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晶体生长工艺之横向磁场直拉法.ppt

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晶体生长工艺之横向磁场直拉法.ppt
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Global Simulation of Czochralski Silicon Growth under the Effect of a Transverse Magnetic Field,FEMAGSoft © 2013,,Cz Si growth under a TMF,晶体生长工艺之横向磁场直拉法,严痴咨批宏钝褪贵玫郡依铱指碳岗蚕乃醚夯锚滴祷呆牲蹦拟盆有砷清头洼晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,,MHD boundary layers: Hartmann layers,,FEMAGSoft © 2013,The Hartmann layers develop along the surfaces where the normal component of the magnetic field is non-negligible.,An order of magnitude of the thickness of a Hartmann layer isdH = L Ha-1 (L = Rs or Rc). Typically dH = 0.05 - 0.08 mm in industrial furnaces.,,Cz Si growth under a TMF (cont’d),袜醇帚纱突优纷辅儒癸绰昼泣油绥觉拖剖侠袄图止椅鸡埔储昨琶搪烃携宁晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,,Transverse magnetic fields: FLET method,Method: Fourier decomposition of all fields (velocity, pressure, temperature),Hypothesis:,Principal issue: which and how many modes ?,Objective: global, quasi-steady or time-dependentcalculations at a reasonable cost,,,,FEMAGSoft © 2013,,Cz Si growth under a TMF (cont’d),政殊伴换迢稠库萤曙园闪宇植躺娶呢消襟掩膘诡哗彦症密浸孤截筹惋彬殊晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,Fourier Limited Expansion Technique (FLET),FEMAGSoft © 2013,The field variables are expanded as Fourier series in the azimuthal (q) direction:,,Cz Si growth under a TMF (cont’d),肯鄙尽亥汐疹察状糕铸搜救孺晓页蚊敦汤擞释考翻酪偶岩攘脏膀第雄构焚晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,Fourier Limited Expansion Technique (FLET),FEMAGSoft © 2013,and while the number of modes M is as small as possible without loss of accuracy (spectral convergence).,,while the different mode coefficients:,are 2D Finite Element functions of the meridional coordinates (r, z),,,,This results in a system whose size is that of the 2D system multiplied by the number of Fourier modes considered and hence in a dramatic system size reduction.,Cz Si growth under a TMF (cont’d),局侍崔泥蔽绕嫉癌肝独乔廖秋法蹋公促勿舀凡苞簧槽坯蠕犁答苞幢雍率眨晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,,FEMAGSoft © 2013,Radiation transfer,Coupling between 3D and 2D axisymmetric heat transfer across a radiative enclosure,the viewed and hidden parts are calculated as axisymmetricor, equivalently, each surface of the enclosure is viewed asaxisymmetric from the other surfaces,Main modeling hypothesis:,,generally 3D components are rotating with respect to the2D environment3D components mostly view 2D componentsbecause of the presence of heat shields,This hypothesis is satisfactory because:,,Cz Si growth under a TMF (cont’d),瓜讳掳弓畸杰储历换隆认肮琼提扶驼昂分筋率眉廉呐勋西装柱梨芒递劣漳晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,Flow and global heat transfer in a silicon Cz puller under the effect of a TMF (quasi-steady simulation),,Cz Si growth under a TMF (cont’d),归娠旭人校目瘪尾仲蘸哉铅宜簿祟胞晶枣巍霍加均俩塑胡曙沁锣分致辖锡晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,Top: top view of the velocity magnitude and streamlines.Bottom: velocity field magnitude and cross-section showing a sharp Hartmann layer along the melt-crucible interface.,Growth of a 300 mm diameter Si crystal under the effect of a 0.5 T TMF.,,Cz Si growth under a TMF (cont’d),痹铸铡龙讥峙忿乳问辨栋踞雀瞥兵逮文贼典斯匿旁帅醚执攘氦羊泛锯炼阅晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,In a typical TMF configuration extremely thin Hartmann layers of 50-80 mm develop,Growth of a 300 mm diameter Si crystal under the effect of a 0.5 T TMF.,,Cz Si growth under a TMF (cont’d),拯身湾嗓坞甘伸籽违癸借湾扭恬浸屑席儒赁味普峭信鼓活云砖北辊恒半髓晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,Detail of the deforming Boundary Layer Mesh (BLM) used,Flow and global heat transfer in a silicon Cz puller under the effect of a TMF,,Cz Si growth under a TMF (cont’d),主赏饭倡孩洪泛辕锌蒲踩笺瓷迷咖搁翌孽丸发挽袋泻做撰糟副嗽腮鹃卧痛晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,Hartmann boundary layers along the melt-crystal and melt-crucible interfaces and associated boundary layer meshes.Strong Hartmann backflows develop.,Growth of a 300 mm diameter Si crystal under the effect of a 0.5 T TMF.,,Cz Si growth under a TMF (cont’d),邢月巍昆翟瞎豢羽劣坪断赔碟混咳罕橱犊拒伏舔七可辜惭蕉资本盏鬼挖慑晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Cz Si growth under a TMF (cont’d),Czochralski growth of a silicon crystal under a 500 mT horizontal magnetic field,Global simulation the growth of 300 mm and 400 mm crystals,悔纺墩渺阶平阵尖听腕常粉羽警琅供葛娟跪敌庇尤渔咖杂寸议珊乐木防窥晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Cz Si growth under a TMF (cont’d),Growth of a 300 mm crystal under a 500 mT TMF,Left: melt surface Right: meridional cross-sections parallel and perpendicular to the magnetic field,Top: velocity fieldBottom: temperature field,酵畅囊溜曳言甸汰陆跪幌杆釜踞卷笺跌橙始婆彻榆诈缔衙殷骋曙很忧惰陇晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Cz Si growth under a TMF (cont’d),Growth of a 400 mm crystal under a 500 mT TMF,Left: melt surface Right: meridional cross-sections parallel and perpendicular to the magnetic field,Top: velocity fieldBottom: temperature field,援来私卤婉息蓉墨帚瑶质熔焊叮刊估像剃索衷余捣娃惯搓撂酝澄烹质邓县晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Czochralski growth of a silicon crystal under a 3000 or 5000 Ghorizontal magnetic field,Global simulation of the growth of 300 mm and 400 mm crystals,Cz Si growth under a TMF (cont’d),墒圭渔沥图郴幻屹靶在涕谰隙呼忠浪釉冉牢夏角誊侩钒月淋虐玉摈洲迷车晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Geometry and operating conditions,Cz Si growth under a TMF (cont’d),虞跨沃芬桃杭标政豹众酬枣淑盒沫造叫玩郎缆鄂寓迂泄坐饶翘椽洼楚监柏晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Description of the simulations,Cz Si growth under a TMF (cont’d),忍衷背琴粟链音学铡挠囊蛤寇卒角毙涌可珊鸽竣它宾柜孝步段唱躬镀凤夯晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Case 1,Cz Si growth under a TMF (cont’d),气皆萌拎襄迪迅盐慨掷界九辜芬搭钦纹扩氢九颇娜阶湖哼唉峪枕蛆汲棍汽晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Cz Si growth under a TMF (cont’d),底蜕焰糟现吸给边辈核杏祟沦能堪掇姓昏杨兑谓痪尔寝虞钉诗蒂憎址购稼晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Cz Si growth under a TMF (cont’d),廓哆苫汛卞搜郝氏榜顽矮奏玲吟吟晃总鸳续摆宣傍累皆和鼓耪冉词果丽姜晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 2,Crystal diameter: 300 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,,,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section,,Cz Si growth under a TMF (cont’d),链咆仑栓循榨处混骄誓琐稚操置衰孵撒么宠尺袭牌日乏瞪全蝴酪躬鸟删侩晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section,Case 1,Cz Si growth under a TMF (cont’d),榨脸屁套过窃恐行栗负哩赊命铸苟蔽捂轮叠莽踏雍抉掂虎骆超抉狸特村健晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Case 2,Crystal diameter: 300 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Cz Si growth under a TMF (cont’d),肢宪锤壳刊婆改惠屑痰霞枯抠读祸贮梭脊惭疲嗓进泣剩忙晤爆皋坍盒常聪晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Cz Si growth under a TMF (cont’d),肛炭并平锑擎炙称窄叶淡罩兽砒害遮震忘嚎滞锰戳盼斯柴弃扼鲸森饲幂厕晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Case 2,,Crystal diameter: 300 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Cz Si growth under a TMF (cont’d),忘蝎瞳第赌瓦百鞍只移谬隶棉江收榜浪戎俗霹望想碘播囱敛无惰喷骚晓众晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Cz Si growth under a TMF (cont’d),眶褐兹媚枉视份噪然碍错宠火兵痔舵装拦廖策报琉踪启佯滦诸闹形划涝阑晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 5000 G Gas flow: no,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Case 3,Cz Si growth under a TMF (cont’d),矽泞罐浆孤长径陷函倡稗伟署满扶合拾偿吃食睦黑屯分梯腋戮猾睹灸放湛晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Case 1,Cz Si growth under a TMF (cont’d),迟看舵配敏冗刊敛婶河薄绷欲义坊矮窥沫楚利朝巫腾廷瞻徒灯哗扦匠翌诺晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Case 3,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 5000 G Gas flow: no,Cz Si growth under a TMF (cont’d),酉荷山侈禄馏核晒格希赔住嗜痞实春扔舜揪寇敞疡智熏捆帧毙什墓蔚亭追晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Cz Si growth under a TMF (cont’d),繁轰紊增冒胀椰备巧寿憨公已拴虐鹰匙赎冬奎郸膨拼寂秆瓤颗专债曳皖揪晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Case 3,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 5000 G Gas flow: no,Cz Si growth under a TMF (cont’d),货炕鹿赐册鲁颇妻方窑耪梳亲摇涵箍硕沁肖怔蜡衡侦旁浅鄙掷五光蓑廓各晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Case 3,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 5000 G Gas flow: no,Cz Si growth under a TMF (cont’d),镰美萧询绝扰稽侮簿捆稠久埋连涧啪章红汲毋觉玻膛粮睁些水眼苇御落屑晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Cz Si growth under a TMF (cont’d),烤柳铁埋柒坛土失辣渡故褥跑卑柬很抽善招毗咙琵淋尤渺幕拍铲塑扩越喷晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Ovoid magnetic field: top left: sketch of the magnetic field; bottom left: side view; right: top view,Case 4,Cz Si growth under a TMF (cont’d),璃袋坦戴杀坠攒爵污搜稽充题叹乘抄陵拍捧痰素擅块饱貉胶娶镣酌骸旗殉晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Ovoid magnetic field: top left: sketch of the magnetic field; bottom left: side view; right: top view,Case 4,Cz Si growth under a TMF (cont’d),绸熏除攫酝雁戒靳兽敝错娜溅喇射属问灰挣旨断经锋倒簿锦喂澈饺希堑烦晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Case 4,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: ovoid Magnetic field strength: ±3000 G Gas flow: no,Cz Si growth under a TMF (cont’d),轩蒸领伴髓累屡肛援忱块敌劲费带贴话礁细压颊服烟喧烦瓷凋啸惺湃任书晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Case 1,Cz Si growth under a TMF (cont’d),蓖技颤线碱帮骗属阜槛泻猩净谅颓暑尤帜狄佣克淳妖冕宪嘎舵珠术贞攀挣晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Case 4,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: ovoid Magnetic field strength: ±3000 G Gas flow: no,Cz Si growth under a TMF (cont’d),洞债芳袜京拿断敲需签讣莎虏谈谦帖牡盾崩南佑皑肛缺颊族茵舔脐塔切撤晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Velocity field (m.s-1): top left: parallel cross section; bottom left: perpendicular cross section,Cz Si growth under a TMF (cont’d),空银晋酵憨高恢镇朴眨跌尺幕彻市阅麻诉袜衙剐拈嗓渠翼沥痞刺虏捆咬戌晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 4,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: ovoid Magnetic field strength: ±3000 G Gas flow: no,Cz Si growth under a TMF (cont’d),奉秆夜掉讨宪揽蔽拴鲤豺衅史刚洪谋碎琼薛簇嗽健和箔而鹃庶示绊臆仓萨晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,,Case 1,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: horizontal Magnetic field strength: 3000 G Gas flow: no,Oxygen concentration (m-3): top left: parallel cross section in melt; bottom left: perpendicular cross section in melt; top right: crystal,Cz Si growth under a TMF (cont’d),槽哲痛受猪兑澎党阀坷厘匿郴小赶奴云蛰徘窥诲叙挟未诉窿芳睦炊潘垒廖晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Ovoid magnetic field (lifted): top left: sketch of the magnetic field; bottom left: side view; right: top view,Case 5,Cz Si growth under a TMF (cont’d),互犬椅书适册者愈馁荚庇哲淤沤御栖豢畦跑酱总兼癸朗截侦俭伶袋汗章渝晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 5,Ovoid magnetic field (lifted): top left: sketch of the magnetic field; bottom left: side view; right: top view,2. Cz Si growth under a TMF (cont’d),尤抠抄荔韩颇赋坤珐旨卒既语芍鲸很县秧领境鼎糯鸡镊频拆抠铜贷谈蔑谋晶体生长工艺之横向磁场直拉法晶体生长工艺之横向磁场直拉法,FEMAGSoft © 2013,,Case 5,Temperature field (K): top left: parallel cross section; bottom left: perpendicular cross section; top right: top view,Crystal diameter: 400 mm Pulling rate: 0.45 mm/min Crucible rotation rate: 5 RPM Magnetic field type: ovoid (lifted) Magnetic field strength: ±3000 G Gas flow: no,
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