Recently reported phenomenon of “geometrical thermoelectricity” (GTE) that allows to tune a local Seebeck coefficient in a two-dimensional material (2DM) solely by changing device geometry [1], allows to manufacture thermoelectric (TE) devices such as nanoscale thermocouples [2] and heat management structures from a single material eliminating the need of thermoelectric junctions and multiple materials. It was suggested that this effect that is profound in the nanoscale constrictions have it origin in the modification of the energy dependent majority carriers mean-free path (MFP) in the nano-constriction [1]. The Seebeck coefficient in such a constriction is reduced by up to orders of magnitude, resulting in two opposing TE junctions between the 2DM in the constriction and the unaffected material on the either side of the constriction qualitatively explaining the phenomenon and the experimental results using nanoscale thermal probe [1,2]. At the same time, major questions remained on the a) role of the assymmetry of the constriction (e.g. tapered vs rectangular junctions), b) polarity of charge carriers in GTE phenomenon and c) effect of the tip of the nanoscale probe with previous studies performed on the symmetric graphene devices deposited on the SiO2/Si substrate that is known to provide a significant and not well defined doping of the graphene layer.


Fig 1. STGM map of the encapculated graphene device.
Here we explore outstanding questions of GTE charge and geometry symmetry using a recently developed scanning thermal gate microscopy (STGM) approach where a heated nanoscale scanning probe moves across sample surface while potential difference at the edges of the sample is measured producing STGM “maps” linked to a local Seebeck coefficient variation [3]. We created a monolayer graphene structure sandwiched between two hBN layers on SiO2/Si substrate serving as a back gate that has four nanoscale constriction junctions of approximately 100 nm width – (i) triangular to flat, (ii) flat edge-long constriction (iii) long constriction flat edge, and (iv) flat to triangular construiction that has close to the mirror symmetry with respect to the central line perpendicular to the device axis. The encapsulation allowed to clarify the effects of the carrier polarity (with charge neutrality Dirac point < 1V vs ~20V for the uncovered graphene) and spatial symmetry. By electrically biasing the STGM tip we were able to exclude effects of the tip on the observed TE phenomena. We also explore the effect of the asymmetric Joule heating in the graphene constriction where the heat generated in the junction is asymmetrically displaced due to high average velocity of the charge carriers in the constriction.
References
[1] Harzheim, A. et al, Nano Letters 2018, 18 (12), 7719-7725.
[2] Harzheim, A. et al, Advanced Functional Materials 2020, 30 (22), 2000574.
[3] Harzheim, A. et al, 2D Materials 2020, 7 (4), 041004.