CN107747122B - Method for optimizing solid-liquid interface oxygen distribution regulation in Czochralski silicon single crystal growth process - Google Patents

Method for optimizing solid-liquid interface oxygen distribution regulation in Czochralski silicon single crystal growth process Download PDF

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CN107747122B
CN107747122B CN201710811360.3A CN201710811360A CN107747122B CN 107747122 B CN107747122 B CN 107747122B CN 201710811360 A CN201710811360 A CN 201710811360A CN 107747122 B CN107747122 B CN 107747122B
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oxygen concentration
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CN107747122A (en
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刘丁
任俊超
张新雨
张晶
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Xi'an Xinhui Equipment Technology Co.,Ltd.
Xian Eswin Material Technology Co Ltd
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Xian University of Technology
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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
    • 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
    • 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
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Abstract

The invention discloses a solid-liquid interface oxygen distribution adjusting method for optimizing a czochralski silicon single crystal growth process, which comprises the steps of firstly adjusting superconducting horizontal magnetic field intensity to obtain a solid-liquid interface oxygen concentration distribution curve under different magnetic field intensities, calculating average oxygen concentration of a solid-liquid interface and uniformity of radial oxygen concentration distribution of the solid-liquid interface, selecting a proper magnetic field intensity through comparison, then respectively adjusting crystal rotating speed and crucible rotating speed under the selected magnetic field intensity, obtaining crystal rotating speed and crucible rotating speed which are suitable for reducing solid-liquid interface oxygen concentration and improving the solid-liquid interface oxygen concentration distribution uniformity through comparison simulation results, and finally obtaining the czochralski silicon single crystal interface oxygen concentration distribution information under the superconducting horizontal magnetic field under the combined action of the selected superconducting magnetic field intensity, crystal rotating speed and crucible rotating speed Uneven distribution of oxygen.

Description

Method for optimizing solid-liquid interface oxygen distribution regulation in Czochralski silicon single crystal growth process
Technical Field
The invention belongs to the technical field of adjusting methods of a magnetically controlled Czochralski silicon single crystal solid-liquid interface oxygen distribution growth process, and particularly relates to an adjusting method for optimizing the solid-liquid interface oxygen distribution of the Czochralski silicon single crystal growth process.
Background
The Czochralski method is the main method for preparing silicon single crystal semiconductor materials in the fields of integrated circuits and photovoltaic power generation. The main quality evaluation indexes of silicon single crystals in the semiconductor industry include reduction of various harmful impurity contents (oxygen, carbon) in the wafer and reduction of micro-defects, wherein secondary defects caused by the oxygen impurity content can seriously affect the quality of drawn silicon semiconductor materials and the performance of produced devices. In order to reduce the micro-defects of the crystal as much as possible and ensure the uniformity of the resistivity of the crystal, how to reduce the content of oxygen impurities in a solid-liquid interface (a crystal and melt interface) in the growth process of the large-size crystal and improve the uniformity of oxygen distribution in the solid-liquid interface has important significance.
Because the molten silicon is in a high-temperature and sealed furnace body, the oxygen distribution condition in the crucible melt and the solid-liquid interface cannot be directly obtained. At present, methods for obtaining oxygen distribution in crystals mainly include an infrared absorption method and a numerical simulation method. The infrared absorption method is to analyze the infrared spectrum by measuring the silicon wafer, and quantitatively analyze and calculate the oxygen content and the oxygen distribution uniformity on the silicon wafer according to the peak position and the absorption intensity. The numerical simulation method is characterized in that a single crystal furnace thermal field is modeled by commercial CFD software, and the distribution condition of oxygen content in a melt and in a solid-liquid interface is obtained by solving by adopting a Finite Volume Method (FVM), so that the experiment cost is low, the period is short, and the crystal growth problem can be known better and faster. The existing process adjusting method of high crystal rotating speed and low crystal rotating speed under the conventional horizontal magnetic field in the numerical simulation method easily causes the oxygen content in the crystal to be increased, and the working performance of the manufactured electronic device is seriously influenced. Therefore, the important problem to be solved at present is to provide a method for adjusting the oxygen distribution of the solid-liquid interface in the Czochralski silicon single crystal growth process, so as to reduce the oxygen concentration of the solid-liquid interface and improve the uniformity of the oxygen distribution of the solid-liquid interface in the Czochralski silicon single crystal growth process, and to meet the market demand for high-quality silicon single crystals.
Disclosure of Invention
The invention aims to provide a method for adjusting oxygen distribution of a solid-liquid interface optimized by a czochralski silicon single crystal growth process, which solves the problems that the oxygen content in the crystal is too high and the oxygen distribution is not uniform easily caused when the parameters of the czochralski silicon single crystal growth process are adjusted in the prior art.
The technical scheme adopted by the invention is that the method for optimizing the oxygen distribution adjustment of the solid-liquid interface in the czochralski silicon single crystal growth process is implemented according to the following steps:
step 1, constructing a three-dimensional local physical model required by the growth of silicon single crystal by a Czochralski method;
step 2, importing the three-dimensional local physical model into a CFX fluid simulation module, setting simulation as steady-state simulation, and setting physical parameters and superconducting magnetic field strength of silicon melt, silicon crystal, graphite crucible and quartz crucible;
step 3, solving the radial oxygen concentration distribution condition of the solid-liquid interface under different superconducting horizontal magnetic field strengths;
step 4, analyzing the influence of the crystal rotation speed on the solid-liquid interface shape and the radial temperature distribution in the melt;
step 5, analyzing the influence of the crucible rotation speed on the shape of a solid-liquid interface and the radial temperature distribution in the melt;
and 6, integrating the steps 3-5, and obtaining oxygen concentration distribution information of the solid-liquid interface of the czochralski silicon single crystal under the superconducting horizontal magnetic field under the combined action of the selected superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed.
The present invention is also characterized in that,
the step 1 is implemented according to the following steps:
step 1.1, generating a three-dimensional local physical model for the growth of the silicon single crystal by the Czochralski method by using a Gambit software grid, wherein the three-dimensional local physical model comprises a crystal, a melt, a quartz crucible and a graphite crucible;
step 1.2, setting the radius of a quartz crucible to be 0.306m, the radius of a graphite crucible to be 0.32m, the radius of a melt in the crucible to be 0.3m, rotating the crucible anticlockwise, and setting the rotating speed of the crucible to be omegac(ii) a The radius range of the crystal is 0.15 m-0.225 m, the crystal rotates clockwise, and the rotation speed of the crystal is omegasThe height of the melt is 0.08-0.22 m, the length of the crystal is 0-0.6 m, the feeding amount is 160kg, the free interface is the interface between the silicon melt and the gas, and the solid-liquid interface is the phase interface between the crystal and the melt. Step 1.2 crucible rotation speed omegac0-10 rpm, crystal rotation speed omegasIs 0 to 16 rpm.
The step 2 is implemented according to the following steps:
step 2.1, setting the crucible to rotate anticlockwise, wherein the rotating speed of the crucible is omegacThe crystal rotates clockwise at omegas；
Step 2.2, assuming that the silicon melt is incompressible Newtonian fluid; assuming that the silicon melt satisfies the Boussinesq approximation; setting a solid-liquid interface as a flat surface, wherein a supercooled state does not occur during crystallization of the solid-liquid interface, and the temperature of the solid-liquid interface is 1685K of the melting point of silicon; setting the interface of the melt and argon, namely the free liquid level is a flat surface, the height of the free liquid level is the same as that of the solid-liquid interface, and radiating heat to the external atmosphere environment; the bottom of the quartz crucible, the inner wall of the crucible and the silicon melt meet the condition of no sliding boundary; oxygen transport processes within the melt have negligible effect on melt flow and heat transfer.
In step 2.2, the boundary conditions used in the simulation iterative solution process include an oxygen concentration boundary condition and a temperature boundary condition, wherein the oxygen concentration boundary condition is as follows:
(1) the boundary condition of the oxygen concentration at the boundary of the silicon melt and the inner wall of the quartz crucible is as follows:
Figure BDA0001403971240000031
Figure BDA0001403971240000032
Figure BDA0001403971240000041
wherein N isAIs the alpha-Galois constant of the analog-to-digital converter,
Figure BDA0001403971240000042
is the partial pressure of oxygen, aoIs the volume fraction of oxygen, R is the oxygen gas molar constant, T is the chemical reaction temperature,
Figure BDA0001403971240000043
is a chemical reaction
Figure BDA0001403971240000044
Amount of change in free energy.
(2) Oxygen concentration boundary condition at interface of silicon melt and argon gas:
Figure BDA0001403971240000045
in the formula, COAnd CsurfThe oxygen concentration in the melt and the oxygen concentration at the free liquid level, respectively; cSiIs the silicon melt concentration; dOAnd DSiOThe diffusion coefficient of oxygen in the silicon melt and the diffusion coefficient of SiO gas in the silicon meltDiffusion coefficient in argon; Δ G is the chemical reaction formula (Si)melt+Omelt＝SiOgas) Amount of change in free energy of p0Is the vapor pressure of SiO gas, R is the gas molar constant, T is the chemical reaction temperature; deltagIs the free liquid level boundary layer thickness;
in the actual growth environment of the crystal, the oxygen concentration C of the free liquid surface is blown by argon gassurfOnly the internal oxygen concentration C of the meltOTen thousand of (a), thus the oxygen concentration C of the free liquid surfacesurfNeglecting, the oxygen concentration boundary condition of the free liquid surface is simplified to
CO＝0mol/m3；
(3) Oxygen concentration boundary conditions at solid-liquid interface (crystal growth interface):
Figure BDA0001403971240000046
wherein D is the diffusion coefficient of oxygen, VgThe moving speed of the solid-liquid interface, k is the segregation coefficient of oxygen, CoIs the oxygen concentration in the melt. Experiments show that the segregation coefficient of oxygen is close to unit 1, and more than 99 percent of oxygen is volatilized into argon from a free liquid surface, so that the content of oxygen doped into crystals is ignored in the whole oxygen flux balance of a solid-liquid interface, and the formula is simplified into that
Figure BDA0001403971240000047
In the temperature boundary condition, the bottom of the graphite crucible and the outer wall of the graphite crucible are applied with equal gradient temperature distribution values, and a heat flux density equation is established at the free liquid level, which is as follows:
Figure BDA0001403971240000051
Ql'＝qout,k-qin,k＝σεT4-εqin,k
qin,k＝sumj＝1～N(Fk,jqout,j)
wherein β [ T (r) -T0(r)]1.25Describing the heat loss due to gas convection, Ql' to describe the heat loss of the melt level by radiation, T is the free level temperature, T0Is ambient temperature, KlFor the heat transfer coefficient of the silicon melt, β is the heat loss coefficient of gas convection, r is the free liquid surface radius, ε is the emissivity, σ is the Stefan-Boltzmann constant, Fk,jIs the angular coefficient between the two surfaces of k, j, qout,kIs the heat flow out of the surface, qin,kThe heat flow flowing into the surface is shown, x and z are direction variables of a space rectangular coordinate system, and N is the total number of the surface;
similar heat flux density equations are also established at the top surfaces of the graphite crucible and the quartz crucible, the inner surface of the quartz crucible not in contact with the silicon melt, and the solid surfaces such as the outer surface of the crystal, as follows:
Figure BDA0001403971240000052
Qs'＝qout,k-qin,k＝σεT4-εqin,k
wherein Q iss' to describe the heat loss from a solid surface by radiation, KsThe thermal conductivity of the silicon melt is shown as r, the radius of the crystal or the inner radius of the quartz crucible is shown as r, and y is a direction variable of a space rectangular coordinate system.
In the iterative solution control, the number of iterations is set to 90000, the time factor is set to 1, and the residual value of the convergence curve is set to 1E-06.
Step 3 is specifically implemented according to the following steps:
step 3.1, using a numerical solver of the CFX module to numerically solve the crystal rotation speed omega under different superconducting horizontal magnetic field strengthssAnd the rotational speed omega of the cruciblecBoth flow and heat transfer within the crucible melt at 0 rpm;
step 3.2, obtaining a temperature distribution cloud picture and oxygen concentration of the melt through post-processing of the CFX module after iteration convergenceAnd tracking the position of a isotherm of the solid-liquid interface 1685K on the temperature distribution cloud chart to obtain oxygen concentration distribution data on the solid-liquid interface and obtain a relation curve of the oxygen concentration and the crystal diameter, namely a radial oxygen concentration distribution curve of the solid-liquid interface. According to the average oxygen concentration at solid-liquid interface
Figure BDA0001403971240000061
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOAnd selecting proper superconducting magnetic field intensity as a minimum principle. Wherein the average oxygen concentration
Figure BDA0001403971240000062
Used for measuring the oxygen concentration of the solid-liquid interface, and the mean square error MSEOSum gradient error sum deltaOUsed for measuring the uniformity of oxygen concentration distribution at solid-liquid interface, as shown in the following formula
Figure BDA0001403971240000063
Wherein n is the number of collected oxygen data on the solid-liquid interface, ciIs an oxygen data point, i is an oxygen data independent variable;
Figure BDA0001403971240000064
Figure BDA0001403971240000065
wherein, gradOiIs the gradient, gradO, of each oxygen data point on the solid-liquid interface radial oxygen concentration distribution curveminIs the minimum gradient, gradient error sum delta of the radial oxygen concentration distribution curve of the solid-liquid interfaceOThe smaller the average particle diameter, the more uniform the radial oxygen concentration distribution at the solid-liquid interface.
Step 4 is specifically implemented according to the following steps:
step 4.1, in the CFX pretreatment setting, setting the appropriate magnetic field intensity selected in the step 3, and rotating the crucible at the rotating speedωcSet to 0rpm, adjust different crystal rotation speeds omegasIteratively solving until a residual error curve converges, thereby obtaining oxygen concentration data on a solid-liquid interface 1685K isotherm;
step 4.2, obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a radial oxygen concentration distribution curve of the solid-liquid interface, in order to analyze the influence of the crystal rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, wherein the temperature detection position is taken from the inside of the melt, is 0.08m away from the interface of the melt and argon, has the length of 0.3m, points to a crystal growth axis from the interface of the crucible and the melt in the direction, and points to the crystal growth axis according to the average oxygen concentration of the solid-
Figure BDA0001403971240000071
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOFor the minimum principle, the proper crystal rotation speed is selected.
Step 5 is specifically implemented according to the following steps:
step 5.1, in the CFX pretreatment setting, setting the magnetic field intensity to be the proper magnetic field intensity selected in the step 3, and setting the crystal rotation speed omegasIs 0rpm, the rotating speed omega of the crucible is adjustedcIteratively solving through a numerical solver until a residual error curve converges, thereby obtaining oxygen concentration data on a solid-liquid interface 1685K isotherm;
step 5.2, obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a solid-liquid interface radial oxygen concentration distribution curve, in order to analyze the influence of the crucible rotation speed on the solid-liquid interface shape and the melt internal radial temperature distribution, wherein the temperature detection position is taken from the inside of the melt, the height is 0.08m away from the melt-argon interface, the length is 0.3m, the direction is from the crucible to the melt interface to the crystal growth axis, and the average oxygen concentration of the solid-liquid interface is based on
Figure BDA0001403971240000072
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOFor the minimum principle, the proper crystal rotation speed is selected.
Step 6 is implemented according to the following steps:
step 6.1, in the CFX pretreatment setting, setting the superconducting horizontal magnetic field intensity and the crucible rotating speed as the proper superconducting horizontal magnetic field intensity and the crucible rotating speed selected in the step 3 and the step 5, and because the high crystal rotation is favorable for improving the consistency of a solid-liquid interface, firstly, the crystal rotating speed omega is setsSetting the crystal transition as high crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping;
step 6.2, rotating the crystal at the speed omegasSetting the crystal transition as low crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping;
step 6.3, calculating the crystal rotation speed omega respectivelysThe average oxygen concentration of the solid-liquid interface in the radial oxygen concentration distribution curve of the solid-liquid interface at the time of high crystal transition and low crystal transition
Figure BDA0001403971240000073
And mean square error MSE associated with uniformity of oxygen concentration distributionOSum gradient error sum deltaOThrough quantitative and qualitative comparative analysis, the superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed which are suitable for reducing the oxygen concentration of the solid-liquid interface and improving the radial oxygen concentration distribution uniformity of the solid-liquid interface are obtained through selection.
The method for adjusting the oxygen distribution of the solid-liquid interface optimized by the czochralski silicon single crystal growth process has the advantages that the oxygen concentration distribution state in the crucible melt and the oxygen concentration distribution information of the solid-liquid interface can be intuitively and accurately recognized by establishing a three-dimensional numerical value to simulate the czochralski silicon single crystal growth process, and the oxygen content and the oxygen impurity distribution uniformity in the crystal can be qualitatively analyzed according to the oxygen concentration distribution curve of the solid-liquid interface. And on the basis of quantitative analysis, the arithmetic mean value of oxygen concentration data is used for measuring the oxygen concentration of the solid-liquid interface, the mean square error of the oxygen concentration data and the gradient error of an oxygen concentration distribution curve are used for measuring the uniformity of the oxygen concentration distribution of the solid-liquid interface. The combination of qualitative analysis and quantitative analysis results shows that the process adjusting method of low crystal rotation speed and low crucible rotation speed under the selected proper magnetic field strength can effectively reduce the oxygen concentration of the solid-liquid interface and improve the radial oxygen concentration distribution uniformity of the solid-liquid interface, thereby achieving the purposes of reducing the content of oxygen impurities in the silicon crystal and improving the oxygen distribution uniformity in the crystal, and further improving the quality of the large-size silicon single crystal.
Drawings
FIG. 1 is a three-dimensional numerical simulation silicon single crystal growth schematic diagram of a solid-liquid interface oxygen distribution adjusting method optimized by a czochralski silicon single crystal growth process of the invention;
FIG. 2(a) to FIG. 2(b) are graphs showing the solid-liquid interface oxygen concentration distribution at different superconducting magnetic field strengths in the method for optimizing the solid-liquid interface oxygen distribution regulation in the Czochralski silicon single crystal growth process of the present invention;
FIGS. 3(a) to 3(d) are graphs showing the solid-liquid interface oxygen concentration distribution at different crystal rotation speeds in the method for optimizing the solid-liquid interface oxygen distribution regulation in the Czochralski silicon single crystal growth process of the present invention;
FIGS. 4(a) to 4(d) are graphs showing the solid-liquid interface oxygen concentration distribution at different crucible rotation speeds in the method for optimizing the solid-liquid interface oxygen distribution regulation in the Czochralski silicon single crystal growth process of the present invention;
FIG. 5 is a solid-liquid interface oxygen concentration distribution curve diagram under high crystal rotation and low crucible rotation in the solid-liquid interface oxygen distribution adjusting method optimized by the czochralski silicon single crystal growth process;
FIG. 6 is a solid-liquid interface oxygen concentration distribution curve diagram under low crucible rotation and low crucible rotation in the method for adjusting the solid-liquid interface oxygen distribution optimized by the czochralski silicon single crystal growth process.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a method for adjusting oxygen distribution of an optimized solid-liquid interface of a czochralski silicon single crystal growth process, which is implemented according to the following steps:
step 1, constructing a three-dimensional local physical model required by the growth of the silicon single crystal by the Czochralski method, and specifically implementing the following steps:
step 1.1, as shown in figure 1, utilizing a Gambit software grid to generate a three-dimensional local physical model for the growth of silicon single crystals by a Czochralski method, wherein the three-dimensional local physical model comprises crystals, melts, a quartz crucible and a graphite crucible;
step 1.2, setting the radius of a quartz crucible to be 0.306m, the radius of a graphite crucible to be 0.32m, the radius of a melt in the crucible to be 0.3m, rotating the crucible anticlockwise, and setting the rotating speed of the crucible to be omegac(ii) a The radius range of the crystal is 0.15 m-0.225 m, the crystal rotates clockwise, and the rotation speed of the crystal is omegasThe height of the melt is 0.08-0.22 m, the length of the crystal is 0-0.6 m, the feeding amount is 160kg, the free interface is the interface between the silicon melt and the gas, and the solid-liquid interface is the phase interface between the crystal and the melt. Wherein, the crucible rotating speed omegac0-10 rpm, crystal rotation speed omegasIs 0 to 16 rpm. In the simulation experiment of the present invention, the crystal radius was set to 0.15m and the crystal length was set to 0.2 m.
Step 2, importing the three-dimensional local physical model into a CFX fluid simulation module, setting simulation as steady-state simulation, and setting physical parameters and superconducting magnetic field intensity of silicon melt, silicon crystal, graphite crucible and quartz crucible, wherein the physical parameters are set as shown in Table 1:
TABLE 1 physical Property parameters
Figure BDA0001403971240000101
The method is implemented according to the following steps:
step 2.1, setting the crucible to rotate anticlockwise, wherein the rotating speed of the crucible is omegacThe crystal rotates clockwise at omegas；
Step 2.2, assuming that the silicon melt is incompressible Newtonian fluid; assuming that the silicon melt satisfies the Boussinesq approximation; setting a solid-liquid interface as a flat surface, wherein a supercooled state does not occur during crystallization of the solid-liquid interface, and the temperature of the solid-liquid interface is 1685K of the melting point of silicon; setting the interface of the melt and argon, namely the free liquid level is a flat surface, the height of the free liquid level is the same as that of the solid-liquid interface, and radiating heat to the external atmosphere environment; the bottom of the quartz crucible, the inner wall of the crucible and the silicon melt meet the condition of no sliding boundary; the oxygen transport process in the melt has negligible effect on the melt flow and heat transfer,
in step 2.2, the boundary conditions used in the simulation iterative solution process include an oxygen concentration boundary condition and a temperature boundary condition, wherein the oxygen concentration boundary condition is as follows:
(1) the boundary condition of the oxygen concentration at the boundary of the silicon melt and the inner wall of the quartz crucible is as follows:
Figure BDA0001403971240000111
Figure BDA0001403971240000112
Figure BDA0001403971240000113
wherein N isAIs the alpha-Galois constant of the analog-to-digital converter,
Figure BDA0001403971240000114
is the partial pressure of oxygen, aoIs the volume fraction of oxygen, R is the oxygen gas molar constant, T is the chemical reaction temperature,
Figure BDA0001403971240000115
is a chemical reaction
Figure BDA0001403971240000116
Amount of change in free energy.
(2) Oxygen concentration boundary condition at interface of silicon melt and argon gas:
Figure BDA0001403971240000117
in the formula, COAnd CsurfThe oxygen concentration in the melt and the oxygen concentration at the free liquid level, respectively; cSiIs the silicon melt concentration; dOAnd DSiOThe diffusion coefficient of oxygen in the silicon melt and the diffusion coefficient of SiO gas in argon respectively; Δ G is the chemical reaction formula (Si)melt+Omelt＝SiOgas) Amount of change in free energy of p0Is the vapor pressure of SiO gas, R is the gas molar constant, T isThe temperature of the chemical reaction; deltagIs the free liquid level boundary layer thickness;
in the actual growth environment of the crystal, the oxygen concentration C of the free liquid surface is blown by argon gassurfOnly the internal oxygen concentration C of the meltOTen thousand of (a), thus the oxygen concentration C of the free liquid surfacesurfNeglecting, the oxygen concentration boundary condition of the free liquid surface is simplified to
CO＝0mol/m3；
(3) Oxygen concentration boundary conditions at solid-liquid interface (crystal growth interface):
Figure BDA0001403971240000121
wherein D is the diffusion coefficient of oxygen, VgThe moving speed of the solid-liquid interface, k is the segregation coefficient of oxygen, CoIs the oxygen concentration in the melt. Experiments show that the segregation coefficient of oxygen is close to unit 1, and more than 99 percent of oxygen is volatilized into argon from a free liquid surface, so that the content of oxygen doped into crystals is ignored in the whole oxygen flux balance of a solid-liquid interface, and the formula is simplified into that
Figure BDA0001403971240000122
In the temperature boundary condition, the bottom of the graphite crucible and the outer wall of the graphite crucible are applied with equal gradient temperature distribution values, and a heat flux density equation is established at the free liquid level, which is as follows:
Figure BDA0001403971240000123
Ql'＝qout,k-qin,k＝σεT4-εqin,k
qin,k＝sumj＝1～N(Fk,jqout,j)
wherein β [ T (r) -T0(r)]1.25Describing the heat loss due to gas convection, Ql' use withTo describe the heat loss of the melt level by radiation, T being the free level temperature, T0Is ambient temperature, KlFor the heat transfer coefficient of the silicon melt, β is the heat loss coefficient of gas convection, r is the free liquid surface radius, ε is the emissivity, σ is the Stefan-Boltzmann constant, Fk,jIs the angular coefficient between the two surfaces of k, j, qout,kIs the heat flow out of the surface, qin,kThe heat flow flowing into the surface is shown, x and z are direction variables of a space rectangular coordinate system, and N is the total number of the surface;
similar heat flux density equations are also established at the top surfaces of the graphite crucible and the quartz crucible, the inner surface of the quartz crucible not in contact with the silicon melt, and the solid surfaces such as the outer surface of the crystal, as follows:
Figure BDA0001403971240000131
Qs'＝qout,k-qin,k＝σεT4-εqin,k
wherein Q iss' to describe the heat loss from a solid surface by radiation, KsThe thermal conductivity of the silicon melt is shown as r, the radius of the crystal or the inner radius of the quartz crucible is shown as r, and y is a direction variable of a space rectangular coordinate system.
Setting the iteration times to 90000, the time factor to 1 and the residual error value of the convergence curve to 1E-06 in the iteration solving control;
step 3, solving the radial oxygen concentration distribution condition of the solid-liquid interface under different superconducting horizontal magnetic field strengths, and specifically implementing the following steps:
step 3.1, using a numerical solver of the CFX module to numerically solve the crystal rotation speed omega under different superconducting horizontal magnetic field strengthssAnd the rotational speed omega of the cruciblecBoth flow and heat transfer within the crucible melt at 0 rpm;
step 3.2, obtaining a temperature distribution cloud picture and an oxygen concentration distribution cloud picture of the melt through post-processing of the CFX module after iterative convergence, tracking the position of a temperature line 1685K of the solid-liquid interface on the temperature distribution cloud picture to obtain oxygen concentration distribution data on the solid-liquid interface,obtaining a relation curve of oxygen concentration and crystal diameter, i.e. a radial oxygen concentration distribution curve of the solid-liquid interface, as shown in FIG. 2, wherein FIG. 2(a) is a radial oxygen concentration distribution curve in a plane of 0 to 180 degrees (parallel to the magnetic field direction) of the solid-liquid interface, and FIG. 2(b) is a radial oxygen concentration distribution curve in a plane of 90 to 270 degrees (perpendicular to the magnetic field direction) of the solid-liquid interface, according to the average oxygen concentration of the solid-liquid interface
Figure BDA0001403971240000132
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOSelecting suitable superconducting magnetic field strength for minimum principle, as shown in the following formula
Figure BDA0001403971240000133
Wherein n is the number of collected oxygen data on the solid-liquid interface, ciIs an oxygen data point, i is an oxygen data independent variable;
Figure BDA0001403971240000134
Figure BDA0001403971240000141
wherein, gradOiIs the gradient, gradO, of each oxygen data point on the solid-liquid interface radial oxygen concentration distribution curveminIs the minimum gradient, gradient error sum delta of the radial oxygen concentration distribution curve of the solid-liquid interfaceOThe smaller the oxygen concentration distribution, the more uniform the radial oxygen concentration distribution of the solid-liquid interface is;
step 4, analyzing the influence of the crystal rotation speed on the solid-liquid interface shape and the radial temperature distribution in the melt, and specifically implementing the following steps:
step 4.1, in the CFX pretreatment setting, setting the appropriate magnetic field intensity selected in the step 3, and setting the crucible rotation speed omegacSet to 0rpm, adjust different crystal rotation speeds omegasAnd iteratively solving until the residual error curve converges, thereby obtaining the temperature on the isotherm of the solid-liquid interface 1685KOxygen concentration data of (d);
step 4.2, obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a solid-liquid interface radial oxygen concentration distribution curve, in order to analyze the influence of the crystal rotation speed on the solid-liquid interface shape and the melt internal radial temperature distribution, wherein the temperature detection position is taken from the inside of the melt, is 0.08m away from the melt and argon interface, the length is 0.3m, the direction is from the crucible to the melt interface to the crystal growth axis, and the graphs (a) to (d) in the figures 3 are respectively a solid-liquid interface radial oxygen concentration distribution curve in a 0-180-degree plane, a solid-liquid interface radial oxygen concentration distribution curve in a 90-270-degree plane, a solid-liquid interface shape and a melt internal temperature detection radial temperature distribution curve, according to the solid-liquid interface average oxygen concentration distribution
Figure BDA0001403971240000142
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOSelecting proper crystal rotation speed as a minimum principle;
and 5, analyzing the influence of the crucible rotation speed on the solid-liquid interface shape and the radial temperature distribution in the melt, and specifically implementing the following steps:
step 5.1, in the CFX pretreatment setting, setting the magnetic field intensity to be the proper magnetic field intensity selected in the step 3, and setting the crystal rotation speed omegasIs 0rpm, the rotating speed omega of the crucible is adjustedcIteratively solving through a numerical solver until a residual error curve converges, thereby obtaining oxygen concentration data on a solid-liquid interface 1685K isotherm;
step 5.2, obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a radial oxygen concentration distribution curve of the solid-liquid interface, in order to analyze the influence of the crucible rotation speed on the shape of the solid-liquid interface and the radial temperature distribution in the melt, wherein the temperature detection position is taken from the inside of the melt, the height is 0.08m away from the interface of the melt and the argon, the length is 0.3m, the direction is from the interface of the crucible and the melt to the crystal growth axis, and the graphs in the figures 4(a) to 4(d) are respectively a radial oxygen concentration distribution curve in a 0-180-degree plane of the solid-liquid interface, a radial oxygen concentration distribution curve in a 90-270-degree plane of the solid-liquid interface, and a radial temperature distribution curve at the shape of the solidAccording to the average oxygen concentration at solid-liquid interface
Figure BDA0001403971240000151
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOSelecting proper crystal rotation speed as a minimum principle;
and 6, integrating the steps 3-5, and obtaining oxygen concentration distribution information of a solid-liquid interface of the czochralski silicon single crystal under the superconducting horizontal magnetic field by combining the combined action of the selected superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed, wherein the oxygen concentration distribution information is implemented according to the following steps:
step 6.1, in the CFX pretreatment setting, setting the superconducting horizontal magnetic field intensity and the crucible rotating speed as the proper superconducting horizontal magnetic field intensity and the crucible rotating speed selected in the step 3 and the step 5, and because the high crystal rotation is favorable for improving the consistency of a solid-liquid interface, firstly, the crystal rotating speed omega is setsSetting as high crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping, as shown in FIG. 5;
step 6.2, rotating the crystal at the speed omegasSetting the crystal transition as low crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping, as shown in FIG. 6;
step 6.3, calculating the crystal rotation speed omega respectivelysThe average oxygen concentration of the solid-liquid interface in the radial oxygen concentration distribution curve of the solid-liquid interface at the time of high crystal transition and low crystal transition
Figure BDA0001403971240000152
And mean square error MSE associated with uniformity of oxygen concentration distributionOSum gradient error sum deltaOThrough quantitative and qualitative comparative analysis, the superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed which are suitable for reducing the oxygen concentration of the solid-liquid interface and improving the radial oxygen concentration distribution uniformity of the solid-liquid interface are obtained through selection.
In order to research and analyze the influence of the superconducting magnetic field on the growth of the czochralski silicon single crystal, the numerical simulation model of the invention takes a TDR-120 full-automatic CZ-Si single crystal furnace of the university of Western Anlun as a prototype, and a horizontal superconducting magnetic field is added. For the convenience of numerical calculation, a part of the structure is appropriately simplified. Establishing a three-dimensional physical model in the middle growth period of the czochralski silicon single crystal, wherein the specific physical parameters comprise: the diameter of the crystal is 300mm, the feeding amount is 160kg, the length of the crystal is 200mm, the growth speed of the crystal is 0.52mm/min, the X direction is a horizontal superconducting magnetic field, the Y axis is the growth axis direction of the crystal, and the maximum superconducting magnetic induction intensity can reach 0.5T, as shown in figure 1.
The crucible is rotated to omega by a CFX fluid simulation module in numerical simulation software ANSYScAnd crystal transformation omegasSetting the speed to be 0rpm, adjusting the superconducting magnetic induction intensity to be 0.25T and 0.5T respectively, and obtaining the radial oxygen concentration distribution curve of the solid-liquid interface under different magnetic field strengths, as shown in figure 2, wherein figures 2(a) -2(b) are radial oxygen concentration distribution curves in a 0-180 degree plane and a 90-270 degree plane of the solid-liquid interface respectively. The higher the magnetic field intensity is, the lower the average oxygen concentration of the solid-liquid interface is, and the better the uniformity of the oxygen concentration is; the crucible is rotated to omegacSet at 0rpm, adjusted for crystal rotation omegasRespectively at 6rpm, 8rpm and 16rpm, and obtaining the oxygen concentration distribution information of the solid-liquid interface by iterative solution. Crystal transformation of omegasThe higher the average oxygen concentration at the solid-liquid interface, the worse the uniformity of the oxygen concentration distribution, and FIG. 3(a) to FIG. 3(d) show different crystal transitions ωsRadial oxygen concentration distribution curve in 0-180 degree plane of lower solid-liquid interface, radial oxygen concentration distribution curve in 90-270 degree plane of solid-liquid interface, solid-liquid interface shape and temperature distribution in melt, and then crystal is transformed to omegasSet to 0rpm, adjust crucible rotation omegacRespectively at 0.5rpm, 2rpm and 4rpm, and iteratively solving to obtain the solid-liquid interface oxygen concentration distribution result. Crucible rotation omegacThe higher the oxygen concentration is, the higher the oxygen concentration in the edge region of the solid-liquid interface is, the better the uniformity of the oxygen concentration becomes, and FIGS. 4(a) -4(d) are respectively different crucible rotation omegacThe radial oxygen concentration distribution curve of the lower solid-liquid interface, the shape of the solid-liquid interface and the detection temperature distribution in the melt. By comprehensively considering the principle that the oxygen concentration of the solid-liquid interface is low and the radial oxygen concentration distribution is more uniform, selecting the superconducting magnetic induction intensity of 0.5T and the crucible rotation speed of 0.5rpm, and setting the crystal rotation omegas16rpm, high crystal transition omegasLow crucible rotation omegacThe solid-liquid interface oxygen concentration distribution curve below was set at 0.5T of superconducting induction strength and 0.5rpm of crucible rotation speed, as shown in FIG. 5Crystal setting and omega turningsAt 6rpm, a low crystal transition omega was obtainedsLow crucible rotation omegacThe solid-liquid interface oxygen concentration distribution curve below is shown in FIG. 6.
In FIG. 5, the simulation results for high crystal rotation and low crucible rotation are shown respectively
Figure BDA0001403971240000171
And
Figure BDA0001403971240000172
the average oxygen concentration of the solid-liquid interface is 0-180 DEG plane and 90-270 DEG plane
Figure BDA0001403971240000173
Figure BDA0001403971240000174
Using mean square error MSE respectivelyOSum gradient error sum deltaOThe uniformity of the radial oxygen concentration distribution in the 0-180 DEG plane and the 90-270 DEG plane of the solid-liquid interface is evaluated.
(1) Using MSEOxyAnd MSEOyzRespectively shows the radial oxygen concentration distribution uniformity in a solid-liquid interface plane of 0 to 180 degrees and a plane of 90 to 270 degrees, namely
Figure BDA0001403971240000175
Figure BDA0001403971240000176
(2) Using deltaOxyAnd deltaOyzRespectively shows the radial oxygen concentration distribution uniformity in a solid-liquid interface plane of 0 to 180 degrees and a plane of 90 to 270 degrees, namely
Figure BDA0001403971240000177
Figure BDA0001403971240000178
In FIG. 6, the simulation results for low crystal rotation and low crucible rotation show the average oxygen concentration at the solid-liquid interface
Figure BDA0001403971240000179
And radial oxygen concentration distribution uniformity MSEOAnd deltaOAre respectively as
Figure BDA00014039712400001710
Figure BDA00014039712400001711
MSEOxy＝0.0073,MSEOyz＝0.0020
δOxy＝0.7316,δOyz＝0.6539
Compared with the simulation result under the process regulation of the traditional high crystal rotation and low crucible rotation, the result shows that under the process regulation method of the low crystal rotation and the low crucible rotation, the average oxygen concentration of a solid-liquid interface is lower, the radial oxygen concentration distribution uniformity of the solid-liquid interface is more uniform, and the requirement of large-size electronic grade czochralski silicon single crystal on the content of oxygen impurities in the crystal is met (
Figure BDA0001403971240000181
Magnitude).

Claims (3)

1. A method for adjusting oxygen distribution of a solid-liquid interface optimized by a czochralski silicon single crystal growth process is characterized by comprising the following steps:
step 1, constructing a three-dimensional local physical model required by the growth of silicon single crystal by a Czochralski method;
step 2, importing the three-dimensional local physical model into a CFX fluid simulation module, setting simulation as steady-state simulation, and setting physical parameters and superconducting magnetic field strength of silicon melt, silicon crystal, graphite crucible and quartz crucible;
step 3, solving the radial oxygen concentration distribution condition of the solid-liquid interface under different superconducting horizontal magnetic field strengths;
step 4, analyzing the influence of the crystal rotation speed on the solid-liquid interface shape and the radial temperature distribution in the melt;
step 5, analyzing the influence of the crucible rotation speed on the shape of a solid-liquid interface and the radial temperature distribution in the melt;
step 6, integrating the steps 3-5, and obtaining oxygen concentration distribution information of a solid-liquid interface of the czochralski silicon single crystal under the superconducting horizontal magnetic field under the combined action of the selected superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed;
the step 1 is specifically implemented according to the following steps:
step 1.1, generating a three-dimensional local physical model for the growth of the silicon single crystal by the Czochralski method by using a Gambit software grid, wherein the three-dimensional local physical model comprises a crystal, a melt, a quartz crucible and a graphite crucible;
step 1.2, setting the radius of a quartz crucible to be 0.306m, the radius of a graphite crucible to be 0.32m, the radius of a melt in the crucible to be 0.3m, rotating the crucible anticlockwise, and setting the rotating speed of the crucible to be omegac(ii) a The radius range of the crystal is 0.15 m-0.225 m, the crystal rotates clockwise, and the rotation speed of the crystal is omegasThe height of the melt is 0.08-0.22 m, the length of the crystal is 0-0.6 m, the feeding amount is 160kg, the free interface is a silicon melt and gas interface, and the solid-liquid interface is a phase interface between the crystal and the melt;
the step 2 is specifically implemented according to the following steps:
step 2.1, setting the crucible to rotate anticlockwise, wherein the rotating speed of the crucible is omegacThe crystal rotates clockwise at omegas；
Step 2.2, assuming that the silicon melt is incompressible Newtonian fluid; assuming that the silicon melt satisfies the Boussinesq approximation; setting a solid-liquid interface as a flat surface, wherein a supercooled state does not occur during crystallization of the solid-liquid interface, and the temperature of the solid-liquid interface is 1685K of the melting point of silicon; setting the interface of the melt and argon, namely the free liquid level is a flat surface, the height of the free liquid level is the same as that of the solid-liquid interface, and radiating heat to the external atmosphere environment; the bottom of the quartz crucible, the inner wall of the crucible and the silicon melt meet the condition of no sliding boundary; the influence of the oxygen transport process in the melt on the flow and heat transfer of the melt is ignored;
in the step 2.2, the boundary conditions used in the simulation iterative solution process include an oxygen concentration boundary condition and a temperature boundary condition, wherein the oxygen concentration boundary condition is as follows:
(1) the boundary condition of the oxygen concentration at the boundary of the silicon melt and the inner wall of the quartz crucible is as follows:
Figure FDA0002202734290000021
Figure FDA0002202734290000022
Figure FDA0002202734290000023
wherein N isAIs the alpha-Galois constant of the analog-to-digital converter,
Figure FDA0002202734290000024
is the partial pressure of oxygen, aoIs the volume fraction of oxygen, R is the oxygen gas molar constant, T is the chemical reaction temperature,
Figure FDA0002202734290000025
is a chemical reaction
Figure FDA0002202734290000026
A change in free energy;
(2) oxygen concentration boundary condition at interface of silicon melt and argon gas:
Figure FDA0002202734290000027
in the formula, COAnd CsurfThe oxygen concentration in the melt and the oxygen concentration at the free liquid level, respectively; cSiIs the silicon melt concentration; dOAnd DSiORespectively oxygen in a silicon meltDiffusion coefficient of SiO gas in argon; Δ G is the chemical reaction formula Simelt+Omelt＝SiOgasAmount of change in free energy of p0Is the vapor pressure of SiO gas, R is the gas molar constant, T is the chemical reaction temperature; deltagIs the free liquid level boundary layer thickness;
in the actual growth environment of the crystal, the oxygen concentration C of the free liquid surface is blown by argon gassurfOnly the internal oxygen concentration C of the meltOTen thousand of (a), thus the oxygen concentration C of the free liquid surfacesurfNeglecting, the oxygen concentration boundary condition of the free liquid surface is simplified to
CO＝0mol/m3；
(3) Oxygen concentration boundary conditions at the solid-liquid interface, i.e., the crystal growth interface:
Figure FDA0002202734290000031
wherein D is the diffusion coefficient of oxygen, VgThe moving speed of the solid-liquid interface, k is the segregation coefficient of oxygen, CoExperiments show that the segregation coefficient of oxygen is close to unit 1, and more than 99 percent of oxygen is volatilized into argon from a free liquid surface, so that the content of oxygen doped into crystals is ignored in the whole oxygen flux balance of a solid-liquid interface, and the formula is simplified into that
Figure FDA0002202734290000032
In the temperature boundary condition, the bottom of the graphite crucible and the outer wall of the graphite crucible are applied with equal gradient temperature distribution values, and a heat flux density equation is established at the free liquid level, which is as follows:
Figure FDA0002202734290000033
Q'l＝qout,k-qin,k＝σεT4-εqin,k
qin,k＝sumj＝1～N(Fk,jqout,j)
wherein β [ T (r) -T0(r)]1.25Describing the heat loss due to gas convection, Ql' to describe the heat loss of the melt level by radiation, T is the free level temperature, T0Is ambient temperature, KlFor the heat transfer coefficient of the silicon melt, β is the heat loss coefficient of gas convection, r is the free liquid surface radius, ε is the emissivity, σ is the Stefan-Boltzmann constant, Fk,jIs the angular coefficient between the two surfaces of k, j, qout,kIs the heat flow out of the surface, qin,kThe heat flow flowing into the surface is shown, x and z are direction variables of a space rectangular coordinate system, and N is the total number of the surface;
similar heat flux density equations are also established at the top surfaces of the graphite crucible and the quartz crucible, the inner surface of the quartz crucible not in contact with the silicon melt, and the outer surface of the crystal, as follows:
Figure FDA0002202734290000041
Q's＝qout,k-qin,k＝σεT4-εqin,k
wherein, Q'sFor describing the heat loss from a solid surface by radiation, KsThe heat conduction coefficient of the silicon melt is shown as r is the radius of a crystal or the inner radius of a quartz crucible, and y is the direction variable of a space rectangular coordinate system;
setting the iteration times to 90000, the time factor to 1 and the residual error value of the convergence curve to 1E-06 in the iteration solving control;
the step 3 is specifically implemented according to the following steps:
step 3.1, using a numerical solver of the CFX module to numerically solve the crystal rotation speed omega under different superconducting horizontal magnetic field strengthssAnd the rotational speed omega of the cruciblecBoth flow and heat transfer within the crucible melt at 0 rpm;
step 3.2, after the iteration is converged, passing through a CFX moduleProcessing to obtain a temperature distribution cloud chart and an oxygen concentration distribution cloud chart of the melt, tracking the 1685K isotherm position of the solid-liquid interface on the temperature distribution cloud chart, obtaining the oxygen concentration distribution data on the solid-liquid interface, obtaining a relation curve of the oxygen concentration and the crystal diameter, namely a radial oxygen concentration distribution curve of the solid-liquid interface, and obtaining the average oxygen concentration distribution curve of the solid-liquid interface according to the average oxygen concentration distribution curve of the solid-liquid interface
Figure FDA0002202734290000042
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOSelecting suitable superconducting magnetic field strength for minimum principle, as shown in the following formula
Figure FDA0002202734290000043
Wherein n is the number of collected oxygen data on the solid-liquid interface, ciIs an oxygen data point, i is an oxygen data independent variable;
Figure FDA0002202734290000051
Figure FDA0002202734290000052
wherein, gradOiIs the gradient, gradO, of each oxygen data point on the solid-liquid interface radial oxygen concentration distribution curveminIs the minimum gradient, gradient error sum delta of the radial oxygen concentration distribution curve of the solid-liquid interfaceOThe smaller the oxygen concentration distribution, the more uniform the radial oxygen concentration distribution of the solid-liquid interface is;
the step 4 is specifically implemented according to the following steps:
step 4.1, in the CFX pretreatment setting, setting the appropriate magnetic field intensity selected in the step 3, and setting the crucible rotation speed omegacSet to 0rpm, adjust different crystal rotation speeds omegasIteratively solving until a residual error curve converges, thereby obtaining oxygen concentration data on a solid-liquid interface 1685K isotherm;
step 4.2,Obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a solid-liquid interface radial oxygen concentration distribution curve, in order to analyze the influence of the crystal rotation speed on the solid-liquid interface shape and the melt inner radial temperature distribution, wherein the temperature detection position is taken from the inside of the melt, is 0.08m away from the interface of the melt and the argon gas, has the length of 0.3m, points to a crystal growth axis from the interface of the crucible and the melt in the direction, and according to the average oxygen concentration of the solid-liquid interface
Figure FDA0002202734290000053
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOSelecting proper crystal rotation speed as a minimum principle;
the step 5 is specifically implemented according to the following steps:
step 5.1, in the CFX pretreatment setting, setting the magnetic field intensity to be the proper magnetic field intensity selected in the step 3, and setting the crystal rotation speed omegasIs 0rpm, the rotating speed omega of the crucible is adjustedcIteratively solving through a numerical solver until a residual error curve converges, thereby obtaining oxygen concentration data on a solid-liquid interface 1685K isotherm;
step 5.2, obtaining a relation curve between the oxygen concentration and the crystal diameter, namely a solid-liquid interface radial oxygen concentration distribution curve, in order to analyze the influence of the crucible rotation speed on the solid-liquid interface shape and the melt internal radial temperature distribution, wherein the temperature detection position is taken from the inside of the melt, the height is 0.08m away from the melt-argon interface, the length is 0.3m, the direction is from the crucible to the melt interface to the crystal growth axis, and the average oxygen concentration of the solid-liquid interface is based on
Figure FDA0002202734290000061
Mean square error MSE of radial oxygen concentration profileOSum gradient error sum deltaOFor the minimum principle, the proper crystal rotation speed is selected.
2. The method for optimizing the oxygen distribution at the solid-liquid interface in the Czochralski silicon single crystal growth process as claimed in claim 1, wherein the crucible rotation speed ω in the step 1.2 is set to be higher than the crucible rotation speed ωc0-10 rpm, crystal rotation speed omegasIs 0 to 16 rpm.
3. The method for adjusting the optimized solid-liquid interface oxygen distribution of the czochralski silicon single crystal growth process according to claim 1, wherein the step 6 is specifically implemented according to the following steps:
step 6.1, in the CFX pretreatment setting, setting the superconducting horizontal magnetic field intensity and the crucible rotating speed as the proper superconducting horizontal magnetic field intensity and the crucible rotating speed selected in the step 3 and the step 5, and because the high crystal rotation is favorable for improving the consistency of a solid-liquid interface, firstly, the crystal rotating speed omega is setsSetting the crystal transition as high crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping;
step 6.2, rotating the crystal at the speed omegasSetting the crystal transition as low crystal transition, and obtaining a solid-liquid interface radial oxygen concentration distribution curve through numerical iteration solution and MATLAB mapping;
step 6.3, calculating the crystal rotation speed omega respectivelysThe average oxygen concentration of the solid-liquid interface in the radial oxygen concentration distribution curve of the solid-liquid interface at the time of high crystal transition and low crystal transition
Figure FDA0002202734290000062
And mean square error MSE associated with uniformity of oxygen concentration distributionOSum gradient error sum deltaOThrough quantitative and qualitative comparative analysis, the superconducting horizontal magnetic field intensity, the crystal rotating speed and the crucible rotating speed which are suitable for reducing the oxygen concentration of the solid-liquid interface and improving the radial oxygen concentration distribution uniformity of the solid-liquid interface are obtained through selection.
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