Thermoelectric optimization and quantum-to-classical crossover in gate-controlled two-dimensional semiconducting nanojunctions

TL;DR

This work tackles how to maximize thermoelectric efficiency in gate-controlled 2D semiconducting nanojunctions by examining how gate voltage, temperature, and channel length shape transport mechanisms. It employs a multi-scale first-principles approach combining DFT, NEGF-DFT (via NanoDCAL), and non-equilibrium MD (via LAMMPS) to compute τ(E), Seebeck coefficient, electrical and electronic thermal conductivities, and phonon thermal conductivity for Pt–WSe$_2$–Pt devices with 3–12 nm channels, using an effective gate model to simulate gating. The authors identify a quantum-to-classical crossover from tunneling to thermionic emission as length increases and show that peak ZT occurs near the insulating–conducting transition, especially for the 3 nm junction where ZT exceeds 2.3 at 500 K. The study provides design principles for gate-tunable nanoscale thermoelectrics and emphasizes the critical balance between electronic and phononic heat transport in 2D material junctions for achieving high efficiency.

Abstract

We investigate the thermoelectric performance of 2D nanojunctions with gate tunable architectures and varying channel lengths from 3 to 12 nm using a combination of first principles simulations, including density functional theory, DFT with nonequilibrium Greens function formalism (nanoDCAL), and nonequilibrium molecular dynamics simulations. Our study reveals a gate, temperature, and length dependent transition from quantum to classical in electron transport, transitioning from quantum tunneling in short junctions to thermionic emission in longer ones. We observe nontrivial dependencies of the thermoelectric figure of merit on the Seebeck coefficient, electrical conductivities, and thermal conductivities as a result of this crossover and gate controlling. We identify that maximizing ZT requires tuning the chemical potential just outside the band gap, where the system lies at the transition between insulating and conducting regimes. While extremely large Seebeck coefficients are observed in the insulating state, they do not yield high ZT due to suppressed electrical conductivity and dominant phononic thermal transport. The optimal ZT larger than 2.3 is achieved in the shortest 3 nm junction at 500 K, where quantum tunneling and thermionic emission coexist. These findings offer fundamental insights into transport mechanisms in 2D semiconducting nanojunctions and present design principles for high efficiency nanoscale thermoelectric devices.

Figures (8)

• Figure 1: Schematics of Pt-WSe$_{2}$-Pt nanojunctions. The transmission coefficients $\tau (E)$, conductivity $\sigma$, and electronic thermal conductivity $\kappa_{\mathrm{el}}$ of Pt-WSe$_2$-Pt nanojunctions with channel lengths of (a) 3 nm, (b) 6 nm, (c) 9 nm, and (d) 12 nm are calculated using the NEGF method within the DFT framework with the NANIDcal simulation package. (e) Scheme used to compute the phononic thermal conductivity $\kappa_{\mathrm{ph}}$ via non-equilibrium molecular dynamics (NEMD) using the LAMMPS simulation package. Region A denotes the WSe$_2$ monolayer, regions B represent the thermostatted zones, and atoms in region C are fixed to prevent translational motion.
• Figure 2: $\tau (E)$ and $\kappa_{ph}(T)$ computed from NANODcal and LAMMPS. (a) Transmission function $\tau(E)$ as a function of energy $E$ for Pt–WSe$_2$–Pt nanojunctions at $V_g = 0$, with channel lengths $\mathrm{L}_{\text{ch}}=$ 3 nm (black dotted line), 6 nm (red dash-dotted line), 9 nm (green dashed line), and 12 nm (black solid line). The chemical potential $\mu$ at $V_g = 0$ is set to zero and used as the reference energy. (b) Phononic thermal conductivity $\kappa_{\mathrm{ph}}$ of Pt–WSe$2$–Pt nanojunctions with channel lengths $\mathrm{L}_{\text{ch}}=$ 3 nm (black square), 6 nm (red circle), 9 nm (green upward triangle), and 12 nm (black downward triangle). Solid and dotted lines represent the electronic thermal conductivity $\kappa_{\mathrm{el}}$ at $V_g = 0$ and $V_g = -0.5$ V, respectively, for the same set of channel lengths $\mathrm{L}_{\text{ch}}=$ 3 nm (black), 6 nm (red), 9 nm (green), and 12 nm (blue).
• Figure 3: $ZT$ due to competition between $S^2$ and $\kappa_{ph}/\kappa_{el}$. (a) The black line shows the transmission coefficient $\tau(E)$ as a function of energy $E$ (left vertical axis and top horizontal axis), with the chemical potential $\mu$ set to zero as the reference energy. The red line illustrates how the chemical potential $\mu$ shifts with gate voltage $V_g$ (right vertical axis and bottom horizontal axis), following $\mu(V_g) = \mu + e V_{\mathrm{G}}^{\mathrm{eff}}(V_g)$. (b) The Seebeck coefficient $S$ is plotted as a function of $\mu(V_g)$, showing its evolution with varying $V_g$. (c) The factor $1 + \kappa_{\mathrm{ph}}/\kappa_{\mathrm{el}}$ (left axis) and the factor $S^2/L$ (right axis) are plotted as functions of $\mu(V_g)$, highlighting the competition between phononic and electronic thermal transport and the trade-off between maximizing $S$ and minimizing the denominator in $ZT$. (d) The resulting thermoelectric figure of merit $ZT$ [left (right) axis: linear (log) scale] is plotted as a function of $\mu(V_g)$, reflecting the net outcome of the interplay among $S$, $\kappa_{\mathrm{el}}$, and $\kappa_{\mathrm{ph}}$. The chemical potential $\mu$ at $V_g=0$ is designated as the reference energy, set to zero, while the transmission band gap is defined by $(E_{\mathrm{V}},E_{\mathrm{C}})$.
• Figure 4: Contour plots of $\sigma(T,V_g)$. Contour plots of the electrical conductivity $\sigma(T, V_g)$ are shown as functions of temperature (250–500 K) and gate voltage $V_g$ (–1.5 to 1.5 V) for Pt–WSe$_2$–Pt thermoelectric junctions with channel lengths $\mathrm{L}_{\text{ch}}=$ (a) 3 nm, (b) 6 nm, (c) 9 nm, and (d) 12 nm. The maximum and minimum values of $\sigma$, denoted as $\sigma_{\mathrm{Max}}$ and $\sigma_{\mathrm{Min}}$, respectively, and their corresponding locations within the $T–V_g$ domain are also indicated.
• Figure 5: Contour plots depict the quantum-to-classical transition. Contour plots of $\zeta \equiv (G_{\mathrm{SC}}-G_{\mathrm{QM}})/(G_{\mathrm{SC}}+G_{\mathrm{QM}})$ are shown as functions of temperature (250–500 K) and gate voltage $V_g$ (–1.5 to 1.5 V) for Pt–WSe$_2$–Pt thermoelectric junctions with channel lengths $\mathrm{L}_{\text{ch}}=$ (a) 3 nm, (b) 6 nm, (c) 9 nm, and (d) 12 nm. $\zeta(T,V_g)$ represents competitive strength between quantum mechanical (shown in blue) and semi-classical (represented in red) transport mechanisms.