Modeling Si/Ge Interdiffusion in Si/Si_1-xGe_x/Si Single Quantum Well Structures

Abstract

Recently Silicon Germanium alloy (Si_1-xGe_x) is showing lots of potentials in device fabrication. Most of the structures containing Si_1-xGe_x that are fabricated at present involve Si/Si_1-xGe_x heterostructure. The fabrication process involves several high temperature anneal steps in either inert, oxidizing or nitriding ambient which results the interdiffusion of Si and Ge through the hetero-interfaces. The interdiffusion causes broadening of Si/Si1_xGex interface and changes the physical position of the heterointerface which can cause degradation of device performance. Several studies have so far been done to quantify the amount of Ge interdiffusion in heterostructures. However no study has yet been performed to model this phenomenon. Modeling the interdiffusion mechanism is important for two reasons: (1) it will facilitate to calibrate the device characteristics taking the effect of interdiffusion mechanism into calculations prior to device fabrication; and (2) to get a better insight of the actual mechanism involved in the interdiffusion process. In this study, attempt has been taken to model interdiffusion of Si and Ge in structures having Si/Si_1-xGe_x hetero-interfaces. Mathematical models are proposed to model the behavior and the models are applied to previously published results where samples were annealing in inert, oxidizing and nitriding ambient at different anneal temperatures for different anneal times. First only the contributions of vacancies in the interdiffusion mechanism are considered. This can successfully model the interdiffusion mechanism for samples annealed in inert and oxidizing ambients at low temperatures (below 1050°C). Next the contributions of interstitials along with vacancy in the interdiffusion mechanism are considered. These are able to successfully model the interdiffusion phenomenon for the samples annealed in oxidizing and nitriding ambients at high temperatures (above 1050°C). The success of the modeling is justified by getting good match between the simulated and the experimental interdiffusion profiles along with good match between the fitting parameters used in the simulations compared with previous reported values. Besides modeling the interdiffusion mechanism, for the first time, a mathematical model is proposed for vacancy injection while nitridation of silicon is done.