A p-type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at x = $$\pm$$ 2l_n, where l_n = 10^$$-$$4 cm is the diffusion length of electrons. Assume electronic charge, q = $$-$$1.6 $$\times$$ 10^$$-$$19 C. The profiles of photo-generation rate of carriers and the recombination rate of excess minority carriers (R) are shown. Under these conditions, the magnitude of the current density due to the photo-generated electrons at x = +2_ln is ___________ mA/cm² (rounded off to two decimal places).

For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J_L) is 2.5 mA/cm² and the open-circuit voltage (V$$_{oc}$$) is 0.451 V. consider thermal voltage (V$$_T$$) to be 25 mV. If the intensity of the incident light is increased by 20 times, assuming that the temperature remains unchanged. V$$_{oc}$$ (in volts) will be ______.

Consider the charge profile shown in the figure. The resultant potential distribution is best described by

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 ________.