Isotopic Disorder Research Articles

Elastic electron scattering and localization in a chain with isotopic disorder

Elastic electron scattering and localization in a chain with isotopic disorder

Isotopic effects on in-plane hyperbolic phonon polaritons in MoO3

Abstract Hyperbolic phonon polaritons (HPhPs), hybrids of light and lattice vibrations in polar dielectric crystals, empower nanophotonic applications by enabling the confinement and manipulation of light at the nanoscale. Molybdenum trioxide (α-MoO3) is a naturally hyperbolic material, meaning that its dielectric function deterministically controls the directional propagation of in-plane HPhPs within its reststrahlen bands. Strategies such as substrate engineering, nano- and hetero-structuring, and isotopic enrichment are being developed to alter the intrinsic dielectric functions of natural hyperbolic materials and to control the confinement and propagation of HPhPs. Since isotopic disorder can limit phonon-based processes such as HPhPs, here we synthesize isotopically enriched 92MoO3 (92Mo: 99.93 %) and 100MoO3 (100Mo: 99.01 %) crystals to tune the properties and dispersion of HPhPs with respect to natural α-MoO3, which is composed of seven stable Mo isotopes. Real-space, near-field maps measured with the photothermal induced resonance (PTIR) technique enable comparisons of in-plane HPhPs in α-MoO3 and isotopically enriched analogs within a reststrahlen band (≈820 cm−1 to ≈972 cm−1). Results show that isotopic enrichment (e.g., 92MoO3 and 100MoO3) alters the dielectric function, shifting the HPhP dispersion (HPhP angular wavenumber × thickness vs. IR frequency) by ≈−7 % and ≈+9 %, respectively, and changes the HPhP group velocities by ≈±12 %, while the lifetimes (≈3 ps) in 92MoO3 were found to be slightly improved (≈20 %). The latter improvement is attributed to a decrease in isotopic disorder. Altogether, isotopic enrichment was found to offer fine control over the properties that determine the anisotropic in-plane propagation of HPhPs in α-MoO3, which is essential to its implementation in nanophotonic applications.

Anharmonic effects on the reflectivity of CaS and MgS: a first-principles based study

We employ systematic calculations based on density functional theory to model the reflectivity of CaS and MgS in the infrared region. We show that in addition to the modeling using the harmonic approximation, an accurate spectral description requires the inclusion of anharmonic effects. Due to their conceptual simplicity, CaS and MgS are excellent systems for the explicit consideration of the anharmonicity, which we include here using a perturbative approach up to three-phonon scattering processes, and the consideration of isotopic disorder. All physical quantities, such as Born effective charges and dielectric constant, necessary for the calculation of the reflectivity within the Lorentz model are extracted from our first-principles computations. To validate our predicted optical and transversal modes, and reflectivity spectra, we compare them to available experimental results. We find that the overall agreement is good, which supports the importance of the inclusion of anharmonic terms in the modeling of optical properties in the infrared region.

Isotope Effects on the Optical Phonons of Cubic Boron Phosphide

The ratio of boron isotopes (10B and 11B) affects the thermal conductivity of cubic borides because of the phonon scattering. There are two signals appearing in the Raman spectra of cubic boron phosphide (c‐BP) single crystals with natural boron isotope abundance. One is a sharp peak with high intensity and small linewidth, which has been identified as a TO‐LO‐mixed mode; the other is a small peak in the low‐frequency side with quite low intensity and large linewidth, which is difficult to be observed in isotope‐purified crystals and with an unclear origin. Herein, in order to clarify the isotope effects on optical phonons and to identify the origin of the small peak in c‐BP, the Raman spectra of isotope‐tailored c‐BP single crystals in the range from nearly pure c‐10BP to nearly pure c‐11BP are analyzed in detail. Both the frequency and linewidth of the TO‐LO‐mixed mode are closely related to the boron isotope ratio under the isotopic average mass effect and mass disorder effect. The small Raman peak is also isotope dependent. It originates from LO phonon scattering at the non‐origin of the Brillouin zone under the isotopic mass disorder effect.

Теплопроводность SiC: расчет изотопического эффекта из первых принципов

The thermal conductivity temperature dependence kappa(T) of a hexagonal 2H-SiC silicon carbide crystal was calculated using the first-principle approach for the orientation of the heat flux in the basal plane and along the hexagonal axis c in the temperature range from 100 to 500 K. The effect of silicon and carbon isotopic disorder on thermal conductivity is considered. It was found that, at a temperature of 300 K, the thermal conductivity of isotopically pure 2H-SiC containing 100% 28Si and 100% 12C is higher by 15.2% and 12.4% for directions along and across the basal plane, respectively, than that of crystals with a natural composition of silicon and carbon isotopes. For crystals with a natural mixture of carbon isotopes natC, the isotope effect for silicon is 14.5% and 11.9% for these directions.

SiC thermal conductivity: calculation of the isotope effect from first principles

The thermal conductivity temperature dependence kappa(T) of a hexagonal 2H-SiC silicon carbide crystal was calculated using the first-principle approach for the orientation of the heat flux in the basal plane and along the hexagonal axis c in the temperature range from 100 to 500 K. The effect of silicon and carbon isotopic disorder on thermal conductivity is considered. It was found that, at a temperature of 300 K, the thermal conductivity of isotopically pure 2H-SiC containing 100% 28Si and 100% 12C is higher by 15.2% and 12.4% for directions along and across the basal plane, respectively, than that of crystals with a natural composition of silicon and carbon isotopes. For crystals with a natural mixture of carbon isotopes textnatC, the isotope effect for silicon is 14.5% and 11.9% for these directions. Keywords: single crystal, thermal conductivity, silicon carbide, first principle calculation.

Ultrahard BC5 – An efficient nanoscale heat conductor through dominant contribution of optical phonons

In this work, we study lattice thermal conductivity (k) of BC5, an diamondlike ultra-hard material, using first-principles computations and analyze the effect of both isotopic disorder as well as length scale dependence. k of isotopically pure BC5 is computed to be 169 Wm−1 K−1 (along a-axis) at 300 K; this high k is found to be due to the high frequencies and phonon group velocities of both acoustic and optical phonons owing to the light atomic mass of Carbon (C) and Boron (B) atoms and strong C-C and B-C bonds. We also observe a dominance of optical phonons (∼54%) over acoustic phonons in heat conduction at higher temperatures (∼500 K). This unusually high contribution of optical phonons is found to be due to a unique effect in BC5 related to a weaker temperature dependence of optical phonon scattering rates relative to acoustic phonons. The effect is explained in terms of high frequencies of optical phonons causing decay into other high frequency phonons, where low phonon populations cause the decay term to become insensitive to temperature. The effect further leads to high nanoscale thermal conductivity of 77 Wm−1 K−1 at 100 nm length scale due to optical phonon meanfreepaths being in nanometer regime. These results provide avenues for application of BC5 in nanoscale thermal management.

Isotopic disorder in integer and fractional quantum Hall effects

The energy of the activation gaps in the quantum Hall effect has been thought to be reduced by the broadening of the Landau levels due to disorder. The isotopic mass can affect the electron-phonon interactions and the 0 K renormalization of the conduction and valence bands, leading to appreciable energy offsets between lattice sites with different nuclear masses. The isotopic disorder originating from the natural occurrence of nuclear masses could be the dominant broadening mechanism remaining, leading to the experimentally observed quantum Hall effect gaps in high-mobility devices. The Landau level broadening due to the isotopic disorder has been calculated microscopically without fitting parameters.

Ultrahigh Thermal Conductivity of θ-Phase Tantalum Nitride.

Extracting long-lasting performance from electronic devices and improving their reliability through effective heat management requires good thermal conductors. Taking both three- and four-phonon scattering as well as electron-phonon and isotope scattering into account, we predict that semimetallic θ-phase tantalum nitride (θ-TaN) has an ultrahigh thermal conductivity (κ), of 995 and 820 W m^{-1} K^{-1} at room temperature along the a and c axes, respectively. Phonons are found to be the main heat carriers, and the high κ hinges on a particular combination of factors: weak electron-phonon scattering, low isotopic mass disorder, and a large frequency gap between acoustic and optical phonon modes that, together with acoustic bunching, impedes three-phonon processes. On the other hand, four-phonon scattering is found to be significant. This study provides new insight into heat conduction in semimetallic solids and extends the search for high-κ materials into the realms of semimetals and noncubic crystal structures.

Ab initio Calculation of the Effective Thermal Conductivity Coefficient of a Superlattice Using the Boltzmann Transport Equation

The effective thermal conductivity coefficient of a binary semiconductor heterostructure is calculated by an example of the GaAs/AlAs superlattice at different layer periods and different ambient temperatures. The applicability of the Fourier-law models is strongly limited on the investigated scale, since they do not take into account the quantum-mechanical properties of materials, which leads to a large deviation from the experimental data. However, the use of molecular dynamics methods allows us to obtain accurate solutions; however, these methods are much more demanding of computing resources and require a nontrivial potential selection problem to be solved. In the investigations of the nanostructures, good results are obtained using the methods based on solving the Boltzmann transport equation for phonons; they make it possible to obtain a fairly accurate solution at a lower computational complexity compared with the molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used, which approximates the solution of the Boltzmann transport equation for phonons. The dispersion and phonon scattering parameters are obtained using ab initio calculations. The two-phonon processes related to the isotopic disorder and the barrier three-phonon scattering processes are taken into account. To increase the accuracy of the calculations, the inhomogeneity of the distribution of materials over the superlattice layers is taken into account. A comparison of the results obtained with the experimental data shows their close agreement.

Large substitutional impurity isotope shift in infrared spectra of boron-doped diamond

Isotopic enrichment offers cutting-edge properties of materials opening exciting research and development opportunities. In semiconductors, reached progress of ultimate control in growth and doping techniques follows nowadays the high level isotopic purification. This requires deep understanding of isotopic disorder effects and techniques of their effective determination. Isotopic content of both crystal lattice and impurity centers cause the effects, which can be examined by different optical techniques. While disorder in the host lattice can be straight forward evaluated by inelastic light scattering or by SIMS measurements, determination of isotopic contributions of many orders less presented impurities remains challenging and usually observed in high-resolution photoluminescence or optical absorption spectra. Boron-doped diamonds exhibit complex infrared absorption spectra while boron-related luminescence remains unobserved. Boron, as a most light element acting as a hydrogen-like dopant in elemental semiconductors, has a largest relative difference in its isotope masses, and by this, cause the largest isotopic disorder in semiconductors, including diamond, an elemental semiconductor with the lightest atomic mass of a host lattice. This enables an access to the isotopic constitution of boron in diamond by infrared absorption spectroscopy. By comparison of low-temperature absorption spectra of a natural (20% of 10B and 80% of 11B isotopes) and 11B enriched (up to 99%) doped diamonds we differentiate the intracenter transitions related to 10B and to 11B isotopes. We have found that the isotopic spectral lines of the same boron intracenter transition are separated with the energy of about 0.7 meV. This is the largest impurity isotopic shift ever observed in semiconductors doped by hydrogen-like impurity centers.

Positional, isotopic mass and force constant disorder in molybdate glasses and their parent metal oxides as observed by neutron diffraction and Compton scattering

Neutron Compton scattering and neutron diffraction, augmented by ab initio modelling, have been applied for the characterisation of disorder in molybdate glasses, 20MoO3 + 30Nd2O3 + 50B2O3, 40MoO3 + 30Nd2O3 + 30B2O3, and 50MoO3 + 25Nd2O3 + 25B2O3, along with their parent metal oxides, B2O3, MoO3 and Nd2O3. Softening of the atom-projected vibrational densities of states (apVDOSes) was observed for all constituent nuclei in the metal oxide systems, with respect to the ab initio harmonic lattice dynamics predictions. For the oxygen, the mode softening was attributed to force-constant disorder, and for the boron to the isotopic mass disorder. A universal scale of disorder in oxide glasses has been proposed. The scale relies on the assumption that the amount of disorder-induced phonon softening can be bracketed by two extreme situations: (i) a completely disordered system with no confining potential whose momentum distribution is described by the Maxwell-Boltzmann momentum, and (ii) the compositional average of harmonic lattice dynamics predictions for individual metal oxide systems. The highest degree of disorder on this scale was observed for the boron in the molybdate glasses with the highest amount of B2O3. The distributions of total (summed over all nuclei) effective force constants were found to be at least an order of magnitude wider than their counterparts calculated for the parent metal oxide systems, indicating a much greater degree of positional disorder-induced force constant disorder in the molybdate glasses. The sum of all mean effective forces acting on all constituent nuclei in the molybdates was found to be decreasing with the increasing amount of the glass-former B2O3, clearly showing a systematic softening of the structure of the glasses. The biggest contributions to the total average effective mean force in all three molybdates were found for the molybdenum and neodymium.

Isotopic Disorder: The Prevailing Mechanism in Limiting the Phonon Lifetime in Hexagonal BN.

The phonon linewidth of isotopically controlled hexagonal boron nitride (h-BN) single crystals has been determined by Raman scattering. The scattering by isotopic mass disorder induces a phonon broadening that is largest for boron 11 fractions around 0.65. Lowest-order perturbation theory does not suffice to explain the dependence of the isotopic broadening on isotopic composition. A multiple-scattering theory based on the coherent potential approximation provides a good quantitative account of the phonon shift and broadening with isotopic composition observed in the experiments. Isotopic-disorder scattering is shown to have a prominent role in limiting the optical-phonon lifetime in h-BN.

Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder

We address the general problem of heat conduction in one dimensional harmonic chains, with correlated isotopic disorder, attached at their ends to white noise or Rubin's model of heat baths. The scaling behavior of the thermal conductivity is independent of the heat reservoirs, but depends on the boundary conditions and the low wave-number μ behavior of the power spectrum W(μ) of the fluctuations of the random masses around their common mean value. Thus, by properly tuning W(μ) we are able to control the scaling of the thermal conductivity κ with the system size N. As an example, we show that if W(μ)∼exp⁡(−1/μ)/μ2, then κ∼N/(log⁡N)3 for fixed boundary conditions and κ∼N/log⁡(N) for free boundary conditions, which represent non-standard scalings of the thermal conductivity. In addition, we obtain the asymptotic dependence of the thermal conductivity on the coupling strength between the harmonic chain and the heat baths.

Calculation of the effective thermal conductivity of a superlattice based on the Boltzmann transport equation using first-principle calculations

In this work, we calculate the effective thermal conductivity coefficient for a binary semiconductor heterostructure using the GaAs/AlAs superlattice as an example. Different periods of layers and different ambient temperatures are considered. At the scale under consideration, the use of models based on the Fourier law is very limited, since they do not take into account the quantum-mechanical properties of materials, which gives a strong discrepancy with experimental data. On the other hand, the use of molecular dynamics methods allows us to obtain accurate solutions, but they are significantly more demanding on computing resources and also require solving a non-trivial problem of potential selection. When considering nanostructures, good results were shown by methods based on the solution of the Boltzmann transport equation for phonons; they allow one to obtain a fairly accurate solution, while having less computational complexity than molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used that approximates the solution of the Boltzmann transport equation for phonons. The dispersion parameters and phonon scattering parameters are obtained from first-principle calculations. The work takes into account 2-phonon (associated with isotopic disorder and barriers) and 3-phonon scattering processes. To increase the accuracy of calculations, the non-digital profile of the distribution of materials among the layers of the superlattice is taken into account. The obtained results are compared with experimental data showing good agreement.

Influence of isotopic substitution on the anharmonicity of the interlayer shear mode of h -BN

We present a detailed analysis of the temperature dependence of the interlayer shear mode that reveals a variation of the four-phonon scattering coupling with isotopic mass. Phonon anharmonic decay and isotopic disorder effects are very weak for the low-energy interlayer shear mode, and the overall temperature dependence is mainly governed by the thermal lattice expansion. This allows us to observe systematic differences in the temperature dependence of the low-energy mode with the isotopic mass that are related to the four-phonon scattering contribution in quartic anharmonicity. The change in the quartic anharmonicity coefficient between the isotopically pure samples is larger than would be purely expected from the mass variation.

Isotope-Engineering the Thermal Conductivity of Two-Dimensional MoS2.

Isotopes represent a degree of freedom that might be exploited to tune the physical properties of materials while preserving their chemical behaviors. Here, we demonstrate that the thermal properties of two-dimensional (2D) transition-metal dichalcogenides can be tailored through isotope engineering. Monolayer crystals of MoS2 were synthesized with isotopically pure 100Mo and 92Mo by chemical vapor deposition employing isotopically enriched molybdenum oxide precursors. The in-plane thermal conductivity of the 100MoS2 monolayers, measured using a non-destructive, optothermal Raman technique, is found to be enhanced by ∼50% compared with the MoS2 synthesized using mixed Mo isotopes from naturally occurring molybdenum oxide. The boost of thermal conductivity in isotopically pure MoS2 monolayers is attributed to the combined effects of reduced isotopic disorder and a reduction in defect-related scattering, consistent with observed stronger photoluminescence and longer exciton lifetime. These results shed light on the fundamentals of 2D nanoscale thermal transport important for the optimization of 2D electronic devices.

Infrared reflectance, transmittance, and emittance spectra of MgO from first principles

By using density functional theory calculations we determined the influence of anharmonic effects on the infrared reflectance, transmittance, and emittance of MgO. The goal is to determine the limit of validity of a perturbative (multiphonon) approach. MgO is chosen as a test material because of the availability of different kinds of radiative properties measured experimentally. Nonanalytic terms of the three-phonon scattering coefficients are explicitly calculated and do not provide measurable effects. The agreement is overall very good to such an extent that, already at room temperature, one can clearly identify regions in which four-phonon scattering processes are dominant with respect to the three-phonon ones. The influence of isotopic disorder at cryogenic temperatures is also settled.

Isotopic effects on phonon anharmonicity in layered van der Waals crystals: Isotopically pure hexagonal boron nitride

Hexagonal boron nitride (h-BN) is a layered crystal that is attracting a great deal of attention as a promising material for nanophotonic applications. The strong optical anisotropy of this crystal is key to exploit polaritonic modes for manipulating light-matter interactions in 2D materials. h-BN has also great potential for solid-state neutron detection and neutron imaging devices, given the exceptionally high thermal neutron capture cross section of the boron-10 isotope. A good knowledge of phonons in layered crystals is essential for harnessing long-lived phonon-polariton modes for nanophotonic applications and may prove valuable for developing solid-state 10BN neutron detectors with improved device architectures and higher detection efficiencies. Although phonons in graphene and isoelectronic materials with a similar hexagonal layer structure have been studied, the effect of isotopic substitution on the phonons of such lamellar compounds has not been addressed yet. Here we present a Raman scattering study of the in-plane high-energy Raman active mode on isotopically enriched single-crystal h-BN. Phonon frequency and lifetime are measured in the 80–600-K temperature range for 10B-enriched, 11B-enriched, and natural composition high quality crystals. Their temperature dependence is explained in the light of perturbation theory calculations of the phonon self-energy. The effects of crystal anisotropy, isotopic disorder, and anharmonic phonon-decay channels are investigated in detail. The isotopic-induced changes in the phonon density of states are shown to enhance three-phonon anharmonic decay channels in 10B-enriched crystals, opening the possibility of isotope tuning of the anharmonic phonon decay processes.

Ultrahigh thermal conductivity of isotopically enriched silicon

Most of the stable elements have two and more stable isotopes. The physical properties of materials composed of such elements depend on the isotopic abundance to some extent. A remarkably strong isotope effect is observed in the phonon thermal conductivity, the principal mechanism of heat conduction in nonmetallic crystals. An isotopic disorder due to random distribution of the isotopes in the crystal lattice sites results in a rather strong phonon scattering and, consequently, in a reduction of thermal conductivity. In this paper, we present new results of accurate and precise measurements of thermal conductivity κ(T) for silicon single crystals having three different isotopic compositions at temperatures T from 2.4 to 420 K. The highly enriched crystal containing 99.995% of 28Si, which is one of the most perfect crystals ever synthesized, demonstrates a thermal conductivity of about 450 ± 10 W cm−1 K–1 at 24 K, the highest measured value among bulk dielectrics, which is ten times greater than the one for its counterpart natSi with the natural isotopic constitution. For highly enriched crystal 28Si and crystal natSi, the measurements were performed for two orientations [001] and [011], a magnitude of the phonon focusing effect on thermal conductivity was determined accurately at low temperatures. The anisotropy of thermal conductivity disappears above 31 K. The influence of the boundary scattering on thermal conductivity persists sizable up to much higher temperatures (∼80 K). The κ(T) measured in this work gives the most accurate approximation of the intrinsic thermal conductivity of single crystal silicon which is determined solely by the anharmonic phonon processes and diffusive boundary scattering over a wide temperature range.