Why is gallium nitride used in power electronics? Are there any alternatives available?
There are a number of properties that one would wish from a power electronic device:


Voltage withstand capability
Speed of switching
On-state losses 
Thermal capability


If you look at all the materials that possess semiconducting properties diamond is at the top. The problem is how to get there. Germanium was the 1st material used to create a semiconducting device and as crystal growth tech and doping tech progressed, Silicon became a possibility.



We are now in an annoying place. We have the technology to grow Silicon Carbide crystals BUT the yield is low, really low but we have also reach a point where we cannot realise an increase in power density via silicon alone.

Gallium Nitride is a stepping stone until SiC process improvements are realised. 
Equally there is only a couple of switching types that have been successfully doped and even then they are at low current -> low power.