deletions | additions       diff --git a/subsection_Reduction_to_a_scattering__.tex b/subsection_Reduction_to_a_scattering__.tex  index 66b577a..4d48520 100644  --- a/subsection_Reduction_to_a_scattering__.tex  +++ b/subsection_Reduction_to_a_scattering__.tex 
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$$U(x)-E=\frac{(E_G/2)^2-(q\xi x)^2}{E_G}$$  So, in Sze's approximation, the transmission coefficient for interband tunneling is just given by the transmission coefficient of a particle with a familiar parabolic dispersion (and mass $m^*$) through the above parabolic potential barrier. Conveniently, this coefficient does not even depend on the energy of the tunneling electron (within the WKB approximation, for uniform fields, and ignoring transverse momentum).  Allowing for transverse momentum can be shown to simply raise the parabolic barrier by $E_\perp=\hbar^2k_\perp^2/2m^*$. Including this effect, and evaluating the WKB integral, we find  $$T(E,E_\perp)=\exp\left\{-\frac{\pi\sqrt{m^*}(E_G+2E_\perp)^{3/2}}{2\sqrt{2}q\hbar\xi}\right\}$$