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The one-dimensional (1-D) confined hydrogenic impurity states confined in the InAs quantum-well has been studied due to its wide application in manufacturing high-electron-mobility transistors in semiconductor physics. We calculate the energy levels and wave functions of this system using the linear variational method. Choosing the wave function of a particle confined in a 1-D infinitely deep quantum well as a basis set, we obtain the numerical solutions of the energy levels and wave functions of the hydrogenic impurity states confined at one end of the InAs quantum-well by solving the Hamiltonian matrix equation. It is found when the quantum well is very narrow, the eigen-energy approaches to the exact solution with a small number of basis set functions; whereas for a relatively wide quantum well, it is necessary to use a large number of basis set functions. The confinement effect of the quantum well on the energy level and binding energy of the hydrogenic impurity state has been studied in great detail. Although the linear variational method used in this work has only been applied to the hydrogenic impurity state confined in the quantum well, for the non-hydrogenic confined systems, this method is still applicable. Therefore, our work provides a new method to study the energy level structure of the impurity state confined in the external environment and has some practical applications in the fields of semiconductor physics, material science, etc.

The one-dimensional hydrogenic impurity states confined at one end of the InAs quantum well