Multifunctional structural design of graphene thermoelectrics by Bayesian optimization.

Materials development often confronts a dilemma as it needs to satisfy multifunctional, often conflicting, demands. For example, thermoelectric conversion requires high electrical conductivity, a high Seebeck coefficient, and low thermal conductivity, despite the fact that these three properties are normally closely correlated. Nanostructuring techniques have been shown to break the correlations to some extent; however, optimal design has been a major challenge due to the extraordinarily large degrees of freedom in the structures. By taking graphene nanoribbons (GNRs) as a representative thermoelectric material, we carried out structural optimization by alternating multifunctional (phonon and electron) transport calculations and Bayesian optimization to resolve the trade-off. As a result, we have achieved multifunctional structural optimization with an efficiency more than five times that achieved by random search. The obtained GNRs with optimized antidots significantly enhance the thermoelectric figure of merit by up to 11 times that of the pristine GNR. Knowledge of the optimal structure further provides new physical insights that independent tuning of electron and phonon transport properties can be realized by making use of zigzag edge states and aperiodic nanostructuring. The demonstrated optimization framework is also useful for other multifunctional problems in various applications.