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\begin{equation}  P(E) = \left( 1-\frac{V_t}{V_{dc}}\right) \space exp \left( -\frac{E_0}{E_{dc}} \right) = \left( 1-\frac{V_t}{V_{dc}}\right) \space exp \left( -\frac{V_0}{V_{dc}} \right)  \end{equation}  where $V_0=E_0 l$ and $l$ is the length of the crystal. The threshold electric field $E_{t}=V_{th\}/l$ $E_{t}=V_{th}/l$  and the tunneling contribution is significant if $V_{dc}>V_{t}=\mathcal{E}_gl/e^*L$. $V_{dc}>V_{t}=\mathcal{E}_gl/e^*L$ where  $L$ is the correlation length. length\cite{Bardeen_1979}. The threshold voltage is proportional to the length of the channel in the crystal