JPH05319974A - Production of crystal and production unit therefor - Google Patents
Production of crystal and production unit thereforInfo
- Publication number
- JPH05319974A JPH05319974A JP15560892A JP15560892A JPH05319974A JP H05319974 A JPH05319974 A JP H05319974A JP 15560892 A JP15560892 A JP 15560892A JP 15560892 A JP15560892 A JP 15560892A JP H05319974 A JPH05319974 A JP H05319974A
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- JP
- Japan
- Prior art keywords
- crystal
- solid
- liquid interface
- temperature distribution
- melt
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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- Crystals, And After-Treatments Of Crystals (AREA)
Abstract
Description
【０００１】[0001]
【産業上の利用分野】本発明は数値計算を用いた結晶製
造方法および結晶製造装置に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a crystal manufacturing method and a crystal manufacturing apparatus using numerical calculation.
【０００２】[0002]
【従来の技術】シミュレーション技術を結晶成長に応用
して、最適育成条件や製造炉の設計に役立てる試みが行
われている。代表的な文献としてはM.J.CROCHET, Journ
al ofCrystal Growth 97 (1989) 173等がある。一般
に、結晶成長において、欠陥の少ない高品質の結晶を得
るには固液界面の形状を適正に保つことが重要である。
従って、固液界面を計算機実験（シミュレーション）で
求める手法が種々検討されており、上記文献の研究者等
によっても試みられている。2. Description of the Related Art Attempts have been made to apply simulation techniques to crystal growth to utilize them for optimum growth conditions and manufacturing furnace design. MJCROCHET, Journ as a representative document
al ofCrystal Growth 97 (1989) 173 etc. Generally, in crystal growth, it is important to maintain the shape of the solid-liquid interface appropriately in order to obtain high-quality crystals with few defects.
Therefore, various methods for obtaining the solid-liquid interface by computer experiments (simulations) have been studied, and have been attempted by the researchers of the above literature.
【０００３】従来法の概略を以下に述べる。まず、結晶
製造装置、結晶、融液等を含む系全体を、有限要素法で
いうところの要素（メッシュ）に分割し、結晶製造装置
の温度分布に因って決まる成長結晶および融液が受ける
周辺温度環境（成長結晶および融液表面の温度分布）
を、熱伝導や輻射伝熱等を考慮しながら数値計算により
求める。The outline of the conventional method will be described below. First, the entire system including the crystal manufacturing apparatus, crystal, melt, etc. is divided into elements (mesh) in the finite element method, and the grown crystal and melt determined by the temperature distribution of the crystal manufacturing apparatus receive Ambient temperature environment (temperature distribution on grown crystal and melt surface)
Is calculated by taking into account heat conduction and radiative heat transfer.
【０００４】次に、求めた周辺温度環境下で固液界面形
状を仮定し、この形状で要素を分割し直す。結晶中にお
いては熱伝導方程式を解き、融液中においては流体の運
動方程式を解くようにし、さらに固液界面部では固化時
に発生する潜熱を考慮して計算し、固液界面に融液より
流入する熱流束と結晶側へ逃げる熱流束との差から、仮
定した固液界面形状よりも更に確からしい固液界面形状
を仮定し直す。Next, assuming a solid-liquid interface shape under the determined ambient temperature environment, the elements are redivided in this shape. Solve the heat conduction equation in the crystal, solve the fluid motion equation in the melt, and calculate in consideration of the latent heat generated at the solid-liquid interface at the time of solidification, and then flow from the melt to the solid-liquid interface. The solid-liquid interface shape that is more probable than the assumed solid-liquid interface shape is re-assumed from the difference between the heat flux that is generated and the heat flux that escapes to the crystal side.
【０００５】次に、この仮定し直した固液界面形状で要
素の分割を再度行い、同様の計算で更に確からしい固液
界面形状を求め直す。この計算を、セルフコンシステン
トになるまで、具体的には熱流束の差の面内分布が一様
になるまで繰り返し、固液界面形状を最終的に求める。
この方法により、固液界面形状以外にも結晶製造炉内の
温度分布や、融液の対流の様子などを同時に求めること
ができる。Next, the elements are divided again with this re-assumed solid-liquid interface shape, and a more probable solid-liquid interface shape is calculated again by the same calculation. This calculation is repeated until it becomes self-consistent, specifically, until the in-plane distribution of the heat flux difference becomes uniform, and the solid-liquid interface shape is finally obtained.
By this method, in addition to the solid-liquid interface shape, the temperature distribution in the crystal manufacturing furnace, the state of convection of the melt, and the like can be simultaneously obtained.
【０００６】こうした計算結果を詳細に分析し、また結
晶製造炉の様々な温度分布や結晶製造炉の様々な構造に
おいて上述の計算を行うことにより、知見を得て結晶品
質の向上や結晶製造炉の設計に役立てていると言うもの
であった。また、融液の対流がほとんど無視できる縦型
ブリッジマン法では、計算は融液中も熱伝導方程式で近
似してよく、計算時間も短いことから、結晶製造中に製
造装置の温度分布をモニターしながら固液界面形状と位
置を計算し、結晶製造をその場で制御するという方法も
あった。By analyzing these calculation results in detail and performing the above-mentioned calculations in various temperature distributions of the crystal manufacturing furnace and in various structures of the crystal manufacturing furnace, it is possible to obtain knowledge and improve the crystal quality and to improve the crystal manufacturing furnace. It was said to be useful for the design of. In addition, in the vertical Bridgman method in which the convection of the melt can be almost ignored, the calculation can be approximated by the heat conduction equation even in the melt, and the calculation time is short, so the temperature distribution of the manufacturing equipment can be monitored during crystal manufacture. However, there has also been a method of calculating the solid-liquid interface shape and position and controlling the crystal production on the spot.
【０００７】[0007]
【発明が解決しようとする課題】上記従来技術の問題点
としては以下のようなものがある。計算をセルフコンシ
ステントになるまで繰り返すため、計算に時間を要し、
結晶の製造に迅速にフィードバックをかけ難く、工業的
生産に不向きである。また計算に時間を要するため、結
晶製造中に固液界面形状等を求め、結晶製造装置の温度
分布にフィードバックをかけることがほぼ不可能であっ
た。The problems of the above-mentioned prior art are as follows. The calculation is repeated until it becomes self-consistent, so it takes time to calculate,
It is not suitable for industrial production because it is difficult to give quick feedback to the production of crystals. Further, since it takes time to calculate, it was almost impossible to obtain the solid-liquid interface shape and the like during the crystal production and to feed back the temperature distribution of the crystal production apparatus.
【０００８】計算を何度も繰り返すため、一回の計算に
よる計算誤差を繰り返しの回数だけ含み、このためいく
ら繰り返しても計算がセルフコンシステントに収束しな
い場合がしばしば有る。特に、固液界面形状に対して有
限要素法での要素の分割が不適切な場合に発生しやす
い。この、計算の発散に対応するために、非常に専門的
な計算ノウハウの必要が生じ汎用性に乏しい。Since the calculation is repeated many times, the calculation error due to one calculation is included only for the number of times of repetition, and therefore the calculation often does not converge to self-consistency. In particular, it tends to occur when the element division by the finite element method is inappropriate for the solid-liquid interface shape. In order to cope with this divergence of calculation, very specialized calculation know-how is required, and the versatility is poor.
【０００９】上記問題点は、融液対流が旺盛な結晶成長
方法では一層顕著になる。The above problems become more remarkable in the crystal growth method in which the melt convection is vigorous.
【００１０】また、上記以外に次のような問題点も挙げ
られる。数値計算により、結晶製造装置の温度分布から
結晶と融液の表面温度分布を求めたり、あるいは、逆に
結晶と融液の特定の表面温度分布を与える結晶製造装置
の温度分布状態を求める場合、数値計算では一般に非常
に複雑な結晶製造装置内を有限要素法の要素に分割した
り、複雑な構造の装置と結晶および融液間の熱伝達を計
算する必要があり、その計算にかかる労力、時間、計算
精度等に問題があった。In addition to the above, the following problems are also raised. By numerical calculation, or to obtain the surface temperature distribution of the crystal and the melt from the temperature distribution of the crystal manufacturing apparatus, or conversely, when obtaining the temperature distribution state of the crystal manufacturing apparatus that gives a specific surface temperature distribution of the crystal and the melt, In the numerical calculation, it is generally necessary to divide the inside of a very complicated crystal manufacturing device into elements of the finite element method, and to calculate the heat transfer between the device and the crystal and the melt of the complicated structure, and the labor required for the calculation, There was a problem in time and calculation accuracy.
【００１１】[0011]
【課題を解決するための手段】本発明は、前述の問題点
を解決するためになされたものであり、第１の発明とし
て、結晶成長が融液からの結晶成長でありかつ融液の移
動速度が固液界面の成長速度に比べ１０倍以上速い準定
常状態における結晶製造方法であって、結晶成長の複数
の段階における結晶製造装置の温度分布に対応した固液
界面形状の解を予め数値計算により求めておき、結晶製
造中において最適な固液界面形状に近い固液界面形状の
解に対応した結晶製造装置の前記各段階の温度分布が予
め設定されるように、前記温度分布を調整しつつ結晶成
長させることを特徴とする結晶製造方法を提供するもの
である。The present invention has been made to solve the above-mentioned problems, and as a first invention, crystal growth is crystal growth from a melt and movement of the melt. A method for producing a crystal in a quasi-steady state in which the speed is 10 times or more faster than the growth rate of the solid-liquid interface, and the solution of the shape of the solid-liquid interface corresponding to the temperature distribution of the crystal producing apparatus at multiple stages of crystal growth is numerically calculated in advance. The temperature distribution is adjusted so that the temperature distribution of each stage of the crystal production apparatus corresponding to the solution of the solid-liquid interface shape close to the optimum solid-liquid interface shape during crystal production is preset in advance by calculation. The present invention provides a method for producing a crystal, which is characterized in that the crystal is grown while being grown.
【００１２】第２の発明として、結晶成長が融液からの
結晶成長でありかつ融液の移動速度が固液界面の成長速
度に比べ１０倍以上速い準定常状態における結晶製造方
法であって、結晶製造中の結晶製造装置の温度分布をモ
ニターしつつ、前記温度分布に対応する固液界面形状の
解を数値計算により逐次求め、前記固液界面形状の解が
最適な固液界面形状に近づくように結晶製造装置の温度
分布を制御することを特徴とする結晶製造方法を提供す
るものである。A second invention is a method for producing a crystal in a quasi-steady state in which the crystal growth is from a melt and the moving speed of the melt is 10 times or more faster than the growth speed at the solid-liquid interface. While monitoring the temperature distribution of the crystal manufacturing apparatus during crystal production, the solution of the solid-liquid interface shape corresponding to the temperature distribution is sequentially obtained by numerical calculation, and the solution of the solid-liquid interface shape approaches the optimum solid-liquid interface shape. As described above, the present invention provides a crystal manufacturing method characterized by controlling the temperature distribution of the crystal manufacturing apparatus.
【００１３】第３の発明として、結晶成長が融液からの
結晶成長でありかつ融液の移動速度が固液界面の成長速
度に比べ１０倍以上速い準定常状態で結晶成長させるた
めの結晶製造装置であって、結晶成長の複数の段階にお
ける結晶製造装置の温度分布に対応した固液界面形状の
解を予め数値計算により求めておくコンピューターと、
結晶製造中において最適な固液界面形状に近い固液界面
形状の解に対応した結晶製造装置の前記各段階の温度分
布が予め設定されるように、前記温度分布を調整しつつ
結晶成長させる結晶製造装置の温度分布制御手段とを備
えてなることを特徴とする結晶製造装置を提供するもの
である。As a third aspect of the present invention, the crystal production is for crystal growth from a melt, and the crystal growth is performed in a quasi-steady state in which the moving speed of the melt is at least 10 times faster than the growth speed at the solid-liquid interface. A computer, which is a computer that preliminarily obtains a solution of the solid-liquid interface shape corresponding to the temperature distribution of the crystal manufacturing apparatus in a plurality of stages of crystal growth by numerical calculation,
A crystal that grows while adjusting the temperature distribution so that the temperature distribution of each stage of the crystal production apparatus corresponding to the solution of the solid-liquid interface shape close to the optimum solid-liquid interface shape during crystal production is preset. A crystal production apparatus comprising a temperature distribution control means of the production apparatus.
【００１４】第４の発明として、結晶成長が融液からの
結晶成長でありかつ融液の移動速度が固液界面の成長速
度に比べ１０倍以上速い準定常状態で結晶成長させるた
めの結晶製造装置であって、結晶製造中の結晶製造装置
の温度分布を検出する検出器と、検出された温度分布に
対応する固液界面形状の解を数値計算により逐次求める
コンピューターと、前記固液界面形状の解が最適な固液
界面形状に近づくように結晶製造装置の温度分布を制御
する結晶製造装置の温度分布制御手段とを備えてなるこ
とを特徴とする結晶製造装置を提供するものである。As a fourth invention, crystal production for crystal growth from a melt and crystal growth in a quasi-steady state in which the moving speed of the melt is at least 10 times faster than the growth speed at the solid-liquid interface. The apparatus is a detector for detecting the temperature distribution of the crystal production apparatus during crystal production, a computer for sequentially calculating the solution of the solid-liquid interface shape corresponding to the detected temperature distribution by numerical calculation, and the solid-liquid interface shape And a temperature distribution control means of the crystal manufacturing apparatus for controlling the temperature distribution of the crystal manufacturing apparatus so that the solution of (1) approaches an optimum solid-liquid interface shape.
【００１５】準定常状態における結晶成長とは、融液の
移動速度、特に固液界面から１０ｍｍ程度以内近傍の融
液の移動速度が固液界面の移動速度の１０倍以上の場合
をいうものであり、固液界面の変化が融液の移動速度に
比較して非常に緩やかな場合に相当する。例えば、ボー
ト法によるＧａＡｓ、ＩｎＰ等の３−５族化合物半導体
単結晶、ＺｎＳｅ等の２−６族化合物半導体単結晶の成
長過程、あるいは引き上げ法による前記３−５族、２−
６族化合物半導体単結晶およびＳｉ単結晶の成長過程、
他にはＬｉＮｂＯ3 、ＬｉＴａＯ3 、ＴｂＭｏＯ4 、Ａ
ｌ2 Ｏ3 等の酸化物結晶の成長過程がこれに相当し、本
発明方法および装置はそれら全ての結晶成長に適用でき
るものである。Crystal growth in the quasi-steady state means a case where the moving speed of the melt, especially the moving speed of the melt within about 10 mm from the solid-liquid interface is 10 times or more the moving speed of the solid-liquid interface. Yes, this corresponds to the case where the change in the solid-liquid interface is very gentle compared to the moving speed of the melt. For example, the growth process of a Group 3-5 compound semiconductor single crystal such as GaAs or InP by a boat method, a Group 2-6 compound semiconductor single crystal such as ZnSe, or the above-mentioned Group 3-5, 2 by a pulling method.
Growth process of Group 6 compound semiconductor single crystal and Si single crystal,
Others include LiNbO3, LiTaO3, TbMoO4, A
This corresponds to the growth process of oxide crystals such as l2 O3, and the method and apparatus of the present invention can be applied to the growth of all of them.
【００１６】本発明でいう最適な固液界面形状とは、従
来からの経験則によって見出されたものであり、ボート
内上部の方が下部よりも結晶化が進行している状態であ
り、傾斜したほぼ平面形状か、あるいは前記平面からわ
ずかに融液側に凸またはわずかに凹（極端な凹ではな
い）であるような形状である。The optimum solid-liquid interface shape referred to in the present invention has been found by a conventional empirical rule, and is a state in which the upper part in the boat is more crystallized than the lower part, It has a substantially plane shape that is inclined, or a shape that is slightly convex or slightly concave (not an extremely concave) from the plane to the melt side.
【００１７】本発明において、結晶製造装置の温度分布
制御手段は以下のような機構によって温度分布を制御す
る。一般的に、結晶製造装置は複数のヒーターゾーンを
持っており、それぞれのヒーターゾーンに印加する電力
を制御することで、結晶製造装置中の温度分布を制御す
ることができる。例えばヒーターゾーン毎に印加される
電力を増減すれば、温度分布のきめ細かい制御ができ
る。In the present invention, the temperature distribution control means of the crystal manufacturing apparatus controls the temperature distribution by the following mechanism. Generally, a crystal manufacturing apparatus has a plurality of heater zones, and the temperature distribution in the crystal manufacturing apparatus can be controlled by controlling the electric power applied to each heater zone. For example, the temperature distribution can be finely controlled by increasing or decreasing the power applied to each heater zone.
【００１８】従って、前記温度分布制御手段は、結晶製
造装置の複数のヒーターゾーンに入力される電力量の調
整装置、例えば各ヒーターゾーンへの入力線の抵抗を入
力線に接続された可変抵抗等により調節するような手
段、あるいは電源電圧をコントローラー等で直接調節す
るような手段等でよい。またその調節はコンピューター
等により入力データおよび専用のプログラムに基づいて
行ってもよい。また、固液界面形状を数値計算により求
めるコンピューターを用いて、前記調節を同時並列的に
実行させることもできる。Therefore, the temperature distribution control means is a device for adjusting the amount of electric power input to the plurality of heater zones of the crystal manufacturing apparatus, for example, a variable resistance connected to the input line for the resistance of the input line to each heater zone. Or a means for directly adjusting the power supply voltage with a controller or the like. The adjustment may be performed by a computer or the like based on input data and a dedicated program. Further, the adjustment can be simultaneously executed in parallel by using a computer that obtains the solid-liquid interface shape by numerical calculation.
【００１９】[0019]
【実施例】以下、本発明をボート法によるＧａＡｓ単結
晶の製造に適用した実施例に従って説明する。EXAMPLES The present invention will be described below with reference to examples in which the present invention is applied to the production of a GaAs single crystal by the boat method.
【００２０】まず、ボート法によるＧａＡｓ単結晶の製
造方法を、図９に基づいて説明する。図９において、１
は結晶成長のための温度分布を炉内に設定するヒータ
ー、２はアンプルを収納する炉芯管、３はボートを内蔵
する石英アンプル、４は結晶をその内部で成長させるた
めの石英ボート、５はＧａＡｓ融液、６はＧａＡｓ結
晶、７は結晶と融液との境界面であり結晶成長面でもあ
る固液界面である。First, a method of manufacturing a GaAs single crystal by the boat method will be described with reference to FIG. In FIG. 9, 1
Is a heater for setting the temperature distribution for crystal growth in the furnace, 2 is a furnace core tube for accommodating ampoules, 3 is a quartz ampoule with a built-in boat, 4 is a quartz boat for growing crystals therein, 5 Is a GaAs melt, 6 is a GaAs crystal, and 7 is a solid-liquid interface which is a boundary surface between the crystal and the melt and is also a crystal growth surface.
【００２１】ヒーター１で加熱された炉芯管２からの熱
により、石英アンプル３中に載置された石英ボート４中
のＧａＡｓ融液５と既に結晶成長したＧａＡｓ結晶６と
が加熱されている。ボート法によるＧａＡｓ単結晶の製
造において、高品質な結晶を得るためには、結晶製造中
の固液界面７の形状を好適にたもつことが重要であるこ
とは言うまでもない。固液界面７の形状を計算するのに
必要な熱境界条件は、石英ボート４の表面形状での温度
分布である。The heat from the furnace core tube 2 heated by the heater 1 heats the GaAs melt 5 in the quartz boat 4 mounted in the quartz ampoule 3 and the already grown GaAs crystal 6. .. Needless to say, it is important to have a suitable shape of the solid-liquid interface 7 during crystal production in order to obtain a high-quality crystal in the production of a GaAs single crystal by the boat method. The thermal boundary condition necessary for calculating the shape of the solid-liquid interface 7 is the temperature distribution in the surface shape of the quartz boat 4.
【００２２】この温度分布を得るには、従来例のように
結晶製造装置の温度分布から計算により求めることもで
きるが、製造装置の構造が複雑でかつ計算すべき系が大
きくなるため、分割要素数が膨大になり数値計算に膨大
な時間とコストを必要とすることになる。また、製造装
置を構成する様々な部品について、計算上物性値が必要
であるが、現在必要な物性値のすべてが知られているわ
けではない等の問題もある。In order to obtain this temperature distribution, it is possible to calculate it from the temperature distribution of the crystal manufacturing apparatus as in the conventional example, but since the structure of the manufacturing apparatus is complicated and the system to be calculated becomes large, the dividing element The number becomes enormous, and enormous time and cost are required for numerical calculation. Further, there is a problem in that physical property values are required in calculation for various parts constituting the manufacturing apparatus, but not all physical property values currently required are known.
【００２３】本実施例では、ダミー結晶ブロックを用い
た公知の手法（特開平２−２２９８２５号）により表面
温度を測定し、熱境界条件（結晶および融液表面の温度
分布）を求めた。図３に示した結晶製造に用いる炉内温
度分布（ヒーターの温度分布）の一例Ａ（図中符号１１
で表される温度分布）を用いて測定した熱境界条件の結
果を、図４に示す。ただし、図４はダミー結晶ブロック
の長手方向縦断面の外周温度を示している。上記の温度
条件で、ほぼＧａＡｓの融点（１２３８℃）を与える位
置近傍で、結晶成長方向にほぼ垂直に仮想的な固液界面
を想定する。次に、ボート形状全体（結晶と融液の全体
積）を図５に示すごとく要素に分割する。このとき、仮
想固液界面の近傍は、この固液界面形状にほぼ平行な要
素に分割することが数値計算上都合がよい。In this example, the surface temperature was measured by a known method using a dummy crystal block (JP-A-2-229825) to determine the thermal boundary conditions (temperature distribution on the surface of the crystal and the melt). An example of the temperature distribution in the furnace (temperature distribution of the heater) used in the crystal production shown in FIG.
FIG. 4 shows the results of the thermal boundary condition measured by using the temperature distribution represented by However, FIG. 4 shows the peripheral temperature of the longitudinal cross section of the dummy crystal block. Under the above temperature conditions, a virtual solid-liquid interface is assumed to be substantially perpendicular to the crystal growth direction in the vicinity of the position that gives the melting point of GaAs (1238 ° C.). Next, the entire boat shape (total volume of crystal and melt) is divided into elements as shown in FIG. At this time, it is convenient for numerical calculation to divide the vicinity of the virtual solid-liquid interface into elements substantially parallel to the solid-liquid interface shape.
【００２４】この仮想固液界面から低温側の結晶相当部
分では、下記数１で表される熱伝導方程式をコンピュー
ターを使って数値計算で解き、固液界面での要素につき
温度Ｔｉと、固液界面から一つ手前（結晶側）の要素の
温度Ｔｓを求める。In the portion corresponding to the crystal on the low temperature side from this virtual solid-liquid interface, the heat conduction equation represented by the following mathematical formula 1 is solved by numerical calculation using a computer, and the temperature Ti and the solid-liquid interface are calculated for each element at the solid-liquid interface. The temperature Ts of the element immediately before (on the crystal side) from the interface is obtained.
【００２５】[0025]
【数１】 [Equation 1]
【００２６】このＴｉからＴｓを引いた値を、この二点
間の固液界面に垂直な方向の距離で割り熱流束Ｑｓを求
める。同様に、前記仮想固液界面から高温側の融液相当
部分では、下記数２で表される流体の運動方程式をコン
ピューターを使って数値計算で解き、固液界面での要素
につき温度Ｔｉと、固液界面から一つ手前（融液側）の
要素の温度Ｔｌを求める。The value obtained by subtracting Ts from this Ti is divided by the distance in the direction perpendicular to the solid-liquid interface between these two points to obtain the heat flux Qs. Similarly, in the portion corresponding to the melt on the high temperature side from the virtual solid-liquid interface, the equation of motion of the fluid represented by the following equation 2 is solved by numerical calculation using a computer, and the temperature Ti per element at the solid-liquid interface, The temperature Tl of the element immediately before (melt side) from the solid-liquid interface is obtained.
【００２７】[0027]
【数２】 [Equation 2]
【００２８】このＴｌからＴｉを引いた値を、この二点
間の固液界面に垂直な方向の距離で割り熱流束Ｑｌを求
める。The value obtained by subtracting Ti from T1 is divided by the distance in the direction perpendicular to the solid-liquid interface between these two points to obtain the heat flux Ql.
【００２９】固液界面を境にして隣合ったＱｓ、Ｑｌに
ついて、結晶側へ逃げる単位時間当たりの熱量Ｑｓか
ら、融液から固液界面部分へ与える熱量Ｑｌを減じた値
Ｑｓ−Ｑｌを結晶固化潜熱で割ることにより、結晶成長
界面（固液界面）の成長速度ＧＲを計算することができ
る。これを固液界面を構成する要素全体について行うこ
とで、仮想的な固液界面から界面形状が移り変わってい
く形状を定性的に求めることができる。上記数値計算の
流れをまとめたフローチャートを図８に示す。For Qs and Ql adjacent to each other with the solid-liquid interface as a boundary, a value Qs-Ql obtained by subtracting the amount of heat Ql given to the solid-liquid interface from the melt from the amount of heat Qs escaping to the crystal side per unit time is crystallized. By dividing by the latent heat of solidification, the growth rate GR of the crystal growth interface (solid-liquid interface) can be calculated. By performing this for all the elements constituting the solid-liquid interface, it is possible to qualitatively obtain a shape in which the interface shape changes from the virtual solid-liquid interface. A flow chart summarizing the flow of the numerical calculation is shown in FIG.
【００３０】ところで、結晶固化潜熱は物質固有値であ
るからＱｓ−ＱｌはＧＲに比例し、Ｑｓ−Ｑｌの分布が
界面形状が移り変わっていく形状を定性的に表すことに
なる。図１は、前記結晶製造装置の温度分布の例Ａの場
合に、ダミー結晶ブロックの表面温度を測定し、これに
基づいて計算した固液界面におけるボートの長手方向縦
断面でのＱｓ−Ｑｌを示した。縦軸はボートの深さ方向
であり、横軸は熱流束の差である。Since the latent heat of solidification of crystallization is an intrinsic value of a substance, Qs-Ql is proportional to GR, and the distribution of Qs-Ql qualitatively represents a shape in which the interface shape changes. FIG. 1 shows Qs-Ql in the longitudinal cross section of the boat at the solid-liquid interface, which is calculated based on the measurement of the surface temperature of the dummy crystal block in the case of the temperature distribution example A of the crystal manufacturing apparatus. Indicated. The vertical axis is the depth direction of the boat, and the horizontal axis is the heat flux difference.
【００３１】熱流束の差が＋側ということは、仮想固液
界面（この場合は垂直断面）から結晶は成長する傾向に
あるということであり、その値が大きいということは成
長する傾向が強いあるいは成長速度が早いといえる。ま
た、熱流束の差が−側ということは、仮想固液界面（こ
の場合は垂直断面）から結晶が融ける傾向にあるという
ことであり、その絶対値が大きいということは融解する
傾向が強いといえる。すなわち温度分布Ａでは、固液界
面形状は中央部が激しく−になる傾向があることが分か
った。The fact that the difference in heat flux is on the + side means that the crystal tends to grow from the virtual solid-liquid interface (in this case, the vertical cross section), and the large value thereof means that the crystal tends to grow. Or it can be said that the growth rate is fast. Further, the fact that the difference in heat flux is on the-side means that the crystal tends to melt from the virtual solid-liquid interface (in this case, the vertical cross section), and the large absolute value means that the crystal tends to melt. I can say. That is, in the temperature distribution A, it was found that the shape of the solid-liquid interface tends to be severe in the central part.
【００３２】同様にして、図３に示す結晶製造装置の温
度分布の一例Ｂ（図中符号１２で表される温度分布）の
場合には、図２のようになり、固液界面形状は温度分布
Ａの場合よりは平坦になることがわかった。すなわち、
結晶製造装置の温度分布を図３の１１（Ａ）から１２
（Ｂ）へ変更すると、固液界面形状はより平坦になる傾
向があることが知見として得られた。Similarly, in the case of an example B (temperature distribution represented by reference numeral 12 in the figure) of the temperature distribution of the crystal manufacturing apparatus shown in FIG. 3, the result is as shown in FIG. It was found that the distribution was flatter than in the case of A. That is,
The temperature distribution of the crystal manufacturing apparatus can be changed from 11 (A) to 12 in FIG.
It was found as a finding that the solid-liquid interface shape tends to be flatter when changed to (B).
【００３３】ここで、以下に具体的実施例について説明
する。Specific examples will be described below.
【００３４】（実施例１）図９に示したボート法による
ＧａＡｓ単結晶の製造装置中に、石英アンプルの代わり
にダミー結晶ブロックを入れてその表面温度を測定し
た。次に結晶の成長段階を初期（結晶全長の０〜１／３
が結晶化）、中期（１／３〜２／３が結晶化）、後期
（２／３〜１が結晶化）の３段階に区分し、それぞれの
段階に相当するダミー結晶ブロックと結晶製造炉（ある
温度分布Ｔｃを設けている）の位置関係で、ダミー結晶
ブロックの表面温度分布を測定した。測定は熱電対をダ
ミー結晶ブロック表面に複数設けて行った。Example 1 A dummy crystal block was put in place of the quartz ampoule in the GaAs single crystal manufacturing apparatus by the boat method shown in FIG. 9, and the surface temperature was measured. Next, the initial stage of crystal growth (0-1 / 3 of the total crystal length)
Is crystallized), the middle stage (1/3 to 2/3 is crystallized), and the latter stage (2/3 to 1 is crystallized) are divided into three stages, a dummy crystal block and a crystal production furnace corresponding to each stage. The surface temperature distribution of the dummy crystal block was measured based on the positional relationship (providing a certain temperature distribution Tc). The measurement was performed by providing a plurality of thermocouples on the surface of the dummy crystal block.
【００３５】前記３段階のダミー結晶ブロックの表面温
度分布を、それぞれの熱境界条件として３段階の固液界
面形状を数値計算により算出する。これによると、初期
段階では固液界面が、上部の方が下部よりも結晶化が進
行した傾斜した平面から融液側に大きく凹となった形状
であり、後期段階ではほぼ前記傾斜した平面になってお
り、中期段階では初期と後期の中間的形状であった。The surface temperature distribution of the above-mentioned three-stage dummy crystal block is used as the respective thermal boundary conditions to calculate the three-stage solid-liquid interface shape by numerical calculation. According to this, in the initial stage, the solid-liquid interface has a shape in which the upper part is largely concave toward the melt side from the inclined plane where crystallization progressed more than the lower part, and in the latter stage it is almost the inclined plane. The shape was intermediate between the early and late stages in the middle stage.
【００３６】一般にボート法によるＧａＡｓ単結晶の製
造においては、固液界面形状は前記平面から凹となった
形状は好ましい形状とはいえず、結晶成長のどの時期に
おいても後期段階における平面に近い形状が好ましい。
そこで、再度前記初期に相当するダミー結晶ブロックと
製造炉の位置関係で、製造炉（複数のヒーターゾーン）
の温度分布を数種類変えて設定し、それらの各温度分布
においてダミー結晶ブロックの表面温度分布を測定し、
これらを熱境界条件として固液界面の解を数値計算で算
出する。Generally, in the production of a GaAs single crystal by the boat method, the shape of the solid-liquid interface which is concave from the above-mentioned plane cannot be said to be a preferable shape, and the shape close to the plane in the later stage at any stage of crystal growth. Is preferred.
Therefore, the manufacturing furnace (a plurality of heater zones) is again arranged in the positional relationship between the dummy crystal block corresponding to the initial stage and the manufacturing furnace.
The temperature distribution of the dummy crystal block is measured in each of these temperature distributions.
Using these as thermal boundary conditions, the solution at the solid-liquid interface is calculated by numerical calculation.
【００３７】上記数種類の製造炉の温度分布のうち、そ
の固液界面の解が最も前記傾斜した平面に近い条件Ｔａ
を選び出した。中期段階においても、上記初期段階の手
順と全く同様にして条件Ｔｂを選び出した。ここで、本
実施例の製造プロセスのフローチャートを図６に示し
た。Among the temperature distributions of the above-mentioned several kinds of manufacturing furnaces, the condition Ta where the solution of the solid-liquid interface is closest to the inclined plane is Ta.
I picked out. Also in the middle stage, the condition Tb was selected in exactly the same manner as the procedure in the initial stage. Here, a flow chart of the manufacturing process of this embodiment is shown in FIG.
【００３８】結晶の製造は条件Ｔａで開始し、結晶成長
が中期段階に達した時には条件Ｔｂに滑らかに移行する
ように、温度分布制御専用コンピューターにプログラム
しておく。製造炉の温度分布制御は、各ヒーターゾーン
の電力入力値を電源部のコントローラーおよびそれに接
続された温度分布制御専用コンピューターにより調節す
ることにより行った。また、同様に中期段階から後期段
階にかけては条件ＴｂからＴｃへ滑らかに移行するよう
にコントロールした。以上で結晶製造のプロセスは終了
する。The crystal production is started in the condition Ta, and is programmed in the temperature distribution control dedicated computer so that the crystal is smoothly transferred to the condition Tb when the crystal growth reaches the middle stage. The temperature distribution control of the manufacturing furnace was performed by adjusting the electric power input value of each heater zone by the controller of the power source section and the computer for temperature distribution control connected thereto. Further, similarly, control was performed so that the condition Tb smoothly transitions to Tc from the middle stage to the latter stage. This completes the crystal manufacturing process.
【００３９】上記のように温度分布の条件をＴａ、Ｔ
ｂ、Ｔｃの順に移行するように、あらかじめ温度分布制
御コンピューターに設定することにより、従来は結晶成
長の初期段階〜中期段階において固液界面形状不良（融
液側へ凹形状）によるリネージ等の結晶欠陥密度の増加
が見られていたのが、本実施例では結晶品質の改善がみ
られ結晶欠陥密度の小さい結晶が得られた。As described above, the temperature distribution conditions are Ta, T
By setting the temperature distribution control computer in advance so as to move in the order of b and Tc, conventionally, crystals such as lineage due to the solid-liquid interface shape defect (concave shape to the melt side) in the initial stage to the middle stage of crystal growth have been conventionally used. Although an increase in the defect density was observed, in this example, the crystal quality was improved and a crystal with a small crystal defect density was obtained.
【００４０】（実施例２）図９に示したボート法による
ＧａＡｓ単結晶の製造装置を用いる。本実施例の製造プ
ロセスのフローチャートを図７に示す。製造炉の温度分
布を、炉芯管２の外表面に長手方向に複数設けられた熱
電対（検出器）により温度を検出し、所定の温度分布に
なるようにヒーター１の入力電力を電源部に設定された
コントローラーおよびそれに接続される温度分布制御専
用コンピューターにより制御する。所定の温度分布Ｔｄ
に設定した後、結晶製造を開始する。(Embodiment 2) The apparatus for producing a GaAs single crystal by the boat method shown in FIG. 9 is used. FIG. 7 shows a flowchart of the manufacturing process of this embodiment. With respect to the temperature distribution of the manufacturing furnace, the temperature is detected by a plurality of thermocouples (detectors) provided in the longitudinal direction on the outer surface of the furnace core tube 2, and the input power of the heater 1 is supplied to the power source unit so that the temperature distribution becomes a predetermined temperature distribution. It is controlled by the controller set to and the temperature distribution control dedicated computer connected to it. Predetermined temperature distribution Td
After that, the crystal production is started.
【００４１】前記熱電対の検出温度により炉芯管２の温
度分布を検出でき、この温度分布を熱境界条件としてボ
ート表面（結晶と融液の表面）の温度分布を数値計算に
より算出する。次に、前記ボート表面の温度分布を熱境
界条件として炉芯管の温度分布Ｔｄに対する固液界面の
解を算出する。この固液界面の解がほぼ傾斜した平面
（最適な固液界面形状）であれば、製造炉およびボート
表面の温度分布は問題ないと判断し、そのまま結晶製造
を続行する。もし固液界面の解が最適な固液界面形状と
大きく相違する場合は、結晶成長を一時停止して（炉と
アンプルの相対移動を一時停止して）前記温度分布制御
専用コンピューターへの温度分布入力データを変更し製
造炉の温度分布を調整する。The temperature distribution of the furnace core tube 2 can be detected by the temperature detected by the thermocouple, and the temperature distribution on the boat surface (crystal and melt surface) is calculated by numerical calculation using this temperature distribution as a thermal boundary condition. Next, the solution at the solid-liquid interface with respect to the temperature distribution Td of the furnace core tube is calculated by using the temperature distribution on the boat surface as a thermal boundary condition. If the solution of the solid-liquid interface is a substantially inclined plane (optimal solid-liquid interface shape), it is determined that the temperature distribution on the surface of the production furnace and the boat is not a problem, and the crystal production is continued as it is. If the solution at the solid-liquid interface is significantly different from the optimal solid-liquid interface shape, the crystal growth is temporarily stopped (relative movement of the furnace and ampoule is temporarily stopped), and the temperature distribution to the temperature distribution control computer is distributed. Change the input data and adjust the temperature distribution in the manufacturing furnace.
【００４２】前記温度分布の良否判断は、数値計算で求
めた固液界面の解が、結晶上部の方が下部よりも結晶化
が進行している状態で融液側に対して凹になる形状であ
り、かつ固液界面の凹部に内接する円のうち最小の曲率
半径の円の選び出し、その半径が結晶の高さの１／４以
下の時は不良と判断し、温度分布を調整する。例えば、
図１の場合は温度分布不良であり、図２の場合は問題な
いものと判断する。一般に固液界面形状が、融液側に対
して凸になる形状は凹になる形状よりも好ましいものと
認められているが、固液界面の解が融液側に対して凸に
なる場合はほとんどなく、また実際の結晶成長でも凸に
なることはほとんどない。The quality of the temperature distribution is judged by the shape of the solution of the solid-liquid interface obtained by numerical calculation, in which the upper part of the crystal is concave with respect to the melt side in the state where crystallization is more advanced than the lower part. The circle having the smallest radius of curvature is selected from the circles inscribed in the concave portion of the solid-liquid interface, and when the radius is ¼ or less of the height of the crystal, it is determined as defective and the temperature distribution is adjusted. For example,
In the case of FIG. 1, it is determined that the temperature distribution is poor, and in the case of FIG. 2, there is no problem. It is generally accepted that the shape of a solid-liquid interface is convex toward the melt side is more preferable than the shape of a concave side. However, if the solution at the solid-liquid interface is convex toward the melt side, There is almost no such thing, and there is almost no convexity in actual crystal growth.
【００４３】次に、結晶成長の中期段階において上記と
同様にして固液界面の解を算出した。この時、固液界面
の解は最適な固液界面形状から融液側へ凹気味であり、
良好とはいえないため、一時結晶成長を停止した。この
状態で、炉芯管の温度分布を調整し直し、それに対応す
る固液界面の解を算出し最適な固液界面形状に最も近く
なる炉芯管の温度分布Ｔｅを探索する。次に、温度分布
制御専用コンピューターへの温度分布入力データの設定
値をＴｅに変更し、停止していた結晶成長を再開した。Next, in the middle stage of crystal growth, the solution at the solid-liquid interface was calculated in the same manner as above. At this time, the solution at the solid-liquid interface is concave from the optimum solid-liquid interface shape to the melt side,
Since it was not good, the crystal growth was temporarily stopped. In this state, the temperature distribution of the furnace core tube is readjusted, the solution of the solid-liquid interface corresponding thereto is calculated, and the temperature distribution Te of the furnace core tube that is closest to the optimum solid-liquid interface shape is searched. Next, the set value of the temperature distribution input data to the temperature distribution control dedicated computer was changed to Te, and the stopped crystal growth was restarted.
【００４４】その後、後期段階でも同様に固液界面の解
を算出したが、ほぼ最適な固液界面形状であり、炉芯管
の温度分布に問題ないと判断した。そのまま結晶製造は
終了した。本実施例においても結晶品質の改善がみられ
結晶欠陥密度の小さい結晶が得られた。After that, the solution of the solid-liquid interface was calculated in the same manner in the latter stage, but it was judged that the solution had an almost optimum solid-liquid interface shape and there was no problem in the temperature distribution of the furnace core tube. Crystal production was completed as it was. Also in this example, the crystal quality was improved and a crystal with a low crystal defect density was obtained.
【００４５】（比較例）ボート法によるＧａＡｓ単結晶
の製造において、従来の計算方法により固液界面形状を
計算した場合、計算時間が本発明の１０倍以上かかり、
結晶製造装置の温度分布と固液界面形状の相関関係が明
確に把握できるまでの時間が長く、結晶製造中に固液界
面形状に起因すると思われる欠陥が発生した場合、すぐ
に結晶製造へのフィードバックができず結晶品質の改善
が遅れた。さらに、時間が掛かるため結晶製造中に計算
を行いながらフィードバックをかけることができなかっ
た。(Comparative Example) In the production of a GaAs single crystal by the boat method, when the solid-liquid interface shape was calculated by the conventional calculation method, the calculation time was 10 times or more that of the present invention.
It takes a long time until the correlation between the temperature distribution of the crystal production equipment and the solid-liquid interface shape can be clearly grasped, and if a defect that seems to be due to the solid-liquid interface shape occurs during crystal production, the crystal production is immediately Feedback was not possible and the improvement of crystal quality was delayed. Furthermore, it was not possible to give feedback while making calculations during crystal production because it took time.
【００４６】また、しばしば繰り返し計算の途上で計算
が収束せず、振動状態（固液界面形状が計算の度に明ら
かに相違する複数の解群、例えば解Ｒ１群、解Ｒ２群の
間を行き来し、特定の解群に帰着しない）に陥ることが
あった。この場合、コンピューターの数値計算に熟練し
た専門家無しでは、計算を収束完了させることができな
くなるという事態が生じた。In addition, the calculation often does not converge in the course of iterative calculation, and the vibration state (a plurality of solution groups whose solid-liquid interface shapes are obviously different at each calculation, for example, a solution R1 group and a solution R2 group are traversed. However, it does not result in a specific solution group). In this case, the situation in which the calculation cannot be completed completely without the expert who is skilled in the numerical calculation of the computer occurred.
【００４７】さらに、鋭意努力することにより固液界面
形状を定量的に求めることができたが、実際の結晶製造
条件を改良するためには定量的な結果を求める必要性は
ほとんどなく、計算は無駄な努力が多かった。また、以
上のような定量的計算の煩雑さが予想されるため、少し
でも煩雑さを省略するために、結晶成長系を結晶長手方
向の中心軸に軸対象であると仮定することもできるが、
現実に起こっている現象は軸対象でない場合があり、こ
のような仮定自体が間違っている危険性を含んでいる。Further, although the solid-liquid interface shape could be quantitatively determined by diligent efforts, there is almost no need to obtain a quantitative result in order to improve the actual crystal production conditions, and the calculation is performed. There was a lot of wasted effort. Further, since the complexity of the quantitative calculation as described above is expected, in order to omit the complexity as much as possible, it is possible to assume that the crystal growth system is axially symmetric with respect to the central axis of the crystal longitudinal direction. ,
The phenomenon that is actually occurring may not be axially symmetrical, and there is a risk that such assumptions themselves are wrong.
【００４８】[0048]
【発明の効果】本発明によれば、特に数値計算に熟練し
た人でなくでも比較的容易に計算をあらゆる場合に実行
することができ、しかも短時間で温度分布と固液界面
（結晶成長界面）形状との定性的な関係を計算で把握す
ることができるため、結晶製造の際の好適な育成温度分
布や、好適な育成装置の設計等にすぐにフィードバック
をかけることができる。EFFECTS OF THE INVENTION According to the present invention, it is possible for a person who is not particularly skilled in numerical calculation to perform the calculation relatively easily in all cases, and the temperature distribution and the solid-liquid interface (crystal growth interface) can be obtained in a short time. ) Since the qualitative relationship with the shape can be grasped by calculation, it is possible to immediately give feedback to a suitable growth temperature distribution during crystal production, a suitable growth apparatus design, and the like.
【００４９】また、結晶育成中に温度分布をモニターし
ながら計算することで、より好適な固液界面形状を与え
る製造装置の温度分布を育成中に推定することができ、
その場で結晶成長を制御することができる。つまり、結
晶品質を育成中に短時間で改善していくことが可能であ
り、工業生産的価値は大きい。さらには、計算に用いた
り、製造装置の温度分布を設定したりする熱境界条件
（結晶および融液の表面温度分布）を、ダミー結晶ブロ
ックの表面温度の測定で与えることにより、製造装置の
温度分布から間接的に結晶および融液の表面温度分布を
求めるための膨大な計算を省略することができ、計算時
間、計算コスト面で工業的生産に有効である。Further, by performing the calculation while monitoring the temperature distribution during the crystal growth, the temperature distribution of the manufacturing apparatus which gives a more preferable solid-liquid interface shape can be estimated during the growth,
Crystal growth can be controlled in situ. In other words, it is possible to improve the crystal quality in a short time during the growth, and the industrial production value is great. In addition, the thermal boundary conditions (surface temperature distribution of the crystal and melt) used for calculation and setting the temperature distribution of the manufacturing equipment are given by measuring the surface temperature of the dummy crystal block, thereby It is possible to omit a huge calculation for indirectly obtaining the surface temperature distribution of the crystal and the melt from the distribution, which is effective for industrial production in terms of calculation time and calculation cost.
【図１】本発明の１実施例を示し、製造装置の温度分布
Ａにおいて計算により得られた固液界面付近の熱流束の
差を表すグラフ。FIG. 1 is a graph showing an embodiment of the present invention and showing a difference in heat flux near a solid-liquid interface obtained by calculation in a temperature distribution A of a manufacturing apparatus.
【図２】本発明のもう１つの実施例を示し、製造装置の
温度分布Ｂにおいて計算により得られた熱流束の差を表
すグラフ。FIG. 2 is a graph showing another embodiment of the present invention and showing the difference in heat flux obtained by calculation in the temperature distribution B of the manufacturing apparatus.
【図３】ボート法によるＧａＡｓ単結晶製造装置の温度
分布のグラフ。FIG. 3 is a graph of temperature distribution of a GaAs single crystal manufacturing apparatus by the boat method.
【図４】温度分布Ａにおけるダミー結晶ブロックの表面
温度分布を示す概念図。FIG. 4 is a conceptual diagram showing a surface temperature distribution of a dummy crystal block in a temperature distribution A.
【図５】ボート内結晶および融液の温度分布を有限要素
法で計算するための要素に分割した概念図。FIG. 5 is a conceptual diagram in which the temperature distributions of crystals in the boat and the melt are divided into elements for calculating by the finite element method.
【図６】本発明の１実施例を示し、数値計算を導入した
ＧａＡｓ単結晶製造プロセスのフローチャート。FIG. 6 is a flow chart of a GaAs single crystal manufacturing process in which numerical calculation is introduced, showing one embodiment of the present invention.
【図７】本発明のもう１の実施例を示し、数値計算を導
入したＧａＡｓ単結晶製造プロセスのフローチャート。FIG. 7 is a flow chart of a GaAs single crystal manufacturing process in which numerical calculation is introduced, showing another embodiment of the present invention.
【図８】本発明で用いる数値計算のフローチャート。FIG. 8 is a flowchart of numerical calculation used in the present invention.
【図９】はボート法によるＧａＡｓ単結晶製造装置。FIG. 9 is an apparatus for producing a GaAs single crystal by the boat method.
１：ヒーター ２：炉芯管 ３：石英アンプル ４：石英ボート ５：ＧａＡｓ融液 ６：ＧａＡｓ結晶 ７：固液界面 １１：製造装置の温度分布Ａ １２：製造装置の温度分布Ｂ ２１：仮想固液界面 1: Heater 2: Furnace core tube 3: Quartz ampoule 4: Quartz boat 5: GaAs melt 6: GaAs crystal 7: Solid-liquid interface 11: Temperature distribution of manufacturing equipment A 12: Temperature distribution of manufacturing equipment B 21: Virtual solid Liquid interface
───────────────────────────────────────────────────── フロントページの続き (72)発明者 西浜 二郎 神奈川県横浜市神奈川区羽沢町1150番地 旭硝子株式会社中央研究所内 (72)発明者 佐藤 誠 神奈川県横浜市神奈川区羽沢町松原1160番 地 エイ・ジー・テクノロジー株式会社内 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Jiro Nishihama, 1150 Hazawa-machi, Kanagawa-ku, Yokohama, Kanagawa Prefecture Central Research Laboratory, Asahi Glass Co., Ltd. (72) Makoto Sato, 1160, Matsubara, Hazawa-machi, Kanagawa-ku, Yokohama・ G-Tech Co., Ltd.
Claims (7)
融液の移動速度が固液界面の成長速度に比べ１０倍以上
速い準定常状態における結晶製造方法であって、結晶成
長の複数の段階における結晶製造装置の温度分布に対応
した固液界面形状の解を予め数値計算により求めてお
き、結晶製造中において最適な固液界面形状に近い固液
界面形状の解に対応した結晶製造装置の前記各段階の温
度分布が予め設定されるように、前記温度分布を調整し
つつ結晶成長させることを特徴とする結晶製造方法。1. A method for producing a crystal in a quasi-steady state in which the crystal growth is from a melt and the moving speed of the melt is 10 times or more faster than the growth speed of a solid-liquid interface, and a plurality of crystal growth methods are provided. The solution of the solid-liquid interface shape corresponding to the temperature distribution of the crystal manufacturing equipment at the stage of is calculated in advance by numerical calculation, and the crystal production corresponding to the solution of the solid-liquid interface shape that is close to the optimum solid-liquid interface shape during crystal production A crystal manufacturing method, wherein crystal growth is performed while adjusting the temperature distribution so that the temperature distribution at each of the stages of the apparatus is preset.
融液の移動速度が固液界面の成長速度に比べ１０倍以上
速い準定常状態における結晶製造方法であって、結晶製
造中の結晶製造装置の温度分布をモニターしつつ、前記
温度分布に対応する固液界面形状の解を数値計算により
逐次求め、前記固液界面形状の解が最適な固液界面形状
に近づくように結晶製造装置の温度分布を制御すること
を特徴とする結晶製造方法。2. A method for producing a crystal in a quasi-steady state in which the crystal growth is from a melt and the moving speed of the melt is 10 times or more faster than the growth speed at the solid-liquid interface, While monitoring the temperature distribution of the crystal production equipment, the solution of the solid-liquid interface shape corresponding to the temperature distribution is sequentially obtained by numerical calculation, and the crystal production is performed so that the solution of the solid-liquid interface shape approaches the optimum solid-liquid interface shape. A method for producing a crystal, which comprises controlling a temperature distribution of an apparatus.
液の表面温度分布の融点付近に結晶成長方向にほぼ垂直
な平面を設けこれを仮想固液界面とし、結晶と融液の全
体積を有限要素法に用いる要素に分割し、前記仮想固液
界面から融液側では、流体の運動方程式を結晶と融液の
熱境界条件から解いて仮想固液界面が融液側から受ける
熱流束Ｑｌを求め、前記仮想固液界面から結晶側では、
熱伝導方程式を結晶と融液の熱境界条件から解いて仮想
固液界面から結晶側へ逃げる熱流束Ｑｓを求め、２つの
熱流束の差Ｑｓ−Ｑｌを前記仮想固液界面全体に渡って
計算し、仮想固液界面形状からの変化量を求めて固液界
面形状の解を求める方法である請求項１または２記載の
結晶製造方法。3. The method of numerical calculation according to claim 1, wherein a plane substantially perpendicular to the crystal growth direction is provided near the melting point of the surface temperature distribution of the crystal under growth and the melt, and this is used as a virtual solid-liquid interface, and The total volume is divided into the elements used in the finite element method, and on the melt side from the virtual solid-liquid interface, the equation of motion of the fluid is solved from the thermal boundary condition of the crystal and the melt to receive the virtual solid-liquid interface from the melt side. The heat flux Ql is calculated, and on the crystal side from the virtual solid-liquid interface,
The heat flux Qs escaping from the virtual solid-liquid interface to the crystal side is obtained by solving the heat conduction equation from the thermal boundary condition between the crystal and the melt, and the difference Qs-Ql between the two heat fluxes is calculated over the entire virtual solid-liquid interface. 3. The method for producing a crystal according to claim 1 or 2, which is a method for obtaining a solution of the solid-liquid interface shape by obtaining the amount of change from the virtual solid-liquid interface shape.
は、結晶と融液の外形形状を模したダミー結晶ブロック
の表面温度分布の測定値で与えられる請求項３記載の結
晶製造方法。4. The crystal manufacturing method according to claim 3, wherein in the numerical calculation, the thermal boundary condition is given by a measured value of a surface temperature distribution of a dummy crystal block simulating the outer shapes of the crystal and the melt.
ブロックの表面温度分布を、最適な固液界面形状を与え
る結晶と融液の表面温度分布となるように、結晶製造装
置の温度分布の設定を調整する請求項４記載の結晶製造
方法。5. The temperature of the crystal manufacturing apparatus is adjusted so that the surface temperature distribution of the dummy crystal block simulating the outer shapes of the crystal and the melt becomes the surface temperature distribution of the crystal and the melt that gives the optimum solid-liquid interface shape. The crystal manufacturing method according to claim 4, wherein the setting of the distribution is adjusted.
融液の移動速度が固液界面の成長速度に比べ１０倍以上
速い準定常状態で結晶成長させるための結晶製造装置で
あって、結晶成長の複数の段階における結晶製造装置の
温度分布に対応した固液界面形状の解を予め数値計算に
より求めておくコンピューターと、結晶製造中において
最適な固液界面形状に近い固液界面形状の解に対応した
結晶製造装置の前記各段階の温度分布が予め設定される
ように、前記温度分布を調整しつつ結晶成長させる結晶
製造装置の温度分布制御手段とを備えてなることを特徴
とする結晶製造装置。6. A crystal production apparatus for growing crystals in a quasi-steady state in which the crystal growth is from a melt and the moving speed of the melt is 10 times or more faster than the growth speed of a solid-liquid interface. , A computer that preliminarily obtains a solution of the solid-liquid interface shape corresponding to the temperature distribution of the crystal manufacturing apparatus at multiple stages of crystal growth by numerical calculation, and a solid-liquid interface shape that is close to the optimum solid-liquid interface shape during crystal production In order to preset the temperature distribution of each stage of the crystal manufacturing apparatus corresponding to the solution of, the temperature distribution control means of the crystal manufacturing apparatus for crystal growth while adjusting the temperature distribution is provided. Crystal production equipment.
融液の移動速度が固液界面の成長速度に比べ１０倍以上
速い準定常状態で結晶成長させるための結晶製造装置で
あって結晶製造中の結晶製造装置の温度分布を検出する
検出器と、検出された温度分布に対応する固液界面形状
の解を数値計算により逐次求めるコンピューターと、前
記固液界面形状の解が最適な固液界面形状に近づくよう
に結晶製造装置の温度分布を制御する結晶製造装置の温
度分布制御手段とを備えてなることを特徴とする結晶製
造装置。7. A crystal manufacturing apparatus for growing crystals in a quasi-steady state in which the crystal growth is from a melt and the moving speed of the melt is 10 times or more faster than the growth speed at the solid-liquid interface. A detector that detects the temperature distribution of the crystal manufacturing apparatus during crystal production, a computer that sequentially calculates the solution of the solid-liquid interface shape corresponding to the detected temperature distribution by numerical calculation, and the solution of the solid-liquid interface shape is optimal. A crystal production apparatus, comprising: a temperature distribution control means of the crystal production apparatus for controlling the temperature distribution of the crystal production apparatus so as to approach the solid-liquid interface shape.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP15560892A JPH05319974A (en) | 1992-05-22 | 1992-05-22 | Production of crystal and production unit therefor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP15560892A JPH05319974A (en) | 1992-05-22 | 1992-05-22 | Production of crystal and production unit therefor |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH05319974A true JPH05319974A (en) | 1993-12-03 |
Family
ID=15609747
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP15560892A Withdrawn JPH05319974A (en) | 1992-05-22 | 1992-05-22 | Production of crystal and production unit therefor |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH05319974A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110139951A (en) * | 2017-01-05 | 2019-08-16 | 胜高股份有限公司 | Lifting condition calculation procedure, the modification method of the hot-zone of monocrystalline silicon and the breeding method of monocrystalline silicon of monocrystalline silicon |
-
1992
- 1992-05-22 JP JP15560892A patent/JPH05319974A/en not_active Withdrawn
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110139951A (en) * | 2017-01-05 | 2019-08-16 | 胜高股份有限公司 | Lifting condition calculation procedure, the modification method of the hot-zone of monocrystalline silicon and the breeding method of monocrystalline silicon of monocrystalline silicon |
| US10920339B2 (en) | 2017-01-05 | 2021-02-16 | Sumco Corporation | Silicon single crystal pulling condition calculation program, silicon single crystal hot zone improvement method, and silicon single crystal growing method |
| CN110139951B (en) * | 2017-01-05 | 2021-04-09 | 胜高股份有限公司 | Program for calculating pulling conditions of silicon single crystal, method for improving hot zone of silicon single crystal, and method for growing silicon single crystal |
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