## 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.

The effective density of states for electrons in the conduction band is calculated from:

and the effective density of states for holes in the valence band is obtained from:

The intrinsi carrier density is then obtained from both effective densities if states using:

The resuls are shown in the table below. The same calculation is repeated at 373.15 K = 100 C. Note that the effective densities are dependent on temperature so that they need to be calculated first before the intrinsic density can be obtained.
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