Extensional piezoelectric coefficients of gallium nitride and aluminum nitride

Measurements of piezoelectric coefficients d₃₃ and d₃₁ in wurtzite GaN and AlN using an interferometric technique are presented. We report on the clamped values, d₃₃^c of these coefficients found in GaN and AlN thin films, and we derive the respective bulk values, d₃₃^b. The clamped value of d₃₃^c in GaN single crystal films is 2.8±0.1 pm V^-1 which is 30% higher than in polycrystalline films grown by laser assisted chemical vapor deposition. The value of d₃₃^b in bulk single crystal GaN is found to be 3.7±0.1 pm V^-1. The value of d₃₃^c in plasma assisted and laser assisted chemical vapor deposited AlN films was 3.2±0.3 and 4.0±0.1 pm V^-1, respectively. The bulk value estimate of d₃₃^b in AlN of 5.6±0.2 pm V^-1 was deduced. The values of d₃₁, both clamped and bulk, were calculated for wurtzite GaN and AlN. We have also calculated the values of d₁₄ in cubic phase film and bulk GaN and AlN. Interferometric measurements of the inverse piezoelectric effect provide a simple method of identifying the positive direction of the c axis, which was found to be pointing away from the substrate for all films.