The combined method to investigate the electron spectrum of single n-type δ-doped quantum wells in silicon is proposed. It is based on computing the electron potential energy by means of the Thomas-Fermi method at finite temperatures; then the obtained electron potential energy is applied to the iteration procedure with solving the Schrödinger equations for the electron spectrum and the Poisson one for the potential energy. The many-body corrections to the electron spectrum in the quantum well also have been investigated. The combined method demonstrates a rapid convergence. It is shown that that the simple Thomas-Fermi method gives a good approximation for the electron potential energy and for the total electron concentration within the well.

The application of the Thomas-Fermi method to calculate the electron spectrum in quantum wells formed by highly doped n-Si quantum wires is presented under finite temperatures where the many-body effects, like exchange, are taken into account. The electron potential energy is calculated initially from a single equation. Then the electron energy sub-levels and the wave functions within the potential well are simulated from the Schrödinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schrödinger equation in the case of the anisotropic effective electron mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix.

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