The quantum dots were fabricated using e-beam lithography on epitaxial graphene grown on SiC and following the fabrication procedure described in Refs. [23], [28]. The samples were mounted on a gold plate and placed in a cryostat behind a picarin vacuum window. Filters were inserted to control the optical input power and restrict the wavelength to eliminate thermal blackbody radiation.

Figure 1A shows the temperature dependence of the electrical resistance *R*(*T*) of a 100-nm-diameter quantum dot (red curve). In our previous work [23], we characterized the performance of the graphene quantum-dot bolometers as a function of temperature and dot diameter and showed that the smallest dots (with a diameter smaller than 100 nm) yield the best performance (responsivities higher than 1×10^{10} V W^{−1}) because they have the largest quantum confinement gap and the strongest variation of resistance with temperature. In this work, we focus on the study of the bolometer performance as a function of radiation wavelength and absorbed power, using dots of intermediate size, with diameters ranging from 100 to 200 nm. All the measurements presented here are performed at the base lattice temperature *T*_{0}=3 K. The dependence of the device performance on the base lattice temperature can be found in Ref. [23].

Figure 1: Ultra-broadband bolometric response.

(A) Resistance as a function of temperature for a quantum dot with a diameter of 100 nm. Inset: schematic of the experimental setup and optical image of a typical quantum dot. Scale bar, 3 μm. (B) Sketch of a typical device with broadband radiation. (C) Electron temperature as a function of Joule power for a quantum dot with a diameter of 200 nm. (D) IV characteristic of a 200 nm dot without radiation (OFF, black) and with radiation at 2 mm (red), 1.543 mm (green), and 365 nm (purple) wavelength, having absorbed power of 0.4, 1.0, and 1.4 nW, respectively. Inset: response Δ*V*_{DC} as a function of the current *I*_{DC} at the same wavelengths.

Figure 1D shows the photoresponse of a 200 nm dot. The black curve is the current-voltage (IV) characteristic of the dot with radiation OFF. The curve tends to be nonlinear due to Joule heating: when the bias and the Joule power increase, the resistance decreases, as can be seen in Figure 2A (inset). This qualitative behavior occurs in all the dots; however, the IV curves are very sensitive to the dot diameter and the orientation of the graphene bolometer with respect to the steps between the crystal planes on the surface of the SiC substrate, as these two factors affect the temperature dependence of the bolometer resistance [23]. As a result, the IV curves of devices designed with the same dot diameter such as those in Figures 1D and 2A show some differences due to variations in the actual dot diameter after the fabrication process and in their orientation with respect to the steps on the substrate [23].

Figure 2: Measurements of photovoltage and absorbed power from IV curves.

(A) IV characteristic of a 200 nm dot without radiation (black) and with 2-mm-wavelength radiation (colors) at different values of absorbed power. Dashed lines indicate points in the curves with the same differential resistance. Inset: differential resistance of the curve with radiation OFF at different values of Joule power. (B) Photovoltage measured from the device in (A) at *I*_{DC}=1.9 nA as a function of absorbed power under illumination with a 2-mm-wavelength source (black squares). Inset: responsivity vs. absorbed power for the same device (black squares) and five other devices. The legend indicates the diameter of the quantum dot for each device.

Under illumination, the resistance decreases further. The red, green, and purple curves in Figure 1B show the IV characteristics when the sample is irradiated with light at three different wavelengths ranging from millimeter-wave to ultraviolet (2, 1543, and 365 nm, respectively). The sample clearly shows a response in this wide range of wavelengths. We analyze the response by measuring the power absorbed by our devices from the IV curves. Figure 2A shows the response of a device as a function of power for illumination at 2 mm wavelength (0.15 THz). For every value of incident power, we measure the power absorbed by the bolometer with the same method that we used in Ref. [23].

We first measure the differential resistance at zero bias for the IV characteristic with radiation ON and then find the point in the IV characteristic with radiation OFF that exhibits the same differential resistance. We use the Joule power dissipated in the bolometer at that point, *P*=*I*_{DC}V_{DC}, as a measurement of the radiation power absorbed when the light is ON. We repeat the same procedure for every IV curve that we obtain when varying the power of the incident light.

The photovoltage Δ*V*_{DC} at a fixed current, *I*_{DC}=1.9 nA, for different values of the absorbed power is shown in Figure 2B (black squares). The sublinear dependence of Δ*V*_{DC} (*P*) is expected because the variation of resistance versus temperature is highest at low temperature (see Figure 1A) and becomes weaker when the electron temperature increases due to an increase in the absorbed power. As Δ*V*_{DC} is sublinear as a function of absorbed power, the responsivity decreases with increasing radiation power, but it is still very high for a large range of absorbed power, as shown in Figure 2B (inset), where we include data from six devices, including two small-diameter devices with 30 nm dots.

The responsivity is larger for dots of smaller diameter. Figure 3 shows the power dependence of the responsivity for a 100-nm-diameter dot. Measurements at the lowest values of absorbed power in Figure 3A show that absorbed power below 1 pW can be detected at all the measured wavelengths by measuring changes in *V*_{DC}. Higher sensitivity can be achieved with temporally modulated illumination using lock-in detection.

Figure 3: Power dependence of the response.

(A) Low power dependence of the response from a 100 nm dot under illumination at different wavelengths. (B) Responsivity as a function of absorbed power at different wavelengths. Inset: calculated electrical NEP as a function of absorbed power at various wavelengths.

In all the measurements above, we have reported the absorbed power. Although this gives the ultimate performance of the devices, it is most useful to characterize their performance in terms of incident power. The optical coupling efficiency (the ratio between absorbed power and incident power) varies with radiation wavelength. For our long-wavelength source (2 mm, where the absorption is dominated by the graphene Drude conductivity), it can be optimized by designing antennas that are either broadband or tuned at specific wavelengths [29]. For wavelengths of 1500 nm or shorter, the coupling efficiency is limited by the optical absorption of a single graphene layer (2.3%). Our measured ratio of absorbed to incident power at 1543 nm is a bit higher (2.7%; see Methods) and it is possibly enhanced by the reflection of radiation from the gold plate under the bottom surface of the SiC substrate. Optical cavities can be also used to enhance the detector absorption [30].

We use the measured responsivity at different wavelengths to calculate the total electrical noise equivalent power (NEP) for the bolometers, including contributions from Johnson noise, shot noise, and thermal fluctuations [31] (NEP^{2}=NEP^{2}_{JN}+NEP^{2}_{SN}+NEP^{2}_{TF}=(4*k*_{B}TR)/*r*^{2}+(2*eI*_{DC})*R*^{2}/* r*^{2}+4*k*_{B}T^{2}*G*_{TH}, where *G*_{TH} is extracted from the data using the IV and *R*(*T*) curves [23]). Figure 3 indicates that the responsivity and the NEP are independent of radiation wavelength for photon energies in a very wide range of the radiation spectrum, including photon energies that are orders of magnitude larger than the activation energy of the dot. These behaviors can be explained by considering charge carrier dynamics after light absorption. As mentioned earlier, the timescale for electrons to equilibrate at an effective electron temperature via electron-electron collisions and optical phonon emission is on the order of 10–100 fs. This timescale is extremely fast compared to the charging time of the dot. We can estimate the capacitance of the dot by considering that the charging energy must be larger than the activation energy of the dot. This is because the activation energy depends on the alignment of the Fermi energy of the source and drain electrodes within the quantum confinement gap (it can be tuned to zero by doping the dot and aligning the Fermi energy to the top of the quantum confinement gap). The capacitance corresponding to a charging energy of 10 meV is about 10 aF, giving an RC time of 1 ns for a dot resistance of 100 MΩ. As electrons equilibrate with a much faster timescale, the photon energy and the specific wavelength do not play any role in the quantum transport of charges through the dot. As a result, we find that the absorbed power (regardless of wavelength) and the corresponding electron temperature are the only factors that determine the current through the dot.

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