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.

1.
Carpena
,
P.
,
Coronado
,
A. V.
, and
Bernaola-Galvan
,
P.
, 2000, “
Comparison of Multifractal and Thermodynamical Properties of Fractal and Natural Spectra
,”
Physica A
0378-4371,
287
(
1–2
), pp.
37
48
.
2.
Chaudhari
,
A.
,
Sanders Yan
,
C. C.
, and
Lee
,
S. L.
, 2004, “
Multifractal Analysis of Growing Surfaces
,”
Appl. Surf. Sci.
0169-4332,
238
(
1–4
), pp.
513
517
.
3.
Sarkar
,
N.
, and
Chaudhuri
,
B. B.
, 1992, “
An Efficient Approach to Estimate Fractal Dimensions of Textural Images
,”
Pattern Recogn.
0031-3203,
25
(
9
), pp.
1035
1041
.
4.
Chen
,
Z. W.
,
Wang
,
X. P.
,
Tan
,
S.
,
Zhang
,
S. Y.
,
Hou
,
J. G.
, and
Wu
,
Z. Q.
, 2001, “
Multifractal Behavior of Crystallization on Au/Ge Bilayer Films
,”
Phys. Rev. B
0163-1829,
63
, p.
165413
.
5.
Dong
,
L.
, and
Zhang
,
Y. X.
, 2005, “
Research on Mathematical Expression and Simulation of Multi-Fractal Profiles and Surfaces
,”
Lubr. Eng.
0024-7154,
170
(
2
), pp.
103
105
.
6.
Fang
,
T. H.
, and
Chang
,
W. J.
, 2003, “
Effects of AFM-based Nanomachining Process on Aluminum Surface
,”
J. Phys. Chem. Solids
0022-3697,
64
, pp.
913
918
.
7.
Gan
,
S. Y.
,
Zhou
,
Q.
,
Xu
,
X. D.
,
Hong
,
Y. L.
,
Liu
,
Y.
, and
Fu
,
S. J.
, 2007, “
Study on the Surface Roughness of Substrate With Multi-Fractal Spectra
,”
Microelectron. Eng.
0167-9317,
84
(
5–8
), pp.
1806
1809
.
8.
Han
,
J. H.
,
Shan
,
P.
, and
Hu
,
S. S.
, 2005, “
Fractal Characterization and Simulation of Surface Profiles of Copper Electrodes and Aluminum Sheets
,”
Mater. Sci. Eng., A
0921-5093,
403
(
1–2
), pp.
174
181
.
9.
Jahn
,
R.
, and
Truckenbrodt
,
H.
, 2004, “
A Simple Fractal Analysis Method of the Surface Roughness
,”
J. Mater. Process. Technol.
0924-0136,
145
(
1
), pp.
40
45
.
10.
Jeng
,
Y. R.
,
Tsai
,
P. C.
, and
Fang
,
T. H.
, 2003, “
Nanomeasurement and Fractal Analysis of PZT Ferroelectric Thin Films by Atomic Force Microscopy
,”
Microelectron. Eng.
0167-9317,
65
, pp.
406
415
.
11.
Jeżewski
,
W.
, 2001, “
Complex Multifractal Measures and a Generalized Multifractal Formalism
,”
Physica A
0378-4371,
298
(
3–4
), pp.
419
430
.
12.
Ji
,
L. W.
,
Su
,
Y. K.
,
Chang
,
S. J.
,
Wu
,
L. W.
,
Fang
,
T. H.
,
Chen
,
J. F.
,
Tsai
,
T. Y.
,
Xue
,
Q. K.
, and
Chen
,
S. C.
, 2003, “
Growth of Nanoscale InGaN Self-Assembled Quantum Dots
,”
J. Cryst. Growth
0022-0248,
249
, pp.
144
148
.
13.
Ji
,
L. W.
,
Su
,
Y. K.
,
Chang
,
S. J.
,
Wu
,
L. W.
,
Fang
,
T. H.
,
Xue
,
Q. K.
,
Lai
,
W. C.
, and
Chiou
,
Y. Z.
, 2003, “
A Novel Method to Realize InGaN Self-Assembled Quantum Dots by Metalorganic Chemical Vapor Deposition
,”
Mater. Lett.
0167-577X,
57
, pp.
4218
4221
.
14.
Liu
,
A. Z.
, and
Xie
,
X. P.
, 2005, “
The Application and Researching Development of the Fractal Theory on the Science of Materials
,”
Journal of Anhui Institute of Architecture & Industry
,
13
(
3
), pp.
1
3
.
15.
Mandelbrot
,
B. B.
, 1983,
The Fractal Geometry of Nature
,
3rd ed.
,
Freeman
,
New York
.
16.
Mandelbrot
,
B. B.
,
Passoja
,
D. E.
, and
Paullay
,
A. J.
, 1984, “
Fractal Character of Fracture Surface of Metals
,”
Nature (London)
0028-0836,
308
(
5961
), pp.
721
722
.
17.
Nakamura
,
S.
,
Pearton
,
S.
, and
Fasol
,
G.
, 2000,
The Blue Laser Diode—The Complete Story
,
Springer
,
Berlin
.
18.
Nakamura
,
S.
,
Senoh
,
M.
, and
Mukai
,
T.
, 1994, “
High-Brightness InGaN/AlGaN Double-Heterostructure Blue-Green-Light-Emitting Diodes
,”
J. Appl. Phys.
0021-8979,
76
, p.
8189
.
19.
Park
,
Y. B.
, and
Rhee
,
S. W.
, 1997, “
Growth and Fractal Scaling Nature of Copper Thin Films on TiN Surface by Metal Organic Chemical Vapor Deposition From Hexafluoroacethylacetonate Cu Vinyltrimethylsilane
,”
J. Vac. Sci. Technol. A
0734-2101,
15
, pp.
1995
2000
.
20.
Peyriére
,
J.
, 2003, “
Multifractal Formalisms: Boxed Versus Centered Intervals
,”
Analysis in Theory and Applications
,
19
(
4
), pp.
332
341
.
21.
Rodrigues Neto
,
C.
,
Bube
,
K.
,
Cser
,
A.
,
Otto
,
A.
, and
Feudel
,
U.
, 2004, “
Multifractal Spectra of a Laser Beam Melt Ablation Process
,”
Physica A
0378-4371,
344
(
3–4
), pp.
580
586
.
22.
Silva
,
L. L. G.
,
Ferreira
,
N. G.
,
Dotto
,
M. E. R.
, and
Kleinke
,
M. U.
, 2001, “
The Fractal Dimension of Boron-Doped Diamond Films
,”
Appl. Surf. Sci.
0169-4332,
181
(
3–4
), pp.
327
330
.
23.
Stach
,
S.
, and
Cybo
,
J.
, 2003, “
Multifractal Description of Fracture Morphology: Theoretical Basis
,”
Mater. Charact.
1044-5803,
51
(
1
), pp.
79
86
.
24.
Stach
,
S.
,
Cybo
,
J.
, and
Chmiela
,
J.
, 2001, “
Fracture Surface-Fractal or Multifractal
,”
Mater. Charact.
1044-5803,
26
(
2–3
), pp.
79
86
.
25.
Stanley
,
H. E.
, and
Meakin
,
P.
, 1998, “
Multifractal Phenomena in Physics and Chemistry
,”
Nature (London)
0028-0836,
335
(
3
), pp.
405
409
.
26.
Stupak
,
P. R.
,
Syu
,
C. Y.
, and
Donovan
,
J. A.
, 1992, “
The Effect of Filtering Profilometer Data on Fractal Parameters
,”
Wear
0043-1648,
154
, pp.
109
114
.
27.
Sun
,
C. H.
,
Li
,
F.
,
Ying
,
Z.
,
Liu
,
C.
, and
Cheng
,
H. M.
, 2004, “
Surface Fractal Dimension of Single-Walled Carbon Nanotubes
,”
Phys. Rev. B
0163-1829,
69
(
3
), p.
033404
.
28.
Sun
,
X.
,
Fu
,
Z. X.
, and
Wu
,
Z. Q.
, 2002, “
Fractal Processing of AFM Images of Rough ZnO Films
,”
Mater. Charact.
1044-5803,
48
(
2–3
), pp.
169
175
.
29.
Sun
,
X.
,
Fu
,
Z. X.
, and
Wu
,
Z. Q.
, 2002, “
Multifractal Analysis and Scaling Range of ZnO AFM Images
,”
Physica A
0378-4371,
311
(
3–4
), pp.
327
338
.
30.
Sun
,
Z. F.
, and
Li
,
Y. G.
, 2003, “
Multifractal Analysis of Morphology of TiO2 Nano-Films
,”
Chin. Chem. Lett.
1001-8417,
14
(
5
), pp.
543
546
.
31.
Thomas
,
T. R.
,
Rosen
,
B. G.
, and
Amini
,
N.
, 1999, “
Fractal Characterization of the Anisotropy of Rough Surfaces
,”
Wear
0043-1648,
232
, pp.
41
50
.
32.
Wang
,
B.
,
Wang
,
Y.
, and
Wu
,
Z. Q.
, 1995, “
Multifractal Behavior of Solid-on-Solid Growth
,”
Solid State Commun.
0038-1098,
96
(
2
), pp.
69
72
.
33.
Wehbi
,
D.
,
Roques-Carmes
,
C.
, and
Tricot
,
C.
, 1992, “
The Perturbation Dimension for Describing Rough Surfaces
,”
Int. J. Mach. Tools Manuf.
0890-6955,
32
, pp.
211
216
.
34.
Yordanov
,
O. I.
, and
Ivanova
,
K.
, 1995, “
Description of Surface Roughness as an Approximate Self-Affine Random Structure
,”
Surf. Sci.
0039-6028,
331–333
, pp.
1043
1049
.
35.
Yu
,
H. S.
,
Sun
,
X.
,
Luo
,
S. F.
,
Wang
,
Y. R.
, and
Wu
,
Z. Q.
, 2002, “
Multifractal Spectra of Atomic Force Microscope Images of Amorphous Electroless Ni-Cu-P Alloy
,”
Appl. Surf. Sci.
0169-4332,
191
(
1–4
), pp.
123
127
.
You do not currently have access to this content.