Theoretical Investigations of Electron States in Small-Scale Semiconductor Structures

Citation

Mailhiot, Christian (1984) Theoretical Investigations of Electron States in Small-Scale Semiconductor Structures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0470-nf89. https://resolver.caltech.edu/CaltechETD:etd-01112007-111123

Abstract

The work presented here is concerned with theoretical investigations of electronic states in small-scale semiconductor structures. This last term encompasses layered structures made up of two dissimilar, but lattice-matched, semiconductors. The semiconductors of interest here are mostly the tetrahedrally bonded zincblende semiconductors GaAs and the alloy Ga_1-xAl_xAs. The thesis is subdivided in three major chapters. The first chapter is concerned with electrical doping of Ga_1-xAl_xAs-GaAs-Ga_1-xAl_xAs quantum well structures. The second chapter addresses the question of the transport of electrons through GaAs-Ga_1-xAl_xAs double heterojunction structures. In the final chapter, we develop a theory of the electronic structure of semiconductor superlattices particularly suitable for the study of the optical properties and the recombination mechanisms.

In Chapter 2, we study the energy spectrum of ground state and excited states of shallow donor states in Ga_1-xAl_xAs-GaAs-Ga_1-xAl_xAs quantum well structures. In this system, an impurity atom is located within a GaAs slab of finite thickness. The GaAs slab is, in turn, centered between two semi-infinite layers of Ga_1-xAl_xAs. We use a variational method to solve the effective mass equation for the donor envelope function. We study the variation of the binding energy as a function of

∘ thickness of the GaAs containing the impurity,

∘ alloy composition x in Ga_1-xAl_xAs, and

∘ position of the impurity in the GaAs slab.

Two cases are treated:

(i) In the first case we assume that the potential well is formed by finite conduction band offsets at the GaAs-Ga_1-xAl_xAs interface (imperfect confinement).

(ii) In the second case we consider infinite confining potential at the GaAs-Ga_1-xAl_xAs interface (perfect confinement).

The major result of this study is that the binding energy of the donor ground state is considerably modified as the thickness of the GaAs slab containing the impurity is varied. At large GaAs slab thicknesses, the binding energy is that of shallow donors in bulk GaAs. At small GaAs slab thicknesses, the binding energy is that of shallow donors in bulk Ga_1-xAl_xAs for the case of imperfect confinement, but corresponds to the two-dimensional Coulomb limit in the case of perfect confinement. It is also found that the binding energy depends on the position of the impurity atom within the GaAs slab. Thus, we have a confinement-induced lifting of the Coulomb energy levels.

In Chapter 3, we study the transport characteristics of electrons through GaAs-Ga_1-xAl_xAs-GaAs double heterojunction structures. In this system, a Ga_1-xAl_xAs slab of finite thickness is centered between two semi-infinite layers of GaAs. An electron is incoming from the GaAs onto the Ga_1-xAl_xAs barrier. Transport coefficients are calculated using the formalism of the complex-k energy band structure within the empirical tight-binding method. Transmission into states derived from different energy extrema of the GaAs lowest conduction band obtained. We consider both the (111) and the (100) GaAs-Ga_1-xAl_xAs interfaces. Transport coefficients are calculated as a function of

∘ GaAs conduction band minimum from which the electron state is derived,

∘ energy of the electron incoming on the Ga_1-xAl_xAs barrier,

∘ thickness of the Ga_1-xAl_xAs barrier, and

∘ alloy composition x in the Ga_1-xAl_xAs.

The major result of the study is that states derived from different energy extrema of the GaAs lowest conduction band appear to couple weakly across the GaAs-Ga_1-xAl_xAs interface. Thus, if we consider the (111) interface, is seems possible to reflect the L-point component of the current while transmitting the Γ-point component. There exists two regimes of transport: tunneling transport and propagating transport. In the case where the energy incoming electron is below the energy barrier, transmission is small and the transport occurs via a tunneling process. However, in the case where the energy incoming electron is above the energy barrier, transmission is large and the transport occurs via a propagating process. Depending on the Ga_1-xAl_xAs slab thickness, it is possible to induce resonances whereby the transmission coefficient is unity.

In Chapter 4, we develop a theoretical framework to investigate the electronic structure of semiconductor superlattices. The theoretical formulation is based on the k • p method derived from an accurate local pseudopotential method. The formalism developed is particularly well suited for the study of the optical properties and the investigation of the recombination mechanisms in semiconductor superlattices. Here again, we make extensive use of the complex-k energy band structure obtained via the k • p method. Realistic boundary conditions are imposed on the multi-component superlattice envelope function. From these boundary conditions, the energy spectrum of the superlattice is deduced. For the first time, we develop a scheme whereby the superlattice state function in both solids is expanded in terms of the same set of basis functions. By doing so, we relax the often used approximation that assumed that the basis functions are the same for all zincblende semiconductors.

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