Modeling of nonuniform SiGe heterostructure

Devices containing SiGe alloys are demonstrating improved performance over their silicon counterparts. In fact, the SiGe heterojunction bipolar transistor based on SiGe epitaxial base is up to now the fastest device available on a CMOS integrated circuit, with cutoff frequencies reaching 100 GHz. The superior performance of SiGe HBTs over conventional Si BJTs is due to their key advantage: an increase of collector current density, which leads to increased current gain, reduced base transit time, and higher Early voltage. To understand explicitly how SiGe alloyed devices give rise to these improvements, detailed device modeling can be used. The difficulty, however, is that standard device modeling techniques cannot be directly applied due to the bandgap variation in the alloy. To overcome this difficulty, a new approach for modeling of SiGe nonuniform heterostructures is presented. The method differs from traditional Si device modeling since in nonuniform SiGe heterostructures the bandgap is a function of position. We account for this position dependence of band structure by revising the traditional semiconductor drift-diffusion equations. A newly defined parameter ψ is used in the drift-diffusion model to represent the effects of bandgap narrowing and change of effective masses of SiGe heterostructures resulted from alloying Ge with Si. The new model is discretized using a revised Scharfetter-Gummel type approach and solved numerically with Newton´s method and matrix algebra. Simulation results comparing Si and SiGe PN-junctions as an example show why SiGe devices have significantly improved performance over those of Si. Detailed modeling explains the improved performance to be largely due to the increased minority electron concentration, an accelerating electric field in the SiGe alloyed region, and increased crystal mobility for both electrons and holes