Ids modeling is not easy as you suppose.There are few models on HEMT transistors and each model has its own approximation.
Because Ids is pretty nonlinear just after pinch-offf then continue linearly and then it arrives to saturation region.So, there are basically three zone and a simple equation can not represent these different zones precisely.
You should take a model as a reference and define the equation as you wish but it's quite hard sine you don't have expriences.