Epitaksiyel Olarak Gerilmiş İzotropik İnce Filmlerde Elastik Etkileşim Nedenli Morfolojik Değişimin Doğrusal Kararlılık ve Sayısal Analizi

Yıl 2022, Cilt: 3 Sayı: 1, 21 - 33, 30.06.2022

Aytaç Çelik

https://doi.org/10.53501/rteufemud.1088954

Öz

Bu sistematik sayısal analiz çalışmasında ince film yüzeyinin kararlılığı, elastik dipol etkileri de göz önünde bulunduran matematiksel model ile farklı çeki kuvvetleri altında kararlılığı incelenmiştir. Bu modelde yüzey difüzyonuna gerilmenin etkisi birinci ve ikinci dereceden iki terim ile ifade edilmektedir. İnce film yüzeyinin sinüs dalgası şekillinde olduğu varsayılmış ve bu dalga yapısının yüzeydeki gerilme nedenli difüzyon ile sönümlenme veya büyüme dinamikleri incelenerek kararlılığı test edilmiştir. Elastik dipol etkileşimlerin basma ve çekme gerilmeleri altında farklı yüzey dinamiklerine sebep olduğu, bu farkın kritik basma gerilmesi (σ>100 MPa) üzerindeki basma gerilmesi durumunda çatlak benzeri yapıların oluşmasına neden olduğu gösterilmiştir. Çekme gerilmesine maruz kalan yüzeydeki dalgalı yapının sönümlendiği gözlemlenmiştir. Çatlak yapıların oluşumu sonrası yüzey kinetiği doğrusal kararlılık analizlerinden uzaklaşmaktadır. Uygulanan gerilmeye göre 3 farklı davranış saptanmıştır. Bunlar; sönümlenmenin gerçekleştiği (Ξ >0) çekme kuvveti uygulanan bölge, düşük basma kuvveti (-1,12>Ξ > 0) uygulanan yüzeyin karalı olduğu bölge ve çatlak benzeri oluşumların gözlemlendiği yüksek basma gerilmesinin (Ξ<-1,12) uygulandığı bölgedir. Yapılan simülasyonlarda, çatlak oluşumu sürecinde, çatlak bölgeden difüzyon ile kaçan maddenin tepelerde birikerek yeni tepeler oluşturduğu gözlemlenmiştir. 

Anahtar Kelimeler

İnce film, Difüzyon, Elastik etkileşimler, Uyumsuzluk gerilmesi

Destekleyen Kurum

TUBITAK

Proje Numarası

107M011

Teşekkür

Bu çalışma TUBİTAK tarafından 107M011 nolu proje dahilinde desteklenmiştir.

Linear Instability and Numerical Analysis of Surface Morphology Changes of Epitaxially Strained Thin Films Due to Elastic Interactions

Öz

In this systematic simulation study, thin-film surface stability has been investigated with consideration of elastic dipole interactions under compression and tension. In this model, the effect of stress on surface diffusion is introduced by first and second-order parameters. Preexistent sinusoidal wave formed surface of the thin films is assumed and decay or growth of this form due to the diffusion is investigated with the combined effect of capillary, stress, and elastic dipole interactions. It has been shown that elastic dipole interactions cause the different surface dynamics under the compression and the tension, and this difference caused crack like formations on the surface over critical compression stress (σ>100 MPa). On the other hand, wave-formed thin film surface decays with tensile stress. Three different regions were observed according to the applied stress; the area where decaying has occurred (Ξ >0) under tensile load, the region the surface is stable where the low compression force (-1,12>Ξ > 0) is applied, and the high compressive stress (Ξ<-1,12), where crack-like formations are observed. After the crack formation, surface kinetics deviates from the linear instability analysis. During the crack formation, mass flow due to the diffusion results in creating new crests at the surface or filling in the trough. 

Anahtar Kelimeler

Thin films, Difüzyon, Elastic interactions, Misfit stress

Proje Numarası

107M011

Kaynakça

• Agarwal, R., Trinkle, D.R. (2016). Light-element diffusion in Mg using first-principles calculations: Anisotropy and elastodiffusion. Physical Review B, 94, 054106. DOI:10.1103/PhysRevB.94.054106
• Balluffi, R.W., Allen, S.M., Carter, W.C. (2005). Kinetics of Materials, John Wiley & Sons, Inc., ISBN: 0471246891, Hoboken, New Jersey.
• Barvosa-Carter, W., Aziz, M.J., Gray, L.J., Kaplan, T. (1998). Kinetically driven growth instability in stressed solids. Physical Review Letters, 81, 1445. DOI:10.1103/PhysRevLett.81.1445
• Brebbia, C.A., Dominguez, J. (1994). Boundary Elements: An Introductory Course, WIT Press., ISBN: 1853123498, Southhampton.
• Çelik, A. (2011). Investigation of Electromigration and Stress Induced Surface Dynamics on The Interconnect by Computer Simulation. Ph.D. Thesis, Middle East Technical University, Ankara, Turkey.
• Chen, Y., Billia, B., Li, D.Z., Nguyen-Thi, H., Xiao, N.M., Bogno, A. (2014). Tip-splitting instability and transition to seaweed growth during alloy solidification in anisotropically preferred growth direction. Acta Materialia, 66, 219–231. DOI:10.1016/j.actamat.2013.11.069
• Chuang, T., Fuller, Jr. E.R. (1992). Extended Charles–Hillig theory for stress corrosion cracking of glass. Journal of the American Ceramic Society, 75(3), 540–545. DOI:10.1111/j.1151-2916.1992.tb07839.x
• Clouet, E., Varvenne, C., Jourdan, T. (2018). Elastic modeling of point-defects and their interaction. Computational Materials Science, 147, 49-63. DOI:10.1016/j.commatsci.2018.01.053
• Connétable, D., Maugis, P. (2020). Effect of stress on vacancy formation and diffusion in fcc systems: Comparison between DFT calculations and elasticity theory. Acta Materialia, 200, 869–882. DOI:10.1016/j.actamat.2020.09.053
• Dudarev, S.L., Sutton, A.P. (2017). Elastic interactions between nano-scale defects in irradiated materials. Acta Materialia, 125, 425-430. DOI:10.1016/j.actamat.2016.11.060
• Ogurtani, T.O., Çelik, A., Ören E.E. (2014). Stranski-Krastanow islanding initiated on the stochastic rough surfaces of the epitaxially strained thin films. Journal of Applied Physics, 115, 224307. DOI:10.1063/1.4883295
• Guin, L., Jabbour, M.E., Triantafyllidis, N. (2021a). Revisiting step instabilities on crystal surfaces. Part I: The quasistatic approximation. Journal of the Mechanics and Physics of Solids, 156, 104574. DOI:10.1016/j.jmps.2021.104574
• Guin, L., Jabbour, M.E., Shaabani-Ardali, L., Triantafyllidis, N. (2021b). Revisiting step instabilities on crystal surfaces. Part II: General theory. Journal of the Mechanics and Physics of Solids, 156, 104582. DOI: 10.1016/j.jmps.2021.104582
• Jesson, D.E., Chen, K.M., Pennycook, S.J., Thundat, T., Warmack R.J. (1995). Crack-like sources of dislocation nucleation and multiplication in thin films. Science, 268, 1161-1663. DOI:10.1126/science.268.5214.1161
• Kostyrko, S.A., Shuvalov, G.M. (2015). Morphological stability of multilayer film surface during diffusion processes, International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP), 5-9 October 2015, Russia, Saint-Petersburg, DOI:10.1109/SCP.2015.7342172. Krishnamurty, R., Srolovitz, D.J. (2006). Film/substrate interface stability in thin films. Journal of Applied Physics, 99, 043504. DOI: 10.1063/1.2173047
• Kukta, R.V., Peralta, A., Kouris, D. (2002). Elastic interaction of surface steps: effect of atomic-scale roughness. Physical Review Letters, 88(18), 186102. DOI:10.1103/PhysRevLett.88.186102
• Kukta, R.V., Kouris, D., Sieradzki, K. (2003). Adatoms and their relation to surface stress. Journal of the Mechanics and Physics of Solids, 51, 1243-1266. DOI:10.1016/S0022-5096(03)00024-3
• Lu, G.Q., Nygren, E., Aziz, M.J. (1991). Pressure‐enhanced crystallization kinetics of amorphous Si and Ge: Implications for point‐defect mechanisms. Journal of Applied Physics, 70, 5323. DOI:10.1063/1.350243
• Maroutian, T., Douillard, L., Ernst, H.J. (2001). Morphological instability of Cu vicinal surfaces during step-flow growth. Physical Review B, 83, 165401. DOI:10.1103/PhysRevB.64.165401
• Muller, P., Saul, A. (2004). Elastic effects on surface physics. Surface Science Reports, 54, 157-258. DOI:10.1016/j.surfrep.2004.05.001
• Ogurtani, T.O. (2006). Unified theory of linear instability of anisotropic surfaces and interfaces under capillary, electrostatic, and elastostatic forces: The regrowth of epitaxial amorphous silicon. Physical Review B, 74, 155422. DOI:10.1103/PhysRevB.74.155422
• Ogurtani, T.O., Celik, A., Oren, E.E. (2010). Generic role of the anisotropic surface free energy on the morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate. Journal of Applied Physics, 108(10), 103516. DOI:10.1063/1.3512970
• Polop, C., Hansen, H., Busse, C., Michely, T. (2003). Relevance of nonlocal adatom-adatom interactions in homoepitaxial growth. Physical Review B, 193405. DOI:10.1103/PhysRevB.67.193405
• Ramachandramoorthy, R., Wang, Y., Agheai, A., Richter, G., Cai, W., Espinosa, E.H. (2017). Reliability of single crystal silver nanowire-based systems: stress assisted instabilities. ACS nano, 11(5), 4768-4776. DOI: 10.1021/acsnano.7b01075
• Rice, J.R., Chuang, T.J. (1981). Energy variations in diffusive cavity growth. Journal of the American Ceramic Society vol. 64 (1) pp. 46-53. DOI: 10.1111/j.1151-2916.1981.tb09557.x
• Srolovitz, D. (1989). On the stability of surfaces of stressed solids. Acta Metallurgica, 37(2), 621-625. DOI:10.1016/0001-6160(89)90246-0
• Sun, B., Suo, Z., Evans, A.G. (1994). Emergence of cracks by mass transport in elastic crystals stressed at high temperatures. Journal of the Mechanics and Physics of Solids, 42(11), 1653-1677. DOI:10.1016/0022-5096(94)90066-3
• Suo, Z. (2000). Evolving material structures of small feature sizes. International Journal of Solids and Structures, 37, 367-378. DOI: 10.1016/S0020-7683(99)00100-6
• Tomar, V., Gungor, M.R., Maroudas, D. (2008). Theoretical analysis of texture effects on the surface morphological stability of metallic thin films. Applied Physics Letters, 92, 181905. DOI: 10.1063/1.2912037
• Tomar, V., Gungor, M.R., Maroudas, D. (2009). Rippling instability on surfaces of stressed crystalline conductors. Applied Physics Letters, 94, 181911. DOI:10.1063/1.3130742
• Varvenne, C., Clouet, E. (2017). Elastic dipoles of point defects from atomistic simulations. Physical Review B, 96, 224103. DOI:10.1103/PhysRevB.96.224103
• Xie, Y.H., Gilmer, G.H., Roland, C., Silverman, P.J., Buratto, S.K., Cheng, J.Y., Fitzgerald, E.A., Kortan, A.R., Schuppler, S., Marcus, M.A., Citrin, P.H. (1994). Semiconductor surface roughness: dependence on sign and magnitude of bulk strain. Physical Review Letters, 73, 3006. DOI:10.1103/PhysRevLett.73.3006
• Zhou, W., Li, W. (2019). Instability of Epitaxially Strained Thin Films Based on Nonlocal Elasticity. Chinese Physical Letters, 36(1), 016801. DOI:10.1088/0256-307X/36/1/0168