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The Investigation of Bunching and No Bunching Regions of Sinusoidal Mounds

Year 2024, , 609 - 613, 30.09.2024

Ahmet Türker Tüzemen

https://doi.org/10.17776/csj.1511216

Abstract

We studied the evolution of an initial surface which was sinusoidal mound shaped for Diffusion Limited (DL) regime. We supposed that there were two dimensional concentric circular steps on initial surface and attractive/repulsive interactions between these monoatomic steps. While following the surface's evolution, the equation of motion related to each step radius's change and diffusion equation have been solved. We obtained bunching and no bunching regions of studied initial surfaces in a parameter space with their scaling characteristics. Our results in this examination can be summarized as; bunching (no bunching) region expands (shrinks) with increasing of wavelength or amplitude of the initial surface. The curves separating bunching/no bunching regions scale with each other. In the case of the amplitude (wavelength) is changed, the scaling factor is (A_0⁄(A_0^' ))^(1/6) ((λ⁄λ^' )^(1/2)). When both the wavelength and amplitude of the surface are changed at the same time, the scaling factor is equal to (A_0⁄(A_0^' ))^(1/6)×(λ⁄λ^' )^(1/2).

Keywords

Diffusion Surface structure Semiconducting Materials Step Bunching

References

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  • [5] Pérez León C., Drees H., Wippermann S.M., Marz M., Hoffmann-Vogel R., Atomically resolved scanning force studies of vicinal Si(111), Phys. Rev. B, 95 (2017) 245412.
  • [6] Hecquet P., Stability of vicinal surfaces and role of the surface stress, Surface Science, 604 (2010) 834–852.
  • [7] Mugarza A., Schiller F., Kuntze J., Cord´on J., Ruiz-Os´es M., Ortega J.E., Modelling nanostructures with vicinal surfaces, J. Phys. Condens. Matter, 18 (2006) 27–49.
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  • [9] Persichetti L., Sgarlata A., Fanfoni M., Bernardi M., Balzarotti A., Step-step interaction on vicinal Si(001) surfaces studied by scanning tunneling microscopy, Phys. Rev. B, 80 (2009) 075315.
  • [10]Magri R., Gupta S.K., Rosini M., Step energy and step interactions on the reconstructed GaAs(001) surface, Phys. Rev. B, 90 (2014) 115314.
  • [11] Sawada K., Iwata J.I., Oshiyama A., Origin of repulsive interactions between bunched steps on vicinal solid surfaces, e-J, Surf. Sci. Nanotechnol., 13 (2015) 231–234.
  • [12] Righi G., Franchini A., Magri R., Attractive interactions between like-oriented surface steps from an ab initio perspective: role of the elastic and electrostatic contributions, Phys. Rev. B, 99 (2019) 075311.
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  • [15] Andreev A.F., Sov. Phys. JETP, 53 (1981) 1063.
  • [16] Gruber E.E., Mullins W.W., On the theory of anisotropy of crystalline surface tension, J. Phys. Chem. Solids, 28 (1967) 875–887.
  • [17] Saenz J.J., Garcia N., Classical critical behaviour in crystal surfaces near smooth and sharp edges, Surf. Sci., 155 (1985) 24–30.
  • [18] Metois J.J., Heyraud J.C., Analysis of the critical behaviour of curved regions in equilibrium shapes of in crystals, Surf. Sci., 180 (1987) 647–653.
  • [19] Sudoh K., Iwasaki H., Williams E.D., Facet growth due to attractive step step interactions on vicinal Si(113), Surf. Sci., 452 (2000) 287–292.
  • [20] Shenoy V.B., Zhang S., Saam W.F., Step-bunching transitions on vicinal surfaces with attractive step interactions, Surf. Sci., 467 (2000) 58–84.
  • [21] Jeong H.C., Williams E.D., Steps on surfaces: experiment and theory, Surf. Sci., Rep. 34 (1999) 171–294.
  • [22] Jayaprakash C., Rottman C., Saam W.F., Simple model for crystal shapes: step-step interactions and facet edges, Phys. Rev. B, 30 (1984) 6549.
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  • [24] Frohn J., Giesen M., Poensgen M., Wolf J.F., Ibach H., Attractive interaction between steps, Phys. Rev. Lett., 67 (1991) 3543.
  • [25] Redfield A.C., Zangwill A., Attractive interactions between steps, Phys. Rev. B, 46 (1992) 4289.
  • [26] Fujita K., Ichikawa M., Stoyanov S.S., Size-scaling exponents of current-induced step bunching on silicon surfaces, Phys. Rev. B, 60(23) (1999) 16006.
  • [27] Fok P.-W., Rosales R.R., Margetis D., Unification of step bunching phenomena on vicinal surfaces, Phys. Rev. B, 76 (2007) 033408.
  • [28] Borovikov V., Zangwill A., Step bunching of vicinal 6H-SiC{0001} surfaces, Phys. Rev. B, 79(24) (2009) 245413.
  • [29] Załuska-Kotur M.A., Krzyz˙ewski F., Step bunching process induced by the flow of steps at the sublimated crystal surface, J. App. Phys., 111 (2012) 114311.
  • [30] Tonchev V., Classification of step bunching phenomena, Bulgarian Chemical Communications, 44 (2012) 1-8.
  • [31] Siewierska K., Tonchev V., Scaling of the minimal step-step distance with the step-bunch size: Theoretical predictions and experimental findings, Crystal Growth, 43(4) (2016) 204.
  • [32] Sato M., Step Bunching Induced by Immobile Impurities in a Surface Diffusion Field, Journal of the Physical Society of Japan, 86 (2017) 114603.
  • [33] Popova H., Krzyżewski F., Załuska-Kotur M.A., Tonchev V., Quantifying the Effect of Step−Step Exclusion on Dynamically Unstable Vicinal Surfaces: Step Bunching without Macrostep Formation, Cryst. Growth Des., 20 (2020) 7246−7259.
  • [34] Popova H., Analyzing the Pattern Formation on Vicinal Surfaces in Diffusion-Limited and Kinetics-Limited Growth Regimes: The Effect of Step−Step Exclusion, Cryst. Growth Des., 23 (2023) 8875−8888.
  • [35] Tüzemen A.T., Esen M., Ozdemir M., The investigation of the morphology of a decaying conic mound in the presence of repulsive and attractive step interactions, Journal of Crystal Growth, 501 (2018) 1-6.
  • [36] Tüzemen A.T., Scaling characteristics of bunching and no bunching regions of semiconductor mounds, Journal of Crystal Growth, 546 (2020) 125788.
  • [37] Israeli N., Kandel D., Profile of a decaying crystalline cone, Phys. Rev. B, 60 (1999) 5

Year 2024, , 609 - 613, 30.09.2024

Ahmet Türker Tüzemen

https://doi.org/10.17776/csj.1511216

Abstract

References

  • [1] Guin L., Jabbour M.E., Shaabani-Ardali L., Benoit-Mar´echal L., Triantafyllidis N., Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation, Phys. Rev. Letts., 124 (2020) 036101.
  • [2] Krzyżewski F., Załuska-Kotur M., Krasteva A., Popova H., Tonchev V., Scaling and Dynamic Stability of Model Vicinal Surfaces, Cryst. Growth Des., 19 (2019) 821−831.
  • [3] Misbah C., Pierre-Louis O., Saito Y., Crystal surfaces in and out of equilibrium: A modern view, Rev. Mod. Phys., 82 (2010) 981.
  • [4] Toktarbaiuly O., Usov V., Ó Coileáin C., Siewierska K., Krasnikov S., Norton E., Bozhko S.I., Semenov V.N., Chaika A.N., Murphy B.E., Lübben O., Krzyżewski F., Załuska-Kotur M.A., Krasteva A., Popova H., Tonchev V., Shvets I.V., Step bunching with both directions of the current: Vicinal W(110) surfaces versus atomistic-scale model, Phys. Rev. B, 97 (2018) 035436.
  • [5] Pérez León C., Drees H., Wippermann S.M., Marz M., Hoffmann-Vogel R., Atomically resolved scanning force studies of vicinal Si(111), Phys. Rev. B, 95 (2017) 245412.
  • [6] Hecquet P., Stability of vicinal surfaces and role of the surface stress, Surface Science, 604 (2010) 834–852.
  • [7] Mugarza A., Schiller F., Kuntze J., Cord´on J., Ruiz-Os´es M., Ortega J.E., Modelling nanostructures with vicinal surfaces, J. Phys. Condens. Matter, 18 (2006) 27–49.
  • [8] Ciobanu C.V., Tambe D.T., Shenoy V.B., Wang C.Z., Ho K.M., Atomic-scale perspective on the origin of attractive step interactions on Si(113), Phys. Rev. B, 68 (2003) 201302.
  • [9] Persichetti L., Sgarlata A., Fanfoni M., Bernardi M., Balzarotti A., Step-step interaction on vicinal Si(001) surfaces studied by scanning tunneling microscopy, Phys. Rev. B, 80 (2009) 075315.
  • [10]Magri R., Gupta S.K., Rosini M., Step energy and step interactions on the reconstructed GaAs(001) surface, Phys. Rev. B, 90 (2014) 115314.
  • [11] Sawada K., Iwata J.I., Oshiyama A., Origin of repulsive interactions between bunched steps on vicinal solid surfaces, e-J, Surf. Sci. Nanotechnol., 13 (2015) 231–234.
  • [12] Righi G., Franchini A., Magri R., Attractive interactions between like-oriented surface steps from an ab initio perspective: role of the elastic and electrostatic contributions, Phys. Rev. B, 99 (2019) 075311.
  • [13] Andreev A.F., Kosevich A.Y., Sov. Phys. JETP, 54 (1981) 761.
  • [14] Pearson E.M., Halicioglu T., Tiller W.A., Long-range ledge-ledge interactions on Si(111) surfaces: I. No kinks or surface point defects, Surf. Sci., 184 (1987) 401-424.
  • [15] Andreev A.F., Sov. Phys. JETP, 53 (1981) 1063.
  • [16] Gruber E.E., Mullins W.W., On the theory of anisotropy of crystalline surface tension, J. Phys. Chem. Solids, 28 (1967) 875–887.
  • [17] Saenz J.J., Garcia N., Classical critical behaviour in crystal surfaces near smooth and sharp edges, Surf. Sci., 155 (1985) 24–30.
  • [18] Metois J.J., Heyraud J.C., Analysis of the critical behaviour of curved regions in equilibrium shapes of in crystals, Surf. Sci., 180 (1987) 647–653.
  • [19] Sudoh K., Iwasaki H., Williams E.D., Facet growth due to attractive step step interactions on vicinal Si(113), Surf. Sci., 452 (2000) 287–292.
  • [20] Shenoy V.B., Zhang S., Saam W.F., Step-bunching transitions on vicinal surfaces with attractive step interactions, Surf. Sci., 467 (2000) 58–84.
  • [21] Jeong H.C., Williams E.D., Steps on surfaces: experiment and theory, Surf. Sci., Rep. 34 (1999) 171–294.
  • [22] Jayaprakash C., Rottman C., Saam W.F., Simple model for crystal shapes: step-step interactions and facet edges, Phys. Rev. B, 30 (1984) 6549.
  • [23] Wolf D.E., Villain J., Shape fluctuations of crystal bars, Phys. Rev. B, 41 (1990) 2434.
  • [24] Frohn J., Giesen M., Poensgen M., Wolf J.F., Ibach H., Attractive interaction between steps, Phys. Rev. Lett., 67 (1991) 3543.
  • [25] Redfield A.C., Zangwill A., Attractive interactions between steps, Phys. Rev. B, 46 (1992) 4289.
  • [26] Fujita K., Ichikawa M., Stoyanov S.S., Size-scaling exponents of current-induced step bunching on silicon surfaces, Phys. Rev. B, 60(23) (1999) 16006.
  • [27] Fok P.-W., Rosales R.R., Margetis D., Unification of step bunching phenomena on vicinal surfaces, Phys. Rev. B, 76 (2007) 033408.
  • [28] Borovikov V., Zangwill A., Step bunching of vicinal 6H-SiC{0001} surfaces, Phys. Rev. B, 79(24) (2009) 245413.
  • [29] Załuska-Kotur M.A., Krzyz˙ewski F., Step bunching process induced by the flow of steps at the sublimated crystal surface, J. App. Phys., 111 (2012) 114311.
  • [30] Tonchev V., Classification of step bunching phenomena, Bulgarian Chemical Communications, 44 (2012) 1-8.
  • [31] Siewierska K., Tonchev V., Scaling of the minimal step-step distance with the step-bunch size: Theoretical predictions and experimental findings, Crystal Growth, 43(4) (2016) 204.
  • [32] Sato M., Step Bunching Induced by Immobile Impurities in a Surface Diffusion Field, Journal of the Physical Society of Japan, 86 (2017) 114603.
  • [33] Popova H., Krzyżewski F., Załuska-Kotur M.A., Tonchev V., Quantifying the Effect of Step−Step Exclusion on Dynamically Unstable Vicinal Surfaces: Step Bunching without Macrostep Formation, Cryst. Growth Des., 20 (2020) 7246−7259.
  • [34] Popova H., Analyzing the Pattern Formation on Vicinal Surfaces in Diffusion-Limited and Kinetics-Limited Growth Regimes: The Effect of Step−Step Exclusion, Cryst. Growth Des., 23 (2023) 8875−8888.
  • [35] Tüzemen A.T., Esen M., Ozdemir M., The investigation of the morphology of a decaying conic mound in the presence of repulsive and attractive step interactions, Journal of Crystal Growth, 501 (2018) 1-6.
  • [36] Tüzemen A.T., Scaling characteristics of bunching and no bunching regions of semiconductor mounds, Journal of Crystal Growth, 546 (2020) 125788.
  • [37] Israeli N., Kandel D., Profile of a decaying crystalline cone, Phys. Rev. B, 60 (1999) 5
There are 37 citations in total.

Details

Primary Language English
Subjects Surface Physics
Journal Section Natural Sciences
Authors

Ahmet Türker Tüzemen 0000-0002-6120-6008

Publication Date September 30, 2024
Submission Date July 5, 2024
Acceptance Date September 12, 2024
Published in Issue Year 2024

Cite

APA Tüzemen, A. T. (2024). The Investigation of Bunching and No Bunching Regions of Sinusoidal Mounds. Cumhuriyet Science Journal, 45(3), 609-613. https://doi.org/10.17776/csj.1511216