Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 31 : Electron in a Periodic Potential
 
\includegraphics{fig5.09a.eps}
  The potential is periodic with a period $ a+b$. In this case the electrons diffract from the periodic lattice resulting in some values of $ k$ for which no solution exists. The reason can be traced to formation of standing waves for such values of $ k$. For a crystal with periodicity $ a+b$, as shown above, standing waves would form if the electron wavelength $ \lambda$ is an integral multiple of $ 2(a+b)$. Thus the condition for formation of standing waves is
 
$\displaystyle 2(a+b) = n\lambda = n\frac{2\pi}{k}$
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