Analytical modeling of polycrystalline silicon emitter bipolar transistors under high-level injection

Abstract

We derived an analytical model, focused on injected charge storage, for electron current density J n , hole current density J ps , current gain β, and forward transit time τ f for heavily doped base and emitter with non-uniform band structures. This model can apply in high-level injection regions before the onset of the Kirk effect. By comparing with those results obtained from Sukuki's low-level injection model, it is observed that a new high-level injection term, proportional to the square of the hole current density, appears in the injected hole concentration in the polycrystalline silicon emitter and this term vanishes in the limit of low-level injection. As bias increases, J n and J p s of high-level injection model are less than those of the low-level injection model. In addition, for low-level injection model, β, τ f, the base transit time τ b, the crystalline silicon emitter transit time τ se, and the polycrystalline silicon emitter transit time τ pe keep constant for all injection region. However, for high-level injection model, β and τ b decreases as bias increases, while τ se and τ pe increase with increasing bias. τ f reaches a minimum and then increases. We conclude that the high-level injection model offers significant information for device operations at various electron current levels.