A novel analytical model of the vertical breakdown voltage on impurity concentration in top silicon layer for SOI high voltage devices

Abstract

A novel analytical model of the vertical breakdown voltage (VB , V ) on impurity concentration (Nd ) in top silicon layer for silicon on insulator high voltage devices is first presented in this article. Based on an effective ionisation rate considering the multiplication of threshold energy εT in the electron, a new formula of silicon critical electric field ES , C on Nd is derived by solving a 2D Poisson equation, which increases with the increase in Nd especially at higher impurity concentration, and reaches up to 68.8 V/µm with Nd = 1 × 1017 cm−3 and 157.2 V/µm with Nd = 1 × 1018 cm−3 from the conventional about 30 V/µm, respectively. A new physical concept of critical energy εB is introduced to explain the mechanism of variable high ES , C with heavy impurity concentration. From the ES , C , the expression of VB , V is obtained, which is improved with the increasing Nd due to the enhanced ES , C. VB , V with a dielectric buried layer thickness (tI ) of 2 µm increases from 428 V of 1 × 1017 cm−3 to 951 V of 1 × 1018 cm−3. The dependence of Nd and top silicon layer thickness (tS ) for an optimised device is discussed. 2D simulations and some experimental results are in good agreement with the analytical results.