I know the general structural differences between each one. A MOSFET is a metal, oxide, and semiconductor and you apply voltage to the gate to create an inversion layer in the semiconductor. A MODFET is similar to a MOSFET but its oxide is a doped AlGaAs combined with an undoped GaAs to create a strange dip in the band energy. This (somehow) creates a larger mobility for carriers in the 2-Dimensional Electron Gas layer.
A MESFET, I think, is the most dissimilar to the others because it is just a metal on a semiconductor. And you apply a voltage to create a large enough depletion region to completely deplete the layer so charge can't flow.
But what are the advantages and disadvantages to each one? Why would you want to use a MOSFET when the MODFET supposedly has a higher carrier mobility? Why would you use MODFET over a MESFET?
I am trying to construct a chart comparing and contrasting their characteristics, including (but not limited to): fabrication and structure and strain, parasitic effects, depletion region creation and shape, mobility of carriers, barrier height.