The electronic and thermoelectric properties of one to four monolayers of MoS 2 , MoSe 2 , WS 2 , and WSe 2 are calculated. For few layer thicknesses, the near degeneracies of the conduction band K and Σ valleys and the valence band Γ and K valleys enhance the n-type and p-type thermoelectric performance. The interlayer hybridization and energy level splitting determine how the number of modes within k B T of a valley minimum changes with layer thickness. In all cases, the maximum ZT coincides with the greatest near-degeneracy within k B T of the band edge that results in the sharpest turn-on of the density of modes. The thickness at which this maximum occurs is, in general, not a monolayer. The transition from few layers to bulk is discussed. Effective masses, energy gaps, power-factors, and ZT values are tabulated for all materials and layer thicknesses.

Molybdenum disulfide (MoS2) is a layered semiconductor which has become very important recently as an emerging electronic device material. Being an intrinsic semiconductor the two-dimensional MoS2 has major advantages as the channel material in field-effect transistors. In this work we determine the electronic structures of MoS2 with the highly accurate screened hybrid functional within the density functional theory (DFT) including the spin-orbit coupling. Using the DFT electronic structures as target, we have developed a single generic tight-binding (TB) model that accurately produces the electronic structures for three different forms of MoS2 - bulk, bilayer and monolayer. Our TB model is based on the Slater-Koster method with non-orthogonal sp3d5 orbitals, nearest-neighbor interactions and spin-orbit coupling. The TB model is useful for atomistic modeling of quantum transport in MoS2 based electronic devices

The valence band of a variety of few-layer, two-dimensional materials consists of a ring of states in the Brillouin zone. The energy-momentum relation has the form of a 'Mexican hat' or a Rashba dispersion. The two-dimensional density of states is singular at or near the band edge, and the band-edge density of modes turns on nearly abruptly as a step function. The large band-edge density of modes enhances the Seebeck coefficient, the power factor, and the thermoelectric figure of merit ZT. Electronic and thermoelectric properties are determined from ab initio calculations for few-layer III-VI materials GaS, GaSe, InS, InSe, for Bi 2 Se 3 , for monolayer Bi, and for bilayer graphene as a function of vertical field. The effect of interlayer coupling on these properties in few-layer III-VI materials and Bi 2 Se 3 is described. Analytical models provide insight into the layer dependent trends that are relatively consistent for all of these few-layer materials. Vertically biased bilayer graphene could serve as an experimental test-bed for measuring these effects.

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