Simulation model and generation method thereof, simulation method, electronic device and storage medium

Abstract

Embodiments of the present disclosure relate to simulation models and methods for generating the same, simulation methods, electronic devices, and storage media. The method includes: determining the position of a pseudo-global process corner based on the position of a predetermined global process corner and the correlation between the target parameters of each global process corner, the pseudo-global process corner being used to assist in defining the distribution range of the electrical characteristics of the simulation object; adjusting the process corner model parameters corresponding to each target parameter based on the values ​​of the target parameters at the respective positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of each target parameter are respectively consistent with the target values ​​of the corresponding target parameters; determining the model parameters of the simulation model based on each adjusted process corner model parameter to generate a simulation model. The technical solution of the present disclosure can improve the accuracy of MC simulation.

Description

Technical Field

[0001] Embodiments of the present disclosure generally relate to integrated circuits, and more particularly, to simulation models and methods for generating the same, simulation methods, electronic devices, and storage media. Background Art

[0002] Design Technology Co-Optimization (DTCO) is gaining more and more attention in the industry during the development of new processes. Usually, when developing new processes, semiconductor process device simulation (Technology Computer Aided Design, TCAD) is used to simulate processes and devices to obtain the electrical characteristics of the devices.

[0003] The finite element method used by TCAD requires the generation of a large number of grids to solve discrete equations, which makes it impractical to simulate large-scale circuits. Therefore, it is necessary to fit the electrical simulation results of TCAD through the Simulation Program with Integrated Circuit Emphasis (SPICE) model to obtain the SPICE model for PPA (performance, process, area) simulation verification or even circuit-level simulation verification. In other words, TCAD is used for early process simulation to obtain device characteristics, and SPICE-level circuit simulation is required in the later stage. How to achieve the link from TCAD to SPICE has become a problem that plagues the industry. Summary of the invention

[0004] According to an exemplary embodiment of the present disclosure, a simulation model generation and simulation solution is provided to at least partially overcome the above or other potential defects.

[0005] According to one aspect of the present disclosure, a method for generating a simulation model is provided. The method includes: determining the position of a pseudo-global process corner based on the position of a predetermined global process corner and the correlation between the target parameters of each global process corner, the pseudo-global process corner being used to assist in defining the distribution range of the electrical characteristics of the simulation object; adjusting the process corner model parameters corresponding to each target parameter based on the values ​​of the target parameters at the positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of each target parameter are respectively consistent with the target values ​​of the corresponding target parameters; determining the model parameters of the simulation model based on each adjusted process corner model parameter, so as to generate the simulation model.

[0006] According to a second aspect of the present disclosure, a simulation model generated according to the first aspect is provided.

[0007] According to a third aspect of the present disclosure, a method for performing random simulation using a simulation model is provided, the method comprising: assigning Gaussian distribution values ​​to model parameters of the simulation model in a predetermined number of simulations; and performing simulation with the model parameters assigned Gaussian distribution values ​​to determine the distribution of electrical characteristics of the simulation object.

[0008] In some embodiments, assigning Gaussian distribution values ​​to model parameters of the simulation model in each simulation includes: normalizing the Gaussian distribution values ​​to generate normalized Gaussian distribution values; multiplying the normalized Gaussian distribution values ​​by corresponding weight coefficients to obtain Gaussian parameter distributions of different component sizes; and generating model parameters for random simulation based on a combination of Gaussian parameter distributions of different component sizes.

[0009] In a fourth aspect of the present disclosure, an electronic device is provided. The electronic device includes a processor; and a memory coupled to the processor, the memory having instructions stored therein, and when the instructions are executed by the processor, the device performs an action, the action including: determining the position of a pseudo-global process corner based on the position of a predetermined global process corner and the correlation between the target parameters of each global process corner, the pseudo-global process corner being used to assist in defining the distribution range of the electrical characteristics of the simulation object; adjusting the process corner model parameters corresponding to each target parameter based on the values ​​of the target parameters at the respective positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of each target parameter are respectively consistent with the target values ​​of the corresponding target parameters; determining the model parameters of the simulation model based on each adjusted process corner model parameter to generate the simulation model.

[0010] In some embodiments, the predetermined global process corners include a typical process corner, a fast N fast P process corner, and a slow N slow P process corner, and determining the position of the pseudo-global process corner includes: specifying the value of one of two associated target parameters of each pseudo-global process corner; determining the value of the other of the two associated target parameters corresponding to each pseudo-global process corner based on the difference between the value of one of the target parameters and the value of the corresponding target parameter of the typical process corner and a specified correlation value; and respectively determining the positions corresponding to the values ​​of the two associated target parameters as the positions of each pseudo-global process corner.

[0011] In some embodiments, the location of the pseudo-global process corner is determined based on the following formula:

[0012] ;

[0013] in represents the correlation between the associated target parameters, X and Y each represent one of the two sets of associated target parameters, and x and y represent the values ​​of the two associated target parameters. represents the average value of a set of target parameters represented by X, Represents the average value of a set of target parameters represented by Y.

[0014] In some embodiments, determining the model parameters of the simulation model based on each adjusted process corner model parameter includes: determining a weight coefficient based on each adjusted process corner model parameter, the weight coefficient representing the degree of influence of the adjusted process corner model parameter on the electrical characteristic distribution of the simulation object in different directions; and determining the model parameters of the simulation model based on a combination of each weight coefficient.

[0015] In some embodiments, determining the weight coefficient based on each adjusted process corner model parameter includes: performing principal component analysis on the adjusted process corner model parameters to determine the weight coefficient; or performing singular value decomposition on the adjusted process corner model parameters to determine the weight coefficient.

[0016] In some embodiments, determining weight coefficients based on each adjusted process corner model parameter includes: arranging the adjusted process corner model parameters into an initial matrix; normalizing the initial matrix to generate a standardized matrix; determining a covariance matrix of the standardized matrix; and determining eigenvalues ​​and eigenvectors of the covariance matrix; and determining the ratio of each eigenvalue to the sum of all eigenvalues ​​as the weight coefficient of the eigenvector corresponding to each eigenvalue.

[0017] In some embodiments, the standardization of the initial matrix includes: determining the difference between the value of each element in the initial matrix and the average value of the elements in the same row of the initial matrix; determining the standard deviation of the value of each element in the initial matrix; and determining the ratio of each difference to each standard deviation as each element of the standardized matrix.

[0018] In some embodiments, determining the covariance matrix of the normalized matrix includes: determining the product of the transposed matrix of the normalized matrix and the normalized matrix; and dividing the product by the number of samples of elements in the initial matrix minus one to obtain the covariance matrix.

[0019] In some embodiments, determining the model parameters of the simulation model based on the combination of various weight coefficients includes: selecting a predetermined number of eigenvalues ​​from the eigenvalues ​​in descending order; determining the ratio of the selected eigenvalues ​​to all eigenvalues; and multiplying the ratio of each model parameter by the predetermined parameter as a weight coefficient; and adding the results of each multiplication to generate the model parameters of the simulation model.

[0020] In some embodiments, the method also includes: determining the square root value of the selected eigenvalue; multiplying each square root value by the eigenvector corresponding to the respective eigenvalue to obtain a first vector; multiplying the first vector by the variance of the respective adjusted process angle model parameters of each global process angle to obtain a first result; and dividing the first result by the variance of the respective coefficients of each global process angle to obtain a second result, wherein the second result represents the value of the model parameter of the simulation model.

[0021] In a fifth aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the method according to the first and third aspects of the present disclosure is implemented.

[0022] It will be understood from the following description that the technical solution of the present disclosure can effectively improve the accuracy of MC simulation.

[0023] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the disclosure, nor is it intended to limit the scope of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A schematic diagram of the DTCO process is shown;

[0025] Figure 2 A schematic diagram of the process corner is shown;

[0026] Figure 3 A schematic diagram showing an example environment in which embodiments of the present disclosure can be implemented;

[0027] Figure 4 A flowchart of a method for generating a simulation model according to some embodiments of the present disclosure is shown;

[0028] Figure 5 A schematic diagram showing a configuration file according to some embodiments of the present disclosure;

[0029] Figure 6 A schematic diagram showing PCA configuration information according to some embodiments of the present disclosure is shown;

[0030] Figure 7 A schematic diagram showing MC results of PCA according to some embodiments of the present disclosure;

[0031] Figure 8 A schematic diagram showing a process corner for PCA extraction according to some embodiments of the present disclosure is shown;

[0032] Fig. 9A schematic diagram showing normalized target parameters of process corners for PCA extraction according to some embodiments of the present disclosure;

[0033] Fig.10 A schematic diagram showing process angles and corresponding model parameters according to some embodiments of the present disclosure is shown;

[0034] Fig.11 A schematic diagram showing scaling of parameters of MC according to some embodiments of the present disclosure is shown;

[0035] Fig.12 A schematic diagram showing the comparison between the MC simulation results of vl_lin and idlin and the results of the MC process corner according to some embodiments of the present disclosure is shown;

[0036] Fig.13 A schematic diagram showing a comparison between MC simulation results of vt_sat and idsat and results of MC process corner according to some embodiments of the present disclosure is shown;

[0037] Fig.14 A block diagram of a computing device capable of implementing various embodiments of the present disclosure is shown.

[0038] In the various drawings, the same or corresponding reference numerals represent the same or corresponding parts. DETAILED DESCRIPTION

[0039] The principles of the present disclosure will be described below with reference to the various exemplary embodiments shown in the accompanying drawings. It should be understood that the description of these embodiments is only to enable those skilled in the art to better understand and further implement the present disclosure, and is not intended to limit the scope of the present disclosure in any way. It should be noted that similar or identical reference numerals may be used in the figures where feasible, and similar or identical reference numerals may represent similar or identical functions. Those skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods described herein may be adopted without departing from the principles of the present invention described herein.

[0040] As used herein, the term "including" and its variations mean open inclusion, i.e., "including but not limited to". Unless otherwise stated, the term "or" means "and / or". The term "based on" means "based at least in part on". The terms "an example embodiment" and "an embodiment" mean "at least one example embodiment". The term "another embodiment" means "at least one additional embodiment". The terms "first", "second", etc. may refer to different or the same objects.

[0041] SPICE is a language simulator software used for circuit description and simulation. It is used to detect the integrity of circuit connections and functions, as well as to predict the behavior of circuits. In order to perform SPICE simulation, a device-level SPICE model must be established first, such as the SPICE model of the Metal-Oxide-Semiconductor Field-EffectTransistor (MOSFET) device, so that there is a specific mathematical model in the simulation program to describe the corresponding components. The SPICE model of components is closely related to the semiconductor manufacturing process, and the corresponding device characteristics can be simulated through the SPICE model of components.

[0042] SPICE models usually consist of two parts: model equations and model parameters. When modeling, SPICE modeling engineers usually need to manually change the values ​​of model parameters in the model equations, and then compare the test data with the simulation data until the model parameter values ​​that are closest to the test data and the simulation data are found. This method requires repeated changes in the values ​​of model parameters, and each change requires comparison of test data with simulation data, which is time-consuming and laborious.

[0043] Taking the MOS tube as an example, the initial SPICE model of the MOS tube has a model equation for characterizing the DC characteristics of the MOS device, a model equation for characterizing the AC characteristics of the MOS tube, and a model equation for characterizing other characteristics of the MOS tube (temperature characteristics, noise characteristics, layout characteristics, etc.), each model equation may include at least one equation, and each equation may include at least one model parameter. The model parameters in the initial SPICE model can be used to characterize the electrical characteristics of the target device, such as the model parameters for characterizing the saturation current Idsat, linear current Idlin, off current Idoff, linear threshold voltage Vtlin, and saturation threshold voltage Vtsat of the MOS tube; accordingly, the model parameters in the initial SPICE model can also be used to characterize the physical characteristics of the target device, such as the model parameters for characterizing the channel length, channel width, and gate oxide thickness of the MOS tube, etc.

[0044] Usually, the process design package that designers get is called PDK (Process Design Kit), which is a process simulation package provided by the wafer foundry to the design company. Designers use the process device package in PDK to simulate and design circuits. SPICE model is an important part of DK. Design companies use simulation software (HSPICE) to call model cards and implement device simulation and design in various situations by adding stimulus conditions. Models are generally abstract mathematical formulas, and model cards record the coefficients of abstract formulas in text files, such as forming model cards.

[0045] At present, the SPICE models in the process industry are all based on the Berkeley BSIM model. Among them, the planar models are mainly BSIM3 and 4; the model for FINFET is the Berkeley Short-channel IGFET Model – CommonMulti-Gate, referred to as BSIMCMG. The BSIM model can accurately describe the electrical characteristics of the device at various voltages and temperatures in an analytical way through a series of mathematical and physical formulas. Since these models have many parameters and complex formulas, the current practice in the industry is that EDA companies incorporate these complex mathematical models into the simulation software. Wafer foundries only need a card that provides model coefficients, that is, a model card, and users use SPICE simulation software to call the model card for circuit simulation.

[0046] In addition to AC and DC simulations, SPICE can also perform Monte Carlo simulations to simulate the electrical offset caused by the fluctuation of the electrical parameters of the device within a certain sigma range. Monte Carlo (MC) simulation can more realistically simulate the electrical characteristics of the device. Designers can establish the performance window of the device by simulating the entire circuit MC, and then adjust their design direction.

[0047] In the field of chip design, MC simulation is a powerful tool that can simulate the mismatch between devices on a chip and the mismatch between different wafers. Monte Carlo simulation can provide more comprehensive and accurate simulation results in chip design, helping designers to better optimize the design and improve the yield.

[0048] Process fluctuations are well known for a semiconductor production line. Process fluctuations cause parameter variations for every transistor on the chip. For example, the threshold voltage Vth of a MOS transistor is a parameter related to the gate oxide thickness and the channel doping concentration. Process parameters such as gate oxide thickness and channel doping concentration vary with manufacturing process variations. The actual threshold Vth of a MOS device also varies with process variations and is therefore not a constant value. Usually, due to the complexity of the modeling task, parameter extraction of semiconductor devices uses only a small number of devices for modeling. Statistically speaking, this is a small sample base. Since there is a WAT ​​(wafer accept) test in the manufacturing process, a large amount of statistical data is available, so there is a large sample base statistically. The idea behind the Corner Model is to use the results of process monitoring for modeling. Using WAT data, a model library can be extended with the Corner Model to obtain a realistic representation of the device behavior under real manufacturing process conditions. The Corner Model allows worst-case simulations of circuits to obtain realistic results. The process deviations between lots, wafers, and dies are all global process deviations, which are usually described as global variations in the SPICE model. The impact of local process variation in a die is the error caused by uneven particle injection and uneven etching, which is described as local variation in the SPICE model. Due to the existence of global and local deviations, the speed of complementary metal oxide semiconductors (CMOS) varies, which leads to different speeds of chips. Local and global deviations are usually expressed as random distribution standard deviations. Local and global deviations satisfy the relationship of formula (1):

[0049] (1)

[0050] in represents the square of the standard deviation of the total random distribution; The square of the standard deviation of the global random distribution representing the global deviation above; The square of the standard deviation of the local random distribution representing the above local deviation.

[0051] Chip manufacturing is a physical process, and there are process deviations (including doping concentration, diffusion depth, etching degree, etc.), which lead to differences between different batches, between different wafers in the same batch, and between different chips on the same wafer. The parameters of field effect transistors (MOSFETs) vary greatly. In order to reduce the difficulty of circuit design, process engineers must ensure that the performance of the device is within a certain range. If it exceeds this range, the IC will be scrapped, and the yield of the IC can be guaranteed in this way. This performance range provided to designers is given in the form of "process corners".

[0052] Since the global process deviation has different effects on NMOS and PMOS in CMOS, the process corners can be divided into the following five types according to the speed of the transistor: TT (Typical Typical), SSG, SlowN Slow P Global, FFG, Fast N Fast P Global, SFG, Slow N Fast P Global, and FSG, Fast N Slow P Global. If the influence of local deviation is taken into account, there are four other total process corners: FF, SS, FS, and SF. The only difference between the four total process corners and the other process corners mentioned above except TT is that there is less G at the end. The one with G indicates global, and the one without G here indicates the total process corner. In addition to the above 9 fixed process corners, the corresponding MC model is also very important.

[0053] Therefore, a complete set of MC models requires the establishment of a global MC model and a local MC model. The total deviation of the entire process can be obtained by adding the two. A control switch (flag) can be added to the SPICE model card, so that the MC type to be simulated can be switched through the switch, as shown in formula (2):

[0054] (2)

[0055] represents the total MC deviation, represents the global MC deviation, represents the local MC deviation.

[0056] During the simulation process, you can set the flag parameter of the model card to turn on the local MC and the global MC for superimposed simulation to get the total deviation. Since the local MC has no correlation, you only need to add a sigma function (Gaussian function) to the parameters, and adjust the coefficient of the Gaussian function to get the local random distribution standard deviation. For the extraction of the global MC, in addition to the individual electrical indicators such as vt_lin, vt_sat, idlin, idsat, the sigma also needs to consider the correlation of vt / id and the correlation of NP MOS. Therefore, the extraction (establishment) of the global MC model and how to extract the correlated MC model have become a problem that plagues SPICE model engineers.

[0057] The idea of ​​process corners is to limit the speed fluctuation range of NMOS and PMOS transistors to a rectangle defined by four corners. These four corners are shown below, as mentioned above and further explained here:

[0058] Fast NFET and fast PFET, FF (Fast Fast): Both NMOS and PMOS are in the fastest state, when the switching speed of the device is the fastest.

[0059] Slow NFET and slow PFET, i.e. SS (Slow Slow): Both NMOS and PMOS are in the slowest state, when the switching speed of the device is the slowest.

[0060] Fast NFET and slow PFET, that is, FS (Fast Slow): NMOS is in the fastest state, while PMOS is in the slowest state, or vice versa FS (Slow Fast).

[0061] Slow NFET and fast PFET, that is, SF (Slow Fast): NMOS is in the slowest state, while PMOS is in the fastest state, or vice versa SF (Fast Slow).

[0062] In addition, there is the typical process corner mentioned earlier, namely TT: both NMOS and PMOS are in typical conditions, which are usually used for preliminary circuit design and simulation.

[0063] Simulating the circuit at various process corners and extreme temperature conditions is the basis for determining the yield. For example, transistors with thinner gate oxides and lower threshold voltages fall near the fast corners. When the device models corresponding to each corner are extracted from the wafer, the on-chip NMOS and PMOS test structures show different gate delays, and these corners are actually selected to obtain acceptable yields. Therefore, only wafers that meet these performance indicators are considered qualified. Simulating the circuit at various process corners and extreme temperature conditions is the basis for determining the yield. Process corners help designers evaluate the performance of the circuit under different process conditions and ensure that the circuit can work properly even under the worst conditions.

[0064] Since the global process corner takes into account the correlation between vt and id, it is expected that one MC model can reflect the information of multiple process corner models.

[0065] The traditional MC extraction method usually directly calculates the MC distribution on the three process angles of FFG, SSG and TT. The MC distribution obtained in this way has a strong correlation. Since the three are basically on the same straight line, the obtained correlation is about 1, which does not match the actual distribution. In addition, since the traditional algorithm does not consider the relationship between the correlation of parameters and the correlation of MC distribution, the distribution results of MC of id and vt are offset from the actual angle, affecting its accuracy.

[0066] In view of this, the present disclosure provides an improved solution.

[0067] Some embodiments of the present disclosure provide an improved method for generating a simulation model. The method includes: determining the position of a pseudo-global process corner based on the position of a predetermined global process corner and the correlation between the target parameters of each global process corner, the pseudo-global process corner is used to assist in defining the distribution range of the electrical characteristics of the simulation object; adjusting the process corner model parameters corresponding to each target parameter based on the value of the target parameter at each position of the global process corner and the pseudo-global process corner, so that the simulation value of each target parameter is consistent with the target value of the corresponding target parameter; determining the model parameters of the simulation model based on each adjusted process corner model parameter to generate a simulation model. The embodiments of the present disclosure can effectively improve the accuracy of MC simulation.

[0068] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings.

[0069] Figure 1 The basic process of DTCO is known in the industry and is briefly described below.

[0070] At block 102, a new technical standard is provided.

[0071] At block 104 , TCAD simulation is performed, which includes simulation of transistors and interconnects or connection relationships, and can output, for example, a curve of device characteristics.

[0072] At block 106 , a PDK is shown, which includes DR (design rules), standard cells, and models. The models include compact models and RC (resistance and capacitance).

[0073] At block 108 , a SPICE simulation of the circuit is shown being performed.

[0074] At block 110 , the output from the circuit simulation of block 108 is fed back to block 102 for co-optimization.

[0075] Figure 2 A schematic diagram of the process corner is shown. Figure 2 In the FS, FF, SF and SS shown in the figure, the first letter stands for NMOS and the second letter stands for PMOS. TFS (Typical, Fast, Slow) refers to different concentrations of N-type and P-type doping respectively. Because NMOS and PMOS are made independently in the process, they will not affect each other during manufacturing. However, for the circuit, NMOS and PMOS work at the same time, and the speed of the NMOS and PMOS produced may be fast or slow, which is reflected in the slight inconsistency of the delay of the MOS tube between different batches or different chips, so there will be four situations: FF, SS, FS, and SF.

[0076] Through the adjustment of process injection, the speed of the analog device is adjusted, and different levels of FF and SS are set according to the deviation. Under normal circumstances, most of them are TT, and the above five process angles can cover about 99.73% of the range within ±3σ. This random occurrence conforms to the normal distribution.

[0077] Pay more attention to two parameters, vth and ids. If you want to minimize the risk of the circuit, the circuit must have enough margin and all PVT (process, voltage, temperature) combination simulations must pass. Generally speaking, the worst case is SS, the highest temperature, and the lowest voltage. If this situation can pass the simulation, then the circuit is basically fine.

[0078] There are many reasons for process deviation, such as doping concentration, temperature control during manufacturing, etching degree, etc., which may cause different conditions in different areas of the same wafer and different conditions between different wafers. This kind of random occurrence can only be evaluated through statistical methods to ensure the rationality of coverage.

[0079] Figure 3Schematic diagram of an example environment 300 in which embodiments according to the present disclosure can be implemented. Figure 3 As shown, the example environment 300 includes a computing device 310 and a client 320 .

[0080] In some embodiments, the computing device 310 may interact with the client 320. For example, the computing device 310 may receive an input message from the client 320 and output a feedback message to the client 320. In some embodiments, the input message from the client 320 may be data of a semiconductor process device. The computing device 310 may perform corresponding mathematical operations on the data of the semiconductor process device and output corresponding operation results to the client 320.

[0081] In some embodiments, computing device 310 may include, but is not limited to, a personal computer, a server computer, a handheld or laptop device, a mobile device (such as a mobile phone, a personal digital assistant (PDA), a media player, etc.), consumer electronics, a minicomputer, a mainframe computer, cloud computing resources, etc.

[0082] It should be understood that the structure and function of the example environment 300 are described for exemplary purposes only and are not intended to limit the scope of the subject matter described herein. The subject matter described herein can be implemented in different structures and / or functions. The environment is merely illustrative and is not intended to limit the application environment of the embodiments of the present disclosure.

[0083] In order to explain the principle of the present disclosure more clearly, the following will refer to Figure 4 Let's describe it in more detail.

[0084] Figure 4 A flowchart of a method 400 for generating a simulation model according to some embodiments of the present disclosure is shown.

[0085] At block 402 , the position of a pseudo global process corner is determined based on the positions of predetermined global process corners and the correlation between target parameters of the respective global process corners, where the pseudo global process corner is used to assist in defining the distribution range of electrical characteristics of a simulation object.

[0086] In some embodiments, the predetermined global process angle may include a typical process angle TT, a fast N fast P process angle FFG, and a slow N slow P process angle SSG. It should be understood that the embodiments of the present disclosure are not limited to this, and the predetermined process angle may be changed accordingly as needed. The position of the process angle can be understood as a target parameter, such as the size relationship of vt / id, etc. at different process angles, which is presented on the graph to reflect the position relationship. Therefore, determining the position of the process angle is to determine the position of the target parameter corresponding to the process angle, or the value of the target parameter. In some embodiments, the value of the target parameter of the process angle can be specified to determine the position of the process angle.

[0087] In some embodiments, a pseudo-global process angle is introduced. The pseudo-global process angle is not a process angle known in the industry. The pseudo-global process angle mainly has a mathematical meaning and can be used to assist in defining the distribution range of the electrical characteristics of the simulation object. In a preferred embodiment, the pseudo-global process angle is not in a straight line with the selected predetermined global process angle, so as to obtain a distribution closer to the actual distribution.

[0088] In some embodiments, determining the position of the pseudo-global process corner may include: specifying the value of one of two associated target parameters of each pseudo-global process corner, for example, specifying a value in vt / id; determining the value of the other of the two associated target parameters corresponding to each pseudo-global process corner based on the difference between the value of one of the target parameters and the value of the corresponding target parameter of the typical process corner and a specified correlation value, wherein the correlation may be specified by a user based on actual process conditions and known conditions, for example, 0.6, 0, 8, etc.; determining the positions corresponding to the values ​​of the two associated target parameters as the positions of each pseudo-global process corner, for example, the positions corresponding to the values ​​of the two associated target parameters are respectively determined. Fig. 9 The position of vt=0.235, id=-1 shown in FIG. 1 is determined as the position of a pseudo-global process corner.

[0089] Usually, the model card contains the process corner model information, so that the specific conditions of each process corner can be known through simulation. However, if you want to simulate the distribution (curve distribution) of various electrical characteristics within the range limited by the process corner, it cannot be achieved through several fixed process corner models in the model card. This can be achieved through Monte Carlo simulation. Monte Carlo simulation can describe the real distribution within the range between fixed process corners.

[0090] First refer to Figure 5 , Figure 5 A schematic diagram of a configuration file according to some embodiments of the present disclosure is shown. By configuring the json file, the data file name and data location to be captured are configured, such as Figure 5 As shown. Among them, "corner" represents the process corner, tt, ffg, ssg, ffa, and ssa respectively represent some of the process corners mentioned above. The file also defines the PCA (principle component analysis, PCA for short) file, namely PCA_lib. PCA_lib is a text file containing these fixed process corners. Specifically, PCA_lib can contain which files to grab data from, as well as the proportional coefficients of ffa and ssa. Among them, "corner" can represent the position where parameters need to be extracted. For example, for tt defined under "corner", it can mean extracting the corresponding parameters (model parameters) at the position of the process corner tt.

[0091] Figure 6 Schematic diagram of PCA configuration information according to some embodiments of the present disclosure is shown. The process angle parameters mentioned above for extracting the MC model are defined in the .lib file. For example, Figure 6 As shown in the figure, the .lib ffg and .end ffg keywords contain the delta values ​​of the ffg parameters (phig, dvtp0, u0, a2, etc.) relative to the tt. The delta here indicates the deviation of the model parameters of the process corner compared to the model parameters of the tt process corner, and the rest are similar.

[0092] Figure 7 A schematic diagram showing MC results of PCA according to some embodiments of the present disclosure. Figure 7 Several parameters are shown in the figure, which are denoted as pa0, pa1, pa2, pa3, and pa4. Among them, pa0=p0 means that p0 is assigned to pa0. For pa1 to pa4, and so on. pa0=agauss(0,1,3) means that a Gaussian function value is assigned to the parameter pa0 during the simulation process. For p2 to p4, and so on. As a result, the model parameters are randomly changed during the simulation process, thereby realizing Monte Carlo simulation. About Figure 7 The parameters in the last few lines are described further below.

[0093] In some embodiments, by placing the target file and the .lib file in the same folder, the target file and the .lib file can be selected through the menu interface of the corresponding simulation software. Just select the target file. The software will save the PCA extraction results in the file format of "PCA.lib". The obtained PCA.lib results are integrated into the SPICE model, and the establishment of the MC model is completed. This is described in detail later.

[0094] In some embodiments, the process angle of MC can have two directions: one is FFG&SSG, and the other is FFA&SSA. Among them, FFG&SSG is the 3sigma range value of vt-id corresponding to vt and id under the FFG process angle and SSG process angle, the 3sigma range value of vt is the process angle voltage minus the process angle voltage of tt, and the 3sigma range value of id is the process angle id divided by the id of the process angle tt-1. Since the process angle range of FFG and SSG usually refers to the 3*sigma value in the data of WAT test. For NMOS, the vt value of the FFG process angle is smaller than the median value, and the id value is larger than the median value; for PMOS, the FFG process angle vt value is larger than the median value, and the id value is smaller than the median value; the SSG process angle is opposite to the FFG process angle. The 3sigma range value is obtained according to "vt is the process angle voltage minus tt, and id is the process angle id divided by tt id". 3sigma is the difference between the simulation results of vt and id under the process angle and the simulation results of tt.

[0095] For Monte Carlo simulation, which is to simulate random fluctuations of the device, the 3σ criterion is usually referred to, that is, the error range of the output results. The 3σ criterion first assumes that a set of test data contains only random errors, calculates and processes them to obtain the standard deviation, and determines an interval according to a certain probability. It is believed that any error exceeding this interval is not a random error but a gross error, and the data containing this error should be eliminated. The 3σ principle is: the probability that the value is distributed in (μ-σ, μ+σ) is 0.6827; the probability that the value is distributed in (μ-2σ, μ+2σ) is 0.9545; the probability that the value is distributed in (μ-3σ, μ+3σ) is 0.9973; it can be considered that its values ​​are almost all concentrated in the interval (μ-3σ, μ+3σ), and the possibility of exceeding this range is less than 0.3%. σ represents the standard deviation and μ represents the mean.

[0096] In some embodiments, the process angle range values ​​of FFG and SSG can be normalized. The normalization allows the dimension of each parameter to be reflected, thereby more realistically reflecting the actual situation. Fig. 9 As shown, the following text will Fig. 9 Further description. If only FFG and SSG are retained, the distribution of MC obtained by PCA extraction is approximately a straight line, and the correlation of vt_id is about 1. Therefore, it is necessary to add additional process angle components. In order to simplify the extraction process, two additional process angles are introduced into the algorithm of some embodiments of the present disclosure: ffa & ssa, which are the pseudo process angles mentioned above, and PCA is performed together with FFG & SSG & TT.

[0097] See also Figure 8 , Figure 8A schematic diagram showing process corners for PCA extraction according to some embodiments of the present disclosure is shown. Figure 8 The figure shows five process corners: FFG, TT, SSG, SSA and FFA. The difference between FFG and SSG and FF and SS is that they are followed by a G, which means global. FFG and SSG are determined by process conditions, usually obtained from silicon data or provided by a process integration engineer (PIE) / device manufacturer.

[0098] Figure 8 In the embodiment shown, the difference from the traditional process angle is that two pseudo process angles (called pseudo global process angles) SSA and FFA are also set. SSA and FFA here have no physical meaning but only mathematical meaning. In the embodiment of the present disclosure, by introducing SSA and FFA, it is possible to combine with other process angles to implement Monte Carlo simulation and more accurately determine the random distribution of electrical properties of electronic devices.

[0099] In some embodiments, the positions of SSA and FFA may be obtained by formula (3), respectively.

[0100] (3).

[0101] Indicates the correlation between associated target parameters, or Correl(X, Y) indicates the correlation between two (or two groups of) target parameters. X and Y are arrays, each representing one of the two groups of related target parameters. For example, for Figure 8 For the process angle and target parameters VT and ID shown in , X represents the data set vt (target parameter value), and Y represents the data set id. Then Correl (X, Y) represents the correlation between VT and ID. Among them, x represents the value of each specific target parameter in the data set vt, and y represents the value of each specific target parameter in the data set id. represents the average value of a set of target parameters represented by X. Figure 8 ” corresponds to the average value of the abscissa, and represents the value of TT on the abscissa in this embodiment. The average of a set of target parameters represented by Y is equivalent to Figure 8 ” corresponds to the average value of the ordinate, and in this embodiment represents the value of the ordinate of TT.

[0102] If the relationship between VT and ID can be expressed as a straight line, the correlation between the two is 1. If the relationship between VT and ID can be expressed as a curve, the correlation between the two is less than 1 and greater than 0. When the process conditions are determined, the value of the horizontal axis of TT is determined, so and is known.

[0103] In some embodiments, the user may specify the correlation between the two target parameters according to the actual process conditions, for example, specifying the correlation between VT and ID to be 0.8. It should be understood that the correlation value here is not specified arbitrarily, but is specified within a predetermined range according to the data results of the actual test of the FAB.

[0104] In addition, one of the values ​​of x and y in formula (3) can be specified, for example, Figure 8 As shown in , the y (ordinate) of SSA is equal to the ordinate of SSG. Therefore, there is only one unknown number x on the right side of formula (3), and the value of x can be quickly solved.

[0105] See below Fig. 9 , Fig. 9 A schematic diagram showing the normalized position of process angles for PCA extraction according to some embodiments of the present disclosure. Fig. 9 The relationship between the various process angles is shown, where the specific values ​​of FFA and SSA can be obtained according to formula (3). The five process angles used by MC can be automatically extracted using relevant software (automatically fitting to obtain parameters of different process angles: phig, vsat, etc.). Vt refers to vt_lin and vt_sat, and id refers to idlin and idsat; specifically, when Vt refers to vt_lin, id refers to idlin; when Vt refers to vt_sat, id refers to idsat.

[0106] The meanings of several main electrical parameters involved in some embodiments of the present invention are as follows:

[0107] Phig: Gate work function, which has a linear relationship with vt_lin. When phig increases, vt_lin increases, and when phig decreases, vt_lin decreases.

[0108] Uθ: low field mobility;

[0109] vt_lin: linear threshold voltage;

[0110] vt_sat: saturation threshold voltage

[0111] Idlin: linear current;

[0112] idsat: saturation current.

[0113] Fig. 9 The process angles of FFG and SSG are normalized to the process angle range of FFG and SSG, and the correlation between vt and id is calculated as 0.85 according to formula (3). For example, the process angle range of FFG is -100mv, id +20%; that of SSG is +100mv, id -20%. The range of FFA is -23.5mv, id +20%, and the range of vt of FFA is +23.5mv, id -20%.

[0114] Fig. 9 The first column shows the process corners FFG, FFA, TT, SSA, SSG. The second and third columns show the target parameters VT and ID of each process corner, respectively. Fig. 9 It can be seen that the VT and ID of TT are 0, corresponding to the previously mentioned and are 0 respectively. It should be pointed out that Fig. 9 The values ​​of VT and ID in are normalized values ​​rather than actual values. It should also be pointed out that Fig. 9 The VT and ID shown in represent the target parameter values ​​of each process corner rather than the simulation parameter values. As mentioned above, the position of the process corner is determined by using the target parameter values ​​of each process corner. For example, for vt and id, determining the position of the process corner is to determine the values ​​of vt and id of different process corners. In some embodiments, the value of the target parameter (e.g., vt / id) of the process corner can be specified to determine the position of the process corner.

[0115] Back to Figure 4 Continue with description.

[0116] At block 404 , process corner model parameters corresponding to the respective target parameters are adjusted based on the values ​​of the target parameters at the respective locations of the global process corner and the pseudo-global process corner, so that the simulation values ​​of the respective target parameters are consistent with the target values ​​of the corresponding target parameters.

[0117] In some embodiments, Figure 8 As shown, after determining the position of each process corner, the value of the target parameter corresponding to each position can be known, such as the target value of vt, the target value of id, etc. After obtaining the value (target value) of the target parameter, the model parameter, such as the value of phig, can be adjusted so that the simulation value of vt / id is equal to the target value. Thus, the adjusted model parameters can be obtained. The adjusted model parameters can be used for subsequent processing so that the simulation model can accurately determine the distribution of electrical characteristics.

[0118] For example, for the process corner SSG, its corresponding phig can be adjusted, denoted as phig_ssg, and the simulation value of vt / id corresponding to the process corner SSG is made consistent with the target value by adjusting (which can be achieved manually or by software) phig_ssg. For example, by increasing the value of phig_ssg, it is found that the simulation value of vt / id deviates more from the target value, then the value of phig_ssg is adjusted in the opposite direction, so that through multiple iterations, the simulation value is close to or equal to the target value. The same treatment is performed for the process corners TT and FFG. Similarly, the same treatment can be performed for the pseudo-global process corners SSA and FFA. In the embodiment of the present disclosure, a pseudo-global process corner is additionally introduced in the process of constructing a simulation model to more accurately model the distribution of electrical characteristics. The process of adjusting the pseudo-global process corner here is specifically, for example, for SSA, its corresponding phig is denoted as phig_ssa, and by adjusting phig_ssa, the simulation value of its corresponding vt / id is made consistent with the target value of the vt / id corresponding to the SSA. For each global process corner and pseudo-global process corner itself, the specific method of adjusting its model parameters is the same.

[0119] It should be understood that the consistency between the simulation value of each target parameter and the target value of the corresponding target parameter does not require the two to be completely equal, but the difference between the two can be less than a predetermined threshold.

[0120] At block 406 , model parameters of a simulation model are determined based on the respective adjusted process corner model parameters to generate a simulation model.

[0121] In some embodiments, each adjusted process corner model parameter may be analyzed in a conventional manner to determine the model parameters of the simulation model.

[0122] In some embodiments, a weight coefficient may be determined based on each adjusted process corner model parameter. The weight coefficient represents the influence of the adjusted process corner model parameter on the electrical characteristic distribution of the simulation object in different directions; and the model parameters of the simulation model may be determined based on a combination of each weight coefficient.

[0123] In some embodiments, the principal component analysis (PCA) method can be used to determine the weight coefficient. PCA is a widely used data analysis method, especially in the field of data dimensionality reduction. PCA can map high-dimensional data to low-dimensional space while retaining as much information of the original data as possible. The purpose of principal component analysis is to extract the main component information in the data. The main idea of ​​PCA is to project the original high-dimensional feature space to a new low-dimensional feature space through a linear transformation, while trying to maintain the variance of the original data so that the difference of the data in the new low-dimensional space can be retained. In this way, the original complex dimension is reduced while retaining the information of the original data to the greatest extent. Since dimensionality reduction is involved, it is necessary to find a suitable orthogonal coordinate system so that the variance of the projection of each point of the original data on the new coordinate system is maximized. From the knowledge of linear algebra, it can be known that this coordinate system is to perform eigenvalue decomposition on the covariance of the original data to obtain eigenvalues ​​and eigenvectors.

[0124] The main steps of PCA include: decentralizing and normalizing the data (place the origin of the coordinates in the center of the data for decentralization, and then divide it by the sample standard deviation of a certain characteristic quantity) -> find the covariance matrix of the data -> then find the eigenvector matrix of the covariance matrix > rotate the data in the original coordinate system (after decentralization) through the eigenvector matrix, that is, obtain the coordinates after PCA transformation, and the eigenvector matrix is ​​also the direction of the principal component. The larger the eigenvalue of the covariance matrix, the larger the variance in the corresponding eigenvector direction. This means that the data changes most significantly in these directions, so these directions are called principal components. Covariance represents the degree of correlation between the changes of two variables.

[0125] In some embodiments, principal component analysis may be performed on the adjusted process corner model parameters to determine weight coefficients, wherein the weight coefficients represent the extent to which the adjusted process corner model parameters affect the electrical characteristic distribution of the simulation object in different directions.

[0126] In some embodiments, determining the weight coefficient based on each adjusted process corner model parameter may include: arranging the adjusted process corner model parameters into an initial matrix; normalizing the initial matrix to generate a normalized matrix; determining a covariance matrix of the normalized matrix; and determining eigenvalues ​​and eigenvectors of the covariance matrix; and determining the ratio of each eigenvalue to the sum of all eigenvalues ​​as a weight coefficient of an eigenvector corresponding to each eigenvalue. This is further described below.

[0127] In some embodiments, the eigenvalue decomposition of the symmetric covariance matrix C is as follows:

[0128] (4)

[0129] The dimension of C is m*m, that is, m rows and m columns. It is called an eigenvector, and its dimension is m*m, i.e., m rows and m columns. Λ is an eigenvalue matrix, and its dimension is also m*m. The non-zero elements on the diagonal of the eigenvalue matrix Λ are the eigenvalues ​​of the covariance matrix C. , , … , .

[0130] In some embodiments, the purpose of the MC process corner is to integrate the information of the five process corners and express them using a process corner model (MC corner). This makes it easier to do MC simulation. MC simulation usually adds Gaussian distribution parameters to certain parameters to simulate the real MC. If the MC distribution is only distributed in one direction, it is a straight line and the correlation is 1; however, the correlation in the real situation is not 1. In order to express this correlation, pseudo process corners ffa and ssa are introduced in some embodiments of the present disclosure (it should be noted that the uppercase and lowercase letters representing the process corners ffa and ssa in the present disclosure have the same meaning). The specific value of the Gaussian distribution is generated by the internal mechanism of SPICE during simulation.

[0131] The PCA algorithm is described in detail below.

[0132] What PCA needs to process are the parameters in the model, that is, the parameters that need to be adjusted, such as phig. The dimension of the column in the matrix is ​​the dimension of the process angle (ffg, ssg, tt, ffa, ssa). In some embodiments, the first k eigenvalues ​​can be arranged from large to small. , , … , , calculate Λ*V to obtain the components of the parameter in the first k directions.

[0133] (5)

[0134] X0 is a two-dimensional array. By default, each row represents a variable, such as one of phig, dvtp0, u0, vsat, a2. Specifically, each row in the matrix X0 can represent a variable. For example, the elements of the first row can represent the corresponding phig values ​​at different process angles. For the five process angles, their respective Delta phig relative to the TT corner can be represented, such as phig1 to phig5. Each column represents an observation value. In this embodiment, there are 5 process angles, namely tt, ffg, ssg, ffa, ssa, so the matrix has 5 columns. For example, the observed value of phig under tt is 0, -1 under ff, 1 under ss, and so on.

[0135] The following describes in detail the process of performing PCA processing on the matrix X0.

[0136] Step 1: Standardization. Data standardization is an important pre-step of PCA. In some embodiments, standardizing the initial matrix may include: determining the difference between the value of each element in the initial matrix and the average value of the elements in the same row of the initial matrix; determining the standard deviation of the value of each element in the initial matrix; and determining the ratio of each difference to each standard deviation as each element of the standardized matrix. In this way, the initial matrix is ​​standardized, and the standardization process is to decentralize and normalize the original data.

[0137] The standardized formula is as follows: is the standardized data, is the original data, is the mean of the jth feature, is the standard deviation of the jth feature.

[0138] (6)

[0139] Step 2: Calculate the covariance matrix C of the standardized data matrix Z. In some embodiments, determining the covariance matrix of the standardized matrix may include: determining the product of the transposed matrix of the standardized matrix and the standardized matrix; dividing the product by the number of samples of elements in the initial matrix minus one to obtain the covariance matrix, for example, for a matrix with 5 columns, the number of samples is 5.

[0140] Specifically, the covariance matrix C can be obtained by multiplying the transpose of Z with itself and dividing it by the number of samples n-1:

[0141] (7);

[0142] Step 3: Calculate the eigenvalue and eigenvalue vector. The covariance matrix C is a symmetric matrix, which can be decomposed by eigenvalues. The eigenvalue λ and the corresponding eigenvector v are obtained. The formula for eigenvalue decomposition is:

[0143] (8);

[0144] Among them, λ is the eigenvalue and v is the corresponding eigenvector.

[0145] Step 4: Sort the obtained eigenvalues ​​from large to small, and select the top 3-5 eigenvalues ​​and their corresponding eigenvectors. The size of each eigenvalue represents the proportion of its component in the overall component, which can be obtained by formula (9).

[0146] (9);

[0147] According to formula (9), the first three main components are calculated as follows: pa0: 61.585%, pa1: 21.201%, pa2: 17.214%; where pa0, pa1, and pa2 represent the corresponding components. From the data results, we can see that the first three main components basically account for 99.9%. Therefore, selecting the first three eigenvectors as projection vectors can express 99.9% of the original data information. In practice, the number of eigenvalues ​​can be selected according to needs.

[0148] In fact, the eigenvector corresponding to the maximum eigenvalue is the direction of the first principal component. The direction perpendicular to the first principal component direction is the direction of the second principal component. The first principal component can indicate that each model parameter has the greatest influence on the electrical characteristic distribution in the first direction.

[0149] In some embodiments, the previously obtained results may be further processed, namely: determining the square root value of the selected eigenvalue; multiplying each square root value by the eigenvector corresponding to the respective eigenvalue to obtain a first vector; multiplying the first vector by the standard deviation of each adjusted process angle model parameter of each global process angle to obtain a first result; and dividing the first result by the standard deviation of each coefficient of each global process angle to obtain a second result, wherein the second result represents the value of the model parameter of the simulation model. The details are as follows.

[0150] Step 5: In order to make the result of MC's 3sigma consistent with the 3sigma of ffg and ssg, in some embodiments of the present disclosure, each parameter can be scaled twice. Since the parameters have been normalized before (during the standardization process), it is necessary to take the square root (singular value) of the previous eigenvalue λ (the selected λ) and multiply it by the eigenvector v, that is, sqrt(λ)*v, and then multiply it by the sigma_raw_$ of each parameter of the original data: stdev($_ffg, $_ssg, $_tt, $_ffa, $_ssa) for the first scaling, where $ represents the parameters used in the MC process angle, such as phig, vsat, etc. stdev (StandardDeviation) means to calculate the standard deviation of the coefficients of each parameter in (TT, FFG, SSG, FFA, SSA). Due to the addition of the ffa and ssa process angles, the 3sigma in the long axis direction of the MC distribution is smaller than the 3sigma in the long axis direction of the two fixed process angles ffg and ssg. Therefore, the result after the first scaling is divided by sigma_co = stdev (-1, -0.235, 0, 0.235, 1) for the second scaling to obtain the final MC parameter result:

[0151] (10)

[0152] The expressions of various parameters of the MC process angle can be obtained by using formula (10). Figure 7 , Figure 7 The phig_mc shown in is obtained by equation (10). Figure 7 It can be seen (see the last five rows for details) that the parameters of the five process angles are simplified to one MC process angle. One parameter has five components, and the proportion of the components is mainly concentrated in the first three parameters par0, par1, and par2. Figure 7 The parameter expression phig_mc shown in the last five lines integrates the parameters phig of the five process angles together, that is, unifies them into one phig.

[0153] Scaling is to multiply the entire thing by a certain coefficient at the same time. The proportional component remains unchanged, and what is affected is the size of all the previous coefficients such as pa0, pa1, etc.

[0154] Fig.10 Schematic diagram of process angles and corresponding MC parameters according to some embodiments of the present disclosure is shown. Each process angle has its own corresponding parameters, such as phig, Vsat, etc. Fig.10 As shown, five process angles and their corresponding parameters phig are shown. For each process angle model, phig is the parameter of the model. By adjusting the parameters of the model, different simulation values ​​can be obtained. Adjusting the model parameters to appropriate values ​​can make the simulation value equal to the target value.

[0155] As mentioned above, the position of the process corner refers to the position of the set vt_id; the position of the parameter refers to the position of the model parameter. Fig.10 As shown: the position of each process corner is shown as a dot, and the model parameters corresponding to each process corner are shown as phig_ffa, phig_ssa, etc.

[0156] The adjusted model parameters are actually the coefficients in the equations that describe the electrical characteristics. The SPICE simulation after adjusting the coefficients makes the simulated vt / id results consistent with the set target values. The target values ​​are usually iv (current voltage) or cv (capacitance voltage) curves and vt_lin, vt_sat, idlin, idsat, etc. Determining the position of the process corner means determining the position of vt and id at different process corners. If the simulation results of the model are to match the target values, the model parameters need to be adjusted.

[0157] Fig.11 A schematic diagram showing scaling of parameters for MC according to some embodiments of the present disclosure is shown. Fig.11 The inner ellipse in the middle represents the curve diagram of VT / ID correlation obtained after the first scaling; Fig.11The outer ellipse in the middle represents the curve diagram of the VT / ID correlation obtained after the second scaling. In some embodiments of the present disclosure, after MC simulation, the following can be obtained: Fig.11 The elliptical shape shown. In some embodiments of the present disclosure, after two scalings, the 3sigma result of MC can be made consistent with the 3sigma results of ffg and ssg. The 3sigma of ffg and the 3sigma of ssg have the same value, but the direction is different (opposite). Therefore, it can be said that the correlation between vt and id matches that of silicon. It is equivalent to a distribution similar to a real situation, which is very close to the actual situation. This shows that the simulation accuracy of MC is accurate enough.

[0158] In some embodiments of the present disclosure, the originally scattered parameters are combined into one parameter through the above method. For example, each of the five process angles has a parameter phig. Figure 7 The parameter expression phig_mc shown in integrates the parameters phig of the five process corners, that is, unifies them into one phig. In this way, the comprehensive information of the five process corners can be expressed by directly calling the information of this process corner. In other words, the information of the five points is integrated together by MC. Originally, the five process corners are independent and cannot be coupled with random variables at the same time. The method disclosed in this disclosure can realize the coupling of random parameters at the same time and thus generate a coupled distribution.

[0159] MC mainly performs random simulation. The characteristic of MC simulation is the introduction of changing random parameters. The parameters of each simulation are changing, thus generating a lot of simulation results.

[0160] During simulation, each component will be multiplied by a Gaussian distribution function. For example, if you build a model for two points, you can directly build a model with a linear relationship, such as a linear equation. But if you are targeting a series of distributed points, such as the randomly occurring states in the MC process corner, you need to describe this series of points, and obviously the model should not be a linear model. For example, for phig, assuming it is equal to the value a, if you add a MC random variable to a, a will become a Gaussian distribution value centered on a. In other words, the phig parameter of each process corner originally has a value, and after assigning the Gaussian distribution value, it fluctuates randomly around its original value.

[0161] Figure 7In the example, pa0=p0 is a fixed operation for random numbers to prevent random sequence disorder during simulation. p0=agauss(0,1,3) means passing the Gaussian function to p0; the coefficients after pax (where x is 0,1,2,3,4) are the proportion coefficients of these components. In other words, parameters pa0, pa1, etc. are used to pass into the Gaussian function. The coefficients of par0 and pa1 are the sizes of the final effects of each component on the Gaussian component. Since the Gaussian distribution is normalized, multiplying by the corresponding coefficients can get the Gaussian parameter distribution of different component sizes. The actual parameter distribution effect is finally obtained by superimposing these components.

[0162] Fig.12 A schematic diagram comparing the MC simulation results of vl_lin and idlin and the results of the MC process corner according to some embodiments of the present disclosure is shown. Fig.13 A schematic diagram showing a comparison between MC simulation results of vt_sat and idsat and results of MC process corner according to some embodiments of the present disclosure is shown. Fig.12 and Fig.13 The dots in the figure represent the positions of the five defined process corners, and the square dots are the discrete points obtained by 1000 MC simulations. The MC process corner extraction is achieved through the optimization algorithm of the embodiment of the present disclosure, and the correlation meets the expected results. The result of calculating 3sigma for MC is: the difference between VC of MC and FFG&SSG is within 3mV, and ID is within 3%.

[0163] In some embodiments of the present disclosure, a method of MC modeling of a SPICE model is implemented. The optimized MC algorithm makes the simulation results well consistent with the global process angle in terms of correlation and sigma value. In some embodiments of the present disclosure, the method of MC modeling can be implemented based on self-developed software.

[0164] The role of MC simulation is to describe the random distribution state of the device, which is essentially a part of the SPICE model and a description of the characteristics of the SPICE device, specifically describing a simulated random distribution. In some embodiments of the present disclosure, the information of the MC process angle can be combined with the information of the typical model to realize the MC simulation.

[0165] As mentioned earlier, since the local models themselves have no correlation, only the global MC needs to be established.

[0166] In some embodiments of the present disclosure, the correlation between VT and ID is used as an example for explanation, but it should be understood that the present disclosure is not limited thereto, and for example, the MC model may also be determined based on the correlation between gm and rout, where gm is the transconductance of the MOSFET and rout is the output resistance of the MOSFET.

[0167] In the above embodiment, it is mainly introduced that the principal component analysis of the adjusted process angle model parameters is performed by PCA to determine the weight coefficient. The embodiment of the present disclosure is not limited to this, but other algorithms can also be used to determine the weight coefficient. For example, the matrix or the adjusted process angle model parameters can also be subjected to singular value decomposition to determine the weight coefficient. The singular value decomposition method itself is known to those skilled in the art. Based on the description of the present disclosure, those skilled in the art understand that the singular value decomposition method can be applied to the objects described in the embodiments of the present disclosure. For this reason, the specific process is not described in the present disclosure.

[0168] In some embodiments, determining the model parameters of the simulation model based on the combination of various weight coefficients may include: selecting a predetermined number of eigenvalues ​​from the eigenvalues ​​in descending order, for example, selecting three values ​​with the largest eigenvalues ​​as needed; determining the ratio of the selected eigenvalues ​​to all eigenvalues; multiplying the ratio of each model parameter by the predetermined parameter as a weight coefficient; and adding the results of each multiplication to generate the model parameters of the simulation model.

[0169] As mentioned earlier, from Figure 7 It can be seen that the parameters of the five process corners are simplified into one MC process corner. One parameter has five components, and the proportion of the components is mainly concentrated in the first three parameters pa0, pa1, and pa2. Figure 7 The parameter expression phig_mc shown in the last five lines integrates the parameters phig of the five process corners into one phig. In some embodiments, pa0, pa1, pa2, pa3, pa4 are used to transfer Gaussian distribution values. The coefficient multiplied by pa0, pa1, pa2, pa3, pa4 is the weight coefficient. The weight coefficient is combined by pa0, pa1, pa2, pa3, pa4. It should be understood that the specific combination method is not limited to Figure 7 The weight coefficients can be combined according to actual needs.

[0170] Figure 7 The phig_mc etc. shown in are the parameters of the simulation model obtained by equation (10). Once the simulation model layer parameters are determined, the simulation model is determined.

[0171] Some embodiments of the present disclosure provide a method for generating a simulation model. Some embodiments of the present disclosure provide a simulation model generated according to the aforementioned method.

[0172] Some embodiments of the present disclosure also provide a method for performing random simulation using a simulation model, the method comprising: assigning Gaussian distribution values ​​to model parameters of the simulation model in a predetermined number of simulations; and performing simulation with the model parameters assigned Gaussian distribution values ​​to determine the distribution of electrical characteristics of the simulation object.

[0173] In some embodiments, assigning Gaussian distribution values ​​to model parameters of the simulation model in each simulation includes: normalizing the Gaussian distribution values ​​to generate normalized Gaussian distribution values; multiplying the normalized Gaussian distribution values ​​by corresponding weight coefficients to obtain Gaussian parameter distributions of different component sizes; and generating model parameters for random simulation based on a combination of Gaussian parameter distributions of different component sizes.

[0174] An electronic device is also disclosed in an embodiment of the present disclosure. The electronic device includes: a processor; and a memory coupled to the processor, the memory having instructions stored therein, and when the instructions are executed by the processor, the device performs an action, the action including: determining the position of a pseudo-global process corner based on the position of a predetermined global process corner and the correlation between the target parameters of each global process corner, the pseudo-global process corner is used to assist in defining the distribution range of the electrical characteristics of the simulation object; adjusting the process corner model parameters corresponding to each target parameter based on the values ​​of the target parameters at the respective positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of each target parameter are respectively consistent with the target values ​​of the corresponding target parameters; determining the model parameters of the simulation model based on each adjusted process corner model parameter to generate a simulation model.

[0175] The embodiments of the present disclosure further disclose a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the method according to the embodiments of the present disclosure is implemented.

[0176] The solutions of some embodiments of the present disclosure can achieve accurate simulation of the electrical performance distribution of semiconductor devices.

[0177] It should be noted that the examples given in the above embodiments are only for illustrating the solutions of the embodiments of the present disclosure, and are not intended to limit the solutions of the present disclosure. In some embodiments, Monte Carlo simulation and its model are used as examples for illustration, but the embodiments of the present disclosure are not limited thereto and can be modified based on the teachings of the present disclosure, such as using other simulation models for simulation.

[0178] It should be understood that the embodiments shown in the drawings are only for schematically illustrating the solutions of some embodiments of the present disclosure and are not intended to limit the present disclosure. The embodiments of the present disclosure may also have various other forms.

[0179] Fig.14A schematic block diagram of an electronic device according to some exemplary embodiments of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0180] like Fig.14 As shown, the device 1400 includes a CPU 1401, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 1402 or a computer program loaded from a storage unit 1408 into a random access memory (RAM) 1403. In the RAM 1403, various programs and data required for the operation of the device 1400 can also be stored. The CPU 1401, the ROM 1402, and the RAM 1403 are connected to each other via a bus 1404. An input / output (I / O) interface 1405 is also connected to the bus 1404.

[0181] Multiple components in the device 1400 are connected to the I / O interface 1405, including: an input unit 1406, such as a keyboard, a mouse, etc.; an output unit 1407, such as various types of displays, speakers, etc.; a storage unit 1408, such as a disk, an optical disk, etc.; and a communication unit 1409, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 1409 allows the device 1400 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0182] The various processes and processing described above, such as method 400, may be executed by CPU 1401. For example, in some embodiments, method 400 may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as storage unit 1408. In some embodiments, part or all of the computer program may be loaded and / or installed on device 1400 via ROM 1402 and / or communication unit 1409. When the computer program is loaded into RAM 1403 and executed by CPU 1401, one or more steps in method 400 described above may be performed.

[0183] The scheme according to the embodiment of the present disclosure may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium on which computer-readable program instructions for executing various aspects of the present disclosure are loaded. The computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. The computer-readable program instructions may be downloaded from the computer-readable storage medium to various computing / processing devices, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network and / or a wireless network.

[0184] Various embodiments of the present disclosure have been described above, and the above descriptions are exemplary and are only optional embodiments of the present disclosure, not exhaustive, and are not intended to limit the present disclosure. Although the claims in this application have been formulated for specific combinations of features, it should be understood that the scope of the present disclosure also includes any novel features or any novel combination of features disclosed herein, whether or not it relates to the same scheme in any claim currently claimed for protection. The applicant hereby informs that new claims may be formulated into these features and / or combinations of these features during the examination of this application or in any further application derived therefrom.

[0185] The terms used in this article are selected to best explain the principles of each embodiment, practical application or technical improvement in the market, or to enable other ordinary technicians in the field to understand the embodiments disclosed herein. For those skilled in the art, the present disclosure may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the scope of protection of the present disclosure.

Claims

1. A method for generating a simulation model, comprising: Determine the position of the pseudo-global process corner based on the position of the predetermined global process corner and the correlation between the target parameters of the respective global process corners, wherein the pseudo-global process corner is used to assist in defining the distribution range of the electrical characteristics of the simulation object; Adjusting the process corner model parameters corresponding to the respective target parameters based on the values ​​of the target parameters at the respective positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of the respective target parameters are consistent with the target values ​​of the corresponding target parameters; as well as Determining model parameters of the simulation model based on the adjusted process corner model parameters to generate the simulation model; The predetermined global process angle includes a typical process angle, and determining the position of the pseudo global process angle includes: specifying a value of one of two associated target parameters of each of the pseudo-global process corners; Determining the value of the other target parameter of the two associated target parameters corresponding to each of the pseudo-global process corners based on the difference between the value of one of the target parameters and the value of the corresponding target parameter of the typical process corner and a specified correlation value; and Positions corresponding to the values ​​of the two associated target parameters are respectively determined as positions of the pseudo-global process corners.

2. The method according to claim 1, wherein the position of the pseudo-global process corner is determined based on the following formula: ； in represents the correlation between the associated target parameters, X and Y each represent one of the two sets of associated target parameters, and x and y represent the values ​​of the two associated target parameters, represents the average value of a set of target parameters represented by X, Represents the average value of a set of target parameters represented by Y.

3. The method according to claim 1, wherein determining the model parameters of the simulation model based on the respective adjusted process corner model parameters comprises: Determining a weight coefficient based on each adjusted process corner model parameter, wherein the weight coefficient represents the influence of the adjusted process corner model parameter on the electrical characteristic distribution of the simulation object in different directions; as well as The model parameters of the simulation model are determined based on the combination of the weight coefficients.

4. The method according to claim 3, wherein determining the weight coefficient based on each adjusted process corner model parameter comprises: Performing principal component analysis on the adjusted process angle model parameters to determine the weight coefficients; or Singular value decomposition is performed on the adjusted process corner model parameters to determine the weight coefficients.

5. The method according to claim 4, wherein determining the weight coefficient based on each adjusted process corner model parameter comprises: Arranging the adjusted process angle model parameters into an initial matrix; Performing a normalization process on the initial matrix to generate a normalized matrix; determining a covariance matrix of the standardized matrix; as well as Determining eigenvalues ​​and eigenvectors of the covariance matrix; as well as The ratio of each of the eigenvalues ​​to the sum of all the eigenvalues ​​is determined as a weight coefficient of the eigenvector corresponding to each eigenvalue.

6. The method according to claim 5, wherein normalizing the initial matrix comprises: Determine the difference between the value of each element in the initial matrix and the average value of the elements in the same row of the initial matrix; determining a standard deviation of the values ​​of each element in the initial matrix; as well as The ratios of the respective differences to the respective standard deviations are respectively determined as the respective elements of the standardization matrix.

7. The method of claim 5, wherein determining the covariance matrix of the standardized matrix comprises: Determining the product of a transposed matrix of the normalized matrix and the normalized matrix; as well as The covariance matrix is ​​obtained by dividing the product by the number of samples of the elements in the initial matrix minus one.

8. The method according to claim 5, wherein determining the model parameters of the simulation model based on the combination of the weight coefficients comprises: selecting a predetermined number of eigenvalues ​​from the eigenvalues ​​in descending order; Determine the ratio of the selected eigenvalue to all eigenvalues; The ratios of the model parameters are taken as the weight coefficients and multiplied by the predetermined parameters respectively; as well as The results of the respective multiplications are added together to generate the model parameters of the simulation model.

9. The method according to claim 8, further comprising: Determine the square root value of the selected eigenvalue; Multiplying each of the square root values ​​by an eigenvector corresponding to the respective eigenvalue to obtain a first vector; Multiplying the first vector by the variance of the adjusted process corner model parameters of each of the global process corners to obtain a first result; as well as The first result is divided by the variance of the respective coefficients of the global process corners to obtain a second result, wherein the second result represents a value of a model parameter of the simulation model.

10. A simulation model generated by the method according to any one of claims 1 to 9.

11. A method for performing random simulation using the simulation model according to claim 10, the method comprising: assigning Gaussian distribution values ​​to model parameters of the simulation model in a predetermined number of simulations; as well as A simulation is performed with the model parameters assigned the Gaussian distribution values ​​to determine the distribution of electrical characteristics of the simulation object.

12. The method according to claim 11, wherein assigning Gaussian distribution values ​​to model parameters of the simulation model in each simulation comprises: Normalizing the Gaussian distribution value to generate a normalized Gaussian distribution value; Multiplying the normalized Gaussian distribution value by a corresponding weight coefficient to obtain Gaussian parameter distributions of different component sizes; The model parameters for stochastic simulation are generated based on a combination of Gaussian parameter distributions of different component sizes.

13. An electronic device comprising: processor; as well as A memory coupled to the processor, the memory having instructions stored therein, the instructions causing the device to perform actions when executed by the processor, the actions comprising: Determine the position of the pseudo-global process corner based on the position of the predetermined global process corner and the correlation between the target parameters of the respective global process corners, wherein the pseudo-global process corner is used to assist in defining the distribution range of the electrical characteristics of the simulation object; Adjusting the process corner model parameters corresponding to the respective target parameters based on the values ​​of the target parameters at the respective positions of the global process corner and the pseudo-global process corner, so that the simulation values ​​of the respective target parameters are consistent with the target values ​​of the corresponding target parameters; and Determining model parameters of a simulation model based on each adjusted process corner model parameter to generate the simulation model; The predetermined global process angle includes a typical process angle, and determining the position of the pseudo global process angle includes: specifying a value of one of two associated target parameters of each of the pseudo-global process corners; Determining the value of the other target parameter of the two associated target parameters corresponding to each of the pseudo-global process corners based on the difference between the value of one of the target parameters and the value of the corresponding target parameter of the typical process corner and a specified correlation value; and Positions corresponding to the values ​​of the two associated target parameters are respectively determined as positions of the pseudo-global process corners.

14. The electronic device according to claim 13, wherein the position of the pseudo-global process corner is determined based on the following formula: ； in represents the correlation between the associated target parameters, X and Y each represent one of the two sets of associated target parameters, and x and y represent the values ​​of the two associated target parameters, represents the average value of a set of target parameters represented by X, Represents the average value of a set of target parameters represented by Y.

15. The electronic device according to claim 13, wherein determining the model parameters of the simulation model based on the respective adjusted process corner model parameters comprises: Determining a weight coefficient based on each adjusted process corner model parameter, wherein the weight coefficient represents the influence of the adjusted process corner model parameter on the electrical characteristic distribution of the simulation object in different directions; as well as The model parameters of the simulation model are determined based on the combination of the weight coefficients.

16. The electronic device according to claim 15, wherein determining the weight coefficient based on each adjusted process corner model parameter comprises: Performing principal component analysis on the adjusted process angle model parameters to determine the weight coefficients; or Singular value decomposition is performed on the adjusted process corner model parameters to determine the weight coefficients.

17. The electronic device according to claim 16, wherein determining the weight coefficient based on each adjusted process corner model parameter comprises: Arranging the adjusted process angle model parameters into an initial matrix; Performing a normalization process on the initial matrix to generate a normalized matrix; determining a covariance matrix of the standardized matrix; as well as Determining eigenvalues ​​and eigenvectors of the covariance matrix; as well as The ratio of each of the eigenvalues ​​to the sum of all the eigenvalues ​​is determined as a weight coefficient of the eigenvector corresponding to each eigenvalue.

18. The electronic device according to claim 17, wherein normalizing the initial matrix comprises: Determine the difference between the value of each element in the initial matrix and the average value of the elements in the same row of the initial matrix; determining a standard deviation of the values ​​of each element in the initial matrix; as well as The ratios of the respective differences to the respective standard deviations are respectively determined as the respective elements of the standardization matrix.

19. The electronic device of claim 17, wherein determining a covariance matrix of the normalized matrix comprises: Determining the product of a transposed matrix of the normalized matrix and the normalized matrix; as well as The covariance matrix is ​​obtained by dividing the product by the number of samples of the elements in the initial matrix minus one.

20. A computer-readable storage medium having machine-executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the method according to any one of claims 1-9 and 11-12.

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