Atomistic Green's Function Research Articles

Thermal Boundary Conductance Across Heteroepitaxial ZnO/GaN Interfaces: Assessment of the Phonon Gas Model.

We present experimental measurements of the thermal boundary conductance (TBC) from 78-500 K across isolated heteroepitaxially grown ZnO films on GaN substrates. This data provides an assessment of the underlying assumptions driving phonon gas-based models, such as the diffuse mismatch model (DMM), and atomistic Green's function (AGF) formalisms used to predict TBC. Our measurements, when compared to previous experimental data, suggest that TBC can be influenced by long wavelength, zone center modes in a material on one side of the interface as opposed to the '"vibrational mismatch"' concept assumed in the DMM; this disagreement is pronounced at high temperatures. At room temperature, we measure the ZnO/GaN TBC as 490[+150,-110] MW m-2 K-1. The disagreement among the DMM and AGF, and the experimental data at elevated temperatures, suggests a non-negligible contribution from other types of modes that are not accounted for in the fundamental assumptions of these harmonic based formalisms, which may rely on anharmonicity. Given the high quality of these ZnO/GaN interfaces, these results provide an invaluable, critical, and quantitative assessment of the accuracy of assumptions in the current state of the art computational approaches used to predict phonon TBC across interfaces.

Atomistic S -matrix method for numerical simulation of phonon reflection, transmission, and boundary scattering

The control of phonon scattering by interfaces is critical to the manipulation of heat conduction in composite materials and semiconducting nanostructures. However, one of the factors limiting our understanding of elastic phonon scattering is the lack of a computationally efficient approach for describing the phenomenon in a manner that accounts for the atomistic configuration of the interface and the exact bulk phonon dispersion. Building on the atomistic Green's function (AGF) technique for ballistic phonon transport, we formulate an atomistic S-matrix method that treats bulk phonon modes as the scattering channels and can determine the numerically exact scattering amplitudes for individual two-phonon processes, enabling a highly detailed analysis of the phonon transmission and reflection spectrum as well as the directional dependence of the phonon scattering specularity. Explicit formulas for the individual phonon reflection, absorption and transmission coefficients are given in our formulation. This AGF-based S-matrix approach is illustrated through the investigation of: (1) phonon scattering at the junction between two isotopically different but structurally identical carbon nanotubes, and (2) phonon boundary scattering at the zigzag and armchair edges in graphene. In particular, we uncover the role of edge chirality on phonon scattering specularity and explain why specularity is reduced for the ideal armchair edge. The application of the method can shed new light on the relationship between phonon scattering and the atomistic structure of interfaces.

Tutorial: Concepts and numerical techniques for modeling individual phonon transmission at interfaces

At the nanoscale, thermal transport across the interface between two lattice insulators can be described by the transmission of bulk phonons and depends on the crystallographic structure of the interface and the bulk crystal lattice. In this tutorial, we give an account of how an extension of the Atomistic Green’s Function (AGF) method based on the concept of the Bloch matrix can be used to model the transmission of individual phonon modes and allows us to determine the wavelength and polarization dependence of the phonon transmission. Within this framework, we can explicitly establish the relationship between the phonon transmission coefficient and dispersion. Details of the numerical methods used in the extended AGF method are provided. To illustrate how the extended AGF method can be applied to yield insights into individual phonon transmission, we study the (16,0)/(8,0) carbon nanotube intramolecular junction. The method presented here sheds light on the modal contribution to interfacial thermal transport between solids.

Interplay between total thickness and period thickness in the phonon thermal conductivity of superlattices from the nanoscale to the microscale: Coherent versus incoherent phonon transport

We report on the room temperature thermal conductivity of AlAs-GaAs superlattices (SLs), in which we systematically vary the period thickness and total thickness between $2--24\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ and $20.1--2,160\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, respectively. The thermal conductivity increases with the SL thickness and plateaus at a thickness around 200 nm, showing a clear transition from a quasiballistic to a diffusive phonon transport regime. These results demonstrate the existence of classical size effects in SLs, even at the highest interface density samples. We use harmonic atomistic Green's function calculations to capture incoherence in phonon transport by averaging the calculated transmission over several purely coherent simulations of independent SL with different random mixing at the AlAs-GaAs interfaces. These simulations demonstrate the significant contribution of incoherent phonon transport through the decrease in the transmission and conductance in the SLs as the number of interfaces increases. In spite of this conductance decrease, our simulations show a quasilinear increase in thermal conductivity with the superlattice thickness. This suggests that the observation of a quasilinear increase in thermal conductivity can have important contributions from incoherent phonon transport. Furthermore, this seemingly linear slope in thermal conductivity versus SL thickness data may actually be nonlinear when extended to a larger number of periods, which is a signature of incoherent effects. Indeed, this trend for superlattices with interatomic mixing at the interfaces could easily be interpreted as linear when the number of periods is small. Our results reveal that the change in thermal conductivity with period thickness is dominated by incoherent (particlelike) phonons, whose properties are not dictated by changes in the AlAs or GaAs phonon dispersion relations. This work demonstrates the importance of studying both period and sample thickness dependencies of thermal conductivity to understand the relative contributions of coherent and incoherent phonon transport in the thermal conductivity in SLs.

Ultimate Confinement of Phonon Propagation in Silicon Nanocrystalline Structure.

Temperature-dependent thermal conductivity of epitaxial silicon nanocrystalline (SiNC) structures composed of nanometer-sized grains separated by ultrathin silicon-oxide (SiO_{2}) films (∼0.3 nm) is measured by the time domain thermoreflectance technique in the range from 50 to 300K. The thermal conductivity of SiNC structures with a grain size of 3 and 5nm is anomalously low at the entire temperature range, significantly below the values of bulk amorphous Si and SiO_{2}. The phonon gas kinetic model, with intrinsic transport properties obtained by first-principles-based anharmonic lattice dynamics and phonon transmittance across ultrathin SiO_{2} films obtained by atomistic Green's function, reproduces the measured thermal conductivity without any fitting parameters. The analysis reveals that mean free paths of acoustic phonons in the SiNC structures are equivalent or even below half the phonon wavelength, i.e., the minimum thermal conductivity scenario. The result demonstrates that the nanostructures with extremely small length scales and a controlled interface can give rise to ultimate classical confinement of thermal phonon propagation.

First-Principle-Based Phonon Transport Properties of Nanoscale Graphene Grain Boundaries.

The integrity of phonon transport properties of large graphene (linear and curved) grain boundaries (GBs) is investigated under the influence of structural and dynamical disorder. To do this, density functional tight‐binding (DFTB) method is combined with atomistic Green's function technique. The results show that curved GBs have lower thermal conductance than linear GBs. Its magnitude depends on the length of the curvature and out‐of‐plane structural distortions at the boundary, having stronger influence the latter one. Moreover, it is found that by increasing the defects at the boundary, the transport properties can strongly be reduced in comparison to the effect produced by heating up the boundary region. This is due to the large reduction of the phonon transmission for in‐plane and out‐of‐plane vibrational modes after increasing the structural disorder in the GBs.

Phonon-eigenspectrum-based formulation of the atomistic Green's function method

While the atomistic Green's function (AGF) method has the potential to compute spectrally resolved phonon transport across interfaces, most prior formulations of the AGF method provide only the total phonon transmission function that includes contributions from all phonon branches or channels. In this work, we present a formulation of the conventional AGF technique in terms of phonon eigenspectra that provides a natural decomposition of the total transmission function into contributions from various phonon modes. The method involves the use of Dyson and Lippmann-Schwinger equations to determine surface Green's functions from the phonon eigenspectrum of the bulk, and establishes a direct connection between the transmission function and the bulk phonon spectra of the materials forming the interface. We elucidate our formulation of the AGF technique through its application to a microscopic picture of phonon mode conversion at Si-Ge interfaces with atomic intermixing. Intermixing of atoms near the interface is shown to increase the phase space available for phonon mode conversion and to enhance thermal interface conductance at moderate levels of atomic mixing. The eigenspectrum-based AGF (EAGF) method should be useful in determination of microscopic mechanisms of phonon scattering and identification of the specific modes that dominate thermal transport across an interface.

Ab initio study of mode-resolved phonon transmission at Si/Ge interfaces using atomistic Green's functions

Solid interfaces with exceptionally low or high thermal conductance are of intense scientific and practical interest. However, realizing such interfaces is challenging due to a lack of knowledge of the phonon transmission coefficients between specific modes on each side of the interface and how the coefficients are affected by atomic scale structure. Here, we report an ab initio based study of phonon transmission at Si/Ge interfaces using a recent extension of the atomistic Green's function method that resolves transmission coefficients by mode. These results provide a detailed framework to investigate the precise transmission and reflection processes that lead to thermal resistance and how they depend on phonon frequency as well as incident angle. We find that the transmission and reflection processes can be partly explained with familiar concepts such as conservation of transverse momentum, but we also find that numerous phonons have zero transmission coefficient despite the existence of modes that satisfy transverse momentum conservation. This work provides detailed insights into precisely which phonons transmit or reflect at interfaces, knowledge necessary to design solid interfaces with extreme values of thermal conductance for thermoelectricity and heat management applications.

Designing Nanostructures for Phonon Transport via Bayesian Optimization

We demonstrate optimization of thermal conductance across nanostructures by developing a method combining atomistic Green's function and Bayesian optimization. With an aim to minimize and maximize the interfacial thermal conductance (ITC) across Si-Si and Si-Ge interfaces by means of Si/Ge composite interfacial structure, the method identifies the optimal structures from calculations of only a few percent of the entire candidates (over 60,000 structures). The obtained optimal interfacial structures are non-intuitive and impacting: the minimum-ITC structure is an aperiodic superlattice that realizes 50% reduction from the best periodic superlattice. The physical mechanism of the minimum ITC can be understood in terms of crossover of the two effects on phonon transport: as the layer thickness in superlattice increases, the impact of Fabry-P\'erot interference increases, and the rate of reflection at the layer-interfaces decreases. Aperiodic superlattice with spatial variation in the layer thickness has a degree of freedom to realize optimal balance between the above two competing mechanism. Furthermore, aperiodicity breaks the constructive phonon interference between the interfaces inhibiting the coherent phonon transport. The present work shows the effectiveness and advantage of material informatics in designing nanostructures to control heat conduction, which can be extended to other interfacial structures.

Relative effect of edge versus basal plane functionalization on graphene/polymer interfacial thermal conductance - Role of in-plane phonons

We compare the effectiveness of functionalization on the edge with that on the basal plane of graphene in enhancing interfacial thermal transport between polyethylene and graphene using an atomistic Green's function method. Harmonic interatomic force constants needed for the method are derived from the density-functional theory to provide a first-principles estimate of thermal conductance comparison. Computations reveal the thermal conductance for the edge functionalization to be 75% higher relative to the basal plane case at 300 K. Polarization specific transmission calculations are used to provide understanding of these differences.

Thermal transport across metal silicide-silicon interfaces: First-principles calculations and Green's function transport simulations

In this work, we use a combination of first-principles calculations under the density functional theory framework and heat transport simulations using the atomistic Green's function (AGF) method to quantitatively predict the contribution of the different scattering mechanisms to the thermal interface conductance of epitaxial CoSi$_2$-Si interfaces. An important development in the present work is the direct computation of interfacial bonding from density functional perturbation theory (DFPT) and hence the avoidance of commonly used `mixing rules' to obtain the cross-interface force constants from bulk material force constants. Another important algorithmic development is the integration of the recursive Green's function (RGF) method with B\"{u}ttiker probe scattering that enables computationally efficient simulations of inelastic phonon scattering and its contribution to the thermal interface conductance. First-principles calculations of electron-phonon coupling reveal that cross-interface energy transfer between metal electrons and atomic vibrations in the semiconductor is mediated by delocalized acoustic phonon modes that extend on both sides of the interface, and phonon modes that are localized inside the semiconductor region of the interface exhibit negligible coupling with electrons in the metal. We also provide a direct comparison between simulation predictions and experimental measurements of thermal interface conductance of epitaxial CoSi$_2$-Si interfaces using the time-domain thermoreflectance technique. Importantly, the experimental results, performed across a wide temperature range, only agree well with predictions that include all transport processes: elastic and inelastic phonon scattering, electron-phonon coupling in the metal, and electron-phonon coupling across the interface.

Thermal transport across metal silicide-silicon interfaces: An experimental comparison between epitaxial and nonepitaxial interfaces

Silicides are used extensively in nano- and microdevices due to their low electrical resistivity, low contact resistance to silicon, and their process compatibility. In this work, the thermal interface conductance of TiSi$_2$, CoSi$_2$, NiSi and PtSi are studied using time-domain thermoreflectance. Exploiting the fact that most silicides formed on Si(111) substrates grow epitaxially, while most silicides on Si(100) do not, we study the effect of epitaxy, and show that for a wide variety of interfaces there is no difference in the thermal interface conductance of epitaxial and non-epitaxial silicide/silicon interfaces. The effect of substrate carrier concentration is also investigated over a wide range of p- and n-type doping, and is found to be independent of carrier concentration, regardless of whether the interface is epitaxial and regardless of silicide type. In the case of epitaxial CoSi$_2$, a comparison of temperature dependant experimental data is made with two detailed computational models using (1) full-dispersion diffuse mismatch modeling (DMM) including the effect of near-interfacial strain and (2) an atomistic Green' function (AGF) approach that integrates near-interface changes in the interatomic force constants obtained through density functional perturbation theory. At temperatures above 100K, the AGF approach greatly underpredicts the CoSi$_2$ data, while the DMM prediction matches the data well. The full-dispersion DMM is also found to closely predict the experimentally observed temperature-dependent interface conductance for epitaxial NiSi/Si and non-epitaxial TiSi$_2$/Si interfaces. In the case of epitaxial PtSi/Si interfaces, full dispersion DMM significantly overpredicts the experimental data.

The Role of Interfacial Electronic Properties on Phonon Transport in Two-Dimensional MoS2 on Metal Substrates.

We investigate the role of interfacial electronic properties on the phonon transport in two-dimensional MoS2 adsorbed on metal substrates (Au and Sc) using first-principles density functional theory and the atomistic Green's function method. Our study reveals that the different degree of orbital hybridization and electronic charge distribution between MoS2 and metal substrates play a significant role in determining the overall phonon-phonon coupling and phonon transmission. The charge transfer caused by the adsorption of MoS2 on Sc substrate can significantly weaken the Mo-S bond strength and change the phonon properties of MoS2, which result in a significant change in thermal boundary conductance (TBC) from one lattice-stacking configuration to another for same metallic substrate. In a lattice-stacking configuration of MoS2/Sc, weakening of the Mo-S bond strength due to charge redistribution results in decrease in the force constant between Mo and S atoms and substantial redistribution of phonon density of states to low-frequency region which affects overall phonon transmission leading to 60% decrease in TBC compared to another configuration of MoS2/Sc. Strong chemical coupling between MoS2 and the Sc substrate leads to a significantly (∼19 times) higher TBC than that of the weakly bound MoS2/Au system. Our findings demonstrate the inherent connection among the interfacial electronic structure, the phonon distribution, and TBC, which helps us understand the mechanism of phonon transport at the MoS2/metal interfaces. The results provide insights for the future design of MoS2-based electronics and a way of enhancing heat dissipation at the interfaces of MoS2-based nanoelectronic devices.

Nano-cross-junction effect on phonon transport in silicon nanowire cages

Wave effects of phonons can give rise to controllability of heat conduction beyond that by particle scattering at surfaces and interfaces. In this work, we propose a new class of 3D nanostructure: a silicon-nanowire-cage (SiNWC) structure consisting of silicon nanowires (SiNWs) connected by nano-cross-junctions (NCJs). We perform equilibrium molecular dynamics (MD) simulations, and find an ultralow value of thermal conductivity of SiNWC, 0.173 Wm-1K-1, which is one order lower than that of SiNWs. By further modal analysis and atomistic Green's function calculations, we identify that the large reduction is due to significant phonon localization induced by the phonon local resonance and hybridization at the junction part in a wide range of phonon modes. This localization effect does not require the cage to be periodic, unlike the phononic crystals, and can be realized in structures that are easier to synthesize, for instance in a form of randomly oriented SiNWs network.

Controlling the thermal conductance ofgraphene/h−BNlateral interface with strain and structure engineering

Although phonon-mediated thermal conduction in pristine graphene and hexagonal boron nitride is well understood, less is known about phonon transport in single-sheet graphene-hexagonal boron nitride ($\mathrm{Gr}/h\ensuremath{-}\mathrm{BN}$) lateral heterostructures, where the thermal resistance of the interfaces plays an important role in the overall thermal conductivity. We apply the newly developed extended atomistic Green's function method to analyze with detail the effect of strain and structure engineering on the thermal conductance ${G}_{\mathrm{int}}$ of the $\mathrm{Gr}/h\ensuremath{-}\mathrm{BN}$ interface. Our calculations show that longitudinal tensile strain leads to significant ${G}_{\mathrm{int}}$ enhancement (up to $25%$ at 300 K) primarily through the improved alignment of the flexural acoustic phonon bands, despite the reduction in the longitudinal acoustic (LA) and transverse acoustic phonon velocities. In addition, we find that alternating C-N zigzag bonds along the zigzag interface lead to a greater ${G}_{\mathrm{int}}$ than C-B bonds through more effective transmission of high-frequency LA and transverse optical phonons, especially at high strain levels. We also demonstrate how the interfacial structure dramatically affects the orientation of the transmitted optical phonons, a phenomenon that is neither seen for acoustic phonons nor predictable from conventional acoustic wave scattering theory. Insights from our paper can provide the basis for manipulating the interfacial thermal conductance in other two-dimensional heterostructures.

A framework for solving atomistic phonon-structure scattering problems in the frequency domain using perfectly matched layer boundaries

We present a numerical approach to the solution of elastic phonon-interface and phonon-nanostructure scattering problems based on a frequency-domain decomposition of the atomistic equations of motion and the use of perfectly matched layer (PML) boundaries. Unlike molecular dynamic wavepacket analysis, the current approach provides the ability to simulate scattering from individual phonon modes, including wavevectors in highly dispersive regimes. Like the atomistic Green's function method, the technique reduces scattering problems to a system of linear algebraic equations via a sparse, tightly banded matrix regardless of dimensionality. However, the use of PML boundaries enables rapid absorption of scattered wave energies at the boundaries and provides a simple and inexpensive interpretation of the scattered phonon energy flux calculated from the energy dissipation rate in the PML. The accuracy of the method is demonstrated on connected monoatomic chains, for which an analytic solution is known. The parameters defining the PML are found to affect the performance and guidelines for selecting optimal parameters are given. The method is used to study the energy transmission coefficient for connected diatomic chains over all available wavevectors for both optical and longitudinal phonons; it is found that when there is discontinuity between sublattices, even connected chains of equivalent acoustic impedance have near-zero transmission coefficient for short wavelengths. The phonon scattering cross section of an embedded nanocylinder is calculated in 2D for a wide range of frequencies to demonstrate the extension of the method to high dimensions. The calculations match continuum theory for long-wavelength phonons and large cylinder radii, but otherwise show complex physics associated with discreteness of the lattice. Examples include Mie oscillations which terminate when incident phonon frequencies exceed the maximum available frequency in the embedded nanocylinder, and scattering efficiencies larger than two near the Brillouin zone edge.

Phonon transmission acrossMg2Si/Mg2Si1−xSnxinterfaces: A first-principles-based atomistic Green's function study

Phonon transmission across interfaces of dissimilar materials has been studied intensively in recent years by using atomistic simulation tools due to its importance in determining the effective thermal conductivity of nanostructured materials. The atomistic Green's function method with interatomic force constants from the first-principles calculations has evolved to be a promising approach to study phonon transmission in many material systems that have not been well studied. However, the direct first-principles calculation for interatomic force constants becomes infeasible when the system involves atomic disorder. Mass approximation is usually used, but its validity has not been tested. In this paper, we employ the higher-order force constant model to extract harmonic force constants from the first-principles calculations, which originates from the virtual crystal approximation but considers the local force-field difference. As a feasibility demonstration of the proposed method that integrates higher-order force constant model from the first-principles calculations with the atomistic Green's function, we study the phonon transmission in the ${\mathrm{Mg}}_{2}\mathrm{Si}/{\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ systems. When integrated with the atomistic Green's function, the widely used mass approximation is found to overpredict phonon transmission across the ${\mathrm{Mg}}_{2}{\mathrm{Si}/\mathrm{Mg}}_{2}\mathrm{Sn}$ interface. The difference can be attributed to the absence of local strain field-induced scattering in the mass approximation, which makes the high-frequency phonons less scattered. The frequency-dependent phonon transmission across an interface between a crystal and an alloy, which often appears in high-efficiency ``nanoparticle in alloy'' thermoelectric materials, is studied. The interfacial thermal resistance across ${\mathrm{Mg}}_{2}\mathrm{Si}/{\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ interface is found to be weakly dependent on the composition of Sn when the composition of $\mathrm{x}$ is less than 40% but increases rapidly when it is larger than 40% due to the transition of high-frequency phonon DOS in ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ alloys. This work could have a great impact on the design of novel nanostructures with tunable thermal properties.

Efficient approach for modeling phonon transmission probability in nanoscale interfacial thermal transport

The Kapitza or interfacial thermal resistance at the boundary of two different insulating solids depends on the transmission of phonons across the interface and the phonon dispersion of either material. We extend the existing atomistic Green's function (AGF) method to compute the probability for individual phonon modes to be transmitted across the interface. The extended method is based on the concept of the Bloch matrix and allows us to determine the wavelength and polarization dependence of the phonon transmission as well as to analyze efficiently the contribution of individual acoustic and optical phonon modes to interfacial thermal transport. The relationship between the phonon transmission probability and dispersion is explicitly established. A detailed description of the method is given and key formulas are provided. To illustrate the role of the phonon dispersion in interfacial thermal conduction, we apply the method to study phonon transmission and thermal transport at the armchair interface between monolayer graphene and hexagonal boron nitride. We find that the phonon transmission probability is high for longitudinal (LA) and flexural (ZA) acoustic phonons at normal and oblique incidence to the interface. At room temperature, the dominant contribution to interfacial thermal transport comes from the transverse-polarized phonons in graphene (45.5%) and longitudinal-polarized phonons in boron nitride (47.4%).

Thermally‐Active Screw Dislocations in Si Nanowires and Nanotubes

that in bulk, dislocations can lead to a signifi cant decrease in κ in the direction perpendicular to the dislocation line. The widely-used theory of Klemens [ 11 ] accounts for this result with perturbation theory, by including scattering of the phonon states (eigenstates of the harmonic crystal) on the linear and non-linear elastic strain regions localized around the dislocation line. By contrast, in SD NWs and NTs, we encounter the unexplored case of thermal transport along the dislocation line. In this work we combine modern theories based on atomistic simulations in order to understand how the thermal properties of Si NWs and NTs accommodating axial SDs with closed and opened cores might differ from the more studied pristine forms. After computing the SD NW and NT structures with objective molecular dynamics [ 12 ] (MD), we used two main methods, the direct method [ 13 ] and the atomistic Green function (AGF) method [ 14 ] (See simulation section), to reveal an important reduction in κ . This fi nding presents signifi cant interest for nanoscale thermoelectricity. We simulated a set of pristine and SD Si NWs and NTs with cubic diamond structure and hexagonal cross sections. The number of 111 layers L in the cross-section was taken to be 12, 16, 20 and 30, so that the radii of the created NWs ranged from 18.8 A to 47.1 A. Next, from the pristine L = 12 NW we created a set of (L,h) NTs, by systematically removing central atomic layers. We label by h the number of 111 inner layers that have been removed. Finally, in all these structures we introduce SDs with the axis located at the center. We considered minimal Burgers vector of magnitude b = 3.8 A and multiples of it, 2b and 3b. In 1b NWs, the created core structure is the Hornstra core, where all atoms remain fourfold coordinated. SDs twist NWs and NTs. This is the Eshelby twist [ 15 ] γ E , which is well known at the macroscale. The presence of γ E creates challenges for the atomistic simulations as it prevents the applicability of the standard periodic boundary conditions. Here, in order to fi nd optimal morphologies (corresponding to minimum energy) we used objective MD [ 12 ]

Phonon transmission and thermal conductance across graphene/Cu interface

We investigate phonon transmission and thermal boundary conductance (TBC) across graphene/Cu interface using density functional theory and atomistic Green's function method. The analysis of phonon dispersions and density of states of single layer graphene (SLG) shows that even weak SLG/Cu interaction can soften the transverse optical and longitudinal optical modes and suppress low frequency out-of-plane acoustic (ZA) modes. Our calculations predict that a small stretching of the SLG lattice (∼1.6%) significantly enhances the SLG/Cu interaction which is reflected in larger band-gap for ZA/ZO phonon mode and a remarkable increase in TBC (∼59%).