CN107747122A - A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method - Google Patents
A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method Download PDFInfo
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- CN107747122A CN107747122A CN201710811360.3A CN201710811360A CN107747122A CN 107747122 A CN107747122 A CN 107747122A CN 201710811360 A CN201710811360 A CN 201710811360A CN 107747122 A CN107747122 A CN 107747122A
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- C—CHEMISTRY; METALLURGY
- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B15/00—Single-crystal growth by pulling from a melt, e.g. Czochralski method
- C30B15/20—Controlling or regulating
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- C—CHEMISTRY; METALLURGY
- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B29/00—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
- C30B29/02—Elements
- C30B29/06—Silicon
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- C—CHEMISTRY; METALLURGY
- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B30/00—Production of single crystals or homogeneous polycrystalline material with defined structure characterised by the action of electric or magnetic fields, wave energy or other specific physical conditions
- C30B30/04—Production of single crystals or homogeneous polycrystalline material with defined structure characterised by the action of electric or magnetic fields, wave energy or other specific physical conditions using magnetic fields
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Abstract
The invention discloses a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method,Superconduction horizontal magnetic intensity is adjusted first,Obtain the solid liquid interface oxygen concentration distribution curve under different magnetic field intensity,Calculate the average oxygen concentration of solid liquid interface and the uniformity of solid liquid interface radial direction oxygen concentration distribution,Suitable magnetic field intensity is selected by contrast,Next to that crystal rotation and crucible rotation are adjusted respectively under the magnetic field intensity of selection,Obtain being adapted to reduce solid liquid interface oxygen concentration by contrast simulation result and improve the crystal rotation and crucible rotation of solid liquid interface oxygen concentration distributing homogeneity,Finally in selected cryogenic magnetic field intensity,Under the collective effect of crystal rotation and crucible rotation three,Obtain czochralski silicon monocrystal solid liquid interface oxygen concentration distributed intelligence under superconduction horizontal magnetic field,The present invention solves when Modelling of Crystal Growth in CZ-Si Pulling technological parameter present in prior art is adjusted and easily causes too high oxygen level in crystal,The problem of oxygen distribution is uneven.
Description
Technical field
The invention belongs to magnetic control czochralski silicon monocrystal solid liquid interface oxygen distribution growth technique adjusting method technical field, specifically relate to
A kind of and Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method.
Background technology
Vertical pulling method is to prepare the main method of integrated circuit and field of photovoltaic power generation silicon single crystal semi-conducting material.Semiconductor row
Industry includes to the prevailing quality evaluation index of silicon single crystal to be reduced various objectionable impurities contents (oxygen, carbon) in wafer and reduces micro-
Defect, the wherein secondary defect caused by oxygen impurities content can have a strong impact on quality and the production of the silicon semiconductor material of drawing
Device performance.In order to reduce the microdefect of crystal as far as possible and ensure the uniformity of crystal resistivity, so how to reduce big chi
The oxygen impurities content of solid liquid interface in very little crystal growing process (crystal and melt interface) and raising solid liquid interface oxygen distribution
Uniformity, tool is of great significance.
Because molten silicon is in high temperature, the body of heater sealed, it is impossible to directly obtain the oxygen in crucible melt with solid liquid interface
Distribution situation.At present, the method for obtaining oxygen distribution in crystal mainly has infrared absorption method and Method for Numerical.Infrared absorption method is
By measuring silicon wafer, infrared spectrum is analyzed, carrying out quantitative analysis according to peak position, absorption intensity goes out silicon wafer
Oxygen content and oxygen distribution uniformity on disk, because the method for multiple crystal pulling experiment wastes time and energy, cost is very big, can only be directly perceived
Ground understands experimental phenomena.Method for Numerical is by being modeled by commercial CFD software to thermal field of single crystal furnace, using limited body
Area method (FVM), which solves, to be obtained in melt and the distribution situation of solid liquid interface oxygen content, and experimental cost is low, the cycle is short, Neng Gougeng
It is good quickly to recognize crystal growth problem.High crystal rotation, low crystal rotation under conventional levels magnetic field in Method for Numerical at present
Process adjustments method easily cause in crystal oxygen content to raise, have a strong impact on manufactured electronic device service behaviour.Therefore,
A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method is proposed, is dropped during Modelling of Crystal Growth in CZ-Si Pulling
The oxygen concentration of low solid liquid interface and the uniformity for improving solid liquid interface oxygen distribution, to meet the needs of market is to high quality silicon monocrystalline
It is major issue urgently to be resolved hurrily at present.
The content of the invention
It is an object of the invention to provide a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method, solution
Determine when Modelling of Crystal Growth in CZ-Si Pulling technological parameter present in prior art is adjusted and easily caused too high oxygen level in crystal, oxygen
The problem of cloth is uneven.
The technical solution adopted in the present invention is a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution regulation
Method, specifically implement according to following steps：
Three-dimensional Local physical model needed for step 1, structure crystal for straight drawing monocrystal growth；
Step 2, by three-dimensional Local physical model import CFX fluid emulation modules, setting analogue simulation is steady-state simulation, and
The physical parameter and cryogenic magnetic field intensity of silicon melt, silicon crystal, graphite crucible and silica crucible are set；
Step 3, solve solid liquid interface radial direction oxygen concentration distribution situation under different superconduction horizontal magnetic intensities；
The influence of step 4, analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt；
The influence of step 5, analysis crucible rotation to radial temperature profile in solid-liquid interface shape and melt；
Step 6, combining step 3~5, with reference to selected superconduction horizontal magnetic intensity, crystal rotation and crucible rotation three
Under the collective effect of person, czochralski silicon monocrystal solid liquid interface oxygen concentration distributed intelligence under superconduction horizontal magnetic field is obtained.
The features of the present invention also resides in,
Step 1 is specifically implemented according to following steps：
Step 1.1, the three-dimensional Local physical model using Gambit software mess generation crystal for straight drawing monocrystal growth, comprising
Crystal, melt, silica crucible and graphite crucible；
Step 1.2, to set silica crucible radius be 0.306m, and graphite crucible radius is 0.32m, and melt radius is in crucible
0.3m, crucible rotate counterclockwise, crucible rotation ωc；Crystal radius scope is 0.15m~0.225m, and crystal turns clockwise,
Crystal rotation is ωs, melt height is 0.08m~0.22m, and crystal length is 0m~0.6m, inventory 160kg, free interface
For silicon melt and gas interface, boundary of the solid liquid interface between crystal and melt.Crucible rotation ω in step 1.2cFor 0
~10rpm, crystal rotation ωsFor 0~16rpm.
Step 2 is specifically implemented according to following steps：
Step 2.1, setting crucible are rotate counterclockwise, crucible rotation ωc, crystal turns clockwise, and crystal rotation is
ωs；
Step 2.2, hypothesis silicon melt are incompressible Newtonian fluid；Assuming that silicon melt meets Boussinesq approximations；
Setting solid liquid interface is flat face, and supercooled state does not occur when solid liquid interface crystallizes, and the temperature of solid liquid interface is the fusing point temperature of silicon
Spend 1685K；Melt and argon gas interface are set, i.e. free surface is flat face, and its position height is highly identical with solid liquid interface,
And outwardly atmosphere radiations heat energy；Silica crucible bottom and crucible internal walls meet without slip boundary condition with silicon melt；It is molten
Internal oxygen transport process is ignored to melt flows with the influence conducted heat.
In step 2.2, used boundary condition includes oxygen concentration boundary condition and temperature in iteration of simulations solution procedure
Boundary condition is spent, wherein oxygen concentration boundary condition is as follows：
(1) the oxygen concentration boundary condition of melted silicon and inner wall of quartz crucible intersection：
Wherein, NAFor Avgadro constant,For partial pressure of oxygen, aoFor oxysome fraction, R is carrier of oxygen mole constant, T
For chemical reaction temperature,For chemical reactionGibbs free amount.
(2) melted silicon and the oxygen concentration boundary condition at argon gas interface：
In formula, COAnd CsurfIt is the oxygen concentration of oxygen concentration in melt and free surface respectively；CSiIt is melted silicon concentration；DO
And DSiOIt is diffusion coefficient and SiO gas diffusion coefficient in argon gas of the oxygen in silicon melt respectively；Δ G is chemical equation
(Simelt+Omelt=SiOgas) Gibbs free amount, p0It is the steam pressure of silicon monoxide gas, R is gas molar constant, T
It is chemical reaction temperature；δgIt is free surface boundary layer thickness；
During the actual growing environment of crystal, the oxygen of free surface is under the brushing of argon gas, the oxygen concentration of free surface
CsurfOxygen concentration C only inside meltOCount very much, therefore by the oxygen concentration C of free surfacesurfIgnore, then free surface
Oxygen concentration boundary condition be reduced to
CO=0mol/m3；
(3) the oxygen concentration boundary condition at solid liquid interface (crystal growth interface) place：
In formula, D be oxygen diffusion coefficient, VgFor the translational speed of solid liquid interface, k is the segregation coefficient of oxygen, CoFor in melt
Oxygen concentration.Experiment discloses the segregation coefficient of oxygen close to unit 1, and the oxygen more than 99% evaporate into argon gas from free surface and worked as
In, so the oxygen content being incorporated into crystal is ignored in solid liquid interface Whole Oxygen flux equilibrium, above formula is reduced to
Graphite crucible bottom and graphite crucible outer wall apply constant gradient Temperature Distribution value in temperature boundary condition, in free liquid
Heat flow density equation, such as following formula are established at face：
Ql'=qout,k-qin,k=σ ε T4-εqin,k
qin,k=sumJ=1~N(Fk,jqout,j)
In formula, β [T (r)-T0(r)]1.25For describing due to gaseous exchange and caused thermal losses, Ql' be used for describing to melt
The caused thermal losses by radiation of body fluid face, T are free surface temperature, T0For environment temperature, KlFor the silicon melt coefficient of heat conduction, β
For the thermal losses coefficient of gaseous exchange, r is free surface radius, and ε is radiation coefficient, and σ is Stefan-Boltzmann constants,
Fk,jFor k, the ascent between two surfaces of j, qout,kIt is the heat flow of flux surface, qin,kBe flow into surface heat flow, x,
Z is rectangular coordinate system in space direction variable, and N is surface total number；
Outside the inner surface and crystal that graphite crucible and the top surface of silica crucible, silica crucible do not contact with silicon melt
The surfaces of solids such as surface, also establish similar heat flow density equation, such as following formula：
Qs'=qout,k-qin,k=σ ε T4-εqin,k
Wherein, Qs' be used for describing the surface of solids caused thermal losses by radiation, KsFor the silicon melt coefficient of heat conduction, r is
The inside radius of crystal radius or silica crucible, y are rectangular coordinate system in space direction variable.
It is 90000 that iterations is set in iterative controls, time factor 1, and the residual values of convergence curve are set
For 1E-06.
Step 3 is specifically implemented according to following steps：
Step 3.1, the numerical solver using CFX modules, under numerical solution difference superconduction horizontal magnetic intensity, crystal turns
Fast ωsWith crucible rotation ωcFlowing and heat transfer when being 0rpm in crucible melt；
Step 3.2, after iteration convergence by the post processing of CFX modules obtain melt Temperature Distribution cloud atlas and oxygen it is dense
Cloud charts are spent, solid liquid interface 1685K isothermal line positions are followed the trail of on Temperature Distribution cloud atlas, obtain the oxygen concentration in solid liquid interface
Distributed data, obtain the relation curve of oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve.According to solid-liquid
Interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor minimum principle, choosing
Take suitable cryogenic magnetic field intensity.Wherein, average oxygen concentrationFor weighing the height of solid liquid interface oxygen concentration, mean square error
MSEOWith gradient error and δOFor weighing the uniformity of solid liquid interface oxygen concentration distribution, such as following formula
Wherein, n is the oxygen data amount check in collected solid liquid interface, ciFor oxygen data point, i is oxygen data arguments；
Wherein, gradOiIt is the gradient of each oxygen data point on solid liquid interface radial direction oxygen concentration distribution curve, gradOminIt is solid
The minimal gradient of liquid interface radial direction oxygen concentration distribution curve, gradient error and δOIt is smaller, then illustrate solid liquid interface radial direction oxygen concentration
The uniformity of distribution is more uniform.
Step 4 is specifically implemented according to following steps：
Step 4.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, will
Crucible rotation ωc0rpm is arranged to, adjusts different crystal rotational speed omegas, iterative to residual error curve convergence, so as to obtain solid-liquid
Oxygen concentration data on the 1685K thermoisopleths of interface；
Step 4.2, the relation curve between oxygen concentration and crystal diameter is obtained, i.e. solid liquid interface radial direction oxygen concentration distribution is bent
Line, for influence of the analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from
Inside melt, apart from melt and argon gas interface 0.08m, length 0.3m, crystal is pointed in direction by crucible and melt interface
Growth axis, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and
δOFor minimum principle, suitable crystal rotation is chosen.
Step 5 is specifically implemented according to following steps：
Step 5.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, if
Put crystal rotation ωsFor 0rpm, regulation crucible rotation ωc, by numerical solver iterative to residual error curve convergence, so that
Obtain the oxygen concentration data on solid liquid interface 1685K thermoisopleths；
Step 5.2, the relation curve between oxygen concentration and crystal diameter is obtained, i.e. solid liquid interface radial direction oxygen concentration distribution is bent
Line, in order to analyze influence of the crucible rotation to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from
Inside melt, height distance melt and argon gas interface are 0.08m, and length 0.3m, direction is referred to by crucible and melt interface
To crystal growth axis, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOAnd gradient
Error and δOFor minimum principle, suitable crystal rotation is chosen.
Step 6 is specifically implemented according to following steps：
Step 6.1, during processing is set before CFX, superconduction horizontal magnetic intensity and crucible rotation are set for step 3, step 5
Selected suitable superconduction horizontal magnetic intensity and crucible rotation, because Gao Jingzhuan is advantageous to improve the uniformity of solid liquid interface,
So first by crystal rotation ωsGao Jingzhuan is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface footpath
To oxygen concentration distribution curve；
Step 6.2, by crystal rotation ωsLow brilliant turn is arranged to, is solved by iterative numerical and MATLAB maps and consolidated
Liquid interface radial direction oxygen concentration distribution curve；
Step 6.3, crystal rotation ω is calculated respectivelysThe oxygen concentration distribution of solid liquid interface radial direction is bent when turning for high brilliant turn with low crystalline substance
The average oxygen concentration of solid liquid interface in lineThe mean square error MSE related to oxygen concentration distributing homogeneityOWith gradient error and
δO, by comparative analysis qualitatively and quantitatively, selection is both adapted to reduce solid liquid interface oxygen concentration and can raising solid liquid interface
Superconduction horizontal magnetic intensity, crystal rotation and the crucible rotation of radial direction oxygen concentration distributing homogeneity.
The invention has the advantages that a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method,
By establishing Three-dimensional simulation Modelling of Crystal Growth in CZ-Si Pulling process, more intuitively accurate oxygen concentration point in crucible melt can must be recognized
Cloth state and solid liquid interface oxygen concentration distributed intelligence, and according to solid liquid interface oxygen concentration distribution curve, can qualitatively analyze
The height of oxygen content and the uniformity of oxygen impurities distribution among crystal.And oxygen concentration number is utilized from quantitative analysis foundation
According to arithmetic mean of instantaneous value weigh solid liquid interface oxygen concentration height and using oxygen concentration data mean square error and oxygen concentration distribution
The gradient error of curve and the uniformity for weighing the distribution of solid liquid interface oxygen concentration.Sent out with reference to qualitative analysis and quantitative analysis results
It is existing, the process adjustments method of low crystal rotation and low crucible rotation under selected suitable magnetic field intensity, can effectively it reduce
The oxygen concentration of solid liquid interface and the uniformity for improving the distribution of solid liquid interface radial direction oxygen concentration, reaching reduces oxygen impurities in silicon crystal
Content and the purpose for improving oxygen distribution uniformity in crystal, so as to improve large scale silicon single crystal quality.
Brief description of the drawings
Fig. 1 is a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method three-dimensional numerical value mould of the present invention
Intend silicon monocrystal growth schematic diagram；
Fig. 2 (a)~Fig. 2 (b) is a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution regulation side of the present invention
Solid liquid interface oxygen concentration scatter chart under different cryogenic magnetic field intensity in method；
Fig. 3 (a)~Fig. 3 (d) is a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution regulation side of the present invention
Solid liquid interface oxygen concentration scatter chart under different crystal rotating speed in method；
Fig. 4 (a)~Fig. 4 (d) is a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution regulation side of the present invention
Solid liquid interface oxygen concentration scatter chart under different crucible rotations in method；
Fig. 5 be Gao Jingzhuan in a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method of the present invention,
Low crucible turns lower solid liquid interface oxygen concentration scatter chart；
Fig. 6 be in a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method of the present invention it is low it is brilliant turn,
Low crucible turns lower solid liquid interface oxygen concentration scatter chart.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and detailed description.
A kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method of the present invention, specifically according to following step
It is rapid to implement：
Three-dimensional Local physical model needed for step 1, structure crystal for straight drawing monocrystal growth, it is specifically real according to following steps
Apply：
Step 1.1, as shown in figure 1, three-dimensional local thing using Gambit software mess generation crystal for straight drawing monocrystal growth
Model is managed, includes crystal, melt, silica crucible and graphite crucible；
Step 1.2, to set silica crucible radius be 0.306m, and graphite crucible radius is 0.32m, and melt radius is in crucible
0.3m, crucible rotate counterclockwise, crucible rotation ωc；Crystal radius scope is 0.15m~0.225m, and crystal turns clockwise,
Crystal rotation is ωs, melt height is 0.08m~0.22m, and crystal length is 0m~0.6m, inventory 160kg, free interface
For silicon melt and gas interface, boundary of the solid liquid interface between crystal and melt.Wherein, crucible rotation ωcFor 0~
10rpm, crystal rotation ωsFor 0~16rpm.In emulation experiment of the present invention, crystal radius are arranged to 0.15m, and crystal length is set
It is set to 0.2m.
Step 2, by three-dimensional Local physical model import CFX fluid emulation modules, setting analogue simulation is steady-state simulation, and
The physical parameter and cryogenic magnetic field intensity of silicon melt, silicon crystal, graphite crucible and silica crucible are set, and wherein physical parameter is set
As shown in table 1：
The physical parameter of table 1
Specifically implement according to following steps：
Step 2.1, setting crucible are rotate counterclockwise, crucible rotation ωc, crystal turns clockwise, and crystal rotation is
ωs；
Step 2.2, hypothesis silicon melt are incompressible Newtonian fluid；Assuming that silicon melt meets Boussinesq approximations；
Setting solid liquid interface is flat face, and supercooled state does not occur when solid liquid interface crystallizes, and the temperature of solid liquid interface is the fusing point temperature of silicon
Spend 1685K；Melt and argon gas interface are set, i.e. free surface is flat face, and its position height is highly identical with solid liquid interface,
And outwardly atmosphere radiations heat energy；Silica crucible bottom and crucible internal walls meet without slip boundary condition with silicon melt；It is molten
Internal oxygen transport process is ignored to melt flows with the influence conducted heat,
In step 2.2, used boundary condition includes oxygen concentration boundary condition and temperature in iteration of simulations solution procedure
Boundary condition is spent, wherein oxygen concentration boundary condition is as follows：
(1) the oxygen concentration boundary condition of melted silicon and inner wall of quartz crucible intersection：
Wherein, NAFor Avgadro constant,For partial pressure of oxygen, aoFor oxysome fraction, R is carrier of oxygen mole constant, T
For chemical reaction temperature,For chemical reactionGibbs free amount.
(2) melted silicon and the oxygen concentration boundary condition at argon gas interface：
In formula, COAnd CsurfIt is the oxygen concentration of oxygen concentration in melt and free surface respectively；CSiIt is melted silicon concentration；DO
And DSiOIt is diffusion coefficient and SiO gas diffusion coefficient in argon gas of the oxygen in silicon melt respectively；Δ G is chemical equation
(Simelt+Omelt=SiOgas) Gibbs free amount, p0It is the steam pressure of silicon monoxide gas, R is gas molar constant, T
It is chemical reaction temperature；δgIt is free surface boundary layer thickness；
During the actual growing environment of crystal, the oxygen of free surface is under the brushing of argon gas, the oxygen concentration of free surface
CsurfOxygen concentration C only inside meltOCount very much, therefore by the oxygen concentration C of free surfacesurfIgnore, then free surface
Oxygen concentration boundary condition be reduced to
CO=0mol/m3；
(3) the oxygen concentration boundary condition at solid liquid interface (crystal growth interface) place：
In formula, D be oxygen diffusion coefficient, VgFor the translational speed of solid liquid interface, k is the segregation coefficient of oxygen, CoFor in melt
Oxygen concentration.Experiment discloses the segregation coefficient of oxygen close to unit 1, and the oxygen more than 99% evaporate into argon gas from free surface and worked as
In, so the oxygen content being incorporated into crystal is ignored in solid liquid interface Whole Oxygen flux equilibrium, above formula is reduced to
Graphite crucible bottom and graphite crucible outer wall apply constant gradient Temperature Distribution value in temperature boundary condition, in free liquid
Heat flow density equation, such as following formula are established at face：
Ql'=qout,k-qin,k=σ ε T4-εqin,k
qin,k=sumJ=1~N(Fk,jqout,j)
In formula, β [T (r)-T0(r)]1.25For describing due to gaseous exchange and caused thermal losses, Ql' be used for describing to melt
The caused thermal losses by radiation of body fluid face, T are free surface temperature, T0For environment temperature, KlFor the silicon melt coefficient of heat conduction, β
For the thermal losses coefficient of gaseous exchange, r is free surface radius, and ε is radiation coefficient, and σ is Stefan-Boltzmann constants,
Fk,jFor k, the ascent between two surfaces of j, qout,kIt is the heat flow of flux surface, qin,kBe flow into surface heat flow, x,
Z is rectangular coordinate system in space direction variable, and N is surface total number；
Outside the inner surface and crystal that graphite crucible and the top surface of silica crucible, silica crucible do not contact with silicon melt
The surfaces of solids such as surface, also establish similar heat flow density equation, such as following formula：
Qs'=qout,k-qin,k=σ ε T4-εqin,k
Wherein, Qs' be used for describing the surface of solids caused thermal losses by radiation, KsFor the silicon melt coefficient of heat conduction, r is
The inside radius of crystal radius or silica crucible, y are rectangular coordinate system in space direction variable.
It is 90000 that iterations is set in iterative controls, time factor 1, and the residual values of convergence curve are set
For 1E-06；
Step 3, solve solid liquid interface radial direction oxygen concentration distribution situation under different superconduction horizontal magnetic intensities, specifically according to
Lower step is implemented：
Step 3.1, the numerical solver using CFX modules, under numerical solution difference superconduction horizontal magnetic intensity, crystal turns
Fast ωsWith crucible rotation ωcFlowing and heat transfer when being 0rpm in crucible melt；
Step 3.2, after iteration convergence by the post processing of CFX modules obtain melt Temperature Distribution cloud atlas and oxygen it is dense
Cloud charts are spent, solid liquid interface 1685K isothermal line positions are followed the trail of on Temperature Distribution cloud atlas, obtain the oxygen concentration in solid liquid interface
Distributed data, the relation curve of oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, such as Fig. 2 institutes
Show, wherein Fig. 2 (a) be in 0 ° of -180 ° of plane of solid liquid interface (parallel to magnetic direction) radial direction oxygen concentration distribution curve, Fig. 2 (b)
Be in 90 ° of -270 ° of planes of solid liquid interface (perpendicular to magnetic direction) radial direction oxygen concentration distribution curve, according to solid liquid interface averaged oxygen
ConcentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor minimum principle, choose suitable super
Magnetic conduction field intensity, such as following formula
Wherein, n is the oxygen data amount check in collected solid liquid interface, ciFor oxygen data point, i is oxygen data arguments；
Wherein, gradOiIt is the gradient of each oxygen data point on solid liquid interface radial direction oxygen concentration distribution curve, gradOminIt is solid
The minimal gradient of liquid interface radial direction oxygen concentration distribution curve, gradient error and δOIt is smaller, then illustrate solid liquid interface radial direction oxygen concentration
The uniformity of distribution is more uniform；
The influence of step 4, analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt, specifically according to
Lower step is implemented：
Step 4.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, will
Crucible rotation ωc0rpm is arranged to, adjusts different crystal rotational speed omegas, iterative to residual error curve convergence, so as to obtain solid-liquid
Oxygen concentration data on the 1685K thermoisopleths of interface；
Step 4.2, the relation curve between oxygen concentration and crystal diameter is obtained, i.e. solid liquid interface radial direction oxygen concentration distribution is bent
Line, for influence of the analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from
Inside melt, apart from melt and argon gas interface 0.08m, length 0.3m, crystal is pointed in direction by crucible and melt interface
Growth axis, Fig. 3 (a) -3 (d) be respectively radial direction oxygen concentration distribution curve, 90 ° of solid liquid interface in 0 ° of -180 ° of plane of solid liquid interface -
Radial temperature profile is bent at temperature detection in radial direction oxygen concentration distribution curve and solid-liquid interface shape and melt in 270 ° of planes
Line, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor
Minimum principle, choose suitable crystal rotation；
Step 5, influence of the analysis crucible rotation to radial temperature profile in solid-liquid interface shape and melt, specifically according to
Lower step is implemented：
Step 5.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, if
Put crystal rotation ωsFor 0rpm, regulation crucible rotation ωc, by numerical solver iterative to residual error curve convergence, so that
Obtain the oxygen concentration data on solid liquid interface 1685K thermoisopleths；
Step 5.2, the relation curve between oxygen concentration and crystal diameter is obtained, i.e. solid liquid interface radial direction oxygen concentration distribution is bent
Line, in order to analyze influence of the crucible rotation to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from
Inside melt, height distance melt and argon gas interface are 0.08m, and length 0.3m, direction is referred to by crucible and melt interface
To crystal growth axis, Fig. 4 (a) -4 (d) is that radial direction oxygen concentration divides in 0 ° of -180 ° of plane of solid liquid interface under different crucible rotations respectively
Radial direction oxygen concentration distribution curve and solid-liquid interface shape and the inspection of molten body temperature in 90 ° of cloth curve, solid liquid interface -270 ° of planes
Radial temperature profile curve at survey, according to solid liquid interface average oxygen concentrationThe mean square error of radial direction oxygen concentration distribution curve
MSEOWith gradient error and δOFor minimum principle, suitable crystal rotation is chosen；
Step 6, combining step 3~5, with reference to selected superconduction horizontal magnetic intensity, crystal rotation and crucible rotation three
Under the collective effect of person, obtain czochralski silicon monocrystal solid liquid interface oxygen concentration distributed intelligence under superconduction horizontal magnetic field, specifically according to
Lower step is implemented：
Step 6.1, during processing is set before CFX, superconduction horizontal magnetic intensity and crucible rotation are set for step 3, step 5
Selected suitable superconduction horizontal magnetic intensity and crucible rotation, because Gao Jingzhuan is advantageous to improve the uniformity of solid liquid interface,
So first by crystal rotation ωsGao Jingzhuan is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface footpath
To oxygen concentration distribution curve, as shown in Figure 5；
Step 6.2, by crystal rotation ωsLow brilliant turn is arranged to, is solved by iterative numerical and MATLAB maps and consolidated
Liquid interface radial direction oxygen concentration distribution curve, as shown in Figure 6；
Step 6.3, crystal rotation ω is calculated respectivelysThe oxygen concentration distribution of solid liquid interface radial direction is bent when turning for high brilliant turn with low crystalline substance
The average oxygen concentration of solid liquid interface in lineThe mean square error MSE related to oxygen concentration distributing homogeneityOWith gradient error and
δO, by comparative analysis qualitatively and quantitatively, selection is both adapted to reduce solid liquid interface oxygen concentration and can raising solid liquid interface
Superconduction horizontal magnetic intensity, crystal rotation and the crucible rotation of radial direction oxygen concentration distributing homogeneity.
In order to research and analyse influence of the cryogenic magnetic field to Modelling of Crystal Growth in CZ-Si Pulling, numerical simulation model of the invention is with Xi'an
The full-automatic CZ-Si single crystal growing furnaces of Polytechnics TDR-120 are prototype, add horizontal cryogenic magnetic field.In order to which numerical computations are convenient, to portion
Separation structure suitably simplify.The three-dimensional physical model of Modelling of Crystal Growth in CZ-Si Pulling mid-term is established, specific physical parameter includes：Crystal
Diameter 300mm, inventory 160kg, crystal length 200mm, rate of crystalline growth 0.52mm/min, X-direction are horizontal superconduction
Magnetic field, Y-axis are crystal growth direction of principal axis, and superconduction magnetic induction intensity reaches as high as 0.5T, as shown in Figure 1.
By the CFX fluid emulation modules in numerical simulation software ANSYS, crucible is turned into ωcTurn ω with crystalline substancesIt is arranged to 0rpm,
Superconduction magnetic induction intensity is adjusted respectively in 0.25T and 0.5T, is obtained solid liquid interface radial direction oxygen concentration under different magnetic field intensity and is distributed
Curve, as shown in Fig. 2 Fig. 2 (a) -2 (b) is radial direction oxygen concentration in 0 ° of -180 ° of plane of solid liquid interface and 90 ° of -270 ° of planes respectively
Distribution curve.Magnetic field intensity is higher, and solid liquid interface average oxygen concentration is lower, and oxygen concentration uniformity is better；Crucible is turned into ωcIt is arranged to
0rpm, regulation crystalline substance turn ωsRespectively 6rpm, 8rpm and 16rpm, iterative obtain solid liquid interface oxygen concentration distributed intelligence.It is brilliant
Turn ωsHigher, solid liquid interface average oxygen concentration is higher, and the uniformity of oxygen concentration distribution is poorer, and Fig. 3 (a) -3 (d) is different respectively
Crystalline substance turns ωsRadial direction oxygen in 90 ° of radial direction oxygen concentration distribution curve, solid liquid interface -270 ° of planes in lower 0 ° of -180 ° of plane of solid liquid interface
Detection temperature is distributed in concentration profile, solid-liquid interface shape and melt, then crystalline substance is turned into ωs0rpm is arranged to, regulation crucible turns
ωcRespectively 0.5rpm, 2rpm and 4rpm, iterative obtain solid liquid interface oxygen concentration distribution results.Crucible turns ωcIt is higher, then it is solid
The oxygen concentration rise of liquid interface edge region, oxygen concentration uniformity improve, and Fig. 4 (a) -4 (d) is that different crucibles turn ω respectivelycLower solid-liquid
Detection temperature is distributed in interface radial direction oxygen concentration distribution curve, solid-liquid interface shape and melt.By considering solid liquid interface
The low principle being more evenly distributed with radial direction oxygen concentration of oxygen concentration, chooses superconduction magnetic induction intensity 0.5T and crucible rotation 0.5rpm,
Crystalline substance is set to turn ωsFor 16rpm, obtain high crystalline substance and turn ωs, low crucible turn ωcUnder solid liquid interface oxygen concentration distribution curve, such as Fig. 5 institutes
Show, under same superconduction magnetic induction intensity 0.5T and crucible rotation 0.5rpm, set crystalline substance to turn ωsFor 6rpm, low brilliant turn is obtained
ωs, low crucible turn ωcUnder solid liquid interface oxygen concentration distribution curve, as shown in Figure 6.
In Figure 5, the simulation result under turning for Gao Jingzhuan, low crucible, is used respectivelyWith0 ° of solid liquid interface of expression-
The average oxygen concentration of 180 ° of planes and 90 ° of -270 ° of planes is
Mean square error MSE is used respectivelyOWith gradient error and δOCarry out evaluating 0 ° of -180 ° of plane of solid liquid interface and 90 ° -270 °
The uniformity that radial direction oxygen concentration is distributed in plane.
(1) MSE is utilizedOxyAnd MSEOyzRadial direction oxygen in 0 ° of -180 ° of plane of solid liquid interface and 90 ° of -270 ° of planes is represented respectively
Uniform concentration distribution, i.e.,
(2) δ is utilizedOxyAnd δOyzRadial direction oxygen concentration in 0 ° of -180 ° of plane of solid liquid interface and 90 ° of -270 ° of planes is represented respectively
Distributing homogeneity, i.e.,
And in figure 6, the simulation result under turning for low brilliant turn, low crucible, the average oxygen concentration of solid liquid interfaceAnd radially
Oxygen concentration distributing homogeneity MSEOAnd δORespectively
MSEOxy=0.0073, MSEOyz=0.0020
δOxy=0.7316, δOyz=0.6539
By the simulation result contrast under the process adjustments that turn with traditional Gao Jingzhuan, low crucible, as a result find it is low it is brilliant turn, low crucible
Under the process adjustments method turned, the average oxygen concentration of solid liquid interface is lower, and solid liquid interface radial direction oxygen concentration distributing homogeneity is more
Uniformly, at the same meet large scale electron level czochralski silicon monocrystal to oxygen impurities content in crystal requirement (Amount
Level).
Claims (9)
- A kind of 1. Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method, it is characterised in that specifically according to Lower step is implemented：Three-dimensional Local physical model needed for step 1, structure crystal for straight drawing monocrystal growth；Step 2, by three-dimensional Local physical model import CFX fluid emulation modules, setting analogue simulation is steady-state simulation, and is set Silicon melt, silicon crystal, the physical parameter and cryogenic magnetic field intensity of graphite crucible and silica crucible；Step 3, solve solid liquid interface radial direction oxygen concentration distribution situation under different superconduction horizontal magnetic intensities；The influence of step 4, analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt；The influence of step 5, analysis crucible rotation to radial temperature profile in solid-liquid interface shape and melt；Step 6, combining step 3~5, with reference to selected superconduction horizontal magnetic intensity, crystal rotation and crucible rotation three Under collective effect, czochralski silicon monocrystal solid liquid interface oxygen concentration distributed intelligence under superconduction horizontal magnetic field is obtained.
- 2. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 1 is specifically implemented according to following steps：Step 1.1, the three-dimensional Local physical model using Gambit software mess generation crystal for straight drawing monocrystal growth, include crystalline substance Body, melt, silica crucible and graphite crucible；Step 1.2, to set silica crucible radius be 0.306m, and graphite crucible radius is 0.32m, and melt radius is in crucible 0.3m, crucible rotate counterclockwise, crucible rotation ωc；Crystal radius scope is 0.15m~0.225m, and crystal turns clockwise, Crystal rotation is ωs, melt height is 0.08m~0.22m, and crystal length is 0m~0.6m, inventory 160kg, free interface For silicon melt and gas interface, boundary of the solid liquid interface between crystal and melt.
- 3. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 2, its It is characterised by, crucible rotation ω in the step 1.2cFor 0~10rpm, crystal rotation ωsFor 0~16rpm.
- 4. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 2 is specifically implemented according to following steps：Step 2.1, setting crucible are rotate counterclockwise, crucible rotation ωc, crystal turns clockwise, crystal rotation ωs；Step 2.2, hypothesis silicon melt are incompressible Newtonian fluid；Assuming that silicon melt meets Boussinesq approximations；Set Solid liquid interface is flat face, and supercooled state does not occur when solid liquid interface crystallizes, and the temperature of solid liquid interface is the melting temperature of silicon 1685K；Melt and argon gas interface are set, i.e. free surface is flat face, and its position height is highly identical with solid liquid interface, and Outwardly atmosphere radiations heat energy；Silica crucible bottom and crucible internal walls meet without slip boundary condition with silicon melt；Melt Interior oxygen transport process is ignored to melt flows with the influence conducted heat.
- 5. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 4, its It is characterised by, in the step 2.2, used boundary condition includes oxygen concentration boundary condition in iteration of simulations solution procedure And temperature boundary condition, wherein oxygen concentration boundary condition are as follows：(1) the oxygen concentration boundary condition of melted silicon and inner wall of quartz crucible intersection：<mrow> <msub> <mi>C</mi> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.5</mn> <mo>&times;</mo> <msup> <mn>10</mn> <mn>23</mn> </msup> </mrow> <msub> <mi>N</mi> <mi>A</mi> </msub> </mfrac> <mo>&times;</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> <mo>&times;</mo> <mfrac> <msub> <mi>a</mi> <mi>O</mi> </msub> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>a</mi> <mi>O</mi> </msub> </mrow> </mfrac> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo>/</mo> <msup> <mi>m</mi> <mn>3</mn> </msup> </mrow><mrow> <msub> <mi>a</mi> <mi>O</mi> </msub> <mo>=</mo> <msqrt> <msub> <mi>P</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </msub> </msqrt> <mo>&CenterDot;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msubsup> <mi>&Delta;G</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>3200</mn> <mo>/</mo> <mi>T</mi> <mo>-</mo> <mn>8.19</mn> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mi>P</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> </msub> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>113.826</mn> <mo>/</mo> <mi>T</mi> <mo>+</mo> <mn>24.32</mn> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>&Delta;G</mi> <mn>2</mn> <mn>0</mn> </msubsup> <mo>=</mo> <mo>-</mo> <mn>446570</mn> <mo>+</mo> <mn>169.19</mn> <mi>T</mi> <mo>.</mo> </mrow>Wherein, NAFor Avgadro constant,For partial pressure of oxygen, aoFor oxysome fraction, R is carrier of oxygen mole constant, and T is change Learn reaction temperature,For chemical reactionGibbs free amount.(2) melted silicon and the oxygen concentration boundary condition at argon gas interface：<mrow> <mo>-</mo> <msub> <mi>D</mi> <mi>O</mi> </msub> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>D</mi> <mrow> <mi>S</mi> <mi>i</mi> <mi>O</mi> </mrow> </msub> <mrow> <msub> <mi>RT&delta;</mi> <mi>g</mi> </msub> </mrow> </mfrac> <mfrac> <msub> <mi>p</mi> <mn>0</mn> </msub> <msub> <mi>C</mi> <mrow> <mi>S</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mrow> <mi>&Delta;</mi> <mi>G</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>C</mi> <mrow> <mi>s</mi> <mi>u</mi> <mi>r</mi> <mi>f</mi> </mrow> </msub> </mrow>In formula, COAnd CsurfIt is the oxygen concentration of oxygen concentration in melt and free surface respectively；CSiIt is melted silicon concentration；DOAnd DSiO It is diffusion coefficient and SiO gas diffusion coefficient in argon gas of the oxygen in silicon melt respectively；Δ G is chemical equation (Simelt +Omelt=SiOgas) Gibbs free amount, p0It is the steam pressure of silicon monoxide gas, R is gas molar constant, and T is chemistry Reaction temperature；δgIt is free surface boundary layer thickness；During the actual growing environment of crystal, the oxygen of free surface is under the brushing of argon gas, the oxygen concentration C of free surfacesurfOnly For melt inside oxygen concentration COCount very much, therefore by the oxygen concentration C of free surfacesurfIgnore, then the oxygen of free surface is dense Degree boundary condition is reduced toCO=0mol/m3；(3) the oxygen concentration boundary condition at solid liquid interface (crystal growth interface) place：<mrow> <mi>D</mi> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>V</mi> <mi>g</mi> </msub> <msub> <mi>C</mi> <mi>O</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow>In formula, D be oxygen diffusion coefficient, VgFor the translational speed of solid liquid interface, k is the segregation coefficient of oxygen, CoFor the oxygen in melt Concentration.Experiment discloses the segregation coefficient of oxygen close to unit 1, and the oxygen more than 99% is evaporate among argon gas from free surface, So the oxygen content being incorporated into crystal is ignored in solid liquid interface Whole Oxygen flux equilibrium, above formula is reduced to<mrow> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>C</mi> <mi>O</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mi>m</mi> <mi>o</mi> <mi>l</mi> <mo>/</mo> <msup> <mi>m</mi> <mn>3</mn> </msup> </mrow>Graphite crucible bottom and graphite crucible outer wall apply constant gradient Temperature Distribution value in temperature boundary condition, at free surface Establish heat flow density equation, such as following formula：<mrow> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mi>l</mi> </msub> <mo>&part;</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mi>&beta;</mi> <msup> <mrow> <mo>&lsqb;</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>1.25</mn> </msup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>l</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mi>s</mi> <mi>q</mi> <mi>r</mi> <mi>t</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>Q′l=qout,k-qin,k=σ ε T4-εqin,kqin,k=sumJ=1~N(Fk,jqout,j)In formula, β [T (r)-T0(r)]1.25For describing due to gaseous exchange and caused thermal losses, Q 'lFor describing melt liquid Face caused thermal losses by radiation, T are free surface temperature, T0For environment temperature, KlFor the silicon melt coefficient of heat conduction, β is gas The thermal losses coefficient of body convection current, r are free surface radius, and ε is radiation coefficient, and σ is Stefan-Boltzmann constants, Fk,jFor Ascent between two surfaces of k, j, qout,kIt is the heat flow of flux surface, qin,kIt is the heat flow for flowing into surface, x, z are sky Between rectangular coordinate system direction variable, N is surface total number；The inner surface not contacted in graphite crucible and the top surface of silica crucible, silica crucible with silicon melt and crystal outer surface Deng the surface of solids, similar heat flow density equation, such as following formula are also established：<mrow> <mfrac> <mrow> <mo>-</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mo>&part;</mo> <msub> <mi>T</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&part;</mo> <mi>n</mi> </mrow> </mfrac> <mo>=</mo> <mi>&beta;</mi> <msup> <mrow> <mo>&lsqb;</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>T</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> <mn>1.25</mn> </msup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>s</mi> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>r</mi> <mo>=</mo> <mi>c</mi> <mi>r</mi> <mi>y</mi> <mi>s</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> <mo>/</mo> <mi>c</mi> <mi>r</mi> <mi>u</mi> <mi>c</mi> <mi>i</mi> <mi>b</mi> <mi>l</mi> <mi>e</mi> <mi> </mi> <mi>r</mi> <mi>a</mi> <mi>d</mi> <mi>i</mi> <mi>u</mi> <mi>s</mi> </mrow>Q′s=qout,k-qin,k=σ ε T4-εqin,kWherein, Q 'sFor describing the surface of solids caused thermal losses by radiation, KsFor the silicon melt coefficient of heat conduction, r is crystal The inside radius of radius or silica crucible, y are rectangular coordinate system in space direction variable.It is 90000 that iterations is set in iterative controls, and time factor 1, the residual values of convergence curve are arranged to 1E- 06。
- 6. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 3 is specifically implemented according to following steps：Step 3.1, the numerical solver using CFX modules, under numerical solution difference superconduction horizontal magnetic intensity, crystal rotation ωs With crucible rotation ωcFlowing and heat transfer when being 0rpm in crucible melt；Step 3.2, the Temperature Distribution cloud atlas and oxygen concentration point of melt are obtained by the post processing of CFX modules after iteration convergence Cloth cloud atlas, solid liquid interface 1685K isothermal line positions are followed the trail of on Temperature Distribution cloud atlas, obtain the oxygen concentration distribution in solid liquid interface Data, the relation curve of oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, according to solid liquid interface Average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor minimum principle, choose and close Suitable cryogenic magnetic field intensity, such as following formula<mrow> <msub> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>c</mi> <mi>i</mi> </msub> </mrow>Wherein, n is the oxygen data amount check in collected solid liquid interface, ciFor oxygen data point, i is oxygen data arguments；<mrow> <msub> <mi>MSE</mi> <mi>O</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mover> <mi>c</mi> <mo>&OverBar;</mo> </mover> <mi>O</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow><mrow> <msub> <mi>&delta;</mi> <mi>O</mi> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>gradO</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>gradO</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>Wherein, gradOiIt is the gradient of each oxygen data point on solid liquid interface radial direction oxygen concentration distribution curve, gradOminIt is solid-liquid circle Face diameter is to the minimal gradient of oxygen concentration distribution curve, gradient error and δOIt is smaller, then illustrate that solid liquid interface radial direction oxygen concentration is distributed Uniformity it is more uniform.
- 7. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 4 is specifically implemented according to following steps：Step 4.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, by crucible Rotational speed omegac0rpm is arranged to, adjusts different crystal rotational speed omegas, iterative to residual error curve convergence, so as to obtain solid liquid interface Oxygen concentration data on 1685K thermoisopleths；Step 4.2, the relation curve between oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, For influence of the analyzing crystal rotating speed to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from melt Inside, apart from melt and argon gas interface 0.08m, length 0.3m, crystal growth is pointed in direction by crucible and melt interface Axle, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOWith gradient error and δOFor Minimum principle, choose suitable crystal rotation.
- 8. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 5 is specifically implemented according to following steps：Step 5.1, during processing is set before CFX, suitable magnetic field intensity of the magnetic field intensity selected by step 3 is set, set brilliant Body rotational speed omegasFor 0rpm, regulation crucible rotation ωc, by numerical solver iterative to residual error curve convergence, so as to obtain Oxygen concentration data on solid liquid interface 1685K thermoisopleths；Step 5.2, the relation curve between oxygen concentration and crystal diameter, i.e. solid liquid interface radial direction oxygen concentration distribution curve are obtained, In order to analyze influence of the crucible rotation to radial temperature profile in solid-liquid interface shape and melt, temperature detection loca is derived from melt Inside, height distance melt are 0.08m with argon gas interface, and length 0.3m, direction is pointed to brilliant by crucible and melt interface Body growth axis, according to solid liquid interface average oxygen concentrationThe mean square error MSE of radial direction oxygen concentration distribution curveOAnd gradient error And δOFor minimum principle, suitable crystal rotation is chosen.
- 9. a kind of Modelling of Crystal Growth in CZ-Si Pulling process optimization solid liquid interface oxygen distribution adjusting method according to claim 1, its It is characterised by, the step 6 is specifically implemented according to following steps：Step 6.1, during processing is set before CFX, superconduction horizontal magnetic intensity and crucible rotation are set for selected by step 3, step 5 Suitable the superconduction horizontal magnetic intensity and crucible rotation taken, because Gao Jingzhuan is advantageous to improve the uniformity of solid liquid interface, so First by crystal rotation ωsGao Jingzhuan is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface radial direction oxygen Concentration profile；Step 6.2, by crystal rotation ωsLow brilliant turn is arranged to, is solved by iterative numerical and MATLAB maps to obtain solid liquid interface Radial direction oxygen concentration distribution curve；Step 6.3, crystal rotation ω is calculated respectivelysWhen turning for high brilliant turn with low crystalline substance in solid liquid interface radial direction oxygen concentration distribution curve The average oxygen concentration of solid liquid interfaceThe mean square error MSE related to oxygen concentration distributing homogeneityOWith gradient error and δO, lead to Comparative analysis qualitatively and quantitatively is crossed, selection is both adapted to reduce solid liquid interface oxygen concentration and can raising solid liquid interface radial direction oxygen Superconduction horizontal magnetic intensity, crystal rotation and the crucible rotation of uniform concentration distribution.
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| CN108914201A (en) * | 2018-08-29 | 2018-11-30 | 西安理工大学 | A kind of Modelling of Crystal Growth in CZ-Si Pulling process parameter optimization method |
| CN109576785A (en) * | 2018-12-29 | 2019-04-05 | 徐州鑫晶半导体科技有限公司 | The method of oxygen content during adjusting monocrystalline silicon growing |
| CN110512278A (en) * | 2019-09-12 | 2019-11-29 | 西安奕斯伟硅片技术有限公司 | A kind of crystal pulling apparatus, device and method |
| CN111926384A (en) * | 2020-06-05 | 2020-11-13 | 徐州鑫晶半导体科技有限公司 | Single crystal furnace, method for determining operating parameters of single crystal furnace in growth process of single crystal silicon and method for preparing single crystal silicon |
| CN118658570A (en) * | 2024-08-19 | 2024-09-17 | 西安交通大学 | Method and device for determining shape of inner wall surface of crucible for growing silicon carbide by liquid phase method |
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| CN108914201A (en) * | 2018-08-29 | 2018-11-30 | 西安理工大学 | A kind of Modelling of Crystal Growth in CZ-Si Pulling process parameter optimization method |
| CN108914201B (en) * | 2018-08-29 | 2019-09-27 | 西安理工大学 | A kind of Modelling of Crystal Growth in CZ-Si Pulling process parameter optimization method |
| CN109576785A (en) * | 2018-12-29 | 2019-04-05 | 徐州鑫晶半导体科技有限公司 | The method of oxygen content during adjusting monocrystalline silicon growing |
| CN110512278A (en) * | 2019-09-12 | 2019-11-29 | 西安奕斯伟硅片技术有限公司 | A kind of crystal pulling apparatus, device and method |
| CN111926384A (en) * | 2020-06-05 | 2020-11-13 | 徐州鑫晶半导体科技有限公司 | Single crystal furnace, method for determining operating parameters of single crystal furnace in growth process of single crystal silicon and method for preparing single crystal silicon |
| CN111926384B (en) * | 2020-06-05 | 2022-06-17 | 徐州鑫晶半导体科技有限公司 | Single crystal furnace, method for determining operating parameters of single crystal furnace in growth process of single crystal silicon and method for preparing single crystal silicon |
| CN118658570A (en) * | 2024-08-19 | 2024-09-17 | 西安交通大学 | Method and device for determining shape of inner wall surface of crucible for growing silicon carbide by liquid phase method |
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