David H. Matthiesen

Numerical Simulation of the Effect of Shearing on the Concentration Profile in a Shear Cell

The effect of the action of shearing on the concentration field in a shear cell was investigated numerically. One cylindrical fluid column present in a capillary of a shear cell segment, 1 to 2 mm in diam and 4 to 10 mm long, was modeled. Here only Ga-doped Ge was used, and it was found that the shearing action disrupts the concentration field to a depth of about one capillary diameter from each sheared end. In this disrupted region, the concentration field was mixed to near uniformity. The convection generated by shearing rapidly dissipates and is effectively zero within 10 s after the end of shear. For shear cell segment capillary aspect ratios l/d greater than about 3, the central portion of the fluid column is expected to be unaffected by the shearing action

Void formation in gallium arsenide crystals grown in microgravity

Abstract Two crystals of selenium doped gallium arsenide ( Se GaAs ) were grown in the crystal growth furnace (CGF), during the First United States Microgravity Laboratory (USML-1). Both of these crystals contained voids and three theories were proposed to explain the formation of these voids: (1) Evolution of dissolved argon from the liquid encapsulated Czochralski (LEC) grown crystal could have resulted in the formation of voids during solidification. (2) Vaporization of excess arsenic at the melt/solid interface due to superheating during rapid solidification could have generated bubbles that were trapped as voids during solidification. (3) A three-piece charge geometry with nondirectional melting could have generated bubbles which were trapped in the crystal as voids during directional solidification. During the Second United States Microgravity Laboratory (USML-2), two more Se GaAs crystals were grown in the CGF. The USML-2 experiments used one-piece charges which were grown using the same LEC procedure and apparatus as the USML-1 charges, but machined with a new technique. The USML-2 charges were directionally melted and directionally solidified. One of the USML-2 experiments duplicated the fastest growth rate that was used on USML-1. No voids were seen in X-rays of either of the crystals grown on USML-2. From these results, it is reasonable to reject the theories concerning dissolved Ar and excess As vaporization. It can be concluded that the voids found in the USML-1 crystals resulted from the combination of the three-piece charge geometry and nondirectional melting prior to directional solidification.

Lateral or radial segregation in solidification of binary alloy with a curved liquid-solid interface

This paper deals with steady state lateral or radial segregation of solute in solidification of a binary alloy with a curved solid-liquid interface. It is an extension of the work of Coriell and Sekerka and of Coriell et al. for interface shapes that meet the crucible wall at an arbitrary angle, as is commonly found in experiments. This work is limited to the diffusion controlled growth regime in which the Peclet number Pe = Vl/D is large, and where the interface deflection is small. In the definition of Peclet number V is the growth rate, l is a characteristic length, and D is the binary diffusion coefficient of the solute in the liquid. We present analytical expressions for lateral and radial segregation which can be readily evaluated, given the material properties, growth velocity, and an interface shape obtained from experiment.

Effect of void location on segregation patterns in microgravity solidification

Three recent microgravity experiments have been hampered by convection caused by unwanted voids and/or bubbles in the melt. In this work, we present a numerical study to describe how thermocapillary convection generated by a void or bubble can affect a typical microgravity solidification process. A detailed numerical model for the Bridgman solidification of a doped single crystal from its dilute binary melt is developed which solves the quasi-steady Navier Stokes equations together with the conservation equations for transport of energy and species. The complicating effects of thermocapillary convection generated by the void and solutal rejection at the melt-solid interface are included. Numerical simulations indicate that void-generated thermocapillary convection can affect segregation patterns drastically, especially, if the thermocapillary vortex penetrates the solutal boundary layer at the growth interface. Two lateral void positions are considered with the void placed either in the center of the ampoule or on the side wall. From a transport point of view, three different segregation regimes are identified for each lateral void location based on the distance between the void and the growth interface. These range from a diffusion-controlled regime where most of the radial nonuniformity in the interfacial composition is due to the interface curvature with minimal convective effects to a fully mixed regime where the penetration of the solutal boundary layer by the thermocapillary vortex tends to homogenize the interfacial compositions drastically. Naturally, the extent of each of these regions will not only depend on the size and lateral position of the void but also on the material and growth properties of the system under consideration.

Physical Modeling of the Effect of Shearing on the Concentration Profile in a Shear Cell

The effect of the action of shearing a column of molten gallium (Ga) doped germanium (Ge) on the gallium concentration field in a shear cell segment was experimentally investigated using a physical model. A physical model is an experimental system that is different from the system of interest but connected by scaling relations. Water was used as the fluid in the physical model in place of the molten germanium, and methylene blue dye was used as a tracer in place of the gallium dopant to determine the extent of mixing. Two adjacent cylindrical fluid segments in a capillary of a shear cell were studied with the physical model. These fluid segment dimensions were scaled by a factor of seven for the physical model, since the kinematic viscosity of water at 22.6°C is seven times that of Ge at 950°C, A small amount of mixing between adjacent segments was measured due to the initial fluid-fluid shear. The mass transfer between the top and bottom segments of the physical model during the fluid-fluid shear was found to be less than 2% for all shear rates in the range 0.1-2.0 cm/s. The average mass transfer between adjacent segments due to the fluid-fluid shear in that shearing range was 1.2%.

Determination of the Peltier coefficient of germanium in a vertical Bridgman-Stockbarger furnace

The Peltier effect is the fundamental mechanism that makes interface demarcation through current pulsing possible. If a method for calculating the necessary current density for effective demarcation is to be developed, it will be necessary to know the value of the Peltier coefficient. This study determined experimentally the value of the Peltier coefficient for gallium-doped germanium by comparing the change in average growth rates between current-on and current-off periods. Current-on and current-off layer thickness measurements were made using differential interference contrast microscopy and atomic force microscopy. It was found that the Joule and Thomson effects could not be neglected. Peltier coefficients calculated from the experimental data with an analysis that accounts for Joule, Thomson, and Peltier effects yielded an average value for the Peltier coefficient of 0.076 ± 0.015 V.

An innovative method for preparing semiconductor charges used in crystal growth and shear cell diffusion experiments

An innovative technique for machining semiconductors has been developed. This technique was used to prepare semiconductor charges for crystal growth and shear cell diffusion experiments. The technique allows brittle semiconductor materials to be quickly and accurately machined. Lightly doping the semiconductor material increases the conductivity enough to allow the material to be shaped by an electrical discharge machine (EDM).

NUMERICAL SIMULATION OF HEAT TRANSPORT AND FLUID FLOW IN DIRECTIONAL CRYSTAL GROWTH OF GaAs

Recent progress in numerical modeling of the transient heat transport and fluid flow in the GTE GaAs space experiment is reported. The vertical gradient freeze crystal growth system is simulated using a simplified axisymmetric finite element model. The enthalpy method is used to model the phase change, and numerical solutions are computed on a fixed grid using the CFD code FIDAP. The numerical results suggest that the shape and melt-back position of the meti-crystal interface are greatly affected by the melting history, therefore making it necessary to model the whole melting and solidification process. The simulated interface evolution for the flight experiment predicts a delay of about 25 min for the actual growth to start after the power reduction begins, which is in good agreement with the experiment. Some numerical issues, such as the advantages and limitations of the fixed domain approach, are also discussed.

The total pressure of arsenic over molten gallium arsenide at 1260°C

In the design of Bridgman type growth systems for the growth of GaAs, the use of a hermetically sealed fused quartz ampoule is often required. In addition, if the sample id to be directionally solidified in some manner, the melt is usually held at a temperature above the melting point of 1238°C, such as 1260°C. The literature generally supports the value of 0.97 atm for the total pressure of As over molten GaAs at the melting point, although there is not agreement on the ratio of the As2 and As4 species. However, only Richman [J. Phys. Chem. Solids 24 (1963) 1131] lists any data for the total pressure of aresenic over GaAs at temperatures above the melting point. His data indicate a value of 1.2 atm at 1260δC. In this paper several experiments are reported, which were conducted using a pressurized furnance and any subsequent deformation of the fused quartz ampoule, which at 1260δC is in viscous flow, was observed. Thus, for no deformation of the ampoule to occur, the internal ampoule pressure due to the total pressure of arsenic over the molten GaAs must be balanced by the externally applied pressure. Based on the results of these experiments, a value of 2.2 atm (18 psig) was measured for the total pressure of arsenic over molten GaAs at 1260δC. The value was used to construct ampoules for several different growth systems, all of which yielded successful ampoules with no deformation.

Design of ceramic springs for use in semiconductor crystal growth in microgravity

Segregation studies can be done in microgravity to reduce buoyancy-driven convection and investigate diffusion-controlled growth during the growth of semiconductor crystals. During these experiments, it is necessary to prevent free surface formation in order to avoid surface tension driven convection (Marangoni convection). Semiconductor materials such as gallium arsenide and germanium shrink upon melting, so a spring is necessary to reduce the volume of the growth chamber and prevent the formation of a free surface when the sample melts. A spring used in this application must be able to withstand both the high temperature and the processing atmosphere. During the growth of gallium arsenide crystals during the GTE Labs/USAF/NASA GaAs GAS Program and during the CWRU GaAs programs aboard the First and Second United States Microgravity Laboratories, springs made of pyrolytic boron nitride (PBN) leaves were used. The mechanical properties of these PBN springs have been investigated and springs having spring constants ranging from 0.25 to 25 N/mm were measured. With this improved understanding comes the ability to design springs for more general applications, and guidelines are given for optimizing the design of PBN springs for crystal growth applications.