A.A. Nazarenko - Post-graduate Student, Moscow State University of Information Technologies, Radioengineering and Electronics. Е-mail: alexandrnazarenco@gmail.com O.S. Kiselevskiy - Ph.D. (Eng.), Senior Research Scientist, Belarusian State University of Transport, Homel A.A. Ragachev - Ph.D. (Eng.), Senior Research Scientist, Belarusian State University of Transport, Homel. Е-mail: rogachevfv@mail.ru Р.А. Luchnikov - Senior Research Scientist, Moscow State University of Information Technologies, Radioengineering and Electronics. Е-mail: xamdex@gmail.com S.N. Akilov - Senior Research Scientist, ZNIRTI, Moscow

The results of physical fractals based analysis of methods of description of structural properties of nano-size polymer coatings is pre-sented. The coating structure self-organization was observed at the coating synthesis from gaseous phase with manifestation of polymer fractality in the layer. The polymer structure is shown to be governed by its growth regimes: layer by layer or islands formation. The application of algorithms for pinpointing the characteristic cross-section and caculating dimentional and fractal characteristic features of the coating with using the cluster marker method substantially increases the accuracy of monofractal dimentionality calculations. There are given examples of calculation of mono- and multi-fractal dimentionalities for characteristic cross-section of test structures of island -like film structure with fractal dimentionalities from 2 up to 3.

 

1. Nikolis G., Prigozhin I. Samoorganizacija v neravnovesnykh sistemakh: ot dissipativnykh struktur k uporjadocheniju cherez fluktuacii. M.: Mir. 1979. 512 s.
2. Glensdorf P.,Prigozhin I. Termodinamicheskaja teorija struktury ustojjchivosti i fluktuacijj / Per. s angl. M.: Mir. 1973. 280 s.
3. EHbeling V. Obrazovanie struktur pri neobratimykh processakh. M.: Mir. 1979. 279 s.
4. Klimontovich JU.L. Kriterii otnositelnojj stepeni uporjadochennosti otkrytykh sistem // Uspekhi fizicheskikh nauk. 1996. T. 166. № 11. S. 1231-1243.
5. Antonov A.S., Batenin V.M., Vinogradov A.P. EHlektrofizicheskie svojjstva perkoljacionnykh sistem. M.: IVTAN. 1990. 124 s.
6. ZHabreev V.A. i dr.  Zol-gel tekhnologija. SPb.: Izd-vo SPbGEHTU. 2005. 156 s.
7. Mandelbrot B.B. The fractal geometry nature. NY.: Freeman. 1983. 480 p.
8. Feder J.Fractals. NY.: Plenum. 1988. 221 p.
9. Zotoukhin I.V. Fraktaly v fizike tverdogo tela // Sorovskijj obrazovatelnyjj zhurnal. 1998. № 7. C. 108-113
10. Mandelbrot B.B. Self-affine fractals and fractal dimension // Phys. Scr. 1985. V. 32. P. 257-260.
11. Roldugin V.I.Fraktalnye struktury v dispersnykh sistemakh // Uspekhi khimii. 2003. T. 72. № 10. S. 931-959.
12. VitjazP.A., GordienkoA.I., Mrochek ZH.A., KHejjfec M.L., Golubev O.P. Multifraktalnyjj analiz mnogokomponentnykh plazmenno-vakuumnykh pokrytijj // Doklady NAN Belarusi. 2006. T. 50. № 5. S. 98-100.
13. Smirnov B.M. Fizika fraktalnykh klasterov. M. 1991. 133 s.
14. Gribov B.G., Domracheev G.A., ZHuk B.V. Osazhdenie pljonok i pokrytijj razlozheniem metallo-organicheskikh soedinenijj. M.: Nauka. 1991. 322 s.
15. Zyn V.I., Molchatskijj S.L.  Issledovanie fraktalnojj struktury poverkhnosti po-limernykh pljonok stirola i oktametiltrisiloksana // Poverkhnost. 1999. № 4. S. 66-69.
16. Xagas A.P.,et all. Preparation, fractal surfase morphology and photocatalytic properties of TiO₂ films // Thin solid films. 1999. № 357. P. 173-178.
17. Li J.M.et all. Self-affine nature of thin film surface // Appl. Surf. Sci. 2000. № 161. P. 187-193.
18. Kobelev V.L., Kobelev L.JA., Kobelev JA.L. O zavisimosti fraktalnojj razmernosti poverkhnosti rastushhego segnetoehlektricheskogo kristalla ot vremeni rosta // Poverkhnost. 1999. № 4. C. 42-46.
19. Helin Wei, Zuli Liu, Kailun Yao.Influence of microstructure of substrate surface on early stage of thin film growth // Vacuum. 2000. № 56. P. 185-190.
20. Zolotukhin I.V. Fraktaly v fizike tvjordogo tela // Sorosovskijj obrazovatelnyjj zhurnal. 1998. № 7. S. 108-113.
21. Bieganski P.P. et al. Fractal dimension of discontinuous copper films // Vacuum. 1995. V. 46. № 5/6. P. 513-516.
22. Trojan V.I.i dr. Formirovanie fraktalnykh nanoklasterov Au pri impulsnom lazernom osazhdenii na poverkhnost grafita // Sb. dokladov XIV Mezhdunar. simpoziuma «Tonkie pljonki v optike i ehlektronike». KHarkov, 2002. CH. 1. S. 6-10.
23. Sun Xia, Fu Zhuxi, Wu Ziqin. Fractal processing of AFM images of rough ZnO films // Materials Characterization. 2002. V. 48. P. 169-175.
24. Novikov V.U., Kozlov G.V. Struktura i svojjstva polimerov v ramkakh fraktalnogo podkhoda // Uspekhi khimii. 2000. T. 69. № 6. S. 572-598.
25. Lin C.W., Du Y.C. Effect of surface topographies of PTFE and polyimide as characterized by ASM on the heterogeneous nucleation of isotactic polypropylene // Materials Chemistry and Physics. 1999. V. 58. P. 268-275.
26. Rogachev A.A. Fiziko-khimija polimernykh pokrytijj, osazhdaemykh iz aktivnojj gazovojj fazy. M.: Nauchnyjj mir. 2014. 287 s.
27. Durand H.A.et al. Effect of energy on direct ion beam deposition of carbon thin films: induced defects and graphitization // Surface and coating technology. 2000. V. 125. P. 57? 62.
28. Dobbelaere T., Roy A.K., Vereecken P. Detavernier C. Atomic Layer Deposition of Aluminum Phosphate Based on the Plasma Polymerization of Trimethyl Phosphate // Chem. Mater. 2014. V. 26. P. 6863−6871.
29. De Vriendt V., Felten A., Blondeau J.-P., Maseri F., Pireaux J.-J., Lucas S. Deposition of superhydrophobic structures by magnetron discharge // Surface & Coatings Technology. 2001. V. 205. P. 582-585.
30. Meyer zu Heringdorf, F.-J., Reuter M.C., Tromp R.M.Growth dynamics of pentacene thin films // Nature. V. 412. № 2. P. 517-520.
31. Bieganski P.et al. Fractal dimension of discontinuous copper films // Vacuum. 1995. V. 46. № 5/6. P. 513-516.
32. Dremin I.M., Ivanov O.V., Nechitajjlo V.A. Vejjvlety i ikh ispolzovanie // Uspekhi fizicheskikh nauk. 2001. T. 171. № 5. S. 465-501.
33. Vstovskijj G.V., Kolmakov A.G., Bunin I.ZH. Vvedenie v multifraktalnuju parametrizaciju struktur materialov. M.-Izhevsk: Nauchno-izdatelskijj centr «Reguljarnaja i khaoticheskaja dinamika». 2001. 116 s.
34. Sinergetika i fraktaly v materialovedenii / V.S. Ivanova, A.S. Balankin, I.ZH. Bunin, A.A. Oksogoev / otv. red. N.P. Ljakishev. M.: Nauka. 1994. 382 s.
35. Nejjmark A.V. Opredelenie poverkhnostnojj fraktalnojj razmernosti po dannym adsorbcionnogo ehksperimenta // ZHFKH. 1990. T. 64. Vyp. 10. S. 2593-2605.
36. Nejjmark A.V. Termodinamicheskijj metod raschjota poverkhnostnojj fraktalnojj razmernosti // Pisma v ZHEHTF. 1990. T. 51. Vyp. 10. S. 535-538.
37. Li J.M.et all. Self-affine nature of thin film surface // Appl. Surf. Sci. 2000. № 161. P. 187-193.
38. Rogachjov A.A. Morfologija i molekuljarnaja struktura nanorazmernykh zashhitnykh polimernykh pokrytijj, osazhdjonnykh iz aktivnojj gazovojj fazy: Avtoref. diss. - kand. tekhn. nauk. Gomel: IMMS NAN Belarusi. 2006. 22 s.
39. McRae G.A., Maguire M.A., Jeffrey C.A. A comparison of fractal dimensions determined from atomic force microscopy and impedance spectroscopy of anodic oxides on Zr-2.5Nb // Appl. Surf. Sci. 2002. V. 191. P. 94-105
40. Sayles R.S., Thomas T.R. Surface topography as a nonstationary random process // Nature. 1978. V. 271. P. 431-434.
41. Mandelbrot B.B., Passoja D.E., Paullay A.J.  Fractal character of fracture surfaces of metals // Nature. 1984. V. 308. P. 721-722.
42. Kiselevskijj O.S. Fraktalnaja struktura poverkhnosti almazopodobnykh i nikelevykh pokrytijj tribotekhnicheskogo naznachenija: Avtoref. diss. - kand. tekh. nauk. Gomel: IMMS NAN Belarusi. 2007. 24 s.
43. Almqvist N. Fractal analisis of scanning probe microscopy images // Surf. Sci. 1996. V. 355. P. 221-228.
44. Nazarenko A.A. Fraktalnyjj analiz vakuumnykh polimernykh pokrytijj. Metod markirovki // Fundamentalnye problemy radioehlektronnogo priborostroenija. 2015. T. 15. № 3. S. 231-243.
45. Luchnikov, P.A., Nazarenko A.A., Rogachev A.A. Fraktalnost relefa poverkhnosti vakuumnykh polimernykh plenok na osnove 2Cl-PPK // Nelinejjnyjj mir. 2014. T. 12. № 1. S. 64-67.
46. Lancev A.N., Luchnikov P.A., Nazarenko A.A. Issledovanie strukturnykh i ehlektricheskikh svojjstv polimernykh plenok ppk metodom ehlektretno-termicheskogo analiza // Vestnik nauki Sibiri. 2012. № 4(5). S. 34-41.
47. Luchnikov P.A., Nazarenko A.A., Rogachev A.A. Morfologija i molekuljarnaja struktura tonkikh pokrytijj polidikhlorparaksililena // Nanomaterialy i nanostruktury - XXI vek. 2013. T. 4.№ 2. S. 15-21.
48. Lancev A.N., Luchnikov A.P., Luchnikov P.A., Nazarenko A.A. Vlijanie termicheskojj obrabotki na strukturnye svojjstva vakuumnykh pokrytijj na osnove poliparaksililena // Naukoemkie tekhnologii. 2013. T. 14. № 1. S. 13-20.
49. Luchnikov P.A., Rogachev A.A., Luchnikov A.P. Nanostrukturnye i morfologicheskie svojjstva vakuumnykh ftorpolimernykh plenok na kremnii// Nano- i mikrosistemnaja tekhnika. 2007. № 10. S. 6-11.
50. Luchnikov P.A., Rogachev A.A., Luchnikov A.P. Modifikacija poverkhnostnogo relefa vakuumnykh ftorpolimernykh plenok v processe ikh rosta napravlennojj ehlektronnojj obrabotkojj // Izvestija vysshikh uchebnykh zavedenijj. Fizika. 2008. № 11-3. S. 145.
51. Luchnikov A.P., Luchnikov P.A., Sigov A.S. Mikrostruktura i ehlektrofizicheskie svojjstva vakuumnykh ftorpolimernykh plenok dlja mehms i nanoehlektroniki // Nano- i mikrosistemnaja tekhnika. 2007. № 12. S. 34-40.