Materials Fundamentals of Molecular Beam Epitaxy

Jeffrey Y. Tsao

• Publisher: Academic Press
• Year: 2012
• Print ISBN: 9780127016252
• eBook ISBN: 9780080571355
• Topic: Technologie et ingénierie
• Subtopic: Ingénierie de l'électricité et des télécommunications

The technology of crystal growth has advanced enormously during the past two decades. Among, these advances, the development and refinement of molecular beam epitaxy (MBE) has been among the msot important. Crystals grown by MBE are more precisely controlled than those grown by any other method, and today they form the basis for the most advanced device structures in solid-state physics, electronics, and optoelectronics. As an example, Figure 0.1 shows a vertical-cavity surface emitting laser structure grown by MBE.* Provides comprehensive treatment of the basic materials and surface science principles that apply to molecular beam epitaxy* Thorough enough to benefit molecular beam epitaxy researchers* Broad enough to benefit materials, surface, and device researchers* Referenes articles at the forefront of modern research as well as those of historical interest

II

Thin Film Structure and Microstructure

Introduction to Thin Film Structure and Microstructure

In Part I, we described the thermodynamic properties of bulk condensed and vapor phases. These properties determine whether epitaxy will occur at all, and are of primary importance in choosing growth conditions.

In this part, we describe modifications to the thermodynamic properties of bulk phases when the phases are constrained to grow as epitaxial thin films. These modifications are of secondary importance in choosing growth conditions, but are nevertheless crucial in determining the detailed structure and microstructure of the epitaxial phases as they condense. Indeed, even if a coarse view reveals only that the desired phase is condensing, a finer view may reveal a wide range of properties.

We begin, in Chapter 4, by discussing the tendency of epitaxial alloy phases to order and cluster. Then, in Chapter 5, we discuss the tendency of lattice-mismatched epitaxial phases to at first grow coherently with their underlying substrate, but then later to grow semi-coherently, through the introduction of misfit dislocations.

Chapter 4

Ordering and Clustering

In this chapter, we discuss the tendency of alloy phases, constrained to grow as epitaxial thin films, to order and cluster. We would like to know whether, during MBE of alloy phases, the individual components will tend on a microscopic scale to attract or repel each other, so that there is short-range order. We would also like to know whether the individual components will tend on a macroscopic scale to cluster into ordered or disordered phases of particular stoichiometries.

For concreteness, our discussion will center on “pseudobinary” III/V alloys — alloys composed of binary mixtures of two distinct III/V compounds. These alloys are exceedingly useful to device engineers because their lattice constants and electronic properties can be tuned continuously by adjusting the relative fractions of the two III/V compounds. These alloys are also characterized by positive enthalpies of mixing, and hence have a tendency to “unmix.”¹ Those enthalpies of mixing originate mainly from microscopic strain caused by the different bond lengths of the two III/V compounds. Therefore, we begin the chapter by describing, in Section 4.1, how to estimate the strain in microscopic clusters using what are known as “valence force field” (VFF) models. If these microscopic clusters are embedded in an epitaxial thin film on a substrate with a different lattice constant, then they will also be “externally” strained. In Section 4.2, we discuss how to estimate that external strain.

In Section 4.3, we introduce a powerful technique, the cluster variation method, for building a macroscopic description of alloy thermodynamics from statistical combinations of such microscopic clusters. In Section 4.4, we apply this method in an approximate way to In_1−x Ga_x As, a pseudobinary alloy of current technological interest. We will find that the thermodynamic properties of In_1−x Ga_x As depend greatly on whether the alloy is coherent or incoherent with the substrate, i.e., on whether the interface between the epitaxial film and the substrate is crystallographically perfect or not.² If the alloy is incoherent with the substrate, then it is free to adopt the in-plane lattice constant that minimizes its free energy. If the alloy is coherent with the substrate, then it must adopt the in-plane lattice constant of the substrate; the resulting elastic strain energy can increase its overall free energy significantly.

In fact, such coherency constraints greatly suppress the tendency for alloys to separate into their pure-component “endpoint” phases, and at the same time greatly enhance their tendency to form ordered compounds at certain stoichiometric compositions. These tendencies can be understood quantitatively from the full cluster variation method calculation, but they can also be understood semiquantitatively through simpler semi-empirical models. We end the chapter, therefore, with a simple analytical treatment in Section 4.5 of coherency-constrained clustering and ordering.

4.1 Microscopic Strain

Let us start, in this section, by discussing microscopic strain in pseudobinary III/V alloys. We begin, in Subsection 4.1.1, by introducing a simple bond stretching and bond bending force field model for c...

Table of contents

• Cover image
• Title page
• Table of Contents
• Inside Front Cover
• Copyright
• Dedication
• Preface
• List of Figures
• List of Tables
• I: Bulk Phase Equilibria
• II: Thin Film Structure and Microstructure
• III: Surface Morphology and Composition
• Index