Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 31 : Electron in a Periodic Potential
Another way of stating Laue condition is
 
$\displaystyle \vec k-\vec k^\prime = \vec G$
  Squaring both sides and using $ \mid k\mid = \mid k^\prime\mid$, we get
 
$\displaystyle \vec k\cdot\vec G = -\frac{1}{2}G^2$
  Since $ -\vec G$ is also a reciprocal lattice vector, one can rewrite the above equation as
 
$\displaystyle \vec k\cdot\vec G = \frac{1}{2}G^2$
  Geometrically, this implies that Laue condition is satisfied if $ \vec k$ lies in a plane that bisects $ \vec G$ perpendicularly.
 
\includegraphics{bragg1.eps}
 
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