Geometrically Enhanced Thermoelectric Effects in Graphene Nanoconstrictions

Abstract

The influence of nanostructuring and quantum confinement on the thermoelectric properties of materials has been extensively studied. While this has made possible multiple breakthroughs in the achievable figure of merit, classical confinement, and its effect on the local Seebeck coefficient has mostly been neglected, as has the Peltier effect in general due to the complexity of measuring small temperature gradients locally. Here we report that reducing the width of a graphene channel to 100 nm changes the Seebeck coefficient by orders of magnitude. Using a scanning thermal microscope allows us to probe the local temperature of electrically contacted graphene two-terminal devices or to locally heat the sample. We show that constrictions in mono- and bilayer graphene facilitate a spatially correlated gradient in the Seebeck and Peltier coefficient, as evidenced by the pronounced thermovoltage Vth and heating/cooling response ΔTPeltier, respectively. This geometry dependent effect, which has not been reported previously in 2D materials, has important implications for measurements of patterned nanostructures in graphene and points to novel solutions for effective thermal management in electronic graphene devices or concepts for single material thermocouples.

Single‐Material Graphene Thermocouples

“…We find c n = 0.96, l 0 = 248 nm, n = 1.08 and U = 0.99, which is similar to previously found values from measurements of the thermopower width dependence in CVD grown graphene. [ 14 ] The U value of ≈1 points toward long‐range Coulomb interaction being the determining factor in the mean free path, consistent with scattering centres along the graphene edges. [ 24,25 ] Differences in signal strength between the long and short devices, as well as for individual devices (see Figure 3a), can be attributed to the unpredictable nature of the defects in the narrow graphene legs, ultimately determining the size of S w .…”

“…The origin of the signal can be explained by a change in the Seebeck coefficient ( to S w ) when varying the leg width from w 0 = 1.5 μm to a narrower width w . [ 14 ] This change in the Seebeck coefficient is due to the increased influence of scattering from the edges on the mean free path as the width of the channel is reduced. As scattering is more prominent in the narrow channel the mean free path decreases.…”

“…Following a previously developed theory for CVD graphene in the diffusive transport regime [ 14 ] it is then possible to arrive at a width dependent expression for the mean free path where l 0 is the bulk mean free path and c n and n are numerical coefficients specifying the transport mode and the influence of scattering on the mean free path. We can then combine Equation (2) with the Mott formula for the Seebeck coefficient given by , where R ( ϵ ) is the energy dependent resistance in graphene.…”

“…To this end, we make use of our recent discovery that similar to metals, the Seebeck coefficient in graphene can be influenced by geometrical constraint, which changes the mean free path locally. [ 14 ] The advantage of using graphene compared to previous approaches is its high bulk Seebeck coefficient [ 15 ] and its long electron mean free path even at room temperature. [ 16 ] This allows for the fabrication of highly sensitive thermocouples with the possibility of wafer‐scale integration, as current research efforts are directed at the use of graphene in 2D van der Waals structures using wafer‐scale fabrication methods.…”

Developments on Thermometric Techniques in Probing Micro- and Nano-heat

“…(c) Schematic of the Scanning Thermal 118 microscopy setup with lock-in technique for studying thermoelectric effect of graphene (as shown in (d) ) Reprinted with permission from Ref. [118]. temperature determined through the Raman 2D peak shift on the same 104 sample.…”