Ефекти електроміграції при епітаксіальному рості тонких плівок: моделювання методом фазового поля

Автор(и)

  • A.V. Dvornichenko Sumy State University

DOI:

https://doi.org/10.15407/ujpe66.5.439

Ключові слова:

метод фазового поля, епiтаксiальний рiст, поверхневi структури, електромiграцiя, числовi симуляцiї, статистичнi властивостi

Анотація

У роботi проводиться теоретичне дослiдження процесу росту тонких плiвок при епiтаксiї з урахуванням анiзотропiї поверхневої дифузiї адсорбату, iндукованої ефектами електромiграцiї, в рамках теорiї фазового поля з використанням процедури числового моделювання. Встановлено вплив коефiцiєнта iндукованої анiзотропної дифузiї, пропорцiйного до напруженостi пiдведеного електричного поля, на динамiку росту товщини плiвки та висоти поверхневих структур, морфологiю зростаючої поверхнi, статистичнi властивостi поверхневих багатошарових структур адсорбату та розподiл поверхневих структур за висотою.

Посилання

J.R. Black. Electromigration - A brief survey and some recent results. IEEE Trans. Electr. Dev. 16, 338 (1969).

https://doi.org/10.1109/T-ED.1969.16754

P.S. Ho, T. Kwok. Electromigration in metals. Rep. Prog. Phys. 52, 301 (1989).

https://doi.org/10.1088/0034-4885/52/3/002

Y. Homma, R.J. Mcclelland, H. Hibino. DC-resistive-heating-induced step bunching on vicinal Si (111). Jap. J. Appl. Phys. 29, L2254 (1990).

https://doi.org/10.1143/JJAP.29.L2254

E.D. Williams, E. Fu, Y.N. Yang et al. Measurement of the anisotropy ratio during current-induced step bunching. Surf. Sci. 336, L746 (1995).

https://doi.org/10.1016/0039-6028(95)00551-X

B.J. Gibbons, J. Noff singer, J.P. Pelz. Influence of Si deposition on the electromigration induced step bunching instability on Si(111). Surf. Sci. 575, L51 (2005).

https://doi.org/10.1016/j.susc.2004.11.020

S. Lin, Y. Liu, S. Chiu et al. The electromigration effect revisited: non-uniform local tensile stress-driven diffusion. Sci. Rep. 7, 3082 (2017).

https://doi.org/10.1038/s41598-017-03324-5

F. Leroy, D. Karashanova, M. Dufay et al. Step bunching to step-meandering transition induced by electromigration on Si(111) vicinal surface. Surf. Sci. 603, 507 (2009).

https://doi.org/10.1016/j.susc.2008.12.016

V. Usov, C.O. Coileain, I.V. Shvets. Influence of electromigration fi eld on the step bunching process on Si(111). Phys. Rev. B 82, 153301 (2010).

https://doi.org/10.1103/PhysRevB.82.153301

O. Toktarbaiuly, V. Usov, C.O. Coileain et al. Step bunching with both directions of the current: Vicinal W(110)

surfaces versus atomistic-scale model. Phys. Rev. B 97 035436 (2018).

A.A. Shklyaev, A.V. Latyshev. Electromigration effect on the surface morphology during the Ge deposition on

Si(111) at high temperatures. Appl. Surf. Sci. 465, 10 (2019).

https://doi.org/10.1016/j.apsusc.2018.09.119

B. Voigtlander. Fundamental processes in Si/Si and Ge/Si epitaxy studied by scanning tunneling microscopy during growth. Surf. Sci. Rep. 43, 127 (2001).

https://doi.org/10.1016/S0167-5729(01)00012-7

A.A. Shklyaev, M. Ichikawa. Extremely dense arrays of germanium and silicon nanostructures. Phys. Usp. 51, 133 (2008).

https://doi.org/10.1070/PU2008v051n02ABEH006344

A.A. Shklyaev, K.N. Romanyuk, S.S. Kosolobov. Surface morphology of Ge layers epitaxially grown on bare and

oxidized Si(001) and Si(111) substrates. Surf. Sci. 625, 50 (2014).

https://doi.org/10.1016/j.susc.2014.03.013

S.A. Teys. Diff erent growth mechanisms of Ge by Stranski-Krastanow on Si (111) and (001) surfaces: An STM study. Appl. Surf. Sci. 392, 1017 (2017).

https://doi.org/10.1016/j.apsusc.2016.09.124

J.M. MacLeod, J.A. Lipton-Duffin, U. Lanke et al. Shape transition in very large germanium islands on Si(111). Appl. Phys. Lett. 94, 103109 (2009).

https://doi.org/10.1063/1.3093674

A. Shklyaev, L. Bolotov, V. Poborchii et al. Properties of three-dimensional structures prepared by Ge dewetting

from Si(111) at high temperatures. J. Appl. Phys. 117, 205303 (2015).

https://doi.org/10.1063/1.4921596

A. Voigt. Multiscale Modeling in Epitaxial Growth (Birkh¨auser, 2000) [ISBN: 3-7643-7208-7].

C. Ratsch, P. Puggerone, M. Scheffl er. Surface Diffusion: Atomistic and Collective Processes (Plenum, 1997) [ISBN: 978-1-4899-0262-7].

H. Metiu, Y.-T. Lu, Z.Y. Zhang. Epitaxial growth and the art of computer simulations. Science 255, 1088 (1992).

https://doi.org/10.1126/science.255.5048.1088

C. Ratsch, M.F. Gyure, R.E. Cafl isch et al. Level-set method for island dynamics in epitaxial growth. Phys. Rev. B 65, 195403 (2002).

https://doi.org/10.1103/PhysRevB.65.195403

S. Park, H. Jeong, B. Kahng. Numerical test of the damping time of layer-by-layer growth on stochastic models. Phys. Rev. E 59, 6184 (1999).

https://doi.org/10.1103/PhysRevE.59.6184

D.O. Kharchenko, V.O. Kharchenko, I.O. Lysenko et al. Stochastic eff ects at ripple formation processes in

anisotropic systems with multiplicative noise. Phys. Rev. E 82, 061108 (2010).

F. Liu, H. Metiu. Stability and kinetics of step motion on crystal surfaces. Phys. Rev. E 49, 2601 (1994).

https://doi.org/10.1103/PhysRevE.49.2601

A. Karma, M. Plapp. Spiral surface growth without desorption. Phys. Rev. Lett. 81, 4444 (1998).

https://doi.org/10.1103/PhysRevLett.81.4444

V.O. Kharchenko, D.O. Kharchenko, A.V. Dvornichenko. Scaling properties of pyramidal islands formation process at epitaxial growth. Eur. Phys. J. B 88, 3 (2015).

https://doi.org/10.1140/epjb/e2014-50327-6

D. Kandel, E. Kaxiras. Microscopic theory of electromigration on semiconductor surfaces. Phys. Rev. Lett. 76, 1114 (1996).

https://doi.org/10.1103/PhysRevLett.76.1114

S. Stoyanov, V. Tonchev. Properties and dynamic interaction of step density waves at a crystal surface during electromigration aff ected sublimation. Phys. Rev. B 58, 1590 (1998).

https://doi.org/10.1103/PhysRevB.58.1590

V. Popkov, J. Krug. Dynamic phase transitions in electromigration-induced step bunching. Phys. Rev. B 73, 235430 (2006).

https://doi.org/10.1103/PhysRevB.73.235430

B. Ranguelov, S. Stoyanov. Instability of vicinal crystal surfaces with transparent steps: Transient kinetics and

non-local electromigration. Surf. Sci. 603, 2907 (2009).

https://doi.org/10.1016/j.susc.2009.07.040

D.O. Kharchenko, V.O. Kharchenko, I.O. Lysenko. Phase-field modeling of epitaxial growth in stochastic systems with interacting adsorbate. Phys. Scr. 83, 045802 (2011).

https://doi.org/10.1088/0031-8949/83/04/045802

D.O. Kharchenko, V.O. Kharchenko, T. Zhylenko et al. A study of pyramidal islands formation in epitaxy within

the generalized phase-field model. Eur. Phys. J. B 86, 175 (2013).

V.O. Kharchenko, D.O. Kharchenko. Nanosize structure formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate. Phys. Rev. E 86, 041143 (2012).

https://doi.org/10.1103/PhysRevE.86.041143

V.O. Kharchenko, D.O. Kharchenko, S.V. Kokhan et al. Properties of nano-islands formation in nonequilibrium reaction-diffusion systems with memory eff ects. Phys. Scr. 86, 055401 (2012). https://doi.org/10.1088/0031-8949/86/05/055401

V.O. Kharchenko, D.O. Kharchenko, A.V. Dvornichenko. Statistical properties of nanosized clusters on a surface

in overdamped stochastic reaction-Cattaneo systems. Surf. Sci. 630, 158 (2014). https://doi.org/10.1016/j.susc.2014.08.008

V.O. Kharchenko, D.O. Kharchenko. Noise-induced structure formation in system of point defects subjected to irradiation. Eur. Phys. J. B 85, 383 (2012). https://doi.org/10.1140/epjb/e2012-30522-3

V.O. Kharchenko, D.O. Kharchenko. Abnormal grain growth in nonequilibrium systems: Effects of point defect structureing. Phys. Rev. E 89, 042133 (2014).

F. Cucker, P.G. Ciarlet. Handbook of Numerical Analysis. Vol. 11. Special Volume: Foundations of Computational Mathematics (Amsterdam, 2003) [ISBN: 9780444512475].

G. Strang. Introduction to Applied Mathematics (Wellesley-Cambridge Press, 1986) [ISBN: 978-0961408800].

E.S. Gadelmawla, M.M. Koura, T.M.A. Maksoud et al. Roughness parameters. J. Mater. Process. Tech. 123, 133 (2002). https://doi.org/10.1016/S0924-0136(02)00060-2

G. Muraleedharan, C.G. Soares, C. Lucas. Characteristic and moment generating functions of generalised extreme value distribution (GeV). In: Sea Level Rise, Coastal Engineering, Shorelines and Tides. Edited by L.L. Wright (Nova Science Publishers, 2009), p. 269 [ISBN 978-1-61728-655-1].

Опубліковано

2021-05-28

Як цитувати

Dvornichenko, A. (2021). Ефекти електроміграції при епітаксіальному рості тонких плівок: моделювання методом фазового поля. Український фізичний журнал, 66(5), 439. https://doi.org/10.15407/ujpe66.5.439

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