Physical Model of Incomplete Ionization for Silicon Device Simulation

An empirical model of incomplete ionization (ii) in phosphorus-, arsenic-, and boron-doped crystalline silicon is derived from photoluminescence, conductance, and mobility measurements. It is found that up to 25% of phosphorus and boron atoms and up to 35% of arsenic atoms are non-ionized at room temperature near the Mott transition, whereas there is no significant amount of ii at dopant densities far above the Mott transition. Simplified equations of ii suitable for implementation in device simulators are exploited to study the effect of ii on the performance of bipolar and MOS devices. It is demonstrated that ii can increase the current gain of bipolar transistors by up to 25%