We present the results of the band structure calculations for a gated AlGaN/GaN heterostructure with undoped AlGaN layer and a lightly doped p-type GaN layer. These calculations are based on the analytical selfconsistent solution of the Poisson and Schrodinger equations at the heterointerface and on the calculations of the spontaneous and piezoelectric polarizations as functions of the lattice mismatch based on the theory of elasticity. The results confirm that piezoelectric and pyroelectric charge can induce the 2D hole gas at the AlGaN/GaN heterointerface. The densities of the 2D hole gas exceeding 10(13) cm(-2) can be obtained in a p-type or even in a nominally undoped GaN. (Our calculations show that in an it-type GaN, the hole 2D gas might be very difficult to induce.) The metal/AlGaN/GaN band structures have been calculated for different gate biases with and without accounting for the effects of spontaneous polarization. The results suggest that a piezoelectrically induced 2D hole gas can be used for the reduction of the base spreading resistance in AlGaN/GaN-based Heterostructure Bipolar Transistors.