Multifractal Spectra of INGaN/GaN Self-Assembled Quantum Dots Films

The surface shape and microstructure of semiconductor thin films, especially nanometer thin films, have important influence to construct physical characteristics, such as electricity, magnetic, and optics nature to the thin films. In this work, we use the multifractal spectra to study the surface morphology of InGaN/GaN self-assembled quantum dot films after the annealed process. Samples used in this study were grown on the (0001)-oriented sapphire $(Al2O3)$ substrates in a vertical low-pressure metal-organic chemical vapor deposition reactor with a high-speed rotation disk. The fractal dimension and multifractal spectra can be used to describe the influence of different annealed conditions on surface characterization. Fractal analysis reveals that both the average surface roughness and root-mean-square roughness of nanostructure surfaces are decreased after the thermal annealing process. It can be seen that a smoother surface was obtained under an annealing temperature at $800°C$⁠, and it implies that the surface roughness of this case is minimum in all tests. The results of this paper also described a mathematical modeling method for the observation of the fractal and multifractal characteristics in a semiconductor nanostructure films.