Semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer

Abstract

The invention relates to the technical field of semiconductor device parameter extraction, in particular to a semiconductor device parameter extraction method based on a reinforcement learning enhanced equalization optimizer, and the method comprises the steps: constructing a semiconductor device model, and determining input, output and optimization targets based on the semiconductor device model; and starting a parameter extraction algorithm based on the input, the output and the optimization target, and obtaining the optimal parameter of the semiconductor device, the parameter extraction algorithm being constructed by combining reinforcement learning with an equalization optimizer. According to the method, the efficiency and the precision of MOSFET parameter extraction can be improved by adaptively adjusting the iteration parameters of the optimization algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of semiconductor device parameter extraction, and in particular to a semiconductor device parameter extraction method based on a reinforcement learning enhanced equalizer optimizer. Background Art

[0002] At present, MOSFET parameter extraction methods mainly include heuristic algorithms based on genetic algorithm (GA), particle swarm optimization algorithm (PSO), and some algorithms based on reinforcement learning.

[0003] Genetic Algorithm (GA) is an optimization algorithm that simulates the biological evolution process. It iteratively updates the population through selection, crossover and mutation operations to find the global optimal solution. The application of GA in MOSFET parameter extraction extracts device parameters by fitting experimental data. GA has slow iteration and update speed in complex multi-dimensional parameter space, resulting in slow convergence speed; in complex nonlinear optimization problems, GA is prone to fall into local optimal solutions and it is difficult to find the global optimal solution; it requires a lot of computing resources, especially when dealing with large-scale parameter extraction problems, the computing overhead increases significantly.

[0004] Particle swarm optimization (PSO) is an optimization technology based on swarm intelligence. It simulates the foraging behavior of bird flocks and uses information sharing between particles to find the best solution. The application of PSO in MOSFET parameter extraction approximates the optimal parameter value by updating the speed and position of particles. PSO performs well in the early stage of search, but it is easy to fall into premature convergence in the later stage, causing the algorithm to stop at the local optimum; the performance of PSO is highly sensitive to parameter settings (such as inertia weight and learning factor), and different problems require different parameter tuning; in high-dimensional parameter space, the search efficiency of PSO is significantly reduced, and it is difficult to handle complex multi-dimensional optimization problems.

[0005] Some studies have tried to use reinforcement learning algorithms such as Q-learning to optimize the parameter extraction process, for example, by adjusting the iteration step and direction to improve the accuracy and efficiency of parameter extraction. Existing parameter extraction methods based on reinforcement learning usually use a fixed iteration step, resulting in insufficient flexibility and adaptability in the search process; since reinforcement learning algorithms rely on historical experience during the search process, they may fall into local optimal solutions; in complex parameter extraction tasks, existing reinforcement learning algorithms are difficult to guarantee high-precision parameter extraction results.

[0006] The shortcomings of the above algorithm are mainly due to the limitations of the algorithm itself and the lack of adaptive mechanism in the optimization process. When faced with complex and changeable optimization problems, it is difficult for heuristic algorithms to balance the capabilities of global search and local search. However, the existing reinforcement learning algorithms lack full utilization of environmental status and historical experience in parameter updating and search strategies, resulting in limited algorithm performance. In addition, the above algorithm steps are relatively fixed and lack adaptive adjustment to dynamic changes in the iterative process, resulting in limited efficiency and accuracy of the search process. Therefore, the present invention proposes a semiconductor device parameter extraction method based on reinforcement learning enhanced equalizer optimizer. Summary of the invention

[0007] The purpose of the present invention is to provide a semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer, overcome the shortcomings of the prior art, and improve the efficiency and accuracy of MOSFET parameter extraction by adaptively adjusting the iterative parameters of the optimization algorithm.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] A semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer, comprising:

[0010] Constructing a semiconductor device model, and determining input, output, and optimization targets based on the semiconductor device model;

[0011] A parameter extraction algorithm is started based on the input, output and optimization target to obtain optimal parameters of the semiconductor device, wherein the parameter extraction algorithm is constructed by combining reinforcement learning with a balanced optimizer.

[0012] Optionally, obtaining the optimal parameters of the semiconductor device includes:

[0013] Initialize the population concentration and population fitness, and preset the parameters of the parameter extraction algorithm {a 1 ,a 2 ,GP}, and use it as a coefficient to build an intelligent agent and start the first round of search, where a 1 is the exploration amount of the parameter extraction algorithm, a 2 is the control development characteristic of the parameter extraction algorithm, GP is the generation probability of the parameter extraction algorithm;

[0014] Calculate individual fitness and use exponential weighted average to determine the change trend of the individual fitness;

[0015] The agent is updated and controlled according to the change trend, the individual position is obtained and the next round of search is carried out until a preset number of iterations is reached, and the final position of the individual and the optimal individual are output.

[0016] Optionally, using exponential weighted average to judge the change trend of the individual fitness includes:

[0017]

[0018] in, represents the exponentially weighted average of the i-th individual at the t-th iteration time step, represents the fitness of the i-th individual at the t-th iteration time step, represents the exponentially weighted average of the i-th individual at the time step of the t-1 iteration, and n represents the window length.

[0019] Optionally, updating and controlling the agent according to the change trend includes:

[0020] If the change in individual fitness shows a decreasing trend, then a 1 Reduce, a 2 Increase, GP decreases;

[0021] If the change in individual fitness shows an increasing trend, then a 1 Increase, a 2 decreases and GP increases.

[0022] Optionally, the method for updating and controlling the agent according to the change trend is:

[0023]

[0024] in, represents the number of intelligent systems a of the i-th individual 1 , max(t) represents the maximum number of iterations, r represents a random number between 0 and 1, and t represents the tth iteration. represents the exponentially weighted average of the i-th individual at the t-th iteration time step, represents the exponentially weighted average of the i-th individual at the time step of the t+1 iteration, represents the number of intelligent systems a of the i-th individual 2 , G.P. i represents the number of intelligent systems GP of the i-th individual, and τ represents the constant that controls the iteration step size.

[0025] Optionally, the final position of the individual is output as:

[0026]

[0027] in, represents the final position of the individual, represents the equilibrium concentration, κ 1 and κ 2 represents the proportionality coefficient, represents the average equilibrium concentration, represents the correction factor, represents the reaction rate, represents flow rate and V represents volume.

[0028] The beneficial effects of the present invention are:

[0029] The present invention can (1) improve the convergence speed: by introducing the reinforcement learning algorithm, the iteration step size and direction of the EO algorithm can be dynamically adjusted to accelerate the convergence speed of parameter extraction. The reinforcement learning algorithm can use historical experience and current status to achieve adaptive adjustment, thereby improving the efficiency of the optimization process; (2) avoid local optimality: by combining reinforcement learning with the EO algorithm, the reinforcement learning algorithm is used to adaptively adjust the parameters during the iteration process, thereby enhancing the global search capability of the algorithm and reducing the probability of falling into the local optimality. By introducing a pre-trained reinforcement learning model, the parameters of the EO algorithm can be optimized at different stages, thereby improving the intelligence and flexibility of the algorithm. (3) Reducing computational overhead: By introducing a reinforcement learning algorithm, computing resources can be used more effectively during the optimization process, unnecessary calculations can be reduced, and the overall computational overhead can be reduced. The adaptive adjustment mechanism makes the parameter extraction process more efficient, thereby obtaining better optimization results with the same computing resources. (4) Improving parameter extraction accuracy: By combining the reinforcement learning algorithm with the EO algorithm, experimental data can be fitted more accurately, and the accuracy of parameter extraction can be improved. By introducing RMSE (root mean square error) as the optimization objective function, the extracted parameters can be ensured to have higher accuracy in model fitting. (5) Enhancing the adaptability of the algorithm: The adaptive adjustment of the EO algorithm is achieved through the reinforcement learning algorithm, so that the algorithm can be adjusted according to different optimization problems and stages, thereby improving the adaptability and robustness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 It is a flow chart of a semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer according to an embodiment of the present invention;

[0032] Figure 2 The balance optimizer algorithm flow of the embodiment of the present invention;

[0033] Figure 3A comparison diagram of convergence curves of SIC MOSFET parameter extraction using different optimization algorithms on an N-th power law model according to an embodiment of the present invention;

[0034] Figure 4 It is a fitting effect diagram of SIC MOSFET parameter extraction on an N-order power law model using different optimization algorithms according to an embodiment of the present invention;

[0035] Figure 5 A comparison diagram of convergence curves of NMOS parameter extraction performed on a compact device model BSIM4 using different optimization algorithms according to an embodiment of the present invention;

[0036] Figure 6 This is a fitting effect diagram of NMOS parameter extraction on the compact device model BSIM4 using different optimization algorithms according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] This embodiment provides a semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer, such as Figure 1 As shown, including:

[0040] Build a semiconductor device model and determine the input, output and optimization targets based on the semiconductor device model.

[0041] A parameter extraction algorithm is started based on input, output and optimization target to obtain the optimal parameters of the semiconductor device, wherein the parameter extraction algorithm is constructed by combining reinforcement learning with a balanced optimizer.

[0042] Among them, the extraction process of the parameter extraction algorithm includes:

[0043] Initialize the population concentration and population fitness, and preset the parameters of the parameter extraction algorithm {a 1 ,a 2 ,GP}, and use it as a coefficient to build an intelligent agent and start the first round of search, where a 1 is the exploration amount of the parameter extraction algorithm, a 2is the control development characteristic of the parameter extraction algorithm, GP is the generation probability of the parameter extraction algorithm;

[0044] Calculate individual fitness and use exponential weighted average to determine the change trend of the individual fitness;

[0045] The intelligent agent is updated and controlled through the changing trend, the individual position is obtained and the next round of search is carried out until the preset number of iterations is reached, and the final position of the individual and the optimal individual are output.

[0046] Specifically, this embodiment combines the reinforcement learning algorithm with the EO algorithm to propose a new MOSFET model parameter extraction method RLEO, which effectively overcomes the shortcomings of the prior art. By introducing the reinforcement learning algorithm, adaptive adjustment of parameters is achieved, the efficiency and accuracy of the optimization process are improved, the computational overhead is reduced, and the adaptability and intelligence of the algorithm are enhanced. Compared with traditional genetic algorithms, particle swarm optimization algorithms and existing reinforcement learning algorithms, this method has significant advantages in speed, accuracy and global search capability of MOSFET model parameter extraction, and provides an efficient and accurate MOSFET parameter extraction solution.

[0047] This embodiment uses two MOSFET models for parameter extraction. The first is the standard compact model BSIM4, which is used to simulate N-type metal oxide semiconductor (NMOS) transistors. The second is an N-th power law model, which is used to fit silicon carbide (SiC) power MOSFETs.

[0048] BSIM4 Compact Model:

[0049] BSIM4 is a physical model for MOS transistors, which is built by fitting process parameters and test data. It can accurately describe various physical effects in deep submicron CMOS processes, including short channel effects, narrow channel effects, and quantum effects. The model contains dozens of parameters that can be extracted to describe the DC / AC characteristics and transient response of MOS transistors. BSIM4 is compatible with SPICE circuit simulation software and can be used for the simulation and design of integrated circuits. The basic equation of the model is as follows:

[0050]

[0051] Among them, I DS is the drain-source current, μ is the mobility, C ox is the oxide capacitance, W and L are the width and length of the MOSFET respectively, V gs is the gate-source voltage, V th is the threshold voltage, λ is the channel length modulation coefficient, V ds is the drain-source voltage. BSIM4 defines small signal parameter equations, including transconductance (gm ) and transconductance generation (g ds ) expression:

[0052]

[0053] Among them, L DS is the distance between the source and drain of the MOSFET.

[0054] This is part of the equations in the BSIM4 model. The actual BSIM4 model involves numerous parameters and equations to describe the various characteristics of the MOSFET. The extracted model is based on the core parameters of the BSIM4 model, as shown in Table 1.

[0055] Table 1

[0056]

[0057]

[0058] N-th power law model:

[0059] In this model, the drain current is calculated based on the threshold voltage VTH of the MOSFET. ds,sat and saturation current I d,sat The definition is as follows:

[0060] V ds,sat = J(V gs -VTH) M (3)

[0061] I d,sat =K(V gs -VTH) N (4)

[0062] The expression involves fitting parameters J and M, which are used to calculate the current in the linear region, and additional fitting parameters K and N, which are applied in the saturation region. ds,mod As V ds to depict a seamless transition between the linear and saturation regions.

[0063]

[0064] DELTA is a control V ds,mod and V ds,sat The drain current I sim is determined by considering channel length modulation and mobility degradation as follows:

[0065]

[0066] The detailed parameters of the model are listed in Table 2.

[0067] Table 2

[0068] parameter describe VTH Threshold voltage K / M Fitting parameters in the linear region J / N Fitting parameters in the saturation region LAMDA Channel length modulation THETA Mobility degradation DELTA Smoothing parameter for smooth transition between linear and saturation regions

[0069] like Figure 2 As shown in the figure, it is based on the principles of mass conservation and concentration balance in physical chemistry, and searches for the optimal solution by simulating the dynamic changes in the concentration of substances in the system. EO uses a simple mixing model to describe the concentration changes of non-reactive components in the control volume. Through this dynamic equilibrium process, the system gradually approaches the optimal state. The algorithm first initializes the population, and then adjusts the position of individuals according to the fitness of individuals in the population through continuous iterations to achieve the global optimal solution. EO effectively avoids falling into the local optimum through appropriate balanced exploration and development.

[0070] In this process, the parameter a 1 、a 2 and the generation probability GP have important implications for the exploration and exploitation mechanisms. Specifically, a 1 Controls the amount of exploration of the algorithm. The larger the value, the stronger the exploration ability. However, if it exceeds 3, the performance will be significantly reduced. 2 Controls the development characteristics and determines the degree of mining around the optimal solution; the generation probability GP controls the probability of participation in the generation rate when the concentration is updated. When GP = 1, it emphasizes high exploration ability, when GP = 0, it increases the probability of local optimal stagnation, and GP = 0.5 provides a good balance between exploration and development. In addition, the sign function sgn (r-0.5) controls the direction of exploration and development, and the uniformly distributed random number r ensures equal probability in the positive and negative directions.

[0071] Parameter a 1 、a 2 The generation probability GP has a great influence on the convergence speed and stability of the algorithm, and all individuals in the group share the same set of algorithm parameters {a 1 ,a 2 ,GP}, which not only affects the convergence speed of the algorithm, but also easily causes the group to fall into the local optimal solution. Therefore, a reinforcement learning-based solution is proposed to give each individual a unique algorithm parameter a 1 ,a 2 ,GP, thereby independently adjusting the balance between individual search and inheritance. Simply comparing the fitness difference of two time steps cannot well deduce the trend of the individual search direction. Therefore, the idea of ​​exponential weighted average (EMA) is adopted to judge the trend of individual fitness change through window sampling, and the intelligent agent is updated and controlled according to the change trend: if the change of individual fitness shows a decreasing trend, then a 1 Reduce, a 2increases, GP decreases; if the change in individual fitness shows an increasing trend, then a 1 Increase, a 2 decreases and GP increases.

[0072] As shown in (7), where n represents the window length, here n is equal to 4. If the EMA of the current time step is greater than the EMA of the previous time step, it means that the individual's fitness is on an upward trend in the short term.

[0073]

[0074] Among them, r represents a random number between 0 and 1, max(t) represents the maximum number of iterations, represents the fitness of the ith individual at the time step of the tth iteration. (8) indicates that if the fitness trend of the individual increases after the iteration, it means that there is still room for further exploration. Otherwise, it means that the remaining space for exploration is limited and needs to be adjusted. 1 Perform appropriate attenuation. Similarly, we can get a 2 The update strategy is shown in (10), which indicates that when the group iteration produces a trend of decreasing fitness, a should be increased. 2 This will enhance the tendency of individuals to move closer to the group's optimal solution. The core process of the algorithm can be Figure 1 In other words, the agent determines the "reward" through the EMA trend, takes corresponding actions based on the reward, and completes the adjustment of independent parameters in the search space to adapt to the algorithm optimization direction.

[0075]

[0076] Similarly, the update rule of GP is defined as (11):

[0077]

[0078] Among them, τ is a constant that controls the iteration step size, which is 0.01. This shows that GP will increase positive feedback with the "reward" obtained from exploration, thereby strengthening the exploration level of individuals and achieving a positive feedback effect.

[0079] At the same time, the individual update strategy of the EO algorithm is only guided by a random individual of the current optimal solution, which not only destroys the directionality of the optimization algorithm, but also easily leads to the process of falling into the local optimal solution. Therefore, equation (12) is improved to obtain (13), where κ is a combination of normal distribution and 1. In this way, the exploration direction of the individual considers both the guidance of random excellent individuals and the common trend of the average individuals in the optimization pool.

[0080]

[0081] Experimental verification:

[0082] In order to verify the effectiveness of the algorithm proposed in this embodiment, two MOSFET models are selected for parameter extraction and compared with other optimization algorithms to verify the effectiveness of the algorithm. The comparison methods include differential evolution algorithm (DE), particle swarm optimization (PSO), neural network optimization (NNA), and balanced optimizer (EO).

[0083] Model V ds 、V gs The input is the parameter p, and the output is the drain current Id. The root mean square error (RMSE) is used as the optimization target and can be expressed as:

[0084]

[0085] Where f is the device model function, M is the optional model, and N is the number of benchmark data. o Experimental measurement data from NMOS and SiC MOSFET.

[0086] The parameter extraction test of SIC MOSFET is carried out on the N-th power law model. The model has 6 parameters. The convergence curve and fitting effect diagram are shown as follows: Figure 3 , Figure 4 shown.

[0087] The parameter extraction test of NMOS is carried out on the compact device model BSIM4. The model has 10 parameters. The convergence curve and fitting effect diagram are shown as follows: Figure 5 , Figure 6 shown.

[0088] From the above content, we can see that Figure 3 and Figure 5 It can be observed that the semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer proposed in this embodiment achieves fast convergence and high precision in parameter extraction of both models and the proposed method has the fastest convergence speed in both parameter extraction examples. Figure 4 and Figure 6 The original IV experimental data and the data after parameter extraction are shown. Figure 4 In the figure, the Vgs voltages from bottom to top are 0.6V, 0.8V, 1.0V, 1.2V, 1.4V, and 1.6V respectively. Figure 6 Middle, V from bottom to top g The voltages are 6V, 8V, 10V, 12V, and 14V respectively. Figure 4 and Figure 6 The data after parameter extraction are consistent with the measured values, which accurately reflects the parameter extraction results.

[0089] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer, characterized in that: include: Constructing a semiconductor device model, and determining input, output, and optimization targets based on the semiconductor device model; A parameter extraction algorithm is started based on the input, output and optimization target to obtain optimal parameters of the semiconductor device, wherein the parameter extraction algorithm is constructed by combining reinforcement learning with a balanced optimizer.

2. The semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer according to claim 1, characterized in that: Obtaining the optimal parameters of the semiconductor device includes: Initialize the population concentration and population fitness, preset the parameters {a1, a2, GP} of the parameter extraction algorithm, and use them as coefficients to construct an agent and start the first round of search, where a1 is the exploration amount of the parameter extraction algorithm, a2 is the control development characteristic of the parameter extraction algorithm, and GP is the generation probability of the parameter extraction algorithm; Calculate individual fitness and use exponential weighted average to determine the change trend of the individual fitness; The agent is updated and controlled according to the change trend, the individual position is obtained and the next round of search is carried out until a preset number of iterations is reached, and the final position of the individual and the optimal individual are output.

3. The semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer according to claim 2, characterized in that: The exponentially weighted average is used to judge the changing trend of the individual fitness, including: in, represents the exponentially weighted average of the i-th individual at the t-th iteration time step, represents the fitness of the i-th individual at the t-th iteration time step, represents the exponentially weighted average of the i-th individual at the time step of the t-1 iteration, and n represents the window length.

4. The method for extracting semiconductor device parameters based on reinforcement learning enhanced equalization optimizer according to claim 3, characterized in that: The updating control of the agent according to the change trend includes: If the change in individual fitness shows a decreasing trend, a1 decreases, a2 increases, and GP decreases; If the change in individual fitness shows an increasing trend, a1 increases, a2 decreases, and GP increases.

5. The semiconductor device parameter extraction method based on reinforcement learning enhanced equalization optimizer according to claim 4 is characterized in that: The method for updating and controlling the agent according to the change trend is: in, represents the number of intelligent systems a1 of the i-th individual, max(t) represents the maximum number of iterations, r represents a random number between 0 and 1, and t represents the t-th iteration. represents the exponentially weighted average of the i-th individual at the t-th iteration time step, represents the exponentially weighted average of the i-th individual at the time step of the t+1 iteration, represents the number of intelligent systems of the ith individual a2, GP i represents the number of intelligent systems GP of the i-th individual, and τ represents the constant that controls the iteration step size.

6. The method for extracting semiconductor device parameters based on reinforcement learning enhanced equalization optimizer according to claim 5, characterized in that: Output the final position of the individual: in, represents the final position of the individual, represents the equilibrium concentration, κ1 and κ2 represent the proportionality coefficients, represents the average equilibrium concentration, represents the correction factor, represents the reaction rate, represents flow rate and V represents container volume.

Images