Question

Caluate the Fermi function for energy KBT above the Fermi energy. Solution [F(E) = 0.2689]​

Answer 1

Answer:

1. A Presentation on Problems on Fermi -Dirac distribution function By Ms.Chetana Magadum Smt. Kasturbai Walchand College,Sangli

2.  Problems on Fermi –Dirac distribution function:- 1. The Fermi level for potassium is 2.1eV. Calculate the velocity of the electron at the Fermi level. Solution:- We have the formula, = 1 2 2 Therefore, = 2 1 2 = 2 × 2.1 × 1.602 × 10−19 / 9.11 × 10−31 1 2 = 8.6 × 10 5 /.

3. 2. In a solid, consider the energy level lying 0.01 eV below Fermi level. What was is the probability of this level not being occupied by an electron? Given : Energy Difference − = 0.01 Thermal energy at room temperature, kT=0.026eV Solution:- We have the formula, = 1 1 + −( −)/ = 1 1 + −0.01/0.026 = 1 1 + −0.3846 = 0.595 Therefore, = 1 − = 1 − 0.595 = 0.405

Answer 2

Answer:

Fermi distribution function$F(E)=0.2689$

Explanation:

A probability distribution function is the Fermi function. Only be used if the environment is in a state of equilibrium. The Fermi function calculates the likelihood of an energy state (E) being filled with electrons. The Fermi level (EF) aids in the calculation of carrier dispersion.

We know Fermi Function $\quad F(E)=\frac{1}{1+e^{\left(E-E_{F}\right) K_{B} T}}$

For an energy $\mathrm{K}_{\mathrm{B}} \mathrm{T}$

above Fermi energy

$\begin{aligned}\mathrm{E}-\mathrm{E}_{\mathrm{F}} &=\mathrm{K}_{\mathrm{B}} \mathrm{T} \\\mathrm{F}(\mathrm{E}) &=\frac{1}{1+\mathrm{e}^{1}}=\frac{1}{1+2.7183}\end{aligned}$

Fermi distribution function $\quad \mathrm{F}(\mathrm{E})=0.2689$