15th April 2004 - 08:19 PM
Pretty basic question here. Let's say I have a slab of intrinsic Si
just above 0 Kelvin so thermal effects are negligible, the valence
band is full and the conduction band is empty. To get an electron out
of the valence band would it just be a matter of me applying about a
1.2 V drop (minimum band gap voltage) across just one Si atom to rip
out a valence electron bond and get it into the conduction band? So
we're talking a field of about 1.2 V/2A = 6e9 V/m (assuming we take
the diameter of the Si atom and its electron cloud to be 2 A). I
suppose this would be a back-of-the-envelope description of intrinsic
breakdown. Can the energy-level diagram be even remotely considered
for such calculations?
15th April 2004 - 08:20 PM
What you are talking about is Zener tunneling (also called Esaki
tunneling if it happens in a pn junction). It occurs at a field
magnitude of more like (bandgap energy) / 10 A. And yes, the
energy-band profile is still meaningful when this starts, you just
have to interpret it as a 1-bit-greyscale local-density-of states plot.
The 10 A length comes from the decay constant of the evanescent wavefunctions
that exist within the energy band gap. (That is the simple picture, which
works for direct-gap semiconductors such as GaAs. Si, being indirect gap,
is more complicated as the direct and phonon-assisted tunneling rates are
similar.) Actually calculating these things has to be done with a model that
reproduces the full bandstructure. See C. Rivas, et al., "Full band modeling of
the excess current in a delta-doped silicon tunnel diode," J. Appl. Phys.
Vol. 94, pp. 5005-5013 (2003).