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.
| 1-d | 2-d | 3-d |
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
 | 
| 
| 
|
Entropy
 | 
| 
| 
|