Valence Force Field Model Research Articles

Size-Dependent Strain Relaxation and Optical Characteristics of InGaN/GaN Nanorod LEDs

In this paper, InGaN/GaN nanorod LEDs with various sizes are fabricated using self-assembled Ni nanomasks and inductively coupled plasma-reactive ion etching. Photoluminescence (PL) characteristics exhibit size-dependent, wavelength blue shifts of the emission spectra from the nanorod LEDs. Numerical analyses using a valence force field model and a self-consistent Poisson, Schrodinger, and drift-diffusion solver quantitatively describe the correlation between the wavelength blue shifts and the strain relaxation of multiple quantum wells embedded in nanorods with different averaged sizes. Time-resolved PL studies confirm that the array with a smaller size exhibits a shorter carrier lifetime at low temperature, giving rise to a stronger PL intensity. However, the PL intensity deteriorates at room temperature, compared to that of a larger size, possibly due to an increased number of surface states, which decreases the nonradiative lifetime, and hence reduces the internal quantum efficiency.

Resonant coherent phonon spectroscopy of single-walled carbon nanotubes

Using femtosecond pump-probe spectroscopy with pulse shaping techniques, one can generate and detect coherent phonons in chirality-specific semiconducting single-walled carbon nanotubes. The signals are resonantly enhanced when the pump photon energy coincides with an interband exciton resonance, and analysis of such data provides a wealth of information on the chirality-dependence of light absorption, phonon generation, and phonon-induced band structure modulations. To explain our experimental results, we have developed a microscopic theory for the generation and detection of coherent phonons in single-walled carbon nanotubes using a tight-binding model for the electronic states and a valence force field model for the phonons. We find that the coherent phonon amplitudes satisfy a driven oscillator equation with the driving term depending on photoexcited carrier density. We compared our theoretical results with experimental results on mod 2 nanotubes and found that our model provides satisfactory overall trends in the relative strengths of the coherent phonon signal both within and between different mod 2 families. We also find that the coherent phonon intensities are considerably weaker in mod 1 nanotubes in comparison with mod~2 nanotubes, which is also in excellent agreement with experiment.

Electronic and optical properties of InGaN quantum dot based light emitters for solid state lighting

In this paper, we have made a systematic study of the electronic and optical properties of InGaN based quantum dot light emitters. The valence force field model and 6×6k⋅p method have been applied to study the band structures in InGaN or InN quantum dot devices. Piezoelectric and spontaneous polarization effects are included. A comparison with InGaN quantum wells shows that InGaN quantum dots can provide better electron-hole overlap and reduce radiative lifetime. We also find that variation in dot sizes can lead to emission spectrum that can cover the whole visible light range. For high carrier density injection conditions, a self-consistent method for solving quantum dot devices is applied for better estimation of device performance. Consequences of variations in dot sizes, shapes, and composition have been studied in this paper. The results suggest that InGaN quantum dots would have superior performance in white light emitters.

Calculations of the structural and thermodynamic characteristics of copper carbonates by quantum-chemical methods

The possibility of using the PM5 semiempirical method and the LADY program for calculations of the vibrational properties and thermodynamic characteristics of copper carbonates, malachite and azurite, was considered. The infrared and Raman spectra of these minerals were calculated using the valence force field model of the theory of crystal lattice dynamics with varying force constants. The results closely agreed with the calorimetric and spectroscopic experimental data.

Strain relaxation and band-gap tunability in ternaryInxGa1−xNnanowires

The alloy formation enthalpy and band structure of InGaN nanowires were studied by a combined approach of the valence-force field model, Monte Carlo simulation, and density-functional theory (DFT). For both random and ground-state structures of the coherent InGaN alloy, the nanowire configuration was found to be more favorable for the strain relaxation than the bulk alloy. We proposed an analytical formula for computing the band gap of any InGaN nanowires based on the results from the screened exchange hybrid DFT calculations, which in turn reveals a better band-gap tunability in ternary InGaN nanowires than the bulk alloy.

Modeling the compositional dependence of electron diffraction in dilute GaAs- and GaP-based compound semiconductors

The change in the intensity of the (200) electron-beam reflection induced by the incorporation of isovalent impurities in GaAs and GaP is studied theoretically. Calculations are performed in the framework of the kinematical scattering theory. The structure factor of random alloys was obtained using atomic form factors calculated with the density-functional theory and an empirical-potential valence force-field model for the structure relaxation. The calculations include the effect of redistribution of the electron density on the electron-scattering amplitudes as well as the effect of the local lattice distortions associated with the impurity sites. We propose a way to calculate these distortions analytically and to introduce them in a simple form to the expression for the structure factor. This method is an alternative to the simulations, which invoke demanding computations for atomic relaxation, and enables quantitative prediction of the compositional variation of the structure factor for dilute alloys taking into account static atomic displacements. The implications of the results for quantification of composition fluctuations in heterostructures using dark-field transmission electron microscopy are discussed. The effect of nitrogen and boron incorporation on the intensity of the (200) reflection is found to be partly compensated by the static atomic displacements they cause. Neglecting this effect would lead to an underestimation of the impurity content by approximately a factor of two. The redistribution of the electron density is found to be less crucial for the evaluation of the chemical composition leading to a relative error in the (200) scattering amplitude of about 16%.

Size effect of thermal conductivity of Si nanocrystals

Thermal conductivities of spherical Si nanocrystals (NCs) are investigated with three different models: a macroscopic approximation, a semi-microscopic model that calculates the heat capacity of NCs with a microscopic Valence–Force–Field Model (VFFM), and a full microscopic description of phonon thermal conduction that calculate both heat capacity and phonon group velocity by the VFFM. The results are compared, and the advantages and limitations of each of these models are discussed. It is shown that for spherical Si NCs, the macroscopic approximation is quite good for NCs with a diameter larger than 1.33 nm. For smaller NCs, the VFFM predicts that the thermal conductivity increases quickly when the size decreases, opposite to the macroscopic approximation, and VFFM also predicts that the minimum of thermal conductivity for spherical Si NCs occurs at a diameter of 1.33 nm, the limit at which the macroscopic approximation applies.

Rashba spin splitting of the minibands of coupled InAs∕GaAs pyramid quantum dots

The Rashba spin splitting of the minibands of coupled InAs∕GaAs pyramid quantum dots is investigated using the k⋅p method and valence force field model. The Rashba splitting of the two dimensional miniband in the lateral directions is found due to the structure inversion asymmetry in the vertical direction while the miniband in the vertical direction has no Rashba spin splitting. As the space between dots increases, the Rashba coefficients decrease and the conduction-band effective mass increases. This Rashba spin splitting of the minibands will significantly affect the spin transport properties between quantum dots.

Formation Mechanism and Properties of CdS-Ag2S Nanorod Superlattices

The mechanism of formation of recently fabricated CdS-Ag(2)S nanorod superlattices is considered and their elastic properties are predicted theoretically based on experimental structural data. We consider different possible mechanisms for the spontaneous ordering observed in these 1D nanostructures, such as diffusion-limited growth and ordering due to epitaxial strain. A simplified model suggests that diffusion-limited growth partially contributes to the observed ordering, but cannot account for the full extent of the ordering alone. The elastic properties of bulk Ag(2)S are predicted using a first principles method and are fed into a classical valence force field (VFF) model of the nanostructure. The VFF results show significant repulsion between Ag(2)S segments, strongly suggesting that the interplay between the chemical interface energy and strain due to the lattice mismatch between the two materials drives the spontaneous pattern formation.

Molecular simulation study of the structural properties in InxGa1−xAs alloys: Comparison between Valence Force Field and Tersoff potential models

The thermodynamic and structural properties of compound semiconductor alloys have been generally modelled using either the Valence Force Field model or the Tersoff potential model. This work compares the properties, such as lattice constant and bond length, of the InxGa1−xAs alloy as predicted by Monte Carlo simulations in the semigrand isothermal isobaric ensemble using both the potential models, with experimental data. The lattice constants are expected to follow the Vegard’s law at any given temperature. Valence Force Field model predicts bond length data which follows the experimentally determined values at 300K; whereas the Tersoff model forecasts that the virtual crystal approximation will be followed. The VFF model, with its experimentally determined parameters, is found to be better for modelling the alloy at room temperature. The Tersoff model, with its fitted parameters, on the other hand predicts the effect of temperature on the microscopic structure of the alloy better. The parameters of the Tersoff potential characterizing the In–Ga interactions can be further improved to predict bond lengths more accurately.

Zero m phonons in metal chalcogenide nanotubes

Phonon dispersions of single-wall MoS2 and WS2 nanotubes are calculated within a full symmetry implemented valence force-field model. Tubular structure is found to be characterized by two Raman active modes: by the in-phase breathing modes (in full analogy to carbon nanotubes) with frequency approaching Brillouin scattering domain (as diameter approaches nm), and by the high-energy breathing mode with sulfur shells breathing in phase, but out of phase relative to the Mo/W atoms. Likewise, the longitudinal rigid-shell mode, where sulfur shells vibrate out of phase whilst Mo/W atoms barely move, is predicted to be a fingerprint of the cylindrical configuration in infrared spectra. It is also found that twisting rigid-layer modes characterize chirality of the tubes. Finally, the large diameter limit is discussed and related to the measured Raman and infrared spectra of the layered structures.

RAMAN SPECTRA AND ELECTRONIC STRUCTURE OF GeXS1-X CHALCOGENIDE GLASSES

The influence of technological synthesis conditions of GeS2 glass on structural changes in g-GeS2 has been investigated. In the Raman spectra of glass synthesized with the increased melt temperature the new vibration modes characteristic Raman modes of c-GeS at polarization ba+(ca) were observed. Taking into account the evolution of Raman spectra of GeS2 glasses synthesized by melt quenching from different temperatures the complex mode at 200-300 cm-1 can be interpreted as superposition of modes characteristic of a-Ge ³ c-GeS. With the high- and low- temperature modifications of germanium disulphide and the calculations of chain vibrations in valence force field model (approximation) the vibrations of deformed A1 GeS4/2 tetrahedral can be associated with most intensive Raman modes at 362 cm-1 in the spectra of β-GeS2 . Using a method based on method of linear combination of atomic orbitals and method of pseudopotential the energy levels of top of the valence band (EV) and bottom of the conduction band (AN) of Gen Sm were calculated. The energy levels of electronic states of Ge4p atoms, Gesp3 clusters, and Sn clusters were calculated. The hypothetical dependence of EV and AN energies versus interatomic distance and calculated energies of electronic states of Es , EGe-Ge, EGesp3 and Fermi levels EF were constructed. For the GeS2 compositions in the energy diagram the calculated probable energy levels of Sn , α-GeS2 , Ge2 S3 , Ge-Ge, Gesp3 phases and LP-states of sulfur were shown.

Building semiconductor nanostructures atom by atom

We present an atomistic tight-binding approach to calculating the electronic structure of semiconductor nanostructures. We start by deriving the strain distribution in the structure using the valence force field model. The strain field is incorporated into the tight-binding electronic structure calculation carried out in the frame of the effective bond orbital model and the fully atomistic sp3d5s* approach. We apply the method to a vertically coupled self-assembled double-dot molecule. Using the effective mass approach, we establish the existence of electronic bonding and antibonding molecular orbitals for electrons and holes, whose probability density is shared equally between the dots. In the atomistic calculation we recover the molecular character of electron orbitals, but find that structural and atomistic details of the sample modify the hole orbitals, leading to a strongly asymmetric distribution of the probability density between the dots.

Effect of post-growth annealing on the optical properties of InAs/GaAs quantum dots: A tight-binding study

We present an atomistic study of the strain field, the one-particle electronic spectrum and the oscillator strength of the fundamental optical transition in chemically disordered InxGa1−xAs pyramidal quantum dots (QDs). Interdiffusion across the interfaces of an originally “pure” InAs dot buried in a GaAs matrix is simulated through a simple model, leading to atomic configurations where the abrupt heterointerfaces are replaced by a spatially inhomogeneous composition profile x. Structural relaxation and the strain field calculations are performed through the Keating valence force field model, while the electronic and optical properties are determined within the empirical tight-binding approach. We analyze the relative impact of two different aspects of the chemical disorder, namely: (i) the effect of the strain relief inside the QD, and (ii) the purely chemical effect due to the group-III atomic species interdiffusion. We find that these effects may be quantitatively comparable, significantly affecting the electronic and optical properties of the dot. Our results are discussed in comparison with recent luminescence studies of intermixed QDs.

General Elasticity Theory for Graphene Membranes Based on Molecular Dynamics

ABSTRACTWe have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (EMD) as a function of external forces. For the continuum description, we use the expression Econt = Estretching + Ebending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering Econt are determined by requiring that Econt = EMD for a set of deformations.Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.

Theory of interface structure, energetics, and electronic properties of embedded Si/a-SiO 2 nanocrystals

We examine the interrelation of the structural and bonding alterations, when Si nanocrystals are embedded in amorphous silicon dioxide, with the electronic properties of the resulting nanocomposite system. Monte Carlo simulations using a valence force-field model obtain the equilibrium structure of the interface, and investigate its energetics, stability and disorder as a function of the nanocrystal size. It is found that when the size is smaller than 2 nm, the embedded nanocrystals get heavily distorted. First-principles calculations of such small nanocrystals reveal a drastic reduction of the energy gap compared to the free-standing case. The origin of this pinning is attributed to the structural deformations, while oxygen states at the interface seem to play a minor role.

Heterocyclic aromatic amines in H-bonded complexes (1:1 and 1:2 composition) in solutions with various proton acceptors

The influence of the position and number of the nitrogen atoms in the aromatic ring on the proton donation ability in intermolecular H-bond, spectral, geometrical, force, electrooptic and energetic characteristics of the amino group was investigated for free and H-bonded (1:1 and 1:2, with various proton acceptors) molecules of 2-aminopyrazine (I) and 3-amino-1,2,4-triazine (II). Acetonitrile, dioxane, tetrahydrofourane, dimethylformamide, dimethylsulfoxide and hexamethylphosphoramide were used as proton acceptors. Their proton accepting properties vary in a wide range. In the range of the amino group stretching and deformation vibrations, within the temperature interval 285–330 K, IR spectra of free and H-bonded (1:1) molecules of compounds I, II in CCl 4 were studied. Complexes of 1:2 composition were studied in the undiluted aprotic solvents. The following absorption band spectral characteristics were determined: M (0) – zero spectral moment (integrated intensity B), M (1) – first spectral moment (the centre of gravity of the band), M (2) – second central moment related to the effective half width (Δ ν 1/2) eff = 2(M (2)) 1/2. It was shown that within the explored temperature interval the absorption band spectral characteristics of the monomers and complexes are well approximated by the linear functions Y = aT + b ( Y = B, M (1), 2( M (2)) 1/2). The linear regression parameters for these equations were determined. The vibrational and electro-optic problems for free and H-bonded molecules of compounds I, II were solved in approximation of the R-NH 2 valence force field model. Valence angles γ (HNH), force constants K (NH), electro-optic parameters ∂ μ/∂ q (derivative of the dipole moment by the length of the corresponding bond) and ∂ μ/∂ q′ (derivative of the dipole moment by the length of the neighboring bond) were determined. It was shown that the absorption band spectral characteristics of the amino group stretching vibrations of the examined compounds in CCl 4 are most sensitive to the o-position of nitrogen atoms in the aromatic ring relatively to the amino group. Increasing the number of the nitrogen atoms in the ring leads to increasing the force constants K (NH), valence angle γ (HNH), and electrooptic parameters ∂ μ/∂ q and ∂ μ/∂ q′. The linear correlations were obtained between spectral, geometrical, force and electrooptic characteristics of amino group of free and H-bonded (1:1 and 1:2) molecules. The comparative analysis was performed on the dependence of the correlation relations on the position and number of the nitrogen atoms in the aromatic ring. The dependence of the monomer-complex (1:1) equilibrium constants on the temperature was examined. The thermodynamical characteristics of the complex: entropy and enthalpy of the complex formation were obtained on the basis of the Vant–Hoff equation. The H-bond enthalpy in complexes of 1:2 composition was calculated using A.V. Iogansen’s “intensities rule”. The basic regularities observed in the spectra of free molecules of compounds I, II are confirmed by the quantum mechanical calculations in the DFT-B3LYP/6-31G** approximation and ab initio MP2/6-31G**.

Hydrogen bonds of 2-aminothiazoles in intermolecular complexes (1:1 and 1:2) with proton acceptors in solutions

IR spectra of the free molecules of 2-aminothiazole and 2-aminobenzothiazole and their H-bonded complexes of 1:1 composition with acetonitrile, dioxane, tetrahydrofourane, dimethylformamide, dimethylsulfoxide and hexamethyl-phosphoramide in CCl 4 were studied in the range of stretching and deformational vibrations of the amino group. The complexes of 1:2 compositions were studied in undiluted aprotic solvents. The absorption band spectral characteristics of monomers and complexes were determined: M (0)—zero spectral moment (integrated band intensity B), M (1)—first spectral moment (band gravity center) and effective half-width (Δ ν 1/2) eff which is related to the second central moment M (2): (Δ ν 1/2) eff=2( M (2)) 1/2. The temperature influence on the absorption band spectral characteristics of the amino group stretching vibrations for monomers and 1:1 complexes were studied in the interval 283–323 K. It was shown that within the range mentioned above, spectral characteristics have practically linear dependence on temperature. Parameters of the linear regression equation Y= aT+ b ( Y= B, M (1), 2( M (2)) 1/2) were determined. It was stated that the temperature sensitivity a= ∂Y/ ∂T of spectral characteristics for 1:1 complexes of 2-aminothiazoles with proton acceptors is approximately 10 times higher than for monomers. The monomer-complex equilibrium constants K( T) (1:1) were calculated and the thermodynamical characteristics –Δ H and Δ S were determined, based on Vant-Hoff equation. For free (R–NH 2, R–NHD, R–ND 2) and H-bonded (1:1 and 1:2, with various proton acceptors) molecules of 2-aminothiazoles, the vibrational and electro optic problems were solved in the approximation of the six-coordinate valence force field model. The valence angles γ(HNH), force constants K(NH), electro optic parameters ∂ μ/ ∂ q (derivative of the dipole moment by the length of NH-bond) and ∂ μ/ ∂ q′ (derivative of the dipole moment by the length of the neighboring NH-bond) were determined. The correlations were stated between spectral, geometrical, force and electro optic parameters of free and bonded molecules. In the approximation of DFT-B3LYP/6-31G** and ab initio MP2/6-31G**, the atom charge distribution (according to Mulliken), geometrical and force characteristics and dipole moments μ 0 of 2-aminothiazoles were calculated. The quantum mechanical calculations, valence force field calculations and the experimental results were shown to be in good agreement.

Theory of strain states in InAs quantum dots and dependence on their capping layers

The dependence of strain states in InAs self-assembled quantum dots (QDs) on their capping layers was investigated by valence-force field model calculations. An InAs QD on (001) GaAs and embedded in a GaNAs capping layer and the one with its dot surface terminated with nitrogen (N) and embedded in a GaAs capping layer show reduced compressive strain within the QDs in the (001) growth plane due to the lateral expansion of the QDs, while the one embedded in an InGaAs capping layer shows enhanced tensile strain along the [001] growth direction. The strain energies around the center of the InAs QDs with the GaNAs capping layer and with the N-surface termination are lowered compared with those for conventional GaAs capping layers. The burying conditions of InAs QDs also modify the sizes of QDs. The stress distributions obtained by strain energy mapping showed that In atoms around the top of QDs undergo inward stress. This inward stress prevents In segregation and explains the experimentally observed improved optical properties of GaNAs-embedded and N-terminated QDs.

Effects of hydrogenation on the local structure ofInxGa1−xAs1−yNyquantum wells andGaAs1−yNyepilayers

We address in this paper the issue of the effects of hydrogenation on the local structure of In{sub x}Ga{sub 1-x}As{sub 1-y}N{sub y} quantum wells by combining In K-edge x-ray absorption and Ga K-edge x-ray diffraction anomalous fine structure experiments. We found that the cation-As bond lengths in hydrogenated samples are systematically longer than the values predicted by a valence force field model corrected for the epitaxial strain. We interpret this bond lengths stretching as a local effect of the formation of N-H complexes very recently predicted by theoretical calculations. By analyzing the Debye-Waller factor of the Ga-As bond length distribution, we observed that hydrogenation removes the static disorder induced by N incorporation in GaAs; this effect is due to the unique characteristics of the N substitutional anion and to the breaking of the ionic Ga-N bonds upon hydrogenation.