SaM - Fermi Dirac Distribution

Memory Card

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We started by saying that at $0$ Kelvin all the electrons are here in the Valence Band, and no electrons are in the Conduction Band. What happens when we go to a temperature which is different from $0$ Kelvin? To understand this, we have to look at the probability that an electron occupies a given energy state (or level).

==The Fermi-Dirac distribution $f_e(E)$ gives the probability that given a certain energy state with an energy level value $E$, this value $E$ is occupied by the electron==, and it is defined as follows:$f_e(E)=\frac{1}{1+e^{\frac{E-E_f}{kT}}}$Where:

• $E$ is the energy that the electron takes.
• $k$ is the Boltzmann constant $=1.380649\cdot 10^{-23}\frac{\text{J}}{\text{K}}$.
• $T$ is the temperature in Kelvin.
• Whereas $E_F$ is a special energy level, which is called “Fermi Energy”, this quantity also changes with temperature.