An integrated circuit yield estimation method and memory

Abstract

The application provides an integrated circuit yield estimation method and a memory, and the method comprises the following steps: formulating a boundary of a success region and a failure region of an integrated circuit performance in a parameter space, and representing the boundary as a boundary surface formula equation; calculating a size of a space defined by the boundary surface formula equation and a boundary surface formed by each parameter axis; and calculating a ratio of the size of the space defined by the boundary surface formula equation and the boundary surface formed by each parameter axis to a size of a space formed by each parameter range, to obtain an estimated yield. The technical scheme of the application can improve the estimation efficiency of the integrated circuit yield.

Description

Technical Field

[0001] This invention relates to the field of integrated circuits, and more particularly to a method for estimating the yield of integrated circuits and a memory. Background Technology

[0002] In integrated circuit manufacturing, variations in process parameters are unavoidable. These variations have become a major challenge in the design and fabrication of nanoscale analog circuits. The uncertainties introduced during manufacturing, such as photolithography, chemical mechanical polishing (CMP), and etching, can cause circuit performance parameters to deviate from design specifications. There is a need to find a standard that allows designers to quickly and accurately estimate the quality of circuit designs, especially important for circuits that require expensive and high-precision simulations during the design process. Yield estimation is a crucial indicator of the robustness of circuit designs.

[0003] Currently, in circuit design, the Monte Carlo (MC) method is frequently used for simulation to obtain circuit yield. This method first generates tens of thousands of samples of probability distributions for variable parameters. Then, it performs circuit simulation on each sample to evaluate the performance value of interest. Under given performance constraints, the Monte Carlo method can identify successful or acceptable samples, and the yield can then be estimated using the percentage of successful samples. The Monte Carlo method is simple and general; it can be applied to parameters and performance advantages of any distribution without any prior knowledge. However, achieving high accuracy using this method is very time-consuming, making it unsuitable for practical applications and unable to meet the yield estimation needs of designs with a large number of components.

[0004] Furthermore, when dealing with surfaces that have successfully and unsuccessfully segmented regions, the Newton-Raphson method is often used to find points on the surface, approximating the solution by calculating the Jacobian matrix. However, in black-box systems where the surface equations are ambiguous, the Newton-Raphson method becomes unusable; and in surface equations with a large number of parameters, calculations such as differentiation significantly increase computational time costs. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing integrated circuit yield estimation algorithms, such as low efficiency and long processing time, by providing an efficient integrated circuit yield estimation method.

[0006] In this embodiment of the invention, a method for estimating the yield of integrated circuits is proposed, which includes:

[0007] The boundary between the successful and unsuccessful regions of integrated circuit performance is formulated in parameter space and expressed as a boundary surface formula equation.

[0008] Calculate the size of the space defined by the boundary surface formula equation and the boundary surface formed by each parameter axis;

[0009] The estimated yield is obtained by calculating the ratio of the space size defined by the boundary surface formula equation and the boundary surface formed by each parameter axis to the space size formed by the range of each parameter.

[0010] In this embodiment of the invention, the formulaic equation for the boundary surface is as follows:

[0011]

[0012] in, This represents a parameter vector, where m represents the number of parameters. The number of f m Indicates circuit performance.

[0013] In this embodiment of the invention, calculating the size of the space defined by the boundary surface formed by the boundary surface and each parameter axis includes:

[0014] Solve the formalized equation of the boundary surface to obtain the coordinates of the intersection points of each parameter axis and the boundary surface;

[0015] The spatial size V0 of the simplex formed by the multiple intersection points and the zero points of the parameter axes is calculated according to the analytical volume calculation formula, and the following iteration is performed:

[0016] According to the parametric equations Find the next point on the boundary surface, where p0 is the centroid of the N known and adjacent points on the boundary surface, u is the normal vector, s is the length along the unit vector u, and N is the number of parametric axes;

[0017] The spatial size Vi of the simplex formed by the newly discovered point and the multiple points used to find the point is calculated according to the analytical volume calculation formula, where i is the i-th newly discovered point;

[0018] When the absolute value of Vi is less than the set threshold, the iteration stops, and the spatial size V = ∑Vi is calculated by the boundary surface formula equation and the boundary surface defined by each parameter axis.

[0019] In this embodiment of the invention, the formula for calculating the analytical volume is as follows:

[0020]

[0021]

[0022] Where, x N，1 x N，2 , ..., x N，N These represent the coordinates of the Nth point in each of the N parameter dimensions.

[0023] In this embodiment of the invention, a memory is also provided, which stores a computer program. When the computer program is executed, it implements the above-described integrated circuit yield estimation method.

[0024] Compared to existing technologies, the integrated circuit yield estimation method of this invention estimates yield by using the area / volume ratio of the bounded region formed by the performance surface to the entire parameter domain. This avoids large-scale sampling and, theoretically, can be hundreds of times faster than the Monte Carlo method under specified accuracy conditions, achieving better efficiency in device parameter yield estimation. Even in black-box systems where the surface equations of the successfully partitioned region are unclear, the method of this invention can still accurately determine points on the surface and perform region calculations. Furthermore, given the surface equations and numerous parameters, compared to computationally expensive methods such as Newton's iteration method, the method of this invention is more flexible, avoids extensive derivative calculations, and accelerates computation. Attached Figure Description

[0025] Figure 1 This is a schematic diagram illustrating the integrated circuit yield estimation method of this invention in the parameter domain for finding the yield boundary.

[0026] Figure 2 This is a schematic diagram showing the ratio of the effective region to the parameter region in the integrated circuit yield estimation method of this invention.

[0027] Figure 3 This is a flowchart illustrating the integrated circuit yield estimation method according to an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram of the parametric equations for the integrated circuit yield estimation method according to an embodiment of the present invention;

[0029] Figure 5(a) is a schematic diagram of the initial iteration of the integrated circuit yield estimation method for finding boundary points according to an embodiment of the present invention;

[0030] Figure 5(b) is a schematic diagram of the second iteration of the integrated circuit yield estimation method for finding boundary points according to an embodiment of the present invention;

[0031] Figure 6 This is a schematic diagram illustrating the calculation of the effective region volume in the integrated circuit yield estimation method according to an embodiment of the present invention. Detailed Implementation

[0032] This invention provides a method for estimating integrated circuit yield by using the area / volume ratio of a bounded region formed by a performance surface to the entire parameter domain. It should be noted that the performance domain is defined as a space encompassing all possible performance parameters (i.e., voltage, gain, bandwidth, etc.), while the parameter domain is the space spanned by all circuit parameters (i.e., channel width, threshold voltage, etc.). The parameter domain considers parameter settings; multiple parameters in a circuit may fluctuate within a certain range. These parameter variations ultimately affect the performance in the performance domain, reflected in the quality of the circuit, with their minimum and maximum values ​​as boundaries. In both domains, successful sampling forms a bounded region called the "yield volume" or "success region," and the nonlinear boundary separating the successful and unsuccessful regions is called the "yield boundary." Therefore, the percentage of satisfactory sampling in these two domains can be used to equivalently estimate yield.

[0033] like Figure 1 As shown by midpoints A, B, C, and D, the performance surface can be defined as follows: each point on the surface corresponds to a sampling point in the parameter domain. Under given performance constraints, this surface can be divided into success regions and failure regions, which are separated by the intersection points of these two surfaces (called "yield boundaries," e.g., ...). Figure 1 (As shown by the curve in the middle). Therefore, yield can be estimated by the ratio of the size (area or volume) of the bounded region to the entire parameter domain, such as... Figure 2 As shown.

[0034] Specifically, such as Figure 3 As shown, the integrated circuit yield estimation method provided in this embodiment of the invention includes steps S1-S3. These will be described below.

[0035] Step S1: Formulate the boundary between the successful and unsuccessful regions of integrated circuit performance in parameter space, and express it as the boundary surface formula equation.

[0036] Specifically, the formulaic equation for the boundary surface is as follows:

[0037]

[0038] in, This represents a parameter vector, where m represents the number of parameters. The number of f m Indicates circuit performance.

[0039] It should be noted that, without a clear boundary equation, the boundary equation can be regarded as a black box system, and the points on the surface boundary can be determined by using the Jacobian-Free method based on simple input and output results.

[0040] Step S2: Calculate the size of the space defined by the boundary surface formula equation and the boundary surface formed by each parameter axis.

[0041] It should be noted that if only one parameter can be changed to alter circuit performance, then there will always be one parameter value that causes circuit failure. Therefore, the boundary surface of the boundary surface formula equation must intersect the parameter axes. Thus, when calculating the size of the computational space, we can first find multiple intersection points between each parameter axis and the boundary surface formula equation. Then, using these intersection points, we can further find more points on the boundary surface of the boundary surface formula equation. Through iteration, the calculated size of the computational space continuously approximates the size of the bounded region.

[0042] Specifically, in this embodiment of the invention, calculating the size of the space defined by the boundary surface formed by the boundary surface and each parameter axis includes:

[0043] Solve the formalized equation of the boundary surface to obtain the coordinates of the intersection points of each parameter axis and the boundary surface;

[0044] The spatial size V0 of the simplex formed by the multiple intersection points and the zero points of the parameter axes is calculated according to the analytical volume calculation formula, and the following iteration is performed:

[0045] According to the parametric equations Find the next point P on the boundary surface, where p0 is the centroid of the N known and adjacent points on the boundary surface, u is the normal vector, s is the length along the unit vector u, and N is the number of parametric axes.

[0046] The spatial size Vi of the simplex formed by the newly discovered point and the multiple points used to find the point is calculated according to the analytical volume calculation formula, where i is the i-th newly discovered point. The analytical volume calculation formula is as follows:

[0047]

[0048]

[0049] Where, x N，1 x N，2 , ..., x N，N These represent the coordinates of the Nth point in the Nth parameter dimensions, respectively;

[0050] When the absolute value of Vi is less than the set threshold, the iteration stops, and the spatial size V = ∑Vi is calculated by the boundary surface formula equation and the boundary surface defined by each parameter axis.

[0051] The following is combined Figures 4-6 The above iterative process will be illustrated using an example with only two parameter axes.

[0052] like Figure 4 As shown, assuming the boundary curve of the formalized boundary surface equation intersects the X-axis and Y-axis at points P01 and P02 respectively, according to the parametric equation... The midpoint of points P01 and P02 (for a line segment, the mass point is the midpoint of the line segment), P1guess, is p0 in the formula. The intersection of the normal vector u with the boundary curve of the formalized boundary surface equation is P1. Therefore, based on the parametric equation and the formalized boundary surface equation, more points can be found iteratively on the boundary curve. The specific iterative process is shown in Figures 5(a) and 5(b). First, P1 is obtained from P01 and P02, then P2 is obtained from P1 and P02, and P3 is obtained from P1 and P01. This iteration can be repeated continuously to obtain more points.

[0053] like Figure 6 As shown, the area of ​​the shape defined by the boundary curve and each parameter axis is calculated as follows:

[0054] S total=SO+S1+S2+S3+……+Si,

[0055] Where S0 is the area of ​​the triangle formed by the origin of the coordinate axes, P01, and P02; S1 is the area of ​​the triangle formed by P01, P02, and P1; S2 is the area of ​​the triangle formed by P1, P2, and P02; S3 is the area of ​​the triangle formed by P01, P1, and P3; and Si is the area of ​​the i-th triangle. It should be noted that when calculating the areas of these triangles, the analytical volume calculation formula is used, and the result may be negative. The sign indicates the direction. Through continuous iteration, the final calculated result S_total can be made infinitely close to the image area defined by the boundary curve and the coordinate axes. When the absolute value of Si is less than a set threshold, it indicates that the calculation of S_total has met the set accuracy, and the iteration stops.

[0056] It should be noted that the above explanation is based on two parameter axes. If there are three parameter axes, the calculated space size is the volume of a tetrahedron formed by four points. If there are more parameter axes, the calculated space size is the hypervolume of a simple shape formed by multiple points.

[0057] Step S3: Calculate the ratio of the space size defined by the boundary surface formula equation and the boundary surface formed by each parameter axis to the space size formed by the range of each parameter, and obtain the estimated yield.

[0058] Furthermore, the present invention also provides a memory in which a computer program is stored, which, when executed, implements the above-described integrated circuit yield estimation method.

[0059] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating the yield of integrated circuits, characterized in that, include: The boundary between the successful and unsuccessful regions of integrated circuit performance is formulated in parameter space as a boundary surface formula equation, which is as follows: ， in, This represents a parameter vector, where m represents the number of parameters. The number of Indicates circuit performance; Calculate the size of the space defined by the boundary surface formula equation and the boundary surface formed by each parameter axis; The estimated yield is obtained by calculating the ratio of the spatial size defined by the boundary surface formula equation and the boundary surface formed by each parameter axis to the spatial size of the hypercube formed by each parameter range, to obtain the estimated yield. Specifically, this includes: Solve the formalized equation of the boundary surface to obtain the coordinates of the intersection points of each parameter axis and the boundary surface; The spatial size V0 of the simplex formed by the multiple intersection points and the zero points of the parameter axes is calculated according to the analytical volume calculation formula, and the following iteration is performed: According to the parametric equations Find the next point on the boundary surface, where p0 is the centroid of the N known and adjacent intersection points on the boundary surface, u is the normal vector, s is the length along the unit vector u, and N is the number of parametric axes; The spatial size Vi of the simplex formed by the newly discovered point and the multiple points used to find the point is calculated according to the analytical volume calculation formula, where i is the i-th newly discovered point; When the absolute value of Vi is less than the set threshold, the iteration stops, and the spatial size V defined by the boundary surface formula equation and the boundary surface formed by each parameter axis is calculated. .

2. The integrated circuit yield estimation method as described in claim 1, characterized in that, The formula for calculating the analytical volume is as follows: ， in, , ,..., These represent the coordinates of the 1st, 2nd, ..., Nth points in the N parameter dimensions, respectively.

3. A memory, characterized in that, The memory stores a computer program, which, when executed, implements the integrated circuit yield estimation method as described in any one of claims 1-2.

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