Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces.

Fractal and multifractal characteristics of self-affine surfaces of BaF2 thin films, deposited on crystalline Si ⟨1 1 1⟩ substrate at room temperature, were studied. Self-affine surfaces were prepared by irradiation of 120 MeV Ag(9+) ions which modified the surface morphology at nanometer scale. The surface morphology of virgin thin film and those irradiated with different ion fluences are characterized by atomic force microscopy technique. The surface roughness (interface width) shows monotonic decrease with ion fluences, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension, did not show either monotonic decrease or increase in nature. The self-affine nature of the films is further confirmed by autocorrelation function. The power spectral density of thin films surfaces exhibits inverse power law variation with spatial frequency, suggesting the existence of fractal component in surface morphology. The multifractal detrended fluctuation analysis based on the partition function approach is also performed on virgin and irradiated thin films. It is found that the partition function exhibits the power law behavior with the segment size. Moreover, it is also seen that the scaling exponents vary nonlinearly with the moment, thereby exhibiting the multifractal nature.

[1]  F. Wang,et al.  A new image segmentation method based on multifractal detrended moving average analysis , 2015 .

[2]  F. Wang,et al.  Local multifractal detrended fluctuation analysis for non-stationary image's texture segmentation , 2014 .

[3]  Fang Wang,et al.  Multifractal detrended moving average analysis for texture representation. , 2014, Chaos.

[4]  R. P. Yadav,et al.  Investigating the nanostructured gold thin films using the multifractal analysis , 2014 .

[5]  R. P. Yadav,et al.  On the scaling law analysis of nanodimensional LiF thin film surfaces , 2014 .

[6]  Avinash C. Pandey,et al.  Analyzing the LiF thin films deposited at different substrate temperatures using multifractal technique , 2014 .

[7]  Fang Wang,et al.  Multifractal Detrended fluctuation Analysis for Image Texture Feature Representation , 2014, Int. J. Pattern Recognit. Artif. Intell..

[8]  Wen Shi,et al.  Leaf image segmentation method based on multifractal detrended fluctuation analysis , 2013 .

[9]  A. C. Pandey,et al.  Multifractal analysis of sputtered CaF2 thin films , 2013 .

[10]  R. P. Yadav,et al.  Fractal and multifractal analysis of LiF thin film surface , 2012 .

[11]  Wei-Xing Zhou,et al.  Detrending moving average algorithm for multifractals. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  A. C. Pandey,et al.  Substrate effect on electronic sputtering yield in polycrystalline fluoride (LiF, CaF2 and BaF2) thin films , 2010 .

[13]  S. S. Camargo,et al.  Scaling law analysis of paraffin thin films on different surfaces , 2010 .

[14]  A. Carbone,et al.  Fractal heterogeneous media. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Anna Carbone,et al.  Algorithm to estimate the Hurst exponent of high-dimensional fractals. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Wei‐Xing Zhou,et al.  Multifractal detrended fluctuation analysis of combustion flames in four-burner impinging entrained-flow gasifier , 2007, 0710.5214.

[17]  A. C. Pandey,et al.  Size effect on electronic sputtering of LiF thin films , 2007 .

[18]  Wei-Xing Zhou,et al.  Detrended fluctuation analysis for fractals and multifractals in higher dimensions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. C. Pandey,et al.  Studies of swift heavy ion induced colour centres in LIF thin films deposited on silica substrates , 2006 .

[20]  D. Paramanik,et al.  Surface characterization and electronic structure of HgTe nanocrystalline thin films , 2005 .

[21]  D. Goswami,et al.  Nanoscale self-affine surface smoothing by ion bombardment and the morphology of nanostructures grown on ion-bombarded surfaces , 2005 .

[22]  S. Khan,et al.  Swift heavy ion induced structural and optical modifications in LiF thin film , 2005 .

[23]  H. Stanley,et al.  Time-dependent Hurst exponent in financial time series , 2004 .

[24]  D. Goswami,et al.  Ge growth on ion-irradiated Si self-affine fractal surfaces , 2004, cond-mat/0403241.

[25]  D. Goswami,et al.  Nanoscale self-affine surface smoothing by ion bombardment , 2002, cond-mat/0212563.

[26]  A. Carbone,et al.  Second-order moving average and scaling of stochastic time series , 2002 .

[27]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[28]  G. Niklasson,et al.  Surface smoothing and roughening in sputtered SnO2 films , 2001 .

[29]  D. Avasthi,et al.  Large electronically mediated sputtering in gold films , 2001 .

[30]  T. Tiedje,et al.  Evidence from the surface morphology for nonlinear growth of epitaxial GaAs films. , 2001, Physical review letters.

[31]  K. Lieb,et al.  NANOMETER RIPPLE FORMATION AND SELF-AFFINE ROUGHENING OF ION-BEAM-ERODED GRAPHITE SURFACES , 1999 .

[32]  R. Zamboni,et al.  SCALING BEHAVIOR OF ANISOTROPIC ORGANIC THIN FILMS GROWN IN HIGH VACUUM , 1997 .

[33]  Y. Bruynseraede,et al.  Scanning tunneling microscopy observation of self-affine fractal roughness in ion-bombarded film surfaces. , 1993, Physical review letters.

[34]  Eklund,et al.  Submicron-scale surface roughening induced by ion bombardment. , 1991, Physical review letters.

[35]  James C. Wyant,et al.  A new three-dimensional non-contact digital optical profiler , 1988 .

[36]  B. Mandelbrot.  Self-Affine Fractals and Fractal Dimension , 1985 .

[37]  Jose Alvarez-Ramirez,et al.  Correlation of optical properties with the fractal microstructure of black molybdenum coatings , 2010 .