Measurement of second order susceptibilities of GaN and AlGaN

Rotational Maker fringes, scaled with respect to χ 11 ( 2 ) of crystalline quartz, were used to determine the second order susceptibilities χ 31 ( 2 ) and χ 33 ( 2 ) for samples of thin Al x Ga 1 − x N films, a thicker GaN film, and a free-standing GaN platelets. The pump wavelength was 1064 nm . The Al x Ga 1 − x N samples, ranging in thickness from roughly 0.5 to 4.4 μ m , were grown by metalorganic chemical vapor deposition (MOCVD) and hydride vapor-phase epitaxy (HVPE) on (0001) sapphire substrates. The Al mole fractions x were 0, 0.419, 0.507, 0.618, 0.660, and 0.666, for the MOCVD-grown samples, and x = 0 , 0.279, 0.363, and 0.593 for the HVPE-grown samples. An additional HVPE-grown GaN sample ∼ 70 μ m thick was also examined. The free-standing bulk GaN platelets consisted of an HVPE grown film ∼ 226 μ m thick removed from its growth substrate, and a crystal ∼ 160 μ m thick grown by high-pressure techniques. For the Al x Ga 1 − x N samples, the magnitudes of χ 31 ( 2 ) and χ 33 ( 2 ) decrease roughly linearly with increasing x and extrapolate to ∼ 0 for x = 1 . Furthermore, the constraint expected for a perfect wurtzite structure, namely χ 33 ( 2 ) = − 2 χ 31 ( 2 ) , was seldom observed, and the samples with x = 0.660 and x = 0.666 showed χ 31 ( 2 ) and χ 33 ( 2 ) having the same sign. These results are consistent with the theoretical studies of nonlinear susceptibilities for AlN and GaN performed by Chen [ Appl. Phys. Lett. 66 , 1129 ( 1995 )] . The thicker bulk GaN samples displayed a complex superposition of high- and low-frequency Maker fringes due to the multiple-pass interference of the pump and second-harmonic generation beams, and the nonlinear coefficients were approximately consistent with those measured for the thin-film GaN sample.