Numerical Study on Flow Field and Temperature Distribution in Growth Process of 200 mm Czochralski Silicon Crystals

The melt flow and temperature distribution in a 200 mm silicon Czochralski furnace with a cusp magnetic field was modeled and simulated by using a finite-volume based FLUTRAPP ( Fluid Flow and Transport Phenomena Program) code. The melt flow in the crucible was focused, which is a result of the competition of buoyancy, the centrifugal forces caused by the rotations of the crucible and crystal, the thermocapillary force on the free surfaces and the Lorentz force induced by the cusp magnetic field. The zonal method for radiative heat transfer was used in the growth chamber, which was confined by the crystal surface, melt surface, crucible, heat shield, and pull chamber. It was found that the cusp magnetic field could strength the dominant counter-rotating swirling flow cell in the crucible and reduce the flow oscillation and the pulling-rate fluctuation. The fluctuation of dopant and oxygen concentration in the growing crystal could thus be smoothed.

3D Finite Volume Scheme for Czochralski Crystal Growth

A general three-dimensional model is developed for simulation of the growth process of silicon single crystals by Czochralski technique. The numerical scheme is based on the curvilinear non-orthogonal finite volume discretization. Numerical solutions show that the flow and temperature fields in the melt are asymmetric and unsteady for 8’’ silicon growth. The effects of rotation of crystal on the flow structure are studied. The rotation of crystal forms the Ekman layer in which the temperature gradient along solid/melt surface is small.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Effect of plasma temperature on electrostatic shock generation and ion acceleration by laser

The effect of plasma temperature on electrostatic shock generated by a circularly polarized laser pulse in overdense plasma is studied by particle-in-cell simulation. Ion reflection and transmission in the collisionless electrostatic shock (CES) are investigated analytically. As the initial ion temperature is varied, a distinct transition from the laser-driven piston scenario with all ions being reflected to the CES scenario with partial ion reflection is found. The results show that at low but finite temperatures the ions are much more accelerated than if they were cold.

Finite element analysis on a circular wedge prism with 400 mm diameter

The paper comprehensively analyzes the distortions of a circular wedge prism with 400 mm diameter in a scanner by method of optical-mechanical-thermal integrating analysis. The structure and intensity of the prism assembly is verified and checked, and the surface deformations of the prism under gravity load, as well as the thermo-elastic distortions of the prism, are analyzed in detail and evaluated, which is finally contrasted with the measured values of Zygo Mark interferometer. The results show: the maximal distortion of the prism assembly is 10 nm magnitude and the maximal stress is 0.441 Mpa, which has much tolerance to the precision requirement of structure and the admissible stress of material; the influence of heat effect on the surface deformations of prism is proved to be far greater than the influence of gravity load, so some strict temperature-controlled measures are to be considered when the scanner is used. (c) 2006 Elsevier GmbH. All rights reserved.

Optimization of thermal environment during crystal growth of large-sized Nd : YAG by Temperature Gradient Technique

A finite-element model is employed to analysis the thermal environments in Temperature Gradient Technique (TGT) furnace during the growth of large-sized Nd:YAG crystal. The obtained results show that when the crucible is located at the lower position inside of the heater, a flatter solid-liquid interface is established, which makes it easier to obtain the core-free Nd:YAG crystal. Meanwhile, the lower crucible position can induce higher axial temperature gradient, which is beneficial to the release of latent heat. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Room-temperature photonic crystal laser in H3 cavity on InGaAsP/InP slab

We fabricate and investigate two-dimensional photonic crystal H3 microcavities in an InGaAsP slab. The lasing action at room temperature is observed. The lasering threshold is 7mW under the pulsed pump of 0.75% duty cycle. The Q factor and the lasing mode characteristics are simulated by three-dimensional finite difference time domain method. The simulation result matches well with the experiment.

Study on growth mechanism of low-temperature prepared microcrystalline Si thin films

Microcrystalline silicon thin films at different growth stages were prepared by hot wire chemical vapor deposition. Atomic force microscopy has been applied to investigate the evolution of surface topography of these films. According to the fractal analysis I it was found that, the growth of Si film deposited on glass substrate is the zero-diffused stochastic deposition; while for the film on Si substrate, it is the finite diffused deposition on the initial growth stage, and transforms to the zero-diffused stochastic deposition when the film thickness reaches a certain value. The film thickness dependence of island density shows that a maximum of island density appears at the critical film thickness for both substrates. The data of Raman spectra approve that, on the glass substrate, the a-Si: H/mu c-Si:H transition is related to the critical film thickness. Different substrate materials directly affect the surface diffusion ability of radicals, resulting in the difference of growth modes on the earlier growth stage.

Cyclotron resonance mass of magnetopolaron in a polar crystal slab at finite temperatures

Using the Green function method, we have studied the cyclotron resonance of an electron interacting with bulk longitudinal optical(BO) phonons as well as surface optical(SO) phonons in a polar crystal slab at finite temperatures. It is found that the temperature dependence of magnetopolaron depends strongly on the strength of the magnetic field. The numerical results show that the cyclotron resonance mass of polaron in a slab is an increasing or decreasing function of temperature when the magnetic field is lower or higher than the resonant magnetic field region, respectively. The magnetic field and slab width dependence of cyclotron resonance mass are also studied in this paper. (C) 1999 Elsevier Science B.V. All rights reserved.

Analysis of Si/GaAs Bonding Stresses with the Finite Element Method

In conjunction with ANSYS, we use the finite element method to analyze the bonding stresses of Si/GaAs. We also apply a numerical model to investigate a contour map and the distribution of normal stress,shearing stress,and peeling stress,taking into full consideration the thermal expansion coefficient as a function of temperature. Novel bonding structures are proposed for reducing the effect of thermal stress as compared with conventional structures. Calculations show the validity of this new structure.

Fiber Bragg Grating Sensor for Strain Sensing in Low Temperature Superconducting Magnet

Fiber Bragg grating (FBG) sensor for monitoring the electromagnetic strain in a low temperature superconducting (LTS) magnet was studied. Before used to LTS magnet strain sensing, the strain response of the sensor with 1.54-mu m wavelength at liquid helium was experimentally studied. It was found that the wavelength shift showed good linearity with longitudinal applied loads and the strain sensitivity is constant at 4.2 K. And then, the hoop strain measurement of a LTS magnet was carried out on the basis of measured results. Furthermore, the finite element method (FEM) was used to simulate the magnet strain. The difference between the experimental and numerical analysis results is very small.

Fiber Bragg Grating Sensor for Strain Sensing in Low Temperature Superconducting Magnet

Fiber Bragg grating (FBG) sensor for monitoring the electromagnetic strain in a low temperature superconducting (LTS) magnet was studied. Before used to LTS magnet strain sensing, the strain response of the sensor with 1.54-mu m wavelength at liquid helium was experimentally studied. It was found that the wavelength shift showed good linearity with longitudinal applied loads and the strain sensitivity is constant at 4.2 K. And then, the hoop strain measurement of a LTS magnet was carried out on the basis of measured results. Furthermore, the finite element method (FEM) was used to simulate the magnet strain. The difference between the experimental and numerical analysis results is very small.

3D quench simulation using finite element method for CR superconducting magnet's strand

The CR superconducting magnet is a dipole of the FAIR project of GSI in Germany. The quench of the strand is simulated using FEM software ANSYS. From the simulation, the quench propagation can be visualized. Programming with APDL, the value of propagation velocity of normal zone is calculated. Also the voltage increasing over time of the strand is computed and pictured. Furthermore, the Minimum Propagation Zone (MPZ) is studied. At last, the relation between the current and the propagation velocity of normal zone, and the influence of initial temperature on quench propagation are studied.