Thomas-Fermi approximation in a tight-binding calculation of $\delta$-doped quantum wells in GaAs

We present a tight-binding calculation of the electronic structure of $\delta$-doped quantum wells in GaAs. A self-consistent potential obtained in the Thomas-Fermi approximation is considered as an external potential in our tight-binding model. A spin-dependent ${\mathrm{sp}}^3{s}^{*}$ basis is used and nearest neighbors are considered to treat GaAs bulk crystals doped with Si or Be. We change the semiempirical Hamiltonian matrix of the (001) direction in each atomic layer, adding the value of the self-consistent external potential in this layer to all diagonal elements of the matrix. The inhomogeneous $\delta$-doped finite region is matched with two semi-infinite homogeneous GaAs barriers within the framework of the surface Green-function matching method. We compare the tight-binding results with the results obtained in the envelope-function approximation and with the experimental data available for the Si- and Be-doped GaAs.