† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61675032 and 11604019) and the National Basic Research Program of China (Grant No. 2014CB643900).
The electrical properties and thermoelectric (TE) properties of monolayer In-VA are investigated theoretically by combining first-principles method with Boltzmann transport theory. The ultralow intrinsic thermal conductivities of 2.64 W·m−1·K−1 (InP), 1.31 W·m−1·K−1 (InAs), 0.87 W·m−1·K−1 (InSb), and 0.62 W·m−1K−1 (InBi) evaluated at room temperature are close to typical thermal conductivity values of good TE materials (κ < 2 W·m−1·K−1). The maximal ZT values of 0.779, 0.583, 0.696, 0.727, and 0.373 for InN, InP, InAs, InSb, and InBi at p-type level are calculated at 900 K, which makes In-VA potential TE material working at medium-high temperature.
Motivated by graphene,[1] one has taken a great interest in other two-dimensional (2D) layered materials, such as hexagonal boron nitride (h-BN),[2,3] black phosphorus,[4–6] silicene,[7,8] and stanene.[9] The 2D materials often present novel and versatile electronic, optical, and mechanical properties, which make them useful in fundamental science and engineering applications. In particular, due to their unexceptionable electrical and thermal transport properties, 2D materials have shown great potential applications in thermal management, thermoelectric (TE) energy generation, and heat-to-electricity conversion.[10]
The TE properties of materials are characterized by the TE figure of merit ZT, which is defined as ZT = σS2T/κe + κl, where σ is the electric conductivity, S is the Seebeck coefficient, T is the absolute temperature, κe and κl are the electronic and lattice thermal conductivity, respectively. The power factor is defined as PF = σS2, which characterizes electric power output. Large ZT values for TE materials are significant for practical device applications. In 2007, Dragoman D and Dragoman M put forward graphene as TE material[11] with a maximum S value of 30 mV/K. After that, the potentials of 2D allotropes of group-IV (silicene, germanene, stanene) and group-V (arsenene, black and blue phosphorus) materials[12, 13] for TE applications have also been explored.
Due to an extensive range of direct band gaps and stability at high temperature, the III–V compound semiconductor family is one of the most commonly used groups of semiconductors. Bulk III–nitrides have been receiving attention as potential high-temperature TE materials.[14–19] Their thin films[20] and thin-film-based nanostructures[21] have shown enhanced in-plane TE conductivity compared with that of the corresponding bulks. An unprecedented high ZT of 1.28 at 773 K was obtained in the InSb-based alloys by optimizing the eutectic content.[22] Recently, a large number of 2D materials in group III–V family, such as AlN, GaN, and InAs, have been predicted to be structurally stable.[23–25] Experimentally, 2D H-BN[26] and h-AlN[27] have been fabricated, impelling the research of 2D III–V materials. Huang et al.[28] studied the relative peak power factors of group-III nitride (BN, AlN, and GaN) atomic sheets under strain. Among 2D group III–V materials, indium-VA possesses the smallest effective mass and the highest electron mobility, which could cause large electronic conductivities and high ZT.
While previous efforts focused on the structural and electronic properties of 2D III–V materials, TE properties of these materials are seldom studied. Therefore, in this paper, the structural, electronic, phonon and TE properties of 2D In–VA compound are investigated by first-principles method combining with Boltzmann transport approach. Among 2D In–VA, monolayer InN exhibits planar (PL) hexagonal structure like graphene while others (InX (X = P, As, Sb, and Bi)) show low buckled (LB) hexagonal structure like silicene. The InX (X = P, As, Sb, and Bi) are found to have significantly lower thermal conductivities than InN, because of the strong coupling between out-of-plane modes and in-plane modes. For TE properties, we also investigate their temperature dependence, showing that ZT values increase with temperature rising from 300 K up to 900 K. Finally, we obtain a maximal ZT value of 0.779 for PL structural InN, which is mainly determined by high power factor.
We start with investigating structural stability and electronic properties of 2D hexagonal In–VA materials by using the first-principles method as implemented in Vienna ab-initio Simulation Package (VASP)[29] code within the framework of the density functional theory (DFT). Perdew–Burke–Ernzerhof (PBE) within the generalized gradient approximation (GGA)[30] is employed to calculate the exchange–correlation potential. The cut-off energy is set to be 400 eV. A Monkhorst–Pack k-mesh of 30 × 30 × 1 is used to sample the Brillouin zone (BZ) in reciprocal space during structural relaxation for the unit cell, with limiting to an energy convergence precision of 1 × 10−8 eV and a force convergence precision of 1 × 10−6 eV/Å. For electronic properties, a denser k-point grid of 40 × 40 × 1 is employed after structural optimization.
In order to identify the dynamical stabilities of 2D hexagonal In–VA materials, we calculate their phonon spectra based on the force-constant approach with the package of Phonopy.[31] We compute the second-order harmonic interatomic force constants (IFCs)[32] by using the 7 × 7 × 1 supercells with k-point meshes of 5 × 5 × 1. The electronic coefficients are calculated by using semi-classical Boltzmann transport theory with the relaxation time approximation as implemented in the BoltzTraPl.[33] We obtain the Seebeck coefficient S which is independent of the relaxation time τ, the electrical conductivity σ and the electronic thermal conductivity κe which are are divided by relaxation time τ. By applying ShengBTE code,[34] we calculate the third-order anharmonic IFCs. The supercells are defined as 6 × 6 × 1 containing 72 atoms with k-point meshes of 5 × 5 × 1.
We cleave the initial structures of the 2D In–VA materials from the (110) face of the ZB semiconductor In–VA compounds. The atomic structures and lattice constants of the cleaved 2D structures then are both fully optimized. Figure
Figure
The calculated band structures of single-layer In–VA and their corresponding total densities of states (DOSs) are plotted in Figs.
Figure
The dynamical stability of the hexagonal 2D In–VA is determined by the phonon spectra shown in Fig.
According to the calculated electronic structures, we are able to evaluate the electronic transport coefficients by using the Boltzmann transport equation within constant relaxation time approximation. The Seebeck coefficient S can be calculated to be independent of the relaxation time τ, while the electrical conductivity σ is divided by τ, so what we obtain is σ/τ. The relaxation time is usually obtained by fitting to the experimental data.[42] Since there are no clear experimental values against which these compounds can be measured, we assume τ = 2 × 10−14 s in the present calculations, which is reasonable.[43] The Seebeck coefficient S and electrical conductivity σ are given by[44, 45]
The Seebeck coefficients of the single-layer In–VA as a function of chemical potential (μ) at different temperatures are plotted in Fig.
In Fig.
In Fig.
The electronic thermal conductivity is addressed in Fig.
Next, we will investigate the doping effect on the thermal transport property of the In–VA monolayer. The intrinsic lattice thermal conductivities of the single-layered In–VA at different temperatures are estimated by using the ShengBTE[35] code based on the phonon Boltzmann transport equation, and the results are shown in Fig.
With all the transport coefficients available, ZT values of the single-layered In–VA as a function of chemical potential at different temperatures are obtained as shown in Fig.
In order to investigate TE properties and their temperature relationships of In–VA more intuitively, we plot Seebeck coefficients, electrical conductivities, PF trend, ZT values versus temperature at a carrier density of 4.8 × 1020 cm−3 as shown in Fig.
Figure
The ZT values as a function of temperature are shown in Fig.
Using ab initio calculations, electronic properties of In–VA in monolayer form are studied, and TE properties are analyzed by using Boltzmann transport equations for the electrons and phonons. The TE response of InN turns out to be superior to those of InX (X = N, P, As, Sb, Bi), and the origin of this difference is ascertained to be relevant to the structural and electronic properties. The ultralow intrinsic thermal conductivities of 2.64 W⋅m−1⋅K−1 (InP), 1.31 W⋅m−1K−1 (InAs), 0.87 W⋅m−1⋅K−1 (InSb), and 0.62 Wm−1⋅K−1 (InBi) evaluated at room temperature are close to the typical thermal conductivities of good TE materials (κ < 2 W⋅m−1⋅K−1). The high figures of merit of monolayer In–VA in a wide temperature range are interesting from the point of view of application. The present study not only provides various unexpected properties of In–VA, but also gives the hints that it could be used to explore the TE effects of the 2D III–V materials.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] | |
[40] | |
[41] | |
[42] | |
[43] | |
[44] | |
[45] | |
[46] |