Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm^$$-$$3 and the intrinsic carrier concentration is 10¹⁰ cm^$$-$$3. Electron and hole diffusion lengthss are 2 $$\mu$$m and 1 $$\mu$$m, respectively. The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the bandgap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 10¹⁴ cm^$$-$$3 due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 $$\mu$$m, is _____________.

In a non-degenerate bulk semiconductor with electron density n = 10¹⁶ cm^$$-$$3, the value of E_C $$-$$ E_Fn = 200 meV, where E_C and E_Fn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 10¹⁰ cm^$$-$$3. For n = 0.5 $$\times$$ 10¹⁶ cm^$$-$$3, the closest approximation of the value of (E_C $$-$$ E_Fn), among the given options is _________.

A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV . The intrinsic Fermi level is shifted from midbandgap energy level by