Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 32 : Covalent Bond
  Example 4
The $ E-k$ relationship near the conduction band of GaAS is given by
 
$\displaystyle E = E_c + Ak^2 - Bk^4$
  where $ A, B >0$. How does it affect the effective mass of electrons near the conduction band minimum ?
  Solution
  We have
 
$\displaystyle \frac{dE}{dk}$ $\displaystyle =$ $\displaystyle 2Ak-4Bk^3$
$\displaystyle \frac{d^2E}{dk^2}$ $\displaystyle =$ $\displaystyle 2A-12Bk^2$
  Thus
 
$\displaystyle \frac{1}{m^\ast} = \frac{1}{\hbar^2}\frac{d^2E}{dk^2} = 2A - 12 Bk^2$
  For values of $ k$ removed from $ k=0$, $ m^\ast$ increases with $ k$.
 

    Back