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Nano-structuring is an extremely promising path to high performancethermoelectrics. Favorable improvements in thermal conductivity are attainablein many material systems, and theoretical work points to large improvements inelectronic properties. However, realization of the electronic benefits inpractical materials has been elusive experimentally. A key challenge is thatexperimental identification of the quantum confinement length, below which thethermoelectric power factor is significantly enhanced, remains elusive due tolack of simultaneous control of size and carrier density. Here we investigategate tunable and temperature-dependent thermoelectric transport in $\gamma$phase indium selenide ($\gamma$ InSe, n type semiconductor) samples withthickness varying from 7 to 29 nm. This allows us to properly map out dimensionand doping space. Combining theoretical and experimental studies, we revealthat the sharper pre-edge of the conduction-band density of states arising fromquantum confinement gives rise to an enhancement of the Seebeck coefficient andthe power factor in the thinner InSe samples. Most importantly, weexperimentally identify the role of the competition between quantum confinementlength and thermal de Broglie wavelength in the enhancement of power factor.Our results provide an important and general experimental guideline foroptimizing the power factor and improving the thermoelectric performance oftwo-dimensional layered semiconductors.

Experimental identification of critical condition for drastically enhancing thermoelectric power factor of two-dimensional layered materials