To be specific, what is the thermal conductivity of Si[100] and Si[111]?
Are they the same? If not, can someone explain with references?
Thank you, in advance.
Yes, because the distance between atoms (lattice planes) is not the same for the different crystal orientations... this will result in non-isotropic phonon spectra.
There is a vast amount of (theoretical) studies about this phenomena, e.g. in nanowires grown in different orientations. I found this one:
http://arxiv.org/pdf/1304.1401.pdf
Yes, because the distance between atoms (lattice planes) is not the same for the different crystal orientations... this will result in non-isotropic phonon spectra.
There is a vast amount of (theoretical) studies about this phenomena, e.g. in nanowires grown in different orientations. I found this one:
http://arxiv.org/pdf/1304.1401.pdf
Dear Dr. Jinscheck
Thank you for your response. I also believe that packing fraction is depends on crystal orientation which is turn in change of thermal conductivity. But I want the value of thermal conductivity for those two substrates at room temperature.
Most likely you have to look for rather 'old' papers, e.g.
A. K. McCurdy, H. J. Maris, and C. Elbaum, Anisotropic Heat Conduction in Cubic Crystals in the Boundary Scattering Regime, Phys. Rev. B 2, 4077 (1970)
DOI: http://dx.doi.org/10.1103/PhysRevB.2.4077
So I can come to conclusion from the above mentioned reference that crystal orientation dependent thermal conductivity is true for low temperature. in 25-45 C, thermal conductivities of Si are almost independent of crystal orientation. So what is happening to the anisotropic phonon in this temperature range along the direction of crystal planes?
Obviously thermal conductivity depends on the heat flux direction and to the phonons that contribute to heat conduction. This is true at all temperatures. If the material is isotropic in two different directions, then thermal conductivity is expected to be the same. However, any anisotropy of the material is expected to influence its thermal conductivity.
Dear Fthenakis,
I need reference, where someone has calculated thermal conductivity (K) for both the orientation of Si substrates. I have reference for K of Si(100), but I need to know K for Si(111).
Thank you for your response.
And thanks to Jinscheck
Let me clear the purpose of asking this question. I wanted to correlate the substrates property with the growth of material. For example, growth rates of GaN/ carbon nanotube(CNT) is higher on the Si(111) than the Si(100). Is the thermal conductivity of Si(111) is higher than that of Si(100)? Is it the reason behind the higher growth rate of GaN/CNT on Si(111)?
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