scholarly journals Nanoscale Quantum Thermal Conductance at Water Interface: Green’s Function Approach Based on One-Dimensional Phonon Model

Molecules ◽  
2020 ◽  
Vol 25 (5) ◽  
pp. 1185
Author(s):  
Toshihito Umegaki ◽  
Shigenori Tanaka
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Transmission Probability ◽  
Phonon Transport ◽  
Tunnel Effect ◽  
Water Molecules ◽  
One Dimensional ◽  
Phonon Model

We have derived the fundamental formula of phonon transport in water for the evaluation of quantum thermal conductance by using a one-dimensional phonon model based on the nonequilibrium Green’s function method. In our model, phonons are excited as quantum waves from the left or right reservoir and propagate from left to right of H 2 O layer or vice versa. We have assumed these reservoirs as being of periodic structures, whereas we can also model the H 2 O sandwiched between these reservoirs as having aperiodic structures of liquid containing N water molecules. We have extracted the dispersion curves from the experimental absorption spectra of the OH stretching and intermolecular modes of water molecules, and calculated phonon transmission function and quantum thermal conductance. In addition, we have simplified the formulation of the transmission function by employing a case of one water molecule (N=1). From this calculation, we have obtained the characteristic that the transmission probability is almost unity at the frequency bands of acoustic and optical modes, and the transmission probability vanishes by the phonon attenuation reflecting the quantum tunnel effect outside the bands of these two modes. The classical limit of the thermal conductance calculated by our formula agreed with the literature value (order of 10 − 10 W/K) in high temperature regime (>300 K). The present approach is powerful enough to be applicable to molecular systems containing proteins as well, and to evaluate their thermal conductive characteristics.

Simulation of Interfacial Phonon Transport in Si–Ge Heterostructures Using an Atomistic Green’s Function Method

2006 ◽  
Vol 129 (4) ◽  
pp. 483-491 ◽  
Author(s):  
W. Zhang ◽  
T. S. Fisher ◽  
N. Mingo
Keyword(s):  
Thin Film ◽  
Thermal Resistance ◽  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Phonon Transport ◽  
Silicon Thin Film ◽  
Green’S Function Method

An atomistic Green’s function method is developed to simulate phonon transport across a strained germanium (or silicon) thin film between two semi-infinite silicon (or germanium) contacts. A plane-wave formulation is employed to handle the translational symmetry in directions parallel to the interfaces. The phonon transmission function and thermal conductance across the thin film are evaluated for various atomic configurations. The contributions from lattice straining and material heterogeneity are evaluated separately, and their relative magnitudes are characterized. The dependence of thermal conductance on film thickness is also calculated, verifying that the thermal conductance reaches an asymptotic value for very thick films. The thermal boundary resistance of a single Si∕Ge interface is computed and agrees well with analytical model predictions. Multiple-interface effects on thermal resistance are investigated, and the results indicate that the first few interfaces have the most significant effect on the overall thermal resistance.

Simulation of Phonon Transmission Through Graphene With a Green’s Function Method

2009 ◽  
Author(s):  
Zhen Huang ◽  
Timothy Fisher ◽  
Jayathi Murthy
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
First Principles ◽  
Nearest Neighbor ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Phonon Transport ◽  
Future Research ◽  
First Principles Calculations ◽  
Best Fit

In this paper, phonon transmission through a graphene sheet is investigated using an atomistic Green’s function (AGF) method. Reported best-fit results from first-principles calculations using a 4th nearest neighbor force-constant (4NNFC) model are used to establish the matrices that describe the interactions among carbon atoms. Calculations reveal that graphene dispersion curves so obtained are in good agreement with experiments as well as other published first-principles calculations. The effect of carbon isotopes on thermal conductance is investigated, and the results reveal that isotopic doping moderately reduces both phonon transmission function and thermal conductance. The phonon transmission function of each vibrational branch in the heterogeneous interface is also calculated based on a method described in recent work, and comparisons indicate the major and minor channels of phonon transport through graphene. The results herein offer a useful reference and suggest directions for future research on thermal applications of this material.

Simulation of Phonon Transmission at Semiconductor Interfaces Using an Atomistic Green’s Function Method

2008 ◽  
Author(s):  
Lin Sun ◽  
Jayathi Y. Murthy ◽  
Zhen Huang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Local Density ◽  
Cutoff Frequency ◽  
Transmission Function ◽  
Phonon Transport ◽  
Atomic Scale ◽  
Rough Interface ◽  
Green’S Function Method

An atomistic Green’s function method is applied to study phonon transport across interfaces between two semi-infinite semiconductors. We investigate the dependence of phonon transmission function on interface atomic configuration, roughness layer thickness and phonon frequency. The transmission function is obtained for a number of interface configurations, including Si/Ge/Si confined structures and a single Si/Ge interface. An interface with a regularly-patterned roughness is investigated to illustrate how the rough interface influences phonon transmission. The results show that the cutoff frequency and the local density of states are modified due to the rough interface. The transmission function is found to strongly dependent on the presence of atomic-scale roughness.

Thermal transport of small systems

2017 ◽  
Author(s):  
Takahiro Yamamoto ◽  
Kazuyuki Watanabe ◽  
Satoshi Watanabe
Keyword(s):  
Thermal Transport ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Fourier Law ◽  
Small Systems ◽  
One Dimensional ◽  
Sample Dimension ◽  
The Mean

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

Electron transport through two one-dimensional multi-quantum dot arrays coupled to four leads

2018 ◽  
Vol 32 (27) ◽  
pp. 1850333 ◽  
Author(s):  
Zelong He ◽  
Kongfa Chen ◽  
Mengchun Lu ◽  
Qiang Li
Keyword(s):  
Quantum Dots ◽  
Quantum Dot ◽  
Green’S Function ◽  
Green's Function ◽  
Energy Levels ◽  
Transmission Probability ◽  
Function Technique ◽  
One Dimensional ◽  
Resonance Band ◽  
Dc Current

Employing the non-equilibrium Green’s function technique, we have obtained the formula for dc current of two one-dimensional multi-quantum dot arrays, which couple to each other via tunneling coupling between two quantum dots connected to four leads, respectively. The retarded Green’s function is a staircase type, terminating at the four leads. Furthermore, the four quantum dots case is demonstrated. The influence of inter-dot coupling strength and quantum dot energy level on the transmission probability for TL, TM and TN branches is investigated. A non-resonant band is observed. By adjusting energy levels of quantum dots, a resonance emerges in the region of the non-resonance band. The system can be used as a quantum switch.

scholarly journals Predicting Phonon Thermal Conductance at Atomic Junctions: Nonequilibrium Green’s Function Approach Compared to Semiclassical Methods

2008 ◽  
Author(s):  
Patrick E. Hopkins ◽  
Pamela M. Norris ◽  
Mikiyas S. Tsegaye ◽  
Avik W. Ghosh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Transport Theory ◽  
Thermal Conductance ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Nonequilibrium Green's Function ◽  
Quantum Transport Theory ◽  
Nonequilibrium Green’S Function ◽  
Phonon Thermal Conductance

Phonon thermal conductance, λ, in nanostructures is a thermophysical property that is becoming increasingly difficult to accurately predict, especially as thermal management at interfaces of different materials is becoming a major engineering concern. The most widely used models for λ prediction are based on the Boltzmann Transport Equation (BTE), and the when junctions between two different materials enter the picture, the most common BTE-based models to predict the interfacial conductance are the Acoustic Mismatch Model (AMM) and Diffuse Mismatch Model (DMM). The models are developed with equilibrium assumptions. However, thermal transport is clearly nonequilibrium phenomenon. Recently, the Nonequilibrium Green’s Function (NEGF) formalism has been extended to phonon transport. The NEGF formalism is rooted in nonequilibrium quantum transport theory, making it ideal to study energy transfer applications, especially in nanosystems where the concept of thermal equilibrium breaks down due to the small dimensions of the transport regions. The purpose of this paper is to derive, from first principles, the NEGF formalism of thermal conductivity, and compare the assumptions of this formalism to the semi-classical Boltzmann models. The NEGF formalism is applied to a 1D atomic chain with varying masses and compared to similar predictions from BTE-based models.

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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