HRTEM contrast simulation of GaN with Cs = −12 nm in and projection directions as dependent on the sample thickness and defocus settings. The insets show the crystal structures of GaN in the respective projection.
First HRTEM image of the series showing the region of the quantum well.
Sketch of the analysis process.
(a) Color coded lattice parameter map for a single HRTEM image. (b) Histogram of the measured c-lattice parameters in the GaN layers.
Decrease of the STD in the GaN layer with increasing number of averaged images. Black squares are data obtained from the evaluation of the experimental series; red dots correspond to image simulations taking amorphous surface layers into account.
Simulated TEM images of GaN accounting for the modulation transfer function and the resolution of the CCD. The simulations were done for a sample thickness of 8 nm, a spherical aberration of −12 μm, and a Scherzer defocus of +6 nm. (a) Plain simulation without noise. (b) Simulated TEM image with a superimposed noise recorded in a region showing vacuum. (c) Simulated TEM image with a superimposed noise due to an amorphous layer. (d) A section of the experimental image.
Power spectra from different sections of the experimental HRTEM image showing vacuum, amorphous area, and GaN.
Color coded lattice parameter map for the averaged HRTEM image series showing (a) the c-lattice parameters and (b) the a-lattice parameter.
(a) Mean and standard deviation of the c-lattice parameter averaged along the 〈1120〉 direction. (b) Mean and STD of the a-lattice parameter averaged along the 〈1120〉 direction for the averaged HRTEM image series.
Histograms of the measured c-lattice in (a) the GaN layer, (b) the In0.09Ga0.91N layers, and (c) the In0.16Ga0.83N of the QW structure for the averaged HRTEM image series. The data were taken from the areas indicated by the white frames in Fig. 9.
Difference between the local c-lattice parameters of the first and the last image of the series. The deviation of the c-lattice parameter is equally noisy over the whole image indicating no measurable beam damage during series acquisition.
Lattice and elastic constants of GaN and InN used for the calculations.
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