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Research Paper

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

[+] Author and Article Information
Artde D. K. T. Lam

Department of Information Communication, Leader University, Tainan, Taiwan 70901, Republic of China

J. Nanotechnol. Eng. Med 1(3), 031002 (Jun 30, 2010) (7 pages) doi:10.1115/1.4001789 History: Received December 15, 2009; Revised May 01, 2010; Published June 30, 2010; Online June 30, 2010

## Abstract

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.

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## Figures

Figure 1

InGaN/GaN SAQDs films: (a) interrupted, (b) annealed at 750°C, and (c) annealed at 800°C

Figure 2

The height of horizontal section zh dependence of D for samples A–C

Figure 3

The AFM image of sample A with the height of horizontal section zh=0.4

Figure 4

The series of ln χq(ε)−ln ε curves for sample A with the height of horizontal section zh=0.4

Figure 5

The curve of the generalized fractal dimension Dq versus q for sample A with the height of horizontal section zh=0.4

Figure 6

The multifractal spectra f(α)−α for sample A with the height of horizontal section zh=0.4

Figure 7

The multifractal spectra f(α)−α for sample A with the height of different horizontal sections zh

Figure 8

The multifractal spectra f(α)−α for sample B with the height of different horizontal sections zh

Figure 9

The multifractal spectra f(α)−α for sample C with the height of different horizontal sections zh

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