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Electrogeneration of EHPs

Discussion in 'General Electronics' started by [email protected], Apr 11, 2004.

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  1. Guest


    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?

  2. 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).

    - Bill Frensley
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