Effective Schottky Barrier Height Model for N-Polar and Ga-Polar GaN by Polarization-Induced Surface Charges with Finite Thickness

The nitrogen-polar GaN material system is a promising candidate for high-frequency applications, such as those in the millimeter-wave range. Schottky barrier height is one of fundamental parameters necessary for device applications of N-polar GaN. Herein, vertical Schottky diodes for both N-polar and Ga-polar GaN are prepared, and it is found through experiments that the barrier height of N-polar GaN is smaller than that of Ga-polar GaN by 0.21 V. This difference in the barrier height stems from the polarization-induced surface charge layer of a few angstroms thickness under the surface. Numerical calculation of band profiles suggests that a significant band bending caused by the large amount of polarization charges pushes the conduction band energy downward (upward) in the N-polar (Ga-polar) surface depending on the sign of the polarization charges, which results in two different effective Schottky barrier heights. This difference is explained by assuming the polarization-charge layer thickness of about 5 angstrom. A simple analytical model to estimate the difference in barrier heights between the two polarities is also proposed.