基于LM算法改进BP神经网络的薄膜电阻高精度测量  

High-precision Measurement of Thin Film Resistance Based on LM Algorithm to Improve BP Neural Network

作　　者：张钰 王琰 彭正凤 马俊杰 王静 ZHANG Yu;WANG Yan;PENG Zhengfeng;MA Junjie;WANG Jing(School of Communication Engineering,Tongda College of Nanjing University of Posts and Telecommunications,Yangzhou 225127,China;School of Computer Engineering,Tongda College of Nanjing University of Posts and Telecommunications,Yangzhou 225127,China;Department of Basic Education,Tongda College of Nanjing University of Posts and Telecommunications,Yangzhou 225127,China)

机构地区：[1]南京邮电大学通达学院通信工程学院,江苏扬州225127 [2]南京邮电大学通达学院计算机工程学院,江苏扬州225127 [3]南京邮电大学通达学院基础教学部,江苏扬州225127

出　　处：《大学物理实验》2025年第2期64-69,共6页Physical Experiment of College

基　　金：江苏省高等学校自然科学基金(20KJB140006);南京邮电大学通达学院大学生科技创新训练计划(202413989022Y)。

摘　　要：在半导体工艺中,电阻测量极其关键。传统四探针法在测量薄膜的电阻时,需对范德堡函数进行非线性拟合,不仅耗时较长,且精度较差。针对该现象提出了一种基于Levenberg-Marquardt(LM)算法的Back propagation neural network(BPNN)神经网络模型。LM算法结合了梯度下降法和牛顿法的优点,在迭代过程中快速接近全局最小值,且对于局部最小值的陷落情况优于纯梯度下降法,结合BP神经网络的反向传播误差来调整权重,从而实现复杂非线性函数的拟合。对含反双曲余弦的超越函数(范德堡函数)的局部参数进行非线性拟合,得到最大偏差为2.08×10^(-5),相对标准偏差为2.16×10^(-8)的神经网络拟合模型,对比规范化多项式拟合方法精度提升99.5%。此改进方法,可极大提高测量结果的稳定性与精确性,将模型运用于实验测量过程,有效改善了电阻率测试精度。Resistance measurement is extremely critical in semiconductor technology.When measuring the resistance of thin films by the traditional four-probe method,nonlinear fitting of the Van der Pauw function is required,which is not only time-consuming but also has poor accuracy.In view of this phenomenon,a Back propagation neural network(BPNN)neural network model based on the Levenberg-Marquardt(LM)algorithm is proposed.The LM algorithm combines the advantages of the gradient descent method and the Newton method,quickly approaches the global minimum during the iteration process,and is better than the pure gradient descent method in the case of local minimum fall.The weight is adjusted by combining the back propagation error of the BP neural network to achieve the fitting of complex nonlinear functions.The local parameters of the transcendental function(Van der Pauw function)containing the inverse hyperbolic cosine are nonlinearly fitted,and a neural network fitting model with a maximum deviation of 2.08×10^(-5)and a relative standard deviation of 2.16×10^(-8)is obtained.Compared with the normalized polynomial fitting method,the accuracy is improved by 99.5%.This improved method can greatly improve the stability and accuracy of the measurement results.The model is applied to the experimental measurement process,which effectively improves the resistivity test accuracy.

关 键 词：BP神经网络 范德堡法 非线性函数拟合 电阻率测量 LM算法 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]