Semiconductor quatum well find band gap question

[brocq_18]

Hiya, been given this question which I am having problems with.

Semi conductor quantum well structure contains a 100A thick layer of GaAs between thick AlGaAs layers. Find the band gap for the structure, where GaAs has the following parameters; conduction band effective mass 0.067 me, heavy hole mass 0.45me, band gap 1.519 eV. Assume conduction and valence bands offset at the GaAs/AlGaAs interfaces are infinite.

I have gotten that electron energy at the lowest level of conduction band is =Ec+(hbar(2)k(2))/2m0me. How do i progress from here?

Thanks

 

[member 553083]

in advanceThe band gap for the structure can be found by subtracting the energy at the lowest level of the conduction band from the energy at the highest level of the valence band. Since you know the electron energy at the lowest level of the conduction band, you just need to find the energy at the highest level of the valence band. This can be done using the effective mass and band gap of the GaAs layer.The energy at the highest level of the valence band is equal to the band gap of the GaAs layer minus the total kinetic energy of the heavy hole:E_v = (1.519 eV) - (hbar^2 * k^2) / (2 * m_hh)where k is the wave vector of the heavy hole and m_hh is the effective mass of the heavy hole.Subtracting E_c from E_v gives the band gap of the quantum well structure:Band Gap = E_v - E_c = (1.519 eV) - (hbar^2 * k^2) / (2 * m_hh) - E_c