GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

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

Given $\mathit{q}=1.6\times {10}^{-19}$ coulomb, ${\mathit{E}}_{\mathit{o}}=8.85\times {10}^{-14}\mathit{F}∕\mathit{c}\mathit{m},{\mathit{E}}_{\mathit{r}}=11.7$ for silicon, the value of $\mathit{L}\left(\mathit{i}\mathit{n}\mathit{n}\mathit{m}\right)$  is ________.