Log homes often have stick frame additions.  Here is a great example of a stick framed addition with spray in expanding foam insulation. 

Spray in foam is very efficient, rated at around R7 per inch versus the R3 per inch of fiberglass insulation.  With fiberglass you also need a vapor barrier, but with spray foam you don't (which conserves materials).  Spray in foam is also more effective at sealing air leaks, making it a more effective at preventing heat loss.  Some spray foams are made from soybean shells, making them very green friendly.