Single-Electron States in Cylindrical Nanolayers in the Presence of External Uniform Electrostatic Field

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.

Keywords: Adiabatic approximation, Boundary conditions, Cylindrical nanolayer, Effective mass, Energy spectrum, Moderate field, Nanotube, Perturbation theory, Probability distribution, Quantized layer, Quantum well, Space separation, Stark-effect, Strong field, Strong quantization, Uniform field, Variation method, Wave function, Weak field.