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Interfacial overheating during melting of Si at 190 m/s

Published online by Cambridge University Press:  31 January 2011

J. Y. Tsao ,
P. S. Peercy  and
Michael O. Thompson
J. Y. Tsao
Affiliation:
Sandia National Laboratories, Albuquerque, New Mexico 87185
P. S. Peercy
Affiliation:
Sandia National Laboratories, Albuquerque, New Mexico 87185
Michael O. Thompson
Affiliation:
Cornell University, Ithaca, New York 14850
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Abstract

An upper limit is placed on the overheating at the liquid/solid interface during melting of (100) Si at high interface velocity. The limit is based on an energy-balance analysis of melt depths measured in real time during pulsed-laser melting of Si on sapphire. When combined with previous measurements of the freezing kinetics of Si, this limit indicates that the kinetics of melting and freezing are nonlinear, i.e., the undercooling required to freeze at modest (15 m/s) velocities is proportionately much greater than the overheating required to melt at high (190 m/s) velocities.

Type
Articles
Information
Journal of Materials Research , Volume 2 , Issue 1 , February 1987 , pp. 91 - 95
Copyright
Copyright © Materials Research Society 1987

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References

REFERENCES

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13This can be seen by differentiation: (d/dt)(lδT) = (IδT) + 1δT = (Dv)/(vβ) - (Dvv)/(v2β) = 0. Physically, an increase in the interface overheating is offset by an accompanying decrease, due to an increased interface velocity, in the length scale /over which the temperature profile decays.Google Scholar
14The values used to evaluate this equation are δH = 4206 J/cm3, cp = 2.56 J/(cm3 K), x = 230 nm, l = 700 nm, v = 190 m/s, and δT mc = 1685 K - 300 K = 1385 K. The thermal conductivity of the liquid K 1, is not known accurately; here we use a conservative upper estimate of 1.0 W/(cm K).Google Scholar
15In units of δH, this has been evaluated (Ref. 9) to be , where c, (T) is the temperature-dependent specific heat of solid Si.Google Scholar
16We use the values D = 0.1 cm2/s and v = 190 m/s.Google Scholar
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18Here, The timing uncertainty of ± 0.3 ns between the laser pulse and the transient-conductance trace implies a potentially large uncertainty in this integral (205 nm ± 50 nm). Because the velocity profile follows so closely the laser profile, as discussed in the first half of this article, the time t 1, at which the velocity is maximum, would actually appear to be nearer the time t = 0, at which the laser intensity is maximum. The integral would therefore be at the upper end of its estimated range, thereby tightening further the bound on the overheating. Here, however, in order to establish the most conservative possible bound, we evaluate the integral at the lower end of its estimated range.Google Scholar