We propose a novel AlN/GaN insulated gate heterostructure field effect transistor (FET) with modulation doping. The vertical structure of the FET was AlN(1)/AlGaN(2)/InGaN(3)/AlGaN(4)/AlGaN(5)/GaN(substrate)(6). The typical widths of gate insulator (1) and channel (3) are 4 and 5 nm, respectively. Charge control in the FET was simulated in one dimension by solving Poisson and Schrodinger equations self-consistently. The dependence of transconductance (G(m)) and the cutoff frequency (f(T)) on the gate voltage (V-gs) was obtained, then the optimum structure was determined. We found: (i) In the above structure, without the electron supplying layer AlGaN(2) in the gate side, the FET has high G(m) (max=2.9 S/mm) and f(T) (max=120 GHz; Lg (gate length)=2.5 mu m) values in the broad V-gs region (about 3 V) in G(m) - V-gs and f(T) - V-gs characteristics. (ii) Both G(m) - V-gs and f(T) - V-gs characteristics show high values in the V-gs region, which becomes broader as the conduction band discontinuity between the channel (3) and electron supplying layers, (2) and (4), increases. (iii) The optimum channel width (w) is 2 nm less than or equal to w less than or equal to 10 nm for the structure with only an electron supplying layer (4). This condition prevents lowering of G(m) in the low V-gs region, and keeps the parasitic resistance between gate and source/drain low. (iv) There is an optimum doping concentration and an optimum width of the electron supplying layer, which depend on the conduction band; discontinuity between the channel and the electron supplying layer. (v) Channel doping reduces intrinsic G(m) and f(T) in the low V-gs region in G(m) - V-gs and f(T) - V-gs characteristics and does not necessarily increase significantly the equilibrium two-dimensional electron gas concentration. (C) 1997 American Institute of Physics.