A bottom-up route to enhance thermoelectric figures of merit in graphene nanoribbons

Abstract

We propose a hybrid nano-structuring scheme for tailoring thermal and thermoelectric transport properties of graphene nanoribbons. Geometrical structuring and isotope cluster engineering are the elements that constitute the proposed scheme. Using first-principles based force constants and Hamiltonians, we show that the thermal conductance of graphene nanoribbons can be reduced by 98.8% at room temperature and the thermoelectric figure of merit, ZT, can be as high as 3.25 at T = 800 K. The proposed scheme relies on a recently developed bottom-up fabrication method, which is proven to be feasible for synthesizing graphene nanoribbons with an atomic precision.

Figure 1. Structural aspects, isotope distribution types, and ballistic transmission spectra of bottom-up fabricated graphene nanoribbons (GNRs).

(a) Structures of precursors and corresponding straight and chevron type graphene nanoribbons, s-GNR and c-GNR. (b) Heavy isotopes can be distributed at the atomic or precursor level. Grey, ¹²C; black, ¹⁴C; white H. Ballistic phonon (c) and electron (d) transmission spectra are plotted for both GNR types, where mini band formation due to the geometry of c-GNR is evident.

Figure 2. Phonon transport through isotopically disordered GNRs.

Thermal conductance per cross section area (κ/A) are plotted as functions of temperature in (a) and ribbon length (L) in (b), for s-GNR (blue) and c-GNR (red). Thermal conductance is minimum for maximal disorder (d = 50%) for a given distribution type. Precursor distribution always yields lower κ/A for a given isotope density for s-GNR. For c-GNR, precursor distribution yields larger κ/A at low density and short L. For long systems, even a low density of heavy precursors give rise to stronger suppression of phonon transport than that of atomic distribution of isotopes. Solid lines in (b) depict κ/A in the absence of ¹⁴C isotopes.

Figure 3. Thermoelectric figure of merit, ZT, for chevron-type GNR with randomly distributed heavy precursors.

ZT is plotted as a function of chemical potential (μ) and length (L) at T = 800 K, (a). The heavy precursor density is d = 50%. Local maxima appear close to the band edges, and the maximum value is obtained inside the band gap for all lengths. ZT for optimum system lengths are plotted at T = 300 K (blue), 500 K (green)and 800 K (red), (b). Electron density of states is depicted in gray. The system lengths are L = 430 nm, 140 nm and 70 nm, respectively. ZT = 3.25 is realized at 800 K.

Figure 4. Maximum ZT as a function of length at different temperatures.

Maximum ZT achievable when Anderson type disorder is introduced in the electronic Hamiltonian. The variation of onsite energies are set equal to the temperature, σ = k_BT. Solid lines represent hole-like transport while the dashed lines are for electron-like charge carriers. The ZT_max values shown are realized inside the band gap, i.e. |μ| < 0.75 eV with respect to the mid-gap, except for the dotted curve (T = 300 K) when |μ| > 1.