Zeeman levels of shallow acceptors in cubic semiconductors

Abstract

A detailed theory for the Zeeman splitting of shallow acceptors in cubic semiconductors is presented, allowing for cubic contributions from the band stmct-, magnetic field orientations B 11 [OOl], [lll], [110] and large magnetic fields B.Practically exact solutions are achieved by taking the contributions of higher angular momenta into account. We calculate the Zeeman splitting of the ground state and the first excited odd-parity states. By also determining the probability for transitions between these states we succeed in a reasonable interpretation of the experimental results for Ge and GaAs. We tabulate g-values for *wide range of Lutt-parame.ters. A description of the Zeeman splitting in terms of a linear field dependence only proves to be accurate for limited field strengths.

Magnetospectroscopy of Be in GaAs

“…The results are in excellent agreement with the previous determinations made using transmission and photoconductivity measurements in a superconducting solenoid to 6 T which yielded g 1 D ϭϪ2.81 and g 2 D ϭϩ1.40. 22 The values are somewhat smaller in magnitude than, but agree, within error, with the experimental results of Atzmüller et al 7 for GaAs:C, which in turn are smaller in magnitude than the theoretical values calculated by Schmitt et al 14 for a generic acceptor in GaAs.…”

“…A detailed numerical theory of the Zeeman effect on acceptor states, including those in GaAs, has been presented by Schmitt et al 14 The calculation takes into account contributions of states with high angular momentum to improve accuracy. These authors present in detail the behavior of the ground state and the first five odd-parity excited states over the field range 0-10 T and give g factors for the ground state and for the first two odd-parity excited states.…”

“…In the notation of Schmitt et al 14 the order of the states is reversed. For example ͑7,8͒ here is the transition denoted by 8→7 by Schmitt et al 14 The selection rules for Bʈ ͓001͔ allow transitions where iϭ f for EʈB; for EЌB, one of i or f is odd and the other is even.…”

“…The energies of the ground and excited states of generic acceptors in GaAs have been calculated by Baldereschi and Lipari 11 using the spherical Hamiltonian, and also incorporating the cubic and other terms, 12 by Fiorentini, 13 and by Schmitt et al 14 The most detailed results are given by the latter authors who present energy levels for 60 acceptor states. The energies these authors determine for acceptor states in GaAs relevant to the present experiments are illustrated in Fig.…”

Magneto-optical far-infrared absorption spectroscopy of the hole states of indium phosphide

“…Such a criterion appears unduly conservative in light of the experimental data published for these systems. Schmitt et al, 11 in a theoretical study, propose a rule of thumb that the linear terms are adequate in describing the states to about B 0 * /5, or about 12 T in InP. However, it has been demonstrated in experiments in p-GaAs that the splittings of the magnetotransitions often follow a linear dependence to much higher fields and an explanation of that phenomenon given: 33 often the quadratic term is the same for the two excited states and so is eliminated if the difference is calculated.…”