I'm not really a solid state guy--I've learned everything I know about HBTs from my trusty tome by Pulfrey, "Understanding modern transistors and diodes". (Great book, btw.) It says that a lot of the unusual properties of SiGe HBTs come from two features: a heterojunction between base and emitter, and a Ge concentration gradient across the base. The heterojunction produces a much higher barrier for holes than electrons, and so allows much higher doping density in the base without the whole thing going metallic.
The very high doping density produces an impurity band below the conduction band, so that to some degree the majority carriers are delocalized even below the ionization temperature. That may be why the beta doesn't tank below 100K the way it usually does. On the other hand, I may be making all that up. ;)
The concentration gradient more or less eliminates the effect of base narrowing, which gives these devices their amazingly high Early voltage and low capacitance. The datasheet of my fave, the BFP640, has plots where the Early slope goes the other way, i.e. collector current _drops_ slightly towards higher V_CE, but the slopes are all pretty nearly zero. A 40-GHz transistor with super low capacitance, high beta, and a practically infinite V_A lets you do magical things, e.g. a cascoded pHEMT front end with 0.3 nV 1-Hz noise, < 1 pF of capacitance, and an RC-coupled voltage gain of 50 from DC to some ridiculous frequency. (The pHEMT has a 1/f corner of ~10 MHz, unfortunately.)
I posted a circuit like that a year or so back, in the "electrometer front end" thread.
Cheers
Phil Hobbs