Derive the following expression for hole concentration n, in the valence band as a functionof temperature Tin an undoped semiconductor: n_{\mathrm{h}}=2\left(\frac{2 \pi m_{\mathrm{h}}^{*} k_{B} T}{h^{2}}\right)^{3 / 2} \exp \left(\frac{-E_{F}}{k_{B} T}\right)

In your derivation you may use the following expressions for the hole density of states g, perunit volume and the electron Fermi-Dirac distribution f(E): g_{h}=\frac{4 \pi\left(2 m_{\mathrm{h}}^{*}\right)^{\frac{3}{2}}}{h^{3}} \sqrt{-E} f(E)=\frac{1}{1+\exp \left(\frac{E-E_{F}}{k_{B} T}\right)}