Jesse Maassen1
Dalhousie University1
Band engineering is an important strategy that seeks to tailor a material’s electronic and scattering properties to improve its thermoelectric performance. This effectively alters the material’s transport distribution (TD), which is the central quantity that determines the electronic conductivity, Seebeck coefficient and electronic thermal conductivity. The seminal work of Mahan and Sofo [1] concluded that the thermoelectric figure of merit, ZT, is maximized with a delta function TD – an unbounded distribution. Later studies by Zhou et al. [2] and Jeong et al. [3], exploring different band structures and scattering models, found that ZT is maximized when the width of the TD is finite and that the TD always remains bounded. Assuming a bounded TD, a genetic algorithm search by Fan et al. [4] determined that a boxcar TD is best for ZT.<br/> <br/>This talk presents a study that theoretically derives what is the optimal bounded TD and its implications on the limits of thermoelectric performance [5]. To maximize the figure of merit and the power factor the ideal transport distributions are boxcar and Heaviside functions, respectively – the edges of which must be located at specific energies. The optimal power factor is simply limited by the magnitude of the Heaviside TD, and reaches ZT values between 4-5. The optimal figure of merit, which can approach the Carnot limit, is uniquely determined by a key quantity that is proportional to the TD magnitude and temperature, and inversely proportional to the lattice thermal conductivity. These results suggest two general approaches to enhance thermoelectric performance: identify or design materials with TDs that have large magnitude (large distribution of modes, high velocities and/or low scattering) and that possess the ideal boxcar or Heaviside shape (controlled by band structure shape, scattering profile and dimensionality). This study can help guide the search for better thermoelectrics by establishing practical upper limits on performance, and by providing target TDs to guide band and scattering engineering strategies. <br/> <br/>[1] Mahan and Sofo, Proc. Natl. Acad. Sci. USA <b>93</b>, 7436 (1996).<br/>[2] Zhou, Yang, Chen, and Dresselhaus, Phys. Rev. Lett. <b>107</b>, 226601 (2011).<br/>[3] Jeong, Kim, and Lundstrom, J. Appl. Phys. <b>111</b>, 113707 (2012).<br/>[4] Fan, Wang, and Zheng, J. Appl. Phys. <b>109</b>, 073713 (2011).<br/>[5] Maassen, Phys. Rev. B <b>104</b>, 184301 (2021).<br/> <br/>Acknowledgements: this research was supported by NSERC and Compute Canada.