Evolution of the free energy of the GaN(0001) surface based on first-principles phonon calculations

Kempisty, Paweł; Kangawa, Yoshihiro

doi:10.1103/physrevb.100.085304

Cited by 39 publications

(35 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( 14 )), the step–step attraction is the origin of the discontinuous surface tension. The surface energy corresponds to the surface free -energy, which includes entropy originating from lattice vibrations and distortions 70 . and may soften due to lattice vibrations as the temperature increases.…”

Section: Methodsmentioning

confidence: 99%

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Akutsu

2021

Sci Rep

View full text Add to dashboard Cite

To clarify whether a surface can be rough with faceted macrosteps that maintain their shape on the surface, crystal surface roughness is studied by a Monte Carlo method for a nucleation-limited crystal-growth process. As a surface model, the restricted solid-on-solid (RSOS) model with point-contact-type step–step attraction (p-RSOS model) is adopted. At equilibrium and at sufficiently low temperatures, the vicinal surface of the p-RSOS model consists of faceted macrosteps with (111) side surfaces and smooth terraces with (001) surfaces (the step-faceting zone). We found that a surface with faceted macrosteps has an approximately self-affine-rough structure on a ‘faceted-rough surface’; the surface width is strongly divergent at the step-disassembling point, which is a characteristic driving force for crystal growth. A ‘faceted-rough surface’ is realized in the region between the step-disassembling point and a crossover point where the single nucleation growth changes to poly-nucleation growth.

show abstract

Section: Methodsmentioning

confidence: 99%

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Akutsu

2021

Sci Rep

View full text Add to dashboard Cite

show abstract

“…For first-principles quantum mechanical calculations, or corresponds to the surface free energy, which includes the entropy originating from lattice vibrations and distortions 65 . Hence, or decreases slightly as the temperature increases.…”

Section: Model and Calculationsmentioning

confidence: 99%

Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession

Akutsu

2020

Sci Rep

View full text Add to dashboard Cite

the crossover from a Berezinskii-Kosterlitz-thouless (BKt) rough surface to a Kardar-parisi-Zhang (KpZ) rough surface on a vicinal surface is studied using the Monte carlo method in the non-equilibrium steady state in order to address discrepancies between theoretical results and experiments. the model used is a restricted solid-on-solid model with a discrete Hamiltonian without surface or volume diffusion (interface limited growth/recession). The temperature, driving force for growth, system size, and surface slope dependences of the surface width are calculated for vicinal surfaces tilted between the (001) and (111) surfaces. The surface velocity, kinetic coefficient of the surface, and mean height of the locally merged steps are also calculated. In contrast to the accepted theory for (2 + 1) surfaces, we found that the crossover point from a BKT (logarithmic) rough surface to a KPZ (algebraic) rough surface is different from the kinetic roughening point for the (001) surface. the driving force for crystal growth was found to be a relevant parameter for determining whether the system is in the BKT class or the KPZ class. It was also determined that ad-atoms, ad-holes, islands, and negative-islands block surface fluctuations, which contributes to making a BKT-rough surface.

show abstract

“…where c A (c B ) is the concentration of A atoms (B atoms) and c A0 (c B0 ) is their concentration under the condition in Equation (12). The bulk chemical potentials and the surface energies for the flat (001) surface should be calculated using the first-principles DFT method [45][46][47][48][49][50]. However, the surface model expressed by the Hamiltonian in Equation (7) is slightly more coarse-grained compared to the surface structure considered in the first-principles DFT calculations.…”

Section: Surface Hamiltonianmentioning

confidence: 99%

“…Hence, µ A,crys (µ B,crys ) ≈ z with z = 6, where z is the number of nearest-neighbor sites in the bulk crystal, E A,surf ≈ E B,surf ≈ . According to a recent study by Kempisty et al [50], the surface free energy decreases as the temperature increases due to the entropy caused by distortions or vibrations. Hence, , P A0 , P B0 , c A0 , and c B0 depend on temperature.…”

Section: Surface Hamiltonianmentioning

confidence: 99%

“…The basic quantity of the st-RSOS model is the microscopic ledge energy and the bulk chemical potentials of the ambient and crystal phases, namely µ ambient and µ crys , respectively. The st-RSOS model is a slightly more coarse-grained model compared to the atomic model for the first-principles density functional theory (DFT) method [45][46][47][48][49][50]. An "atom" in the st-RSOS model is about a half-unit cell in the DFT model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Surface Roughness Changes Induced by Stoichiometric Deviation in Ambient Phase for Two-Component Semiconductor Crystals

2020

View full text Add to dashboard Cite

The effects of a deviation in the fraction of the components in the ambient phase of a stoichiometric AB compound, such as GaN or SiC crystals, on the surface roughness and step self-assembly and disassembly on a vicinal surface are studied using the Monte Carlo method based on a staggered restricted solid-on-solid (st-RSOS) model at equilibrium. The (001) and (111) surfaces are typical examples of non-polar and polar surfaces, respectively. Although a stoichiometric deviation of the ambient phase does not affect the surface energy of a non-polar surface, it affects that of polar surfaces such as the (111) A and (111) B surfaces. We found that the vicinal surface of an AB compound is atomically smooth and globally rough. Globally, the vicinal surface is not affected by a stoichiometric deviation in the ambient phase. In contrast, in a small area, the structure of the vicinal surface is affected by a stoichiometric deviation in the ambient phase. The vicinal surface consists of local double and quadruple steps. The characteristic length L MFL , which separates the global length scale region and the local length scale region, has a maximum value of 156a in the present study, where a is the lattice constant. When temperature decreases, L MFL can become large.

show abstract

Evolution of the free energy of the GaN(0001) surface based on first-principles phonon calculations

Cited by 39 publications

References 50 publications

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession

Surface Roughness Changes Induced by Stoichiometric Deviation in Ambient Phase for Two-Component Semiconductor Crystals

Contact Info

Product

Resources

About