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

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

Solutions of the Peierls-Boltzmann transport equation using inputs from density functional theory calculations have been successful in predicting the thermal conductivity in a wide range of materials. In the case of two-dimensional (2D) materials, the accuracy of this method can depend highly on the shape of the dispersion curve for flexural phonon (ZA). As a universal feature, very recent theoretical studies have shown that the ZA branch of 2D materials is quadratic. However, many prior thermal conductivity studies and conclusions are based on a ZA branch with linear components. In this paper, we systematically study the impact of the long-wavelength dispersion of the ZA branch in graphene, silicene, and $\ensuremath{\alpha}$-nitrophosphorene to highlight its role on thermal conductivity predictions. Our results show that the predicted $\ensuremath{\kappa}$ value, its convergence and anisotropy, as well as phonon lifetimes and mean free path can change substantially even with small linear to pure quadratic corrections to the shape of the long-wavelength ZA branch. Also, having a pure quadratic ZA dispersion can improve the convergence speed and reduce uncertainty in this computational framework when different exchange-correlation functionals are used in the density functional theory calculations. Our findings may provide a helpful guideline for more accurate and efficient thermal conductivity estimation in mono- and few-layer 2D materials.

Importance of quadratic dispersion in acoustic flexural phonons for thermal transport of two-dimensional materials

In this paper, thermal conductivity of crystalline GaAs is calculated using first-principles lattice dynamics. The harmonic and cubic force constants are obtained by fitting them to the force-displacement data from density functional theory calculations. Phonon dispersion is calculated from dynamical matrix constructed using the harmonic force constants and phonon relaxation times are calculated using Fermi Golden rule. The calculated GaAs thermal conductivity agrees well with experimental data. Thermal conductivity accumulations as a function of phonon mean free path and as a function of wavelength are obtained. Our results predict significant size effect on the GaAs thermal conductivity in the nanoscale. Relaxation times of optical phonons and their contributions from different scattering channels are also studied. Such information will help understanding hot phonon effects in GaAs-based devices.

Gallium Arsenide Thermal Conductivity from First-Principles Calculations

Recently, a novel two-dimensional (2D) Dirac material BeN4 monolayer has been fabricated experimentally through high-pressure synthesis. In this work, we investigate the thermal properties of a new class of 2D materials with a chemical formula of MN4 (M = Be and Mg) using first-principles calculations. First, the cohesive energy and phonon dispersion curve confirm the dynamical stability of BeN4 and MgN4 monolayers. Besides, BeN4 and MgN4 monolayers have the anisotropic lattice thermal conductivities of 842.75 (615.97) W m–1 K–1 and 52.66 (21.76) W m–1 K–1 along the armchair (zigzag) direction, respectively. The main contribution of the lattice thermal conductivities of BeN4 and MgN4 monolayers are from the low frequency phonon branches. Moreover, the average phonon heat capacity, phonon group velocity, and phonon lifetime of BeN4 monolayer are 3.54 × 105 J K–1 m–3, 3.61 km s–1, and 13.64 ps, which are larger than those of MgN4 monolayer (3.42 × 105 J K–1 m–3, 3.27 km s–1, and 1.70 ps), indicating the larger lattice thermal conductivities of BeN4 monolayer. Furthermore, the mode weighted accumulative Grüneisen parameters (MWGPs) of BeN4 and MgN4 monolayers are 2.84 and 5.62, which proves that MgN4 monolayer has stronger phonon scattering. This investigation will enhance an understanding of thermal properties of MN4 monolayers and drive the applications of MN4 monolayers in nanoelectronic devices.

https://pubs.acs.org/doi/pdf/10.1021/acsomega.2c00785

Thermal Properties of 2D Dirac Materials MN4 (M = Be and Mg): A First-Principles Study

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.

Neelesh Gupta

Papers

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

Thermoelectric performance of silicene under uniform biaxial strain: A first principles study

Effect of electron–phonon coupling on transport properties of monolayer germanene: A thermoelectric perspective