Hydrostatic-pressure-induced Γ-X mixing in delta-doped AlxGa1-xAs

The mixing between Gamma and X points in the conduction band is known to manifest in GaAs/AlxGa1-xAs heterostructures. Application of hydrostatic pressure leads to the variation of both the Gamma- and X-energy gaps in such a way that a round P = 39 kbar, the GaAs becomes an indirect gap one. With in a narrow interval of P around this value, both minima remain almost energetically aligned. Therefore, it can be expected that some kind of mixing between the states corresponding to the delta-quantum-wells formed at those points should manifest. In this work, we investigate the occurrence of Gamma-X mixing induced by the application of hydrostatic pressure in n-type delta doped AlxGa1-xAs, by means of a variational scheme that uses a 2 x 2 Hamiltonian with the or-diagonal element being a variational potential energy. Diagonal Schrodinger-like effective mass elements are written with potential functions given by the Thomas-Fermi approximation. The erect of the hydrostatic pressure is incorporated via the dependence on P of the different input parameters in the system: energy gaps, effective masses and dielectric constant. We report the variation of the ground state of the system as a function of P.