Acceleration of solving drift-diffusion equations enabled by estimation of initial value at nonequilibrium

Chunlin Du; Yu Zhang; Haolan Qu; Haowen Guo; Xinbo Zou; Chunlin Du; Yu Zhang; Haolan Qu; Haowen Guo; Xinbo Zou

doi:10.3934/nhm.2024020

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 456-474. doi: 10.3934/nhm.2024020

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Acceleration of solving drift-diffusion equations enabled by estimation of initial value at nonequilibrium

1.
School of Information Science and Technology, Shanghaitech University, Shanghai 201210, China
2.
School of Microelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of sciences, Shanghai 200050, China

Received: 27 January 2024 Revised: 28 March 2024 Accepted: 02 April 2024 Published: 15 April 2024

In this study, a novel method enabled by estimation of initial value guess at nonequilibrium was proposed to accelerate drift-diffusion equations in semiconductor device simulation. The initial value guess was obtained by solving analytical model about electrical potential with the decoupling algorithm. By obtaining the initial value directly at the target bias voltage, the proposed method eliminated time-consuming bias ramping process in the classical method starting from the equilibrium state, thereby accelerating the whole process. The method has been applied to a junction barrier Schottky (JBS) diode for validation. Numerical results showed that the proposed method achieves convergence within 10 iterations at several reverse bias voltages, achieving significant reduction of iteration number compared to the classical method using the bias ramping process. It demonstrated that the proposed method holds high feasibility to facilitate the semiconductor device property prediction in relatively regular device structure in the case of low current. With further improvements, this method can also be applied to more complex devices.
- drift-diffusion equations,
- finite element method,
- nonlinear iteration,
- nonequilibrium initial guess,
- semiconductor device simulation
Citation: Chunlin Du, Yu Zhang, Haolan Qu, Haowen Guo, Xinbo Zou. Acceleration of solving drift-diffusion equations enabled by estimation of initial value at nonequilibrium[J]. Networks and Heterogeneous Media, 2024, 19(1): 456-474. doi: 10.3934/nhm.2024020

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Abstract

In this study, a novel method enabled by estimation of initial value guess at nonequilibrium was proposed to accelerate drift-diffusion equations in semiconductor device simulation. The initial value guess was obtained by solving analytical model about electrical potential with the decoupling algorithm. By obtaining the initial value directly at the target bias voltage, the proposed method eliminated time-consuming bias ramping process in the classical method starting from the equilibrium state, thereby accelerating the whole process. The method has been applied to a junction barrier Schottky (JBS) diode for validation. Numerical results showed that the proposed method achieves convergence within 10 iterations at several reverse bias voltages, achieving significant reduction of iteration number compared to the classical method using the bias ramping process. It demonstrated that the proposed method holds high feasibility to facilitate the semiconductor device property prediction in relatively regular device structure in the case of low current. With further improvements, this method can also be applied to more complex devices.

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