Si/SiO2 Multiple Quantum Wells: Electronic and Optical Properties

Theoretical investigation of the size effect in Si/SiO2 multiple quantum wells (MQW) is undertaken. Two modifications of the standard rectangular potential well model are introduced that provides satisfactory fit of the experimentally observed size effect in samples with extremely thin silicon layers. Both linear and nonlinear conductivity tensors of the Si/SiO2 MQW are calculated. Generalized optical transfer matrix technique is outlined. Within the frame of the technique the influence of electromagnetic interactions between the silicon layers on nonlinear optical response is analyzed. Introduction Multiple quantum wells (MQW) are structures consisting of alternating layers of materials of two different types. Typical thicknesses of the layers are about several nanometers, therefore, a quantisation effect coming from confinement of the electron motion in the direction perpendicular to the boundaries of layers is present. The effect depends on the thicknesses of layers, hence, varying the thicknesses of layers one can affect the microscopic properties of MQW structures. The distinguishing feature of MQW structures is that there is no tunneling of electrons between neighboring layers of the same type. This can be achieved if the widthes of electronic band gaps of the materials forming the structure differ a great deal. At present time there is an increasing interest in investigation of MQW structures in modern solid state physics. First of all, MQW structures are interesting by itself because they form a new type of artificial materials with controllable microscopic properties. Second, this materials can be used in laser technology as an active media with a controllable value of the resonant energy. And third, an investigation of a MQW structure provides an information about microscopic properties of the materials forming the structure. In this paper we investigate MQW structures consisting of amorphous silicon (a-Si) layers placed in the oxide of silicon SiO2 host. One of the key problem of the theoretical investigation of Si/SiO2 MQW structures is an explanation of the such called size effect, that is the dependence of the energy difference between levels that contribute to the optical response of the thickness of a-Si layers. The size effect observed in Si/SiO2 MQW with thicknesses of a-Si layers lying in the range from 1nm to 3nm was satisfactory fitted within the frame of the rectangular potential well model [1]. But in the case of the thicknesses lying in subnanometer range the model predicts much stronger size effect than that observed in the experiment [2]. In the paper we analyze possible reasons of the discrepancy and introduce modified rectangular potential well models that provide a substantially steeper thickness dependence. In the paper we also calculate both linear and nonlinear conductivity tensors of the MQW within the frames of the described microscopic models. Finally, we introduce the generalized optical transfer matrix technique that provides precise and quick calculations of both linear and nonlinear optical response of MQW structures. Within the frame of the technique we calculate the second harmonic (SH) response of the Si/SiO2 MQW and analyze the role of polariton effects. Size effect In a Si/SiO2 MQW structure the electron tunneling between neighboring quantum wells can be neglected. Therefore, the problem concerning the energy spectrum of an electron moving in the z direction, that is the direction perpendicular to the boundaries of the layers, reduces to that for a single Si quantum well in a SiO2 host (see Fig.1(a)). Consider the 2-D electron gas in the conduction band of Si (the gas of holes in the valence band). Denote the extremum of the dispersion law of the gas in the conduction band as Ec and that in the valence band as Ev. The main quantity that determines the optical properties of the well is the resonant energy ∆ = Ec −Ev. In order to determine the dependence ∆(d), where d is the thickness of the Si layers the rectangular potential well model is widely used. Within WDS'05 Proceedings of Contributed Papers, Part III, 489–494, 2005. ISBN 80-86732-59-2 © MATFYZPRESS