Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 32 : Covalent Bond
  When an electron moves in a lattice (i.e. in a periodic potential), in addition to the external forces, it is subjected to forces within the lattice. These foreces are generally quite large. We may write the equation of motion for the electron in the lattices as
$\displaystyle m\frac{dv}{dt} = F_{ext} + F_{lattice}\eqno (A)$
  One can define the effective mass of the electron in a lattice to be mass of a particle, which, when subjected to an external force $ F_{ext}$ would give an acceleration $ dv/dt$ defined by eqn. (A), i.e.,
 
$\displaystyle m^\ast\frac{dv}{dt} = F_{ext} $
  Using the expression for $ v$ above, we can write
 
$\displaystyle \frac{dv}{dt}$ $\displaystyle =$ $\displaystyle \frac{1}{\hbar}\frac{d}{dt}\frac{dE}{dk} = \frac{1}{\hbar}\frac{d^2E}{dk^2}\frac{dk}{dt}$
$\displaystyle =$ $\displaystyle \frac{1}{\hbar^2}\frac{d^2E}{dk^2}\frac{d}{dt}(\hbar k)$
$\displaystyle =$ $\displaystyle \frac{1}{\hbar^2}\frac{d^2E}{dk^2}\cdot F_{ext}$
   
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