Tunable Ultrafast Thermal Relaxation in Graphene Measured by Continuous-Wave Photomixing

Hot electron effects in graphene are significant because of graphene’s small electronic heat capacity and weak electron-phonon coupling, yet the dynamics and cooling mechanisms of hot electrons in graphene are not completely understood. We describe a novel photocurrent spectroscopy method that uses the mixing of continuous-wave lasers in a graphene photothermal detector to measure the frequency dependence and nonlinearity of hot-electron cooling in graphene as a function of the carrier concentration and temperature. The method offers unparalleled sensitivity to the nonlinearity, and probes the ultrafast cooling of hot carriers with an optical fluence that is orders of magnitude smaller than in conventional time-domain methods, allowing for accurate characterization of electron-phonon cooling near charge neutrality. Our measurements reveal that near the charge neutral point the nonlinear power dependence of the electron cooling is dominated by disorder-assisted collisions, while at higher carrier concentrations conventional momentum-conserving cooling prevails in the nonlinear dependence. The relative contribution of these competing mechanisms can be electrostatically tuned through the application of a gate voltage—an effect that is unique to graphene.

Figure 1

Diagram of heterodyne photomixing experiment. (a) Two near-IR continuous-wave beams, one with a tunable wavelength, are modulated at two different frequencies $f_1$ and $f_2$, then overlapped and focused down to the graphene photodetector. The photovoltages produced by laser 1 ($V_1$) and the mixing of two beams ($V_{\mathrm{\Delta }}$) are detected at the modulation frequencies $f_1$ and $f_1-f_2$, respectively. (b) Diagram of the HBN-encapsulated graphene (top) and exfoliated graphene (bottom) photodetector devices. The optical beams are illuminated close to one of the metal contacts, and the carrier density of graphene is altered by applying an electrostatic voltage ($V_g$) between the doped silicon substrate and graphene.

Figure 2

Photovoltage vs carrier concentration and incident power, measured at room temperature. (a) Single-laser photovoltage ($V_1$), and nonlinear photomixing signal ($V_{\mathrm{\Delta }}$) measured vs the applied gate voltage $V_g$. $V_{\mathrm{CNP}}$ denotes the charge neutral point. The red ($V_1{V}_{\mathrm{\Delta }}>0$) and blue ($V_1{V}_{\mathrm{\Delta }}<0$) regions indicate the conditions where super- and sublinear power dependence is observed. (b) Measured photovoltage $V_1$ of a single laser vs incident optical power at two different gate voltages, showing sublinear and superlinear behavior. (c) Calculated photothermoelectric voltage (in arbitrary units) vs input optical power for the case of ${\beta }_1=0$ (blue) and ${\beta }_3=0$ (red), illustrating the sublinear and superlinear behavior, respectively. Inset: energy diagram illustrating the two different cooling mechanisms.

Figure 3

Heterodyne photomixing response for the nonencapsulated device, measured at room temperature. (a) The nonlinear photomixing signal ($V_{\mathrm{\Delta }}$) as a function of the difference frequency ($\mathrm{\Omega }$) and gate voltage ($V_g$). At each gate voltage, $V_{\mathrm{\Delta }}$ exhibits a Lorentzian-shaped dependence on the heterodyne difference frequency $\mathrm{\Omega }$. (b) $V_{\mathrm{\Delta }}$ vs $\mathrm{\Omega }$ for $V_g=4\mathrm{V}$. The dashed curve is the theoretical calculation of the photomixing voltage based on a photothermoelectric effect. From the Lorentzian fit, the hot electron cooling time is estimated to be ${\gamma }^{-1}=1.42\mathrm{ps}$.

Figure 4

Temperature dependence of the cooling rate. (a) The two-beam mixing signal as a function of the difference frequency measured close to the charge neutral point (sublinear power dependence regime) at different temperatures for the exfoliated sample on ${\mathrm{Si}\mathrm{O}}_2$. The dashed curves are Lorentzian fits. (b) The black circles are the extracted hot electron cooling time constant $\tau \equiv {\gamma }^{-1}$ from the Lorentzian fits in panel (a). The blue (red) curve is the theory fit for the low (high) temperature.