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Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $N_{d}^{+}=10^{17} cm^{-3}.$ The electric field at $x = 0$ is $0\: V/cm$ and the electric field at $x=L$ is $50$ $kV/cm$ in the positive $x$ direction, Assume that the electric field is zero in the $y$ and $z$ directions at all points.

Given $q=1.6\times 10^{-19}$ coulomb, $\epsilon _{0}=8.85\times 10^{-14}F/cm,$ $\epsilon _{r}=11.7$ for silicon, the value of $L$ in $nm$ is ___________