Scaling properties of equilibrating semiconductor mounds of various initial shapes

Tüzemen, A. Türker; Esen, Mehmet; Özdemir, M.

doi:10.1016/j.jcrysgro.2017.04.022

Cited by 4 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of this, the scaling characteristics obtained in equations ( 13) and ( 15) are the same with found out ones in Ref. [12] as expected. While the slope of the 𝑙𝑜𝑔(ℎ(0) − ℎ(𝜏)) − 𝑙𝑜𝑔(𝜏) curves belonging to the studied sinusoidal surfaces was found as 𝛼 ≈ 0.36 in Ref.…”

Section: Resultssupporting

confidence: 87%

“…While the slope of the 𝑙𝑜𝑔(ℎ(0) − ℎ(𝜏)) − 𝑙𝑜𝑔(𝜏) curves belonging to the studied sinusoidal surfaces was found as 𝛼 ≈ 0.36 in Ref. [12], it was found as 𝛼 ≈ 0.35 for the sinusoidal surfaces studied here. The 𝛼 values are close to each other due to the surface similarity.…”

Section: Resultsmentioning

confidence: 56%

“…In this part of the investigation, we acquired the same scaling behaviors and the 𝛼 values for 𝑔 = 10 −5 , 10 −4 and 10 −3 values under the same initial surface conditions. In our old study [12], we have examined a sinusoidal initial surface similar to the one studied here. Because of this, the scaling characteristics obtained in equations ( 13) and ( 15) are the same with found out ones in Ref.…”

Section: Resultsmentioning

confidence: 99%

“…Esen et al [11] put forth a study about the equilibration of a conic shaped surface using the Kinetic Monte Carlo method. In Diffusion Limited (DL) regime, the different shaped surfaces owned circular monoatomic steps have been examined by Tüzemen et al [12]. They have assumed that there were only repulsive interactions between the steps.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analyzing of the Evolution and the Scaling Properties of a Sinusoidal Mound

Tüzemen

2023

Cumhuriyet Science Journal

View full text Add to dashboard Cite

The evolution of an initial surface (below its roughening temperature) bounded by a sinusoidal function and consisting of concentric circular steps in two dimensions has been investigated in the Diffusion Limited (DL) regime. Assuming that there were entropic interactions between steps and the local mass transfer took place due to the surface diffusion, the solution of the diffusion equation has been obtained by using polar coordinates in two dimensions. The results obtained in this investigation with analyzing the surface height’s evolution as a function of time are as follows: The surface’s height approximately decreases as τ^α (α≈0.35) and α is independent of the amplitude and the wavelength of the initial surface. The variations in the heights of the surfaces which have different amplitudes (A_01,A_02 ) and wavelengths (λ_1,λ_2 ) scale as (A_01⁄A_02 ) (λ_1⁄λ_2 )^3.

show abstract

Section: Resultssupporting

confidence: 87%

Section: Resultsmentioning

confidence: 56%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analyzing of the Evolution and the Scaling Properties of a Sinusoidal Mound

Tüzemen

2023

Cumhuriyet Science Journal

View full text Add to dashboard Cite

show abstract

“…These equations are obtained in Ref. [24] by taking into account repulsive interaction between steps only. In this study, besides repulsive step-step interaction of the form [5,25,26] it is suggested an attractive interaction expression.…”

Section: Theorymentioning

confidence: 99%

İtici ve Çekici Etkileşimlerin Basamaklı Yüzeyler Üzerinde Oluşan Basamak Gruplaşmaları Üzerindeki Etkileri

Tüzemen¹

2018

Cumhuriyet Science Journal

View full text Add to dashboard Cite

A surface which consists concentric circular monoatomic steps in two dimensions and below its roughening temperature is discussed. Repulsive and attractive interactions between steps on the surface are considered. It is supposed that repulsive and attractive interactions vary as −2 and −1 respectively. Here indicates the terrace width between monoatomic steps. The solution of diffusion equation is achieved in twodimension by using polar coordinates. While the initial surface evolves, it is supposed that the local mass transfer exists because of the surface diffusion only under the step-flow model. In the study initial surfaces bounded by envelope functions which have the form of are dealt. In the case of only repulsive interaction between steps surfaces evolve properly. When both repulsive and attractive interactions between steps are accepted step bunchings separated by large flat terraces occur on the surface. While the surface morphology and the evolution of the height of surface in time are investigated for all surface structures in Diffusion-Limited (DL) regime, a parameter space of bunching and no bunching regions is derived.Özet. İki boyutta eş merkezli dairesel monoatomik basamaklardan oluşan pürüzlülük sıcaklığı altında olan bir yüzey tartışılmıştır. Yüzey üzerindeki basamaklar arasında çekici ve itici etkileşimlerin olduğu varsayılmıştır. Çekici ve itici etkileşimlerin sırasıyla −2 ve −1 şeklinde değiştikleri düşünülmüştür. Buradaki monoatomik basamaklar arasındaki teras genişliğini göstermektedir. Difüzyon denkleminin çözümü kutupsal koordinatlar kullanılarak iki boyutta elde edilmiştir. İlk yüzey gelişirken, yerel kütle transferinin sadece yüzey difüzyonu nedeniyle basamak akış modeli altında gerçekleştiği farz edilmiştir. Çalışma içerisinde biçimine sahip zarf fonksiyonları ile sınırlandırılan ilk yüzeyler ele alınmıştır. Basamaklar arasında sadece çekici etkileşimin olduğu durumda yüzeyler düzgün şekilde gelişmiştir. Basamaklar arasında çekici ve itici etkileşimlerin her ikisinin olduğu kabul edildiği zaman yüzey üzerinde geniş düz teraslarla ayrılan basamak gruplaşmaları oluşmuştur. Difüzyon sınırlı düzende (DL) bütün yüzey yapıları için, zaman içerisindeki yüzey morfolojisi ve yüzey yükseklik gelişimi incelenirken, basamak gruplaşmasının olduğu ve basamak gruplaşmasının olmadığı bölgelere ait bir parametre uzayı elde edilmiştir.Anahtar Kelimeler: Yüzey morfolojisi, difüzyon, çekici ve itici etkileşimler, basamak, gruplaşma.

show abstract