Silicon thermophysical properties

Samalam [43] modeled the convective heat transfer in water flowing through microchannels etched in the back of silicon wafers. The problem was reduced to a quasi-two dimensional non-linear differential equation under certain reasonably simplified and physically justifiable conditions, and was solved exactly. The optimum channel dimensions (width and spacing) were obtained analytically for a low thermal resistance. The calculations show that optimizing the channel dimensions for low aspect ratio channels is much more important than for large aspect ratios. However, a crucial approximation that the fluid thermophysical properties are independent of temperature was made, which could be a source of considerable error, especially in microchannels with heat transfer. 

W. K. Rhim and K. Osaka, Thermophysical properties measurement of molten silicon by high-temperature electrostatic levitator density, volume expansion, specific heat capacity, emissivity, surface tension and viscosity, J Ciyst Grovrtft 208, 313-321 (2000). 

Owing to its excellent mechanical, thermal, and thermophysical properties, silicon nitride finds applications in aerospace gas turbines, internal combustion engines, heat engines, and a variety of dies, molds and tools for metal manufacturing and forming (Von Hocking et al., 1994 Riley, 1996 Petzow and Herrmann, 2002 Lin et al., 2006). 

Here v and m denote the volume and mass of the molecule or atom, respectively. The r.h.s of Equation 32 denotes the ground-state energy of a quantum mechanical particle enclosed in a potential well (particle in a box problem [Martin and Leonard, 1970]). This condition is not satisfied for liquid helium and liquid hydrogen, while liquid neon is a borderline case. For the theoretical description of their thermophysical properties, application of the Maxwell-Boltzmann statistics sometimes does not suffice. Another assumption states that the internal degrees of freedom of the molecules or atoms are the same in the gas phase and in the liquid phase. In other words, it is assumed that the molecules can rotate and vibrate freely in the liquid phase, too. Molecular rotation may be hindered in the case of long-chain hydrocarbons or silicone fluids with side groups but also for small, nonspherical molecules such as N2,02, CS2, and others, rotation around two axes is restricted due to steric hindrance. Polar molecules exhibit restricted rotation due to the effect of dipolar orientation. 

Fig. 4.2 I mportance of thermophysical properties of molten silicon (increasing from 0 to 5) required for numerical modeling of crystal growth processes [2].

Table 4.1 Thermophysical properties of silicon actually employed in 44 papers.

Thermal conductivity is one of the most demanding thermophysical properties but difficult to obtain experimentally, because on Earth thermogravitational convection exerts a major effect on heat transfer and it is almost impossible to suppress this effect. There are four methods to obtain the thermal conductivity of molten silicon. Historically, thermal conductivity has been estimated from the measurement of electrical conductivity x and applying the Wiedemann-Franz law, as shown in Eq. (4.2) [5, 8, 52, 53]. Thermal diffusivity was measured also by a laser flash method [7, 24, 54] and is converted into thermal conductivity using density p and mass heat capacity Although transient hot-wire and hot-disk methods assure direct... 

Recommended Thermophysical Property Data for Silicon System... 

Y.-R. Li, and N. Imaishi, 2003, Numerical Simulation for Single Crystal Growth of Silicon and its Thermophysical Properties , J. Jpn. Assoc. Cryst. Growth 30, 357-363 (in Japanese). 

Z.-H. Zhou, S. Mukherjee, and W. K. Rhim, 2003, Measurement of thermophysical properties of molten silicon using an upgraded electrostatic levita-tor , J. Cryst. Growth 257, 350-358. 

A review of measurement of thermophysical properties of silicon melt ,... 

Sensitivity analyses of the thermophysical properties of silicon melt and crystal , Meas. Sci. Technol. 16, 417-425. 

The Stillinger-Weber potential is one of the best model potentials for studying the liquid and supercooled liquid phases of silicon, since the parameters of the model potential are chosen explicitly to predict the structural properties of real liquid silicon. However, whether the model faithfully captures temperature variations of thermophysical, structural, and dynamic properties are unclear, and we should expect that the results obtained from the simulation will be sensitive to the model parameters. The finding of a liquid liquid transition in supercooled silicon using the SW potential has been interrogated by Beaucage and Mousseau... 

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