CN-121997717-A - Semiconductor parametric modeling method based on polynomial regression algorithm

CN121997717ACN 121997717 ACN121997717 ACN 121997717ACN-121997717-A

Abstract

The invention provides a semiconductor parametric modeling method based on a polynomial regression algorithm, belongs to the technical field of semiconductor modeling, and aims at the problems of large calculation amount of traditional TCAD fitting and high demand for machine learning data. Taking a FinFET device as an example, the scheme not only realizes high-precision fitting consistent with measured data in a wide temperature range of-40 ℃ to 120 ℃, but also has excellent extremely low temperature characteristic prediction capability. According to the method, through cooperation of agent model optimization and parameter sensitivity analysis, the efficiency and the accuracy of modeling of the semiconductor device are effectively improved while the calculation cost and the sample collection workload are remarkably reduced.

Inventors

XU JIAHUI
PAN CHONG
CHEN ZE
ZHANG YUNTAO
XIONG BOTAO
LI XIN
TANG DONG
DING YIREN

Assignees

铨力微电子(无锡)有限公司
大连理工大学

Dates

Publication Date: 20260508
Application Date: 20251230

Claims (9)

1. A method for semiconductor parametric modeling based on a polynomial regression algorithm, the method comprising: Extracting characteristic indexes under corresponding different temperature conditions based on the electrical characteristic data provided by the process design suite; Establishing a physical simulation model of the semiconductor device, wherein the physical simulation model comprises a plurality of model parameters, extracting exact values of part of the model parameters based on a process design kit, and determining initial experience values of the rest parameters; Establishing a semiconductor device agent model based on a polynomial regression algorithm based on the change relation, wherein the agent model consists of a plurality of quadratic polynomials, and the quadratic polynomials describe the change relation of the characteristic index and the key parameter in numerical values; And searching an optimal solution of the agent model by adopting a polynomial regression algorithm, wherein the optimal solution is a group of optimal model experience parameters which can enable errors of simulation results of the physical simulation model and fitting targets provided by a process design kit to be within an acceptable range under different temperature conditions.
2. The method of claim 1, wherein the electrical characteristic data comprises current-voltage curves for different temperature conditions, the current-voltage curves being output characteristics for low voltage and operating voltage conditions.
3. The method of claim 1, wherein the different temperature conditions are-40 ℃, and 120 ℃.
4. The method of claim 1, wherein the characteristic measures include threshold voltage, transconductance, and reciprocal subthreshold slope.
5. The method of claim 1, wherein establishing a polynomial regression algorithm based semiconductor device proxy model based on a changing relationship between key parameters and feature indicators comprises: constructing an initial training sample set, and obtaining simulation data of the characteristic index after the key parameter is changed by using the physical simulation model to serve as the initial training sample set; and determining the change relation of the characteristic index and the key parameter in numerical value based on the initial training sample set, combining a theoretical formula of the physics of the semiconductor device, utilizing a quadratic polynomial regression equation to represent the change relation, and determining the undetermined coefficient of the quadratic polynomial regression equation to obtain a semiconductor device proxy model.
6. The method of claim 5, wherein finding an optimal solution for the proxy model using a polynomial regression algorithm comprises: reversely solving the key parameters based on characteristic index data provided by a process design kit under different temperature conditions, substituting target values of the characteristic indexes into the proxy model, and solving to obtain a plurality of groups of possible key parameter candidate solution sets; screening the parameter candidate solution sets by taking physical constraint as boundary condition, and reserving the candidate solution sets conforming to the physical rule; Verifying and evaluating errors by adopting a physical simulation model, taking the screened candidate solution as input of the physical simulation model to simulate, obtaining a model simulation result of the characteristic index corresponding to the solution, comparing the model simulation result of the characteristic index with errors of fitting targets in a process design suite, and if the errors are within an acceptable range, enabling the candidate solution to be effective; And acquiring intersection sets of effective candidate solution sets corresponding to the characteristic indexes respectively, acquiring device simulation data at different temperatures based on a physical simulation model, and comparing the device simulation data with a fitting target under the same conditions extracted by a process kit, wherein index errors are all within an acceptable range, and acquiring an optimal solution.
7. The method of claim 6, wherein the model simulation results of the feature indicators at three different temperature conditions and the error of the fitting targets in the process design suite are not within an acceptable range, adding the set of model simulation data into an initial training sample set, iteratively updating the existing quadratic polynomial regression model based on the expanded initial training sample set, re-searching for the optimal empirical values of the key parameters, and repeating the process until a valid candidate solution is obtained.
8. The method of claim 1, wherein the semiconductor sample device is an N-type FinFET device and a P-type FinFET device, and the model parameters include fin width, fin height, fin pitch, gate length, gate width, gate oxide thickness, channel doping concentration, substrate doping concentration, source/drain doping concentration, work function, series resistance, trap concentration, operating voltage, and drain voltage.
9. The method as recited in claim 1, further comprising: performing simulation test on the electrical characteristic data of the device under the low-temperature condition based on the calibrated physical simulation model; based on a low-temperature integrated circuit reliability test system SCG closed-loop probe station and a semiconductor analyzer, performing electrical characteristic data test on the semiconductor sample device under the same temperature condition; the reliability of the method is determined by comparing simulated test data results with actual test data results at a plurality of different temperature conditions.

Description

Semiconductor parametric modeling method based on polynomial regression algorithm Technical Field The invention belongs to the technical field of semiconductor modeling, and particularly relates to a semiconductor parametric modeling method adopting a polynomial regression algorithm. Background Integrated circuit technology is used as the basis of modern electronic industry, and in the design process, various factors such as device reliability, performance index and manufacturing cost need to be comprehensively considered. In the development stage of semiconductor technology, TCAD (technical computer aided design) simulation tools have become an important means for evaluating device characteristics due to the high cost and long period of actual tape-out. The simulation method based on the physical model can accurately simulate the electrical characteristics of various semiconductor devices such as MOSFET, BJT and the like under different working conditions, and has remarkable advantages particularly when researching the application scene of semiconductor modeling under the environment of radiation effect and extremely low temperature. The application of the current TCAD tool has obvious technical bottlenecks, and the problem of efficiency of a model calibration link is mainly embodied. The traditional calibration method requires engineers to manually adjust device structure parameters and doping distribution, and current-voltage output characteristics and transfer characteristic curves of TCAD output are matched with process design library (PDK) data through repeated iterative simulation. Not only does this manual calibration process require a significant amount of experience from the operator, it typically takes weeks for each complete calibration. More importantly, when the process conditions or calibration targets change slightly, the whole calibration process must be re-executed, and the repeated work severely limits the development efficiency. The lack of effective automated calibration means in the prior art has led to limited application of TCAD tools in rapid process development. Disclosure of Invention In view of this, the present invention provides a semiconductor parametric modeling method using a polynomial regression algorithm, so as to solve the problem that in the prior art, when a TCAD tool is used to perform simulation study on an electronic device, it takes a lot of time to calibrate the TCAD model, and verify the reliability of the method by using TCAD modeling of a FinFET device. For this purpose, the invention adopts the following technical scheme: the invention provides a semiconductor parametric modeling method based on a polynomial regression algorithm, which comprises the following steps: Extracting characteristic indexes under corresponding different temperature conditions based on the electrical characteristic data provided by the process design suite; Establishing a physical simulation model of the semiconductor device, wherein the physical simulation model comprises a plurality of model parameters, extracting exact values of part of the model parameters based on a process design kit, and determining initial experience values of the rest parameters; Determining key parameters with obvious influence on characteristic indexes in experience value parameters through TCAD simulation analysis and semiconductor physical theory, and establishing a semiconductor device proxy model based on a polynomial regression algorithm on the basis of the change relation between the key parameters and the characteristic indexes, wherein the proxy model is composed of a plurality of quadratic polynomials, the quadratic polynomials describe the change relation between the characteristic indexes and the key parameters in numerical values, and the change relation is obtained by analysis and summarization based on simulation data and semiconductor physical theory; And searching an optimal solution of the agent model by adopting a polynomial regression algorithm, wherein the optimal solution is a group of optimal model experience parameters which can enable errors of simulation results of the physical simulation model and fitting targets provided by a process design kit to be within an acceptable range under different temperature conditions. Further, the electrical characteristic data includes current-voltage curves under different temperature conditions, which are output characteristic curves (leakage current-leakage voltage) under low voltage and operating voltage conditions. Further, the different temperature conditions are-40 ℃, 40 ℃ and 120 ℃. Further, the characteristic index comprises threshold voltage, transconductance and inverse of subthreshold slope. Further, the method for establishing the semiconductor device proxy model based on the polynomial regression algorithm based on the change relation between the key parameters and the characteristic indexes comprises the following steps: constructing