Brian Lent

The effect of applied magnetic field on the growth mechanisms of liquid phase electroepitaxy

Abstract Binary (GaAs) and ternary (InGaAs) single crystals were grown by the growth process of liquid phase electroepitaxial (LPEE) under an applied static magnetic field. The effect of the applied magnetic field on two main growth mechanisms of the LPEE growth process, namely the “electromigration” and “natural convection” in the liquid zone, were examined numerically and experimentally. Numerical results show that the flow and concentration patterns exhibit three distinct stability characteristics: stable structures up to the magnetic field level of 2.0 kG, transitional structures between 2.0 and 3.0 kG, and unstable structures above 3.0 kG. In the stable region, the applied magnetic field suppresses the flow structures, and the intensities decrease with the increasing magnetic field level. In the transitional region, the flow intensity increases dramatically with the magnetic field strength, and concentrations show very different patterns leading to a wavy growth interface. Under strong magnetic field levels, the flows cells are confined to the vicinity of the vertical wall and exhibit significant non-uniformity near the growth interface. Experiments performed under various magnetic field levels show that the growth process at the 4.5 kG field level yields satisfactory growths. However, the growth experiments at higher field levels were unsatisfactory and unstable. Although the crystals were still grown, large wholes were observed in the grown crystals. This observation was attributed to the strong interaction of the applied electric and magnetic fields, making the convective flow in the solution very strong and unstable. However, lower magnetic field and electric current levels had very beneficial effects, namely flat growth interfaces and prolonged growth due to weak convection in the liquid zone, and a substantial increase in the growth rate (about 5–10 times higher) due to the effect of magnetic field on the mechanisms of “electromigration”. Such positive developments give the LPEE growth process the potential of becoming a commercial technique.

FUNDAMENTALS AND PHASE CHANGES

This chapter provides a brief introduction to some of the fundamental principles common to the crystal growth processes, in terms of crystal structure, simple temperature composition phase diagrams, and the concepts of lattice parameter- and bandgap-engineering . These concepts provide device engineers with an opportunity to develop novel device structures for applications in the fields of electronics and optoelectronics by defining the optimum characteristics to better suit the device concept structure. A rationale is presented for the choice of growth method for single crystal materials, mainly with applications in the fields of electronics and optoelectronics, from metallic solutions, rather than the more common melt growth techniques, such as the Czochralski pulling from the melt technique, and variants of gradient freeze processes. The advantages of growth from temperatures below the melting point are discussed. The rationale is presented from simple composition–temperature phase relationships.

Chapter 4 – CRYSTAL GROWTH MODELING

Modeling an electromagnetic continuum is of great interest for many disciplines of engineering sciences. This chapter discusses the thermodynamics and modeling of crystal growth from binary and ternary metallic solutions including the effects of applied magnetic fields. Detailed model and simulation equations are presented for each technique. Constitutive equations for the liquid phase as well as the solid phase are presented and then linearized about a reference state. Details of the development of the constitutive equations are presented step by step, giving emphasis on the physical significance of material coefficients in each growth crystal technique. The basic equations are the well-known Maxwell equations and thermomechanical balance laws of a continuum written for a binary liquid mixture. The associated interface and boundary conditions are presented. Finally, the application of magnetic field is discussed.

TRAVELING HEATER METHOD

Traveling heater method (THM) falls into the category of solution growth, and is a relatively new, promising technique for commercial production of high quality, bulk compound and alloy semiconductors. Due to its importance, a number of experimental and theoretical studies are carried out for the THM growth process. This chapter presents the recent developments in modeling of THM, particularly during the last two decades. The basic theoretical considerations regarding the modeling issues are presented first. Then, two and three dimensional simulation models and numerical simulation results are presented for binary and ternary systems. The challenges in modeling of the THM growth of ternary systems are emphasized. The use of static and rotating magnetic fields has also found a great interest in THM. The models under static and strong magnetic fields, and also those under weak and rotating magnetic fields are analyzed.

LIQUID PHASE ELECTROEPITAXY

The growth process of liquid phase electroepitaxy (LPEE) is quite complex and involves the interactions of various thermomechanical and electromagnetic fields. These include fluid flow, heat and mass transfer, electric and magnetic fields, various thermoelectric effects and their interactions in the liquid phase, and the heat and electric conduction with various thermoelectric effects in the solid phase. In addition, the moving growth and dissolution interfaces with possible finite mass transport rates complicate the process further. This nature of the LPEE growth process has brought about a number challenges for researchers. This chapter presents the numerical simulation models developed for the LPEE growth of semiconductors. The numerical simulations carried out to date for binary and ternary systems are presented in a chronological order. The role of a static vertical magnetic field is also examined, and its effect on the growth process is discussed. The models of lateral overgrowth of semiconductor layers are also presented.

METALLIC SOLUTION GROWTH TECHNIQUES

The driving force behind solution growth technologies as they are applied to semiconducting materials lies in their ability to remove the technological limitations for novel device concepts and structures imposed by the small number of available elemental and compound semiconducting substrates, and a limited number of lattice parameters and bandgaps. A slight mismatch between the lattice parameters of a substrate and epitaxial device layer will lead to the creation and propagation of dislocations from the initial growth interface into the device structure, leading to reduced device efficiency and performance. This chapter provides an introduction to crystal growth techniques: their technological significance, detailed configurations, and growth procedures. Comparisons of these techniques with other vapor and melt techniques are made in terms of crystal quality, composition, and uniformity. The materials considered are mainly the IV–IV materials, the III–V alloys, and the II–VI alloys. Space limitations preclude a complete chronological review of the experimental details of each growth process. The growth technologies are presented in a generalized manner, with specific materials or material systems discussed and results presented by way of examples. Many references are provided for the growth processes, materials systems, and specific devices, and applications.

LIQUID PHASE DIFFUSION

Liquid phase diffusion (LPD) is a solution growth technique within the family of directional solidification . This chapter presents the numerical simulations carried out for LPD growth of SixGe1-x crystals with and without the application of applied magnetic fields. In the models, the application of a static vertical magnetic field was considered to suppress the strong convection observed in the solution in the first few hours of the LPD growth process, and a horizontal rotating magnetic field to obtain a uniform mixing and a flatter growth interface. The Si–Ge system is selected because of the increasing technological interest in the improved device performance attainable with this material. Maximum available furnace operating temperatures in the crystal growth laboratory compels the confinement of research to the high Ge content end of the Si–Ge phase diagram, but the principle may be extended by use of higher operating temperature furnaces.

Chapter 5 – LIQUID PHASE EPITAXY

In liquid phase epitaxy (LPE), the growth cell is normally a rectangular cavity where the solution is placed. Therefore, modeling the LPE growth process is actually a three dimensional problem. However, most models in the literature developed for LPE are two dimensional. This is mainly for two reasons: for simplicity, and due to the physical nature of the growth system. Crystals grown by LPE show 3-D and edge effects in the regions very close to the crucible wall. Except the very edges, the LPE process in general produces uniform and flat crystalline layers. Thus, two-dimensional models provide reasonably accurate predictions for most purposes. This chapter presents the simulation models developed for the LPE growth of semiconductor single crystals. The focus is on the growth of silicon, binary systems, and ternaries. Some models developed for the epitaxial lateral growth and the conversion of semiconductor layers by LPE are introduced. The effect of gravity on convection is studied in an LPE growth system, known as the yo-yo technique. Various simulation results are presented and discussed.