Analysis of the diameteral response of a czochralski crystal II. The melt temperature — furnace temperature relation

The paper is the second in a series which presentes results on the small-signal diametral response of a Czochralski crystal grown in a resistively heated furnace to variations in heater temperature and pull rate. Here it is shown that the small-signal bulk melt temperature variation is related to the small-signal furnace temperature variation via a first order linear differential equation.     

Process design for the shape control of crystals grown by Kyropoulos or SAPMAC method

A mathematical model has been proposed to design the process for growing a shaped crystals by Kyropoulos method or SAPMAC method. Crystal shape evolution behaviours under various processes were analysed. The results show that the crystal would go through a transitory shoulder‐expanding stage after which the crystal diameter rapidly decreases under a constant pulling rate and a constant heater temperature. Reducing pulling rate and heater temperature could depress the decrease of crystal diameter after the shoulder‐expanding stage so that enhance the length of crystal. However, the crystal diameter is more sensitive to pulling rate than to heater temperature, and an equal‐diameter crystal can not be grown in non‐undercooled melt by soley reducing the heater temperature. That means that adjusting the pulling rate is the most effective and convenient approach for controlling crystal diameter evolution and simultaneously decreasing both the pulling rate and the heater temperature is the optimal process for growing an equal‐diameter crystal. Moreover, a numerical approach for quantifactional designing crystal shape and corresponding growth processes was proposed according to the model, an example of crystal shape design was given out. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the Diametral Response of a Czochralski Crystal (III) Solution of the Equation Set. Transfer Functions

The paper is the third in a series which presents results on the small-signal diametral response of a Czochralski crystal grown in a resistively heated furnace to variations in heater temperature and pull rate. For typical growth conditions and a wide range of materials it has been shown that this response is obtained by solving a set of linear differential equations. Conditions for normal response, i.e. the diameter increasing on heater temperature and/or pull rate decrease, have been established and shown to hold for most practical cases. The transfer function obtained is consistent with previous results for an inductively heated growth apparatus.     

声光晶体TeO2的生长及缺陷研究

本文研究了直接ＴeO２晶体中的主要晶体缺陷形成机理,讨论分析了Ｔ eO2单晶生长的工艺参数对晶体缺陷的影响,结果表明：晶体裂缝的主要与温度梯度有关,温度梯度大于２０－２５℃/cm及出现界面翻转时,易造成晶全的开裂,位错密度增加,晶体中的包裹体主要为气态包裹全,它的形成主要与籽晶的转速和晶体的提拉速率有关,转速１５－１８r/min,拉速０.55mm/h,固液界面微凹,可以减少晶体中的气态包裹体,晶体台阶由晶体生长过程中温度和生长速度的引起伏引起,当台阶间距较宽时,易形成包裹体。     

A novel method of temperature control for a crystal growth puller

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.     

Growth of SiGe bulk crystals with uniform composition by utilizing feedback control system of the crystal–melt interface position for precise control of the growth temperature

We developed an automatic feedback control system of the crystal–melt interface position to keep the temperature at the interface constant during growth, and demonstrate its successful application to grow Ge-rich SiGe bulk crystals with uniform composition. In this system, the position of the crystal–melt interface was automatically detected by analyzing the images captured using in situ monitoring system based on charge-coupled-devices camera, and the pulling rate of the crucible was corrected at every 1 min. The system was found to be effective to keep the crystal–melt interface position during growth even when the variation of the growth rate is quite large. Especially, the interface position was kept for 470 h during growth of Ge-rich SiGe bulk crystal when we started with a long growth melt of 80 mm. As a result, a 23 mm-long Si_0.22Ge_0.78 bulk crystal with uniform composition was obtained thanks to the constancy of the growth temperature during growth through the control of the interface position. Our technique opens a possibility to put multicomponent bulk crystal in a practical use.     

Compositional variation in Si-rich SiGe single crystals grown by multi-component zone melting method using Si seed and source crystals

The effect of the supply of depleted Si solute elements on the compositional variation in the Si-rich SiGe bulk crystals was studied using the method which was used to grow Ge-rich SiGe single crystals with a uniform composition. By selecting the proper pulling rate, we can obtain Si-rich Si_1−xGe_x bulk crystals with uniform composition of x=0.1 without using the supply mechanism of depleted Si solute elements. When the supply mechanism of Si solute elements was used, the initial composition in Si-rich SiGe crystals can be much more easily determined by controlling the growth temperature than that in Ge-rich crystals because the Si seed crystal is not melted down. The supply of Si solute elements is very effective to change the compositional variation even for Si-rich SiGe crystals.     

Effects of growth rates on the defect generation in KCl crystals grown by the czochralski method

The effects of the growth rates on the perfection of KCl crystals grown by the Czochralski method were investigated in the range of the pulling rate from 1 to 27.3 mm/hr using the etch pit method. It was found that the density of random dislocation within subgrains was almost independent on the pulling rate but the length of subboundaries in the unit area was decreased with an increase of the pulling rate. The shape of the solid-liquid interface changed from convex towards the melt to flat with an increase of the pulling rates. It was found that the leading factor in producing subboundaries is the shape of the solid-liquid interface, and that the pulling rate alone does not always determine the perfection.     

Crystallization Rate Behaviour under Change of Czochralski Growth System Parameters

A comparative analysis of growth system parameters' (pulling rate, melt temperature and crucible position or melt level) change influence on crystallization rate in Czochralski growth system is represented.     

Crystal growth of β-Phthalocyanines from the vapour phase in closed ampoules

An influence of temperature gradient, inert gas pressure and pulling rate on the growth parameters of β-phthalocyanine single crystals grown in the closed ampoules is investigated. The morphology and structure — sensitive properties of β-CuPc crystals grown under different conditions are compared.     

Mechanism for generating interstitial atoms by thermal stress during silicon crystal growth

It has been known that, in growing silicon from melts, vacancies (Vs) predominantly exist in crystals obtained by high-rate growth, while interstitial atoms (Is) predominantly exist in crystals obtained by low-rate growth. To reveal the cause, the temperature distributions in growing crystal surfaces were measured. From this result, it was presumed that the high-rate growth causes a small temperature gradient between the growth interface and the interior of the crystal; in contrast, the low-rate growth causes a large temperature gradient between the growth interface and the interior of the crystal. However, this presumption is opposite to the commonly-accepted notion in melt growth. In order to experimentally demonstrate that the low-rate growth increases the temperature gradient and consequently generates Is, crystals were filled with vacancies by the high-rate growth, and then the pulling was stopped as the extreme condition of the low-rate growth. Nevertheless, the crystals continued to grow spontaneously after the pulling was stopped. Hence, simultaneously with the pulling-stop, the temperature of the melts was increased to melt the spontaneously grown portions, so that the diameters were restored to sizes at the moment of pulling-stop. Then, the crystals were cooled as the cooling time elapsed, and the temperature gradient in the crystals was increased. By using X-ray topographs before and after oxygen precipitation in combination with a minority carrier lifetime distribution, a time-dependent change in the defect type distribution was successfully observed in a three-dimensional manner from the growth interface to the low-temperature portion where the cooling progressed. This result revealed that Vs are uniformly introduced in a grown crystal regardless of the pulling rate as long as the growth continues, and the Vs agglomerate as a void and remain in the crystal, unless recombined with Is. On the other hand, Is are generated only in a region where the temperature gradient is large by low-rate growth. In particular, the generation starts near the peripheral portion in the vicinity of the solid–liquid interface. First, the generated Is are recombined with Vs introduced into the growth interface, so that a recombination region is always formed which is regarded as substantially defect free. Excessively generated Is after the recombination agglomerate and form a dislocation loop region. Unlike conventional Voronkov's diffusion model, Is hardly diffuse over a long distance. Is are generated by re-heating after growth.[In a steady state, the crystal growth rate is synonymous with the pulling rate. Meanwhile, when an atypical operation is performed, the pulling rate is specifically used.]This review on point defects formation intends to contribute further silicon crystals development, because electronic devices are aimed to have finer structures, and there is a demand for more perfect crystals with controlled point defects.     

On the dependence of the critical crystallization rate on the initial impurity concentration in melt

The dependence of the critical crystallization rate on the initial impurity concentration in melt is derived by determining the condition at which a nonplanar solution to the stationary diffusion problem arises. It is suggested that the conditions at which defects arise at the interface differ from those obtained when crystallization becomes stationary. The initial transient process of binary melt solidification under crystal pulling at a constant rate has been studied numerically within a 1D model. It is shown that the character of the time dependence of the crystallization rate is determined by the ratio of the crystal pulling rate to solidification rate V _c, when a constitutional supercooling zone is formed in the melt.     

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.     

On the void distribution and size in shaped sapphire crystals

Ribbon and rod sapphire pulling has been performed in three different crystal growth equipments in order to study the effect of the installation, of the atmosphere, of the die shape, of the feed material and of the pulling rate on the distribution, number and diameter of the characteristic voids (micro‐bubbles) in the crystals. The location of the bubbles in the crystals depends on the die geometry; however, in most cases they are essentially located close to the crystal periphery and then can be efficiently removed by lapping. After statistical analysis of the results, it is demonstrated that the number of gas moles incorporated in the crystals, inside the voids, is totally independent of any growth parameter. It is also shown that the bubble diameter depends only on the pulling rate. Consequently, for a given pulling rate, the number of bubbles auto‐adjusts in order to satisfy the constant molar gas incorporation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CZ法生长参数对TeO2晶体质量的影响

本文主要讨论CZ法生长TeO2晶体中温度梯度、拉速、转速等工艺参数对晶体质量的影响,分析了晶体开裂、包裹物等宏观缺陷以及位错等微观缺陷的形成机理.从晶体形态、包裹体和位错密度变化等方面探讨了晶体生长参数与晶体缺陷之间的内在关系.     

Working point of the EFG process

A theoretical investigation of the EFG process working point based on the meniscus height control is carried out. The link between the two control parameters, which are the pulling rate and the upper die temperature, is found from the thermal equilibrium at the crystallization interface. Using the pressure equilibrium in the film and considering the meniscus shape, the change in meniscus height depending on the crystal radius is analyzed. Limited to small crystal radii, an algebraic formulation of the temperature gradient at the interface is established. Some die design parameters are taken into account and their impacts on the process working point are discussed.     

Dynamik der Phasengrenze beim Ziehen von Kupfereinkristallen aus der Schmelze

During growth of copper crystals by pulling out of the melt the height of the phase boundary has been studied as a function of melt temperature and after sudden changes of pulling speed and temperature. The phase boundary always reaches a new stable position after a change of the parameters with time constants between 20 and 120 s. The behaviour can be described by a model of the heat balance at the phase boundary. According to this model the temperature gradient in the melt below the boundary is 17 degrees/cm in vacuum and 50 degrees/cm in 760 Torr hydrogen gas.     

激光晶体提拉生长模糊PID控制系统

本文设计了基于ARM Cortex-M3核、针对上称重法激光晶体的生长的控制方案硬件平台,运用模糊PID自适应控制算法对称重信号进行模糊处理确定晶体生长瞬间所需的温度场,根据生长模型在理论上进行了仿真,并实际运用到TDL-J50型激光单晶炉设备,实现了激光晶体的瞬时生长速率的精确而平稳的自动控制.     

On the Iso‐Diameter Growth of β ‐BaB2O4 (BBO) Crystals by Flux Pulling Method

The iso‐diameter growth of β ‐BaB₂O₄ (BBO) crystals by the flux pulling method have been studied based on the phase equilibrium diagram in the BaB₂O₄‐Na₂O pseudo‐binary system and from the interface stability. The mathematical expressions for the cooling rate in the growth of the crystals with constant diameter under stable growth conditions are derived, the experimental phenomena such as diameter contraction and difficulty to grow a lengthy crystal by the flux pulling method are explained, the prerequisite for iso‐diameter BBO crystal growth from the flux is suggested; a new continuous charging flux pulling method is introduced to grow large‐sized high quality crystals with a relative high growth rate.     

φ200mm蓝宝石晶体生长工艺研究

采用单晶提拉炉成功生长出φ200mm ×180mm大尺寸Al2O3晶体.探讨了晶体生长工艺参数和晶体开裂之间的关系,并讨论了晶体中的热应力、热应变、温度梯度、提拉速度之间的关系,分析了影响晶体质量主要是晶体开裂的原因,设计出生长大尺寸Al2O3晶体的最佳工艺条件.