Capillary shaping of crystals pulled downward from a melt by the crucibleless AHP method

A model is proposed for capillary shaping of a crystal in the crucibleless variant of the AHP (axial heat flux close to the phase interface) method when the melt in the form of a film flowing over the AHP heater is fed to a meniscus. The meniscus and the film of the melt are described by the same equation with a discontinuous right-hand side. The dependences of the crystal radius and the thickness of the melt film on the parameters of the process are numerically investigated, and the capillary stability of the pulling process is analyzed. It is demonstrated that, in this method, the thickness of the melt layer between the crystal and the heater can be considerably larger than the capillary constant.     

Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Effect of meniscus shape

A global model of heat transfer analysis for the Czochralski crystal growth of oxides, in which a three-dimensional unsteady melt flow was taken into account, was developed in our recent study. In the model, however, the focal point was the methodology of formulating the model by coupling a conventional global model of heat transfer, which is based on a pseudosteady axisymmetric assumption, with a model of a three-dimensional, unsteady melt flow via two interface models. Therefore, for simplicity, the shape of the melt free surface was assumed to be flat. In this study, the global model was further developed by considering the meniscus of the melt free surface. It was found that the meniscus of the melt free surface caused the melt flow to be more unstable and shifted the critical Reynolds number at which the melt/crystal interface inversion occurs toward a much lower value.     

Control over gas bubble distribution in shaped sapphire crystals

Bubble distribution in shaped sapphire crystals grown by Stepanov technique is found to depend on the field of velocities of the melt flows between the top surface of a die and the crystallization front. A die design defining the flows in the meniscus is a tool for control over the bubble distribution.     

Behavior of phosphorus impurities during Czochralski growth of high‐purity germanium single crystals

The effect of evaporation of phosphorus impurities from the melt is investigated as well as the contaminating effect of quartz glass crucibles on residual content and distribution of this impurities by length of high‐purity germanium single crystals. The residual content of phosphorus impurities is mainly influenced by the contaminating effect of crucible material and its distribution by length of crystals is described by the model accounting for the impurities income from crucible material. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automated growing of large single crystals controlled by melt level sensor

The process of single crystal pulling is considered with simultaneous starting material make-up into the melt and heater temperature control in response to a signal generated by the electronic contact melt level sensor, viz.: (i) conditions ensuring the radial broadening steadiness; (ii) effect of melt level displacement, melt temperature changes, changes of solid/liquid interface shape, melt evaporation on the growing crystal diameter; (iii) conditions of crystal purification from impurities and uniform distribution of dopant.     

Modeling the distribution of Ga and Sb impurities in Ge‒Si single crystals grown by double feeding of the melt: Growth conditions for homogeneous single crystals

Mathematical modeling of the distribution of Ga and Sb impurities in homogeneous (with respect to the content of the main components) single crystals of Ge–Si alloys, grown by double feeding of the melt, has been performed in the Pfann approximation. It is shown that the axial gradient of impurity concentration in Ge–Si crystals can be controlled in wide limits by changing the ratio of crystallization rate and the rates of feeding of the melt by silicon and germanium rods. The conditions for growing alloy single crystals, homogeneous both with respect to the content of the main components and to the impurity concentration distribution, have been determined.     

On the theory of the weighing method for automatic crystal shape control in czochralski growth

We derive the exact analytical expression for the meniscus volume in terms of the crystal radius R, the melt contact angle θ_L, and the meniscus height h for the axisymmetric planar growth interface Czochralski configuration. This relation is applied together with motion and mass balance considerations to find the general rate of change in the force experience by the weighing cell in a standard diameter control arrangement. In contrast to the classical work of Bardsley et al. (1977), which is limited to the close viscinity of stationary right cylinder growth, our results are valid for growth developing any crystal profile. In addition, they also account for the fall of melt level due to finite crucible size. The magnitudes of the capillary contributions to the force, and their implications for diameter servo control, are discussed over a wide range of profile parameters using the Tsivinskii formula for h = h (R, θ_L).     

The influence of the intensity of melt stirring on the radial impurity distribution in proustite single crystals grown by the Stockbarger method using ACRT

The influence of the intensity of melt stirring on the radial impurity distribution and optical quality of proustite single crystals grown by the Stockbarger method using ACRT is studied by the example of Cu, Sb and Mg impurities. We report results obtained in a wide range of Taylor numbers (1.9×10⁵<Ta<7.12×10⁷). The studies revealed that the ACRT can be applied validly to decrease the impurity content during the growing of high-quality single crystals.     

Formation of longitudinal aggregation of inclusions in bulk sapphire and yttrium‐aluminum garnet grown by horizontal directed crystallization method

It is shown that the formation of longitudinal aggregation of inclusions in bulk sapphire and yttrium‐aluminum garnet (YAG) grown by the method of HDC is caused by local accumulation of impurities, disturbance of morphological stability of the crystallization front and capture of inclusions and impurities in the nodal region of the melt two‐vortex convection. Studied is the influence of thermal and geometrical parameters of the melt and the shape of the crystallization front on the conditions of the formation of the capture of inclusions.     

Distribution of Al and in impurities along homogeneous Ge-Si crystals grown by the Czochralski method using Si feeding rod

A distribution of Al and In impurities in Ge_{1 ? x} Si _x crystals (0 ≤ x ≤ 0.3) grown by a modified Czochralski method (with continuous feeding of melt using a Si rod) have been studied experimentally and theoretically. Experimental Al and In concentrations along homogeneous crystals have been determined from Hall measurements. The problem of Al and In impurity distribution in homogeneous Ge-Si single crystals grown in the same way is solved within the Pfann approximation. A set of dependences of Al and In concentrations on the crystal length obtained within this approximation demonstrates a good correspondence between the experimental and theoretical data.     

Influence of reaction between silica crucible and graphite susceptor on impurities of multicrystalline silicon in a unidirectional solidification furnace

The influence of silica crucible reaction with graphite susceptor on carbon and oxygen impurities in multicrystalline silicon was studied by global numerical simulations. Results showed that the crucible reaction has a marked effect on carbon and oxygen impurities in the crystal. When the activity of carbon on the surface of the graphite susceptor increases, both oxygen and carbon impurities in the melt increase rapidly. Therefore, the production of high-purity multicrystalline silicon requires setting a free space between the silica crucible and the graphite susceptor or depositing a layer of SiC film on the surface of susceptor to prevent reaction between them.     

Spontaneous crystallization of diamonds in the nickel-manganese system with admixtures of group IV elements

The regularities in the changes in the average size, yield, and impurity composition of diamond crystals synthesized in the nickel-manganese system with admixtures of group IV elements are established. It is found that the average size of crystals in a set increases with increasing Ti concentration. It is shown that the yield of the diamond phase is affected significantly by impurities and almost independent of the metallic melt composition.     

The influence of melt stirring intensity on the axial impurity distribution in proustite single crystals grown by the Stockbarger method using ACRT

The influence of modulated crucible rotation on the axial distribution of Cu, Mg and Si impurities in proustite single crystals grown by the Stockbarger method using ACRT is studied in a wide range of Taylor numbers (1.9·10⁵ < Ta < 7.12·10⁷). The impurity content in the upper part and in the tail portion of the grown crystals is measured using X‐ray‐phase analysis. Micro and macrostriations are observed in the grown crystals. The wavelengths of impurity content fluctuations have been determined. The microfluctuations of axial impurity content are caused by modulated crucible rotation. The studies have revealed that the ACRT provides an effective removal of impurities from the main part of the grown crystal at high intensity of melt stirring, and consequently, the ACRT can be applied validly to decrease the impurity content during the growing of high‐quality proustite single crystals. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physical and physicochemical processes accompanying powder synthesis,growth of PbMoO<Subscript>4</Subscript> crystals,and their annealing in various media: III. Methods of controlling the crystallization front shape

Different methods of controlling the crystallization front shape are considered: variation in a crucible position in a heater, rotation of a crystal, introduction of impurities absorbing melt radiation, and formation of forced convection under dominant free convection in the melt.     

Wachstumsmorphologie von LiNbO3-einkristallen bei der züchtung nach dem czochralski-verfahren unter der einwirkung eines elektrischen feldes

The growth morphology of Czochralski-grown lithium niobate single crystals is described as resulting from interactions of atomary rough and atomary smooth surfaces (facets). The interfacial tension between crystal and melt at smooth faces is considerably larger than at rough ones, causing for appropriately oriented facets a capillary depression of the meniscus. Due to the resulting hydrostatic instabilities spontaneous nucleation may occur that leads to the formation of polycrystals. If an electrical field is applied between crystal and melt the interface tension is reduced. Among other effects, the wetting of facets by the melt is improved and the formation of polycrystals is suppressed.     

Silicon Tubes for Microelectronic Applications Grown Directly from the Melt

A die-free technique for growing large diameter silicon tubes (5–15cm) directly from the melt has been developed. The attained result was a constant tube wall thickness for a range of 7 to 0.2 mm at 1500 mm length limited by the equipment pulling stroke. It is shown that the inner pressure of the tube is function of the meniscus height at the growth interface. A speed is also presented. By means of experiments the thermal gradient at the solid-liquid interfaces is determined.     

Liquid phase epitaxial growth of undoped gallium arsenide from bismuth and gallium melts

Electrical properties of undoped GaAs layers grown from Ga and Bi melts under identical conditions are compared as a function of growth temperature and pregrowth baking time. Identification of residual shallow donors and acceptors is performed by means of laser photoelectrical magnetic spectroscopy and low temperature photoluminescence. It is shown that a change of solvent metal results in complete alteration of major background impurities in grown epilayers due, mainly, to changes of distribution coefficients of these impurities. High purity, low compensation n-GaAs layers can be grown from Bi melt (epilayers with the Hall mobility of electrons μ77K ≈ 150000 cm²/V · sat n = 2.5 · 10¹⁴ cm⁻³ has been grown).     

Existence,stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

A thermocapillary model is used to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the menisci bounding the melt. The positions of the menisci and phase-change boundary are computed to satisfy the conservation laws rigorously. A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal–melt–gas triple phase line, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic shape stability is clarified.     

Phosphoric acid purification by suspension melt crystallization: Parametric study of the crystallization and sweating steps

In order to purify phosphoric acid, the suspension melt crystallization process was studied. The suspension crystallization experiments were carried out with 80, 84 and 88 wt% phosphoric acid melt at the cooling rates of 0.05, 0.1 and 0.2 K/min, respectively. Sweating experiments were executed for various crystals obtained in suspension crystallization step. The purification effects of the sweating parameters including sweating time, initial inclusion amount and initial impurity content were studied. The inclusion fraction increases with the increase in cooling rate. The inclusion fraction of the crystals which were formed with feed concentration of 84 wt% phosphoric acid melt is lowest among the three feed concentrations. Different impurities have different purification performances during sweating. High inclusion amount and low impurity concentration favor the purification of H₃PO₄·0.5H₂O crystals during sweating.     

旋转磁场对空间浮区内流场及浓度场的影响

采用全浮区模型数值研究了旋转磁场作用下熔区内热毛细对流流动特性,分析了磁场强度对流场及浓度场的影响.研究发现,无磁场时,熔体内杂质浓度场和流场呈现三涡胞对称振荡特征;温度场主要由扩散作用决定,呈对称分布.旋转磁场作用下,Ma数基本保持不变.当磁场强度B0≤1 mT时,熔体内杂质浓度场和流场与无磁场时结构类似,但旋转磁场的搅拌作用使得熔体内周期性振荡提前出现,且当旋转磁场产生的洛伦兹力相对较大时,表面张力产生的三维振荡对流得到很好地抑制.B0=5 mT时,周向波动被完全抑制,熔区内流场和浓度场呈二维轴对称分布.旋转磁场对熔体流动产生的轴向抑制作用和周向搅拌作用,都有助于熔体流动的稳定性、浓度分布以及温度分布的均匀性,从而有利于高质量晶体的生长.