Dimension Expansion Of Multivariate Rational Regression And Its Application In Semiconductor Device Modeling

With the limit of Morel Law and the era of Internet of Thing,people are trying new semiconductor device and their application.Device modeling is a must for new semiconductor device to be applied into circuit design.Traditional physic-based semiconductor device model,such as BSIM mode of Berkeley,have advantages of high precision,high transfe rable,high numerical stability.But it also has the disadvantages such as long operation term and high human cost.It's inefficient and risk to invest huge money to build physical model.In this circumstance of semiconductor modeling,the data-driven semiconductor black box modeling becomes a viable solution for physical modeling.The concern of semiconductor modeling mainly focus on curve fitting task,such as the characteristic curve and performance curve of semiconductor devices.The curve of semiconductor modeling has highly non-linear character and the current regression models such as linear regression model and LASSO model are not fit for these tasks.Rational equation is a naturally highly nonlinear curve fitting models.In this paper,we propose multi-variate rational regression model for semiconductor modeling.The model has highly nonlinear ability,which use SK iteration and least linear square method to process measured data and finish semiconductor modeling task.We provide three models,single-pole MRR,double-pole MRR and edited double-pole MRR for the use of semiconductor modeling.In order to prove the performance of model,we use MRR to fit MOSFET,CNT,Fin-FET,GFET and performance model of SRAM.The experiment results show MRR outperforms traditional linear regression methods in precision and convergence stability.The paper discuss es the processing methods of sparse data and choose of basis function.