Wave functions and energies of shallow acceptor states in germanium |
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| Affiliation: | 1. Department of Chemistry, University of Agriculture, Faisalabad, 38000, Pakistan;2. Department of Physics, College of Science, King Khalid University, Abha, 61413, P.O. Box 9004, Saudi Arabia;3. Department of Chemistry, COMSAT University, Abbottabad Campus, KPK, 22060, Pakistan;4. Punjab Bio-energy Institute, University of Agriculture, Faisalabad, 38000, Pakistan;1. State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China;2. Department of Mechanical Engineering and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China;3. Frontier Science Center for Quantum Information, Beijing 100084, China;4. Institute for Advanced Study, Tsinghua University, Beijing 100084, China;1. Department of Physics, Chemistry and Biology, Linköping University, Linköping, Sweden;2. Wigner Research Centre for Physics, Budapest, Hungary;1. ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain;2. CPHT, École polytechnique, CNRS, Université Paris-Saclay, route de Saclay, 91128 Palaiseau cedex, France;1. Department of Chemistry, Saarland University, Saarbrücken 66123, Saarland, Germany;2. London Centre of Nanotechnology, University College London, London WC1H 0AH, United Kingdom;3. Department of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom |
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| Abstract: | Approximate wave functions and energies of shallow acceptor states in germanium have been obtained by solving the effective mass equations in the limit of very strong spin-orbit coupling. The variational approach used by Schechter was followed, but with more general trial functions that allow a more complete calculation of the energy spectrum of the acceptor. The new trial functions are constructed from terms with the angular dependence derived by Schechter, each multiplied by an arbitrary radial function. The variational procedure leads to systems of differential equations for the radial functions and energies of the states.Degenerate wave functions for a given acceptor level transform as a basis for a Γ6, Γ7 or Γ8 irreducible representation of the double tetrahedral group. Energies and wave functions were obtained for the ground state, which has Γ8 symmetry and envelope functions with even parity, and for the first excited state having the same symmetry and parity. Energies and wave functions were also obtained for excited states with Γ6, Γ7 and Γ8 symmetries and envelopes with odd parity. States with Γ6 or Γ7 symmetry and envelope functions with even parity were not considered. The resulting energies show fair agreement with the experimental energies. As the new trial functions are quite flexible, it appears that the remaining discrepancy may be due to the inadequacy of the effective mass approximation. |
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