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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
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