Frederick M. Carlson

Transport modes during crystal growth in a centrifuge

Abstract A fully nonlinear three-dimensional numerical model for a centrifugal crystal growth experiment is presented. The model includes ampoule geometry and the experimentally obtained thermal profiles for the inner furnace steel cartridge insert. Results are presented based on both steady-state and fully transient models. The flow modes are presented resulting from Coriolis effects and from average resulting acceleration and the acceleration gradient, both acting on radial and axial thermal gradients. Thus far the model has been used to simulate growth at a particular experimental g equal to the value at which non-convective type impurity profiles were obtained. The flow modes resulting from different combinations of these forces can be of the same order of magnitude and interact with one another. The importance of the gradient acceleration is determined by the value of a new nondimensional number, called Ad. Thus, Coriolis effects and g gradients may have to be included in the model in order to obtain physically meaningful results. Implications of the resulting flow and thermal fields on the growing crystal at conditions available during centrifuge processing are also discussed.

Finite element analysis of the control of interface shape in Bridgman crystal growth

Abstract Numerical experiments were performed on a vertical Bridgman crystal growth system. The thermal field was studied in the absence of fluid motion by solving the steady state energy equation using a finite element method. Key parameters were isolated and their influence on the interface curvature was assessed. These included insulation zone thickness, system temperatures, Biot numbers, solid-liquid thermal conductivity ratio, and ampoule location in the furnace. It was concluded that interface curvature could be controlled by the crystal grower to achieve any desired shape.

Thermal convection during Bridgman crystal growth

Abstract Numerical experiments are used to study thermally driven flows which occur during vertical Bridgman crystal growth of a single component fluid. The solid-liquid interface was specified as parabolic and flow patterns were calculated for various insulation thicknesses, Grashof, Prandtl and Biot numbers. When the melt is on top and the gravity vector is axially downward it was shown that flow persists as long as a radial temperature gradient is present. If the interface is convex, as viewed from the liquid, a single cell is observed. A concave interface exhibits multiple counterrotating cells. The insulation thickness and Grashof, Prandtl and Biot numbers influence the flow in a quantitative manner.

Computed stress fields in GaAs during vertical Bridgman growth

Abstract The thermoelastic stress field of GaAs crystals grown by the vertical Bridgman method has been approximated using a linear elastic, axisymmetric stress model. The model included the effects due to the thermal field and the gravitational field, as well as the interaction with the ampoule, but did not fully account for the elastic anisotropy of the crystal. Realistic thermal fields for different furnace temperatures and insulation zone thickness were computed with a similar model. The difference between the Von Mises stress and the critical resolved shear stress (CRSS) was used as a measure of the number of dislocations present. Different sets of growth parameters were examined to determine which produced the lowest amount of stress in the crystal. Results show that the crystal-ampoule interaction is the most important parameter in dislocation generation. In addition, for the same sticking boundary conditions, concave interfaces have lower stress than convex interfaces.

Monitoring vertical Bridgman-Stockbarger growth of cadmium telluride by an eddy current technique

The electric conductivity of indium-doped cadmium telluride (CdTe) in the temperature range 600–1080°C was 163 to 1203 Ω-1m-1.In-situ monitoring of vertical Bridgman-Stockbarger growth showed an unexpected step change in the voltage response vs height. Differential thermal analysis of CdTe showed both Cd and Te melting peaks as well as an exothermic reaction above 790°C.

Producibility improvements suggested by a validated process model of seeded CdZnTe vertical Bridgman growth

We have successfully validated theoretical models of seeded vertical Bridgman-Stockbarger CdZnTe crystal growth and post-solidification processing, using in-situ thermal monitoring and innovative material characterization techniques. The models predict the thermal gradients, interface shape, fluid flow and solute redistribution during solidification, as well as the distributions of accumulated excess stress that causes defect generation and redistribution. Data from the furnace and ampoule wall have validated predictions from the thermal model. Results are compared to predictions of the thermal and thermo-solutal models. We explain the measured initial, change-of-rate, and terminal compositional transients as well as the macrosegregation. Macro and micro-defect distributions have been imaged on CdZnTe wafers from 40 mm diameter boules. Superposition of topographic defect images and predicted excess stress patterns suggests the origin of some frequently encountered defects, particularly on a macro scale, to result from the applied and accumulated stress fields and the anisotropic nature of the CdZnTe crystal. Implications of these findings with respect to producibility are discussed.

Particle motion in the fluid experiment system in microgravity

Abstract Polystyrene spherical particles were used to trace the fluid motion in an experiment of crystal growth from aqueous solutions in space. This paper presents the particle motion derived from the images reconstructed from holograms taken in the space experiment. The particle mechanics is also discussed. It was observed that some particles can independently move in different directions; some particles can move much faster than the others, and some small particles may have the same speed as large ones. Particles may individually have the behavior of the inertial random walk. But more importantly, there are non-random motion so that particles may keep moving in certain directions. It becomes difficult to estimate g and g-jitter from these particle motions as expected. This also leads to a doubt that the particles in the fluid experiment system are subjected to g and g-jitter, which have been considered as only a function of time.

Thermomechanical analysis in directional solidification of CdTe

Thermoelastic calculations for CdTe grown by the vertical Bridgman method are presented. Finite element calculations are verified by some experimental data. Solidification interface velocity, charge temperature and stress distributions are computed for prescribed ampoule withdrawal rates and several ampoule support systems. The support systems include various materials and seed-wafer transition zone geometries. Crystal stress in excess of the critical resolved shear stress is used as the figure of merit to judge the performance of a particular system. Emphasis is focused on the transition region between the seed and wafer. A processing strategy is proposed and desirable support system characteristics are presented.

Finite Element Analysis of Thermal and Stress Fields During Directional Solidification of Cadmium Telluride

The thermal field and resulting thermoelastic stress field were simulated for the vertical Bridgman growth of Cadmium Telluride (CdTe) crystals. The calculated temperature distribution agrees well with the data taken from the experiment. The computed excess stress distribution based on the calculated temperature field in the solid also agrees qualitatively with synchrotron contour topography on a slice taken from the growth ingot.

The Role of Thermal Stress In Vertical Bridgman Growth of CdZnTe Crystals

Computational studies of thermal fields and resulting thermoelastic stress fields were undertaken for the vertical Bridgman-Stockbarger growth of CdZnTe crystals. Companion experimental studies included the growth of crystals grown with the same process parameters and the same geometry as the process modeled in the computations. Characteristics of the crystals grown were compared with the computational predictions. Predictions of growth ampoule outer wall temperatures agree well with thermocouple data taken during the growth experiment. Additionally, the computed excess stress distribution resulting from the thermoelastic stress history in the solid is seen to agree qualitatively with synchrotron contour topography on a slice taken from the grown ingot. The computational models are shown to provide a good tool for the study of the influence of process parameters on the quality of crystals grown by this method, at least as far as thermal stress influences the defect distribution. The influence of low-g and high-g environments on growth is discussed.