Circuit simulation devices and circuit simulation software products

Abstract

This invention provides a circuit simulation apparatus and a circuit simulation program product capable of appropriately evaluating the impact of deviations and predicting circuit characteristics. The circuit simulation apparatus includes: a data input unit that accepts design data input; a standardization calculation unit that standardizes multiple predicted characteristic values; a Mahalanobis distance calculation unit that calculates the Mahalanobis distance from the standardized origin for a group of standardized characteristic values; a threshold setting unit that sets a threshold for the calculated Mahalanobis distance; a fast and slow point calculation unit that calculates the fast and slow points among the multiple standardized characteristic values; an unbalanced angle determination unit that determines a first unbalanced angle point and a second unbalanced angle point in an orthogonal coordinate system; and a parameter calculation unit that calculates the deviation based on the fast point, the slow point, the first unbalanced angle point, and the second unbalanced angle point.

Description

Technical Field

[0001] This disclosure relates to circuit simulation devices and circuit simulation program products. Background Technology

[0002] The characteristics of metal-oxide-semiconductor (MOS) devices inevitably deviate due to the influence of their manufacturing process. Therefore, in the design of circuits containing MOS devices, it is necessary to consider the deviations in the characteristics of MOS devices.

[0003] A common method used for this is the pentagonal model. In the pentagonal model, a principal pentagon (TT, FF, SS, FS, SF) is defined for the combination of values ​​in the P-type and N-type components regarding a certain characteristic (e.g., threshold voltage). For both P-type and N-type components, points corresponding to the principal pentagons are plotted in two-dimensional graphs for one characteristic and the other (e.g., drain current). This yields correlation graphs between the two characteristics for both P-type and N-type components. The circuit is then designed to balance the strength of the correlations in the two correlation graphs.

[0004] There are no specific guidelines for setting the unbalanced angles (FS, SF) in the main five angles. Therefore, the values ​​related to F and S are multiplied by a certain coefficient to determine their numerical values. Summary of the Invention

[0005] In existing technologies, the impact of deviations is sometimes misjudged. This is because a method for appropriately setting coefficients based on relevant conditions has not yet been established. Consequently, deviations on correlation diagrams are sometimes underestimated. As a result, the circuit characteristics anticipated in the design sometimes do not match the characteristics of the actually manufactured circuit.

[0006] This disclosure provides a circuit simulation apparatus and circuit simulation program product that can appropriately evaluate the impact of deviations and predict circuit characteristics to address the above-mentioned problems.

[0007] To achieve the above objectives, in a first aspect, this disclosure provides a circuit simulation apparatus for simulating the characteristic values ​​of metal-oxide-semiconductor (MOS) elements in a semiconductor circuit comprising MOS elements. The circuit simulation apparatus includes: a data input unit for receiving design data of the semiconductor circuit; a standardization calculation unit for standardizing multiple characteristic values ​​predicted for each MOS element when multiple semiconductor circuits are manufactured based on the design data; a Mahalanobis distance calculation unit for calculating the Mahalanobis distance from the standardized origin for each set of standardized MOS elements; a threshold setting unit for setting a threshold for the calculated multiple Mahalanobis distances; and a fast / slow point calculation unit for calculating... In a standardized orthogonal coordinate system of multiple characteristic values, on the trajectory of points whose calculated Mahalanobis distance is equal to a threshold, there are fast points where multiple characteristic values ​​are located on the fast side and have the largest Euclidean distance from the origin, and slow points where multiple characteristic values ​​are located on the slow side and have the largest Euclidean distance from the origin; an imbalance angle determination unit determines a first imbalance angle point and a second imbalance angle point, wherein the first imbalance angle point is located in the orthogonal coordinate system at a position deviating from the line connecting the fast and slow points, and its calculated Mahalanobis distance is equal to or less than the threshold, and the second imbalance angle point is located at a position symmetrical to the first imbalance angle point across the origin; and a parameter calculation unit calculates the deviation of multiple characteristic values ​​based on the fast point, slow point, first imbalance angle point, and second imbalance angle point.

[0008] Secondly, this disclosure provides a circuit simulation program product, including a circuit simulation program that simulates the characteristic values ​​of metal-oxide-semiconductor elements in a semiconductor circuit containing metal-oxide-semiconductor elements using a computer. The circuit simulation program is executed by the computer and includes the following steps: a data input step, accepting design data of the semiconductor circuit as input; a standardization calculation step, standardizing multiple characteristic values ​​predicted for each metal-oxide-semiconductor element when multiple semiconductor circuits are manufactured based on the design data; a Mahalanobis distance calculation step, calculating the Mahalanobis distance from the standardized origin for each group of standardized multiple characteristic values ​​of the metal-oxide-semiconductor element; and a threshold setting step, setting a threshold for the calculated multiple Mahalanobis distances. The fast and slow point calculation steps involve calculating the fast point (where all characteristic values ​​are located on the fast side and have the largest Euclidean distance from the origin) and the slow point (where all characteristic values ​​are located on the slow side and have the largest Euclidean distance from the origin) on the trajectory of points in a standardized orthogonal coordinate system with multiple characteristic values ​​where the calculated Mahalanobis distance is equal to the threshold. The unbalanced angle determination steps involve determining the first and second unbalanced angle points. The first unbalanced angle point is located in the orthogonal coordinate system at a position deviating from the line connecting the fast and slow points, and its calculated Mahalanobis distance is equal to or less than the threshold. The second unbalanced angle point is located symmetrical to the first unbalanced angle point across the origin. Finally, the parameter calculation steps involve calculating the deviation of multiple characteristic values ​​based on the fast point, slow point, first unbalanced angle point, and second unbalanced angle point.

[0009] According to the present disclosure, a circuit simulation device and a circuit simulation program product are provided that can appropriately evaluate the impact of deviations and predict circuit characteristics. Attached Figure Description

[0010] Figure 1 It is a graph representing the Vthn and Vthp values ​​in a pentagonal model.

[0011] Figure 2 It is a graph showing the correlation between the Vthn value and the Idn value.

[0012] Figure 3 This is a block diagram of a circuit simulation device.

[0013] Figure 4 This is a flowchart illustrating the circuit simulation steps of the implementation method.

[0014] Figure 5 This is a graph representing an example of a standardized distribution.

[0015] Figure 6 This is a graph representing an example of lines with equal Mahalanobis distances.

[0016] Figure 7This is a graph representing an example of the frequency distribution of Mahalanobis distance.

[0017] Figure 8 This is a graph illustrating an example of how to determine the imbalance value.

[0018] Figure 9 It is a graph used to illustrate the determination of the unbalance angle.

[0019] Explanation of reference numerals in the attached figures

[0020] 1. Circuit simulation device

[0021] 2. Data Input Section

[0022] 3. Standardization Calculation Department

[0023] 4. Mahalanobis distance calculation department

[0024] 5. Threshold setting section

[0025] 6. Fast / Slow Point Calculation Department

[0026] 7. Unbalance Value Calculation Department

[0027] 8. Vth value and Id value calculation section

[0028] 9. Calculation Result Output Section

[0029] 10. Mapping Data Storage Department

[0030] 11. Display screen. Detailed Implementation

[0031] The basic principles of the technology disclosed herein are explained. Circuits containing PMOS and NMOS elements have various characteristic values. In the pentagonal model, two main characteristic values ​​are used for simulation. As the main characteristic values, the threshold voltage Vth and drain current Id of the MOS element are used in this specification. In the following description, the threshold voltage Vth is sometimes referred to as the first principal component, and the drain current Id is sometimes referred to as the second principal component.

[0032] Even multiple individual components based on the same design and manufactured using the same equipment will exhibit characteristic variations. This is because there are slight differences in manufacturing conditions between wafers or chips. The combination of the threshold voltage Vthp of the PMOS element and the threshold voltage Vthn of the NMOS element in these components is roughly distributed as follows: Figure 1 Within the range of quadrilateral FF-FS-SS-SF.

[0033] "F" stands for "Fast," which corresponds to an excellent characteristic value. "S" stands for "Slow," which corresponds to a poor characteristic value. The meanings of the four angles of the quadrilateral are as follows.

[0034] FF: Both Vthp and Vthn are optimal individuals.

[0035] FS: Vthn is the best individual but Vthp is the worst.

[0036] SS: Vthp and Vthn are both the worst individuals.

[0037] SF: Vthn is the worst individual but Vthp is the best.

[0038] These five points, along with "TT" at the center of the quadrilateral, are called the pentagons. "T" stands for "Typical," referring to the case where both Vthp and Vthn are average characteristic values. FS and SF in the pentagons are called unbalanced angles. Sometimes FF and SS are also simply referred to as Fast and Slow.

[0039] Focusing on the threshold voltage Vthn and drain current Idn of an NMOS device, if we set them as the horizontal and vertical axes, then... Figure 2 As shown, the Fast point, corresponding to the FF angle, is located in the upper left, and the Slow point, corresponding to the SS angle, is located in the lower right. In the individual cases of the FF angle, the NMOS device conducts with a low gate voltage, resulting in a large drain current. On the other hand, in the individual cases of the SS angle, a high gate voltage is required to turn on the NMOS device, resulting in only a small drain current. Hereinafter, Vthn on the horizontal axis will sometimes be referred to as the first component, and Idn on the vertical axis will be referred to as the second component.

[0040] The point corresponding to angle TT is located in the middle of the fast-slow line (i.e., the Fast-Slow line) connecting the fast point (i.e., the Fast point) and the slow point (i.e., the Slow point). Point FS is located between the Fast point and point TT, and point SF is located between the Slow point and point TT. The range from point FS to point SF in the Fast-Slow line is called the unbalanced region.

[0041] This involves calculating a set of predicted values ​​for the threshold voltage Vthn and drain current Idn of the NMOS element in each individual unit manufactured using the same design and equipment. These calculation results are referred to as multi-point measurement results. If the multi-point measurement results are plotted on... Figure 2 In a two-dimensional coordinate system, this is equivalent to the distribution of points of each body along a shape that deviates to some extent from the Fast-Slow line connecting the Fast and Slow points.

[0042] exist Figure 2In the distribution of the Fast-Slow line, in the unbalanced regions outside the vicinity of the two ends, the deviation from the Fast-Slow line is greater compared to the vicinity of the two ends. Therefore, simulation accuracy may decrease in the unbalanced regions. This is because, among the multi-point measurements in these regions, more points are located far from the Fast-Slow line, leading to misclassification.

[0043] Furthermore, the deviation is larger when the NMOS device is small compared to when it is large. This is because the smaller the NMOS device, the greater the impact of deviation. Therefore, analog accuracy is more likely to decrease when the device size is small. Figure 2 The image shows an NMOS element, but it can be said that the same applies to a PMOS element.

[0044] Therefore, in this disclosure, the Mahalanobis distance (also known as the Mahalanobis distance) is utilized. [The following is a separate, unrelated sentence:] Determine... Figure 2 The threshold value in the Mahalanobis distance of such a two-dimensional drawing is used to determine the quality of the design. Therefore, the circuit simulation device 1 involved in this embodiment is as follows... Figure 3 It is constructed as shown. Figure 3 The circuit simulation device 1 includes a data input unit 2, a normalization calculation unit 3, a Mahalanobis distance calculation unit 4, a threshold setting unit 5, a Fast / Slow point calculation unit 6, an imbalance value calculation unit 7, a Vth value and Id value calculation unit 8, and a calculation result output unit 9. The circuit simulation device 1 also includes a mapped data storage unit 10 and a display screen 11.

[0045] The circuit simulation device 1 is a computer with simulation capabilities that calculate predicted values ​​of various characteristics of semiconductor circuits. In the circuit simulation device 1, the aforementioned multi-point measurement results can be calculated using this simulation function. The mapping data storage unit 10 stores the calculated multi-point measurement results.

[0046] Figure 3 The data input unit 2 is used to accept data input by the user for calculations required in the circuit simulation device 1. To calculate multi-point measurement results, the user inputs the design data of the circuit to be simulated, as well as the accuracy data of the predetermined manufacturing equipment used in its production (hereinafter collectively referred to as "raw data"), into the data input unit 2. The standardization calculation unit 3 is a functional part that performs standardized calculations based on the data input from the data input unit 2. The calculation processing in the standardization calculation unit 3 also includes the calculation of the covariance matrix.

[0047] The Mahalanobis distance calculation unit 4 is a functional unit that performs the aforementioned Mahalanobis distance calculation. Specifically, the Mahalanobis distance calculation unit 4 calculates the Mahalanobis distance for each point in the multi-point measurement results. The threshold setting unit 5 is a functional unit that determines whether the calculated Mahalanobis distance is set appropriately.

[0048] The Fast / Slow point calculation unit 6 is a functional unit that determines the Fast and Slow points in the orthogonal coordinate system of standardized Vth and Id values. The imbalance value calculation unit 7 is a functional unit that calculates the imbalance value in this orthogonal coordinate system. The Vth and Id value calculation unit 8 is a functional unit that calculates the Vth and Id values. The calculation result output unit 9 is a unit that processes and outputs the calculation results to the user. The display screen 11 is a unit that displays the output results in a way that allows the user to visually recognize them.

[0049] pass Figure 4 The steps of circuit simulation in circuit simulation device 1 are explained. The purpose of this step is to determine the four corner points corresponding to the aforementioned four corners in the standardized orthogonal coordinate system, and to determine the quality of the distribution based on these corner points.

[0050] First, multi-point measurement (S1) is performed. This is a simulation that predicts the Vth and Id values, including inter-individual deviations, when multiple semiconductor circuits are manufactured based on raw data. The raw data required for the simulation is input in advance by the user using the data input unit 2 and stored in the mapping data storage unit 10. The results of the multi-point measurement, i.e., multiple Vth and Id values, are recorded in the mapping data storage unit 10.

[0051] Next, the multi-point measurement results are read (S2). From this, the following results are obtained: Figure 2 The diagram shows a two-dimensional distribution based on Vth and Id values. Two distribution diagrams are obtained: one for Vthp and Idp values ​​in a PMOS element, and another for Vthn and Idn values ​​in an NMOS element. In the following description, the values ​​for PMOS and NMOS elements will be omitting the distinction and simply referred to as Vth and Id. However, in reality, both exist separately.

[0052] Next, standardization and covariance matrix calculation are performed (S3). This process is carried out by the standardization calculation unit 3. Standardization refers to adjusting the scaling of the horizontal and vertical axes in the two-dimensional distribution plot. Specifically, the mean of both the horizontal and vertical axes is zero, and the variance is 1.

[0053] Table 1. Raw data and standardized data

[0054]

[0055] Table 1 shows a partial example of Vth and Id values ​​before and after standardization. In Table 1, "Vth" and "Id" in the "Original Data" column represent the Vth and Id values ​​before standardization. In Table 1, "Vthst" and "Idst" in the "Standardized" column represent the Vth and Id values ​​after standardization. Figure 5 An example of a standardized distribution plot is shown. Figure 5 In the table, points where both Vth and Id values ​​are zero are designated as the origin. Numbers 1-10 in Table 1 are... Figure 5 The middle corresponds to the 10 drawing points located near the top left. The N in Table 1, where "Number" is... Figure 5 The middle point is equivalent to a drawing point located near the bottom right.

[0056] The covariance matrix is ​​the matrix shown in Equation 1. Each component of the covariance matrix in Equation 1 is the standard deviation of the distribution. The covariance matrix reflects the correlation of the distributions. Calculating the standard deviations based on the standardized distribution plot is the calculation of the covariance matrix. The subscript "n" of each component corresponds to the total number of points plotted.

[0057] [Equation 1]

[0058] Next, the Mahalanobis distance is calculated (S4). This process is performed by the Mahalanobis distance calculation unit 4. Mahalanobis distance is... Figure 5 The distances of each point in such a distribution plot from the origin are determined by taking into account the correlation of the distribution. Table 1 also shows the Mahalanobis distances of each point. Figure 6 The two ellipses shown by the dashed lines represent examples of the loci of points whose Mahalanobis distance from the origin is equal to the Mahalanobis distances of the Fast and Slow points, respectively, illustrating strong and weak correlations. The shape of the ellipses varies depending on the strength of the correlation. The Mahalanobis distance d(p,q) of the point at coordinates (p,q) is calculated using Equation 2. Equation 2 uses the inverse of the covariance matrix from Equation 1. Additionally, the transpose matrix of each point is used.

[0059] [Equation 2]

[0060] Next, the threshold is determined (S5). This process is performed by the threshold setting unit 5. The threshold determined here is not the threshold voltage Vth of the MOS element, but the value of the Mahalanobis distance. It is a threshold used to determine whether the above multi-point measurement results are appropriate. This threshold can be arbitrarily determined by the user. For example, the value of 3 times the standard deviation σ of the Mahalanobis distance of each point calculated in S4 (3σ) can be specified as the threshold.

[0061] Alternatively, it can also be used Figure 7 The threshold is determined by the frequency distribution of Mahalanobis distance as shown. Figure 7The horizontal axis represents the Mahalanobis distance between points. Figure 7 The bar chart in the image represents the number of data points in each interval with a width of 0.5 on the horizontal axis. Figure 7 The line graph in the image represents the cumulative value from the smallest value relative to the whole. Figure 7 The frequency of occurrence increases in the intervals around 1.0~1.5, 1.5~2.0, and 2.0~2.5. Near these intervals, the slope of the line graph becomes steeper. When using... Figure 7 When a threshold is determined, for example, the Mahalanobis distance within a high-frequency interval can be specified as the threshold.

[0062] The threshold can be determined by the user or automatically by the circuit simulation device 1. When the user specifies the threshold, for example, it can be displayed on the display screen 11. Figure 7 Such a frequency distribution chart allows the user to specify the position on the horizontal axis of the screen as the threshold. Relative to... Figure 7 The frequency distribution plot can also show the position corresponding to 3σ on the horizontal axis.

[0063] In the case of automatic operation, a method for determining the threshold of the frequency distribution for the obtained Mahalanobis distance is predetermined. For example, in Figure 7 In a bar chart, the center value of the interval with the highest frequency can be set as the threshold. Alternatively, in... Figure 7 In a line graph, the steepest slope can be used as a threshold. The system can also display automatically determined thresholds like these and allow users to change them.

[0064] Next, the Fast and Slow points among the four corner points are determined (S6). This process is performed by the Fast / Slow point calculation unit 6. Figure 8 Explain how to determine the Fast and Slow points. Figure 8 In this context, the locus of points with the distribution example and the threshold determined in S5 above as Mahalanobis distance is represented by an ellipse superposition. Figure 8 The Fast and Slow points in the graph are the points on the ellipse with the greatest Euclidean distance from the origin. The Vth and Id values ​​are both for points on the Fast side. Figure 8 The middle (top left) is the Fast point, and the Vth and Id values ​​are both on the Slow side. Figure 8 The middle (bottom right) is the Slow point.

[0065] Next, the imbalance value is determined (S7). The imbalance value refers to the value used in... Figure 8The offset from the origin of the corner point corresponding to the imbalance angles FS and SF is determined. The imbalance value is a value (UF1, US1) that is smaller than or greater than zero in the vertical or horizontal component (here, the horizontal component) of the coordinates of the Fast and Slow points, and can be arbitrarily determined by the user. For example, in order to make Figure 8 The curve depicted in a way that the ellipse is tilted and the major axis is horizontal. Figure 9 In this process, values ​​at half the Fast and Slow points on the horizontal axis can be identified as unbalanced values. This is achieved, for example, by displaying on display screen 11. Figure 9 The graph is displayed with points on the horizontal axis specified by the user as the imbalance value. Alternatively, it can be displayed... Figure 8 The distribution map is set by the user at the point on the major axis of the ellipse that serves as the imbalance value.

[0066] Next, the Mahalanobis equivalent points in the orthogonal directions are calculated (S8). This is based on the imbalance values ​​determined in S7. That is, in Figure 9 Starting from a point on the horizontal axis corresponding to the imbalance value, draw a line from that point in a direction orthogonal to the horizontal axis, i.e., parallel to the vertical axis. Determine the intersection point of this line with the ellipse. This intersection point is the Mahalanobis equivalent point in the orthogonal direction. Figure 8 In the equation, the Mahalanobis equivalent point is the point between the origin and the point between the Fast point, the Slow point and the origin, and the point on which the line drawn from the origin in a direction orthogonal to the major axis of the ellipse intersects the ellipse.

[0067] Set the coordinates (UF2, US2) of the second component (Id) of the Mahalanobis equivalent point. The points (UF1, UF2) and (US1, US2) determined by the coordinates (UF1, US1) and (UF2, US2) are designated as the first unbalanced angle point and the second unbalanced angle point, respectively, corresponding to the unbalanced angles FS and SF.

[0068] The determined first and second unbalanced corner points are both located at Figure 8 The inner side of the ellipse. That is, the Mahalanobis distance of these points is less than the threshold of S5. These points are also offset from the... Figure 8 The line connecting the Fast and Slow points in the ellipse is the major axis of the ellipse. Furthermore, the first and second unbalanced angle points are located separated by a distance... Figure 8 The position is symmetrical to the origin. The processing of S7 and S8 above is performed by the unbalance value calculation unit 7. The unbalance value calculation unit 7 also functions as an unbalance angle determination unit.

[0069] Once all four corner points are ready, the inverse operation of the Vth and Id values ​​is performed (S9). This process is handled by the Vth and Id value calculation unit 8. That is, using the four corner points determined in S6 to S8, the structure is reconstructed. Figure 1The angular model shown. Accompanying this, Figure 8 The positions of the distribution points in the graph have also been adjusted, resulting in a slight decrease in overall deviation. This is because the unbalance angles FS and SF, defined in S8, are located inside the ellipse in the graph.

[0070] The results are displayed on the display screen 11 via the calculation result output unit 9. The displayed results are simulations of deviations in various characteristic values ​​when manufacturing semiconductor circuits based on the original data, plotted on a two-dimensional coordinate system of Vth and Id values. Figure 2 The graph shown.

[0071] Then, the displayed result is judged to determine whether it is appropriate (S10). The judgment criteria are predetermined. If the judgment result is OK, the process ends. Figure 4 The process is as follows. A result of "OK" indicates that the distribution area of ​​the plotted points in the displayed graph is smaller than the allowable limits in both the Fast-Slow direction (major axis) and the imbalance direction (minor axis). In this case, it means that the original design data of the semiconductor circuit is good relative to its manufacturing equipment. Therefore, it is determined that it can be directly manufactured using the original design and the manufacturing equipment.

[0072] If the result of S10 is NG, the process continues without ending. Figure 4 The process is being reconfigured. Therefore, we return to a point midway through the process. The return target varies depending on the content of the NG (Not Found). In this case, the original data design is unsuitable for the manufacturing equipment; direct manufacturing could result in many defective products.

[0073] If the deviation in the Fast-Slow direction of the distribution area in the displayed curve is too large, return to the threshold determination in S5. In the returned S5, set the threshold to be lower than the threshold in the previous S5. Then, repeat S6~S10.

[0074] If the deviation in the Fast-Slow direction is within the allowable limits but the deviation in the unbalanced direction is too large, return to S7 to determine the unbalance value. In the returned S7, set the unbalance value to be smaller than the unbalance value in the previous S7. Then, repeat S8~S10. In this S8, compared to the previous S8, the starting point is located closer to the origin.

[0075] If the readjustment is deemed appropriate and deemed OK, then the process ends. Figure 4The process involves repeatedly re-adjusting a design that is deemed NG (Not Acceptable) until it is deemed OK. Once an OK designation is achieved, the changes made in settings S5 and S7 are reflected in the original design data. Based on the reflected design data, good manufacturing can be expected.

[0076] The circuit simulation program product of this embodiment includes a circuit simulation program, which is executed by a computer and includes a data input step, a standardization calculation step, a Mahalanobis distance calculation step, a threshold setting step, a Fast point / Slow point calculation step, an unbalanced angle determination step, and a parameter calculation step.

[0077] In the data input step, the computer accepts design data for the semiconductor circuit. In the standardization calculation step, various predicted characteristic values ​​(e.g., Vth and Id values) for each MOS element in the case of manufacturing multiple semiconductor circuits based on the design data are calculated. These values ​​are then standardized. In the Mahalanobis distance calculation step, the Mahalanobis distance from the standardized origin is calculated for each set of standardized characteristic values ​​for each MOS element.

[0078] In the threshold setting step, thresholds are set for the calculated Mahalanobis distances. Specifically, the user can input a value to be set as the threshold, and then set the input value as the threshold. Alternatively, the user can be prompted with initial candidate values ​​to be set as the threshold, and if the user does not change these initial candidate values, they can be directly set as the threshold.

[0079] In the Fast and Slow point calculation steps, Fast and Slow points are calculated. Specifically, in a standardized orthogonal coordinate system with multiple characteristic values, on the trajectory of points whose calculated Mahalanobis distance equals the threshold, the point with the largest Euclidean distance from the origin and all multiple characteristic values ​​being on the Fast side is identified. This point is designated as the Fast point. Similarly, the point with the largest Euclidean distance from the origin within the region where all multiple characteristic values ​​are on the Slow side is identified. This point is designated as the Slow point.

[0080] In the imbalance angle determination step, in an orthogonal coordinate system, a first imbalance angle point is determined that is located off-center from the line connecting the Fast and Slow points, and whose calculated Mahalanobis distance is equal to or less than a threshold. Additionally, a second imbalance angle point is determined, located symmetrically across the origin from the first imbalance angle point. Specifically, the user inputs information to determine the first imbalance angle point, and the first imbalance angle point is determined based on the input information. Alternatively, the user can be prompted with initial candidate points to be identified as the first imbalance angle point, and these initial candidate points can be directly determined as the first imbalance angle point if the user does not change them. If the first imbalance angle point is determined, the second imbalance angle point can be automatically determined based on it.

[0081] In the parameter calculation step, deviations of various characteristic values ​​are calculated based on the Fast point, Slow point, first unbalanced angle point, and second unbalanced angle point. These calculated deviations can serve as indicators for judging the quality of the input design data.

[0082] In the above-mentioned unbalance angle determination step, the computer can perform the following processing, for example: in an orthogonal coordinate system, taking the point between the Fast point and the Slow point and the origin as the starting point, draw a line from the starting point in a direction orthogonal to the major axis of the trajectory of the point whose Mahalanobis distance from the origin is equal to a threshold, determine the intersection point of the drawn line and the trajectory, and determine the first unbalance angle point and the second unbalance angle point based on the coordinate value of the intersection point.

[0083] The "points between the Fast point and the origin" and "points between the Slow point and the origin" mentioned here can be entered by the user. Alternatively, the user can be prompted with candidate points for the above points, and the candidate points can be used without the user changing them.

[0084] In the above parameter calculation steps, for example, the calculated deviation can be compared with a predetermined judgment standard. If it is unqualified, the computer can reset at least one of the following: setting the threshold, determining the first unbalanced corner point, and determining the second unbalanced corner point, and recalculate the deviation of multiple characteristic values.

[0085] Here, the judgment criteria may include allowable limits in the Fast-Slow direction and allowable limits in the unbalance direction regarding the calculated deviation. In this case, during the parameter calculation step, if the calculated deviation does not meet the allowable limit in the Fast-Slow direction, the threshold is reset in the direction of narrowing; if the calculated deviation does not meet the allowable limit in the unbalance direction, the threshold is reset in a way that brings the starting point closer to the origin.

[0086] As explained in detail above, according to this embodiment, Mahalanobis distance is used to simulate the deviation of characteristic values. Therefore, it is possible to predict circuit characteristics while considering the correlation between deviations of multiple characteristic values.

[0087] This embodiment is merely illustrative and does not limit the scope of the present disclosure in any way. Therefore, the present disclosure can naturally be modified and varied in various ways without departing from its spirit. For example, the target MOS element is mainly a field-effect transistor, but it is not limited to this; any element with a MOS structure is acceptable. It can also be an insulated-gate bipolar transistor, an insulated-gate thyristor, etc.

[0088] As various characteristic values ​​for MOS devices, threshold voltage Vth and drain current Id are listed, but not limited to these. Gain, parasitic capacitance, parasitic resistance, etc., can also be included. Furthermore, it is not limited to two; more than three can be used.

[0089] The methods for determining the first and second unbalanced angle points are not limited to those described above. For example, the intersection of the line drawn from the starting point in a direction orthogonal to the major axis of the ellipse with the ellipse can be directly determined as the first and second unbalanced angle points. Alternatively, the unbalanced value can be specified on the vertical axis instead of the horizontal axis. In this case, Figure 9 The starting point is located on the vertical axis. It can also be based on data originating from that starting point. Figure 9 The coordinates of the intersection of the horizontal line and the ellipse are used to determine the first and second unbalanced corner points.

[0090] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0091] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A circuit simulation device, characterized in that, The characteristic values ​​of the metal-oxide-semiconductor element in the semiconductor circuit containing the metal-oxide-semiconductor element are simulated. The circuit simulation device includes: The data input section accepts the design data of the semiconductor circuit as input; The standardization calculation unit standardizes various characteristic values ​​predicted for each of the metal-oxide-semiconductor elements when manufacturing multiple semiconductor circuits based on the design data. The Mahalanobis distance calculation unit calculates the Mahalanobis distance from the standardized origin for each of the metal-oxide-semiconductor elements based on a set of standardized multiple characteristic values. The threshold setting unit sets a threshold for the calculated multiple Mahalanobis distances; The fast and slow point calculation unit calculates the fast point and the slow point on the trajectory of the points whose calculated Mahalanobis distance is equal to the threshold in the orthogonal coordinate system of the standardized multiple characteristic values. The fast point is located on the fast side and has the largest Euclidean distance from the origin, and the slow point is located on the slow side and has the largest Euclidean distance from the origin. The imbalance angle determination unit determines a first imbalance angle point and a second imbalance angle point in an orthogonal coordinate system. The first imbalance angle point is located off-center from the line connecting the fast point and the slow point, and the calculated Mahalanobis distance is equal to or less than a threshold. The second imbalance angle point is located symmetrical to the first imbalance angle point across the origin. The parameter calculation unit calculates the deviation of the various characteristic values ​​based on the fast point, the slow point, the first unbalanced corner point, and the second unbalanced corner point.

2. The circuit simulation device according to claim 1, characterized in that, The unbalance angle determination part is in the orthogonal coordinate system. Taking the point between the fast point and the slow point and the origin as the starting point, Draw a line from the starting point in a direction orthogonal to the major axis of the locus of points whose Mahalanobis distance from the origin is equal to the threshold. Determine the intersection point of the line and the trajectory. Based on the coordinates of the intersection points, the first unbalanced corner point and the second unbalanced corner point are determined.

3. The circuit simulation device according to claim 2, characterized in that, The parameter calculation unit also compares the calculated deviation with a predetermined judgment standard. If the condition is not met, at least one of the following should be repeated: setting the threshold, determining the first unbalanced corner point, and determining the second unbalanced corner point. The deviations of the various characteristic values ​​are recalculated.

4. The circuit simulation device according to claim 3, characterized in that, The judgment criteria include permissible limits for the calculated deviation in the fast-slow direction and permissible limits for the unbalanced direction. If the calculated deviation is not within the allowable limit in the fast-slow direction, the parameter calculation unit resets the parameter in the direction of reducing the threshold. If the calculated deviation is not within the allowable limit relative to the direction of imbalance, the starting point is reset in a manner that brings the starting point closer to the origin.

5. The circuit simulation device according to claim 1, characterized in that, The characteristic values ​​of the metal-oxide-semiconductor device include at least one of the following: threshold voltage, drain current, gain, parasitic capacitance, and parasitic resistance.

6. A circuit simulation program product, comprising a circuit simulation program, characterized in that, The characteristic values ​​of the metal-oxide-semiconductor element in the semiconductor circuit containing the metal-oxide-semiconductor element are simulated. The circuit simulation program is executed by a computer and includes the following steps: The data input step accepts the input of the design data for the semiconductor circuit. The standardized calculation steps standardize the various characteristic values ​​predicted for each of the metal-oxide-semiconductor elements when manufacturing multiple of the semiconductor circuits based on the design data. The Mahalanobis distance calculation step involves calculating the Mahalanobis distance from the standardized origin for each group of standardized characteristic values ​​of the metal-oxide-semiconductor element. The threshold setting step involves setting thresholds for the calculated multiple Mahalanobis distances; The fast and slow calculation steps involve calculating the trajectory of points whose calculated Mahalanobis distance is equal to the threshold in an orthogonal coordinate system of the standardized multiple characteristic values. The fast point where all the multiple characteristic values ​​are located on the fast side and have the largest Euclidean distance from the origin, and the slow point where all the multiple characteristic values ​​are located on the slow side and have the largest Euclidean distance from the origin; The imbalance angle determination step involves identifying a first imbalance angle point and a second imbalance angle point in an orthogonal coordinate system. The first imbalance angle point is located off-center from the line connecting the fast point and the slow point. The calculated Mahalanobis distance is equal to or less than the threshold value. The second unbalanced corner point is located symmetrical to the first unbalanced corner point across the origin; and The parameter calculation step involves calculating the deviation of the various characteristic values ​​based on the fast point, the slow point, the first unbalanced corner point, and the second unbalanced corner point.

7. The circuit simulation program product according to claim 6, characterized in that, The circuit simulation program is executed by a computer, and the unbalance angle determination step includes: In the orthogonal coordinate system, Taking the point between the fast point and the slow point and the origin as the starting point, Draw a line from the starting point in a direction orthogonal to the major axis of the locus of points whose Mahalanobis distance from the origin is equal to the threshold. Determine the intersection point of the line and the trajectory. Based on the coordinates of the intersection points, the first unbalanced corner point and the second unbalanced corner point are determined.

8. The circuit simulation program product according to claim 7, characterized in that, The circuit simulation program is executed by a computer, and the parameter calculation step includes: The calculated deviation will also be compared with a predetermined judgment standard. If the condition is not met, at least one of the following should be repeated: setting the threshold, determining the first unbalanced corner point, and determining the second unbalanced corner point. The deviations of the various characteristic values ​​are recalculated.

9. The circuit simulation program product according to claim 8, characterized in that, The judgment criteria include permissible limits for the calculated deviation in the fast-slow direction and permissible limits for the unbalanced direction. The circuit simulation program enables the computer to perform the calculation steps in the parameter calculation steps: If the calculated deviation fails to meet the allowable limit relative to the fast-slow direction, the threshold is reset in the direction of reducing it. If the calculated deviation is not within the allowable limit relative to the direction of imbalance, the starting point is reset in a manner that brings it closer to the origin.

10. The circuit simulation program product according to claim 6, characterized in that, The characteristic values ​​of the metal-oxide-semiconductor device include at least one of the following: threshold voltage, drain current, gain, parasitic capacitance, and parasitic resistance.

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