Electronic structure and terahertz intersubband absorption spectra of phosphorus donor in silicon using a variationally optimized diagonalization method

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The electronic structure and terahertz (THz) intersubband absorption spectra of phosphorus (P) donor in silicon (Si) are theoretically investigated using a variationally optimized diagonalization method based on the three-dimensional (3D) nonorthogonal associated Laguerre basis set, the basis set of eigenfunctions of 3D hydrogen atom and the basis set of eigenfunctions of 3D isotropic harmonic oscillator. A fully analytical expression of the matrix elements of the Hamiltonian is derived. Due to the large band anisotropy of Si, the donor electron series appear in an anomalous energy-level order and interval of the orbital angular momentum. The donor electron energy levels with even a small number of basis functions are in excellent agreement with those reported in the previous literature. Compared to two different basis sets of eigenfunctions of 3D hydrogen atom and isotropic harmonic oscillator, my proposed variationally optimized diagonalization method based on the 3D nonorthogonal associated Laguerre basis set is proven to be more efficient and reliable in calculating highly accurate impurity states of anisotropic 3D materials. The intersubband absorption spectra of P donor electron involving transitions from the 1s to excited states are strongly dependent on the orientations of the valley and the polarization vector of the incident light, which results from the fact that the large band anisotropy of Si induces strong mixing of the donor electron states. Their absorption frequencies are found to fall into the THz part of the electromagnetic spectrum. These results show that P donor in Si provides a material platform that enables intersubband devices operating in the THz frequency domain. • A fully analytical expression of the matrix elements of the donor Hamiltonian is derived. • The donor electron energy levels are in excellent agreement with those reported in the previous literature. • The intersubband absorption spectra of P donor electron are strongly dependent on the orientations of the incident light polarization. • P donor in Si provides a material platform that enables optoelectronic devices operating in the THz frequency domain. • The 3D nonorthogonal Laguerre basis is more efficient and reliable in calculating impurity states of anisotropic 3D materials.