Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 32 : Covalent Bond
Effective Mass

For a free electron moving under the action of an external force $ F_{ext}$ the equation of motion is given by

 
$\displaystyle m\frac{dv}{dt} = F_{ext}$
  Identifying $ \hbar k$ as the momentum of the particle, we have
 
$\displaystyle E = \frac{\hbar^2k^2}{2m}$
  We may, therefore, express the mass of the particle in terms of the second derivative of the energy with respect to the wavenumber $ k$
 
$\displaystyle m^{-1} = \frac{1}{\hbar^2}\frac{d^2E}{dk^2}$
  The velocity of the particle can be expressed as
 
$\displaystyle v = \frac{\hbar k}{m} = \frac{1}{\hbar}\frac{dE}{dk}$
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