Fermi-Dirac Distribution
#Physics
Video Explaining Fermi-Dirac Statistics
Topics
- Fermi Energy
$\displaystyle f(E)=\frac{1}{1+e^{(E-E_{f})/kT}}$
- Probability of find a particle at a certain energy $\displaystyle E$
- $\displaystyle E_{f}$ is the fermi level
- $\displaystyle T$ is the temperature of the gas. For $\displaystyle T=0$, the function approaches a step function, indicating you'll have 0 probability of finding particles above $\displaystyle E_{f}$
Desmos Demo
Statistical Mechanics
$\displaystyle f(\varepsilon)\equiv {\left\langle{N(\varepsilon)}\right\rangle}=\frac{1}{e^{\beta(\varepsilon-\mu)}+1}$
- Denotes the average occupancy
- Same as above equation, but with
$\displaystyle \mathbb{Z}=e^{\beta(\mu-\varepsilon)}+1=\lambda e^{-\beta\varepsilon}+1$
- $\displaystyle \mathbb{Z}$ is the grand partition function
- $\displaystyle \lambda$ is the absolute activity