This paper reports a systematic theoretical study of Al0.23Ga0.77N/GaN/AlxGa1‐xN double‐heterojunction high electron mobility transistors (DH‐HEMTs) with a boron‐doped GaN cap layer under the gate. Boron containing GaN is a desired replacement for Schottky gate in DH‐HEMT to improve the resistivity and surface qualities of GaN cap with good structural properties, and the influence of polarization field in the GaN cap layer can be used to lift up the conduction band for normally OFF operation of the device. This study shows that the B‐doped GaN cap layer offers excellent device characteristics such as high threshold voltage VT of 1.92 V, steep subthreshold slope of ~ 72 mV/dec, high ON/OFF drain current ratio of ~ 107, extremely low subthreshold drain current Ids,LL ~ 10−9 A/mm, and low gate leakage current, Igs,LL less than 10−15 A/mm. For an Al0.07Ga0.93N back‐barrier/buffer, a high OFF‐state breakdown voltage (VBR,OFF) of 865 V is achieved at Ids = 1 mA/mm and Vgs = 0 V with substrate grounded and gate‐to‐drain distance and gate field plate length of 10 and 5 μm, respectively. The simulated high VT and VBR,OFF values are achieved due to the presence of increased back‐barrier height of the AlxGa1‐xN buffer and high Schottky barrier between the Boron‐doped GaN cap and gate metal. Finally, a DC to AC full‐bridge inverter circuit is designed to evaluate the benefit of B‐doped DH‐HEMTs based switching devices for an ultra‐low‐loss inverter circuit.