A novel doping design has been proposed that yields high two-dimensional electron gas (2DEG) densities in the AlGaN/GaN heterostructure field-effect transistors (HFETs) even when the AlGaN barrier layers are designed to be very thin. In the novel doping design, an asymmetric double-heterostructure is employed, and donor atoms are doped not only in the surface-side AlGaN layer but also in the underlying AlGaN layer. In this structure, electrons are efficiently supplied also from the back-doped AlGaN barrier layer to the GaN channel, with the help of the negative polarization charges at the heterointerface between the GaN channel and the underlying AlGaN barrier layer. High 2DEG densities can thus be obtained. Moreover, relatively high 2DEG mobilities can be obtained for high 2DEG densities, because back-doped donor atoms are sufficiently remote from the position of the 2DEG so that the 2DEG is less subjected to the ionized impurity scattering due to the relevant donor atoms. By using this back-doping design, a very high 2DEG density of 2.8x1013 cm-2 (2DEG mobility is 850 cm2/Vs) has been obtained at 300 K in the Al0.3Ga0.7N/GaN HFET whose barrier layer (Al0.3Ga0.7N) is as thin as 120 Å. Thus, the back-doping design is effective to obtain high 2DEG densities in the HFETs with thin barrier layers, and promising for high-power applications.