Effective density of states - Example

  1. Calculate the effective density of states for electrons and holes in germanium, silicon and gallium arsenide. Use the effective masses provided in the table below.
  2. Calculate the intrinsic carrier density in germanium, silicon and gallium arsenide at room temperature (300 K). Repeat at 100 ° C. Assume that the energy bandgap is independent of temperature and given by the values provided below.

Answer:

Name Symbol Germanium Silicon Gallium Arsenide
Energy bandgap at 300 K Eg (eV) 0.66 1.12 1.424
Effective mass for density of states calculations
Electrons me*,dos/m0 0.56 1.08 0.067
Holes mh*,dos/m0 0.29 0.81 0.47
Effective density of states in the conduction band at 300 K NC (cm-3) 1.05 x 1019 2.82 x 1019 4.37 x 1017
Effective density of states in the valence band at 300 K NV (cm-3) 3.92 x 1018 1.83 x 1019 8.68 x 1018
Intrinsic carrier density at 300 K ni (cm-3) 1.83 x 1013 8.81 x 109 2.03 x 106
Effective density of states in the conduction band at 100 ° C (373.15 K) NC (cm-3) 1.46 x 1019 3.91 x 1019 6.04 x 1017
Effective density of states in the valence band at 100 ° C NV (cm-3) 5.44 x 1018 2.54 x 1019 1.12 x 1019
Intrinsic carrier density at 100 ° C ni (cm-3) 3.1 x 1014 8.55 x 1011 6.24 x 108
Examples
© Bart J. Van Zeghbroeck, 1997