Ultrafast second-harmonic generation spectroscopy of GaN thin films on sapphire

We have performed ultrafast second-harmonic generation spectroscopy of GaN/Al₂O₃. A formalism was developed to calculate the nonlinear response of thin nonlinear films excited by an ultrashort laser source (Ti:Al₂O₃), and then used to extract χzxx⁽²⁾(ω=2ωₒ) and χxzx⁽²⁾(ω=2ωₒ) from our SHG measurements over a two-photon energy range of 2.6--3.4 eV. The spectra are compared to theory [J. L. P. Hughes, Y. Wang, and J. E. Sipe, Phys. Rev. B 55, 13 630 (1997)]. A weak sub-band-gap enhancement of χzxx⁽²⁾(ω=2ωₒ) was observed at a two-photon energy of 2.80 eV; it was not present in χxzx⁽²⁾(ω=2ωₒ). The enhancement, which may result from a three-photon process involving a midgap defect state, was independent of the carrier concentration, intentional doping, and the presence of the ``yellow luminescence band'' defects. In addition, we determined sample miscuts by rotational SHG; the miscuts did not generate observable strain induced nonlinearities. The linear optical properties of GaN from 1.38 to 3.35 eV were also determined.