Here you can find such calculations for AlGaN/GaN system and then it should be easy to recalcultae it for AlN/GaN system.

"Two dimensional electron gases induced by spontaneous and piezoelectric polarization undoped and doped AlGaN/GaN heterostructures", O. Ambacher JAP 2000, Article Two dimensional electron gases induced by spontaneous and pi...

I recommend using the freeware BandEng, useful for computing III-nitride band structure and carrier profiles.

http://my.ece.ucsb.edu/mgrundmann/bandeng.htm

The standard material file includes GaN and AlGaN (including AlN, available by adjusting the AlGaN composition).

Additionally, it is possible to include user-defined materials, so you could experiment with lattice parameters and constants relating to piezoelectric polarization. You can also turn polarization off completely, and compare the results.

Good luck!

I totally agree with Matthew. This software is really good. This should help you.

Matthew D. Smith Dear Matthew D. Smith.

I posted a question about AlN and Gan polarization on researhchgate. Thank you very much for your answer. I would like to ask you to help me give more instructions on how to use this software. Or a related example for calculating the polarization of ALN and GaN.Thank you！

Chen Cai Dear Chen Chai,

I suggest that you play around with the software in order to get familiar with it, and then use it to solve your specific problem. You will need to load the material file using the Materials tab --> Open, and load the matl3.dat file that is downloaded with the software. Then build your structure using the Layers tab.

You may also find this recent paper from Ambacher et al. useful. The total, spontaneous and piezoelectric polarization components are separated out for different heterostructure systems, including AlGaN/GaN, which includes AlN/GaN.

Article Polarization induced interface and electron sheet charges of...

Best of luck

Matthew D. Smith Thank you！