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).

A $p n$ junction solar cell of area $1.0 \mathrm{~cm}^2$, illuminated uniformly with $100 \mathrm{mWcm}^{-2}$; has the following parameter : Efficiency $=15 \%$, open circuit voltage $=0.7 \mathrm{~V}$, fill factor $=0.8$, and thickness $=200 \mu \mathrm{~m}$. The charge of an electron is $1.6 \times 10^{-19} \mathrm{C}$. The average optical generation rate ( $\mathrm{in} \mathrm{cm}^{-3} \mathrm{~s}^{-1}$ ) is

A one-sided abrupt $p n$ junction diode has a depletion capacitance $C_D$ of 50 pF at a reverse bias 0.2 V . The plot of $\frac{1}{C_D^2}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is $\_\_\_\_$ $\times 10^{20} \mathrm{~F}^{-2} \mathrm{~V}^{-1}$.