Problem $5\mathrm{.}1$

Consider an intrinsic GaAs semiconductor with an electron mass of $m_e^{**}=0\mathrm{.}067m_o,$ a heavy$-$hole mass of $m_{hh}^{**}=0\mathrm{.}55m_0,$ and a light$-$hole mass of $m_{lh}^{**}=0\mathrm{.}067m_o$; assume the band gap at $T=0K$ is $E_g=1\mathrm{.}43$ eV $.$ Optical pumping creates $5{10}^{18}c{m}^{-3}$ electrons in the conduction band, leaving an equal number of holes in the valence band. For the questions below, assume $T=0K.$

a$)$ What is the position of the electron quasi$-$Fermi level, $F_e,$ relative to the conduction band$-$edge?

b$)$ What is the position of the hole quasi$-$Fermi level, $F_h,$ relative to the valence band$-$edge?

c$)$ What are the densities of the light$-$ and heavy$-$holes?