Introduction
(Indirect Recombination via a deep energy level)

An energy state, Et, in the band gap can act either as a recombination/generation center or as a carrier trapping center. This is determined primarily by the charge of this gap state and by the separation of Et from the band edge (Ec or Ev).  The charge state determines the center's ability to capture a carrier (i.e., the capture cross section).  The energy separation determines the likelyhood for a captured carrier to be thermally re-excited into the band (when the energy separation is small) or to remain with the center for a long time (thereby giving the time for the opposite charge carrier to be captured also).  The charge state of a recombination center is especially important and it must be attractive to the minority carriers because the minority carriers are so scarce (e.g., in p-Si with Na = 1E18 cm-3, we have 100 electrons and  one million trillions of holes for every cm3 of volume.  Assume ni = 1E10 cm-3).  The majority carriers are much more readily available.

For example, in n-type semiconductor, a center with charge state -1 is likely to be a recombination center because, once a minority carrier (hole) is captured by this center (the -1 charge is attractive to hole), it is easy to capture an electron (because there are so many of them and the state with charge 0 is not repulsive to electron). However, in n-type semiconductor, a deep level center with -2 charge is likely to be a hole trap because, once a minority carrier hole is trapped (-2 charge is attractive to hole), the charge is still -1 which is repulsive to the majority carrier electron and makes it hard to subsequently capture an electron. Therefore, if the separation of Et from Ev is small, then the captured hole could be thermally re-excited into the valence band before an electron is captured, which makes it a hole trap.

The capture efficiency of carriers by these gap states (associated with chemical impurities or structural defects) depends on the capture cross section, which is a measure of the probability of the capturing event. The cross section of attractive centers is 1E-12 to 1E-15 cm2; the cross section of neutral centers is 1E-15 to 1E-17 cm2; and the cross section of repulsive centers is ~1E-22 cm2 [ref.1].

In the applet, the four basic processes (en, cn, ep, and cp) of the Shockley-Read-Hall statistics are introduced, and the recombination/generation and the carrier trapping processes are shown visually. I showed the processes using only the electrons. It should, however, be understood that an electron falling from Et down to the Valence Band is equivalent to a hole rising from the Valence Band up to the trap level Et. (In a separate applet, I will show the processes using both electron and hole, indicating the charge state of the gap states also.)

In summary,

Recombination Center

  1. the center is attractive to the minority carrier.   ( large capture cross section for the minority carrier.)
  2. after the capture of a minority carrier, the charge state becomes not repulsive to the majority carrier.
  3. The energy position, Et, is separated far away from the band edge of the minority carrier. (thermal excitation probability, exp(-Ea/kT), is small, and thus gives enough time for the capture of a majority carrier.  Here, Ea is the difference between Et and the band edge of the minority carrier.)
  4. Example : Au impurity atom in Si semiconductor crystal.
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ref.1: J.W.Mayer and S.S.Lau, "ELECTRONIC MATERIALS SCIENCE: For Integrated Circuits in Si and GaAs", Macmillan Publishing, New York, 1990.


Copyright (c) 1997-1998, Chu R. Wie, SUNY-Buffalo