System of Mathematical Models for the Analysis of Industrial FZ-Si-Crystal Growth Processes

A system of coupled mathematical models and the corresponding program package is developed to study the interface shape, heat transfer, thermal stresses, fluid flow as well as the transient dopant segregation in the floating zone (FZ) growth of large silicon crystals (diameter more than 100mm) grown by the needle-eye technique. The floating zone method with needle-eye technique is used to produce high-purity silicon single crystals for semiconductor devices to overcome the problems resulting from the use of crucibles. The high frequency electric current induced by the pancake induction coil, the temperature gradients and the feed/crystal rotation determine the free surface shape of the molten zone and cause the fluid motion. The quality of the growing crystal depends on the shape of the growth interface, the temperature gradients and corresponding thermal stresses in the single crystal, the fluid flow, and especially on the dopant segregation near the growth interface. From the calculated transient dopant concentration fields in the molten zone the macroscopic and microscopic resistivity distribution in the single crystal is derived. The numerical results of the resistivity distributions are compared with the resistivity distributions measured in the grown crystal.     

The Properties of Undoped InP and GaP Bulk Crystals Prepared by Floating Zone Melting

Undoped GaP and InP crystals which are produced by floating zone melting without a crucible were investigated. The background concentration was 10¹⁵cm⁻³ after several passages of the molten zone. The fundamental residual impurities are carbon and silicon penetrating into the crystals during the crystallization process. After purification, the electron mobility of GaP was 200 cm²/V. s, and for InP – 4000 cm²/Vs. The compensation decreased to 20%. A very effective purification was observed with respect to the carbon atoms, but for silicon this result is observed only after several passages of the molten zone. GaP and InP are basic materials for optoelectronic devices and it is important to investigate the possibility for production of pure bulk crystals. A proper method for this aim is the floating zone melting, where the crucible effect is removed and the influence of residual impurities is observed. In this work the influence of the number of floating zone passages on the electrical and luminescence properties of InP and GAP bulk crystals has been investigated.     

Simulation of dopant zone-leveling in a solid ingot

Simple simulation procedure permitting to perform accurate calculations of the dopant distribution in an ingot after desired number of passes of the molten zone is presented. The results obtained for various distribution coefficients and various widths of the molten zone are discussed. It is shown that the number of passes indispensable for the dopant concentration leveling drastically decreases with the width of the molten zone even for the most disadvantageous range of the distribution coefficients.     

On the combined action of magnetic field and electric current on silicon plasticity

The specific features of the deformation behavior of low-resistivity p-type silicon single crystals have been studied using nontraditional methods of plastic deformation. Under the conditions of the combined action of a weak magnetic field and a direct electric current, a significant decrease in the plasticity of silicon is found during its active deformation when compared to the deformation in the absence of a magnetic field. An increase in the electrical conductivity of silicon samples subjected to active plastic deformation is found. The data that are obtained are compared with the previous data on single-crystal germanium. A possible explanation for the observed effects is given.     

Power Consumption of Skull Melting,Part II: Numerical Calculation of the Shape of the Molten Zone and Comparison with Experiment

A mathematical model for the numerical calculation of the shape of the molten zone during high frequency (HF) inductive Skull melting of ceramic materials in the cold crucible is presented. The mutual interaction between the molten zone and the HF electromagnetic field of the inductor is considered by an axisymmetric model because of the good electromagnetic transparency of the slitted crucible wall (see part I). By means of the developed corresponding Finite-Element program package the shape of the molten zone and corresponding power consumption of the system are calculated. The dependence of the shape of the molten zone on system parameters is analysed numerically and compared with experimental data. Additionally, some further investigations on stability of the molten zone are performed.     

重掺硅衬底片的内吸除效应

本文研究了重掺p型(B)和重掺n型(P、As、Sb)硅单晶的内吸除效应.发现在本实验条件下,经过改进的内吸杂(IG)处理后,不同掺杂剂的重掺硅单晶片都出现了氧沉淀增强现象,但不同掺杂剂的重掺硅单晶中氧沉淀形态不同.且发现砷增强了硅片近表层区氧的外扩散.在相同的热处理条件下,不同掺杂剂的重掺硅清洁区宽度不同,重掺硼硅片的清洁区最窄,重掺砷的最宽.     

Investigation of influential factors on the purification of zone‐refined germanium ingot

Zone refining is one of the most important procedures to purify germanium crystals for the fabrication of detectors in our laboratory. In order to properly zone refine high‐purity germanium crystals, it is important to develop perfect cleaning procedures for raw materials, quartz tubes, and the containers holding raw materials. Additionally, vacuum levels, container types, the correct combination of ambient gases, the speed of zone travel, and the ratio of ingot length to molten zone length, all need to be carefully studied in order to obtain the best results possible. In this work, we investigate a number of influential factors in perfecting high‐purity germanium crystal growth, specifically: cleaning procedures, boat composition, vacuum levels in the chamber, zone travel speed, and the ratio of ingot length to molten zone length. Using the van der Pauw Hall technique, we were able to measure the electrical properties of zone‐refined ingots and analyze the origin and distribution of three main impurity elements (boron, aluminum and phosphorus) thereby allowing us to study potential contamination sources. After detailed analysis on the various influential factors, we were able to optimize the zone‐refining procedures.     

Simulation of dopant zone-leveling for variable distribution coefficient in KCl: EuCl2 system

Experimental data of Eu²⁺ distribution in EuCl₂-doped KCl ingots are analyzed. After settling the relation between variable distribution coefficient and the dopant concentration in the melt, the simulation of the dopant zone-leveling for various molten zone widths is performed. It is shown that owing to the decrease of the distribution coefficient caused by increasing dopant concentration in the molten zone, the number of the zone passes after which the dopant concentration levels off undergoes significant reduction.     

Connection of the Thermocapillary Flow Characteristics and the Impurity Distribution Pattern in Floating Zone Molten Molybdenum Single Crystals

The results of the impurity distribution in W-doped Molybdenum single crystals grown by electron beam floating zone melting are related to the characteristics of computed steady thermocapillary flow and impurity distribution within the molten zone. Particularly the influence of the number and the strength of eddies in the molten zone on the impurity distribution pattern in the grown crystal for different aspect ratios is considered.     

Density and structure of undercooled molten silicon using synchrotron radiation combined with an electromagnetic levitation technique

X-ray diffraction and density measurements have been simultaneously performed to investigate the atomic structure of molten silicon in the undercooled temperature region with the use of an electromagnetic levitation technique. The density was obtained from the levitated sample shape by a non-contact method based on an image analysis technique. From structural analysis of the undercooled molten silicon, the first nearest neighbor coordination number and interatomic distance were determined to be about 5 and 2.48 Å, respectively. There are no temperature dependence of both the first nearest neighbor coordination number and interatomic distance, but a small change observed on the side of the first peak with the structure factor in the temperature range of 1550–1900 K. From these results, we conclude that the short-range order based on tetrahedral bonds of the undercooled molten silicon did not change with the degree of undercooling, however, the medium-range order was changed by the degree of undercooling.     

Fluctuation of crystallization at center part of floating molten zone under reduced gravity condition

Fluctuation of crystallization was observed at floating molten zone under reduced gravity condition on airplane. The zone material was Ba(B_0.9Al_0.1)₂O₄. A pair of Pt tubes was used at the upper and the lower positions, and the molten zone was formed between two Pt tubes. Double peak temperature profile could be performed using two Pt tubes. Crystallization of the molten Ba(B_0.9Al_0.1)₂O₄ was started at center part of side surface of floating molten zone under reduced gravity condition. The formed crystal was melted again during the crystallization by the gravity fluctuation at the center part of the floating molten zone. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Field-assisted ion exchange between molten alloys and soda lime glass

Using molten alloys, the electrolysis of soda lime glass has been studied. Ions from a molten anode can be driven into soda lime glass by applying a modest electric potential. The anode current densities have been measured. The temperature and potential dependences have also been measured. The current-time behavior depends on the ion exchange. In a molten alloy the most easily oxidized metal is suited for exchange.     

Nucleation and growth of crystalline diamond particles on silicon tips

The data on the deposition, structure, and electric properties of crystalline diamond particles at silicon tips grown on single-crystal silicon substrates obtained over the last decade, mainly at the Institute of Crystallography of the Russian Academy of Sciences, have been reviewed. It is shown that silicon emitters coated with crystalline diamond are highly electrically stable. They are used to prepare long-life cathodoluminescence light sources.     

Modulating dopant segregation in floating-zone silicon growth in magnetic fields using rotation

The feasibility of modulating dopant segregation using rotation for floating-zone silicon growth in axisymmetric magnetic fields is investigated through computer simulation. In the model, heat and mass transfer, fluid flow, magnetic fields, melt/solid interfaces, and the free surface are solved globally by a robust finte-volume/Newton's method. Different rotation modes, single- and counter-rotations, are applied to the growth under both axial and cusp magnetic fields. Under the magnetic fields, it is observed that dopant mixing is poor in the quiescent core region of the molten zone, and the weak convection there is responsible for the segregation. Under an axial magnetic field, moderate counter-rotation or crystal rotation improves dopant uniformity. However, excess counter-rotation or feed rotation alone results in more complicated flow structures, and thus induces larger radial segregation. For the cusp fields, rotation can enhance more easily the dopant mixing in the core melt and thus improve dopant uniformity.     

Temperature Distribution of a Floating Zone in Electron Beam Zone Melting of Molybdenum

The temperature distribution in the molten zone for the electron beam zone melting of molybdenum was calculated on the basis of a heat flow model of the rod. Input parameters were the measured axial electron beam density distribution at the rod surface and the supplied power. The calculated zone shape is compared with experiments. Conclusions are drawn on the magnitude of the dimensionless hydrodynamic parameters of the floating zone in dependence on the experimental conditions.     

Analysis of the dopant segregation effects at the floating zone growth of large silicon crystals

A computer simulation is carried out to study the dopant concentration fields in the molten zone and in the growing crystal for the floating zone (FZ) growth of large (> 100 mm) Si crystals with the needle-eye technique and with feed/crystal rotation. The mathematical model developed in the previous work is used to calculate the shape of the molten zone and the velocity field in the melt. The influence of melt convection on the dopant concentration field is considered. The significance of the rotation scheme of the feed rod and crystal on the dopant distribution is investigated. The calculated dopant concentration directly at the growth interface is used to determine the normalized lateral resistivity distribution in the single crystal. The calculated resistivity distributions are compared with lateral spreading resistivity measurements in the single crystal.     

Solubility and metastable zone width of DL‐tartaric acid in aqueous solution

Solubility and metastable zone width (MSZW) of DL‐tartaric acid (DL‐TA) in aqueous solution have been determined. Solubility of DL‐TA was measured in the temperature range from 0 to 50 °C at atmospheric pressure by means of the conventional polythermal method using Turbidity Monitoring Technique, which was verified by a gravimetric method. The dissolution enthalpy and entropy of DL‐TA were then calculated from the solubility data using van't Hoff equation. Two approaches was used to estimate the nucleation kinetics from the measured metastable zone width data, the self‐consistent approach and the approach based on 3D nucleation. In addition, the metastable zone width slightly decreases with increasing agitation rate and was independent of working volume.     

Singular ring‐shaped distribution of Nd in NdxY1‐xVO4 crystals grown by floating zone method

A singular ring‐shaped distribution of high Nd concentration was observed in Nd‐doped YVO₄ single crystals grown by the floating zone (FZ) method. The ring‐shaped distribution appeared 500‐1000 μm inside from the rim of the crystals. Results of growth experiments by the anisotropic heating floating zone (AHFZ) method showed that the Nd concentration was high at the high‐temperature side of the grown crystals. We found a small concave projection at a part of the convex solid‐liquid interface by quenching the molten zone during growth. The cause of the singular ring‐shaped distribution of the Nd‐rich area was discussed in relation with the concave projection at the interface and the convection in the molten zone. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dislocation microwave electrical conductivity of semiconductors and electron-dislocation spectrum

The experimental data are presented on the microwave electrical conductivity of dislocated silicon and germanium as well as on the effect of light on the dislocation ESR signal. Based on the results obtained the new scheme of dislocation electron energy spectrum is suggested.     

Solidification characteristics of textured 123 phase in YBCO by laser floating zone leveling (LFZL) method

Because of incongruent melting in YBa₂Cu₃O_7-x, it is difficult to grow the textured 123 phase directly from the laser-heated molten zone in the laser floating zone (LFZ) method. To overcome this problem, the laser floating zone leveling (LFZL) method was utilized following a pseudo-binary diagram along the Y₂BaCuO₅−YBa₂Cu₃O_7−x tie line and a crystal rod of textured 123 phases was directly grown from the molten zone. Experimental results indicate that the orientation of the textured tetragonal 123 phases is perpendicular to the c-axis and that the T_c of the grown crystal rod is 91.2 K after annealing at 550°C for 40 h in flowing oxygen. Also, the solidified morphologies of some crystal rods grown at different growth rates were observed.