Single-Electron States in Quantum Well (Quantum Film) in the Presence of External Uniform Electrostatic Field

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”.

Keywords: Analytical solution, Boundary conditions, Charge carriers, Effective mass, Energy spectrum, Moderate field, Numerical calculation, Perturbation theory, Probability distribution, Quantum film, Quantum well, Space separation, Stark-effect, Strong field, Strong quantization, Uniform field, Variation method, Wave function, Weak field, WKB-method.