Effects of quantum size on the thermoelectric properties of bismuth.

First principles and the Boltzmann transport equation have been combined to investigate the effects of quantum size L / λ , the ratio of quantum confinement length L to thermal de Broglie wavelength λ , on the thermoelectric properties of 2D β-bismuth. It is revealed that the thermoelectric properties of 2D β-bismuth are highly influenced by quantum size, especially when the L / λ is less than 0.1. Specifically, the Seebeck coefficients of both electrons and holes decrease as the L / λ ratio increases, while the electrical and thermal conductivity show the opposite trend. The results also show that 2D bismuth with three or more layers has semimetal properties, with the first observation of a semiconductor-semimetal transition in 2D bismuth. Moreover, the electron affinity, ionization energy, and work function of 2D β-bismuth do not exhibit a significant variation or trend with quantum size effects. The detailed electronic structures provide a fundamental understanding of the thermoelectric properties of bismuth, and the obtained results may provide a deep understanding of the relationship between the quantum size and the thermoelectric properties of 2D β-bismuth.