Consider a homojunction solar cell with a thin n+ layer on the top (emitter), followed by a thick p-type layer (base)

Consider a homojunction solar cell with a thin n+ layer on the top (emitter), followed by a thick p-type layer (base). The emitter region is significantly wider than the base region, so that it can be considered that that the photogeneration completely happens in the base.
1)               Show that under the assumption of high level injection (HLI) and flat quasi-fermi level, the recombination current in the emitter is given by ,
, where, Joe   is the emitter recombination current density, Δn is the excess carrier concentration and ni  is the intrinsic carrier concentration.
2)                Assume that the HLI bulk lifetime for p-type silicon is, τHLI and the Auger recombination can be modeled with the ambipolar Auger model (CA is the ambipolar Auger coefficient). The rear surface of p-type base is perfectly passivated. Assume, radiative recombination is negligible. Under the assumption of flat quasi-fermi level, derive the mathematical relationship of the recombination current of the complete solar cell that includes the emitter and the base region
3)                Under the assumption of flat quasi fermi level and HLI, find the values of recombination current at V=0.2 V, 0.6 V and 0.7 V. Consider that Joe=  100 fA/cm2, CA= 1x10-30 cm6/s, τHLI= 1 ms. The thickness of the emitter is 0.5 micron and the base is 300 micron. If Jsc= 35 mA/cm2, following the standard convention, in which quadrants the voltage points, 0.2 V, 0.6 V and 0.7 V lie.