Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $${\mathrm N}_\mathrm d^+=10^{17}\;\mathrm{cm}^{-3}$$. 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 × 10⁻¹⁹ coulomb, $$\varepsilon$$₀ = 8.85 × 10⁻¹⁴ F/cm, $$\varepsilon$$_r = 11.7 for silicon, the value of L in nm is ________.

The electric field profile in the depletion region of a p-n junction in equilibrium is shown in the figure. Which one of the following statements is NOT TRUE?

The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance (C_J) at a reverse bias (V_R) of 1.25V is 5pF, the value of C_J (in pF) when V_R = 7.25V is ___________.

Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width X_n on the N-side of the junction is 0.2 µm and the permittivity of silicon (ε_si) is 1.044×10^-12 F/cm. At the junction, the approximate value of the peak electric field (in kV/cm) is _________.