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1.
Phys Chem Chem Phys ; 25(1): 796-805, 2022 Dec 21.
Artigo em Inglês | MEDLINE | ID: mdl-36510741

RESUMO

Coexistence of intrinsic ferromagnetism and piezoelectricity, namely piezoelectric ferromagnetism (PFM), is crucial to advance multifunctional spintronic technologies. In this work, we demonstrate that Janus monolayer YBrI is a PFM, which is dynamically, mechanically and thermally stable. The electronic correlation effects on the physical properties of YBrI are investigated by using generalized gradient approximation plus U (GGA+U) approach. For out-of-plane magnetic anisotropy, YBrI is a ferrovalley (FV) material, and its valley splitting is larger than 82 meV within the considered U range. The anomalous valley Hall effect (AVHE) can be achieved under an in-plane electric field. However, for in-plane magnetic anisotropy, YBrI is a common ferromagnetic (FM) semiconductor. When considering intrinsic magnetic anisotropy, the easy axis of YBrI is always in-plane, and its magnetic anisotropy energy (MAE) varies from 0.309 meV to 0.237 meV (U = 0.0 eV to 3.0 eV). However, the magnetization can be adjusted from the in-plane to out-of-plane direction by an external magnetic field, and then lead to the occurrence of valley polarization. Moreover, the missing centrosymmetry along with broken mirror symmetry results in both in-plane and out-of-plane piezoelectricity in the YBrI monolayer. At a typical U = 2.0 eV, the piezoelectric strain coefficient d11 is predicted to be -5.61 pm V-1, which is higher than or comparable with the ones of other known two-dimensional (2D) materials. The electronic and piezoelectric properties of YBrI can be effectively tuned by applying biaxial strain. For example, tensile strain can enhance valley splitting and d11 (absolute value). The predicted magnetic transition temperature of YBrI is higher than those of experimentally synthesized 2D FM materials CrI3 and Cr2Ge2Te6. Our findings of these distinctive properties could pave the way for designing multifunctional spintronic devices, and bring forward a new perspective for constructing 2D materials.

2.
Phys Chem Chem Phys ; 24(33): 19965-19974, 2022 Aug 24.
Artigo em Inglês | MEDLINE | ID: mdl-35971867

RESUMO

The combination of piezoelectricity with a nontrivial topological insulating phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall insulators (PQSHI), is intriguing for exploring novel topological states toward the development of high-speed and dissipationless electronic devices. In this work, we predict a PQSHI Janus monolayer VCClBr constructed from VCCl2, which is dynamically, mechanically and thermally stable. In the absence of spin orbital coupling (SOC), VCClBr is a narrow gap semiconductor with a gap value of 57 meV, which is different from Dirac semimetal VCCl2. The gap of VCClBr is due to a built-in electric field caused by asymmetrical upper and lower atomic layers, which is further confirmed by the external-electric-field induced gap in VCCl2. When including SOC, the gap of VCClBr is increased to 76 meV, which is larger than the thermal energy of room temperature (25 meV). The VCClBr is a 2D topological insulator (TI), which is confirmed by Z2 topological invariant and nontrivial one-dimensional edge states. It is proved that the nontrivial topological properties of VCClBr are robust against strain (biaxial and uniaxial cases) and external electric fields. Due to broken horizontal mirror symmetry, only an out-of-plane piezoelectric response can be observed, when a biaxial or uniaxial in-plane strain is applied. The predicted piezoelectric strain coefficients d31 and d32 are -0.425 pm V-1 and -0.219 pm V-1, respectively, and they are higher than or compared with those of many 2D materials. Finally, Janus monolayer VCFBr and VCFCl (dynamically unstable) are also constructed, and they are still PQSHIs. Moreover, the d31 and d32 of VCFBr and VCFCl are higher than those of VCClBr, and the d31 (absolute value) of VCFBr is larger than one. According to out-of-plane piezoelectric coefficients of VCXY (X ≠ Y = F, Cl and Br), CrX1.5Y1.5 (X = F, Cl and Br; Y = I) and NiXY (X ≠ Y = Cl, Br and I), it is concluded that the size of the out-of-plane piezoelectric coefficient has a positive relation with the electronegativity difference of X and Y atoms. Our studies enrich the diversity of Janus 2D materials, and open a new avenue in the search for PQSHI with a large out-of-plane piezoelectric response, which provides a potential platform in nanoelectronics.

3.
Nanotechnology ; 33(45)2022 Aug 23.
Artigo em Inglês | MEDLINE | ID: mdl-35905699

RESUMO

Two-dimensional (2D) semiconducting transition metal dichalcogenides can be used to make high-performance electronic, spintronic, and optoelectronic devices. Recently, room-temperature ferromagnetism and semiconduction in 2D VSe2nanoflakes were attributed to the stable 2H-phase of VSe2in the 2D limit. Here, our first-principles investigation shows that a metastable semiconducting H' phase can be formed from the H VSe2 monolayer through uniaxial stress or uniaxial strain. The calculated phonon spectra indicate the dynamical stability of the metastable H' VSe2and the path of phase switching between the H and H' VSe2phases is calculated. For the uniaxial stress (or strain) scheme, the H' phase can become lower in total energy than the H phase at a transition point. The H' phase has stronger ferromagnetism and its Curier temperature can be enhanced by applying uniaxial stress or strain. Applying uniaxial stress or strain can substantially change spin-resolved electronic structures, energy band edges, and effective carrier masses for both of the H and H' phases, and can cause some flat bands near the band edges in the strained H' phase. Further analysis indicates that one of the Se-Se bonds in the H' phase can be shortened by 19% and the related Se-V-Se bond angles are reduced by 23% with respect to those of the H phase, which is believed to increase the Se-Se covalence feature and reduce the valence of the nearby V atoms. Therefore, structural and bond reconstruction can be realized by applying uniaxial stress in such 2D ferromagnetic semiconductors for potential spintronic and optoelectronic applications.

4.
Phys Chem Chem Phys ; 24(2): 715-723, 2022 Jan 04.
Artigo em Inglês | MEDLINE | ID: mdl-34935017

RESUMO

The valley degree of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize valley polarization. Here, we propose a model that the valley polarization transition at different valley points (-K and K points) is produced by biaxial strain. Using first-principles calculations, we illustrate our idea with a concrete example of a Janus GdClF monolayer. The predicted GdClF monolayer is dynamically, mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor with perpendicular magnetic anisotropy (PMA), valence band maximum (VBM) at valley points and a high Curie temperature (TC). Due to its intrinsic ferromagnetism and spin-orbit coupling (SOC), a spontaneous valley polarization will be induced, but the valley splitting is only -3.1 meV, which provides an opportunity to achieve valley polarization transition at different valley points by strain. In the considered strain range (a/a0: 0.94-1.06), the strained GdClF monolayer always has an energy bandgap, strong FM coupling and PMA. The compressive strain is in favour of -K valley polarization, while the tensile strain is favorable for K valley polarization. The corresponding valley splittings at 0.96 and 1.04 strains are -44.5 meV and 29.4 meV, respectively, which are higher than the thermal energy at room temperature (25 meV). Due to its special Janus structure, both in-plane and out-of-plane piezoelectric polarizations can be observed. It is found that the direction of in-plane piezoelectric polarization can be overturned by strain, and the d11 values at 0.96 and 1.04 strains are -1.37 pm V-1 and 2.05 pm V-1, respectively. Our work paves the way to design ferrovalley materials for application in multifunctional valleytronic and piezoelectric devices by strain.

5.
Phys Chem Chem Phys ; 23(45): 25994-26003, 2021 Nov 24.
Artigo em Inglês | MEDLINE | ID: mdl-34783808

RESUMO

To easily synthesize a piezoelectric quantum anomalous Hall insulator (PQAHI), the Janus monolayer Fe2IBr (FeI0.5Br0.5) as a representative PQAHI, is generalized to monolayer FeI1-xBrx (x = 0.25 and 0.75) with α and ß phases. By first-principles calculations, it is proved that monolayer FeI1-xBrx (x = 0.25 and 0.75) are dynamically, mechanically and thermally stable. They are excellent room-temperature PQAHIs with high Curie temperatures, sizable gaps and high Chern number (C = 2). Because the considered crystal structures of α and ß phases possess Mx and My mirror symmetries, the topological properties of monolayer FeI1-xBrx (x = 0.25 and 0.75) are maintained. Namely, if the constructed structures have Mx and My mirror symmetries, the mixing ratio of Br and I atoms can be generalized for other proportions. It is also found that different crystal phases have important effects on the out-of-plane piezoelectric response, and the piezoelectric strain coefficient, d32, of the ß phase is higher than or comparable with those of other known two-dimensional (2D) materials. To further confirm this idea, the physical and chemical properties of monolayer LiFeSe0.75S0.25 with α and ß phases, as a generalization of PQAHI LiFeSe0.5S0.5, is investigated, as it has a similar electronic structure, magnetic and topological properties as LiFeSe0.5S0.5. Our work provides a practical guide to achieve PQAHIs experimentally, and the combination of piezoelectricity, topological and ferromagnetic (FM) orders makes Fe2I2-based monolayers a potential platform for multi-functional spintronics and piezoelectric electronics.

6.
Nanoscale ; 13(30): 12956-12965, 2021 Aug 14.
Artigo em Inglês | MEDLINE | ID: mdl-34477779

RESUMO

A two-dimensional (2D) material with piezoelectricity, topological and ferromagnetic (FM) properties, namely a 2D piezoelectric quantum anomalous hall insulator (PQAHI), may open new opportunities to realize novel physics and applications. Here, by first-principles calculations, a family of 2D Janus monolayer Fe2IX (X = Cl and Br) with dynamic, mechanical, and thermal stabilities is predicted to be a room-temperature PQAHI. In the absence of spin-orbit coupling (SOC), the monolayer Fe2IX (X = Cl and Br) is in a half Dirac semimetal state. When the SOC is included, these monolayers become quantum anomalous Hall (QAH) states with sizable gaps (more than 200 meV) and two chiral edge modes (Chern number C = 2). It is also found that the monolayer Fe2IX (X = Cl and Br) possesses robust QAH states against the biaxial strain. By symmetry analysis, it is found that only an out-of-plane piezoelectric response can be induced by a uniaxial strain in the basal plane. The calculated out-of-plane d31 of Fe2ICl (Fe2IBr) is 0.467 pm V-1 (0.384 pm V-1), which is higher than or comparable with those of other 2D known materials. Meanwhile, using Monte Carlo (MC) simulations, the Curie temperature TC is estimated to be 429/403 K for the monolayer Fe2ICl/Fe2IBr at the FM ground state, which is above room temperature. Finally, the interplay of electronic correlations with nontrivial band topology is studied to confirm the robustness of the QAH state. The combination of piezoelectricity, topological and FM orders makes the monolayer Fe2IX (X = Cl and Br) become a potential platform for multi-functional spintronic applications with a large gap and high TC. Our work provides the possibility to use the piezotronic effect to control QAH effects, and can stimulate further experimental works.

7.
Nanotechnology ; 32(14): 145705, 2021 Apr 02.
Artigo em Inglês | MEDLINE | ID: mdl-33333502

RESUMO

It is highly desirable to search for promising two-dimensional (2D) monolayer materials for obtaining deep insight of 2D materials and developing device applications. We use first-principles method to investigate tetragonal perovskite oxide monolayers as 2D materials, and find three stable freestanding 2D monolayer materials from important perovskite oxides (ABO3), namely SrTiO3, LaAlO3, and KTaO3, denoting them as STO-ML, LAO-ML, and KTO-ML. Such an oxide monolayer consists of one AO and one BO2 atomic layers. Further study shows that the three monolayers are 2D wide-gap semiconducotors, and there is a large electrostatic potential energy difference between the two sides, reflecting a large out-of-plane dipole, in each of the monolayers. We also investigate optical properties of the three monolayer semiconductors and compare them with graphene and MoS2 monolayer. These make a series of 2D monolayer materials, and should be useful in novel electronic and optoelectronic devices considering emerging phenomena in perovskite oxide heterostructures.

8.
RSC Adv ; 10(72): 44088-44095, 2020 Dec 09.
Artigo em Inglês | MEDLINE | ID: mdl-35517182

RESUMO

Strong Rashba effects at semiconductor surfaces and interfaces have attracted great attention for basic scientific exploration and practical applications. Here, we show through first-principles investigation that applying biaxial stress can cause tunable and giant Rashba effects in ultrathin KTaO3 (KTO) (001) films with the most stable surfaces. When increasing the in-plane compressive strain to -5%, the Rashba spin splitting energy reaches E R = 140 meV, corresponding to the Rashba coupling constant α R = 1.3 eV Å. We investigate its strain-dependent crystal structures, energy bands, and related properties, and thereby elucidate the mechanism for the giant Rashba effects. Further calculations show that the giant Rashba spin splitting can remain or be enhanced when capping layer and/or Si substrate are added, and a SrTiO3 capping can make the Rashba spin splitting energy reach the record 190 meV. Furthermore, it is elucidated that strong circular photogalvanic effect can be achieved for spin-polarized photocurrents in the KTO thin films or related heterostructures, which is promising for future spintronic and optoelectronic applications.

9.
Nanotechnology ; 30(19): 195704, 2019 May 10.
Artigo em Inglês | MEDLINE | ID: mdl-30699392

RESUMO

Periodically driven systems can host many interesting phenomena. Two-dimensional Dirac systems irradiated by circularly polarized light are especially attractive thanks to the special absorption and emission of photons near Dirac cones. Here, letting the light travel in the two-dimensional plane, we treat the light-driven Dirac systems by using a unitary transformation, instead of usual Floquet theory, to capture the photon-mediated electronic correlation effects. In this approach, the direct electron-photon interaction terms can be removed and the resulting effective electron-electron interactions can produce important effects. The effective interactions can produce topological band structure in the case of irradiated 2D Dirac fermion system, and can lift the energy degeneracy of the Dirac cones for irradiated graphene. This method can be applied to other light-driven Dirac systems to investigate their photon-mediated electronic effects. These phenomena would be observed with ultraviolet light in some effective two-dimensional Dirac systems of honeycomb long-period superstructures.

10.
Phys Chem Chem Phys ; 20(37): 24257-24262, 2018 Oct 07.
Artigo em Inglês | MEDLINE | ID: mdl-30211411

RESUMO

Since the discovery of a two-dimensional (2D) electron gas at the LaAlO3/SrTiO3 interface, 2D carrier gases at such oxide interfaces and surfaces have attracted great attention because they can host many important phenomena and may produce novel functional devices. Here, we show through first-principles investigations that the surface 2D electron and hole gases in a KTaO3 (KTO) thin film can be tuned by applying biaxial stress. When increasing compressive in-plane strain, the 2D carrier concentrations decrease down to zero and then a new pair of surface 2D electron and hole gases appears in which the carrier types are switched to the opposite ones. Our analysis indicates that this carrier-type switching occurs because the increasing compressive strain reverses the slope of monolayer-resolved electrostatic potential along the [001] direction. We also present strain-dependent carrier concentrations and effective masses, and explore their thickness dependence. It is further shown that the 2D carrier gases and their strain-driven carrier-type switching across the KTO layer still remain true in the presence of overlayers and epitaxial substrates. These phenomena should be useful to design novel functional devices.

11.
Nanotechnology ; 29(32): 325401, 2018 Aug 10.
Artigo em Inglês | MEDLINE | ID: mdl-29790854

RESUMO

Excellent monolayer electrode materials can be used to design high-performance alkali-metal-ion batteries. Here, we propose two-dimensional ReN2 monolayers as superior sodium-ion battery materials. Our total energy optimization results in a buckled tetragonal structure for the ReN2 monolayer, and our phonon spectrum and elastic moduli prove that it is dynamically and mechanically stable. Further investigations show that it is metallic and still keeps its metallic feature after the adsorption of Na or K atoms, and the adsorption of Na (or K) atoms changes the lattice parameters by 3.2% (or 3.8%) at most. Its maximum capacity reaches 751 mA h g-1 for Na-ion batteries or 250 mA h g-1 for K-ion batteries, and the diffusion barrier is only 0.027 eV for the Na atom or 0.127 eV for the K atom. The small lattice changes, high storage capacity, metallic feature, and extremely low ion diffusion barriers make the ReN2 monolayers a superior electrode material for Na-ion rechargeable batteries with ultrafast charging/discharging processes.

12.
Nanoscale ; 10(13): 5990-5996, 2018 Mar 29.
Artigo em Inglês | MEDLINE | ID: mdl-29542759

RESUMO

We propose through first-principles investigation that the GaTeCl monolayer is an excellent two-dimensional (2D) multiferroic with giant mechanical anisotropy. The calculated phonon spectrum, molecular dynamic simulations, and elastic moduli confirm its dynamic and mechanical stability, and our cleavage energy analysis shows that exfoliating one GaTeCl monolayer from the existing GaTeCl bulk is feasible. The calculated in-plane ferroelectric polarization reaches 578 pC m-1. The energy barriers per formula unit of the ferroelastic 90° rotational and ferroelectric reversal transitions are 476 meV and 754 meV, respectively, being the greatest in the 2D multiferroics family so far. Importantly, on the other hand, a tensile stress of 4.7 N m-1 perpendicular to the polarization can drive the polarization to rotate by 90°. These can make the GaTeCl monolayer have not only robust ferroelasticity and ferroelectricity but also easy mechanical controllability. Furthermore, the GaTeCl monolayer has giant piezoelectricity and optical second harmonic generation, especially in the range of visible light, and a tensile stress of 0.3 N m-1 along the polarization can make the indirect gap transit to the direct gap. These interesting mechanical, electronic, and optical properties of the GaTeCl monolayer show its great potential in high-performance multi-functional applications.

13.
J Phys Condens Matter ; 30(10): 105701, 2018 03 14.
Artigo em Inglês | MEDLINE | ID: mdl-29376833

RESUMO

Topological semimetals may have potential applications such as in topological qubits, spintronics and quantum computations. Efficient heat dissipation is a key factor for the reliability and stability of topological semimetal-based nano-electronics devices, which is closely related to high thermal conductivity. In this work, the elastic properties and lattice thermal conductivity of TaN are investigated using first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation. According to the calculated bulk modulus, shear modulus and C 44, TaN can be regarded as a potential incompressible and hard material. The room-temperature lattice thermal conductivity is predicted to be 838.62 [Formula: see text] along the a axis and 1080.40 [Formula: see text] along the c axis, showing very strong anisotropy. It is found that the lattice thermal conductivity of TaN is several tens of times higher than other topological semimetals, such as TaAs, MoP and ZrTe, which is due to the very longer phonon lifetimes for TaN than other topological semimetals. The very different atomic masses of Ta and N atoms lead to a very large acoustic-optical band gap, and then prohibit the scattering between acoustic and optical phonon modes, which gives rise to very long phonon lifetimes. Calculated results show that isotope scattering has little effect on lattice thermal conductivity, and that phonons with mean free paths larger than 20 (80) [Formula: see text] along the c direction at 300 K have little contribution to the total lattice thermal conductivity. This work implies that TaN-based nano-electronics devices may be more stable and reliable due to efficient heat dissipation, and motivates further experimental works to study lattice thermal conductivity of TaN.

14.
Phys Chem Chem Phys ; 19(21): 13432-13437, 2017 May 31.
Artigo em Inglês | MEDLINE | ID: mdl-28534567

RESUMO

The electronic, magnetic, and topological properties of a CoBr2 monolayer are studied in the framework of density-functional theory (DFT) combined with tight-binding (TB) modeling in terms of the Wannier basis. Our DFT investigation and Monte Carlo simulation show that there exists intrinsic two-dimensional ferromagnetism in the CoBr2 monolayer, thanks to the large out-of-plane magnetocrystalline anisotropic energy. Our further study indicates that the spin-orbit coupling makes it become a topologically nontrivial insulator with a quantum anomalous Hall effect and topological Chern number [script C] = 4 and its edge states can be manipulated by changing the width of its nanoribbons and applying strains. The CoBr2 monolayer can be exfoliated from the layered CoBr2 bulk material because its exfoliation energy is between those of graphene and the MoS2 monolayer and it is dynamically stable. These results make us believe that the CoBr2 monolayer can make a promising spintronic material for future high-performance devices.

15.
J Phys Condens Matter ; 24(4): 045502, 2012 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-22214598

RESUMO

We investigate the electronic structures of the ferromagnetic semiconductor HgCr(2)Se(4) by using a modified Becke and Johnson exchange potential. The energy gap calculated with the experimental lattice structure is in good agreement with the experimental value. When the pressure reaches 9.0 GPa, HgCr(2)Se(4) becomes a so-called spin gapless semiconductor due to the closure of the spin non-conservation energy gap, and when the pressure increases to 11.4 GPa, the spin conservation energy gap closes, leading to a semiconductor-semimetal transition.

16.
J Phys Condens Matter ; 21(11): 115701, 2009 Mar 18.
Artigo em Inglês | MEDLINE | ID: mdl-21693924

RESUMO

We use the state-of-the-art density-functional-theory method to study various magnetic orders and their effects on the electronic structures of FeSe. Our calculated results show that, for the spins of the single Fe layer, the striped antiferromagnetic orders with distortion are more favorable in total energy than the checkerboard antiferromagnetic orders with tetragonal symmetry, which is consistent with known experimental data, and the interlayer magnetic interaction is very weak. We investigate the electronic structures and magnetic property of the distorted phases. We also present our calculated spin coupling constants and discuss the reduction of the Fe magnetic moment by quantum many-body effects. These results are useful in understanding the structural, magnetic and electronic properties of FeSe, and may have some helpful implications for other FeAs-based materials.

17.
J Phys Condens Matter ; 21(19): 195701, 2009 May 13.
Artigo em Inglês | MEDLINE | ID: mdl-21825495

RESUMO

We use a Green's function method to study the temperature-dependent average moment and magnetic phase-transition temperature of the striped antiferromagnetism of LaFeAsO, and other similar compounds, as the parents of FeAs-based superconductors. We consider the nearest and the next-nearest couplings in the FeAs layer, and the nearest coupling for inter-layer spin interaction. The dependence of the transition temperature T(N) and the zero-temperature average spin on the interaction constants is investigated. We obtain an analytical expression for T(N) and determine our temperature-dependent average spin from zero temperature to T(N) in terms of unified self-consistent equations. For LaFeAsO, we obtain a reasonable estimation of the coupling interactions with the experimental transition temperature T(N) = 138 K. Our results also show that a non-zero antiferromagnetic (AFM) inter-layer coupling is essential for the existence of a non-zero T(N), and the many-body AFM fluctuations reduce substantially the low-temperature magnetic moment per Fe towards the experimental value. Our Green's function approach can be used for other FeAs-based parent compounds and these results should be useful to understand the physical properties of FeAs-based superconductors.

18.
J Phys Condens Matter ; 21(44): 446005, 2009 Nov 04.
Artigo em Inglês | MEDLINE | ID: mdl-21832478

RESUMO

We explore how much the RKKY spin interaction can contribute to the high-temperature ferromagnetism in cubic (Ga, Mn)N diluted magnetic semiconductors. The usual coupling constant is used and effective carriers are considered independent of doped magnetic atoms, as is shown experimentally. Our Monte Carlo simulated results show that maximal Curie temperature is reached at the optimal carrier concentration for a given Mn concentration, equaling 373 K for 5% Mn and 703 K for 8% Mn. Because such a Monte Carlo method does not overestimate transition temperatures, these calculations indicate that the RKKY spin interaction alone can yield high-enough Curie temperatures in cubic (Ga, Mn)N under optimized conditions.

19.
Ultramicroscopy ; 108(9): 816-20, 2008 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-18579308

RESUMO

Strained-silicon p-type metal-oxide-semiconductor field effect transistors (pMOSFETs) have been investigated by large angle convergent-beam electron diffraction (LACBED). Longitudinal compressive strain is induced into the channel region of a p-type strained-silicon channel metal-oxide-semiconductor field effect transistor by a low-cost Ge pre-amorphization implantation for source/drain extension flow. Anomalously large longitudinal compressive strain, up to 2.5 x 10(-2), in the nanometer scale channel region of pMOSFETs has been measured using LACBED. We propose a novel scaling effect for the giant strain enhancement. Our experimental results and model analysis together reveal that the channel strain is inversely proportional to the shrinking channel length.

20.
Phys Rev Lett ; 100(5): 056103, 2008 Feb 08.
Artigo em Inglês | MEDLINE | ID: mdl-18352395

RESUMO

We propose a natural two-speed model for the phase dynamics of Si(111) 7 x 7 phase transition to high-temperature unreconstructed phase. We formulate the phase dynamics by using phase-field method and adaptive mesh refinement. Our simulated results show that a 7 x 7 island decays with its shape kept unchanged, and its area decay rate is shown to be a constant increasing with its initial area. Low-energy electron microscopy experiments concerned are explained, which confirms that the dimer chains and corner holes are broken first in the transition, and then the stacking fault is remedied slowly. This phase-field method is a reliable approach to phase dynamics of surface phase transitions.

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