Probing the electrostatic potential of charged dislocations inn−GaNandn−ZnOepilayers by transmission electron holography

Abstract

Epitaxial layers frequently contain a high density of threading dislocations, which may exceed values of ${10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ for ZnO and GaN. To study the electrical activity of single dislocations off-axis electron holography in a transmission electron microscope was applied. The electrostatic potential in the vicinity of charged dislocations was determined from the reconstructed phase of the electron wave, which also provides access to the charge density at the dislocation. On the basis of the electrostatic potential for a screened line charge given by Read [Philos. Mag. 45, 775 (1954)] a refined model is proposed in which a charge density with a finite spatial distribution at the dislocation core is assumed. Comparing the measured and theoretically expected potential, charge densities between $5\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}\phantom{\rule{0.3em}{0ex}}\mathrm{and}\phantom{\rule{0.3em}{0ex}}5\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ in cylinders with radii up to $5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ around the dislocation lines were found. An important aspect of our work is the analysis of dislocations in cross-section transmission electron microscopy samples where the dislocation lines are oriented perpendicular to the electron beam. The advantages and drawbacks of the cross-section geometry are discussed. Electrostatic potentials due to piezoelectric charges in the dislocation strain field are considered and found to be insignificant with respect to dislocation charges.