Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 30 : Quantum Mechanical Concepts
 
$\displaystyle E_F = \frac{\hbar^2 k_F^2}{2m}$
The volume of Fermi sphere being $ 4\pi k_F^3/3$, the number of electrons $ N$ that lie within such a sphere is
 
$\displaystyle N = \frac{4\pi}{3}k_F^3\times\frac{V}{4\pi^3}\equiv \frac{V}{3\pi^2} \left(\frac{2mE_F}{\hbar^2}\right)^{3/2}\eqno(C) $
  which gives the density $ n$ as equal to
 
$\displaystyle n=\frac{N}{V}= \frac{k_F^3}{3\pi^2}$
  Using eqn. (C), we can obtain an expression for the density of states $ n(E)$. Since, by definition, $ n(E)dE$ is the number of states lying within energy interval $ E$ and $ E+dE$, we may simply subtract the number of states below energy $ E$ from the number below $ E+dE$. We have
   
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