Effect of Static Electric Fields on The Electronic And Optical Properties of Layered Semiconductor Nanostructures

External static electric fields are one of the powerful modulating factors that may significantly affect the quasi-particle states in low-dimensional semiconductors. In this chapter we will consider the influence only of the external uniform electrostatic field on the sample. The change of charge carriers’ states under the influence of a uniform electric field which is directed along the quantization axis of the system in low dimensional semiconductors was first examined in semiconductor quantized films. From a purely physical point of view, the essence of this phenomenon is the following: a uniform external field applied along the quantization axis alters the profile of the bottom of the quantum well and in a certain way modifies both the energy spectrum of the charge carriers and their wave functions. Under the influence of the field the coordinate of the center of gravity of the electron cloud in quantum well is shifted, thereby the area of overlap of wave functions is also changed. Under the influence of the field also the shift in the energy levels of the charge carriers in the well takes place (quantum-confined Stark - effect). In this chapter we present analytical calculations for the energy spectrum and the envelope wave functions of single-electron states in a quantum well in the presence of a uniform electrostatic field transversal to the plane of the well. Calculations are performed for three different intervals of the external field in which we conventionally define the field as “weak”, “moderate” and “strong”.

In this chapter, we "curl up" the quantized semiconductor film into a tube. As a result, we obtain the quantized semiconductor nano-cylindrical layer or, as it is also called, a semiconductor nanotube (SNT). Thereafter, we investigate theoretically the influence of lateral uniform electrostatic field on the energy spectrum of charge carriers in this SNT. We first consider the single-particle states in SNT in the absence of an external field. Investigation was conducted at different ratios between the thickness of the layer and its inner radius. Explicit expressions are obtained for the energy spectrum and envelope wave functions of single-particle states in the layer in the absence of an external field. After that the states of charge carriers in SNT in the presence of weak (perturbing), moderate and strong electrostatic fields are considered in each case separately. For each of these cases the corresponding theoretical approach is presented and explicit analytical expressions are obtained for the energy and particle envelope wave functions of charge carriers in the nanotube in the presence of a perpendicular to the axis of symmetry of the system uniform electrostatic field. If necessary, the analytical results are also compared with the results of numerical calculations. An explicit dependence of the Stark splitting on the geometric dimensions of the sample and the intensity of the external field are obtained. On the example of InSb cylindrical nanolayer the behavior of the charge carriers in the narrow-gap SNT in the presence of strong lateral electric field is also considered.

The single-particle states in a semiconductor cylindrical nanolayer (nanotube) in the presence of lateral-radial electrical field are considered. It is assumed, that the regime of strong quantization for radial motion of charge carriers in the nanotube takes place. The explicit analytic forms of the energy spectrum and envelope wave functions of the single-electron states are obtained in the cases of weak and strong radial electric fields, respectively. The comparison of results of analytical and numerical calculations is carried out. The degree of agreement of these results shows the adequacy of the choice of such theoretical approach for the solution of the considered problems. The single-particle states in a wide-gap semiconductor cylindrical nanotube placed in the field of a uniformely charged ring are considered theoretically in the effective-mass approximation. It is shown, that the electrostatic field of the charged ring creates in the tube an additional quantum well along the symmetry axes of the system. It is shown also, that this quantum well can be described as onedimensional modified Coulomb-like potential. By using a variation-method the wave functions and energy levels of the first two states of charge carriers in this well were obtained. The electronic states are considered for the narrow gap InSb nanotube in the field of homogeneously charged ring. The problem is also solved in the framework of the variational approach. Energy spectrum and wave functions for heavy and light charge carriers in the presence of charged ring’s field are obtained in the explicit analytical form.

The states of interacting electron-hole pair in semiconductor nanotube in the presence of strong lateral homogeneous electric field are considered theoretically. It is shown in single-particle approximation that along with the size-quantization of charge carriers` motion by the radial direction the external strong electric field leads to the additional (field) localization of particles also by the angular variable. At the same time the strong external field polarizes the electron–hole pair and traps them on the opposite ends of tube`s diameter. Consequently, the excitonic complex with transversal dimensions of the order of the system`s diameter is formed in a nanotube. By using the variation approach the binding energies and wave functions of the first two states of such field exciton-like complex (FELC) in the tube are calculated. The specificities of interacting electron-hole pair states in semiconductor quantum ring in the presence of strong lateral homogeneous electrostatic field are also considered. The influence of the longitudinal uniform electrostatic field on two- dimensional and one-dimensional excitonic states in the quantum film and quantum wire are considered, respectively. In the quasiclassical approximation the probabilities of ionization of two-dimensional and one-dimensional excitons under the influence of a longitudinal external electric field are calculated. The dependence of the ionization probability on the external field strength is obtained in the explicit analytical form. The results show that when the dimensionality of the system is reduced, the dependence of the exciton ionization probability on the value external field as compared to the three-dimensional case is weakened.

In the strong quantization regime the single-particle states in quantum heterostructures core/layer/clad in conditions when the localization of charge carriers in the layer-component of composition takes place, are considered. Investigation was conducted both in the absence of an external field and in the presence of weak and strong homogeneous electrostatic fields as well as when the radially symmetric electric field is present. In the case of weak fields the confinement Stark effect in the layer is considered. Correspondingly, the energy shifts of the radial and orbital motions of charge carriers in the layer and corresponding perturbated envelope single-electron wave functions are calculated under the external homogeneous electrical field. The calculations are carried out separately for both cases of perturbation of the radial and orbital motions of charge carriers in the layer. The influence of a strong homogeneous electric field on the states of charge carriers in the structure of quantum dot-quantum well (QDQW) is studied theoretically. It is shown that a strong external field changes radically the character of carrier motion in the structure and leads to an additional fieldlocalization of the particle along the polarangle variable. An explicit form of the wave functions and energy spectrum of single-particle states in the structure in the presence of an external field is obtained. The possibilities of experimental and operational applications of the theoretical results obtained for the study of core/layer/shell structures as well as of hollow spheres are also shown. Explicit analytical expressions for the energy spectrum and the envelope wave functions in the presence of a source of the radial electrostatic field in the center of the heterostructure are obtained. The quantitative estimations for concrete CdS/HgS/CdS structure are given as well.