A method for predicting the metal work function fluctuation effect of semiconductor field effect transistors

Abstract

The present invention provides a method for predicting the metal work function fluctuation effect of semiconductor field-effect transistors. The method comprises solving for target devices under multiple sets of metal work function conditions, extracting electrical characteristic parameters during device operation, and forming a data set required for constructing a metal work function fluctuation effect prediction model. Based on the fitting relationship between different electrical characteristic parameters and metal work functions in the data set, a fitting function for the metal work function fluctuation effect prediction model is calculated and verified to obtain a verified prediction model. A metal work function fluctuation distribution probability model is established based on the mechanism of metal work function fluctuation during the production process, and a random distribution sample of metal work function fluctuation is generated. The random distribution sample of metal work function fluctuation of the device to be predicted is input into the verified prediction model to obtain the fluctuation distribution of the electrical characteristic parameters of the device under metal work function fluctuation. The present invention can quickly and accurately predict the effect of metal work function fluctuation on device performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of MOS device simulation, and in particular relates to a method for rapidly predicting fluctuation effects of metal work functions of field effect transistors. Background Art

[0002] Field-Effect Transistor (FET) is a very common semiconductor device and is widely used in integrated circuits.

[0003] Taking the Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) as an example, during the process of production, since the grains of the metal gate material in the device usually have two or more crystal orientations, when the metal material is deposited on the high-K dielectric material using atomic layer deposition technology, the grains of different metal crystal orientations on the interface of the high-K dielectric material are randomly distributed. The number ratio and distribution of grains corresponding to different crystal orientations lead to fluctuations in the metal gate work function. In the production process of field-effect transistors, the above-mentioned random fluctuations are inevitable, and the random fluctuations of the metal work function will cause fluctuations in the electrical performance of the device. As the process size of semiconductor devices continues to shrink, the impact of the metal work function fluctuation effect has become increasingly important.

[0004] Currently, there are two common methods for calculating the fluctuation effect of the metal work function of field-effect transistors. The first relies on TCAD software to calculate a large number of random samples and then collect the results of the random samples. The second method treats the fluctuation of the metal work function as a noise perturbation of the device and calculates the linear response of the device current to the noise perturbation to obtain the change of the device's electrical characteristic parameters. The former requires huge computational and time costs during the calculation process, while the latter has certain deviations in the calculation results and is technically difficult to implement. Summary of the Invention

[0005] Technical Problem: To address the shortcomings of the aforementioned existing technologies, the present invention proposes a method for quickly and easily predicting the effects of metal work function fluctuations in semiconductor field-effect transistors. By using the known grain orientation properties of the device's metal material, the distribution of a series of electrical characteristic parameters, such as the threshold voltage, operating current, and off-state current, can be quickly predicted with high accuracy at a specified operating voltage.

[0006] Technical solution: To achieve the above-mentioned purpose, the method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor adopted by the present invention comprises the following steps:

[0007] Step 1: Solve the target device under multiple sets of metal work function conditions, obtain the drain current and gate voltage relationship curve of the target device under the corresponding drain voltage, and extract the electrical characteristic parameters of the target device such as threshold voltage, operating current, and off current from it, and build the data set required for the model to predict electrical parameters;

[0008] Step 2: Calculate the fitting function of the target device's different electrical characteristic parameter vector groups and the metal work function W based on the above data set to obtain the fitting function of the metal work function fluctuation effect prediction model. And the actual value of the above data set is matched with the prediction model fitting function The mean square error (MSE) and correlation coefficient of the values ​​verify the fitting function of the metal work function fluctuation effect prediction model rationality;

[0009] Step 3: Establish a metal work function fluctuation distribution probability model based on the mechanism of metal work function fluctuation during the production process, and generate a random distribution sample of metal work function fluctuation based on this probability model;

[0010] Step 4: Input the randomly distributed sample of the metal work function fluctuation of the target device to be predicted into the verified metal work function fluctuation effect prediction model to obtain the fluctuation distribution of the electrical characteristic parameters such as threshold voltage, operating current, and off current of the device under the metal work function process fluctuation.

[0011] in,

[0012] The step 1 is specifically as follows:

[0013] According to the physical properties of the metal gate material of the target device, metal work function sample values ​​are selected within the metal work function range corresponding to different crystal orientations of the field effect tube metal gate material to form a metal work function vector group. Where n is the number of selected samples: n = 10 to 30; use TCAD software to obtain the relationship between the drain current and gate voltage Id-Vg of each element of the sample metal work function vector group, namely Id-V g1, Id-V g2, ... Id-V g n ) curve group; finally, the linear region threshold voltage V of the device is extracted from the drain current and gate voltage relationship curve group of the device obtained above. th,lin , saturation threshold voltage V th,sat , linear region working current I on,lin , saturation zone working current I on,sat , linear region shutdown current I off,lin , saturation region turn-off current I off,sat , linear region subthreshold swing SS lin , saturation region subthreshold swing SS satand the vector group of electrical characteristic parameters of the drain-induced barrier lowering effect DIBL

[0014] The data set required for constructing the model for predicting electrical parameters is to divide the data of the device's sample metal work function, threshold voltage, operating current and off current into a training set and a validation set in a ratio of approximately 1:1, where the training set is composed of the selected training set metal work function vector group And the training set linear region threshold voltage vector group obtained by solving it Training set saturation region threshold voltage vector group Training set linear region working current vector group Training set saturation region working current vector group Training set linear region turn-off current vector group And the training set saturation region turn-off current vector group The electrical characteristic parameter vector group is composed of the validation set; the validation set consists of the selected validation set metal work function vector group And the verification set linear region threshold voltage vector group obtained by its solution Verify the saturation threshold voltage vector group Verification set linear region working current vector group Verify the working current vector group in the saturation region Verification set linear region turn-off current vector group and verification set saturation region turn-off current vector group The electrical characteristic parameter vector group is composed of

[0015] The step 2 is specifically as follows: first, the electrical characteristic parameter vector group in the training set is fitted with the corresponding metal work function vector group to obtain the metal work function fluctuation effect prediction model fitting function The fitting function is preliminarily estimated by calculating the mean square error (MSE) between the actual value of the training set and the corresponding fitting function value. The rationality of the final calculation is done by comparing the actual value of the validation set with the corresponding fitting function. The correlation coefficient R2 between the predicted values ​​is greater than 0.9, which verifies the fitting function of the metal work function fluctuation effect prediction model. The rationality of the metal work function fluctuation effect prediction model has been verified.

[0016] The R2 is expressed as Calculate, where N is the number of validation set samples, A i 、B i are the i-th element of the parameter vector group for verifying the electrical characteristics of the collector and the fitting function of the metal work function fluctuation effect prediction model. Obtain the electrical characteristic parameter results corresponding to the i-th element of the metal work function vector group of the verification set; μ A 、μ B , σ A , σ B Verify the electrical characteristic parameter vector group and the fitting function of the metal work function fluctuation effect prediction model respectively Obtain the mean and variance of the corresponding electrical characteristic parameter results obtained from the verification set metal work function vector group.

[0017] Fitting function of the metal work function fluctuation effect prediction model in step 2 The specific solution method is implemented using a variety of numerical fitting methods, including but not limited to polynomial fitting algorithm, Fourier series fitting algorithm, Smooth smoothing fitting algorithm, and least squares fitting algorithm.

[0018] Step 3 is specifically as follows: based on the generation mechanism of the metal gate during the device production process and the metal particle size of the metal gate material, the gate oxide interface is gridded, and random grains are generated at each grid point according to the distribution probability of the crystal orientation of the metal material grains. Finally, the equivalent work function of the metal gate is calculated based on the metal work functions corresponding to the grains with different crystal orientations and their random distribution.

[0019] Step 4 is specifically: fitting the function to the metal work function fluctuation effect prediction model verified in step 2 Input the random distribution sample of the metal work function fluctuation of the device to be predicted, specifically in the fitting function of the above metal work function fluctuation effect prediction model The random distribution sample set of metal work function fluctuations generated by the distribution probability model of metal grains with different crystal orientations on the metal-oxide interface of the device to be predicted is input. The fitting function of the metal work function fluctuation effect prediction model obtained in step 2 The calculated fluctuation distribution of the electrical characteristic parameters of the device under the random distribution sample of the metal work function fluctuation.

[0020] Beneficial Effects: The present invention proposes a simple and rapid method for predicting the metal work function fluctuation effects of semiconductor field effect transistors. By collecting and preprocessing a small sample of data on the relationship between the metal work function of the device and electrical characteristic parameters such as threshold voltage, operating current, and off current, a prediction model is established to quickly and accurately predict the effects of metal work function fluctuations on device performance. Compared with traditional calculation methods that require repeated calculation of a large number of fluctuation samples, the method for rapidly predicting the metal work function fluctuation effects of semiconductor field effect transistors proposed in the present invention can rapidly predict the metal work function fluctuation effects of the device by only calculating a data set obtained from a small number of samples, reducing the time cost of calculation by more than two orders of magnitude. At the same time, compared with the statistical impedance field method, the calculation results have high accuracy and are easy to implement.

[0021] This invention aims to provide a time-efficient, highly accurate, and computationally efficient solution for simulating field-effect transistor (FET) process fluctuations. This solution is applicable not only to conventional 2D MOSFETs but also to predicting metal work function fluctuations in emerging small, complex FETs, such as FinFETs, GAAFETs, and FDSOI MOSFETs. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A schematic flow chart of a method provided by the present invention for predicting the influence of metal work function fluctuations on the electrical characteristics of semiconductor field effect transistors during process production;

[0023] Figure 2 A schematic diagram of the structure of a 14nm SOI FinFET device used in Example 1 of the present invention;

[0024] Figure 3 The relationship between the fitting function curves of the electrical characteristic parameter vector groups and the metal work function vector groups in Example 1 of the present invention and the training set and the verification set. Among them, (a) is the fitting function of the linear region threshold voltage vector group of the training set and the metal work function vector group and the linear region threshold voltage vector group of the verification set, (b) is the fitting function of the saturation region threshold voltage vector group of the training set and the metal work function vector group and the saturation region threshold voltage vector group of the verification set, (c) is the fitting function of the linear region working current vector group of the training set and the metal work function vector group and the linear region working current vector group of the verification set, (d) is the fitting function of the saturation region working current vector group of the training set and the metal work function vector group and the saturation region working current vector group of the verification set, (e) is the fitting function of the linear region turn-off current vector group of the training set and the metal work function vector group and the linear region turn-off current vector group of the verification set, (f) is the fitting function of the saturation region turn-off current vector group of the training set and the metal work function vector group and the saturation region turn-off current vector group of the verification set;

[0025] Figure 4A schematic diagram of establishing a gate oxide layer grid in Example 1 of the present invention;

[0026] Figure 5 The histogram of the random distribution samples of the equivalent metal work function fluctuation generated in Example 1 of the present invention and the Gaussian distribution curve fitted thereto are shown.

[0027] Figure 6 The electrical characteristic parameter distribution histogram, the Gaussian distribution curve obtained by histogram fitting, and the parameters in the Gaussian distribution function corresponding to the random distribution sample of the equivalent metal work function fluctuation in Example 1 of the present invention are shown. Among them, (a) is the threshold voltage distribution histogram, Gaussian distribution curve, and parameters in the linear region, (b) is the threshold voltage distribution histogram, Gaussian distribution curve, and parameters in the saturation region, (c) is the operating current distribution histogram, Gaussian distribution curve, and parameters in the linear region, (d) is the operating current distribution histogram, Gaussian distribution curve, and parameters in the saturation region, (e) is the off-current distribution histogram, Gaussian distribution curve, and parameters in the linear region, and (f) is the off-current distribution histogram, Gaussian distribution curve, and parameters in the saturation region;

[0028] Figure 7 A schematic diagram of the structure of a predicted ultra-thin body-box (UTBB) fully depleted silicon-on-insulator (FDSOI) device used in Example 2 of the present invention;

[0029] Figure 8 The histogram of the random distribution samples of the equivalent metal work function fluctuation generated in Example 2 of the present invention and the Gaussian distribution curve fitted thereto are shown.

[0030] Figure 9 The electrical characteristic parameter distribution histogram, Gaussian distribution curve obtained by histogram fitting, and parameters in the Gaussian distribution function corresponding to the random distribution sample of equivalent metal work function fluctuation in Example 2 of the present invention are shown. Among them, (a) is the threshold voltage distribution histogram, Gaussian distribution curve, and parameters in the linear region, (b) is the threshold voltage distribution histogram, Gaussian distribution curve, and parameters in the saturation region, (c) is the operating current distribution histogram, Gaussian distribution curve, and parameters in the linear region, (d) is the operating current distribution histogram, Gaussian distribution curve, and parameters in the saturation region, (e) is the off-current distribution histogram, Gaussian distribution curve, and parameters in the linear region, and (f) is the off-current distribution histogram, Gaussian distribution curve, and parameters in the saturation region;

[0031] The figure includes: substrate 1, insulating layer 2, source region 3, gate 4, spacer 5, drain region 6; gate oxide interface partition 401, gate oxide interface partition 402, and gate oxide interface partition 403. DETAILED DESCRIPTION

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] Example 1:

[0034] See also Figure 1 An embodiment of the present invention provides a method for rapidly predicting the metal work function fluctuation effect of a 14nm SOIFinFET device based on a simple probability distribution model. The method includes steps S1 to S4.

[0035] Figure 2 A schematic diagram of the structure of a FinFET device used in an embodiment of the present invention includes a substrate 1, an insulating layer 2, a source region 3, a gate 4, a spacer 5, and a drain region 6. The specific parameters of the FinFET device are as follows: gate length 14nm, gate height 29nm, source-drain length 50nm, source-drain extension region length 10nm, Fin height 26nm, Fin width 6.5nm, source region doping concentration 1×10 21 / cm 3 , the drain region doping concentration is 1×10 21 / cm 3 The doping distribution of the source and drain extension regions is Gaussian, and the channel doping concentration is 1×10 15 / cm 3 , the substrate doping concentration is 1×10 17 / cm 3 The device gate oxide material is hafnium dioxide, the gate metal material is titanium nitride, and the expected value of the work function is 4.32eV.

[0036] S1. Select a set of uniformly distributed work function values ​​from the work function fluctuation range of the metal gate material of the FinFET device described in this embodiment. The FinFET device model corresponding to each work function value is constructed using TCAD software and the drain current and gate voltage relationship curve group (Id-Vg1, Id-Vg2, ... Id-Vg) of each FinFET device model is solved under two fixed drain voltages of 0.05V and 0.8V and the gate voltage range is from 0V to 0.8V. 19 ), and finally extract the threshold voltage vector group of the device's electrical characteristic parameters in the two working modes from the device drain current and gate voltage relationship curve corresponding to this set of work function values Working current vector group Turn off current vector group

[0037] S2. The electrical characteristic parameter values ​​corresponding to the uniformly distributed work function obtained in S1 are divided into a training set and a validation set in a ratio of 10:9. The training set is used to calculate the fitting function of the metal gate work function of the device of this embodiment within a reasonable fluctuation range and the electrical characteristic parameters, thereby establishing a fitting function for the device's metal work function fluctuation effect prediction model. The validation set data is used to verify the accuracy of the prediction model fitting function. Polynomial fitting can accurately fit the threshold voltage and operating current vector groups to the metal work function vector group. The fitting relationship between the off-current vector group and the metal work function vector group is approximately exponential. Therefore, the off-current vector group is logarithmized to the base 10 and then the polynomial fitting relationship between it and the metal work function vector group is solved. The fitting function expressions and correlation coefficients of the various electrical characteristic parameter vector groups and the metal work function vector group are as follows:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] S3, meshing and modeling the gate oxide material interface of the FinFET device in this embodiment. Figure 4 As shown, the process of grid division refers to the average grain size of the metal gate material of the device of this embodiment, titanium nitride TiNitride, and sets the metal grain size of titanium nitride in the process of growth to 5 nanometers, and the grid division method is determined accordingly. The establishment of the metal work function fluctuation distribution probability model refers to the crystal orientation distribution probability and corresponding work function of titanium nitride in the growth process, and sets the probability of the occurrence of crystal orientation grains with corresponding work functions of 4.2eV, 4.3eV and 4.65eV to 50%, 30% and 20% respectively. After generating 10,000 random distribution samples of titanium nitride grains according to the above principle, the equivalent metal work function value corresponding to each randomly distributed sample is calculated by weighted average. The histogram of the equivalent metal work function fluctuation random distribution sample and its fitted Gaussian distribution curve are shown in Figure 2. Figure 5 As shown, the Gaussian distribution function of the metal work function fluctuation random distribution sample fitting is The value of μ is 4.320 and the value of σ is 0.022.

[0045] S4, fitting function to the metal work function fluctuation effect prediction model established in S2 By inputting 10,000 random distribution samples of equivalent metal work function fluctuations generated in S3, the prediction model can quickly calculate the electrical characteristic parameter distribution corresponding to the equivalent metal work function samples through the fitting parameters of various electrical characteristic parameters and metal work function, the electrical characteristic parameter distribution histogram, the Gaussian distribution curve obtained by histogram fitting, and the parameters in the Gaussian distribution function as shown in the figure. Figure 6 As shown, the impact of random fluctuations in the metal work function during the process production on the electrical characteristics of the device can be predicted.

[0046] Example 2:

[0047] See also Figure 1 An embodiment of the present invention provides a method for rapidly predicting the metal work function fluctuation effect of an ultra-thin body-box (UTBB) fully depleted silicon-on-insulator (FDSOI) device based on a simple probability distribution model. The method includes steps S1 to S4.

[0048] Figure 7 This is a schematic diagram of a fast prediction ultra-thin box fully depleted silicon-on-insulator device structure used in an embodiment of the present invention, including a substrate 1, an insulating layer 2, a source region 3, a gate 4, a spacer 5, and a drain region 6. The specific parameters of the FDSOI device are as follows: gate length 12nm, buried oxide thickness 10nm, ultra-thin silicon channel thickness 5nm, equivalent gate oxide thickness 1nm, source region doping concentration 1×10 21 / cm 3 , the drain region doping concentration is 1×10 21 / cm 3 , the channel doping concentration is 1×10 15 / cm 3 , the substrate doping concentration is 1×10 17 / cm 3 The device gate oxide material is hafnium dioxide, the gate metal material is titanium nitride, and the expected value of the work function is 4.205eV.

[0049] S1. Select a set of uniformly distributed work function values ​​from the work function fluctuation range of the metal gate material of the FDSOI device described in this embodiment. TCAD software was used to construct the FDSOI device model corresponding to each work function value and solve the drain current and gate voltage relationship curve group (Id-Vg1, Id-Vg2, ... Id-Vg) of each FDSOI device model under two fixed drain voltages of 0.05V and 0.8V and the gate voltage range of 0V to 1.0V. 17 ), and finally extract the threshold voltage vector group of the device's electrical characteristic parameters in the two working modes from the device drain current and gate voltage relationship curve corresponding to this set of work function values. Working current vector group Turn off current vector group

[0050] S2. The electrical characteristic parameter values ​​corresponding to the uniformly distributed work function obtained in S1 are divided into a training set and a validation set in a ratio of 9:8. The training set is used to calculate the fitting function of the metal gate work function of the device of this embodiment within a reasonable fluctuation range and each electrical characteristic parameter, thereby establishing a metal work function fluctuation effect prediction model for the device. The validation set data is used to verify the accuracy of the fitting function of the prediction model. In this embodiment, the threshold voltage and working current vector group and the metal work function vector group can be fitted more accurately using polynomial fitting. The fitting relationship between the turn-off current vector group and the metal work function vector group is approximately an exponential relationship. Therefore, the turn-off current vector group is logarithmized to the base 10 and then the polynomial fitting relationship between it and the metal work function vector group is solved. The fitting function expressions and correlation coefficients of each electrical characteristic parameter vector group and the metal work function vector group are as follows:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] S3. The gate oxide material interface of the FDSOI device in this embodiment is meshed and modeled. The meshing process refers to the average grain size of the metal gate material titanium nitride TiN of the device in this embodiment. The metal grain size of titanium nitride during the process growth is set to 1 nanometer and the meshing method is determined accordingly. The establishment of the metal work function fluctuation distribution probability model refers to the crystal orientation distribution probability and corresponding work function of titanium nitride in the growth process. The probability of the occurrence of crystal orientation grains with corresponding work functions of 4.0eV, 4.15eV and 4.8eV is set to 50%, 30% and 20% respectively. After generating 10,000 random distribution samples of titanium nitride grains according to the above principle, the equivalent metal work function value corresponding to each randomly distributed sample is calculated by weighted average. The histogram of the equivalent metal work function fluctuation random distribution sample and its fitted Gaussian distribution curve are shown as follows. Figure 8 As shown, the Gaussian distribution function of the metal work function fluctuation random distribution sample fitting is The value of μ is 4.205 and the value of σ is 0.049.

[0058] S4. Input the 10,000 equivalent metal work function fluctuation random distribution samples generated in S3 into the metal work function fluctuation effect prediction model established in S2. The prediction model can quickly calculate the electrical characteristic parameter distribution corresponding to the equivalent metal work function sample through the fitting parameters of each electrical characteristic parameter and the metal work function. The electrical characteristic parameter distribution histogram, the Gaussian distribution curve obtained by histogram fitting and its Gaussian distribution parameters are as follows: Figure 9 As shown, the impact of random fluctuations in the metal work function during the process production on the electrical characteristics of the device can be predicted.

Claims

1. A method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor, characterized in that: The method comprises the following steps: Step 1: Solve the target device under multiple sets of metal work function conditions, obtain the drain current and gate voltage relationship curve of the target device under the corresponding drain voltage, and extract the electrical characteristic parameters of the target device such as threshold voltage, operating current, and off current from it, and build the data set required for the model to predict electrical parameters; Extract the linear region threshold voltage V of the device from the drain current and gate voltage relationship curve group obtained above. th,lin , saturation threshold voltage V th,sat , linear region working current I on,lin , saturation zone working current I on,sat , linear region shutdown current I off,lin , saturation region turn-off current I off,sat , linear region subthreshold swing SS lin , saturation region subthreshold swing SS sat and the vector group of electrical characteristic parameters of the drain-induced barrier lowering effect DIBL Step 2: Calculate the fitting function of the target device's different electrical characteristic parameter vector groups and the metal work function W based on the above data set to obtain the fitting function of the metal work function fluctuation effect prediction model. And the actual value of the above data set is matched with the prediction model fitting function The mean square error (MSE) and correlation coefficient of the values ​​verify the fitting function of the metal work function fluctuation effect prediction model The rationality of the metal work function fluctuation effect prediction model fitting function The specific solution method is implemented using a variety of numerical fitting methods, including polynomial fitting algorithm, Fourier series fitting algorithm, Smooth smoothing fitting algorithm, and least squares fitting algorithm; Step 3: Establish a metal work function fluctuation distribution probability model based on the mechanism of metal work function fluctuation during the production process, and generate a random distribution sample of metal work function fluctuation based on this probability model; Step 4: Input the randomly distributed sample of the metal work function fluctuation of the target device to be predicted into the verified metal work function fluctuation effect prediction model to obtain the fluctuation distribution of the electrical characteristic parameters of the device such as threshold voltage, operating current, and off current under the metal work function process fluctuation.

2. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 1, characterized in that: The step 1 is specifically as follows: According to the physical properties of the metal gate material of the target device, metal work function sample values ​​are selected within the metal work function range corresponding to different crystal orientations of the field effect tube metal gate material to form a metal work function vector group. Where n is the number of selected samples: n = 10 to 30; use TCAD software to obtain the relationship between the drain current and gate voltage Id-Vg of each element of the sample metal work function vector group, namely Id-V g1, Id-V g2, ... Id-V g n ) curve group.

3. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 1, characterized in that: The data set required for constructing the model for predicting electrical parameters is to divide the data of the device's sample metal work function, threshold voltage, operating current and off current into a training set and a validation set in a 1:1 ratio, where the training set is composed of the selected training set metal work function vector group And the training set linear region threshold voltage vector group obtained by solving it Training set saturation region threshold voltage vector group Training set linear region working current vector group Training set saturation region working current vector group Training set linear region turn-off current vector group And the training set saturation region turn-off current vector group The electrical characteristic parameter vector group is composed of the validation set; the validation set consists of the selected validation set metal work function vector group And the verification set linear region threshold voltage vector group obtained by its solution Verify the saturation threshold voltage vector group Verification set linear region working current vector group Verify the working current vector group in the saturation region Verification set linear region turn-off current vector group and verification set saturation region turn-off current vector group The electrical characteristic parameter vector group is composed of 4. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 1, characterized in that: The step 2 is specifically as follows: first, the electrical characteristic parameter vector group in the training set is fitted with the corresponding metal work function vector group to obtain the metal work function fluctuation effect prediction model fitting function The fitting function is preliminarily estimated by calculating the mean square error (MSE) between the actual value of the training set and the corresponding fitting function value. The rationality of the final calculation is done by comparing the actual value of the validation set with the corresponding fitting function. The correlation coefficient R2 between the predicted values ​​is greater than 0.9, which verifies the fitting function of the metal work function fluctuation effect prediction model. The rationality of the metal work function fluctuation effect prediction model has been verified.

5. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 4, characterized in that: The R2 is expressed as Calculate, where N is the number of validation set samples, A i 、B i are the i-th element of the parameter vector group for verifying the electrical characteristics of the collector and the fitting function of the metal work function fluctuation effect prediction model. Obtain the electrical characteristic parameter results corresponding to the i-th element of the metal work function vector group of the verification set; μ A 、μ B , σ A , σ B Verify the electrical characteristic parameter vector group and the fitting function of the metal work function fluctuation effect prediction model respectively Obtain the mean and variance of the corresponding electrical characteristic parameter results obtained from the verification set metal work function vector group.

6. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 1, characterized in that: Step 3 is specifically as follows: based on the generation mechanism of the metal gate during the device production process and the metal particle size of the metal gate material, the gate oxide interface is gridded, and random grains are generated at each grid point according to the distribution probability of the crystal orientation of the metal material grains. Finally, the equivalent work function of the metal gate is calculated based on the metal work functions corresponding to the grains with different crystal orientations and their random distribution.

7. The method for predicting the metal work function fluctuation effect of a semiconductor field effect transistor according to claim 1, characterized in that: Step 4 is specifically: fitting the function to the metal work function fluctuation effect prediction model verified in step 2 Input the random distribution sample of the metal work function fluctuation of the device to be predicted, specifically in the fitting function of the above metal work function fluctuation effect prediction model The random distribution sample set of metal work function fluctuations generated by the distribution probability model of metal grains with different crystal orientations on the metal-oxide interface of the device to be predicted is input. The fitting function of the metal work function fluctuation effect prediction model obtained in step 2 The calculated fluctuation distribution of the electrical characteristic parameters of the device under the random distribution sample of the metal work function fluctuation.

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