Decoupling thermoelectric coefficients of multilayer graphene by nanomeshing

TL;DR

This work demonstrates decoupling of thermoelectric coefficients in multilayer graphene by introducing a hexagonal nanomesh that preserves electrical transport while strongly scattering phonons. Using a dual-region device (GN and GNNM) and modulated thermoreflectance, the authors show $PF = S^2 \sigma$ increases by about $40$% and thermal conductivity $k$ decreases by nearly a factor of $3$ at room temperature, with $k_{\parallel}$ reduced from ~$2016$ to ~$723$ W m$^{-1}$ K$^{-1}$. The classical Maxwell–Eucken model underpredicts the reduction, indicating the neck width is comparable to or smaller than the phonon MFP, highlighting nanoscale phonon filtering. Overall, nanomeshing enables significant control over 2D thermoelectric properties, offering a viable route for energy conversion and thermal management in graphene-based devices.

Abstract

Nanostructuring materials at small scales enables control over their physical properties, revealing behaviors not observed at larger dimensions. This strategy is particularly effective in two-dimensional (2D) materials, where surface effects dominate, and has been applied in the thermoelectric field. Here, we use multilayer graphene (4-6 nm thick) as a test platform to study the effect of nanomeshing on its thermoelectric properties. The nanomesh consists of a hexagonal array of holes, with a measured diameter and neck-width of ~360 nm and ~160 nm, respectively. The multilayer graphene is integrated into field-effect transistor-like devices supported by hexagonal boron nitride (hBN), allowing simultaneous electric and thermoelectric measurements, with nanomeshing applied to only part of the material. We use modulated thermoreflectance to investigate thermal transport in equivalent nanomeshed and pristine graphene flakes, extracting key parameters that affect thermoelectric performance. The nanomesh geometry suppresses thermal transport without significantly impacting charge transport, highlighting the different scattering lengths of phonons and electrons while enhancing the thermopower response. We observe a twofold improvement in the device power factor, PF = S^2 sigma (with S the Seebeck coefficient and sigma the electrical conductivity), at room temperature, along with a nearly threefold reduction in thermal conductivity k. The results show that nanomeshing can significantly improve the thermoelectric performance of multilayer graphene, paving the way for novel energy conversion strategies using 2D materials.

Figures (4)

• Figure 1: (a) Scanning electron microcope (SEM) image of a typical FET-like device including multilayer graphene (GN) where nanomeshing has been applied to a portion of it (GNNM). (b) Zoomed-in SEM image of the nanomeshed graphene (GNNM). (c) Artistic view of the device illustrating details for the electrical transport measurements of the GN and GNNM regions. (d) Artistic view of the device illustrating details for the thermopower measurements of the GN and GNNM regions.
• Figure 2: (a) Atomic force microscopy (AFM) image of the presented device indicating the different parts (electrodes, micro-heater, gate, flakes). The border of the hBN flake is highlithed by the dashed white line. (b) Averaged AFM line profile of the hBN flake (bottom panel) and GN flake (top panel) of the device in (a) allowing the flakes thicknesses extraction. (c) Zoomed-in AFM image of the GNNM region. (d) AFM line profile cut along the with dotted line in (c) allowing to extract a hole depth of $\sim$ 6 nm. (e) Raman spectra ($\lambda$=532 nm, Witec) of GN (black data) and GNNM (red data) parts respectively, showing multiple well-defined peaks. The correspondent phonon modes are indicated. (f) Zoom of the Raman spectra around the D band at 1362 cm$^{-1}$ allowing to detect the signature of an increased disorder in the GNNM. (g) Zoom of the Raman spectra around the D' band at 1621 cm$^{-1}$ visible only in the spectra of GNNM (red curve) confirming an increased disorder. Note that not always the GN and GNNM spectra are distinghuishable, the presented data are related to a different sample than the one discussed.
• Figure 3: (a) Electrical conductivity $\sigma$ of the GN (open symbols) and GNNM regions (solid symbols) as a function of the gate voltage V$_G$. The continous red line is the expected $\sigma$ redicton calculated by the Maxwell-Eucken model. (b) Seebeck coefficient $S$ for the GN region (open symbols) and the GNNM region (solid symbols) as a function of the gate voltage, showing an enhanced response in the presence of the nanomeshed network. (c) Power factor $PF=S^2\sigma$ for the GN region (open symbols) and the GNNM region (solid symbols) as a function of the gate voltage, showing enhanced values in the nanomeshed case.
• Figure 4: (a) Optical image of the GNNM-based device for MTR measurements. The location and direction of the MTR scans is performed over GNNM is indicated by the green dotted lines. The green spot indicates the zero scan position. The Gaussian beam profile of the green laser is schematically represented. (b) MTR amplitude and (c) phase data measured at 500 kHz for the GN (open symbols) and GNNM regions (solid symbols), along with the corresponding best-fit curves (solid lines). For clarity, the data and fits are vertically offset.