Compact Modeling of the Temperature Dependence of Parasitic Resistances in SiGe HBTs Down to 30 K

In this paper, we investigate the physics and modeling of temperature dependence of various parasitic resistances in SiGe heterojunction bipolar transistors down to 30 K. Carrier freezeout is shown to be the dominant contributor to increased resistances at cryogenic temperatures for lightly-doped and moderately-doped regions, whereas the temperature dependence of the mobility is the dominant contributor to the temperature dependence of heavily-doped regions. Two incomplete ionization models, the classic model with a doping dependent activation energy and the recent model of Altermatt , are shown to underestimate and overestimate incomplete ionization rate below 100 K for intrinsic base doping, respectively. Analysis of experimental data shows that the bound state fraction factor is temperature dependent and including this temperature dependence enables compact modeling of resistances from 30 to 300 K for moderately-doped regions. For heavily-doped regions, a dual power law mobility approximation with complete ionization is shown to work well down to 30 K. An alternative approach is also presented for heavily-doped resistors which allows one to use the same model equation for all regions.