The investigation of shallow impurity and excitonic states in various confined systems, such as quantum wells, quantum well wires (QWW) and quantum dots (QD) [1–3] in external magnetic and electric fields are of great interest for a better understanding of their properties, as well as for their potential application in optoelectronic devices [4, 5].
Photospectroscopy experiments, carried out on n-type GaAs in magnetic fields, have revealed transitions involving the so-called metastable impurity states . These states, associated with the free electron Landau levels, modified by the Coulomb interaction between the donor ion and electron, are known as Landau-like states .
In earlier work, Zhilich and Monozon  variational procedure to calculate the energies of Landau-like states of shallow donors is used. However, this method applies only for extreme values of magnetic field. The variational method of investigating these states were developed in [9–16] as well as in  for a semiconductor with parabolic bands.
At present the stage of experimental and theoretical investigations of Landau-like states in bulk semiconductors and their heterostructures, may be considered completed. Of great interest is the study of Landau-like states in low-dimensional semiconductors, since the reduction of dimensionality leads to an increase in binding energy of Landau-like states. Investigations in magnetic fields are of particular interest for understanding the basic physical properties of nanostructures, in particular, of QWW. Here, magnetic confinement potential competes with the geometric confinement potential depending on the strength and orientation of B . The magnetic length can be varied from values which are larger than the typical lateral dimensions of QWW and QD, to values which are smaller than these dimensions.
The binding energy of the ground state of a hydgrogenic donor in a GaAs QWW in the presence of a uniform magnetic field has been calculated in . The calculations were performed for an axial localization of the impurity for the cases of both infinite and finite potential barriers.
The calculation in [18–22] are carried out within the framework of the effective-mass approximation for the semiconductor QWW with parabolic bands. The calculations of the binding energy of the hydrogen-like impurity in magnetic field in a QWW of A
5 semiconductors with nonparabolic bands is of great interest. A
5 semiconductors usually have small effective masses, great dielectrical constant χ, which means that the Bohr radius of the impurity is larger in comparison with QWW radius achievable at present. It should be noted that the binding energy of the hydrogen-like impurity increases when the size of the confining potential is of the order or less of than the Bohr radius .
The binding energy of the hydrogen-like impurity in a QWW of A
5 semiconductors has been calculated in  as a function of the radius of the wire and the location of the impurity with respect to the axis of the wire, using a variational approach. It is shown that the binding energy in Kanes semiconductors  is larger than in standard case for all values of the shift parameter.
As it is known , the nonparabolicity of the dispersion law leads to a considerable increase of the binding energy in the magnetic field, as well as to a more rapid nonlinear growth of binding energy with B.
The binding energy of a hydrogen-like impurity in a thin size-quantized wire of InSb/GaAs semiconductors  with Kane’s dispersion law has been calculated as a function of the radius of the wire and the location of the impurity with respect to the axis of the wire, using a variational approach. It is shown that when wire radius is less than the Bohr radius of the impurity, the nonparabolicity of dispersion law of charge carriers leads to a considerable increase of the binding energy.
In this paper this analogy is applied for the investigation of binding energy of hydrogenlike shallow donor in a thin size-quantized wire of the InSb/GaAs semiconductors in a magnetic field, parallel to the wire axis. Calculations have been performed using the variational approach, developed in .