Effect of doping on hot-carrier thermal breakdown in perforated graphene metasurfaces

TL;DR

This work investigates hot-carrier-induced electrothermal breakdown in perforated graphene metasurfaces (PGMs) under chemical doping. By extending the PGM model to include doping via acceptor density $ ext{Σ}_A$ and doping voltage $ ext{V}_A$, the authors derive a coupled set of transport and energy-balance equations using a Landauer-Buttiker framework and optical-phonon-limited relaxation to obtain parametric relations between carrier temperatures $T^{-}$, $T^{+}$ and bias $V_G$. Doping introduces electron-hole asymmetry, causing a split in $T^{-}(V_G)$ and $T^{+}(V_G)$ and more pronounced changes in partial currents $J_{GMR}^{-}$ and $J_{GMR}^{+}$, while the overall onset of hot-carrier breakdown (threshold $V_G^{th}$) remains tied to the number of GNR bridges $(2N-1)$. The findings demonstrate that the S-shaped I–V characteristics associated with electrothermal instability persist across a range of doping levels and bridge counts, enabling potential applications in fast switches, incandescent emitters, and terahertz detectors, with a quantitative framework for optimizing GMR/GNR-based devices.

Abstract

We examine the robustness of the S-shaped current-voltage characteristics associated with hot-carrier-induced electrical breakdown in perforated graphene metasurfaces (PGMs) as a function of doping. The perforation of the graphene layer forms interdigital arrays of graphene microribbons (GMRs) interconnected by graphene nanoribbon (GNR) bridges. These GNR constrictions act as energy barriers for electrons and holes emitted from the GMRs and govern the inter-GMR thermionic current under an applied bias voltage. The doping and the voltage bias establish distinct electron and hole populations in adjacent GMRs. Peltier heating of these carriers within the GMRs increases their effective temperatures, thereby enhancing the inter-GMR current. The resulting positive feedback between carrier heating and current amplification can trigger an electrothermal breakdown, transforming a superlinear current-voltage dependence into an S-shaped characteristic exhibiting negative differential resistance. The degree of electron-hole asymmetry significantly influences this positive feedback and strongly modifies the overall current-voltage response. These results provide a framework for optimizing PGM-based devices employing GMR/GNR architectures, including voltage-controlled fast switches, incandescent emitters, and terahertz bolometric detectors.

Figures (5)

• Figure 1: (a) Top view of a PGM with metal contact electrodes, (b) its band diagram corresponding to cross-sections of the inter-GNR bridges at $V_G =0$ and (c) at $V_G > V_A$.
• Figure 2: Voltage dependences of carrier temperatures $T^-$ and $T^+$ in the PGMs with different numbers, $(2N-1) =1,\, 3,\, 5,\, 7$ of the GNR bridges (indicated in rectangles) and different doping voltages: $V_A = 0$ ($T^-=T^+ = T$) , $V_A = 25$ mV, and $V_A = 50$ mV (acceptor surface densities $\Sigma_A =0$, $\Sigma_A \simeq 3.47\times 10^{11}$ cm$^2$, and $\Sigma_A \simeq 6.94\times 10^{11}$ cm$^2$).
• Figure 3: Voltage dependences of partial currents of $J_{GMR}^-/M$ and $J_{GMR}^+/M$ normalized by the number, $M$, of the GMR pairs in the PGMs with different numbers, $(2N-1)$, of the GNR bridges and different doping voltages $V_A$.
• Figure 4: Normalized current-voltage characteristics $J_{GMR}/M$ of the PGMs with different $(2N-1)$ and $V_A$.
• Figure 5: Threshold voltage $V_G^{th}$(top panel) and threshold normalized current $J_{GMR}^{th}$ (bottom panel) as functions of the doping voltage $V_A$ for the PGMs with different $(2N-1)$.