Direct observation of piezoelectric fields in GaN/InGaN/GaN strained quantum wells

Off-axis electron holography is used to examine a single thin InGaN quantum well in GaN viewed in cross-section. The results show a phase offset across the well, which, under weakly diffracting conditions, is an approximately linear function of specimen thickness. This phase offset is ascribed to a change Delta V-0 in the specimen mean inner potential V-0 caused by a piezoelectric field induced by misfit strains in the InGaN layer. This paper examines the dependence of the phase offset on the diffracting conditions and on thin foil relaxation effects. It is shown that relaxation is negligible for the film thicknesses involved. Using a range of weakly diffracting conditions, the phase offset is measured as Delta V-0/V-0 = 0.042 +/- 0.012. Zone axis convergent beam electron diffraction patterns were taken and compared to simulations to determine the crystal polarity, showing the magnitude of the inner potential increased in the [0001] direction. By using dark-field displacement fringes to measure the InGaN layer thickness, and recent estimates of V-0, the magnitude of the piezoelectric field is determined. This paper assesses the accuracy and limitations of electron holography for the studies of electric fields in other GaN structures.