Doping effect on thermoelectric properties of MoS$_2$

TL;DR

This work addresses how doping tunes the thermoelectric performance of layered MoS$_2$. By combining EV-GGA electronic structure (via LAPW/WIEN2K) with Boltzmann transport theory (BoltzTraP) and an energy-independent scattering time, the authors compute thermopower, electrical conductivity, and thermal conductivities for in-plane and cross-plane directions. They identify an optimal hole-doping level around $1\times10^{19}$ cm$^{-3}$, reveal strong anisotropy in electrical and electronic thermal transport caused by anisotropic scattering, and predict a maximum ZT of about $0.3$ at $700$ K in the in-plane direction, with potential gains if lattice thermal conductivity is reduced (e.g., via restacking). The findings guide doping strategies and suggest that in-plane MoS$_2$ offers the most practical thermoelectric performance, highlighting the role of anisotropic scattering and the balance between $\kappa_e$ and $\kappa_l$ in engineering high efficiency materials.

Abstract

We systematically study thermoelectric properties of layered MoS$_2$ by doping, based on Boltzmann transport theory and first-principles calculations. We obtain optimal doping region (around 10$^{19}$ cm$^{-3}$) by looking closely to the temperature and doping level dependent thermopower, electrical conductivity, power factor (PF) and ultimately figure of merit (ZT) coefficient along in-plane and cross-plane directions. MoS$_2$ has a vanishingly small anisotropy of thermopower but a big anisotropy of electrical conductivity and electronic thermal conductivity in optimal doping region. $κ_e$ is comparable to $κ_l$ in the plane while $κ_l$ dominates over $κ_e$ across the plane. ZT can reach as high as 0.3 at around 700 K. In-plane direction is demonstrated to be more preferable for thermoelectric applications of MoS$_2$ by doping.

Figures (6)

• Figure 1: (Color online) EV-GGA electronic band structure of MoS$_2$ along high-symmetry lines (a) $\Gamma$-M-K-$\Gamma$ in plane and (b) $\Gamma$-A across plane in the hexagonal Brillouin zone (BZ). The valence-band edge is set as zero and marked with a dashed line. Electronic density of states in (c) shows a comparatively higher value at the conduction band edge than at the valence band edge.
• Figure 2: (Color online) (a) Temperature dependence of calculated in-plane thermopower S$_{xx}$ of MoS$_2$, compared with experimental data by Mansfield and Salam PPSB1953 at two doping levels p = 1.6 $\times$ 10$^{16}$ (filled triangle) and 3.4 $\times$ 10$^{16}$ (empty circle) holes per cm$^{3}$. Doping level dependence of (b) in-plane thermopower S$_{xx}$(p, T), (c) ratio of cross-plane S$_{zz}$(p, T) over in-plane S$_{xx}$(p, T) and (d) in-plane S$_{xx}(n, T)$ at different temperatures. The temperature ranges from 100K to 700K for some practical reason. Hole and electron doping are respectively used in (a-c) and (d). Experimental data with p = 7.6 $\times$ 10$^{16}$ and 1.0 $\times$ 10$^{17}$ cm$^{-3}$ at 200K by Mansfield and Salam PPSB1953 is respectively marked by filled triangle and square in (b).
• Figure 3: (Color online) Doping level dependence of (a) in-plane $\sigma_{xx}/\tau_{xx}$, (b) in-plane electrical conductivity $\sigma_{xx}$, (c) ratio of cross-plane $\sigma_{zz}/\tau_{zz}$ over in-plane $\sigma_{xx}/\tau_{xx}$ and (d) cross-plane $\sigma_{zz}$, at different temperatures. Isotropic and anisotropic electronic scattering time $\tau$ are respectively assumed in (c), for instance, $\tau_{zz}/\tau_{xx} = 1$ and 0.024 with the anisotropic one fitting well the experimental data in blue square from Thakurta et. al. JPCS1983 and thereby used to derive $\sigma_{zz}$ in (d).
• Figure 4: (Color online) Doping level dependence of (a) power factor $\sigma_{xx} S^2_{xx}$ and (b) $\sigma_{zz} S^2_{zz}$ of p-type MoS$_2$ at different temperatures.
• Figure 5: (Color online) (a) In-plane electronic thermal conductivity $\kappa^e_{xx}$, (b) cross-plane $\kappa^e_{zz}$ and (c) in-plane L/L$_0$ as function of doping and temperature. L = $\kappa$/($\sigma$ T) and L$_0$ is the Lorenz number 2.44$\times$10$^{-8}$ W$\Omega$K$^{-2}$. (d) Temperature dependence of thermal conductivity $\kappa$ from experiment by Kim et. al. kappa2, which are presented by filled circles and fitted by $\kappa$ = 183.103/T + 0.412671 in dashed line.