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

Far-infrared photoconductivity measurements on n-GaAs using a far-infrared laser and a Fourier-transform spectrometer are reported. They extend previous measurements to higher magnetic fields (14 T) and higher laser energies (330 cm-1) and, in particular, give results in those regions of the spectra where resonant polaron effects on transitions to metastable states are clearly present. To describe the field dependence of the transition energies, a new variational-type approach for the calculation of the energies of the metastable states has been developed. As such an approach yields analytical expressions for the wave functions, the effects of resonant polaron interactions on the transition energies can be calculated. Experimental and theoretical transition energies are compared for the more important transitions to metastable states, including resonant polaron effects, and very good agreement is obtained even though the theoretical model is very simple.

A theoretical method for calculating the energies and wave functions of an electron bound to a shallow donor in a semiconductor, subject to an applied magnetic field, is presented. This approach is particularly useful for describing highly excited Landau-like states, which cannot be dealt with properly using most other theoretical models. First, an adiabatic high-field approximation is used where mixing between different Landau-like states is neglected. Solving the one-electron Schrödinger equation is then reduced to finding solutions to a one-dimensional differential equation for motion along the field axis. We present results in which a finite-difference technique is used to solve this equation numerically. Values for the electron wave function at discrete points along the field axis are then determined. By calculating the discrete Fourier transform of this set of values, an analytical form for the wave function in terms of sines and cosines is obtained. These resultant wave functions are then used to calculate a Hamiltonian matrix in which mixing between different high-field states is included. Diagonalization of this matrix yields improved values for the energies of the impurity states. Where previous results exist, our results are compared with those of other theoretical approaches and from experiments on the donor in GaAs. The advantage of our approach is that it enables both energies and wave functions to be determined without any prior assumptions of the form of the wave function in the field direction. This includes expressions for highly excited states which are difficult to obtain by other means. The results demonstrate the validity of the present method of calculation. ͓S0163-1829͑98͒08315-5͔

Calculations are made of the energies of the dominant transition (1s to 2p+1-like) of a hydrogenic donor impurity in a multi-quantum-well (MQW) system subject to a magnetic field applied at an angle theta to the direction of growth of the MQW layers. The model used involves constructing suitable basis states, and then performing a matrix diagonalization procedure. The results are compared to the available experimental data, including the extreme cases of fields perpendicular ( theta =0 degrees ) and parallel ( theta =90 degrees ) to the layers. The results are also found to compare well with the results of existing variational calculations.

A method is presented for the calculation of the energy eigenvalues and eigenstates of the electron associated with a shallow donor impurity in a GaAs/GaAlAs multi-quantum well structure in the presence of a magnetic field parallel to the layers. Compared to the case of an impurity in a magnetic field directed perpendicular to the layers, the problem is complicated by the lack of cylindrical symmetry. This lack of symmetry is reflected in the form chosen here for the basis states that describe the donor electron. By formulating the Hamiltonian and operating on these states, the energies and orthonormal ground and excited state wavefunctions of the donor electron are determined by matrix diagonalization procedures. Calculations of the transition probability between the ground and excited states yield the theoretically most probable transition energy for a given magnetic field. These calculated values are compared to available experimental data and deviations between the theory and experiments at large fields are discussed.