The role of dimensionality on the electronic performance of thermoelectric devices is clarified using the Landauer formalism, which shows that the thermoelectric coefficients are related to the transmission, T(E), and how the conducing channels, M(E), are distributed in energy. The Landauer formalism applies from the ballistic to diffusive limits and provides a clear way to compare performance in different dimensions. It also provides a physical interpretation of the "transport distribution," a quantity that arises in the Boltzmann transport equation approach. Quantitative comparison of thermoelectric coefficients in one, two, and three dimension shows that the channels may be utilized more effectively in lower-dimensions. To realize the advantage of lower dimensionality, however, the packing density must be very high, so the thicknesses of the quantum wells or wires must be small. The potential benefits of engineering M(E) into a delta-function are also investigated. When compared to a bulk semiconductor, we find the potential for ~50 % improvement in performance. The shape of M(E) improves as dimensionality decreases, but lower dimensionality itself does not guarantee better performance because it is controlled by both the shape and the magnitude of M(E). The benefits of engineering the shape of M(E) appear to be modest, but approaches to increase the magnitude of M(E) could pay large dividends.

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Influence of Dimensionality on Thermoelectric Device Performance

Thermoelectric properties of γ-graphyne from first-principles calculations

We uncover the constitutive relation of graphene and probe the physics of its optical phonons by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly degenerate E(2g) optical mode splits in two components: one polarized along the strain and the other perpendicular. This splits the G peak into two bands, which we call G(+) and G(-), by analogy with the effect of curvature on the nanotube G peak. Both peaks redshift with increasing strain and their splitting increases, in excellent agreement with first-principles calculations. Their relative intensities are found to depend on light polarization, which provides a useful tool to probe the graphene crystallographic orientation with respect to the strain. The 2D and 2D(') bands also redshift but do not split for small strains. We study the Gruneisen parameters for the phonons responsible for the G, D, and D(') peaks. These can be used to measure the amount of uniaxial or biaxial strain, providing a fundamental tool for nanoelectronics, where strain monitoring is of paramount importance.

Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation

Effect of polystyrene grafted graphene nanoplatelets on the physical and chemical properties of asphalt binder

The two-dimensional graphene-like carbon allotrope, graphyne, has been recently fabricated and exhibits many interesting electronic properties. In this work, we investigate the thermoelectric properties of {\gamma}-graphyne by performing first-principles calculations combined with Boltzmann transport theory for both electron and phonon. The carrier relaxation time is accurately evaluated from the ultra-dense electron-phonon coupling matrix elements calculated by adopting the density functional perturbation theory and Wannier interpolation, rather than the generally used deformation potential theory which only considers the electron-acoustic phonon scattering. It is found that the thermoelectric performance of {\gamma}-graphyne exhibits a strong dependence on the temperature and carrier type. At an intermediate temperature of 600 K, a maximum ZT value of 1.5 and 1.0 can be achieved for the p- and n-type systems, respectively.

Thermoelectric properties of graphyne from first-principles calculations

We investigate the thermoelectric (TE) figure-of-merit of a single-layer graphene (SLG) sheet by a physics-based analytical technique. We first develop analytical models of electrical and thermal resistances and the Seebeck coefficient of SLG by considering electron interactions with the in-plane and flexural phonons. Using those models, we show that both the figure-of-merit and the TE efficiency can be substantially increased with the addition of isotope doping as it significantly reduces the phonon-dominated thermal conductivity. In addition, we report that the TE open circuit output voltage and output power depends weakly on the SLG sheet dimensions and sheet concentration in the strongly diffusive regime. Proposed models agree well with the available experimental data and demonstrate the immense potential of graphene for waste-heat recovery application.

Thermoelectric Performance of a Single-Layer Graphene Sheet for Energy Harvesting

In this paper, we address a physics-based analytical model of electric-field-dependent electron mobility (μ) in a single-layer graphene sheet using the formulation of Landauer and Mc Kelvey's carrier flux approach under finite temperature and quasi-ballistic regime. The energy-dependent, near-elastic scattering rate of in-plane and out-of-plane (flexural) phonons with the electrons are considered to estimate μ over a wide range of temperature. We also demonstrate the variation of μ with carrier concentration as well as the longitudinal electric field. We find that at high electric field , the mobility falls sharply, exhibiting the scattering between the electrons and flexural phonons. We also note here that under quasi-ballistic transport, the mobility tends to a constant value at low temperature, rather than in between T-2 and T-1 in strongly diffusive regime. Our analytical results agree well with the available experimental data, while the methodologies are put forward to estimate the other carrier-transmission-dependent transport properties.

Modeling of Temperature and Field-Dependent Electron Mobility in a Single-Layer Graphene Sheet

In this paper, we address a closed-form analytical solution of the Joule-heating equation for metallic single-walled carbon nanotubes (SWCNTs). Temperature-dependent thermal conductivity κ has been considered on the basis of second-order three-phonon Umklapp, mass difference, and boundary scattering phenomena. It is found that κ , in case of pure SWCNT, leads to a low rising in the temperature profile along the via length. However, in an impure SWCNT, κ reduces due to the presence of mass difference scattering, which significantly elevates the temperature. With an increase in impurity, there is a significant shift of the hot spot location toward the higher temperature end point contact. Our analytical model, as presented in this study, agrees well with the numerical solution and can be treated as a method for obtaining an accurate analysis of the temperature profile along the CNT-based interconnects.

Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects

In this paper, we investigate the thermoelectric transport coefficients namely the Seebeck coefficient, the electrical conductivity, the electronic thermal conductivity and the lattice thermal conductivity using first-principles calculations in density functional theory. We also estimate the figure-of-merit for both intrinsic as well as extrinsic low-buckled monolayer silicene. Using Electron-Phonon Wannier function, we calculate the average scattering time in the reduced Brillouin zone as a function of temperature. The scattering time of electrons in the conduction band is found to be slightly higher than that of holes in the valence band. Also, the out-of-plane acoustic phonon modes scatter more strongly than the in-pane acoustic modes and hence contributes less in lattice thermal conductivity. We observe that the lattice thermal conductivity of monolayer intrinsic silicene comes out of the order of 9.2 W m − 1 K − 1 and the figure-of-merit in n-type material is almost twice to that of the p-type at around 1200 K. We compare the results obtained with HSE06 hybrid functional and PBE functional and find that there is a significant improvement in the values of those transport coefficients calculated using HSE06.

First-principles study of thermoelectric transport properties in low-buckled monolayer silicene

In this paper, we address a physics-based closed-form analytical model of flexural phonon-dependent diffusive thermal conductivity (kappa) of suspended rectangular single layer graphene sheet. A quadratic dependence of the out-of-plane phonon frequency, generally called flexural phonons, on the phonon wave vector has been taken into account to analyze the behavior of kappa at lower temperatures. Such a dependence has further been used for the determination of second-order three-phonon Umklapp and isotopic scatterings. We find that these behaviors in our model are best explained through the upper limit of Debye cut-off frequency in the second-order three-phonon Umklapp scattering of the long phonon waves that actually remove the thermal conductivity singularity by contributing a constant scattering rate at low frequencies and note that the out-of-plane Gruneisen parameter for these modes need not be too high. Using this, we clearly demonstrate that. follows a T-1.5 and T-2 law at lower and higher temperatures in the absence of isotopes, respectively. However in their presence, the behavior of kappa sharply deviates from the T-2 law at higher temperatures. The present geometry-dependent model of kappa is found to possess an excellent match with various experimental data over a wide range of temperatures which can be put forward for efficient electro-thermal analyses of encased/supported graphene.

http://iopscience.iop.org/article/10.1088/0268-1242/28/1/015009/pdf

Rekha Verma

Papers

Thermoelectric Performance of a Single-Layer Graphene Sheet for Energy Harvesting

Modeling of Temperature and Field-Dependent Electron Mobility in a Single-Layer Graphene Sheet

Analytical Solution of Joule-Heating Equation for Metallic Single-Walled Carbon Nanotube Interconnects

First-principles study of thermoelectric transport properties in low-buckled monolayer silicene

A physics-based flexural phonon-dependent thermal conductivity model for single layer graphene