Thickness-dependent anisotropic transport of phonons and charges in few-layered PdSe₂

So far, layered PdSe₂ has attracted much attention due to its completely tunable band-gap with varying layer numbers, yet the thickness-dependent transporting properties have been rarely studied. We have systematically studied the electronic structures, phonon and charge transport properties, and thermoelectric properties of few-layered (from 1L to 4L) and bulk PdSe₂ by first-principles calculations and Boltzmann transport theory. As the thickness increases, the energy levels of band edges relative to 4s of selenium move oppositely due to their different bonding states, leading to the power-law decrease of the band-gap. Meanwhile, the electron effective mass decreases rapidly while the hole effective mass increases significantly compared with those unperturbed. Calculations on elastic constants reveal that both bulk and few-layered PdSe₂ are mechanically stable, and the bulk is ductile with a Poisson's ratio of 0.27. The shifts of Raman active modes with respect to the thickness as well as their Gruneisen parameters are analyzed and the underlying physics is discussed. At room temperature, the thermal conductivities of the bulk are 7.7, 10.1 and 0.9 W m^-1 K^-1 along the a, b and c axes, respectively. It is found that the low-frequency modes (<2.0 THz) contribute about 80% of in-plane thermal conductivities. Due to the enhanced contribution from the ZA mode, the thermal conductivity of few-layered PdSe₂ is much larger than that of the bulk. The ZA mode is mainly scattered by itself and the Umklapp scattering dominates in the process as the thickness increases. Calculations on charge transport reveal that the electron mobility increases from 2.5-13.2 (1L) to 121.9-167.8 (4L) cm² V^-1 s^-1 with the decreasing anisotropy μ_b/μ_a, while the hole mobility remains to be ∼20 cm² V^-1 s^-1, which is in good agreement with the experimental results. Calculations on the thermoelectric properties reveal that the ZT value as well as the power factor increases largely as the thickness increases and it gets to be optimum for the triple layer. Interestingly, the transport of electrons and phonons is decoupled along the out-of-plane direction, which makes bulk PdSe₂ exhibit good thermoelectric performance along the c axis.