Kedar P. Gupta

Numerical and experimental study of a solid pellet feed continuous Czochralski growth process for silicon single crystals

Abstract A polysilicon pellets (≅1 mm diameter) feed continuous Czochralski (CCZ) growth process for silicon single crystals is proposed and investigated. Experiments in an industrial puller (14–18 inch diameter crucible) successfully demonstrate the feasibility of this process. The advantages of the proposed scheme are: a steady state growth process, a low aspect ratio melt, uniformity of heat addition and a growth apparatus with single crucible and no baffle(s). The addition of dopant with the solid charge will allow a better control of oxygen concentration leading to crystals of uniform properties and better quality. This paper presents theoretical results on melting of fully and partially immersed silicon spheres and numerical solutions on temperature and flow fields in low aspect ration melts with and without the addition of solid pellets. The theoretical and experimental results obtained thus far show a great promise for the proposed scheme.

Oscillatory convection in low aspect ratio Czochralski melts

Abstract Modeling of the crucible in bulk crystal growth simulations as a right circular cylinder may be adequate for high aspect ratio melts but this may be unrealistic when the melt height is low. Low melt height is a unique feature of a solid feed continuous Czochralski growth process for silicon single crystals currently under investigation. At low melt heights, the crucible bottom curvature has a dampening effect on the buoyancy-induced oscillations, a source of inhomogeneities in the grown crystal. The numerical results demonstrate how the mode of convection changes from vertical wall-dominated recirculating flows to Benard convection as the aspect ratio is lowered. This phenomenon is strongly dependent on the boundary condition at the free surface of the melt, which has been generally considered to be either adiabatic or radiatively cooled. A comparison of the flow oscillations in crucibles with and without curved bottoms at aspect ratios in the range of 0.25 to 0.50, and at realistic Grashof numbers (10 7 8 ) illustrate that changing the shape of the crucible may be an effective means of suppressing oscillations and controlling the melt flow.

Towards an Integrated Approach for Analysis and Design of Wafer Slicing by a Wire Saw

Crystalline and polycrystalline ingots of silicon and other materials need to be cut into thin wafers for microelectronics, photovoltaics, and many other applications. For slicing process to be cost-effective, the kerf loss should be minimum and the surface finish should be of a high quality. Wire saw can meet these demands and is considered to be a potentially better technology than the inner diameter (ID) saw. An initial study of the current technology shows that the wire saw cutting is a poorly understood process, and no model exists for simulation, design, and control of this process. The wire saw slicing process can be well modeled as a cutting process, where the initial fracture occurs because of the stress distribution between the two surfaces subjected to compressive loading and sliding friction. A preliminary analysis is carried out using a standard finite element method to develop a better understanding of this process and to determine possible ways of improving the process design. The results of vibration (modal) and thermal stress analyses show that an accurate prediction of the effects of process parameters would help in improving the wire saw design. Similarly, a proper feedback control algorithm would enable a better control of the process by using on-line information on wire tension and stiffness, temperature, and other relevant quantities. A methodology for systematic approach to analysis and design of an advanced wire saw process is also outlined.

Role of crucible partition in improving Czochralski melt conditions

Many of the inhomogeneities and defects in the crystal grown from a pool of melt are because of the inherent unsteady growth kinetics and flow instabilities of the process. A scaled up version of the Czochralski process induces oscillatory and turbulent conditions in the melt, thereby resulting in the production of non-uniform silicon crystals. This numerical study reveals that a crucible partition shorter than the melt height can significantly improve the melt conditions. The obstruction at the bottom of the crucible is helpful but the variations in heat flux and flow patterns remain random. However, when the obstruction is introduced at the top of the melt, the flow conditions become much more desirable and oscillations are greatly suppressed. It is also found that a full-melt height partition or a double-crucible may not be a good choice. An optimal size of the blockage and its location to produce the most desirable process conditions will depend on the growth parameters including the melt height and the crucible diameter. These findings should be particularly useful in designing a solid polysilicon pellets-feed continuous Czochralski process for Si crystals.

A new high-pressure system for synthesis and crystal growth of large diameter InP

An advanced high-pressure crystal growth system for one-step synthesis and growth has been constructed from a design based on numerical simulations and experiments. Experimental work reported previously, optimizing the one-step in-situ process for synthesis and growth, served as a basis for developing the new furnace. A global model developed to simulate growth conditions in the prototype system, has contributed to our understanding of complex transport phenomena such as thermoelastic strain and dopant incorporation. Using both the experimental and the simulation results, we have designed a system to produce large diameter, high purity, low defect density compound semiconductor crystals at low cost.

A comprehensive model for high pressure growth of InP crystals

We have developed a comprehensive model that accounts for oscillatory, laminar and turbulent flows caused by buoyancy and surface tension forces; forced convection due to crucible and crystal rotations; and complex thermal boundary conditions. The model also accounts for magnetohydrodynamics and sophisticated radiation heat exchange. Thermal elastic stress in the InP crystal is simultaneously calculated using the temperature distribution and crystal/melt interface shape obtained from the thermal transport simulation. A sophisticated adaptive grid generation technique together with the curvilinear finite volume discretization and several other high resolution numerical schemes have made it possible to simulate the growth of a compound crystal in a high pressure system.