P.-H. Chang and B. K. Nikolic, Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high-ZT thermoelectrics , Phys. Rev. B 86, 041406(R) (2012). [PDF] B. K. Nikolic, K. K. Saha, T. Markussen, and K. S. Thygesen First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes , J. Comp. Electronics 11, 78 (2012); mini-review article for the special issue of the Journal of Computational Electronics on "Simulation of Thermal, Thermoelectric, and Electrothermal Phenomena in Nanostructures." [PDF] K. K. Saha, T. Markussen, K. S. Thygesen, and B. K. Nikolic, Multiterminal single-molecule–graphene-nanoribbon junctions with the thermoelectric figure of merit optimized via evanescent mode transport and gate voltage, Phys. Rev. B 84, 041412(R) (2011). [PDF]
Thermoelectrics transform temperature gradients into electric voltage and vice versa. Although a plethora of widespread applications has been envisioned, such as generation of electricity from waste heat to improve vehicle fuel efficiency or solid-state Peltier coolers for electronic circuits, their usage is presently limited by their small efficiency. Thus, careful tradeoffs are required to optimize the dimensionless figure of merit ZT=S2GT/K quantifying the maximum efficiency of a thermoelectric cycle conversion because ZT contains unfavorable combination of the thermopower S, average temperature T, electrical conductance G and total thermal conductance K =Kel + Kph which has contributions from both electrons Kel and phonons Kph. The devices with ZT > 1 are regarded as good thermoelectrics, but ZT > 3 is required to compete with conventional generators.
The major experimental efforts to increase ZT have been directed toward suppressing the lattice thermal conductivity Kph using either complex (through disorder in the unit cell) bulk materials or bulk nanostructured materials. A complementary approach engineers electronic density of states to obtain a sharp singularity near the Fermi energy which can enhance the power factor S2G (e.g., as in PbTe doped with Tl reaching ZT ~ 1.5 at 775 K).
In recent years, there has been a growing experimental and theoretical interest to explore nanowires and devices where a single molecule is attached to metallic or semiconducting electrodes for thermoelectric applications. In such devices, the dimensionality reduction (e.g., rough silicon nanowires can act as efficient thermoelectric materials although bulk silicon is not) and possible strong electronic correlations can make it possible to increase S concurrently with diminishing Kph while keeping the nanodevice disorder-free.
For example, creation of sharp transmission resonances near the Fermi energy EF by tuning the chemical properties of the molecule and molecule-electrode contact can substantially enhance the thermopower S which depends on the derivative of the conductance near EF. At the same time, the presence of a molecule in the electrode-molecule-electrode heterojunction severely disrupts phonon propagation when compared to homogenous wires made of the same electrode material.
A set of four general criteria that any nanoscale device must satisfy in order to reach optimized value for ZT can be delineated as follows:
- its electronic transmission function Tel(E) should exhibit fast changes (such as peaks or resonances) near the device Fermi energy EF,
- since hole-like [Tel(E) for E<EF] and electron-like [Tel(E) for E>EF] contribution to the thermopower S compensate each other due to opposite sign, one of these contributions must be suprressed,
- its phonon conductance Kph should be suppressed as much as possible by disrupting homogeneity of the device while trying to keep it disorder-free in order to avoid localization effects for very narrow wires,
- the decrease in the thermal conductance due to disorder and defects should not be outweighed by the decrease in the electronic conductance which should remain as high as possible.
Our first-principles quantum transport modeling of thermoelectric devices is focused on graphene nanoribbons (GNRs) and heterojunctions involving GNRs. The recent experiments measuring the thermopower S of micron-size graphene sheets have ignited theoretical studies of thermoelectric properties of large-area graphene. However the 2D graphene has extremely high thermal conductivity dominated by phonons, which actually outperforms all other known materials (e.g., graphene thermal conductivity is about ten times larger than that of copper at room temperature). Thus, the design of efficient graphene-based thermoelectric device requires to overcome the high thermal conductivity where quasi-one-dimensional GNRs with their edges might play an important role.
- molecular junctions-based thermoelectric devices,
- graphene nanoribbons in thermoelectric appplications,
- first-principles methods for phonon transport through nanostructures.