Recently, crystal engineers seem to pay attention to numerical simulation of melt flow, heat transfer and thermal stress in crystal growth processes. Here, some results of simple numerical simulations are used to explain the effects of thermophysical properties of materials on the characteristics of Cz apparatus and macroscopic shape of grown crystals.
Two typical measurements of the thermal conductivies of crystalline and melt silicon were reviewed. Shashkov and Grishin determined them from the heat balance at the crystallization front in the Czochralski method. Yamamoto et al. measured by a laser flash method, and deter-mined the thermal conductivies of the crystal and the melt silicon at the melting point to be 27.3±0.3 and 56±1 W/mK, respectively. They also reported an anomaly at melting. In the present study, the formula for the thermal conductivity of silicon crystal in the temperature range from 300 K to the melting point were derived on the basis of the data measured by Yamamoto et al. and the thermophysical properties.
A mathematical model for Czochralski (CZ) crystal growth has been developed. The model is based on the assumptions of axial symmetry, diffuse-gray radiation, and conduction dominated heat transfer in the melt. The model (l) includes global radiative heat exchange, (2) is a transient model, (3) requires only physical properties and complete geometry, and (4) permits fast calculation of the view factors based on a novel computation method. Good agreement was obtained between the model and experimental results for the heater power of a 2" puller. Thermal histories of 2" and 6" crystals were calculated.
On CZ silicon crystal growth, melt flow affects formation of microdefects as well as formation of striations in the crystal. Furthermore, when large diameter crystal is produced, this plays a quite important role. There are many studies on CZ melt flow, however, mechanism of complex flow has not been clear. In order to clarify the mechanism for the origin of temperature fluctuation in the CZ silicon melt, temperature fluctuation in the melt has been mesured. Spectral analysis of these data showed that baroclinic waves exist in the melt. The results of numerical simulations also showed that baroclinic waves may be present in the melt. According to Fein's experiments and Eady's theory, present experimental condition is in the baroclinic wave region.
Direct observation on molten silicon convection during Czochralski crystal growth was carried out using doublebeam X-ray radiography system with solid tracer method. The observed particle path had a torus like pattern for crystal and crucible rotation rates as +1 and -1 rpm, respectively. The root-mean-square velocity for one specific tracer was 21 mm/sec. Moreover, it is found that a flow field with larger azimuthal velocity than the rotational velocity of the crucible exists just beneath the crystal, while the flow field with smaller or negative azimuthal velocity exists near the crucible wall. Numerical simulation containing fluid flow, heat conduction and heat exchange by radiation has been performed using the geometry of the same as furnace used for experiment. The calculated flow velocity and particle path were almost the same as the experimental results. It has also become clear from a comparison of flow-velocity field between experimental and calculated results that the modulation of azimuthal-flow field is caused by the Colioris force.
This paper reviews the recent development of the silicon continuous-charging Czochralski (CCZ) process with a double-crucible method and discusses some problems and their solutions based on the author's work. The newly developed double-crucible (DC) method, which characterizes an inner crucible held at an upper portion during the meltdown process, is effective to avoid the troubles usually caused in conventional DC methods. The dopant concentration of the CCZ crystal could be precisely controlled by setting the concentration of the inner and the outer melts equal before starting the pulling. Granular polysilicon was used as continuous-charging material in the pulling. The accumulation of heavy-metal impurities in the melt was evaluated by a numerical calculation considering both the resolution of quartz crucibles and the inherent concentration of continuously charged poly-silicon. The CCZ crystals showed the same contamination level with the conventional CZ crystals at the top and the tail portion, though they showed a little higher concentration at the middle portion. The possibility of a long CCZ crystal growth was also investigated by using an incidence of structure-loss.
The effect of crystal/melt interface on single crystal growth of GaAs and InP by LEG method has been studied. The mechanism of polycrystallization of GaAs crystals has been investigated related to the concave interface at the edge of crystals. Gathered dislocations at the concave edge result in generation of grain boundaries. The position of the center of concavity has been found to strongly relate to the propagation and the gathering of dislocations. The measurement of the center position of concavity is useful to evaluate growth conditions. GaAs 'single' crystals with modified interfacial concavity, 500 mm-long with 3-inch diamerer and 350 mm-long with 4-inch diameter, have been grown. The formation of twins in OOO) InP crystals has been in-vestigated, focussing on the precise observation of edge facets. Irregularity of edge facets strongly relates to the generation of twins. Regularity of edge facets, which means the stability of growth conditions, is essential for the growth of twin-free InP crystals.
The reported measurements of the viscosity of molten LiNbO_3 were surveyed. Advantages and disadvantages of each of the employed methods were discussed. The activation energies for viscous flow calculated from the temperature dependences of the viscosity under various conditions were compared with each other. The relation-ship between the viscous flow unit and the local ordering, which was suggested by an X-ray scattering experiment, in LiNbO_3 melt in air, was discussed. The variations of the energy and the unit size were interpreted in terms of the variation in number of oxygen atoms bridging the niobium atoms. Necessity of the research of melt proper-ties in relation to crystal growth was emphasized to be carried out by two or more different methods.
Effects of the impurities and defects on the promising optical properties of LiNbO_3 are reviewed from our studies. The crystals grown at nitrogen gas ambient which contains 0.001 vol% oxygen, just after the growth, had a strong and broad optical absorption around 500 nm, which was perfectly vanished after a few minutes of the heat treatment in air. The optical absorption in the range of 400-500 nm increased with the partial pressure of oxygen during the crystal growth. However, the absorption in this range could not be reduced by heat treatment in air even for more than 100 h. The origin of this optical absorption is considered not to be Fe^<2+>, but to be intrinsic defects, which are remarkably reduced by the crystal growth in the poor oxygen atmosphere. The photorefractive effect of LiNbO_3, at least in the bulk form, had no relation to the atmosphere during the growth. Large suppression of the optical damage is characteristic for the Ti-diffused waveguides of the crystal which was grown in low oxygen concentration. In Zn doped LiNbO_3, the optical absorption around 400-500 nm was also reduced. High Zn doping could strongly suppress the optical damage as Mg doping. But the refractive indices of Zn doped crystals are different from those of Mg doped ones. The ordinary refractive index is increased with Zn content, and the extraordinary one shows nonmonotonic dependence.
Ferroelectric crystal LiNbO_3 has first utilized as nonlinear optical devices in 1960's. With development in surface accoustic wave (SAW) applications, the utility of this crystal has spread out to the region of high frequency niters. LiNbO_3 has a wide solid solution range between Li_2O and Nb_2O_5, and the SAW velocity significantly changes with the crystal composition. The determination of the congruent composition is thus essential for obtaining uniform SAW velocity in the crystals when they are grown from the melt. Since the starting reagents Li_2CO_3 and Nb2O_5 contain a considerable amount of impurities and water, the constituent in the melt often deviates from the desired, congruent composition, and consequently, a nonuniform SAW velocity is observed in the obtained crystals. The deviation is easily checked by measuring the SAW frequency on the obtained crystal wafers using newly developed equipment, and is eliminated by a suitable complement of deficiency in the composition. Finaly, the variety in the central SAW frequencies becomes less than 0.1%.
The technique for growing low dislocation density GaAs crystal was studied with computer simulation and experiments. The studies consist of the following three subjects. (1) The thermal stress induced in the temperature range between 1100℃ and 1200℃ after solidification was investigated with simulation using finite element method. The low temperature gradient in the crystal after solidification and the direction of crystal growth were found to be effective for reducing dislocation density. (2) The dependence of EPD on crystal diameter and crystal cooling rate in the temperature range between 900℃ and 1200℃ was observed. (3) The correlation between the deviation of solid-liquid (S/L) interface from a flat plane and the dislocation density was found. By applying to 3T-HB method the results of the thermal stress analysis, the slow cooling rate and the control of S/L interface, Si doped GaAs with EPD≦400 cm^<-2> throughout the ingot has been grown.
We report on the successful growth of undoped semi-insulating GaAs single crystals with low dislocation densities by the vertical gradient freeze (VGF) method using a proper quantity of B_2O_3 and precisely controlling the As-pressure. Impurity analysis shows that the use of B2C>3 is effective in preventing contamination with silicon from the quartz ampoule and also in reducing carbon concentration in the crystal, and that high purity GaAs crystals are obtained by using B_2O_3. Hall measurements give the activation energy as 0.8 eV for the annealed samples having the resistivity of 10^8Ω・cm. The average melt composition was estimated by monitoring the As-pressure during crystal growth. It was confirmed that the EL2 concentration depended on the melt composition in the same fashion as for LEG (Liquid Encapsulated Czochralski)-grown crystals. This observation, combined with the spatial distribution of EL2, indicates that the gradient of melt composition in the vertical direction is important in controlling the stoichiometry.
The (100) and (001) thin films of β-Sn (99.999% purity) were partially melted and regrown in a transmission electron microscope at an average cooling rate of 8.3×10^<-3> to 2.7×10^<-1>K/s in order to observe the melt growth process in-situ. The growing interface was somewhat concave toward the melt and it showed the similar curvature irrespective of the film orientation and cooling rate. The average velocity of the interface first increased rapidly and then slowly as the cooling rate was raised. During the melt growth, only lineage defects, which might be composed of a dislocation array, were introduced in the grown (100) films. Most of them were formed in the solid part near the depression of solid-liquid interface and they were propagated into the newly grown crystals, while a few of them were generated in the last solidified part of a liquid pool which was left behind solid crystal. The average length of the lineage defects formed amounted to the order of 10^5 m/m^2 at any cooling rates. On the other hand, none of defects was observed in the (001) films.