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Sam Bader edited Computationally_this_method_is_straightforward__.tex
over 8 years ago
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\textbf{HHHHHHHHHH}
Computationally, this method is straightforward to apply even when the assumptions underlying its simple analytical forms are removed. Starting from a given band diagram, the procedure is as follows. For each $\vec{k}$ in the valence band that could tunnel to the conduction band (while conserving energy and transverse momentum), find the start and end of the tunnel region (where $k_x=0$). Then, choosing some determination of $k$ (either Sze's formula, or a band structure model) evaluate \ref{WKB}. Once $T$ is known for all $k$'s, integrate over the band to find a tunnel current.