0000000000049219
AUTHOR
A. Sabanskis
showing 12 related works from this author
3D modeling of doping from the atmosphere in floating zone silicon crystal growth
2017
Abstract Three-dimensional numerical simulations of the inert gas flow, melt flow and dopant transport in both phases are carried out for silicon single crystal growth using the floating zone method. The mathematical model allows to predict the cooling heat flux density at silicon surfaces and realistically describes the dopant transport in case of doping from the atmosphere. A very good agreement with experiment is obtained for the radial resistivity variation profiles by taking into account the temperature dependence of chemical reaction processes at the free surface.
Simulation of the influence of gas flow on melt convection and phase boundaries in FZ silicon single crystal growth
2015
Abstract Axisymmetric calculations of inert gas flow in a floating zone puller are carried out using an open source software package OpenFOAM. Transient axisymmetric melt flow in liquid silicon and quasi-stationary shape of silicon phase boundaries are calculated using a specialized program FZone. Additional heat losses at silicon surfaces caused by the gas flow are taken into account for argon and helium, while maintaining the height of molten zone by adjusting inductor current. Cooling causes an increase of electromagnetic force, heat sources and more intense melt flow, while crystallization interface deflection decreases. The shear stress of gas flow is found to be an order of magnitude …
Crystal shape 2D modeling for transient CZ silicon crystal growth
2013
Abstract A non-stationary axisymmetric model of Czochralski silicon single crystal growth is presented. The model describes transient behavior of crystal–melt, melt–gas and crystal–gas interfaces in connection with PID-based control of crystal diameter by changing crystal pulling velocity and heater power. To calculate significant crystal shape changes, unstructured finite element mesh is used in crystal and melt together with automatic element size control. Heater temperature changes are modeled with a simplified integral model. A numerical simulation example of start cone growth is given.
Modelling of thermal field and point defect dynamics during silicon single crystal growth using CZ technique
2018
Abstract Silicon single crystal growth by the Czochralski (CZ) technique is studied numerically using non-stationary mathematical models which allow to predict the evolution of the CZ system in time, including Dash neck, cone and cylindrical growth stages. The focus is on the point defect dynamics, also considering the effect of the thermal stresses. During the cylindrical stage, the crystal pull rate is temporarily reduced as in experiments by Abe et al. The crystal radius and heater power change is explicitly considered in the calculations for crystal diameters of 50, 100 and 200 mm and the agreement with experiments is discussed.
Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field
2010
Abstract To examine the applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic fields, LES calculations with Smagorinsky–Lilly turbulence model and van Driest damping at the solid walls are carried out. The program package for the calculations was developed on the basis of the open-source code library OpenFOAM ® . A previously published laboratory model with low temperature melt InGaSn, a 20” crucible, and process parameters corresponding to industrial Czochralski silicon systems is considered. Flow regimes with two crystal and crucible rotation rates and with different strengths of the traveling magnetic field “down” are analyzed. The calcula…
Experimental and Numerical Analysis of Air Flow, Heat Transfer and Thermal Comfort in Buildings with Different Heating Systems
2016
Abstract Monitoring of temperature, humidity and air flow velocity is performed in 5 experimental buildings with the inner size of 3×3×3 m3 located in Riga, Latvia. The buildings are equipped with different heating systems, such as an air-air heat pump, air-water heat pump, capillary heating mat on the ceiling and electric heater. Numerical simulation of air flow and heat transfer by convection, conduction and radiation is carried out using OpenFOAM software and compared with experimental data. Results are analysed regarding the temperature and air flow distribution as well as thermal comfort.
Study of silicon crystal surface formation based on molecular dynamics simulation results
2014
Abstract The equilibrium shape of 〈 110 〉 -oriented single crystal silicon nanowire, 8 nm in cross-section, was found from molecular dynamics simulations using LAMMPS molecular dynamics package. The calculated shape agrees well to the shape predicted from experimental observations of nanocavities in silicon crystals. By parametrization of the shape and scaling to a known value of { 111 } surface energy, Wulff form for solid-vapor interface was obtained. The Wulff form for solid–liquid interface was constructed using the same model of the shape as for the solid–vapor interface. The parameters describing solid–liquid interface shape were found using values of surface energies in low-index dir…
Hydrodynamical aspects of the floating zone silicon crystal growth process
2014
Abstract 3D numerical modeling of dopant transport in the melt is carried out for the 100 mm floating zone silicon single crystal growth process. The axis-symmetric shape of the molten zone is calculated with the program FZone considering the coil and the high frequency (HF) electromagnetic (EM) field in 3D. Time dependent melt flow, temperature and dopant concentration fields are modeled using a specialized solver based on the open source code library OpenFOAM ® . The influence of the Marangoni coefficient in the boundary conditions on the melt velocity field is analyzed. The obtained shapes of the crystallization interface and resistivity profiles in the grown crystal are compared with ex…
Evaluation of the Performance of Published Point Defect Parameter Sets in Cone and Body Phase of a 300 mm Czochralski Silicon Crystal
2021
Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been proposed. In this paper the transient temperature, thermal stress and point defect distributions are simulated for 300 mm Czochralski growth of the whole crystal including cone and cylindrical growth phases. Simulations with 12 different published point defect parameter sets are compared to the experimentally measured interstitial–vacancy boundary. The results are evaluated for stand…
Experimental and numerical investigation of laboratory crystal growth furnace for the development of model-based control of CZ process
2019
Abstract The presented study is focused on laboratory Czochralski crystal growth experiments and their mathematical modelling. The developed small-scale CZ crystal growth furnace is described as well as the involved automation systems: crystal radius detection by image recognition, temperature sensors, adjustable heater power and crystal pull rate. The CZ-Trans program is used to model the experimental results – transient, 2D axisymmetric simulation software primarily used for modelling of the industrial-scale silicon crystal growth process. Poor agreement with the experimental results is reached; however, the proven ability to perform affordable, small-scale experiments and successfully mo…
Numerical study of silicon crystal ridge growth
2014
Abstract The size of the ridge-like protrusions appearing on the external surface of dislocation-free 〈 100 〉 silicon crystals grown from a melt was studied theoretically. According to existing models the growth of the ridges is caused by the presence of { 111 } crystal planes at the crystal–melt interface. They affect the height of triple phase line, free surface orientation and the crystal growth angle. A numerical 2-dimensional model was proposed for the calculation of the size of the crystal ridges. The model included the effect of the undercooling of the crystal–melt interface on the crystal growth angle. The numerical model estimated the effect of the ridge size on the free surface at…
Validation of mathematical model for CZ process using small-scale laboratory crystal growth furnace
2018
The present material is focused on the modelling of small-scale laboratory NaCl-RbCl crystal growth furnace. First steps towards fully transient simulations are taken in the form of stationary simulations that deal with the optimization of material properties to match the model to experimental conditions. For this purpose, simulation software primarily used for the modelling of industrial-scale silicon crystal growth process was successfully applied. Finally, transient simulations of the crystal growth are presented, giving a sufficient agreement to experimental results.