Czochralski Silicon Crystal Growth Research Articles

Crystal Growth of Indium-Doped Czochralski Silicon for Photovoltaic Application

In this paper we have investigated the crystal growth of indium-doped Czochralski (CZ) silicon for photovoltaic application. It is found that during the CZ silicon crystal growth the evaporation of indium is rather severe, which makes the accurate control of desired resistivity in the crystal difficult. The rapid indium doping after melting raw poly-silicon materials has been proposed to reduce the indium evaporation. The segregation coefficient of indium in silicon has been verified to be 4.0×10-4 by the method of quenching the crystal growth. With an increase of doping concentration, the electrical activity of indium dopants in silicon is found to become smaller. Beyond a critical doping concentration, the cellular growth of indium-doped CZ silicon crystal generally occurs. These results are of interest for the application of indium-doped silicon solar cells without light-induced degradation in photovoltaics.

Analysis of W-shape melt/crystal interface formation in Czochralski silicon crystal growth

The shape of the melt/crystal interface in Czochralski grown silicon crystal is a result of the interaction of several phenomena. In particular, melt convection plays a key role as it affects the heat and mass transfer inside the melt. Depending on the growth conditions and heat transfer in the melt, the interface shape can evolve from a purely concave or convex shape to a W-shape. The aim of this study is to explore the heat transfer conditions and melt flow patterns leading to the formation of W-shape interfaces. The 2D simulations are performed for 6in. diameter silicon in order to identify conditions leading to W-shape formation. The numerical results show that the formation and development of W-shape interfaces is associated with growth conditions favoring the appearance of a vortex underneath the crystal. This vortex significantly influences the thermal field within the crystallization zone and locally alters the interface deflection. This study suggests that the formation of the W-shape interfaces influences significantly the grown-in defects and crystal quality.

Simulation aided hot zone design for faster growth of CZ silicon mono crystals

Computer simulation was used for optimizing a hot zone for Czochralski (CZ) silicon crystal growth. The heater structure and heat shield material were investigated. With this optimized hot zone, the temperature gradient near the crystal/melt interface increased and the CZ crystal could be grown at a faster rate. It is a great contribution for saving power consumption.

Numerical simulation of oxygen transport during the CZ silicon crystal growth process

In this study, the effect of the flow motion and heat transfer generated by the crystal and crucible rotation on the oxygen distribution inside the melt during Czochralski silicon crystal growth is investigated. When the crucible rotates in a direction opposite to the crystal rotation, Taylor–Proundman vortices appear in the region below the crystal. The diffusion of oxygen impurity from the crucible wall to the crystal–melt interface is suppressed by these Taylor–Proundman vortices, while heat transport from the crucible wall to the crystal–melt interface is blocked by the Taylor–Proundman vortices. With a higher crucible rotation rate, the size of the Taylor–Proundman vortices increases and the size of the buoyancy–thermocapillary vortices decreases. This causes the temperature at the crucible wall to rise and the evaporation of oxygen impurity on the free surface to decrease. Hence, the amount of oxygen impurity that diffuses into the melt towards the crystal–melt interface increases. The suppression from the Taylor–Proundman vortices is dominant for the smaller crucible rotation rate, while the enhancement from the oxygen impurity diffusion prevails for the higher crucible rotation rate. Therefore, there is an optimum combination of crucible and crystal rotation for obtaining the lowest oxygen concentration.

Investigation of nitrogen behaviors during Czochralski silicon crystal growth

The behaviors of nitrogen during Czochralski (CZ) silicon crystal growth have been investigated in this paper. It is found that the nitrogen impurities in silicon mainly exist as nitrogen pair and nitrogen–oxygen complex. The nitrogen concentration can be exactly determined by Fourier transformed infrared spectroscopy (FTIR) after eliminating the thermal donors. Above a critical concentration of 4×1015/cm3, the nitrogen impurities easily form Si3N4 particles, causing the dislocations, grain boundary and cellular structure in the crystal. Meanwhile, with a nitrogen-doped seed, the dislocations due to thermal shocking during the dipping process can be effectively suppressed at the seed/crystal interface, which will allow growing a crystal without a Dash neck. These results are of interest for the CZ silicon crystal growth in semiconductor industry.

Three‐dimensional study of the pressure field and advantages of hemispherical crucible in silicon Czochralski crystal growth

AbstractThe effects of several growth parameters in cylindrical and spherical Czochralski crystal process are studied numerically and particularly, we focus on the influence of the pressure field. We present a set of three‐dimensional computational simulations using the finite volume package Fluent in two different geometries, a new geometry as cylindro‐spherical and the traditional configuration as cylindro‐cylindrical. We found that the evolution of pressure which is has not been studied before; this important function is strongly related to the vorticity in the bulk flow, the free surface and the growth interface. It seems that the pressure is more sensitive to the breaking of symmetry than the other properties that characterize the crystal growth as temperature or velocity fields. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Forced and thermocapillary convection in silicon Czochralski crystal growth in semispherical crucible

In order to understand the influence of a semispherical crucible geometry combined with different convection modes as a thermocapillary convection, natural convection and forced convection, induced by crystal rotation, on melt flow pattern in silicon Czochralski crystal growth process, a set of numerical simulations are conducted using Fluent Software. We solve the system of equations of heat and momentum transfer in classical geometry as cylindrical and modified crystal growth process geometry as cylindro-spherical. In addition, we adopt hypothesis adapted to boundary conditions near the interface and calculations are executed to determine temperature, pressure and velocity fields versus Grashof and Reynolds numbers. The analysis of the obtained results led to conclude that there is advantage to modify geometry in comparison with the traditional one. The absence of the stagnation regions of fluid in the hemispherical crucible corner and the possibility to control the melt flow using the crystal rotation enhances the quality of the process comparatively to the cylindrical one. The pressure field is strongly related to the swirl velocity.

Numerical study of thermal stress during different stages of silicon Czochralski crystal growth

In this paper, the influence of various crystal heights to the crystal/melt interface shape and thermal stresses distribution in the large diameter (300 mm) of the silicon single crystal growth in a Czochralski process was studied numerically. A tow dimensional fluid flow and heat transfer with solidification model was developed. The Navier-Stoks and energy equations in melt and the heat conduction equation in crystal are solved using the control volume-based finite difference method. The thermal elastic stress fields for different stages are calculated from the temperature field by adopting the plane strain model in an axi-symmetric geometry of a cylindrical crystal. It was found that the melt/crystal interface shape becomes more concave and the maximum value of thermal stress in the crystal reduces as the crystal grows. A good agreement between our numerical simulations and those found in the literature is obtained.

Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth

AbstractIn order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis of impurity transport and deposition processes on the furnace elements during Cz silicon growth

Czochralski growth of silicon crystals is always related to transport of impurities. The main impurities are oxygen and carbon. They react with furnace elements with formation of SiO, SiO 2 and SiC deposit layers. Prediction of transport of impurities is important to detect the precise location of areas where impurity deposition may cause considerable difficulties and to avoid excessive deposition above the melt free surface. Detailed analysis of chemical processes, accompanying Cz silicon growth is under discussion in the current paper. The proposed numerical model accounts for oxygen transport in the melt and SiO deposition on the walls of the furnace. Computer analysis was provided for cases with different heat insulation of the furnace walls.

Ga segregation in Czochralski-Si crystal growth with B codoping

Codoping of gallium (Ga) and boron (B) in a Czochralski-silicon (CZ-Si) crystal has been proposed to be an effective way to improve the homogeneity of resistivity over the length of a simply Ga-doped Si crystal, by increasing the very small equilibrium segregation coefficient of Ga ( k 0=0.008). It was observed that the axial resistivity variation in a Ga- and B-codoped Si crystal was smaller than that in simply Ga-doped Si crystals. The segregation behavior of Ga and B in the codoped CZ-Si crystal growth has been investigated in the present study. The effective segregation coefficient of Ga was kept almost constant when the B concentrations were low, but it increased at higher B concentrations. On the other hand, the effective segregation coefficient of B was kept almost constant when the B concentrations were low; however, it decreased at higher B concentrations. It has been analytically demonstrated that there is strong interaction between Ga and B in a Si crystal, which leads to an increase in the segregation coefficient of Ga in Si crystal growth.

Development of oxygen transport model in Czochralski growth of silicon crystals

Oxygen is one of the most important impurities in Czochralski (Cz)-grown silicon crystals. The precise control of oxygen concentration in growing crystal, both in radial and in axial directions, is required to obtain silicon wafers with necessary electronic properties. A modified numerical model of oxygen transport as a way of prediction of oxygen concentration in growing Si crystals is described in this paper. Test calculations for the updated model were performed for a Cz setup with a small crucible diameter and weak turbulent melt flow. The calculated oxygen profile along the crystallization front is compared with available experimental data. 2-D and 3-D calculation results have evaluated the number of finite volumes in 3-D grid, required for precise description of oxygen transport in the small growth system.

Comparison of measurements and simulation results in 300 mm CZ silicon crystal growth

A special thermal modeling tool, CrysVUn, which was developed by Crystal Growth Laboratory (CGL) of Fraunhofer Institute of Integrated Systems and Devices Technology in Erlangen of Germany, was used for numerical analysis of growth interface situation. The heat transportation, argon flow and melt convection have been considered. Cauchy's first and second laws of motion have been the governing partial equations for stress calculation. The measurement results and simulation results were compared and the interface shape and thermal stress distribution during 300 mm Czochralski (CZ) silicon crystal growth with different growth rates were predicted.

3D global analysis of CZ–Si growth in a transverse magnetic field with various crystal growth rates

A series of computations were performed for Czochralski silicon crystal growth in a transverse magnetic field with different crystal growth rates by using a recently developed three-dimensional global model. The effects of the transverse magnetic field and crystal growth rate on the melt–crystal interface were numerically investigated. It was found that the interface shape is three-dimensional when the crystal is not rotating, while it becomes nearly two-dimensional when the crystal is rotating, even at a low rotation rate. The temperature gradient in the axial direction at the melt–crystal interface increases with increase in crystal growth rate except near the crystal edge, where it changes oppositely.

Numerical analysis for transient point defect behavior in Czochralski silicon crystal growth

r− To study the transient point defect distribution in Czochralski-grown silicon single crystals, a contin- uum model of point defect dynamics to predict the concentrati on of interstitial and vacancy is established by estimating expressions for the thermo-physical properties of point defect s and the point defect distribution in silicon crystals. It is well known that the concentration of intrinsic point def ects in growing silicon crystals is a function of the crystal pull rate (V) and the temperature gradient (G) at the solid ification interface inside the crystal, and steady state predictions from point defect dynamics are well agreed with experiment. In this study, finite element simulations have been performed for the growth halt experiment with 150 mm silicon single crystals to study the transient behavior of intrinsic point defects. It has been demonstrated that predicted point defect distributions are in good agreement with experimental results.

A laboratory study of two-dimensional and three-dimensional instabilities in a quasi-two-dimensional flow driven by differential rotation of a cylindrical tank and a disc on the free surface

By laboratory experiments, we investigate instability behaviors in a differential rotation system derived from the Czochralski silicon crystal growth. The experimental apparatus consists of a rotating disc (radius a, rotation rate ω) on the surface of homogeneous salt water contained in a rotating cylindrical tank (radius R>a, rotation rate Ω<ω). The differential rotation induces the vertical Stewartson layer at the disc radius, and various flow patterns appear as the rotation rate difference ω−Ω is increased. At relatively small ω−Ω, the well-known barotropic, or circular shear, instability generates multiple vertically coherent vortices along the Stewartson layer. The number of vortices decreases with increasing ω−Ω. When there are two vortices, irregular vertical motion is observed near the axis beyond certain critical values of ω−Ω. The streamlines near the axis are elliptical and the flow behavior has properties similar to those of the elliptic instability. As ω−Ω is further increased, the irregular motion ceases and the rotation center of the flow below the disc deviates from the machine axis. The rotation center itself orbits around the machine axis. This flow behavior resembles the single-vortex mode of the circular shear instability. We focus on these two instability behaviors: The vertical irregular motion and the off-axis rotation, and examine the instability onset conditions in the light of the elliptic instability and the circular shear instability, respectively.

Transient and quasi‐stationary simulation of heat and mass transfer in Czochralski silicon crystal growth

AbstractThe formation of grown‐in defects in silicon crystals is controlled by the concentration of intrinsic point defects. Under steady state conditions the type of the prevailing point defect species is linked to the ratio of pull rate and temperature gradient in the crystal at the solidification front. It has been shown that this ratio as well as computed point defect distributions are in good agreement with experimental data. In this paper we compare a coupled transient heat transfer and transient point defect transport model with quasi steady state simulations at various time steps. Both simulations show the same qualitative results, quantitative differences in temperature are less than 1 %. But already for constant pull rates the defect distributions show qualitative differences between transient and quasi steady state simulations. Therefore, for a detailed understanding how defects are related to growth conditions, the thermal history should not be neglected.

Hydrogen annealing of grown-in voids in nitrogen-doped Czochralski grown silicon

The effect of nitrogen doping on grown-in crystal originated particles (COPs) in Czochralski (CZ) silicon and COP annihilation during annealing in hydrogen at high temperature has been investigated. It is found that nitrogen doping leads to denser COPs in smaller sizes during CZ silicon crystal growth. Meanwhile, it is clarified that the grown-in COPs in the nitrogen-doped CZ (NCZ) silicon can be annihilated at a much lower temperature compared to those in the CZ silicon, furthermore, the denude zone (DZ) with lower COP density in NCZ silicon was much wider than that in CZ silicon. It is reasonably concluded that the nitrogen doping reduces the supersaturation of vacancies prior to the void formation and thus decreases the onset temperature of void formation, so the size of the void is smaller and the oxide films on the inner walls of the void are assumed to be thinner in NCZ silicon, compared with those in CZ silicon. Therefore, the voids in NCZ silicon can be annihilated more easily by hydrogen annealing.

Using of EM fields during industrial CZ and FZ large silicon crystal growth

The paper describes numerical simulation tools for electromagnetic (EM), hydrodynamic, temperature and concentration fields in industrial Czochralski (CZ) and floating zone (FZ) single silicon crystal growth facilities under the influence of several alternating current (AC) and static DC magnetic fields. Such fields are expected to provide additional means to influence the melt behaviour, especially in the industrial growth of large diameter (200–300 mm) silicon crystals. The simulation tools are based on axisymmetric 2D models for (1) AC and DC magnetic fields in the whole crystal growth facility and (2) hydrodynamics, temperature and mass transport in the melt under the influence of the EM fields. The simulation tools are verified by comparison to temperature and velocity measurements in a laboratory CZ set‐up with eutectics InGaSn model melt and to resistivity measurements in grown silicon crystals.

A continuous Czochralski silicon crystal growth system

Demand for large silicon wafers has driven the growth of silicon crystals from 200 to 300 mm in diameter. With the increasing silicon ingot sizes, melt volume has grown dramatically. Melt flow becomes more turbulent as melt height and volume increase. To suppress turbulent flow in a large silicon melt, a new Czochralski (CZ) growth furnace has been designed that has a shallow melt. In this new design, a crucible consists of a shallow growth compartment in the center and a deep feeding compartment around the periphery. Two compartments are connected with a narrow annular channel. A long crystal may be continuously grown by feeding silicon pellets into the dedicated feeding compartment. We use our numerical model to simulate temperature distribution and velocity field in a conventional 200-mm CZ crystal growth system and also in the new shallow crucible CZ system. By comparison, advantages and disadvantages of the proposed system are observed, operating conditions are determined, and the new system is improved.