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Using first-principles density functional perturbation theory basedcalculations of length-dependent lattice thermal conductivity (\k{appa} L ) andusing our previously calculated results (Phys Rev B 95 085435 (2017)) ofelectrical transport, we report results of thermoelectric figure-of-merit (ZT )of monolayer and bilayer Graphene. We find nearly ten-fold increase in ZT forthe graphene sample doped with boron nitride and reduced sample length. We alsocompare \k{appa} L calculated using the iterative real space method withconventional analytical Callaway-Klemens method and obtain the flexural (ZA)phonon modes to be dominant in thermal transport unlike in the latter method.Our calculations are in good agreement with available experimental data.

Enhancement of thermoelectric figure-of-merit of Graphene upon BN-doping and sample length reduction