Landau-like states in the magneto-optical spectrum of a shallow donor impurity: Theory versus experiment

Abstract

A calculation of the energy levels and the wave functions for a shallow donor impurity in an applied magnetic field is put forward. The behavior of the donor electron in directions perpendicular to the field is described by a basis set of Landau wave functions, and a variational procedure is used to generate approximate forms for the wave function along the field axis. Theoretical values for the ionization energies of the impurity are calculated and a comparison with both existing and new experimental data, also reported here, is made for impurities in bulk GaAs. The model is used to obtain hydrogenlike states of the impurity as well as the so-called ''metastable'' or ''autoionizing'' Landau-like states. A comparison with a ''hydrogenic'' method of calculation is used to highlight the validity of the model. Also, transition probabilities from the ground to excited donor states are deduced. The results obtained are used to identify the various peaks observed in experimental spectra. Differences between theory and experiment are attributed to the occurrence of Fano resonances. A discussion of the behavior of the impurity in an applied magnetic field calls into question the expected ordering of the energy levels of such a system. ͓S0163-1829͑96͒05735-9͔

High-field calculations of Landau-like shallow donor states: A finite-difference approach

“…11 The experimental data has been converted to dimensionless units and stripped of its material-specific character by removing the small band nonparabolicity and nonresonant electron-phonon coupling effects. A correction was also applied to account for the change in effective mass with field and energy.…”

“…These results were then found to agree well with the results of the variational calculations. 11 The variational calculations have recently been repeated and extended to higher excited states and material-specific effects included in the parametrization. 18 These authors also find excellent agreement between these results and experiment.…”

“…First, because of the strong similarity with the hydrogen atom, a common approach for weak-field calculations is to treat the effect of the applied magnetic field starting from the basis of zero-field hydrogenlike states. [4][5][6][7][8][9][10] However, many of the excited electron states observed experimentally in low-temperature bulk donor magneto-spectroscopy [11][12][13][14][15][16][17] cannot be explained within this basis. An alternative view is to consider a strong-field picture in which the Coulomb interaction between the donor electron and the impurity ion is taken to be small.…”

“…Therefore, despite the large amount of work already performed, there is still a continuing interest in formulating a good model for these highly excited states in bulk III-V semiconductors. 11,12,31,32 The model will be developed for shallow donor impurities in bulk semiconductors, and applied particularly to GaAs in order to compare with experimental results. The results will also be compared to those from other theoretical models.…”

Central-cell corrections for Si and S in GaAs in a strong magnetic field

“…An early report gave the difference in chemical shift for two unidentified donors. 15 Other works have used this data 11 or simply a B 2 dependence 16 to model the effect. These reports are limited to fields below 7 T. Even less data are available at high magnetic fields.…”