Re: VRD - electron mobility of silicon

The answer to your question is sort of "easy to say" but much, much more
difficult in the details.  The mobility of electrons, or holes, is a 
function of how the carriers scatter off the lattice and is generally 
determined how many scattering mechanisms (off neutral impurities, off 
charged impurities - including dopants, off the surfaces or interfaces,
off phonons, off other mobile carriers, etc) and how "intense" (how heavily
doped is the crystal, e.g.) they are.  For the moment, let's confine 
ourselves to a "cold" (negligible phonon scattering) perfect crystal with no 
impurities present. In this case, the mobility is limited pretty much by 
scattering off the lattice of the crystal itself.

Free carriers can only exist in certain states (momentum and energy) in a 
crystal lattice. This is a fancy way of saying that they can only move 
around through the lattice in certain directions and speeds, because 
otherwise they will collide with an atom and 'recoil' into a different
momentum, energy state.  The collection of all these states in which free 
carriers can be is called the band structure of the semiconductor. These
bands can be computed from the crystal structure and the quantum mechanical 
properties thereof, but to do so is quite an ugly chore. Each crystal type
will have a different band structure, dependent on the quantum mechanical
properties of its arrangement and its constituent atoms (...and how's that 
for a dense sentence? :-). What this means is that the crystal's structure 
and electronic properties determine the speeds at which carriers can move
through it.

Now, by applying a low field, we do change the momentum and energy of the 
free carriers, thus eventually forcing them to collide with the lattice.
How often and how 'violently' (i.e. how much energy they lose when they do
collide) they collide is determined by the band structure. The carriers 
basically hop around from state to state within the band on their way 
through the crystal. The relative ease with which they do this determines
their velocity for any given applied field. We call the ratio of the 
velocity to the field (cm/sec divided by volt/cm is cm2/volt-sec, the units
of mobility) the mobility.  Each crystal thus has its own set of 
characteristics, and this is why GaAs happens to have an electron mobility
three times higher than silicon does, or why holes move through germanium
faster than through silicon, etc, etc, etc.

For low fields, the 'error' induced by the electric field is pretty small 
with respect to the inherent velocity of the carriers in the crystal, so 
that the system is almost undisturbed, and the relationship between the 
applied field and the induced net drift velocity is roughly linear (this is
similar to Ohm's law for metals) and the mobility is roughly constant of a
range of low fields. Go higher in field intensity, however, and the mobility
begins to decrease. Eventually, with a high enough field, you will reach the 
scatter limit velocity. Beyond that point, additional electric field 
intensity will not increase the average velocity of the carriers.

To go further on this subject, I'm afraid the only recourse is working 
through a text in solid state physics (e.g. Kittel). It's just about as much 
fun as marching through the Great Dismal Swamp without mosquito repellant, 
but you can make it. Others have survived the trek and the trail is at least 
well-marked if not an easy one. Good luck on your quest.