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11 "fermi" - carrier concentrations in doped homogenous semiconductors

"fermi" computes the electron and hole concentrations for a homogeneous semiconductor under a variety of conditions. The user specifies the band gap (including temperature dependence), donor and acceptor binding energies, donor and acceptor concentrations, and the hole and electron effective masses. The program returns a plot of the temperature dependence of the carrier concentrations which illustrates the intrinsic, extrinsic and freeze-out regimes.

"fermi" was programmed by Russ Thompson and Joerg Draeger.

In the Arrhenius plot below, "fermi" shows us the temperature dependence of the carrier concentrations (both majority and minority) in two different n-type semiconductors, red and blue.

Which has the larger energy gap?
Which is doped more heavily?
Which has the higher product of hole and electron effective masses?
Which has the higher donor binding energy?

On the left below are two plots for a differnet sample. The upper is an Arrhenius plot, as above, and below it a plot of the temperature variation of the chemical potential. "fermi" can display the results in several formats. On the right are the same results, but now plotted versus T instead of 1/T, and the carrier concentrations are plotted linearly rather than as a log. Why is it that the chemical potential mu is varying linearly with temperature over the temperature range in which the electron concentration is independent of temperature?
. .

Table of contents for Chapter 11 of Simulations for Solid State Physics
1. Introduction
2. Pure (intrinsic) material
3. Doped (extrinsic) material
  1. Charge neutrality with impurities
  2. Extrinsic regime
  3. Limits of the extrinsic regime
  4. Compensation
4. Summary
5. Appendix: "fermi" -- the program
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