Numerical study of radial temperature distribution in the AlN sublimation growth system

A large radial temperature gradient in the AlN sublimation growth system would lead to non‐uniform growth rate along the radial direction and introduce thermal stress in the as grown crystal. In this paper, we have numerically studied the radial thermal uniformity in the crucible of a AlN sublimation growth system. The temperature difference on the source top surface is insignificant while the radial temperature gradient on the lid surface is too large to be neglected. The simulation results showed that the crucible material with a large thermal conductivity is beneficial to obtain a uniform temperature distribution on the lid surface. Moreover, it was found that the temperature gradient on the lid surface decreases with increased lid thickness and decreased top window size.     

CFD modelling of single crystal growth of potassium dihydrogen phosphate (KDP) from binary water solution at 30 °C

Crystal growth rate depends on both diffusion and surface reaction. In industrial crystallizers, there exist conditions for diffusion-controlled growth and surface reaction-controlled growth. Using mathematical modelling and experimental information obtained from growth studies of single crystals, it is possible to separate these phenomena and study how they are affected by concentration, slip velocities of particles, temperature and finally estimate the parameters for crystal growth models.In this study, a power-law growth model using activity-based driving force is created. Computational fluid dynamics (CFD) was used to evaluate the thickness of a diffusion layer around the crystal. Parameters of the crystal growth model were estimated using a non-linear optimization package KINFIT. Experimental data on growth rate of the (1 0 1) face of a potassium dihydrogen phosphate (KDP) single crystal and simulated data on the thickness of a diffusion layer at the same crystal face were used in parameter estimation. The new surface reaction model was implemented into the CFD code. The model was used to study the effect of flow direction on growth rate of the whole crystal with various slip velocities and solute concentrations.The developed method itself is valid in general but the parameters of crystal growth model are dependent on the system. In this study, the model parameters were estimated and verified for KDP crystal growth from binary water solution.     

The effect of mass transfer on the temperature gradient of a crystal growing from melt

The change in the temperature gradient on the crystal side while the rate of crystal growth from melt is varied has long been debated. Abe and Takahashi have recently reported an unambiguous experimental demonstration that the temperature gradient is a decreasing function of the growth rate, which is different from previous theories, experimental results, and widely held notion of other researchers. The present paper provides a theoretical basis for this seemingly peculiar effect of the growth rate on the temperature gradient. The essential matter is the effect of mass transfer, the role of which had been commonly disregarded in old studies. Although the rate of mass transfer is not large compared to that of heat conduction, it is proven that the temperature gradient is subjected to the mass transfer in a definite manner. Our analysis shows that the effect becomes significant when the crystal diameter is large, which is consistent with the experimental observation. Another effect of the mass transfer is the change in the shape of melt/crystal interface. In old studies, the temperature gradient was determined by Stefan's equation; however, this treatment confuses the cause and effect. The temperature gradient should be determined by the fundamental equation of heat conduction. When the gradient is determined in this way, the shape of the melt/crystal interface spontaneously adjusts to satisfy Stefan's equation.     

数值模拟自然对流对直拉单晶硅的影响

在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。     

Evidence of free carrier concentration gradient along the c-axis for undoped GaN single crystals

Results of measurements of infrared reflectivity and micro-Raman scattering on the undoped GaN high pressure grown single crystals are reported. These crystals have usually a high electron concentration due to unintentional doping by oxygen. We show, by the shift of the plasma edge (infrared reflectivity measurements), that the free electron concentration is always higher on the (0 0 0  )N face of the GaN single crystal than on the (0 0 0 1)Ga face. In order to determine the profile of the free carrier concentration, we performed transverse micro-Raman scattering measurements along the (0 0 0 1) c-axis of the crystal with spatial resolution of 1 μm. Micro-Raman experiments give a quantitative information on the free carrier concentration via the longitudinal optical phonon–plasmon (LPP) coupling modes. Thus, by studying the behavior of the LPP mode along the c-axis, we found the presence of a gradient of free electrons. We suppose that this gradient of electrons is due to the gradient of the main electron donor, in undoped GaN single crystals, i.e. oxygen impurity. We propose a growth model which explains qualitatively the incorporation of oxygen during the growth of GaN crystal under high pressure of nitrogen.     

蓝宝石晶体热性能的各向异性对SAPMAC法晶体生长的影响

采用有限元法对冷心放肩微量提拉法蓝宝石晶体生长过程中晶体内的温度、应力分布进行了模拟计算,结合实验结果讨论了蓝宝石晶体热性能的各向异性对晶体生长的影响.研究结果表明,对于冷心放肩微量提拉蓝宝石晶体生长系统,较大的轴向热导率有利于提高晶体的生长速率和界面稳定性,而稍大的径向热导率则有利于保持微凸的生长界面.晶体内的热应力受径向热膨胀系数的影响显著,随着径向热膨胀系数的增大而增大,最大热应力总是出现在籽晶与新生晶体的界面区域.在实验中选α轴为结晶取向,成功生长出了直径达230mm、高质量蓝宝石晶体.     

PVT法生长SiC过程生长界面形状对热应力的影响

PVT法生长SiC过程中晶体内部的热应力是其位错产生的主要原因,而生长界面的形状对晶体热应力及缺陷的产生都有一定影响.本文对不同生长界面晶体的温场及应力场进行了数值分析,结果显示相对于凸出及平整界面的晶体,微凹界面晶体的轴向温差最小,同时产生缺陷的切应力Τrz及引起开裂的径向正应力σrr值都为最小.     

碳酸钙掺杂对Ⅰb型金刚石沿不同晶面生长行为的影响

作为天然金刚石生长环境的碳酸盐,研究其掺杂对人造金刚石晶体生长行为的影响具有重要的学术价值。本文运用高温高压下的温度梯度法,将碳酸钙(CaCO₃)按照不同比例掺杂到金刚石合成腔体内的碳源中,用以研究其掺杂对金刚石分别沿(100)或(111)晶面生长行为的影响。利用光学显微成像对掺杂合成金刚石晶体形貌的表征表明:随着碳酸钙掺量的增加,沿(100)面生长的金刚石晶形由塔状变为板状且出现了裂晶、连晶现象,晶体颜色先变浅再变黑,内部出现了包裹体;同样,沿(111)面生长的金刚石晶形由板状逐渐变为塔状且出现了裂晶、孪晶现象,晶体颜色逐渐变黑,内部包裹体增多。用激光拉曼光谱对掺杂金刚石晶体质量的表征表明:随着碳酸钙掺量的增加,沿(100)或(111)面生长的掺杂金刚石的拉曼峰位偏移量均增大,半峰全宽均变大。这说明碳酸钙掺杂使得金刚石晶格畸变增加、内应力变大。本文对碳酸钙掺杂影响沿两不同面生长金刚石的晶形、颜色、内部质量等行为的成因进行了分析,为本课题后续研究奠定了基础。     

Thermal stress relaxation phenomenon through forming the interstitial region in CZ silicon pulled with rapid and slow cooling heat shields

This review article aims to clarify a mechanism of point defects formation in a CZ Si crystal through an experimental arrangement using the two kinds of heat shields with different slow-pulling periods. Point defects in a melt grown silicon crystal have been studied for a long time. The author and his co-researchers have reported about “Mechanism for generating interstitial atoms by thermal stress during silicon crystal growth” [in Progress in Crystal Growth and Characterization of Materials, 66 (2019) 36-46]. The experimental arrangement includes constant growing, changing pulling rate and finally detaching crystals from the melt. The two types of heat shields were used to change the cooling history of the grown crystals, for changing a temperature gradient at a bulk part in the grown crystal, G_b. In order to prove that the formation of an interstitial region or a boundary of vacancies (Vs)/interstitials (Is) in a silicon crystal is a phenomenon of relaxing thermal stress, the author explains that a G_b in a crystal forms thermal stress and causes some silicon atoms at lattice positions to move to the closest interstitial sites to relax the stress. The author defines a new term of metastable interstitial atom, I’, or I's as the plural of I’. The I’ coexists with the metastable vacancy V’ from where the I’ is displaced. The plural of V’ is defined to be V's. The author defines the above state to be a complex (I’+ V’), or (I ’+ V’)s as the plural of (I’+ V’), and explains that the (I’+ V’) s convert to Is and form the Is region. The (I’+ V’) is considered as the Frenkel pair-like complex.The crystals were firstly pulled with a high pulling rate, and the pulling rate was consequently decreased to a slow one. Then the crystals were pulled with the slow constant pulling rate for different periods making different cooling processes. Finally, the grown crystals were detached from the melt and cooled rapidly. Characterization of defects, such as Vs, Is, and defect-free (D-F) regions were identified in X-ray topographs (XAOP(s)). Wafer lifetime mapping (WLTM(s)) allows confirming dislocation loop (DL) regions. The results show that the Is are generated depending on the pulling period of the slow pulling and the shapes of the heat shields. The Is and DL regions are formed in a region at temperatures near the melting point. The Is form an Is region through a defect-free (D-F) region, forming the Vs/Is boundary. When the thermal stress weakens, the DL region changes to the Is region; the Is region changes to the D-F region; and the D-F region changes to the Vs region. Temperature gradient distribution is induced toward various directions at different parts of the growing crystal depending on the different slow-pulling periods. The temperature gradient, G_b, includes a temperature gradient from the cooled region shaded by the heat shield to the growth interface and a temperature gradient from the upper surface cooled during the long-time growth to the growth interface. The G_b exceeding a certain threshold at near the melting point forms thermal stress, generating Is to relax the stress.     

Numerical and experimental studies on crack formation in LiNbO3 single crystal

A global analysis of heat transfer was carried out in an inductively heated Czochralski (CZ) furnace which was actually used to grow LiNbO₃ single crystals, and then the temperature profiles obtained were used to calculate the three-dimensional thermal stress field in the crystal. By comparing the numerical results with the experimental ones, it was found that controlling the thermal environment in the CZ furnace so that the thermal stresses at the crystal surface might not exceed a certain value is important to realize the cracking free growth operation. In this study, this was accomplished through some modifications in the furnace design such as insertion of an after-heater into the furnace. These findings were verified by additional numerical simulations and crystal growth experiments for some growth conditions.     

温度梯度法BaY2F8晶体生长中的小面研究

采用温度梯度法生长了BaY2F8晶体,通过X射线定向仪确定晶体自发沿[001]方向生长.通过对不同截面的显微观察和分析,研究认为生长方向与竖直方向不平行是诱发(100)、(130)、(130)等小面生长的重要因素.由于温度的波动和径向温度梯度的存在,会造成晶体生长过程中的组分过冷,引发晶面上出现胞状凸起,影响了晶体的生长质量.     

Transient and quasi‐stationary simulation of heat and mass transfer in Czochralski silicon crystal growth

The formation of grown‐in defects in silicon crystals is controlled by the concentration of intrinsic point defects. Under steady state conditions the type of the prevailing point defect species is linked to the ratio of pull rate and temperature gradient in the crystal at the solidification front. It has been shown that this ratio as well as computed point defect distributions are in good agreement with experimental data. In this paper we compare a coupled transient heat transfer and transient point defect transport model with quasi steady state simulations at various time steps. Both simulations show the same qualitative results, quantitative differences in temperature are less than 1 %. But already for constant pull rates the defect distributions show qualitative differences between transient and quasi steady state simulations. Therefore, for a detailed understanding how defects are related to growth conditions, the thermal history should not be neglected.     

AgGaS2晶体生长裂纹研究

从理论和实验上对AgGaS2晶体生长中易产生裂纹甚至开裂的现象与其热应力、晶体尺寸以及温度梯度、生长速率等生长参数之间的关系进行了研究.结果表明:晶体产生裂纹甚至开裂与生长速率、坩埚旋转速率、冷却速率所造成的热应力和热应变有关.采用改进的Bridgman法成功地生长出尺寸为φ12mm×30mm无裂纹的AgGaS2单晶体,给出了制备无裂纹、大尺寸AgGaS2晶体的较佳生长工艺参数.     

FeNi、NiMnCo及其复合触媒中Ⅰb型金刚石的生长特性

本文以Ni₇₀Mn₂₅Co₅和Fe₆₄Ni₃₆合金及其复合合金作为触媒,采用高温高压温度梯度法在5.6 GPa压力下,对不同温度下沿(100)晶面生长的Ⅰb型金刚石的生长特性进行了研究,研究表明:以Fe₆₄Ni₃₆触媒合成出的金刚石在以(111)晶面为主的晶形高温生长范围内出现了一段约50 K范围的裂晶生长区,而以Ni₇₀Mn₂₅Co₅触媒合成的金刚石在生长温度范围内,特别是在以(111)晶面为主的晶体生长高温区域内容易出现连晶缺陷;高温下Fe₆₄Ni₃₆触媒过度熔融可能是晶体容易产生裂晶的原因,Ni₇₀Mn₂₅Co₅触媒熔体黏性较低可能是容易形成连晶的原因;采用两种触媒复合的方式有效避免了裂晶和连晶的产生;拉曼光谱表征发现连晶的晶体内部质量与单晶的晶体质量相近,裂晶中晶格畸变和杂质较多,晶体内应力较大,复合触媒体系合成的金刚石晶体内应力小,质量好。     

Crystallization mechanisms of acicular crystals

In this contribution, we present an experimental investigation of the growth of four different organic molecules produced at industrial scale with a view to understand the crystallization mechanism of acicular or needle-like crystals. For all organic crystals studied in this article, layer-by-layer growth of the lateral faces is very slow and clear, as soon as the supersaturation is high enough, there is competition between growth and surface-activated secondary nucleation. This gives rise to pseudo-twinned crystals composed of several needle individuals aligned along a crystallographic axis; this is explained by regular over- and inter-growths as in the case of twinning. And when supersaturation is even higher, nucleation is fast and random.In an industrial continuous crystallization, the rapid growth of needle-like crystals is to be avoided as it leads to fragile crystals or needles, which can be partly broken or totally detached from the parent crystals especially along structural anisotropic axis corresponding to weaker chemical bonds, thus leading to slower growing faces. When an activated mechanism is involved such as a secondary surface nucleation, it is no longer possible to obtain a steady state. Therefore, the crystal number, size and habit vary significantly with time, leading to troubles in the downstream processing operations and to modifications of the final solid-specific properties.These results provide valuable information on the unique crystallization mechanisms of acicular crystals, and show that it is important to know these threshold and critical values when running a crystallizer in order to obtain easy-to-handle crystals.     

Study of the dissolution and growth of salt single crystals in inhomogeneous acoustic fields: I. A standing acoustic wave

The growth of the isolated (100) face of a KDP crystal at exposure of the phase boundary to the initial ultrasound field and a standing acoustic wave has been investigated. A significant growth response of this face, exposed to sound normally along the acoustic axis in the near zone of a piston-like half-wave vibrator with f = 20 kHz and tangentially in the pulsed two-frequency (f = 600 and 900 kHz) standing-wave mode, has been revealed. It is shown that the mechanisms of mass exchange enhancement in these acoustic modes are different. The results obtained show a fundamental possibility of controlling crystal growth and dissolution by varying the parameters of inhomogeneous acoustic field.     

KDP晶体生长的溶液流动和物质输运计算

本文采用有限容积法,对KDP晶体生长过程中溶液的流动和物质输运进行了数值模拟.结果表明:随着入口溶液流动速度的增大,籽晶的上表面因自然对流而引起的抽吸作用减小,表面过饱和度的最小值沿x正向发生右移,其上表面的剪切力先减小后增大.随着入口溶液过饱和度的增大,籽晶上表面剪切力增大.不同尺寸的籽晶表面过饱和度的分布差异较大.籽晶的生长边界层厚度与溶液流动密切相关,入口溶液流动速度越大,厚度越小,但其受入口溶液过饱和度的影响较小.     

Growth and characterization of KY(WO4)2 crystals

Single-crystal growth of KY(WO₄)₂ (KYW) by top-seeded solution growth technique has been investigated. The effects of seed orientation, temperature gradient experienced by the growing crystal and rate of crystallization on crystal quality are reported. The best results are obtained when the growth is seeded along the 0 1 0 direction. Minute deviations from this growth direction are found to be detrimental to crystal perfection. The differential thermal analysis shows that the amount of super-cooling required for dissolution and crystallization of KYW in the flux is only 5° and this promotes an easy formation of tiny crystallites in the solution. Consequently, the crystal rotation and the solution cooling rates are found to have pronounced effects on the growth of KYW crystal.     

Global simulation of a Czochralski furnace for silicon crystal growth against the assumed thermophysical properties

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite‐element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)