Hydrogen Impurities In Quantum Well Wires Binding Energy Scale And Optical Ionizing Section,

In the past 20 years, impurity state in low dimensional semiconductor structures have been studied extensively. Impurites play an important role in the transport properties and optical properties of these structures. The fabrication methods such as molecular-beam epitaxy and metal-organic chemical vapor deposition and experimental studies of their properties have been reported, and theoretical studies mainly concentrate on the impurity binding energy varying the size of the wire, the effect of the applied electric field or magnetic field, and photoionization of impurities.In this paper, based on the previous works, we study the quality of a hydrogenic impurity in GaAs/Gai-xAlxAs rectangular quantum wires in detail. Using variational approach, we calculate the binding energy and the photoionization cross-section of the impurity in the system. On choosing the variational wave function, we have considered the correlation between the confined and non-confined directions of the wires in order to make our results more exact. The whole paper is divided into two parts mainly.In the first part, the scaling rule for the hydrogenic impurity binding energy and the virial theorem value (potential- to kinetic- energy) in infinite quantum wells and quantum wires of rectangular cross-section with three different aspect ratios are studied through the variational method. Comparing our results with that of predecessors, we find that (i)there indeed exists a parameter (impurity Bohr radius ajm) on which the impurity binding energy has strong dependence; (ii) the virial theorem value is non-constant but approach 2 from above when the well width is smaller or larger. This is because the origin of the virial theorem value of 2 lies in the inverse square Coulomb force being the only interaction seen by the electron and impurity ion.In the second part, we discuss the binding energy of the impurity in finite GaAs/Gai.xAlxAs quantum wire in the first place, in which the dismatch of effective mass and dielectric constant between the well and the barrier is taken into account. According to the wave function we choose in this paper, the binding energy is larger than that without considering the correlation, especially in the condition of wider wire. One reason for that is the dismatching of effective mass and dielectric constant between the well and the barrier, another important reason is the consideration of the correlation between confined and non-confined direction in the wider well condition. Furthermore, we use the wave function and binding energy obtained from above to calculate the photoionization cross-section of the impurity. We consider two situations: (i)the light is polarized along the z-direction, in which case the first allowed dipole transition is to the first subband (nx -1,ny =1); (ii)thelight is polarized along the x-direction (paralleled to the transverse cross-section of the wire). The first allowed dipole transition is to the second subband nx = 2 relative to the x-direction and to the first subband nr=1 relative to the y-direction of the wire. The shapes of thephotoionization cross-section varying with the photon energy in the two cases are different. We have compared the results with that of previous work.Finally, a specific analysis is made for our results. Because we have considered the correlation between the confined and non-confined direction of the wire, the binding energy is improved and correspondingly the threshold energy is enhanced, which results in the declinement of the photoionization cross-section.