Consider a semiconductor with the conduction-band effective mass (m_{c}^{*}), valence-band effective mass (m_{v}^{*}) with (m_{v}^{*} < 0), and band gap (E_{g} = hbar omega_{g}). You may assume (hat{e} cdot p_{cv}) with (p_{cv}) being independent of (k).
Compute the joint density of states for this material as a function of (as needed) (omega), (omega_{g}), (m_{c}^{*}), (m_{v}^{*}), (p_{cv}) and fundamental physical parameters such as (hbar), (e), (epsilon_{0}), and (m_{e}) (the electron free mass).
Compute the real and imaginary part of the dielectric function, (epsilon') and (epsilon''), as functions of (as needed) (omega), (omega_{g}), (m_{c}^{*}), (m_{v}^{*}), (p_{cv}), and fundamental physical parameters such as (hbar), (e), (epsilon_{0}), and (m_{e}) (the electron free mass). For this part of the problem, you should assume the absorption is zero at frequencies above (omega_{0} > omega_{g}) (due to the finite extent of the bands in energy), and your results should include (omega_{0}) as a parameter. For the computation of (epsilon'), you should do the computation only for frequencies (omega < omega_{g}).