC algorithm to accelerate the yield analysis by sorting the predicted values ​​of a certain variable, because the larger the predicted value of delay, the smaller the gain value, and vice versa; and the smaller the gain value, the smaller the dynamic power consumption, which is even more inconsistent with the The failure condition has been resolved.

[0026] Therefore, if Figure 1 As shown, the invention proposes a sorting method to accelerate the yield analysis of integrated circuits with complex constraints, including the following steps: Step 1: Total decision function Equivalent deformation: for the judgment parameters The evaluation indexes are respectively based on the judgment function 、 ...... The expression of each sub-determinant function is the inequality of the parameter determination index, then the total determination function For each point judgment function 、 ...... When a certain judgment parameter The judgment index is a nonlinear relationship between multiple parameters, then its judgment function is For nonlinear inequality constraints, define an equivalent variable S And make it equal to the judgment function The nonlinear constraint expression of Equal to the equivalent variable S , so the judgment function Transformed into the equivalent variable S The linear inequality constraint of Converted into a logical combination of linear inequality constraints expressed by several decision functions.

[0027] Still taking the failure judgment criteria of the sensitive amplifier as an example: the circuit delay is greater than a And the gain is less than b It is judged as a failure when the circuit dynamic power consumption is greater thanc When the value is less than 0, it is judged as failure regardless of other indicators, and X is used. 1， X2 and X3 represent the indicator delay, gain and static power consumption parameters respectively, and the overall yield determination function is expressed as formula (3):

[0028] (3)

[0029] in is a constant given according to the design specification, for example K is a constant related to the circuit design structure, and its value varies depending on the process node. For example, in the 90nm process SRAM circuit, K is generally 0.01~0.05; while in the 7nm process, K is even smaller, generally 0.0005~0.002.

[0030] In the first step, we need to determine the total decision function Perform equivalent deformation, expressed as formula (4):

[0031] (4)

[0032] in and are simple linear inequality constraints, and Is a complex quadratic surface constraint, at this time we define an equivalent variable S and satisfy them (5), then The equivalent deformation is transformed from formula (4) to formula (6):

[0033]

[0034] (6),

[0035] Then, the total decision function The constraints are transformed into the logical combination of linear inequality constraints expressed by the three sub-decision functions, which can be expressed as formula (7):

[0036] (7).

[0037] Step 2: Data normalization: First, the equivalent variables S The value of is calculated and updated to the new sample data set D; all sample data and the total decision function in the sample data set D are The constant judgment values ​​in are normalized to obtain the judgment parameters The dimensionless value and normalized sample data value of .

[0038] Specifically in this embodiment, formula (5) is used to convert each sample point in the original sample data set into Substitute the corresponding values ​​under the parameters to get the value of each sample point S value, then we get the updated sample data set D. Figure 2 As shown, the original complex constraints The failure region boundary is a quadratic surface, and it is not possible to simply compare the failure probability based on the size of a certain predicted sample value. However, through the equivalent treatment in the first step and the introduction of new sample variables S After that, the quadratic boundary is linearized to obtain Figure 3 , so that the predicted sample value S can be calculated based on the new i Compare the failure probability by size.

[0039] Figure 2 Among them, assuming K=1, for 2 prediction sample data and ,Although ,but , but smaller than , so it is not possible to simply predict the sample or to compare the failure probability.

[0040] and Figure 3 After linearization, for , by the failure probability , so according to the sample data S Sort the samples by the size of the value.

[0041] Since different indicators have different units and cannot be directly compared with each other, it is necessary to normalize all sample data and the constant judgment values ​​in the 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 Z-Score method can be used to normalize the data. The normalization formula is:

[0042] (1)

[0043] in is the sample mean, is the sample deviation. It should be noted that not only the sample value should be normalized, but also the judgment value in each constraint condition in the yield judgment function should be normalized. For example, for (3) , the dimensionless value obtained after normalization of the corresponding sample data set is .

[0044] Because the only thing that matters when sorting is the relative size of the results, this treatment will not change the accuracy of the sort or the final calculation result.

[0045] Step 3: Divide the failure area: According to the total judgment function The logical relationship between the linear inequality constraints of all the sub-determinant functions divides the failure area of ​​the sample space. The rule is: if two constraints are connected by the "and" operator, the two constraints are combined to form a failure area; if two constraints are connected by the "or" operator, the two constraints each form an independent failure area; the failure area can be obtained. A 1、 A 2 ...... A k ， According to the determined failure area, the corresponding failure area is obtained respectively A 1、 A 2 ...... A k Failure boundary a 1、 a 2...... a k ,in k ≤n .

[0046] In this embodiment, according to formula (7), the total decision function It can be divided into two failure areas A1 and A2, where A1 is , A2 is , and the boundary conditions of A1 a 1 Must satisfy greater than a and less than b， The invalid area A1 is the appendix of the instruction manual. Figure 4 The blue part is shown in the middle; the boundary condition of the failure area A2 is a 2 ， and satisfy a 2 ＞c , as detailed in the instruction manual Figure 5 Shown in pink 。

[0047] Assume there is a complex failure discrimination function , according to the priority order of "not" first, then "and" and then "or", it can be divided into three failure areas. According to the constraints of each failure area, three failure areas are obtained:

[0048] .

[0049] Step 4: Calculate the effective directed probability distance from each sample data to the failure boundary d : Taking the direction of failure probability growth as the positive direction, for each sample data, its directed distance to the boundary of each failure area is d1, d2 dk, And the effective directed distance at the boundary of each failure area d The calculation rule is: the failure area composed of two constraints is the effective directed distance d The minimum value of the directed distance from the sample data point to the two failure boundaries; the effective directed distance of the failure region composed of two constraints in parallel is d The maximum value of the directed distance between the sample data point and the two failure boundaries; according to the priority relationship of "and" first and "or", the unique effective directed probability distance corresponding to each sample data is calculated d .

[0050] It is called a directed probability distance because the direction of failure probability growth is defined as the positive direction when calculating the distance. Figure 6 As shown, the coordinates of the sample data points in A1 are ( ),and Figure 6 The failure region A1 in the ＞a and ＜b Combined into, >a is represented by the blue area, and <b is represented by the orange area, and the two constraints need to be satisfied at the same time, that is, Figure 6 The blue and orange overlap. For the first condition ＞a， In the coordinate system x 1 The direction in which the axis increases is the direction in which the failure probability increases, so the sample data point is in the positive direction. x 1 Signed distance in the axial direction d x1= -a As can be seen from the figure, ＞a， Therefore d x1 A value greater than 0 indicates that its direction is the same as the direction of failure probability growth. The larger the absolute value, the higher the failure probability. Figure 6 The second failure condition in x2 ＜b ， In the coordinate system The direction in which the axis decreases is the direction in which the failure probability increases, which is the positive direction. Therefore, the sample data point is Signed distance in the axial direction d x2 =b- ， Depend on Figure 6 It can be seen that b＜ ， Therefore d x2 A value less than 0 indicates that its direction is opposite to the direction of increase in failure probability. The larger the absolute value, the smaller the failure probability.

[0051] As the instruction manual Figure 6 As shown, the failure area A1 is composed of ＞a and ＜b The directed distance is the minimum value of the directed distance from the sample data point to the two failure boundaries, that is, d 1 =min( d x1 ，d x2 ).

[0052] For the failure region formed by logical "or", since it only needs to fall within any one of the constraints, its effective directed distance is the maximum value of the directed distance from the sample data point to the two failure boundaries. 。 As the instruction manual Figure 7 As shown, the failure area A2 is represented by S ＞c Formed, the sample data points are ( S i ), then the sample data point is S Signed distance in the axial direction d 2 = d si 。 From formula (7), we can see that Figure 6 A1 and attached Figure 7 A2 represented in the figure is a parallel relationship, so the effective directed probability distance of the sample data point is d = max(d 1 ，d 2 ).

[0053] When it is composed of multiple logical relationships, according to the priority relationship of "and" first and "or", the two failure area directed probability distance calculation rules are used step by step to calculate the unique effective directed probability distance corresponding to each sample data. d

[0054] For example, the failure discrimination function , the failure boundaries of the three failure regions are: , then the sample data in the failure areas A1, A2 and A3 are calculated to obtain the directed distance d 1、 d 2 and d 3， The relationship between A1, A2 and A3 is logical "or", so the effective directed probability distance is d=max(d 1， d 2 , d 3 ) According to this calculation method, the only valid directed probability distance of each sample data point is calculated. d .

[0055] In this step, the premise for the failure areas to be drawn and compared in the same coordinate system is that they are normalized.

[0056] Step 5: Press effective directed distance d After arranging the algebraic values, simulation: the effective directional probability distance of each sample data obtained in the fourth step is d After being sorted in descending order by algebraic value, the samples are sent to the Monte Carlo simulation algorithm module for simulation. The sample data with a larger algebraic value of the directed probability distance has a greater probability of failure. According to the required accuracy conditions, all failed samples are obtained.

[0057] Because the effective directed probability distance d The larger the algebraic value of , the greater the failure probability of the sample. Therefore, after sorting, samples with high failure probability can be simulated first to speed up the simulation process and find all failed samples more quickly.

[0058] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A ranking method for accelerating yield analysis of integrated circuits with complex constraints, characterized by: The following steps are involved: S1: Total decision function Equivalent deformation: for the judgment parameters The evaluation indexes are respectively based on the judgment function 、 ...... The expression of each sub-determinant function is the inequality of the parameter determination index, then the total determination function is the logical combination of each decision function; When a judgment parameter The judgment index is a nonlinear relationship between multiple parameters, then its judgment function is For nonlinear inequality constraints, define an equivalent variable S And make it equal to the judgment function The nonlinear constraint expression of Equal to the equivalent variable S , so the judgment function Transformed into the equivalent variable S Linear inequality constraints; Then the total decision function Convert to several decision functions 、 ...... Logical combinations of the expressed linear inequality constraints; S2: Data normalization: First, the equivalent variables S The value of is calculated and updated to the new sample data set D; For all sample data in the sample data set D and the total decision function The constant judgment values ​​in are normalized to obtain the judgment parameters The dimensionless value of and the normalized sample data value; S3: Divide the failure area: according to the total judgment function The logical relationship between the linear inequality constraints of all the sub-determinant functions divides the failure area of ​​the sample space. The rules are: Use the "AND" operator to connect two constraints, and the two constraints are combined to form a failure region; Use the "or" operator to connect two constraints, and each constraint forms an independent failure area; Multiple failure regions are obtained A 1 、A 2 ...... A k ， According to the determined failure area, the corresponding failure boundaries are obtained respectively a 1 、a 2...... a k ,in k≤n ; S4: Calculate the effective directed probability distance from each sample data to the failure boundary d : Taking the direction of failure probability growth as the positive direction, for each normalized sample data, its directed distance to the boundary of each failure region is d 1 、d 2 d k ， The calculation rule of the directed distance at the boundary of each failure area is: The failure region formed by combining two constraints has a directed distance that is the minimum of the directed distances from the sample data point to the two failure boundaries. The failure region consists of two constraints in parallel, and its directed distance is the maximum directed distance from the sample data point to the two failure boundaries; According to the priority relationship of "and" first and "or" later, calculate the unique effective directed probability distance corresponding to each sample data d ; S5: The effective directional probability distance of each sample data obtained in S4 d After being sorted in descending order by algebraic value, the samples are sent to the Monte Carlo simulation algorithm module for simulation. The sample data with a larger algebraic value of the directed probability distance has a greater probability of failure. According to the required accuracy conditions, all failed samples are obtained.

2. The method for accelerating yield analysis of integrated circuits with complex constraints according to claim 1, characterized in that: The normalization formula in step S2 is: (1), where is the sample mean, is the sample bias.

3. The method for accelerating yield analysis of integrated circuits with complex constraints according to claim 1, characterized in that: In the failure region, the direction in which the failure probability increases is the positive direction, and the linear inequality of the corresponding determination function is used as the basis.

4. The method for accelerating yield analysis of integrated circuits with complex constraints according to claim 3, characterized in that: In step S4, the distance between the sample data in each failure area and the failure boundary is d 1 、d 2 d k The position of the point and the failure boundary a 1 、a 2 a k The directed difference between .

5. The method for accelerating yield analysis of integrated circuits with complex constraints according to claim 1, characterized in that: The directed distance of the sample data in each failure area in step S4 d 1 、d 2 d k , according to the priority relationship of "and" first and "or" later, merge step by step until a valid directed distance is formed d .

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