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Multifractal analysis of SiO2 surface embedded with Ge nanocrystal

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Abstract

In the present article SiO2/Si layers of thickness 200 nm were implanted with 150 keV Ge ions with different fluences varying from 2.5 × 1016 to 7.5 × 1016 ions/cm2. The implantation-induced disorder was removed via high temperature annealing method in Ar ambience. Transmission electron microscopy (TEM) measurement confirmed the presence of embedded Ge nanocrystals of 5–10 nm size in annealed samples. Topographical studies of implanted as well as annealed samples were captured by the atomic force microscopy (AFM) and parameters such as average roughness and interface width were extracted. Two dimensional multifractal detrended fluctuation analysis (2D-MFDFA) based on the partition function approach was used to study the surfaces of ion implanted and annealed samples. The partition function is used to calculate generalized Hurst exponent with the segment size. A nonlinear variation with moment is observed for generalized Hurst exponents, leading to the multifractal nature. The multifractality of surface is pronounced after annealing for the surface implanted with fluence of 7.5 × 1016 ions/cm2.

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References

  • Ang R, Chen TP, Yang M, Wong JI, Yi MD (2010) The charge trapping and memory effect in SiO2 thin films containing Ge nanocrystals. J Phys D Appl Phys 43:015102

    Article  Google Scholar 

  • Baranwal V, Gerlach JW, Karl H, Rauschenbach B, Kanjilal D, Avasthi DK, Pandey AC (2008) Rapid thermal and swift heavy ion induced annealing of Co ion implanted GaN films. J Appl Phys 103:124904

    Article  Google Scholar 

  • Baranwal V, Gerlach JW, Lotnyk A, Rauschenbach B, Karl H, Ojha S, Avasthi DK, Kanjilal D, Pandey AC (2015) Embedded Ge nanocrystals in SiO2 synthesized by ion implantation. J Appl Phys 118:134303

    Article  Google Scholar 

  • Bogachev MI, Bunde A (2009) Improved risk estimation in multifractal records: application to the value at risk in finance. Phys Rev E 80:026131

    Article  Google Scholar 

  • Drexler H, Leonard D, Hansen W, Kotthaus JP, Petroff PM (1994) Spectroscopy of quantum levels in charge-tunable InGaAs quantum dots. Phys Rev Lett 73:2252

    Article  CAS  Google Scholar 

  • Drozd˙z S, Kwapie´n J, O´swiecimka P, Rak R (2010) The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect. New J Phys 12:105003

    Article  Google Scholar 

  • Gu G-F, Zhou W-X (2006) Detrended fluctuation analysis for fractals and multifractals in higher dimensions. Phys Rev E 74:061104

    Article  Google Scholar 

  • Huffaker DL, Park G, Zou Z, Shchekin OB, Deppe DG (1998) 1.3 μm room-temperature GaAs-based quantum-dot laser. Appl Phys Lett 73:2564

    Article  CAS  Google Scholar 

  • Ihlen EAF, Vereijken B (2013) Multifractal formalisms of human behavior. Human Mov Sci 32:633

    Article  Google Scholar 

  • Jafari GR, Pedram P, Hedayatifar L (2007) Long-range correlation and multifractality in Bach’s Inventions pitches. J Stat Mech 2007:04012

    Article  Google Scholar 

  • Kantelhardt JW, Koscielny-Bunde E, Rybski D, Braun P, Bunde A, Havlin S (2006) Long-term persistence and multifractality of precipitation and river runoff records. J Geophys Res Atmos 111:D01106

    Article  Google Scholar 

  • Lu TZ, Alexe M, Scholz R, Talalaev V, Zhang RJ, Zacharias M (2006) Si nanocrystal based memories: effect of the nanocrystal density. J Appl Phys 100:014310

    Article  Google Scholar 

  • Muzy JF, Bacry E, Baile R, Poggi P (2008) Uncovering latent singularities from multifractal scaling laws in mixed asymptotic regime: application to turbulence. Euro Phys Lett 82:60007

    Article  Google Scholar 

  • Niu M-R, Zhou W-X, Yan Z-Y, Guo Q-H, Liang Q-F, Wang F-C, Yu Z-H (2008) Multifractal detrended fluctuation analysis of combustion flames in four-burner impinging entrained-flow gasifier. Chem Eng J 143:230–235

    Article  CAS  Google Scholar 

  • Oswiecimka P, Kwapien J, Drozdz S (2006) Wavelet versus detrended fluctuation analysis of multifractal structures. Phys Rev E 74:016103

    Article  Google Scholar 

  • Rosas A, Nogueira E Jr, Fontanari JF (2002) Multifractal analysis of DNA walks and trails. Phys Rev E 66:061906

    Article  Google Scholar 

  • Sabarinathan J, Bhattacharya P, Yu PC, Krishna S, Cheng J, Steel DG (2002) An electrically injected InAs/GaAs quantum-dot photonic crystal microcavity light-emitting diode. Appl Phys Lett 81:3876

    Article  CAS  Google Scholar 

  • Sharma P, Singhal R, Vishnoi R, Banerjee MK, Kaushik R, Kamma KV, Lakshmi GBVS, Tripathi A, Avasthi DK (2016) Surface and structural studies of fullerene C70 under ion irradiation. Surf Eng 32:846–852

    Article  CAS  Google Scholar 

  • Singh UB, Yadav RP, Pandey RK, Agarwal DC, Pannu C, Mittal AK (2016) Insight mechanisms of surface structuring and wettability of ion-treated Ag thin films. J Phys Chem C 120:5755–5763

    Article  CAS  Google Scholar 

  • Ţălu S, Stach S, Ghodselahi T, Ghaderi A, Solaymani S, Boochani A, Garczyk Ż (2015) Topographic characterization of Cu-Ni NPs @ a-C: H Films by AFM and multifractal analysis. J Phys Chem B 119:5662–5670

    Article  Google Scholar 

  • Ţălu Ş, Bramowicz M, Kulesza S, Ghaderi A, Dalouji V, Solaymani S, Kenari MF, Ghoranneviss M (2016) Fractal features and surface micromorphology of diamond nanocrystals. J Microsc 264:143–152

    Article  Google Scholar 

  • Ţălu Ş, Yadav RP, Lainović T, Albores AM, Trejo G, Kukuruzović D, Nezafat NB, Shafiekhani A, Solaymani S (2018) The effect of dental LED light-curing unit photoactivation mode on 3D surface morphology of dental nanocomposites evaluated by two-dimensional multifractal detrended fluctuation analysis. Microsc Res Tech 81:1223–1230

    Article  Google Scholar 

  • Talu S, Solaymani S, Bramowicz M, Naseri N, Kulesza S, Ghaderi A (2016) Surface micromorphology and fractal geometry of Co/CP/X (X = Cu, Ti, SM and Ni) nanoflake electrocatalysts. RSC Adv 6:27228

    Article  CAS  Google Scholar 

  • Udovichenko VV, Strizhak PE (2002) Multifractal properties of copper sulfide film formed in self-organizing chemical system. Theor Exp Chem 38:259

    Article  CAS  Google Scholar 

  • Wang F, Li J, Shi W, Liao G (2013) Leaf image segmentation method based on multifractal detrended fluctuation analysis. J Appl Phys 114:214905

    Article  Google Scholar 

  • Wang F, Li Z, Li J (2014) Local multifractal detrended fluctuation analysis for non-stationary image’s texture segmentation. Appl Surf Sci 322:116–125

    Article  CAS  Google Scholar 

  • Wang F, Liao D, Li J, Liao G (2015) Two-dimensional multifractal detrended fluctuation analysis for plant identification. Plant Methods 11:12

    Article  CAS  Google Scholar 

  • Witt A, Malamud BD (2013) Quantification of long-range persistence in geophysical time series: conventional and benchmark-based improvement techniques. Surv Geophys 34:541

    Article  Google Scholar 

  • Yadav RP, Dwivedi S, Mittal AK, Kumar M, Pandey AC (2012) Fractal and multifractal analysis of LiF thin film surface. Appl Surf Sci 261:547–553

    Article  CAS  Google Scholar 

  • Yadav RP, Pandey RK, Mittal AK, Dwivedi S, Pandey AC (2013) Multifractal analysis of sputtered CaF2 thin films. Surf Int Anal 45:1775–1780

    Article  CAS  Google Scholar 

  • Yadav RP, Kumar M, Mittal AK, Dwivedi S, Pandey AC (2014) On the scaling law analysis of nanodimensional LiF thin film surfaces. Mater Lett 126:123–125

    Article  CAS  Google Scholar 

  • Yadav RP, Singh UB, Mittal AK, Dwivedi S (2014) Investigating the nanostructured gold thin films using the multifractal analysis. Appl Phys A 117:2159–2166

    Article  CAS  Google Scholar 

  • Yadav RP, Kumar M, Mittal AK, Pandey AC (2015) Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces. Chaos 25:083115

    Article  CAS  Google Scholar 

  • Yadav RP, Agarwal DC, Kumar M, Rajput P, Tomar DS, Pandey SN, Priya PK, Mittal AK (2017) Effect of angle of deposition on the fractal properties of ZnO thin film surface. Appl Surf Sci 416:51–58

    Article  CAS  Google Scholar 

  • Yang R, Bogdan P (2020) Controlling the multifractal generating measures of complex networks. Sci Rep 10:5541

    Article  Google Scholar 

  • Zhao JP, Huang DX, Chen ZY, Chu WK, Makarenkov B, Jacobson AJ, Bahrim B, Rabalais JW (2008) Amorphous Ge quantum dots embedded in SiO2 formed by low energy ion implantation. J Appl Phys 103:124304

    Article  Google Scholar 

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Acknowledgements

RPY is thankful to Science and Engineering Research Board (SERB) of India for awarding National Postdoctoral Fellowship (PDF/2015/000590). VB is thankful to DST for providing funds under young scientist scheme (SR/FTP/PS-53/2011) and Nanomission scheme (IR/S2/PF/0001/2009).

Funding

This study was funded by Department of Science and Technology, New Delhi (grant number PDF/2015/000590, SR/FTP/PS-53/2011, IR/S2/PF/0001/2009).

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Authors and Affiliations

  1. Department of Physics, Deen Dayal Upadhyay Govt. P.G. College, Saidabad, Allahabad, 221508, India

    R. P. Yadav

  2. Nanotechnology Application Centre, University of Allahabad, Allahabad, 211 002, India

    V. Baranwal & A. C. Pandey

  3. Inter University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi, 110067, India

    Sunil Kumar & A. C. Pandey

  4. Department of Physics, University of Allahabad, Allahabad, 211002, India

    A. K. Mittal

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  1. R. P. Yadav
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  2. V. Baranwal
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  3. Sunil Kumar
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  4. A. C. Pandey
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  5. A. K. Mittal
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Corresponding author

Correspondence to V. Baranwal.

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Conflict of interest

Author R P Yadav has received research grants from SERB, DST (PDF/2015/000590). Author V Baranwal has received research grants from DST (SR/FTP/PS-53/2011). Author Avinash C Pandey has received research grants from Nanomission, DST (IR/S2/PF/0001/2009), Author RPY declares that he has no conflict of interest. Author VB declares that he has no conflict of interest. Author SK declares that he has no conflict of interest. Author ACP declares that he has no conflict of interest. Author AKM declares that he has no conflict of interest.

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Yadav, R.P., Baranwal, V., Kumar, S. et al. Multifractal analysis of SiO2 surface embedded with Ge nanocrystal. Appl Nanosci 13, 247–253 (2023). https://doi.org/10.1007/s13204-020-01626-1

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  • DOI: https://doi.org/10.1007/s13204-020-01626-1

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