My understanding...
Different materials have different co-efficients of thermal expansion (CTE). So, when to items of differing material change temperature (lets say raise), they actually expand. But materials made from different "matter", expand at different rates. So, when you bond two items with different expansion rates or different CTE's, you get a lot of stress between them. Usually the bond fails, but sometimes you can get failure of the materials near the interface, or you cause enough stress to fracture it in other areas.
The SiC matches the CTE of the InGaN fairly well, and falls between the solder/substrate, and the InGaN, so it reduces the stresses at each interface.
There are also some additional advantages for crystal structure, or lattice, and growing the InGaN on SiC substrate, instead of sapphire.
In reality, the bulk material is Silicon, but is also Silicon Carbide. An example is the diagram at the bottom of page 1:
http://www.cree.com/products/pdf/CPR3CC.00c.pdf
Another example:
http://www.creelighting.com/products/pdf/CPR3DC.000.pdf
"Based on Cree's EZBright 1000 LED chip, the XLamp 7090 XR-E is produced on a silicon-carbide (SiC) substrate that has an indium-gallium-nitride (InGaN) epitaxial layer grown on it (Fig. 1). "
http://www.elecdesign.com/Articles/ArticleID/13982/13982.html
Take a look at the patent here:
http://www.freepatentsonline.com/6630690.html
They can directly grow the InGaN right on the SiC.
I don't think the high thermal conductivity of the rather thin SiC ESD diode that CREE uses in the XR-E is much of the equation as far as overall thermal resistance. See my comments later, about comparision to metal.
One would want to look in other areas like the ceramic substrate, which can be made from a variety of fillers.
Notice the low thermal conductivity is silica (silicon) and Alumina.
http://en.wikipedia.org/wiki/Alumina
Notice how the chemical formula is Al2O3. Turns out, that sapphire (mineral glass) is also aluminum oxide. In the crystal form, thermal conductivity of sapphire is only 33% of Silicon Carbide. Silicon Carbide also has 2x the thermal conductivity of pure Silicon.
At room temperature, Silicon Carbide has higher thermal conductivity than any metal.
http://www.cree.com/products/sic_sub_prop.asp
CREE is a leading producer of Silicon Carbide, and Silicon Carbide components, so it makes sense that they'd make their own ESD diodes in house. It is a very tough, and thermally conductive material, and is one of the hardest substances out there, and also performs quite well at elevated temperatures. SiC also has a very high electric field breakdown strength, and a very high maximum current density. It also has a low CTE.
There is a grade of SiC that CREE makes, that is colorless, and is used as a diamond replacement, even in jewelry. I forget the trade name for it off-hand...ah, here it is, Moissanite. It is produced by the C3 division of CREE, the only source of gem grade Moissanite. Even the thermal probe test, used to detect cubic Zirconia, is often fooled by Moissanite. One of the neat things about this material, that differs from diamond, is that it creates double refraction, and demonstrates birefringence. This causes a doubling of the facets cut in it then you look into it. It also has a dispersive power that is 2.5x greater than diamond and creates extra live "fire" than many feel is more beautiful. They are still expensive though, at 569.00 per carot or so.
With diamond at a hardness of 10, SiC at 9.5 Mohs is pretty darn close. The Mohs scale is a non-linear scale.
