Thermally Limited Current Carrying Ability of Graphene Nanoribbons

We investigate high-field transport in graphene nanoribbons (GNRs) on ${\mathrm{SiO}}_2$, up to breakdown. The maximum current density is limited by self-heating, but can reach $>3\mathrm{mA}/\mu \mathrm{m}$ for GNRs $\sim 15\mathrm{nm}$ wide. Comparison with larger, micron-sized graphene devices reveals that narrow GNRs benefit from 3D heat spreading into the ${\mathrm{SiO}}_2$, which enables their higher current density. GNRs also benefit from lateral heat flow to the contacts in short devices ($<\sim 0.3\mu \mathrm{m}$), which allows extraction of a median GNR thermal conductivity (TC), $\sim 80\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at $20°\mathrm{C}$ across our samples, dominated by phonons. The TC of GNRs is an order of magnitude lower than that of micron-sized graphene on ${\mathrm{SiO}}_2$, suggesting strong roles of edge and defect scattering, and the importance of thermal dissipation in small GNR devices.

Figure 1

(a) Schematic of graphene devices used in this work. (b) Measured (symbols) and simulated (lines) current vs voltage up to breakdown of GNRs in air. Solid lines are model with self-heating (SH) and breakdown when $\max (T)>T_{\mathrm{BD}}=873\mathrm{K}$, dashed lines are isothermal model without SH (see text and supplement [12]). Dimensions are $L/W=510/20\mathrm{nm}$ for D1, and $L/W=390/38\mathrm{nm}$ for D2. $V_{GS}=-40\mathrm{V}$ to limit hysteresis effects. (c) Atomic force microscopy (AFM) image of D1 after high-current sweep; arrow shows breakdown location.

Figure 2

Scaling of GNR and “large” XG breakdown power with square root of device footprint, $(WL{)}^{1/2}$. Dashed lines are thermal model with $k=50$ and $500\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, $R_{\mathrm{Cox}}=5\times {10}^{-8}{\mathrm{m}}^2{\mathrm{KW}}^{-1}$ and $L/W=15$. Lateral heat sinking and in-plane GNR thermal conductivity begin to play a role in devices $<\sim 0.3\mu \mathrm{m}$ (also see Fig. 3). A few GNRs were broken in vacuum as a control group (open circles). The inset shows scaling of peak current density vs width at $T_{\mathrm{BD}}$, demonstrating greater current density in narrower GNRs that benefit from 3D heat spreading and lateral heat flow along the GNR. Dashed line drawn to guide the eye.

Figure 3

Thermal conductance of device per unit area (G”) vs width for graphene of varying (a) thermal conductivity and (b) length. Both parameters affect heat sinking along GNRs $<\sim 0.3\mu \mathrm{m}$. Symbols follow the notation of Fig. 2. Horizontal dash-dotted line is the limit $W\to \infty$ which applies to the case in (c), only “vertical” heat sinking through the oxide. The significance of lateral 3D heat spreading from GNRs is shown in (d) and (e), both mechanisms partly leading to higher current density in the Fig. 2 inset.

Figure 4

Thermal conductivity (TC) of GNRs estimated in this work at $T_{\mathrm{BD}}$, compared to large-area samples for supported graphene grown by CVD [23], exfoliated graphene (XG) on ${\mathrm{SiO}}_2$ [24], and suspended XG [25]. The median TC of our GNRs at room temperature is $\sim 80\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ (see text) nearly an order of magnitude lower than “large” XG on ${\mathrm{SiO}}_2$ [24]. The inset shows approximate scaling between TC and electrical sheet conductance, suggesting scattering mechanisms common to both electrons and phonons. The electronic contribution to TC is estimated to be typically $k_e<10\mathrm{W}{{\mathrm{m}}^{-}}^1{{\mathrm{K}}^{-}}^1$ or <10%. Dashed lines show trends to guide the eye.