SaM - Dependence of the Fermi Energy on Temperature

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This is how the Fermi Energy changes with temperature, given the ratio $\frac{n}{n_i}$:$E_F=E_i+kT\ln \left(\frac{n}{n_i}\right)$Where:

• $E_i$ : intrisnic fermi energy.
• $n$ is the density of free electrons in the doped semiconductor.
• $n_i$ is the density of free electrons in the intrinsic semiconductor.
• Now we know that the Fermi-Dirac distribution has an additional dependency on temperature.