晶体生长工艺之横向磁场直拉法(精品).ppt
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1、Global Simulation of Czochralski Silicon Growth under the Effectof a Transverse Magnetic FieldFEMAGSoft 2013Cz Si growth under a TMF 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 layersFEMAGSoft 2013The Hartmann layers develop along the surfaces where the normal component of the magnetic
2、field is non-negligible.An order of magnitude of the thickness of a Hartmann layer is dH=L Ha-1 (L=Rs or Rc).Typically dH=0.05-0.08 mm in industrial furnaces.Cz Si growth under a TMF(contd)Transverse magnetic fields:FLET methodMethod:Fourier decomposition of all fields(velocity,pressure,temperature)
3、Hypothesis:Principal issue:which and how many modes?Objective:global,quasi-steady or time-dependentcalculations at a reasonable costFEMAGSoft 2013 Cz Si growth under a TMF(contd)Fourier Limited Expansion Technique(FLET)FEMAGSoft 2013The field variables are expanded as Fourier series in the azimuthal
4、(q)direction:Cz Si growth under a TMF(contd)Fourier Limited Expansion Technique(FLET)FEMAGSoft 2013and 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 coordinate
5、s (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(contd)FEMAGSoft 2013Radiation transferCoupling between 3D and 2D axisymmetric heat transfer across a radiati
6、ve enclosure-the viewed and hidden parts are calculated as axisymmetric-or,equivalently,each surface of the enclosure is viewed as axisymmetric from the other surfaces Main modeling hypothesis:-generally 3D components are rotating with respect to the 2D environment-3D components mostly view 2D compo
7、nents because of the presence of heat shieldsThis hypothesis is satisfactory because:Cz Si growth under a TMF(contd)FEMAGSoft 2013Flow and global heat transfer in a silicon Cz pullerunder the effect of a TMF(quasi-steady simulation)Cz Si growth under a TMF(contd)FEMAGSoft 2013Top:top view of the vel
8、ocity 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(contd)FEMAGSoft 2013In a typical TMF configuration extrem
9、ely thin Hartmann layersof 50-80 mm developGrowth of a 300 mm diameter Si crystal under the effect of a 0.5 T TMF.Cz Si growth under a TMF(contd)FEMAGSoft 2013Detail of the deforming Boundary Layer Mesh(BLM)usedFlow and global heat transfer in a silicon Cz pullerunder the effect of a TMFCz Si growth
10、 under a TMF(contd)FEMAGSoft 2013Hartmann 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(contd)FEMAGSoft 2013Cz
11、Si growth under a TMF(contd)Czochralski growth of a silicon crystalunder a 500 mT horizontal magnetic fieldGlobal simulation the growth of 300 mm and 400 mm crystalsFEMAGSoft 2013Cz Si growth under a TMF(contd)Growth of a 300 mm crystal under a 500 mT TMFLeft:melt surfaceRight:meridional cross-secti
12、ons parallel and perpendicular to the magnetic fieldTop:velocity fieldBottom:temperature fieldFEMAGSoft 2013Cz Si growth under a TMF(contd)Growth of a 400 mm crystal under a 500 mT TMFLeft:melt surfaceRight:meridional cross-sections parallel and perpendicular to the magnetic fieldTop:velocity fieldB
13、ottom:temperature fieldFEMAGSoft 2013Czochralski growth of a silicon crystalunder a 3000 or 5000 G horizontal magnetic fieldGlobal simulation of the growth of 300 mm and 400 mm crystalsCz Si growth under a TMF(contd)FEMAGSoft 2013Geometry and operating conditionsCz Si growth under a TMF(contd)FEMAGS
14、oft 2013Description of the simulationsCz Si growth under a TMF(contd)FEMAGSoft 2013Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Temperature field(K):top left:parallel cross section;bottom left:perpe
15、ndicular cross section;top right:top viewCase 1Cz Si growth under a TMF(contd)FEMAGSoft 2013Case 1Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Velocity field(m.s-1):top left:parallel cross section;b
16、ottom left:perpendicular cross sectionCz Si growth under a TMF(contd)FEMAGSoft 2013Case 1Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Oxygen concentration(m-3):top left:parallel cross section in mel
17、t;bottom left:perpendicular cross section in melt;top right:crystal Cz Si growth under a TMF(contd)FEMAGSoft 2013Case 2Crystal diameter:300 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Temperature field(K):top left:para
18、llel cross section;bottom left:perpendicular cross section Cz Si growth under a TMF(contd)FEMAGSoft 2013Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Temperature field(K):top left:parallel cross sect
19、ion;bottom left:perpendicular cross sectionCase 1 Cz Si growth under a TMF(contd)FEMAGSoft 2013Velocity field(m.s-1):top left:parallel cross section;bottom left:perpendicular cross sectionCase 2Crystal diameter:300 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalM
20、agnetic field strength:3000 GGas flow:no Cz Si growth under a TMF(contd)FEMAGSoft 2013Case 1Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Velocity field(m.s-1):top left:parallel cross section;bottom
21、left:perpendicular cross section Cz Si growth under a TMF(contd)FEMAGSoft 2013Oxygen concentration(m-3):top left:parallel cross section in melt;bottom left:perpendicular cross section in melt;top right:crystalCase 2Crystal diameter:300 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic f
22、ield type:horizontalMagnetic field strength:3000 GGas flow:no Cz Si growth under a TMF(contd)FEMAGSoft 2013Case 1Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Oxygen concentration(m-3):top left:paral
23、lel cross section in melt;bottom left:perpendicular cross section in melt;top right:crystal Cz Si growth under a TMF(contd)FEMAGSoft 2013Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:5000 GGas flow:no Temperature fiel
24、d(K):top left:parallel cross section;bottom left:perpendicular cross section;top right:top viewCase 3 Cz Si growth under a TMF(contd)FEMAGSoft 2013Crystal diameter:400 mmPulling rate:0.45 mm/minCrucible rotation rate:5 RPMMagnetic field type:horizontalMagnetic field strength:3000 GGas flow:no Temper
25、ature field(K):top left:parallel cross section;bottom left:perpendicular cross section;top right:top viewCase 1 Cz Si growth under a TMF(contd)FEMAGSoft 2013Velocity field(m.s-1):top left:parallel cross section;bottom left:perpendicular cross sectionCase 3Crystal diameter:400 mmPulling rate:0.45 mm/
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