The present invention is directed to high frequency, high power or low noise devices such as low noise amplifiers, amplifiers operating at frequencies in the range of 1 GHz up to 400 GHz, radars, portable phones, satellite broadcasting or communication systems, or other devices and systems that use high electron mobility transistors, also called hetero-structure field-effect transistors. A high electron mobility transistor (HEMT) includes a substrate, a quantum well structure and electrodes. The high electron mobility transistor has a polarization-induced charge of high density. Preferably, the quantum well structure includes an AlN buffer layer, an un-doped GaN layer, and an un-doped InAlN layer.