In AlGaN/GaN as the surface or Schottky barrier height increase, polarization induced sheet charge density reduce in the channel. What is the possible physical reason? For more clarity of the question please see the figure 3 in the attachment file.
The polarization gradient at AlGaN/GaN interface leads for metal-face material to a fixed positive polarization charge. Negative electrons are attracted and form the 2DEG channel layer within the GaN. If one would have flatband conditions in the AlGaN barrier then polarization charge and 2DEG density would be equal.But in reality, the potential increases towards the surface accompanied by an electric field. It lowers the 2DEG density with increasing field strength.
See for example the experimental results and their expalnation:
A.T. Winzer et al., Appl. Phys. Lett. 86, 181912 (2005); doi: 10.1063/1.1923748
A.T. Winzer et al., Appl. Phys. Lett. 88, 024101 (2006); doi: 10.1063/1.2161394
as well references therein, or the work
C. Buchheim et al., Appl. Phys. Lett. 92, 013510 (2008); doi: 10.1063/1.2830836