Strain-induced modification in thermal properties of monolayer 1 T-ZrS2 and ZrS2/ZrSe2 heterojunction

CONTEXT

This paper systematically analyzes the phonon dispersion curves of single-layer ZrS2, ZrSe2, and ZrS2/ZrSe2 heterostructures under different strains. The phonon spectra and thermal parameters of the three structures were obtained based on the density functional perturbation theory method. The upper limits of strain that different monolayers and heterojunctions can withstand were studied. The monolayers ZrSe2 and ZrS2 can withstand up to 8% biaxial tensile strain, and the ZrS2/ZrSe2 heterojunction can withstand up to 6% biaxial tensile strain. In addition, the van der Waals force of the heterojunction may cause phonon tearing in the vertical direction. The application of biaxial tensile strain can adjust the thermal properties of the system to a large extent, which is similar to the strain effect in the pristine case. When the temperature rises, the entropy enthalpy of the three structures also gradually increases, the free energy gradually decreases, and the heat capacity of the system gradually increases until it tends to be stable. Taking single-layer ZrS2 as an example, we analyzed the change curve of thermal properties of single-layer ZrS2 under tensile strain. The results show that with the gradual increase of strain, the crystal's entropy, enthalpy, and free energy change differently. In addition, the heat capacity increases slowly under high temperatures. When all systems reach the limit strain, the phonon spectrum appears to have an imaginary frequency, and the thermal properties decrease significantly.

METHODS

This paper uses the first-principle calculation method based on density functional theory, and the PBE exchange-correlation function based on generalized gradient approximation (GGA) is selected for a specific calculation. The density functional perturbation theory (DFPT) calculates the full kinetic matrix. Because the lattice constants of ZrS2 and ZrSe2 are similar and have similar periodicity, the corresponding unit cells are used for structural optimization and property calculation. The Brillouin zone is integrated using the K points generated by the Monkhorst-pack method. For single-layers ZrS2 and ZrSe2, 8 × 8 × 1 K-point grid is selected, and for ZrS2/ZrSe2 heterojunction, 8 × 8 × 2 K-point grid is selected. A vacuum layer of 30 Å was added in the vertical direction to avoid interlayer interaction. The non-conservative pseudopotential method is used to optimize the structure, and the optimization convergence is set as follows: the cutoff energy is set to 700 eV, the convergence threshold of the maximum force between atoms is 0.01 eV/Å, the convergence threshold of the maximum energy change is set to 1 × 10-9 eV, and the convergence threshold of the maximum displacement is 0.001 Å.

First-Principles Investigation of Simultaneous Thermoelectric Power Generation and Active Cooling in a Bifunctional Semimetal ZrSeTe Janus Structure

Traditional thermoelectric materials often face a trade-off between efficient power generation (high ZT) and cooling performance. Here, we explore the potential of achieving simultaneous thermoelectric power generation and cooling capability in the recently fabricated bulk ZrSeTe Janus structure using first-principles density functional theory (DFT). The layered ZrSeTe Janus structure exhibits a semimetal character with anisotropic transport properties along the in-plane and out-of-plane directions. Our DFT calculations, including the explicit calculation of relaxation time, reveal a maximum ZT of ~0.065 in the out-of-plane direction at 300 K which is one order of magnitude larger than that in the in-plane direction (ZT~0.006). Furthermore, the thermoelectric cooling performance is also investigated. The in-plane direction shows a cooling performance of 13 W/m·K and a coefficient of performance (COPmax) of ~90 with a temperature difference (ΔT) of 30 K, while the out-of-plane direction has a cooling performance of 2.5 W/m·K and COPmax of ~2.5. Thus, the out-of-plane current from the thermoelectric power generation can be utilized as an in-plane current source for active heat pumping. Consequently, we propose that the semimetal ZrSeTe Janus structure can display bifunctional thermoelectric properties for simultaneous thermoelectric power generation and active cooling.

Lattice Transformation from 2D to Quasi 1D and Phonon Properties of Exfoliated ZrS2 and ZrSe2

Recent reports on thermal and thermoelectric properties of emerging 2D materials have shown promising results. Among these materials are Zirconium-based chalcogenides such as zirconium disulfide (ZrS₂ ), zirconium diselenide (ZrSe₂ ), zirconium trisulfide (ZrS₃ ), and zirconium triselenide (ZrSe₃ ). Here, the thermal properties of these materials are investigated using confocal Raman spectroscopy. Two different and distinctive Raman signatures of exfoliated ZrX₂ (where X = S or Se) are observed. For 2D-ZrX₂ , Raman modes are in alignment with those reported in literature. However, for quasi 1D-ZrX₂ , Raman modes are identical to exfoliated ZrX₃ nanosheets, indicating a major lattice transformation from 2D to quasi-1D. Raman temperature dependence for ZrX₂ are also measured. Most Raman modes exhibit a linear downshift dependence with increasing temperature. However, for 2D-ZrS₂ , a blueshift for A1g mode is detected with increasing temperature. Finally, phonon dynamics under optical heating for ZrX₂ are measured. Based on these measurements, the calculated thermal conductivity and the interfacial thermal conductance indicate lower interfacial thermal conductance for quasi 1D-ZrX₂ compared to 2D-ZrX₂ , which can be attributed to the phonon confinement in 1D. The results demonstrate exceptional thermal properties for Zirconium-based materials, making them ideal for thermoelectric device applications and future thermal management strategies.

Janus zirconium halide ZrXY (X, Y = Br, Cl and F) monolayers with high lattice thermal conductivity and strong visible-light absorption

In this work, the structural, mechanical, and electronic properties of Janus zirconium halide monolayers have been systematically investigated using the first-principles calculations. After verifying the mechanical and dynamical stability of these monolayers, their electronic band structures have been predicted. These Janus monolayers have band gaps of 1.51-1.96 eV, which indicates their suitability for visible light absorption. The relaxation time and mobility of charge carriers are estimated using deformation potential theory, and the mobility of these monolayers has been predicted to be of the order ∼10² cm² V^-1 s^-1. The lattice thermal conductivity has been calculated by solving the phonon Boltzmann transport equation using ShengBTE software. At 300 K, the in-plane lattice thermal conductivity has values of 76.94, 54.18, and 95.87 W m^-1 K^-1 for ZrBrCl, ZrBrF, and ZrClF monolayers, respectively. The higher group velocity and small anharmonic three-phonon scattering rate are the main reasons for the high lattice thermal conductivity of the ZrClF monolayer. The real and imaginary parts of the dielectric function are calculated to find the absorption coefficients and these monolayers have a high absorption coefficient of the order ∼10⁶ cm^-1 in the visible light range. Our results show that Janus zirconium halide monolayers are potential candidates for optoelectronic and photocatalytic applications.

Recent progress of two-dimensional heterostructures for thermoelectric applications

The rapid development of synthesis and fabrication techniques has opened up a research upsurge in two-dimensional (2D) material heterostructures, which have received extensive attention due to their superior physical and chemical properties. Currently, thermoelectric energy conversion is an effective means to deal with the energy crisis and increasingly serious environmental pollution. Therefore, an in-depth understanding of thermoelectric transport properties in 2D heterostructures is crucial for the development of micro-nano energy devices. In this review, the recent progress of 2D heterostructures for thermoelectric applications is summarized in detail. Firstly, we systematically introduce diverse theoretical simulations and experimental measurements of the thermoelectric properties of 2D heterostructures. Then, the thermoelectric applications and performance regulation of several common 2D materials, as well as in-plane heterostructures and van der Waals heterostructures, are also discussed. Finally, the challenges of improving the thermoelectric performance of 2D heterostructures materials are summarized, and related prospects are described.

Proximity induced longitudinal and transverse thermoelectric response in graphene-ferromagnetic CrBr3vdW heterostructure

The integration of longitudinal and transverse thermoelectric (TE) fosters various new opportunities in tuning the charge transport behaviour and opens a platform for efficient thermopower devices. The presence of asymmetric electronic structure supposed to accomplish large thermopower and electronic figure of merit. Herein, we investigate magnetic proximity coupled longitudinal and transverse TE behaviour in heterostructure of monolayer semimetal, graphene and a monolayer ferromagnet, CrBr₃under the framework ofab initio-based calculations and employed constant relaxation time approximation (CRTA).The integrated density of states is elevated and asymmetric near Fermi energy region due to seamless proximity integration, depicting mixed character of graphene and CrBr₃. The asymmetric nature of electronic structure significantly affects the Seebeck coefficients (S) and electrical conductivity (σ/τ) of heterostructure. The consistent step-like conductance spectrum influences interfacial polarization due to agile proximity integration. The magnitude of Seebeck coefficient (S) is found to be 653µV K^-1near Fermi level. The heterostructure observes higher electrical conductivity and power factor in n-type region of the order of 10⁶S m^-1and 10²⁰cm^-3at room temperature. The dimensionless electronic figure of merit (zT_e) advocates the heterostructure system to be an ideal TE material. Alongside longitudinal TE, we also find the heterostructure system is sensitive to anomalous Nernst effect (ANE) (transverse TE) with oscillatory nature. The Seebeck and ANE shows high degree of tunability with applied external electric field. The synergistic existence of Seebeck and ANE due to proximity integration in van der Waals atomic crystal at room temperature will provide realistic approach to experimentally fabricate and develop real-time thermopower devices.

First principles study on structural, electronic and optical properties of HfS2(1-x)Se2x and ZrS2(1-x)Se2x ternary alloys

Alloying 2D transition metal dichalcogenides (TMDs) with dopants to achieve ternary alloys is as an efficient and scalable solution for tuning the electronic and optical properties of two-dimensional materials. This study provides a comprehensive study on the electronic and optical properties of ternary HfS_2(1−x)Se_2(x) and ZrS_2(1−x)Se_2(x) [0 ≤ x ≤ 1] alloys, by employing density functional theory calculations along with random phase approximation. Phonon dispersions were also obtained by using density functional perturbation theory. The results indicate that both of the studied ternary families are stable and the increase of Selenium concentration in HfS_2(1−x)Se_2(x) and ZrS_2(1−x)Se_2(x) alloys results in a linear decrease of the electronic bandgap from 2.15 (ev) to 1.40 (ev) for HfS_2(1−x)Se_2(x) and 1.94 (ev) to 1.23 (ev) for ZrS_2(1−x)Se_2(x) based on the HSE06 functional. Increasing the Se concentration in the ternary alloys results in a red shift of the optical absorption spectra such that the main absorption peaks of HfS_2(1−x)Se_2(x) and ZrS_2(1−x)Se_2(x) cover a broad visible range from 3.153 to 2.607 eV and 2.405 to 1.908 eV, respectively. The studied materials appear to be excellent base materials for tunable electronic and optoelectronic devices in the visible range.

Adding Selenium to HfS₂ and ZrS₂ two-dimensional materials allows tuning the optical properties in a wide visible spectrum that can be used in various electronic and optical applications, including solar cells.

Strain-induced enhancement in the electronic and thermal transport properties of the tin sulphide bilayer

The enhancement in the thermoelectric figure of merit (ZT) of a material is limited by the interplay between the electronic transport coefficients. Here we report the greatly enhanced thermoelectric performance of the SnS bilayer with the application of isotropic strain, due to the simultaneous increase in the Seebeck coefficient and low lattice thermal conductivities. Based on first-principles calculations combined with Boltzmann transport theory, we predict that the band structure of the SnS bilayer can be effectively tuned using the strain, and the Seebeck coefficient is significantly improved for the tensile strain. The lattice thermal conductivities for the bilayer under the tensile strain are quite low (0.21-1.89 W m^-1 K^-1 at 300 K) due to the smaller frequencies of the acoustic phonon modes. Along the zigzag (armchair) direction, the room temperature peak ZT value of 4.96 (2.40) is obtained at a strain of 2% (4%), which is 5.3 (2.03) times higher than the peak ZT of the unstrained bilayer along the zigzag (armchair) direction. Thus the strain-tuned SnS bilayer is a good thermoelectric material with low lattice thermal conductivities and promising ZT values at room temperature.

Improved Thermoelectric Performance of Monolayer HfS2 by Strain Engineering

Strain engineering can effectively improve the energy band degeneracy of two-dimensional transition metal dichalcogenides so that they exhibit good thermoelectric properties under strain. In this work, we have studied the phonon, electronic, thermal, and thermoelectric properties of 1T-phase monolayer HfS2 with biaxial strain based on first-principles calculations combined with Boltzmann equations. At 0% strain, the results show that the lattice thermal conductivity of monolayer HfS2 is 5.01 W m-1 K-1 and the electronic thermal conductivities of n-type and p-type doped monolayer HfS2 are 2.94 and 0.39 W m-1 K-1, respectively, when the doping concentration is around 5 × 1012 cm-2. The power factors of the n-type and p-type doped monolayer HfS2 are different, 29.4 and 1.6 mW mK-2, respectively. Finally, the maximum ZT value of the n-type monolayer HfS2 is 1.09, which is higher than 0.09 of the p-type monolayer HfS2. Under biaxial strain, for n-type HfS2, the lattice thermal conductivity, the electronic thermal conductivity, and the power factor are 1.55 W m-1 K-1, 1.44 W m-1 K-1, and 22.9 mW mK-2 at 6% strain, respectively. Based on the above factor, the ZT value reaches its maximum of 2.29 at 6% strain. For p-type HfS2, the lattice thermal conductivity and the electronic thermal conductivity are 1.12 and 1.53 W m-1 K-1 at 7% strain, respectively. Moreover, the power factor is greatly improved to 29.5 mW mK-2. Finally, the maximum ZT value of the p-type monolayer HfS2 is 3.35 at 7% strain. It is obvious that strain can greatly improve the thermoelectric performance of monolayer HfS2, especially for p-type HfS2. We hope that the research results can provide data references for future experimental exploration.

Ultra-low lattice thermal conductivity and giant phonon-electric field coupling in hafnium dichalcogenide monolayers

Phonons in crystalline solids are of utmost importance in governing its lattice thermal conductivity (k L). In this work, k L in hafnium (Hf) dichalcogenide monolayers has been investigated based on ab initio DFT coupled to linearized Boltzmann transport equation together with single-mode relaxation-time approximation. Ultra-low k L found in HfS2 (2.19 W m-1 K-1), HfSe2 (1.23 W m-1 K-1) and HfSSe (1.78 W m-1 K-1) monolayers at 300 K, is comparable to that of the state-of-art bulk thermoelectric materials, such as, Bi2Te3 (1.6 W m-1 K-1), PbTe (2.2 W m-1 K-1) and SnSe (2.6 W m-1 K-1). Gigantic longitudinal-transverse optical (LO-TO) splitting of up to 147.7 cm-1 is noticed at the Brillouin zone-centre (Γ-point), which is much higher than that in MoS2 single layer (∼2 cm-1). It is driven by the colossal phonon-electric field coupling arising from the domination of ionic character in the interatomic bonds and Born effective or dynamical charges as high as 7.4e on the Hf ions, which is seven times that on Mo in MoS2 single layer. Enhancement in k L occurs in HfS2 (2.19 to 4.1 W m-1 K-1), HfSe2 (1.23 to 1.7 W m-1 K-1) and HfSSe (1.78 to 2.2 W m-1 K-1) upon the incorporation of the non-analytic correction term. Furthermore, the mode Grüneisen parameter is calculated to be as high as ∼2.0, at room temperature, indicating a strong anharmonicity. Moreover, the contribution of optical phonons to k L is found to be ∼12%, which is significantly high than that in single-layer MoS2. Large atomic mass of Hf (178.5 u), small phonon group velocities (4-5 km s-1), low Debye temperature (∼166 K), low bond and elastic stiffness (Young's modulus ∼75 N m-1), small phonon lifetimes (∼6 ps), low specific heat capacity (∼17 J K-1 mol-1) and strong anharmonicity are collectively found to be the factors responsible for such a low k L. These findings would be immensely helpful in designing thermoelectric interconnects at the nanoscale and 2D material-based energy harvesters.

Optical and Thermoelectric Properties of Surface-Oxidation Sensitive Layered Zirconium Dichalcogenides ZrS2−xSex (x = 0, 1, 2) Crystals Grown by Chemical Vapor Transport

In this work, structure, optical, and thermoelectric properties of layered ZrS2−xSex single crystals with selenium composition of x = 0, 1, and 2 were examined. Single crystals of zirconium dichalcogenides layer compounds were grown by chemical vapor transport method using I2 as the transport agent. X-ray diffraction (XRD) and high-resolution transmission electron microscope (HRTEM) results indicated that ZrS2−xSex (x = 0, 1, and 2) were crystalized in hexagonal CdI2 structure with one-layer trigonal (1T) stacking type. X-ray photoelectron and energy dispersive X-ray measurements revealed oxidation sensitive behavior of the chalcogenides series. Transmittance and optical absorption showed an indirect optical gap of about 1.78 eV, 1.32 eV, and 1.12 eV for the ZrS2−xSex with x = 0, 1, and 2, respectively. From the result of thermoelectric experiment, ZrSe2 owns the highest figure-of merit (ZT) of ~0.085 among the surface-oxidized ZrS2−xSex series layer crystals at 300 K. The ZT values of the ZrS2−xSex (x = 0, 1, and 2) series also reveal increase with the increase of Se content owing to the increase of carrier concentration and mobility in the highly Se-incorporated zirconium dichalcogenides with surface states.

Interfacing Boron Monophosphide with Molybdenum Disulfide for an Ultrahigh Performance in Thermoelectrics, Two-Dimensional Excitonic Solar Cells, and Nanopiezotronics

A stable ultrathin 2D van der Waals (vdW) heterobilayer, based on the recently synthesized boron monophosphide (BP) and the widely studied molybdenum disulfide (MoS₂), has been systematically explored for the conversion of waste heat, solar energy, and nanomechanical energy into electricity. It shows a gigantic figure of merit (ZT) > 12 (4) for p (n)-type doping at 800 K, which is the highest ever reported till date. At room temperature (300 K), ZT reaches 1.1 (0.3) for p (n)-type doping, which is comparable to experimentally measured ZT = 1.1 on the PbTe-PbSnS₂ nanocomposite at 300 K, while it outweighs the Cu₂Se-CuInSe₂ nanocomposite (ZT = 2.6 at 850 K) and the theoretically calculated ZT = 7 at 600 K on silver halides. Lattice thermal conductivity (κ_l ≈ 49 W m^-1 K^-1) calculated at room temperature is lesser than those of black phosphorene (78 W m^-1 K^-1) and arsenene (61 W m^-1 K^-1). The nearly matched lattice constants in the commensurate lattices of the constituent monolayers help to preserve the direct band gap at the K point in the type II vdW heterobilayer of MoS₂/BP, where BP and MoS₂ serve as donor and acceptor materials, respectively. An ultrahigh carrier mobility of ∼20 × 10³ cm² V^-1 s^-1 is found, which exceeds those of previously reported transition metal dichalcogenide-based vdW heterostructures. The exciton binding energy (0.5 eV) is close to those of MoS₂ (0.54 eV) and C₃N₄ (0.33 eV) single layers. The calculated power conversion efficiency (PCE) in the monolayer MoS₂/BP heterobilayer exceeds 20%. It surpasses the efficiency in MoS₂/p-Si heterojunction solar cells (5.23%) and competes with the theoretically calculated ones, as listed in the manuscript. Furthermore, a high optical absorbance (∼10⁵ cm^-1) of visible light and a small conduction band offset (0.13 eV) make MoS₂/BP very promising in 2D excitonic solar cells. The out-of-plane piezoelectric strain coefficient, d₃₃ ≈ 3.16 pm/V, is found to be enhanced 4-fold (∼14.3 pm/V) upon applying 7% vertical compressive strain on the heterobilayer, which corresponds to ∼1 kbar of hydrostatic pressure. Such a high out-of-plane piezoelectric coefficient, which can tune top-gating effects in ultrathin 2D nanopiezotronics, is a relatively new finding. As BP has been synthesized recently, experimental realization of the multifunctional, versatile MoS₂/BP heterostructure would be highly feasible.

Bilayer MSe2 (M = Zr, Hf) as promising two-dimensional thermoelectric materials: a first-principles study

Motivated by experimental synthesis of two-dimensional MSe₂ (M = Zr, Hf) thin films, we investigate the thermoelectric transport properties of MSe₂ (M = Zr, Hf) bilayers by using first-principles calculations and Boltzmann transport theory.

Isolated highly localized bands in YBi2 monolayer caused by 4f orbitals

The novel electronic structures can induce unique physical properties in two-dimensional (2D) materials. In this work, we report isolated highly localized bands (HLB) in [Formula: see text] monolayer by the first-principle calculations within generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). It is found that [Formula: see text] monolayer is an indirect-gap semiconductor using both GGA and GGA+SOC. The calculations reveal that Yb-4f orbitals constitute isolated HLB below the Fermi level at the absence of SOC, and the bands are split into the j  =  7/2 and j  =  5/2 states with SOC. The isolated HLB can lead to a very large Seebeck coefficient and very low electrical conductivity in p-type doping by producing very large effective mass of the carrier. It is proved that isolated HLB have very strong stability against strain, which is very important for practical application. When the onsite Coulomb interaction is added to the Yb-4f orbitals, isolated HLB persist, and only their relative positions in the gap change. These findings open a new window to search for novel electronic structures in 2D materials.

Monolayer PdSe2: A promising two-dimensional thermoelectric material

Motivated by the recent experimental synthesis of two-dimensional semiconducting film PdSe₂, we investigate the electronic and thermal transport properties of PdSe₂ monolayer by using the density functional theory and semiclassical Boltzmann transport equation. The calculated results reveal anisotropic transport properties. Low lattice thermal conductivity about 3 Wm⁻¹ K ⁻¹ (300K) along the x direction is obtained, and the dimensionless thermoelectric figure of merit can reach 1.1 along the x direction for p-type doping at room temperature, indicating the promising thermoelectric performance of monolayer PdSe₂.