Yu.N. Makarov

Gas flow effect on global heat transport and melt convection in Czochralski silicon growth

We present a model of global heat transfer in Czochralski (CZ) systems for growth of silicon crystals, allowing a self-consistent calculation of radiative and conductive heat exchange, turbulent melt convection, and inert gas flow. The model is verified by comparing the calculated heater power and temperature difference in the melt to available experimental observations. The simulations are used to reveal the gas flow effect on the heat transport, melt convection, and melt/crystal interface geometry in an industrial CZ system. From the analysis of the results obtained, we derive recommendations concerning when the argon gas flow should be necessarily included in the heat transfer calculation.

On mechanisms of sublimation growth of AlN bulk crystals

A novel model of bulk AlN crystal growth by the sublimation technique is developed. The model takes into account both di!usive and convective transport of gaseous Al and N 2 , and the kinetic limitation of nitrogen adsorption/desorption on AlN surfaces. The maximum growth rate is found to be controlled by joint e!ect of enhancement of the convective species transport in a nearly stoichiometric vapor phase and of the suppression of nitrogen incorporation into the crystal due to low N 2 sticking probability. The interplay of these e!ects provides nonmonotonic dependence of the growth rate on pressure. The theoretical predictions agree well with experimental data reported in literature and obtained in this work. ( 2000 Published by Elsevier Science B.V. All rights reserved.

Use of Ta‐Container for Sublimation Growth and Doping of SiC Bulk Crystals and Epitaxial Layers

Analysis of specific features of sublimation growth of bulk SiC crystals in presence of Ta is performed. Control of doping and formation of different SiC polytypes is discussed. Description of mechanisms responsible for generation of micropipes during sublimation growth of bulk crystals is given. It is shown that use of Ta is promising for growth of bulk SiC crystals.

Novel approach to simulation of group-III nitrides growth by MOVPE

Recent studies revealed specific features of chemical processes occurring on the surface of growing group-III nitrides – extremely low sticking probability of molecular nitrogen, low sticking coefficient and incomplete decomposition of ammonia frequently used as the nitrogen precursor. These features (kinetic by nature) result in the growth process going on under conditions remarkably deviated from the gas-solid heterogeneous equilibrium. In this paper we propose a novel approach to modeling of group-III nitride growth by MOVPE taking into account these features. In the model the sticking/evaporation coefficients of N 2 and NH 3 extracted from independent experiments are used allowing adequate description of the kinetic effects. The model is applied to analysis of growth of binary (GaN) and ternary (InGaN) compounds in a horizontal tube reactor. The growth rate and the solid phase composition are predicted theoretically and compared with available experimental data. The modeling results reveal lower ammonia decomposition ratio on the surface of the crystal as compared to thermodynamic expectations. The developed model can be used for optimization of growth process conditions.

Silicon carbide epitaxy in a vertical CVD reactor : Experimental results and numerical process simulation

In this paper an overview is given on the epitaxial growth of SiC in a vertical CVD reactor. Results concerning impurity incorporation and ways to achieve background doping levels as low as 10 14 cm -3 are discussed. Precise control of the C/Si ratio in the gas phase, which is easily achieved in the described reactor, and the use of reduced pressure, lead to good control of dopant incorporation over more than three orders of magnitude, and smooth surface morphology at growth rates higher than 5 μm/h. Doping variations < ±12% across 35 mm wafers can routinely be obtained. The quality of the epilayers is proven by electrical brakdown fields as high as 2 x 10 6 V/cm at N A - N D = 5 x 10 -15 cm -3 achieved in both pn and Schottky diodes and an electron mobility higher than 700 cm 2 /Vs at 300 K (4H-SiC) estimated from the on-resistance of these test devices. Another important experimental boundary condition, the influence of the gas composition at the end of the epitaxial growth process on the surface properties of the epitaxial layer, is described. It will be shown that surfaces nearly resistant against oxidation can be generated in a hydrogen free atmosphere. As a second main topic of this paper, results of an elaborate numerical process simulation will be described including both fluid mechanical and chemical behavior. The influence of the main process parameters like total flow, chamber pressure, and rotation speed on the stability of the flow was investigated. The results achieved are compared with experimental observations showing excellent agreement. The experimental observation of an irradiant layer in the gas phase in front of the wafer under typical process conditions is explained with the help of the numerical model. The usefulness of this specific feature for the optimization of process conditions is discussed.

Global numerical simulation of heat and mass transfer for SiC bulk crystal growth by PVT

Abstract A modeling approach for the numerical simulation of heat and mass transfer during SiC sublimation growth in inductively heated physical vapor transport (PVT) reactors is introduced. The physical model is based on the two-dimensional solution of the coupled differential equations describing mass conservation, momentum conservation, conjugate heat transfer including surface to surface radiation, multicomponent chemical species mass transfer and advective flow. The model also includes the Joule volume heat sources induced by the electromagnetic field. The evolution of the temperature profiles inside the crucible and of the crystallization front is studied. The radial temperature gradient at the crystal/gas interface causes strong radial non-uniformity of the growth rate and, in turn, influences the shape of the growing crystal. Results of calculations are compared to experimental observations to analyse the validity of the modeling approach. Both the computed growth rates, their temporal evolution and the shape of the growing crystal agree with experimental data.

Analysis of sublimation growth of bulk SiC crystals in tantalum container

Abstract Sublimation growth of SiC bulk crystals in tantalum container is studied both experimentally and theoretically. The model of heterogeneous processes occurred on the side wall of the tantalum container proposed recently in Ramm et al. (Mat. Sci. Eng. B 61–62 (1999) 107) is extended to take into account the process of carbon gettering by the container side wall. We formulate a quasi-steady approach for modeling of the bulk crystal growth. Using this concept we predict evolution of the crystal shape and study processes which govern SiC bulk crystal growth. We apply anisotropic thermal elastic analysis to predict stress distribution in the growing crystal. For the first time a model of dislocation formation is applied for SiC bulk growth to compute dislocation density field in highly stressed areas of the growing crystal.

On the flow regimes in VPE reactors

Abstract Computer simulations of gas flows in cold wall vertical and horizontal VPE reactors are carried out. The characteristic features of the forced and natural convection regimes are discussed. The effect of the flow structure on the film thickness uniformity and on the time of change in gas composition is demonstrated for the growth of GaAs from a Ga(CH3)3-AsH3-H2 mixture.

Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of si crystals

We describe a computational model based on Large Eddy Simulation to calculate 3D unsteady turbulent melt convection in Czochralski systems for Si-crystal growth. The model has been verified using temperature measurements inside the melt and along the melt-crucible surface. The effect of the crucible rotation rate on 3D turbulent structures developed in the melt is analyzed. Transformation of the melt flow with increasing argon flow rate is predicted, and the controlling effect of the argon flow on the oxygen content in the crystal is evaluated.

Simulation of Sublimation Growth of SiC Single Crystals

Modelling of sublimation growth of SiC is discussed with the goal to describe the mathematical models necessary to optimize the process and design of the growth system. An analysis of the mechanisms of growth of bulk silicon carbide crystals is performed. Growth conditions which provide stable growth of single SiC crystals without formation of secondary phases are considered. The phase diagram of the formation of extra phases during the sublimation growth of SiC is presented. Modelling of the growth of bulk SiC crystals is considered. Results of modelling the temperature distribution inside the inductively heated system for the growth of bulk SiC crystals are shown. A mechanism of material transport inside the closed Ta container in the absence of an inert gas atmosphere is proposed which is different from that of diffusive or free-molecular transport. First results of the model analysis of chemical processes inside the volume of SiC powder during the sublimation growth are demonstrated. It is shown that the sublimation and re-crystallization of the SiC source is sensitive to the temperature distribution in the source.