An Empirical Composition Dependent Model of Dopant Diffusion Coefficients in Si, Si_1-x Ge_x and Ge Material Systems

I. INTRODUCTION

Previously published fast empirical models for diffusion coefficients in silicon-germanium (Si_1-x Ge_x) [1][2] were not applicable to high germanium content x≥0.5 and hence did not properly extend towards germanium. For some dopants, diffusion coefficients become very small and hence this model cannot be applied to devices containing silicon-germanium with high germanium content or devices containing silicon, silicon-germanium and germanium

In this work we have developed and calibrated a fast empirical model for diffusion coefficients (D) for various dopants in material silicon-germanium (Si_1-x Ge_x) which extends smoothly from silicon to germanium and which is therefore valid for the whole range 0≤x≤1. This model has been implemented in the open material database of Silvaco’s process simulation framework Victory Process [6].

For the calibration task presented in this work, we have used various and more recently published diffusivity data for silicon-germanium as well as germanium. On the other hand, diffusion coefficients for silicon are well established in literature, and hence we have performed the calibration in such a way that it smoothly extends the available data for silicon, which were already available within the open material database of Victory Process. However, it has to be noted that there is a lack of published data for germanium for some dopants and hence the accuracy of the calibration presented in this work can be a little low for very high germanium content for some dopants.