D.T.J. Hurle

The use of magnetic fields in semiconductor crystal growth

The application of a magnetic field to semiconductor crystal growth melts in order to control melt flow and thereby dopant distribution on both macro- and micro-scales is reviewed. Most emphasis is given to Czochralski and LEC growth and the generation of transverse, axial and configured fields is described. Theories predicting flow and segregation in the presence of a magnetic field are outlined and compared with a wide range of published experimental data relating principally to silicon, gallium arsenide and indium phosphide. The technically-important case of oxygen concentration control in Czochralski is considered in detail, including some previously unpublished data. Finally, the published literature on the use of a magnetic field in non-Czochralski growth configurations is reviewed.

Effect of solutal convection on the morphological stability of a binary alloy

The effects of the coupling between the morphological stability of a planar, horizontal crystal-melt interface of a growing crystal and solutal convection in the melt are explored using linear perturbation theory. The results are compared with the Mullins-Sekerka criterion (J. Appl. Phys. 35 (1964) 444) for morphological stability which neglects the effects of convection and with the recent numerical study by Coriell et al. (J. Crystal Growth 49 (1980) 13). It is found that the deformation of the interface due to the onset of solutal convection occurs above a critical value of the solutal Rayleigh number but that, below this critical value, the Mullins-Sekerka criterion for interface breakdown is not significantly altered by the inclusion of the fluid dynamics. An exception to this is the case where the temperature gradient in the melt is extremely small, when some small stabilisation of the interface against breakdown is predicted. Overstable modes of breakdown have been investigated and the form of the bifurcation studied. It is concluded that, under commonly encountered conditions of growth, the stationary instability is the first to occur.

The meniscus in Czochralski growth

The observation by Antonov [Sb. Rost Kristallov 6 (1965) 158, translated in Growth of Crystals, Consultants BureaU, 1968] that the meniscus of a germanium crystal, growing by the Czochralski process, is inclined at 10–20° to the vertical at the solid-liquid interface is explained using thermodynamic theory of surfaces. The effect is shown to imply that molten germanium does not completely wet its own solid and the average value of the surface free energy of solid germanium at its melting point is estimated to be about 740 erg cm-2.

The weighing method of automatic Czochralski crystal growth: I. Basic theory

Abstract Theory relating crystal radius to the time-variation of the force exerted on the pull-rod by the weight of the growing crystal and surface tension forces is developed. The nature of the relationship is investigated for different classes of materials and an anomalous dependence is demonstrated for the case of materials which expand on solidification and/or not completely wetted by their own melts. The consequences for automatic diameter control are considered.

Control of diameter in Czochralski and related crystal growth techniques

Abstract The various published methods for the automatic control of the diameter of crystals growing by the Czochralski technique are critically reviewed. The form of the meniscus in Czochralski growth is described and it is argued that the most successful servo-control techniques are those which sense changes in meniscus shape rather than changes in diameter only.

Convective transport in melt growth systems

Abstract Most melt growth systems are thermal transport controlled, i.e. the kinetic undercooling of the growth surface and the depression of the freezing point due to the added solute are both small. In consequence, the microscopic growth rate and the solute incorporation are very sensitive to time variation in the melt temperature. In this review several aspects of this problem are considered but first the basic pattern of flow in the Czochralski melt is discussed. The spoke pattern which occurs on oxide melts is described and possible explanations reviewed. The catastrophic flow transitions observed in two particular oxide melts are described. Some general considerations of time dependent flow are given and a detailed description of such flow in a floating zone is provided. Finally, recent theoretical and experimental studies of the coupling between morphological and convective instabilities are described.

The weighing method of automatic Czochralski crystal growth: II. Control equipment

Abstract An analogue servo-system for the control of Czochralski crystals from “seed-on” until growth termination is described. Operation of the system with either crystal or crucible weighing is explained. The controller facilitates crystal growth from melts which expand on solidification and/or do not completely wet their own solids even though weight and crystal radius are not well related for these materials.

Striated solute distributions produced by temperature oscillations during crystal growth from the melt

Abstract The effect of sinusoidal temperature fluctuations in the melt on the growth of a crystal is investigated by solving the concentration-diffusion and heat-conduction equations for both solid and liquid phases in a linear approximation. The response of the temperature and concentration at the interface is calculated and the mean concentration and root mean square concentration gradient are found. Results are presented which show how these quantities vary with frequency when the material constants are chosen to be appropriate to metals and to semiconductors.

Developments in the weighing method of automatic crystal pulling

Abstract Application of the crystal weighing technique to the automatic control of diameter from the point of seed-on to completion is described for crystals of gadolinium gallium garnet and lead telluride, the latter material being grown under a liquid encapsulant. For liquid encapsulation growth at high pressures, a crucible weighing technique is described which has been used for the automatic growth of lead telluride, indium phosphide, gallium arsenide, and gallium phosphide. The theory of the weighing process is outlined and it is shown that for melts which do not completely wet and/or are denser than their own solids, weight is not well related to crystals radius. A servo-control system which overcomes this problem and which additionally corrects for thermal delays, crucible levitation effects and buoyancy effects caused by the encapsulant is described. Fully automatic growth of crystals of Ge, GaAs, GaP and InP has been achieved.

Analytical representation of the shape of the meniscus in Czochralski growth

Abstract In order to model heat flow during Czochralski growth, a knowledge of the shape of the meniscus and its dependence on the angle of contact at the three-phase boundary and on the crystal radius is required. An approximate analytical relationship is derived for this purpose which is shown to compare well with the full iterative numerical solution of the Laplace-Young equation for the range of parameters appropriate to the Czochralski growth of germanium.