晶体生长计算与模拟软件之FEMAG

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晶体生长模拟软件FEMAG之晶体生长各种方法

4) Lower LID effect, low feedstock requirements and higher yield.
FEMAGSoft © 2010
VB Growth Method
VB is widely used to grow Si/Ge and compound crystals: （待续）………………
t 1800 1740 1680 1620 1560 1500 1440 1380 1320 1260 1200 1140 1080 1020 960 900 840 780 720 660 600 540 480 420 360 300
2) Part of Germanium crystal grown by CZ method 3) Sappher and lots Compound crystal grown by CZ or its variants, such as Kyropoulos, LEC etc. 4) Market share of CZ wafer in solar market slightly lower than DSS mc wafer
It is assumed that for a certain region of the thermal stresses the crystal is in a metastable state, and a certain perturbation energy is necessary to leave this metastable state. By this model, it can be understood that the crystal can bear higher stresses than the critical values determined by a tensile test. Conforming to the classical idea of dislocation generation it starts somewhere near the growth interface, where the highest stresses are located and then grows deeper into the crystal. At these points of high stress level, the dislocation process may be started due to a perturbation energy resulting from:

晶体生长建模软件FEMAG-模拟策略

Direct dynamic
– calculated crystal shape – precribed heater power history – effect of pull rate and solid-liquid interface deformation on the solidification heat
• To resort to appropriate and up-to-date numerical simulation techniques to couple and solve these models
→ quasi-steady and dynamic models
FEMAGSoft © 2013
Inverse dynamic simulation (imposed crystal shape, calculated heater power): power oscillations resulting from inverse modeling, and smoothed power
FEMAGSoft © 2013
Stream function
psi 7.4E-05 7.1E-05 6.8E-05 6.5E-05 6.2E-05 5.8E-05 5.5E-05 5.2E-05 4.9E-05 4.6E-05 4.3E-05 4.0E-05 3.6E-05 3.3E-05 3.0E-05 2.7E-05 2.4E-05 2.1E-05 1.7E-05 1.4E-05 1.1E-05 8.0E-06 4.8E-06 1.7E-06 -1.5E-06 -4.7E-06
Quasi-steady
– thermal equilibrium – adapted heater power Inverse dynamic to get the prescribed – adapted heater power Quasi-dynamic crystal diameter to grow the prescribed frozen geometry – –heat source on the (except the crystal shape solid-liquid interface) solidification front in – effect of pull rate and to thepower pull to getsolid-liquid interface –proportion adapted heater rate the prescribed crystal diameter deformation on the – effect of pull rate and solid-solidification heat liquid interface deformation on the solidification heat

晶体生长计算软件FEMAG系列之晶体生长方法介绍

可扩展性
软件具有开放性和可扩展性，用户可以根据需要添加新的材料属性和边界条件。
图形界面
提供友好的图形界面，方便用户进行模型建立、参数设置和结果分析。
软件应用领域
半导体晶体生长
用于研究半导体晶体生长过程中的物理和化学行为，优化晶体质量和性能。
光学晶体生长
用于研究光学晶体的生长过程，优化晶体光学性能和加工工艺。
增强可视化功能
为了更好地帮助用户理解和分析计算结果，FEMag软件将增加更强大的可视化功能，如3D图形界面、实时渲染等，使用户能够更直观地查看和操作计算结果。
拓展应用领域和范围
扩大应用领域
随着晶体生长研究的不断发展，FEMag软件的应用领域将不断扩大。未来，FEMag软件将不仅应用于传统的晶体生长研究，还将拓展到其他相关领域，如材料科学、化学、生物学等。
该软件通过建立数学模型，模拟晶体生长过程中各种因素对晶体形态、结构和性能的影响。
FEMag软件提供了丰富的材料属性和边界条件设置，支持多种晶体结构和生长条件。
软件特点
01
02
03
04
高效计算
采用有限元方法进行数值计算，能够快速求解大规模的晶体生长问题。
精确模拟
能够模拟晶体生长过程中的温度场、浓度场、应力场等物理场，以及化学反应过程。
专业和深入。
与实验结果的比较
FEMag与实验的一致性
FEMag软件在模拟晶体生长方面取得了与实验结果高度一致的结果。通过对比实验和模拟数据，可以验证 FEMag软件的准确性和可靠性，进一步推动其在晶体生长研究中的应用。
实验验证的局限性
尽管FEMag软件与实验结果具有较好的一致性，但实验验证仍然存在局限性。实验条件和参数的微小变化可能会对结果产生显著影响，而模拟结果可能无法完全反映这些细微差异。因此，将实验和模拟结果相结合，进行综合分析是更为可靠的方法。

晶体生长仿真软件FEMAG介绍文档(二)--主要功能&技术优势

晶体生长仿真软件FEMAG介绍文档（二）主要功能&技术优势FEMAG软件致力于多物理场数值模拟分析晶体材料的生长过程，为用户提供晶体生长输运过程中的重要信息以及影响晶体质量的工艺信息，提高晶体质量与用户的研发效率。

目前，FEMAG软件产品有：FEMAG/CZ、FEMAG CZ/OX、FEMAG/FZ、FEMAG/DS、FEMAG/VB以及FEMAG/PVT，可有效分析提拉法生长、泡生法生长、区熔法生长、定向凝固、坩埚下降法生长、物理气相传输法生长等工艺过程。

FEMAG软件主要具有以下功能：（1）在设计工程领域，利用FEMAG软件可以设计生长熔炉系统中保温套和反射体的形状、材质和位置，可确定加热器的位置，设计辅助加热器，选择与设计保温层。

（2）在质量控制工程领域，利用FEMAG软件可以分析热应力、控制氧/碳含量分布、掺杂物分布以及缺陷的预测，优化工艺参数，提高晶体生长质量。

（3）在成本控制工程领域，利用FEMAG软件可以评估能耗、气耗，也可以评估原料辅料的成本与使用寿命。

FEMAG软件产品及其典型的应用如下图所示：FEMAG软件产品及其典型应用FEMAG软件的主要技术优势➢求解技术先进、高效，求解精度高晶体生长过程是一个高度非线性的、多尺度的复杂问题，涉及导热、对流、辐射与相变，空间尺度与时间尺度跨度范围大。

例如，熔体与气相的传热、传质，湍流，热辐射相互耦合作用，会显著影响晶体的缺陷形成；熔体与气相中存在扩散、粘性、辐射、热边界层，甚至伴有复杂的缺陷边界层，空间尺度跨度大；晶体生长的时间尺度一般慢于热传导时间尺度两个数量级，慢于对流传热时间尺度六个数量级，时间尺度跨度很大等等。

FEMAG软件通过建立考虑多种耦合效应的传热、湍流等全局有限元模型（包括准稳态模型、与时间相关的逆向动态、直接动态模型），基于非结构化网格而开发的Navier-Stokes求解器，结合Newton-Raphson迭代法，可以准确、快速地求解上述多场、多尺度的复杂问题。

利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图 ppt课件

利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图
利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图
• FEMAG软件是世界上第一款商业的材料晶体生长数值模拟软件，由比利时新鲁汶大学教授Dr. François Dupret于20世纪80年代中期领导开发。
• Dr. François Dupret是第二届晶体生长模型国际研讨会主席、EUROTHERM相变热力学研讨会联合主席、机械工程学位委员会主席，曾担任国际晶体生长（Journal of Crystal Growth）期刊主编。
• FEMAG软件拥有国际上最先进、最高效、最全面的晶体生长工艺模拟技术和多物理场耦合仿真功能，可模拟的晶体生长工艺包括提拉法（柴氏法，Cz 法）、泡生法（Ky法）、区熔法（FZ法）、坩埚下降法（垂直布里兹曼法， VB法）、物理气相传输法（PVT法）等，广泛应用于集成电路、太阳能光伏、半导体、蓝宝石等领域。ON Semiconductor（安森美半导体）、美国 Kayex、Siltronic（世创电子材料）、AXT（美国晶体技术集团）、韩国 Nexolon、LG、韩国汉阳大学、Norut（挪威北方研究所）、日本SUMCO集团、Gritek（有研新材料）、天津环欧半导体材料、中环股份、北京有色金属研究总院、清华大学等企业和科研机构，均是FEMAG软件的用户。
FEMAG定向凝固模拟软件用于设计新的热场，并研发新的方法以满足新的商业需求点，比如： ✓晶体微结构 ✓优化 ✓扩大生产规模
利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图
利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图
利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图
利用晶体生长计算软件FEMAG进行晶体生长计算仿真的结果图

全球半导体晶体生长仿真著名商业软件FEMAG--Optimization of Silicon Ingot Quality

全球半导体晶体生长仿真著名商业软件FEMAGOptimization of Silicon I n go t Q u al it yby the Numerical P r e d i c ti on of Bulk Crystal D e f ec t sF. Loix2*, F. D upr e t1,2*, A. de Potter2, R. R ol i n s ky2, W. L i a ng2, N. Van den B oga e rt21CESAME R e s e a r ch C e nt e r, Uni v e r s i téc at ho li que de L ouva i n,Bât i m e nt EULER, 4 av. Georges L e m aît r e,B-1348 Louva i n-l a-N e uv e,B e l g i um2FEMAGSoft S.A. Company, 7 Rue André Dumont, A x i s Parc, B-1435 Mont-Saint-Guibert, B e l g i umThe growth of S ili c on(Si) i ngot s by the Cz oc hra l s ki(Cz) technique for e l e c t roni c (IC) a ppl i c a t i ons has been governed for more than 50 years by two, somewhat c ont ra di c t ory, t e c hnol ogi c a l obj e c t i ve s.First, the c rys t a l diameter has to be nearly constant and the l a rge s t pos s i bl e according to current market requirements. Second, the product quality has to be pe rfe c t l y c ont rol l e d in terms of c rys t a l defects and composition. On the other hand, grow i ng Cz S i c rys t a l s for phot o-volt a i c(PV) a ppl i c a t i ons requires to m i ni m i z e both the energy c ons umpt i on and the growth dura t i on without, however, gene ra t i ng a too l a rge content of m i c ro-voi ds in the c rys t a l.A c hi e vi ng these goa l s i s by no means easy s i nc e i nc re a s i ng the c rys t a l diameter re qui re s a l a rge r m e l t volume and hence results in a much more complex m e l t flow regime with c om pl i c a t e d heat, momentum and s pe c i e s transport effects, a very s e ns i t i ve s ol i d-li qui d i nt e rfa c e shape (with a l e ss uniform t he rm a l gradient), and in gene ra l an enhanced dynamic s ys t e m behavior. A s i m il a r enhancement of the systemdyna m i c behavior can result from the use of a high pull rate to i nc re a s e the growth speed. Therefore, in gene ra l,de s i gni ng the furnace hot zone will require to i nt roduc e appropriate heat s hi e l ds in order to w e ll-c ont rol the ra di a t i on he a t transfer whi l e a s a t i s fa c t ory m e l t flow pattern can only be obt a i ne d for l a rge diameter c rys t a l s by the a c t i on of transverse or configured m a gne t i c fi e l ds.Moreover the s e l e c t i on of opt i m a l proc e ss parameters (heater power, c rys t a l pulling rate, c rys t a l and c ruc i bl e rot a t i on rates, m a gne t i c fi e l d i nt e ns i ty if any, ambient gas flow rate, etc.) becomes much more difficult in vi e w of the i nc re a s e d system nonl i ne a ri ty and t i m e-depe nde nc y,e s pe c i a ll y during the c ri t i c a l process stages (necking, shouldering, t a il-e nd stage, c rys t a l detachment, …).N one t he l e ss,compared to the high difficulty to address these different t e c hnol ogi c a l i ss ue s,it i s worth observing that huge progress has been achieved in the l a s t decades in s e ve ra l s c i e nt i fi c dom a i ns.F i r s t, the phys i c s of ra di a t i on and c onve c t i on in Cz furnaces, and of defect form a t i on and transport in growing S i c rys t a l s,i s much better known, and hence the m a t he m a t i c a l m ode l s governing Cz S i c ry s t a l growth are better and better e s t a bl i s he d.In spite of the i mport a nt i m prove m e n t s that re m a i n necessary in the m ode li ng of turbulence in the m e l t a nd the ambient gas (i nc l udi ng the m ode li ng of m e l t turbulence under the effect of a m a gne t i c fi e l d) and of the s t ill i ns uffi c i e nt kno w l e dge of the m a t e ri a l parameters governing point-and micro-defect e vol ut i on in S i s i ngl e c rys t a l s,an a l m os t complete picture of the phy s i c s of S i growth today i s a va il a bl e.Secondly, num e ri c a l methods and computers have a l s o quickly progre ss e d s i nc e the de ve l opm e n t ofthe first m ode l s of Cz growth achieved in the 1980’s. Nowadays the qua s i-s t ea dy or t i m e-depe nde nt s i m ul a t i on of the Cz process has become po ss i bl e in an a cc e pt a b l e c om put i ng t i m e,with s uffi c i e nt l y refined meshes to resolve the key de t a il s of the problem, and with appropriate num e ri c a l techniques to handle the system de form i ng ge om e try (which comprises s e ve ra l moving components together with free boundaries such as the m e l t-c rys t a l and m e l t-ga s i nt e rfa c e s).Therefore, having at one’s di s pos a l the appropriate phys i c a l m ode l s, num e ri c a l tools a nd computer hardware, the route i s directly opened to process opt i m i z a t i on by means of num e ri c a l s i m ul a t i on.The obj e c t i ve of the present paper i s to ill us t ra t e how this strategy can be a ppl i e d by use of the FEMAG-CZ software as today co-de ve l ope d by FEMAG Soft S.A. Company and the CESAME research center of the Uni ve rs i téde L ouva i n (Belgium).We will here focus on the S i ingot quality pre di c t i on and i t s opt i m i z a t i on.We present a fully t i m e-depe nde nt m ode l devoted to predict the gl oba l heat transfer in the furnace, the s ol i d-liquid i nt e rfa c e shape, and the re s ult i ng di s t ri but i ons of point-and m i c ro-de fe c t s as c a l c ul a t e d from the S i nno-D ornbe rge r (S-D) model together with an e xt e ns i on of the l um pe d model of Voronkov and Kulkarni. All the t ra ns i e nt s are c ons i de re d including the effects of c rys t a l a nd c ruc i bl e lift, of the heat c a pa c i t i e s of the furnace c ons t i t ue nt s, of the t he rm a l i ne rt i a of the s ol i di fi c a t i on front, and of the dyna m i c defect governing l a w s.We hence show that dynamic effects deeply affect the defect di s t ri but i on inthe c rys t a l(fig 1.). In a ddi t i on to the c l a ss i c a l point-defect e vol ut i on mechanisms, a new l um pe d m ode l i s de ve l ope d to c a l c ul a t e the form a t i on a nd growth of m i c ro-de fe c t s in order to predict their dens i t i e s and s i z e di s t ri but i ons anywhere in the c rys t a l.Another key i ss ue in Cz S i growth i s to control the dens i ty of oxygen and any other s pe c i e s(i nc l udi ng dopants and i m puri t i e s) i ns i de the c rys t a l.M ode li ng i ss ue s will be here a ga i n de t a il e d.Finally, off-line process control pri nc i pl e s will be addressed. Results will ill us t ra t e how this tool can he l p in opt i m i z i ng c rys t a l shape and quality.P r e di c t e d defect de l t a C i-C v di s t r i bu t i on(C i,C v be i ng the c onc e nt r at i on ofi n t e r s t i t i al s , v acan c i e re s p e c t i v e l y) with aquas i-s t e ady (a) and a t i m e-d e pendent （b）simulation. The OSF ring is located at theposition where delta~= 0. This picturehighlights the strong impact on the pointdefect of the transient effects in the growing crystal.。

晶体生长建模软件FEMAG介绍（八）--FEMAGPVT（物理气相传输法）

晶体⽣长建模软件FEMAG介绍（⼋）--FEMAGPVT（物理
⽓相传输法）
FEMAG/PVT软件的主要功能
FEMAG/PVT软件⽤于模拟物理⽓相传输法（Physical Vapor Transport process，PVT）晶体⽣长⼯艺，可以⽤于碳化硅单晶体、氮化铝、氧化锌多晶体等的PVT法⽣长⼯艺过程的模拟。

FEMAG/PVT软件的典型应⽤
FEMAG/PVT软件的典型应⽤是模拟碳化硅单晶的PVT法⽣长过程。

图1是碳化硅晶⽚。

碳化硅（SiC）是⼀种优质的宽带隙半导体材料，具有宽禁带、⾼击穿电场、⾼热导率、⾼饱和电⼦漂移速率等优点，可以满⾜⾼温、⼤功率、低损耗⼤直径器件的需求。

SiC单晶⽆法经过熔融法形成，⽽基于改进型Lely法的升华⽣长技术——物理⽓相传输法是获得SiC单晶的常⽤⽅法。

PVT法制备SiC单晶的⽣长原理是：⾼纯SiC粉源在⾼温下分解形成⽓态物质（主要为Si、SiC2、Si2C），这些⽓态物质在过饱和度的驱动下，升华⾄冷端的籽晶处进⾏⽣长。

过饱和度是由籽晶与粉源之间的温度梯度引起的。

图2是利⽤FEMAG/PVT软件计算碳化硅沉积腔内的温度梯度的结果。

晶体生长仿真软件FEMAG之Float Zone Process (FEMAG-FZ)

晶体生长仿真软件FEMAGFloat Zone Process (FEMAG-FZ)FEMAG区熔法软件（FEMAG-FZ）用于模拟区熔法生长工艺（FZ, PFZ）FEMAG区熔法软件专注于设计新的热场，并研发新的方法以满足新的商业需求点，比如：✓无缺陷晶锭生长✓提高成品率✓节省R&D成本FEMAG区熔法软件因为降低了试验成本而显著节省研发费用。

区熔法工艺的等温线预测无缺陷晶锭生长无缺陷晶体硅生长是世界上最大的难点之一。

FEMAG模拟软件能够帮助工程师运用自己独一无二的技术生长出无缺陷晶体。

半导体晶体缺陷决定了晶锭的市场价格。

通过FEMAG软件的缺陷工程模块，晶体生长行业工作者能够轻松预测晶体炉中生长的晶体质量。

缺陷工程模块能够洞悉硅、锗生长过程中填隙原子，空位和微孔演变过程。

FEMAG-FZ能够成为你的测试平台，试验在不同的操作条件下对于晶体生长质量的影响，如✓热场设计✓晶体和馈送棒的旋转速率✓晶体提拉速度，馈送棒的推送速度一旦研究出上述的依赖关系，就能够控制工艺过程，获得最理想而省时的晶体生长条件。

FEMAG预测区熔法生长晶体缺陷提高成品率您曾经考虑过是什么限制了您的晶体生长生产潜力以达到最大产量吗？您知道这些限制因素对产出的影响吗？FEMAG区熔法模拟软件可以帮助您在晶体生长过程的每一个时刻追踪关键参数的变化。

区熔法模拟软件为工程师们提供了在晶体生长过程中凝固前沿形状，热弹性应力，溶体流动形态等信息。

FEMAG FZ模块的用户可以通过上述的参数信息优化其工艺条件，从而增加凝固生产效率和产出。

节省R&D成本FEMAG区熔法模拟软件能够降低您的研发成本，区熔法生长的领先用户擅于使用FZ模拟软件来减少实验成本并增加投资回报。

这些模拟工作旨在复现固液界面的实验结果，并将数值模拟的结果与晶锭的光扫描观测结果进行对照。

模拟晶体转速对熔体流动的影响。

晶体生长模拟软件FEMAG-CZ之-Czochralski-(CZ)-Process-(FEMAG-

晶体生长模拟软件FEMAG-CZ Czochralski (CZ) Process（FEMAG-CZ）FEMAG直拉法模拟软件（FEMAG-CZ）用于模拟直拉法工艺（包括Cz, MCz, VCz,泡生法）。

FEMAG-CZ直拉法模拟软件用于新的热场设计，并研发新的方法以满足新的商业需求点，比如：✓大直径晶锭生长✓无缺陷硅晶锭生长✓提高成品率✓氧含量控制✓降低碳含量✓晶锭半径和沿轴向的电阻率差异减小✓CCZ工艺仿真✓磁场设计✓蓝宝石生长工艺设计FEMAG-CZ模拟软件通过降低试验成本而节省了R&D消耗。

大直径晶锭生长以期不进行大量昂贵的可行性试验生长大尺寸晶体看起来是不太现实的。

FEMAG-CZ软件提供这种可能性。

为了生产450 mm及以上的大尺寸无缺陷硅晶体，晶体生长工程师通过使用FEMAG-CZ来定义关键的工艺参数，而无需任何材料和能源的消耗。

FEMAG-CZ能够设计新的热场并研发新的工艺技术，在FEMAG直拉法模拟软件的帮助下，晶体生长工程师能够在一个有效的虚拟环境中优化每一个关键参数，比如旋转速率，提拉速度，气体流速，压强和功率消耗等。

FEMAG直拉法模拟还能进一步为晶体生长工程师给出在某一工艺配置下产出的最终成品的质量和成本信息，比如晶体中的温度梯度，氧/碳/掺杂物/微缺陷分布等。

通过软件能够获得硅/锗/蓝宝石晶体质量和产品成本信息，这一模拟过程无需任何材料和能量的消耗。

FEMAG 3D 熔体流动模拟结果FEMAG动态模拟无缺陷硅晶锭生长无缺陷晶体硅生长是世界上最大的难点之一。

FEMAG模拟软件能够帮助工程师运用自己创新的技术生长出无缺陷晶体。

运用FEMAG软件缺陷工程模块可以预测晶体炉或者其他指定直拉法工艺环境中生长的晶体成品质量。

缺陷工程模块能够洞悉硅、锗生长过程中填隙原子，空位和微孔演变过程。

FEMAG-CZ能够成为你的测试平台，试验在不同的操作条件下对晶体生长质量的影响，如✓热场设计✓加热器功率✓晶体和坩埚的旋转速率✓晶体提拉速度，坩埚的位置✓气体流率和压强一旦掌握了晶体生长工艺中的动态规律，就可以找到最优的配置以增加成品率和投资回报。

晶体生长计算软件FEMAG浮区法生长晶体方法

FEMAGSoft © 2011
2. A global simulation tool (cont’d)
Induction Heating in FZ semi-conductor growth
Conduct or
d B
Dissipated power:
Force density:
Alternating magnetic field effects : 1) Heat flux
1. Introduction 2. Global simulation tool
3. Simulation examples
4. Discussion
FEMAGSoft © 2011
2. A global simulation tool
Typical FEMAG-FZ global unstructured mesh for heat transfer and induction heating
FEMAGSoft © 2011
2. A global simulation tool (cont’d)
Prediction of Crystal Defects
FEMAGSoft © 2011
2. A global simulation tool (cont’d)
Quasi-steady simulation of the growth of a 100 mm silicon crystal
Growth of a 100 mm silicon crystal
(1mm/min pull rate) Predicted defect delta -(CI-CV) distribution by means of a quasi-steady simulation

晶体生长模拟软件FEMAG之_Czochralski Crystal Growth Simulation by FEMAGSoft

晶体生长模拟软件FEMAG-CZ之Czochralski Crystal Growth Simulation byFEMAGSoftFEMAG-CZ is a global crystal growth simulation software taking into account the furnace geometry, the materials and the operating conditions in order to provide the user with all the information required for his process development and optimization.Global heat transfer, Thermo-elastic stresses, Defect prediction, Melt flow and Heater power.Features∙»Evolution of the solid/liquid interface shape (dynamic simulation)∙»Thermal gradients in the liquid and solid phase∙»Heat fluxes in the overall furnace∙»Thermal-stresses in the crystal and hotzone components∙»Continuous feeding∙»Species (dopants and impurities) segregation and concentration∙»Magnetic fieldsSupported Languages:EnglishSupported TechnologiesOperating Systems:LinuxProgramming Languages:C/C++Product Type(s):SoftwareAdditional Product InformationFEMAG family products provide so-called ''global calculations'' , meaning that all the constituents of the furnace are taken into account, together with all heat transfer modes within and between them (conduction, convection and radiation).The modelling of conduction includes the possibility of temperature-dependent and anisotropic conductivity. The modelling of radiative heat exchanges assumes diffuse radiation and can take into account semi-transparent materials through wavelength-dependent radiative properties.The flow in the melt phase can be modelized by a laminar and/or turbulent model. It takes into account natural convection, due to temperature-dependent density and surface tension, and forced convection due to crystal, crucible and/or polycrystal - in case of the FZ process - rotations, possibly under the influence of a magnetic field (axial, cusp, rotating or transverse). Melt flow calculation also considers the effect of gas flow and of tangential forces due to induction (if any) on melt surface.The flow in the gas phase, as a result of an imposed flow rate at gas inlet and of temperature-dependent density, can be modelized by a laminar or a turbulent model.The heating of the process is modelized: ohmic heaters (one or several, coupled or independent) or inductors. In the case of multiple heaters, the user has the possibility to control the heating powers by imposing a specific temperature at given control points.The shapes of interfaces and free-surfaces of the system are calculated. The solidification front and melting front - in case of the FZ process - shapes are calculated taking into account heat dissipation (or absorption) proportional to the growth rate. The melt/gas interface is calculated, as a result of a balance of surface tension, gravity and normal forces due to induction (for the FZ process), providing an accurate meniscus shape.The processes can be modelized by a quasi-steady or by a time-dependent model. The quasi-steady model takes into account the effect of growth rate on heat transfer while assuming a fixed position for all constituents. The time-dependent model considers a geometry that evolves due to crystal lengthening and melt shrinking. It also takes into account the transient effects due to the thermal inertia of all constituents, and due to the inertia of the solidification front shape.Global heat transfer. Temperature isolines are separated by 50 K.。