Simulation of dissolution of silicon in an indium solution by spectral methods

Abstract

The results of a numerical simulation of natural convection due to concentration gradients during dissolution of silicon in an indium solution in a horizontal substrate-solution-substrate system are presented. The Chebyshev-Tau spectral method has been used for the simulations. The results are in very good agreement with the experimental data available in the literature. It is concluded that the discrepancies in the dissolution depths between the previous simulations and experimental data, especially at the earlier stages of the process, are mostly due to combined effects of uncertainties in the predicted properties and insufficient numerical accuracy.

Onset of solutal convection in liquid phase epitaxy system

“…It seems evident that convective motion is very weak during t c ≤t≤t o since the related heat transport is well represented by the conduction state. For a silicon (solute)-indium (solvent) LPE system of Sc=15.7, by using computational fluid dynamic method, Saito and Motoyama [6] and Coskun et al [7] determine numerically the onset time of solutal convection as the time when the mean dissolution rate or the mean dissolution depth of the lower substrate deviate from those of upper substrate. Their results are compared with the above theoretical results in Fig.…”

“…By using the Laplace transform method, the exact solution of Eqs. (5) and (6) is obtained as (7) where and erfc is the complementary error function. Based on the above solution, the dimensionless dissolution depths of both substrates can be calculated by using the following relation: (8) where H(τ) is the dissolution depth at time τ.…”

“…Recently, Coskun et al [7] simulated the dissolution of silicon in an indium solution numerically by employing spectral method and compared their results with previous experimental results.…”

Liquid-Phase Epitaxy

“…Sukegawa et al [73,214,215] developed a 'yo-yo' technique for silicon and III-V compounds. Analysis of convectively driven growth in silicon LPE systems has been described by Kimura et al [217][218][219][220], Dost et al [221], and Coşkun et al [222]. The temperature is programmed to cycle between two constant temperature stages.…”

Growth mechanism and dynamics of in-plane solid-liquid-solid silicon nanowires

“…22 From an application point of view, this in-plane growth of SiNWs could provide new opportunities for designing and exploiting various SiNW-based nanodevices, in a way more compatible with the established planar Si architecture. Intrinsically, this IPSLS growth mode can be viewed as a nanoscaled metalinduced crystallization [23][24][25] or a nanoscaled liquidphase-epitaxy 26,27 process. In contrast to its bulk versions, this nanoscale crystallization process produces well-defined nanowires with controllable size, morphology, and even growth path.…”