Impurity States In The Finite Deep Square Quantum Wire

In the past 20 years, hydrogenic impurities in low dimensional semiconductor structures have been studied extensively. Impurities 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 from the size, the effect of the applied electric field or magnetic field, and photoionization of impurities.In this paper, based on the previous works, we studied theproperties of a hydrogenic impurity in the GaAs/Ga1-xAlxAsrectangular single quantum wire in detail. Using variational approach, the binding energy and the photoionization cross section of the impurity in the system are calculated. The envelop function was expressed as the combination of the functions of the one-dimensional well in the previous paper. There were troubles in the continuity of the function and of its-derivative divided by band-mass on the boundary. In the theoretical calculation, the wave function is relative to the physical properties of theimpurity greatly, the envelop function F(x,y) is expanded interms of the one-dimensional linear harmonic oscillator function in this paper. It satisfies the continuity of the function and ofits-derivative divided by the band-mass, so it improves the precision of the function and binding energy. The whole paper is divided into two parts mainly.In the first part, following Ref[27], the expression of the envelop function is obtained. Then, considering the dismatch of effective mass between the well and the barrier, using the variational approach, we calculate the binding energy of hydrogenic impurity.In the second part, using the wave function and binding energy obtained from the first part, the photoionization cross-section of the impurity is calculated. We consider twosituations: (i) the light is polarized in the z-direction;(perpendicular to the cross-section of the wire). (ii)the light ispolarized in the x-direction (parallel to the cross-section of the wire). According to the dipole transition selection rule, it allows the system to transit from the ground state to the first and second sub-band respectively, the shape of the photoionization cross-section varying with the photon energy in the two cases is quite different.Finally, we make a specific analysis for our results, ani compare the result with that of the envelop function in the previous references. We find, in the narrower wire, the binding energy calculated from the envelop function in this paper is better than that from the previous function; in the wider wire, thebinding energy of the three cases is closer because the quantum wire is close to GaAs bulk. It shows that the envelop function in the previous references is good only for wider well in the binding energy calculation. In the calculation of the photoionization cross-section, we find that with the changing of the photon energy, the variation scope of the photoionization cross-section of the envelop function in the previous references is much smaller than that in this paper. It shows that the envelop function in the previous references is not fit to calculate the photoionization cross-section.