Boltzmann approximation

The table below gives the contribution of electrons in intrinsic semiconductors and insulators to some thermodynamic quantities. These results where calculated in the Boltzmann approximation where it is assumed that the chemical potential lies in the band gap more than 3kBT from the band edge. The electronic contribution to the thermodynamic quantities are usually much smaller than the contribution of the phonons and thus the electronic components are often simply ignored.




Density of states
me* and mh* are 'density of states' effective masses

Density of states
Nv and Nc are the effective densities of states

Density of electrons
in the conduction band

Density of holes
in the valence band

Law of mass action

Intrisic carrier density

Chemical potential
Set n = p, solve for μ

Internal energy density

Helmholtz free energy
f = u - Ts

Specific heat