Here are two ways to obtain the piezoelectric tensor using AlN as an example. The first method is to obtain e33 (piezoelectric tensor) by simply inserting the piezoelectric tensor block in the orthorhombic structure and running it. However, in the second method, the piezoelectric tensor block calculates the clamped-ion approximation. I wonder what criteria are used to obtain e33 (piezoelectric tensor) and e33(0) (the clamped ion approximation piezo tensor). I would appreciate it if you could clearly and specifically explain the difference between the two.
I would appreciate your reply.