A method for establishing a transistor statistical model based on an artificial neural network system

Abstract

The application relates to a method for establishing a transistor statistical model based on an artificial neural network system, comprising receiving and generating a nominal model of a standard transistor by using the artificial neural network system based on data in a first data set; screening neurons in the artificial neural network system based on the first data set and the nominal model to obtain final fluctuation neurons; calculating and obtaining the distribution of weights of the final fluctuation neurons and the distribution of threshold voltages in the statistical model based on the change of the weights of the final fluctuation neurons relative to the nominal model, the change of the nominal model relative to threshold voltages, the distribution of drain-source currents and the distribution of gate-source voltages in the first data set; and establishing the statistical model based on the nominal model, the distribution of weights of the final fluctuation neurons and the distribution of threshold voltages.

Description

Technical Field

[0001] This application relates to the field of electronic device simulation model design simulation, and in particular to a method for establishing a transistor statistical model based on an artificial neural network system. Background Technology

[0002] As developments beyond Moore's Law continue, limitations imposed by second-order effects in actual production, such as those resulting from proportional scaling, have led to the introduction of new materials and the development of new structures in devices. The physical mechanisms of these new devices are more complex, posing significant challenges to their modeling.

[0003] During device manufacturing, process parameters such as channel length, mobility, and oxide layer thickness significantly impact the performance of novel devices, including common performance parameters like off-state current, on-state current, subthreshold slope, and threshold voltage. Device simulation models need to consider fluctuations in device process parameters and their impact on device performance, ensuring both technological advancement and the reliability of mass production, especially for novel devices. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this application proposes a method for establishing a transistor statistical model based on an artificial neural network system, comprising: receiving a first dataset, and generating a nominal model of a standard transistor using the artificial neural network system based on the data in the first dataset. The first dataset includes multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of multiple transistors of the same model. The multiple transistors of the same model include the standard transistor and multiple fluctuation transistors. The standard transistor is determined based on the median or average value of the drain-source current data of the multiple transistors of the same model under the same bias conditions, and the rest are called fluctuation transistors. Based on the first dataset and the nominal model, the neurons in the artificial neural network system are screened to obtain the final fluctuation neurons. Based on the changes in the weights of the nominal model relative to the final fluctuation neurons, the changes in the nominal model relative to the threshold voltage, the distribution of drain-source current and the distribution of gate-source voltage in the first dataset, the weight distribution of the final fluctuation neurons and the distribution of the threshold voltage are calculated to obtain the distribution of the weights of the final fluctuation neurons and the distribution of the threshold voltage in the statistical model. Based on the nominal model, the weight distribution of the final fluctuation neurons and the distribution of the threshold voltage, the statistical model is established.

[0005] Specifically, the operation of filtering neurons in the artificial neural network system based on the first dataset and the nominal model to obtain the final fluctuation neurons includes: changing the weight of each neuron in the artificial neural network system in the nominal model until the difference between the intermediate output curve of the neuron after the weight change and the current-voltage characteristic curve of each fluctuation transistor is less than a first threshold, and using the weight of the neuron for the fluctuation transistor as the adjusted weight, wherein the intermediate output curve refers to the output curve obtained after changing the weight of the neuron in the nominal model; for all the fluctuation transistors, calculating the absolute value of the relative change between the adjusted weight of each neuron and the weight of the neuron in the nominal model; for the multiple transistors of the same type, calculating the average value of the absolute value of the relative change of the weight of each neuron in the artificial neural network system and filtering the preliminary fluctuation neurons based on the average value; and filtering the final fluctuation neurons based on the neuron output change amplitude of the preliminary fluctuation neurons.

[0006] Specifically, the first threshold is a value less than or equal to 5% of the drain-source current of the fluctuating transistor being compared.

[0007] Specifically, the initial fluctuation neuron whose output change amplitude is greater than or equal to 0.1 is used as the final fluctuation neuron.

[0008] Specifically, the changes in the weights of the nominal model relative to the final fluctuating neuron include the partial derivatives of the drain-source current in the nominal model with respect to the weights of the final fluctuating neuron and the partial derivatives of the gate-source voltage in the nominal model with respect to the weights of the final fluctuating neuron.

[0009] Specifically, the variation of the nominal model with respect to the threshold voltage includes the partial derivatives of the drain-source current in the nominal model with respect to the threshold voltage and the partial derivatives of the gate-source voltage in the nominal model with respect to the threshold voltage. Specifically, the distributions of the drain-source current and gate-source voltage reflected in the first dataset include the standard deviations of the drain-source current and the gate-source voltage.

[0010] Specifically, the distribution of the weights of the final fluctuation neurons in the statistical model includes the standard deviation of the weights of the final fluctuation neurons, and the distribution of the threshold voltage in the statistical model includes the standard deviation of the threshold voltage.

[0011] This application also proposes a method for applying a transistor statistical model in an artificial neural network system, comprising: receiving a second dataset, the second dataset including gate-source voltage and drain-source voltage data of multiple transistors of the same model, the multiple transistors including standard transistors and multiple fluctuating transistors, wherein the standard transistors are determined based on the median or average of the drain-source current data of the multiple transistors of the same model under the same bias conditions, and the rest are referred to as fluctuating transistors; the second dataset also includes multiple sets of drain-source current data of the standard transistors and some fluctuating transistors; and based on the multiple sets of gate-source voltage data of the standard transistors and some fluctuating transistors in the second dataset... The statistical model is established using gate-source voltage, drain-source voltage, and drain-source current data to obtain the distribution of threshold voltage and the weight distribution of the final fluctuation neurons in the statistical model, wherein the final fluctuation neurons are neurons in the artificial neural network system; multiple threshold voltages are selected from the distribution of threshold voltages, and the corresponding adjusted gate-source voltages are calculated; multiple final fluctuation neuron weights are selected from the distribution of final fluctuation neuron weights; and the drain-source currents of multiple transistors of the same model are generated based on the multiple adjusted gate-source voltages, the multiple selected final fluctuation neuron weights, and the corresponding drain-source voltage data.

[0012] Specifically, the threshold voltage is randomly selected according to a Gaussian distribution in the distribution of the threshold voltage, and the corresponding weight is randomly selected according to a Gaussian distribution in the distribution of the weights of the final fluctuating neurons.

[0013] Specifically, establishing the statistical model based on the data of the standard transistor and some fluctuating transistors in the second dataset includes: generating a nominal model of the standard transistor using an artificial neural network system based on multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and some fluctuating transistors in the second dataset; selecting neurons in the artificial neural network system to obtain final fluctuating neurons based on the multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and some fluctuating transistors in the second dataset and the nominal model; calculating the weight distribution of the final fluctuating neuron and the threshold voltage distribution in the statistical model based on the changes in the weights of the nominal model relative to the final fluctuating neuron, the changes in the nominal model relative to the threshold voltage, the distribution of the drain-source current of the standard transistor and some fluctuating transistors in the second dataset, and the distribution of the gate-source voltage; and establishing the statistical model based on the nominal model, the weight distribution of the final fluctuating neuron, and the threshold voltage distribution. Specifically, the distribution of drain-source current and gate-source voltage of the standard transistor and some fluctuating transistors in the second dataset includes the standard deviation of drain-source current and the standard deviation of gate-source voltage.

[0014] This application also proposes a computer-readable storage medium, including a memory storing a computer program that is executed to perform the aforementioned method for establishing a transistor statistical model based on an artificial neural network system.

[0015] This application also proposes a computer-readable storage medium, including a memory storing a computer program that is executed to perform an application method of a transistor statistical model of an artificial neural network system as described above.

[0016] By adopting the solution of this application, it is possible to accelerate the construction of intensive transistor models, ensure low complexity and high accuracy of the models, capture performance changes caused by process fluctuations, improve the reliability of transistor simulation models, and significantly increase the simulation speed of generating transistor models. Attached Figure Description

[0017] The preferred embodiments of this application will now be described in further detail with reference to the accompanying drawings, wherein: Figure 1A This is a flowchart of a method for establishing a transistor statistical model based on an artificial neural network system according to an embodiment of this application; Figure 1B This is a flowchart of a method for selecting neurons in an artificial neural network system to obtain the final fluctuating neurons according to an embodiment of this application; Figure 2 The first dataset contains current-voltage characteristic curves of multiple transistors according to an embodiment of this application; Figures 3A to 3B These are the output curves of different initial fluctuation neurons according to one embodiment of this application; Figure 4 This is a schematic diagram of the structure of an artificial neural network system for building a transistor statistical model according to an embodiment of this application; Figure 5 This is a flowchart of an application method for a transistor statistical model based on an artificial neural network system according to an embodiment of this application; Figure 6A It is the curve showing the change between the drain-source current and the gate-source voltage as the output. Figure 6B I is obtained using the transistor statistical model of the artificial neural network system of this application. SAT The probability distribution diagram; Figure 7 This is a comparison chart showing the simulation time of the transistor statistical model and the traditional physical model of the artificial neural network system proposed in this application; and Figure 8 The voltage transfer characteristic curve is generated by applying a transistor statistical model according to an embodiment of this application to an inverter circuit. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] In the following detailed description, reference can be made to the accompanying drawings, which form part of this application and illustrate specific embodiments of the present application. In the drawings, similar reference numerals describe substantially similar components in different figures. Specific embodiments of the present application are described in sufficient detail below to enable those skilled in the art to implement the technical solutions of the present application. It should be understood that other embodiments may also be utilized, or structural, logical, or electrical changes may be made to the embodiments of the present application.

[0020] Techniques, methods, and apparatus known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and apparatus should be considered part of the specification. The lines connecting the units in the accompanying drawings are merely for illustrative purposes, indicating that at least the units at both ends of the line are communicating with each other, and are not intended to prevent unconnected units from communicating. Furthermore, the number of lines between two units is intended to indicate at least the number of signals involved in communication between the two units or at least the number of output terminals, and is not intended to limit communication between the two units to only the signals shown in the figures.

[0021] A transistor can refer to any type of transistor, such as a field-effect transistor (FET) or a bipolar junction transistor (BJT). When a transistor is a field-effect transistor, depending on the channel material, it can be hydrogenated amorphous silicon, metal oxide, low-temperature polycrystalline silicon, organic transistors, etc. Based on whether the charge carrier is electrons or holes, they can be divided into N-type transistors and P-type transistors. The gate of a field-effect transistor is its control electrode, and the first electrode can be either the drain or source, while the corresponding second electrode can be either the source or drain. When a transistor is a bipolar junction transistor (BJT), its control electrode is its base, and the first electrode can be either the collector or emitter, while the corresponding second electrode can be either the emitter or collector. Transistors can be manufactured using amorphous silicon, polycrystalline silicon, oxide semiconductors, organic semiconductors, NMOS / PMOS processes, or CMOS processes. Of course, other types of transistors can also be used.

[0022] Existing modeling methods based on artificial neural networks mainly construct condensed models of electronic devices. A condensed model refers to a model obtained by reasonably simplifying the physical model of an electronic device by combining engineering experience or mathematical methods.

[0023] In recent years, artificial neural networks and related technologies have been continuously developing and widely applied in various fields. To address the problems of long simulation times and low model reliability in modeling electronic devices, artificial neural network-based modeling methods have emerged. These methods are often designed for individual devices. How to efficiently model a large number of devices remains a problem to be solved.

[0024] This application proposes a method for establishing a transistor statistical model based on an artificial neural network system. This method takes into account the fluctuations in process parameters of multiple transistors and the resulting output offset problem, which effectively improves the reliability of the transistor model and helps to significantly improve the simulation speed of the transistor model. Thus, it demonstrates the advantages of using artificial neural networks to construct transistor models in large-scale Monte Carlo simulations.

[0025] Figure 1AThe diagram shows a flowchart of a method for establishing a transistor statistical model based on an artificial neural network system according to an embodiment of this application. According to an embodiment of this application, the data in the following dataset may be test data from GAA-FET or test data obtained from other known sources.

[0026] like Figure 1A As shown, the method may include the following operations: According to one embodiment, at step 101: a first dataset is received, and a nominal model of a standard transistor is generated using an artificial neural network system based on a portion of the data in the first dataset. The first dataset may include multiple sets of gate-source voltage, drain-source voltage, and drain-source current data for multiple transistors of the same model, including standard transistors and multiple fluctuating transistors.

[0027] According to an embodiment of this application, the standard transistor can be determined based on the median or average of the drain-source current data of a plurality of transistors of the same model under the same bias conditions in the first dataset.

[0028] The term "same type of transistor" as used here and thereafter refers to the fact that multiple transistors in this article are of the same type, with the same physical structure and manufacturing process. Due to manufacturing processes or other reasons, these transistors (called fluctuation transistors) have certain minor differences from standard transistors, such as size differences, resulting in certain differences in performance, such as threshold voltage and output current. These differences are also referred to as fluctuations in process parameters.

[0029] According to one embodiment, the nominal model refers to a model of a standard transistor generated by training an artificial neural network based on a portion of the data in the first dataset.

[0030] Figure 2 The diagram shows the current-voltage characteristic curves of multiple transistors in a first dataset according to one embodiment. The transistors mentioned here can be three-terminal transistors, for example, with source, drain, and gate. The black solid line represents the voltage-current output characteristic curve corresponding to the nominal model of a standard transistor, and the gray solid line represents the voltage-current output characteristic curves corresponding to multiple transistors of the same type as the standard transistor. Figure 2As shown, due to fluctuations in process parameters, the drain-source currents output by multiple transistors in the first dataset under the same bias conditions differ slightly from the output curves of the nominal model. That is, the voltage-current output characteristic curves are offset relative to the output characteristic curves of the standard transistor. This offset can include an offset along the voltage axis, referring to the difference in gate-source voltages required for multiple transistors to output the same drain-source current; or an offset along the current axis, referring to the difference in drain-source currents generated when multiple transistors are at the same gate-source voltage.

[0031] Depending on the specific implementation, the artificial neural network system to which the nominal model is applied may include different structures, such as one or more artificial neural networks.

[0032] In 102: Based on the first dataset and the nominal model, the neurons in the artificial neural network system are screened to obtain the final fluctuation neurons.

[0033] According to one embodiment, some or all of the neurons in the artificial neural network system can be screened during the above screening operation.

[0034] The ability to filter neurons means that these neurons, during simulation, affect the performance of the transistor model, reflecting fluctuations in the process parameters of the corresponding transistors in actual production. According to one embodiment, for a system consisting of only a single network, the final fluctuation neurons can be filtered from the neurons in the last layer before the output layer. For a system consisting of multiple networks, the final fluctuation neurons can be filtered from all neurons in all networks.

[0035] In 103: Based on the changes in the weights of the nominal model relative to the final fluctuation neuron, the changes in the nominal model relative to the threshold voltage, the distribution of the drain-source current and the distribution of the gate-source voltage in the first dataset, the distribution of the weights of the final fluctuation neuron and the distribution of the threshold voltage in the statistical model are calculated.

[0036] Depending on the specific implementation, the variation referred to here may refer to the variation expressed by partial derivatives or other mathematical calculations. Depending on the specific implementation, the distribution referred to here may be expressed as standard deviation, variance, or other forms.

[0037] In 104: Based on the nominal model, the distribution of the weights of the final fluctuating neurons, and the distribution of the threshold voltage, the transistor statistical model is established.

[0038] Figure 1B The diagram shows a method for selecting neurons in an artificial neural network system to obtain the final fluctuating neurons according to an embodiment of this application.

[0039] Operation 121: Change the weight of each neuron until the difference between the intermediate output curve after the weight change of the neuron and the current-voltage characteristic curve of the fluctuation transistor is less than the first threshold, and use the weight as the adjusted weight of the neuron.

[0040] According to one embodiment, the intermediate output curve refers to the output curve obtained by changing the weights of neurons in the system based on the data in the first dataset and the nominal model. The current-voltage characteristic curve of the fluctuation transistor refers to the curve composed of the current and voltage data corresponding to the fluctuation transistor in the first dataset.

[0041] The data from multiple fluctuating transistors included in the first dataset will produce different drain-source current values ​​than the nominal model under the same gate-source and drain-source voltages. By changing the weights of the neurons to make the output of the nominal model closer to the current data of the fluctuating transistors, the output offset caused by process parameter fluctuations can be translated into changes in the weights and output of the neurons in the model. The adjusted weights of the neurons can be regarded as influencing factors in forming a transistor model within the range of process parameter fluctuations required for production. Multiple transistor models obtained by analyzing the range and magnitude of the changes in neuron weights can be considered transistor models that take into account process parameter fluctuations.

[0042] According to one embodiment, the weight of each neuron can be changed using gradient descent.

[0043] According to one embodiment of this application, after establishing the nominal model, each neuron in the artificial neural network system has its own weights, also known as initial weights. When generating a statistical model of multiple transistors, only the weights of the selected neurons can be changed while the weights of other neurons remain unchanged from their initial weights.

[0044] According to one embodiment of this application, the difference, such as variance, between the intermediate output curve of the nominal model and the current-voltage characteristic curve of the fluctuation transistor after each change of the neuron weight can be used as the loss function, and the decision to stop updating the weights of each neuron can be made based on the relationship between the loss function and a first threshold.

[0045] According to embodiments of this application, multiple iterations can be performed based on the loss function until the final neuron weights result in the difference between the intermediate output curve and the output curve of the fluctuation transistor being less than or equal to a first threshold. According to one embodiment, the first threshold may be, for example, 5% of the fluctuation transistor output. According to embodiments of this application, the maximum number of iterations may be, for example, 10. 5 According to one embodiment, 10 can be performed. 5 Each iteration process, after completing 10... 4In the next iteration, the intermediate output curve is compared with the output curve of the fluctuation transistor. If this is completed in 10 iterations... 4 If, after a certain number of iterations, the difference between the current-voltage characteristic curve of the fluctuation transistor and the intermediate output curve reaches a level less than the first threshold, the calculation can be stopped. If, after reaching the maximum number of iterations, the difference between the two still does not reach a level less than the first threshold, then the calculation result with the smallest difference between the two during all iterations is taken.

[0046] According to different embodiments, when adjusting the weights of neurons, the weights of one or more neurons can be changed simultaneously. According to different embodiments, during the adjustment process, there may be multiple intermediate output curves that meet the conditions for a single neuron. The weight corresponding to the intermediate output curve with the smallest difference from the current-voltage characteristic curve of the fluctuation transistor can be selected as the weight of that neuron.

[0047] Operation 122: For all the data from the fluctuating transistors, calculate the absolute value of the relative change in the weight of each neuron.

[0048] According to one embodiment of this application, since the data in the first dataset corresponds to n transistors (n can be an integer greater than 1), each neuron will have n updated weights, where the weight of the i-th neuron when forming the k-th transistor model is W. i (k) k can be an integer greater than or equal to 1 and less than or equal to n, and i can be an integer greater than or equal to 1. Calculate the absolute value of the relative change in weights of each neuron before and after forming each fluctuation transistor model, such as the absolute value of the relative change in weights of the i-th neuron before and after the weight update, ΔA. i (k) Specifically, the absolute value of the relative change in weight, ΔA. i (k) The following relationship must be satisfied:

[0049] Among them, W i (0) Let be the initial weights of the i-th neuron in the artificial neural network system.

[0050] Operation 123: Select preliminary fluctuating neurons based on the average of the absolute values ​​of the relative changes in the weights of each neuron.

[0051] According to one embodiment of this application, after operation 123, each neuron has n absolute values ​​of relative changes in weights. The average of the absolute values ​​of relative changes in weights of the n neurons is calculated to obtain the average of the absolute values ​​of relative changes in weights of each neuron. Specifically, the average of the absolute values ​​of the relative changes in weights. The following relationship must be satisfied:

[0052] Table 1 shows the average absolute value of the relative changes in the weights of 10 neurons in one embodiment of this application. .

[0053] According to one embodiment of this application, since fluctuations in process parameters have different degrees of impact on current characteristics and different regions (subthreshold region, linear region, and saturation region), the influence of each neuron on the output is also different. The average of the absolute values ​​of the relative changes in weights... The smaller the value, the smaller the magnitude of weight change during the establishment of different fluctuation transistor models, the higher the sensitivity of the neuron's weights to the output, and the stronger the neuron's control over the output of the artificial neural network system. According to one embodiment of this application, it can be based on... The neurons are sorted from smallest to largest to obtain the initial fluctuation neurons. Depending on the implementation, a fixed number of neurons with the smallest average absolute value of the relative change in weights can be selected as the initial fluctuation neurons, or a second threshold can be used to filter the neurons based on the average absolute value of the relative change in weights. For example, neurons with an average absolute value of the relative change in weights less than the second threshold can be used as the initial fluctuation neurons.

[0054] Operation 124: Select the final fluctuation neurons based on the output change amplitude of the initial fluctuation neurons.

[0055] According to one embodiment of this application, the final fluctuation neuron output curve variation range is sufficiently large according to actual production needs. For example, an initial fluctuation neuron with an output curve variation range greater than or equal to a third threshold can be used as the final fluctuation neuron. According to one embodiment, the neuron output curve can be a normalized curve, so for example, the third threshold can be 0.1.

[0056] Figures 3A to 3B These are the output curves of neurons with different initial fluctuations according to an embodiment of this application. Based on the average absolute value of the relative changes in weights in Table 2, it can be seen that neurons 2 and 10 have relatively stronger control capabilities. Furthermore, because... Figure 3A As shown, the output curve of neuron 2 varies within a range of approximately 1, which better matches the current output characteristic curve of an actual transistor, and can be used as the final fluctuation neuron. And as... Figure 3B As shown, the output curve of neuron 10 varies in the range of about 0.04. Therefore, neither of these two is selected as the final fluctuation neuron. In the generation transistor statistical model, neuron 10 will still maintain its initial weights in the nominal model.

[0057] The following describes a method for calculating the distribution of the weights of the final fluctuating neurons and the distribution of the threshold voltages of the plurality of transistors according to an embodiment of this application.

[0058] Depending on the specific implementation, the variation referred to here may refer to the variation expressed by partial derivatives or other mathematical calculations. Depending on the specific implementation, the distribution referred to here may be expressed as standard deviation, variance, or other forms.

[0059] Specifically, after the artificial neural network system completes the final selection of fluctuating neurons, based on the distribution of transistor data in the first dataset, such as I... DS V GS The standard deviation can be used to calculate the distribution of the weights of the final fluctuating neurons in a transistor statistical model. According to one embodiment of this application, the distribution of the final fluctuation neuron's weights and the distribution of the threshold voltage can be calculated using formula (3):

[0060] Since transistors include P-type and N-type transistors, which have different structures, their respective transistor parameters and calculation principles also differ. Therefore, when using the BPV method, the cases for P-type and N-type transistors are calculated separately.

[0061] According to one embodiment of this application, as expressed by formula (3), the distribution of data of multiple transistors, such as the drain-source current data I of multiple transistors, is as follows: DS_data Gate-source voltage data V GS_data Distribution This can be reflected in the changes of each data indicator in the nominal model relative to the final fluctuation neuron weights and relative to the threshold voltage (e.g., the drain-source current I in the nominal model). DS Relative to the changes in the weights of each final fluctuation neuron, the gate-source voltage V in the nominal model GS Relative to the changes in the weights of each final fluctuation neuron, the drain-source current I in the nominal model DS The gate-source voltage V in the nominal model varies relative to the threshold voltage. GS (Changes relative to the threshold voltage) The distribution of weights and threshold voltages of each final fluctuating neuron. The accumulation of.

[0062] According to an embodiment of this application, the above-mentioned gate-source voltage V GS And the gate-source voltage data V in the first dataset GS_dataIt can be the gate-source voltage of a transistor in the subthreshold region.

[0063] According to one embodiment of this application, the gate-source voltage V in the nominal model is... GS The change relative to the threshold voltage can be achieved by transforming the nominal model from an output drain-source current model to an output gate-source voltage model, and calculating the changes of each index in the model relative to the threshold voltage.

[0064] According to one embodiment, when the so-called change is a partial derivative, it can be calculated by the chain rule or by numerical differentiation, depending on the actual production needs.

[0065] According to one embodiment of this application, the data in the first dataset may include data from different V... DS and V GS One or more I under bias DS And in different V DS and I DS One or more V under bias GS Some data are shown in Table 3.

[0066] In formula (3), and This refers to the I of N-type transistors and P-type transistors in the first dataset. DS The distribution of I. As shown in Table 3, I DSt It can be I SAT or I LIN or I SUB One or more of them.

[0067] In formula (3), and This refers to the V values ​​of N-type and P-type transistors in the first dataset. GS The distribution of V. GSt It can be V as shown in Table 3 GS V in GS1 and / or V GS2 .

[0068] In formula (3), I in the nominal model DS The weight W of the final fluctuating neuron m m Find the partial derivative, where I DS It can be I as shown in Table 3 DS One or more of them, such as I SATAccording to one embodiment, the final fluctuation neuron m refers to the m-th neuron among all neurons in the system. When there are multiple final fluctuation neurons, the partial derivative of the weight of each final fluctuation neuron needs to be calculated in formula (3).

[0069] In formula (3), I in the nominal model DS For threshold voltage V th Find the partial derivative, where I DS It can be I as shown in Table 3 SAT or I LIN or I SUB One or more of them. In formula (3), V in the nominal model GS The weight W of the final fluctuating neuron m m Find the partial derivative, where V GS It can be V as shown in Table 3 GS V in GS1 and / or V GS2 .

[0070] In formula (3), V in the nominal model GS For threshold voltage V th Find the partial derivative, where V GS It can be V as shown in Table 3 GS1 and / or V GS2 .

[0071] In formula (3), and The standard deviation of the final fluctuation neuron weights; and This represents the standard deviation of the threshold voltage. According to embodiments of this application, other statistical methods can also be used to calculate the distribution of the threshold voltage and the distribution of the final fluctuating neuron weights.

[0072] Based on the above calculation results, combined with the nominal model, it can serve as a statistical model for multiple transistors of the same model based on the first dataset.

[0073] Figure 4 This is a schematic diagram of the structure of an artificial neural network system for building a transistor statistical model according to an embodiment of this application.

[0074] According to one embodiment, the artificial neural network system 400 may include a threshold voltage adjustment module 401 configured to receive the gate-source voltage V from the dataset when applying the statistical model. GS and the distribution of threshold voltage σV th The threshold voltage adjustment module 401 calculates and generates the adjusted gate-source voltage V.GS_Adjust .

[0075] like Figure 4 As shown, the artificial neural network system 400 may further include an input layer 402, a hidden layer 403, and an output layer 404. These three layers may include multiple neurons capable of transmitting electrical signals.

[0076] According to one embodiment of this application, an artificial neural network system 400 may include a single artificial neural network. Of course, the system may also have other structures, such as including multiple artificial neural networks. Correspondingly, the artificial neural network system 400 may also include multiple hidden layers. The following description uses an embodiment where the artificial neural network system 400 includes only a single artificial neural network as an example.

[0077] like Figure 4 As shown, in the process of applying the transistor statistical model of this application, the input layer 402 can be configured to receive the adjusted gate-source voltage V from the threshold voltage adjustment module. GS_Adjust Drain-source voltage V in the second dataset DS The input layer 402 can be coupled to the hidden layer 403, and the hidden layer 403 is coupled to the output layer 404, transmitting the electrical signals output by the neurons to the output layer 404.

[0078] According to one embodiment, the second dataset may include one or more sets of gate-source voltage and drain-source voltage data for multiple transistors of the same model.

[0079] According to one embodiment of this application, optionally, the artificial neural network system 400 may further include a normalization module (not shown), which may be coupled to the threshold voltage adjustment module 401 and the input layer 402. The normalization module normalizes the input data, and the normalized data is converted into electrical signals that are transmitted to the neurons in the input layer 402 for computation. According to one embodiment of this application, the normalization module may also be configured to process the input data to satisfy the following relationship:

[0080] in, This refers to the drain-source current of the k-th transistor. , This refers to the drain-source voltage of the k-th transistor. .

[0081] Optionally, the artificial neural network system 400 may also include an inverse normalization module (not shown), which may be coupled to the output layer 404 of the artificial neural network. The inverse normalization module performs inverse normalization processing on the calculation results output by the output layer 404 to obtain the drain-source current data obtained by the statistical model of this application.

[0082] Figure 5 The diagram shown is a flowchart of a method for applying a transistor statistical model of an artificial neural network system according to an embodiment of this application.

[0083] like Figure 5 As shown, the method may include the following operations: At 511: Receive the second dataset.

[0084] Taking a three-terminal transistor (GAA-FET) as an example, the second dataset may include gate-source voltage and drain-source voltage data of multiple transistors of the same type. According to one embodiment of this application, the multiple transistors of the same type include a standard transistor and multiple fluctuating transistors, wherein the standard transistor is determined based on the median or average of the drain-source current data of the multiple transistors of the same type under the same bias conditions, and the rest are referred to as fluctuating transistors. According to one embodiment of this application, the second dataset may further include multiple sets of drain-source current data of the standard transistor and some fluctuating transistors. In 512: A statistical model was built based on the data in the second dataset to obtain the final distribution of the weights and threshold voltages of the fluctuating neurons.

[0085] According to an embodiment of this application, the distribution of the weights and the distribution of the threshold voltage of the final fluctuation neuron can be obtained by establishing a statistical model on the data of the standard transistor and some fluctuation transistors in the second dataset using the above-described method.

[0086] According to one embodiment of this application, when the method is applied multiple times based on the same transistor data, the distribution of the final fluctuating neuron's weights and the distribution of the threshold voltage can be received only once.

[0087] In 513: Select multiple threshold voltages from the distribution of threshold voltages and calculate the adjusted gate-source voltage.

[0088] According to embodiments of this application, when the second dataset includes data for s transistors, the statistical model can generate transistor current models corresponding to q transistor data (q can be an integer greater than 1 and less than or equal to s). The threshold voltage of a standard transistor can be used as the reference. Based on this, the distribution σV of the threshold voltage in the model is... th Within the Gaussian distribution, q corresponding threshold voltages are randomly selected. (r can be an integer greater than 1 and less than or equal to q), and calculate the adjusted gate-source voltage V. GS_Adjust Specifically, the adjusted gate-source voltage V GS_Adjust The following relationship must be satisfied:

[0089] According to one embodiment of this application, It can be the threshold voltage corresponding to a standard transistor when the drain-source current is 1μA.

[0090] In 514: Select multiple weights in the distribution of the final fluctuating neurons' weights.

[0091] According to one embodiment of this application, the distribution of weights of the final fluctuating neurons can be... The weights of the q transistors corresponding to each final fluctuation neuron are randomly selected according to a Gaussian distribution. (r can be an integer greater than 1 and less than or equal to q).

[0092] In 515: Drain-source currents of multiple transistors are generated based on the adjusted gate-source voltage, determined weights, and corresponding drain-source voltage data.

[0093] Figure 6A The diagram illustrates the variation curves of the drain-source current relative to the gate-source voltage, which serves as the output. The solid gray line represents the drain-source current curve obtained using the transistor model generated by the BSIM-CMG model based on physical mechanisms, while the dashed black line represents the drain-source current curve obtained using the transistor statistical model in the embodiments of this application. Figure 6A As shown, the regions covered by the drain-source current characteristic curves generated by the two transistor models basically overlap, indicating that the transistor statistical model generated in this application meets expectations.

[0094] Figure 6B The figure shows the I obtained using the transistor statistical model of the artificial neural network system of this application. SAT The probability distribution diagram. Figure 6B Indicator I SAT At the gate-source voltage V GS and drain-source voltage V DS All values ​​represent drain-source currents at VDD. In the figure, dark gray rectangles represent data obtained using the BSIM-CMG model based on physical mechanisms, while light gray striped rectangles represent data obtained using the statistical model of this application. Figure 6B As shown, the probability distribution error (the difference in σ / μ between the probability distribution curves generated by the two models) between the transistor statistical model data generated in this application and the test data in each index does not exceed 1%. In practical applications, such an error of less than 5% indicates that the performance is close to that of traditional models and has high accuracy.

[0095] Figure 7 This is a comparison chart showing the simulation time of the transistor statistical model and the traditional physical model of the artificial neural network system proposed in this application. For example... Figure 7As shown, the simulations are divided into single-tube simulations and multi-tube Monte Carlo simulations. The light gray rectangles represent the simulation time using the proposed artificial neural network statistical model, while the dark gray rectangles represent the simulation time using the physics-based BSIM-CMG model. Figure 7 As shown, the BSIM-CMG model takes 3-4 times longer than the method in this application. Compared with the BSIM-CMG model, the transistor statistical model based on artificial neural network systems in this application achieves a significant improvement in simulation speed.

[0096] Figure 8 This is a voltage transfer characteristic curve generated by applying a transistor statistical model according to an embodiment of this application to an inverter circuit. The gray solid line represents test data generated using the physical mechanism-based BSIM-CMG model, and the black dashed line represents data from the transistor statistical model formed in this application. Figure 8 As shown, the output characteristic curve of the transistor generated by the method of this application, when applied to the inverter circuit, basically matches the reference data, demonstrating high accuracy and practicality.

[0097] This application also provides a simulation tool, which may include a transistor statistical model based on an artificial neural network system. The simulation tool can be applied to simulation software such as SPICE to simulate and test a single transistor, multiple transistors of the same type, or an entire module circuit. During the simulation process, the gate-source voltage and drain-source voltage of the transistor need to be input into the simulation tool.

[0098] This application also provides a computer-readable storage medium, such as a memory storing a computer program that can be executed to complete the steps of the method for establishing a transistor statistical model based on an artificial neural network system provided in any embodiment of this application. The computer storage medium may be a memory such as FRAM, ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface memory, optical disc, or CD ROM; or it may be various devices including one or any combination of the above-mentioned memories.

[0099] This application also provides a computer-readable storage medium, such as a memory storing a computer program that can be executed to perform the application method steps of the transistor statistical model of the artificial neural network system provided in any embodiment of this application. The computer storage medium may be a memory such as FRAM, ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface memory, optical disc, or CD ROM; or it may be various devices including one or any combination of the above-mentioned memories.

[0100] By adopting the solution of this application, it is possible to accelerate the construction of intensive transistor models, ensure low complexity and high accuracy of the models, capture performance changes caused by process fluctuations, improve the reliability of transistor simulation models, and significantly increase the simulation speed of generating transistor models.

[0101] The above embodiments are for illustrative purposes only and are not intended to limit the scope of this application. Those skilled in the art can make various changes and modifications without departing from the scope of this application. Therefore, all equivalent technical solutions should also fall within the scope of this application.

Claims

1. A method for establishing a transistor statistical model based on an artificial neural network system, comprising: The system receives a first dataset and generates a nominal model of a standard transistor using an artificial neural network system based on the data in the first dataset. The first dataset includes multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of multiple transistors of the same model. The multiple transistors of the same model include the standard transistor and multiple fluctuating transistors. The standard transistor is determined based on the median or average value of the drain-source current data of the multiple transistors of the same model under the same bias conditions. The remaining transistors of the multiple transistors of the same model are fluctuating transistors. Based on the first dataset and the nominal model, the neurons in the artificial neural network system are screened to obtain the final fluctuating neurons; Based on the changes in the weights of the nominal model relative to the final fluctuation neuron, the changes in the nominal model relative to the threshold voltage, the distribution of drain-source current and gate-source voltage in the first dataset, the distribution of the weights of the final fluctuation neuron and the distribution of the threshold voltage in the statistical model are calculated; and The statistical model is established based on the nominal model, the distribution of the weights of the final fluctuation neurons, and the distribution of the threshold voltage. The operation of filtering neurons in the artificial neural network system based on the first dataset and the nominal model to obtain the final fluctuation neurons includes: The weights of each neuron in the artificial neural network system in the nominal model are changed until the difference between the intermediate output curve of the neuron after the weight change and the current-voltage characteristic curve of each fluctuation transistor is less than a first threshold. The weights of the neurons in the fluctuation transistor are then used as the adjusted weights of the neurons for that fluctuation transistor. The intermediate output curve refers to the output curve obtained after changing the weights of the neurons in the nominal model. For each of the fluctuation transistors, calculate the absolute value of the relative change between the adjusted weight of each neuron and the weight of that neuron in the nominal model; For the plurality of transistors of the same type, calculate the average of the absolute values ​​of the relative changes in the weights of each neuron in the artificial neural network system, and select preliminary fluctuating neurons based on the average value; and The final fluctuation neurons are selected based on the magnitude of the neuron output changes of the initial fluctuation neurons.

2. The method for establishing according to claim 1, wherein... The first threshold is a value that is less than or equal to 5% of the drain-source current of the fluctuating transistor being compared.

3. The method for establishing according to claim 1, wherein... The initial fluctuation neurons whose output changes by an amplitude greater than or equal to 0.1 are designated as the final fluctuation neurons.

4. The method for establishing according to claim 1, wherein, The changes in the weights of the nominal model relative to the final fluctuating neuron include the partial derivatives of the drain-source current in the nominal model with respect to the weights of the final fluctuating neuron and the partial derivatives of the gate-source voltage in the nominal model with respect to the weights of the final fluctuating neuron.

5. The method for establishing according to claim 1, wherein... The variation of the nominal model with respect to the threshold voltage includes the partial derivative of the drain-source current in the nominal model with respect to the threshold voltage and the partial derivative of the gate-source voltage in the nominal model with respect to the threshold voltage.

6. The method for establishing according to claim 1, wherein... The distribution of drain-source current and gate-source voltage in the first dataset includes the standard deviation of drain-source current and the standard deviation of gate-source voltage.

7. The method for establishing according to claim 1, wherein... The distribution of the weights of the final fluctuation neurons in the statistical model includes the standard deviation of the weights of the final fluctuation neurons, and the distribution of the threshold voltage in the statistical model includes the standard deviation of the threshold voltage.

8. A method for applying a transistor statistical model of an artificial neural network system, comprising: Receive a second dataset, which includes multiple sets of gate-source voltage and drain-source voltage data of multiple transistors of the same model. The multiple transistors of the same model include standard transistors and multiple fluctuating transistors. The standard transistor is determined based on the median or average value of the drain-source current data of the multiple transistors of the same model under the same bias conditions, and the rest are fluctuating transistors. The second dataset also includes multiple sets of drain-source current data of the standard transistor and some of the fluctuating transistors. The statistical model is established based on multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and the partial fluctuation transistor in the second dataset, and the distribution of threshold voltage and the weight distribution of the final fluctuation neuron in the statistical model are obtained, wherein the final fluctuation neuron is a neuron in the artificial neural network system. Multiple threshold voltages are selected from the distribution of threshold voltages, and the corresponding adjusted gate-source voltages are calculated. Select multiple final fluctuation neuron weights from the distribution of the final fluctuation neuron weights; and Based on the multiple adjusted gate-source voltages, the multiple selected final fluctuation neuron weights, and the corresponding drain-source voltage data, the drain-source currents of multiple transistors of the same model are generated. The step of establishing the statistical model based on the data of the standard transistors and some fluctuation transistors in the second dataset includes: Based on multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and the partial fluctuation transistor in the second dataset, a nominal model of the standard transistor is generated using an artificial neural network system. Based on multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and the partial fluctuation transistor in the second dataset, as well as the nominal model, the neurons in the artificial neural network system are screened to obtain the final fluctuation neurons; Based on the changes in the weights of the nominal model relative to the final fluctuation neuron, the changes in the nominal model relative to the threshold voltage, and the distributions of the drain-source currents and gate-source voltages of the standard transistors and some fluctuation transistors in the second dataset, the distributions of the weights of the final fluctuation neuron and the threshold voltages in the statistical model are calculated; and The statistical model is established based on the nominal model, the distribution of the weights of the final fluctuation neurons, and the distribution of the threshold voltage.

9. The application method according to claim 8, wherein The threshold voltage is randomly selected according to a Gaussian distribution in the distribution of the threshold voltage, and the corresponding weight is randomly selected according to a Gaussian distribution in the distribution of the weights of the final fluctuating neurons.

10. The application method according to claim 8, wherein, Based on multiple sets of gate-source voltage, drain-source voltage, and drain-source current data of the standard transistor and the partial fluctuation transistor in the second dataset, as well as the nominal model, the operation of filtering neurons in the artificial neural network system to obtain the final fluctuation neurons includes: The weights of each neuron in the artificial neural network system in the nominal model are changed until the difference between the intermediate output curve of the neuron after the weight change and the current-voltage characteristic curve of each fluctuation transistor is less than a first threshold. The weights of the neurons in the fluctuation transistor are then used as the adjusted weights of the neurons for that fluctuation transistor. The intermediate output curve refers to the output curve obtained after changing the weights of the neurons in the nominal model. For each of the fluctuation transistors, calculate the absolute value of the relative change between the adjusted weight of each neuron and the weight of that neuron in the nominal model; For the plurality of transistors of the same type, calculate the average of the absolute values ​​of the relative changes in the weights of each neuron in the artificial neural network system, and select preliminary fluctuating neurons based on the average value; and The final fluctuation neurons are selected based on the magnitude of the neuron output changes of the initial fluctuation neurons.

11. The application method according to claim 10, wherein, The first threshold is a value that is less than or equal to 5% of the drain-source current of the fluctuating transistor being compared.

12. The application method according to claim 10, wherein The initial fluctuation neurons whose output changes by an amplitude greater than or equal to 0.1 are designated as the final fluctuation neurons.

13. The application method according to claim 8, wherein The changes in the weights of the nominal model relative to the final fluctuating neuron include the partial derivatives of the drain-source current in the nominal model with respect to the weights of the final fluctuating neuron and the partial derivatives of the gate-source voltage in the nominal model with respect to the weights of the final fluctuating neuron.

14. The application method according to claim 8, wherein The variation of the nominal model with respect to the threshold voltage includes the partial derivative of the drain-source current in the nominal model with respect to the threshold voltage and the partial derivative of the gate-source voltage in the nominal model with respect to the threshold voltage.

15. The application method according to claim 8, wherein The distribution of drain-source current and gate-source voltage of the standard transistor and some fluctuating transistors in the second dataset includes the standard deviation of drain-source current and the standard deviation of gate-source voltage.

16. The application method according to claim 8, wherein The distribution of the weights of the final fluctuation neurons in the statistical model includes the standard deviation of the weights of the final fluctuation neurons, and the distribution of the threshold voltage in the statistical model includes the standard deviation of the threshold voltage.

17. A computer-readable storage medium comprising a memory storing a computer program, said computer program being executed to perform the method for establishing a transistor statistical model based on an artificial neural network system as described in any one of claims 1-7.

18. A computer-readable storage medium comprising a memory storing a computer program, said computer program being executed to perform a method for applying a transistor statistical model of an artificial neural network system according to any one of claims 8-16.

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