Numerical analysis of crystal growth of an InAs–GaAs binary semiconductor by the Travelling Liquidus-Zone method under microgravity conditions

Maekawa, Taira; Sugiki, Yoshihiro; Matsumoto, Satoshi; Adachi, Satoshi; Yoda, Shinichi; Kinoshita, Kyôichi

doi:10.1016/j.ijheatmasstransfer.2003.05.002

Cited by 5 publications

(2 citation statements)

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“…The typical values of the Lewis number for binary liquids is 0.01 and less; in computations below we set L = 0.01. The value S ≈ 10 is typical for liquid semiconductors, for example, for gallium-doped germanium [3] and InAs-GaAs [8]. Any other binary liquids we are familiar with have larger values of S, typically S > 100.…”

Section: Background and Methodmentioning

confidence: 99%

Oscillatory Longwave Marangoni Convection in a Binary Liquid. Part 2: Square Patterns

Shklyaev¹,

Nepomnyashchy²,

Oron³

2014

SIAM J. Appl. Math.

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As a natural extension for our recent work [SIAM J. Appl. Math., 73 (2013), pp. 2203-2223] we study pattern selection on a square lattice for longwave oscillatory Marangoni convection in a layer of binary liquid. In contrast to the previous studies dealing with weakly nonlinear dynamics of such systems only, in this recent work we developed a method based on the Fourier transform to describe the dynamics of finite-amplitude perturbations of both temperature and solute concentration. The method is then applied to study simple patterns on a rhombic lattice consisting of four or fewer interacting waves. The present paper is the first implementation of this theory to a problem with multiple interacting waves. In a wide range of parameters, alternating rolls (ARs) are the only stable pattern. For low values of the Schmidt number relevant for liquid semiconductors, a competition between ARs and traveling squares sets in and results in the emergence of a novel "asymmetric" pattern exhibiting properties of both traveling and standing regimes. Busse balloons for these patterns are found.

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Section: Background and Methodmentioning

confidence: 99%

Oscillatory Longwave Marangoni Convection in a Binary Liquid. Part 2: Square Patterns

Shklyaev¹,

Nepomnyashchy²,

Oron³

2014

SIAM J. Appl. Math.

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“…We also make use of the Schmidt number, S = P/L. Characteristic values of the Schmidt number are usually rather high, S > 10 2 ; however, the value S = 10 is typical for some liquid semiconductors, for example, for gallium-doped germanium [4] and InAs-GaAs [10].…”

Section: Problem Formulation and Backgroundmentioning

confidence: 99%

Oscillatory Longwave Marangoni Convection in a Binary Liquid: Rhombic Patterns

Shklyaev¹,

Nepomnyashchy²,

Oron³

2013

SIAM J. Appl. Math.

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Longwave oscillatory Marangoni convection in a planar binary liquid layer is studied. Finite-amplitude regimes with perturbations of temperature and solute concentration of order unity are considered. Both thermocapillary and solutocapillary effects are taken into account. One-and two-dimensional patterns on a rhombic lattice are studied and their stability to the perturbations which do not necessarily belong to the lattice is analyzed. In the framework of the two-dimensional problem, traveling rolls are stable, whereas for a full three-dimensional problem alternating rolls are selected.

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