Gate Tuning of Förster Resonance Energy Transfer in a Graphene - Quantum Dot FET Photo-Detector

Graphene photo-detectors functionalized by colloidal quantum dots (cQDs) have been demonstrated to show effective photo-detection. Although the transfer of charge carriers or energy from the cQDs to graphene is not sufficiently understood, it is clear that the mechanism and efficiency of the transfer depends on the morphology of the interface between cQDs and graphene, which is determined by the shell of the cQDs in combination with its ligands. Here, we present a study of a graphene field-effect transistor (FET), which is functionalized by long-ligand CdSe/ZnS core/shell cQDs. Time-resolved photo-luminescence from the cQDs as a function of the applied gate voltage has been investigated in order to probe transfer dynamics in this system. Thereby, a clear modification of the photo-luminescence lifetime has been observed, indicating a change of the decay channels. Furthermore, we provide responsivities under a Förster-like energy transfer model as a function of the gate voltage in support of our findings. The model shows that by applying a back-gate voltage to the photo-detector, the absorption can be tuned with respect to the photo-luminescence of the cQDs. This leads to a tunable energy transfer rate across the interface of the photo-detector, which offers an opportunity to optimize the photo-detection.

.1 | Photoluminescence and absorbance of cQDs. a) Absorbance (red curve, right axis) and photoluminescence (black curve, left axis) of CdSe/ZnS QDs, respectively. Inset: Histogram of the size distribution of the used cQDs. Here, a representative TEM picture is shown, from which the QD sizes are retrieved. b) Decay of the QDs' photo-luminescence, represented by a logarithmically plotted transient, which has been fitted by a biexponential function. These cQDs have been subject to the studies on the hybrid cQDgraphene system. The inset presents a zoom-out overview on the recorded radiative decay up to 40 µs.

Drop Casting of cQDs onto a graphene transistor channel
Starting from a CAD model, a laser ablation setup was employed to cut the graphene layer on the substrate. The same technique was used to process a shadow mask in aluminium foil for the deposition of electrical contacts.
Following the structuring and processing steps, several field-effect transistor (FET) structures were identified under an optical microscope. Functionalizing of the graphene-transistors was achieved by drop-casting of the aforementioned cQD solution onto the channel region of those FET structures. For individually prepared samples, a representative camera picture is shown which was recorded under UV illumination (see Fig. SI.2a).
To estimate the homogeneity of the QD layer, the brightness of signal in the recorded picture was analysed along the channel axis. A representative cross-section of brightness is presented in Fig  b) The analysis of brightness along the channel axis clearly shows contact-pad regions with a dip in the center, which allows one to distinguish between the gate of a structure and the surrounding contact pads. This is explained by the stronger quenching of signal by the graphene areas compared to the gold-covered regions.
Furthermore, the analysis shows that in the center region, the cQD drop is rather inhomogenous, thus showing strong brightness variation. On the second FET that is neighboring the centrally displayed FET structure, a more homogenous film is obtained.

Electrical contacts
The gold contact pads on the sample were electrically contacted by tungsten needles. Thus, one can expect a contact resistance to affect the channel resistance measurements. Assuming that all pieces of graphene on the sample, i.e. the graphene channels in every structure, exhibit the same resistance, we estimate contact resistances based on the lower limit of the measured source-drain resistance, which can be different in magnitude due to a varying quality of the established electrical contact for each structure. Here, we did not distinguish contact resistances for source and drain contacts and estimate R Contact for the 1 st , 2 nd and 3 rd transistor to be about 0-350, 0-5, and 450-460 Ohms, respectively, with the spread of those attributed to different contact qualities.

Transients of the cQD PL measurements on the graphene FET
The transients of the cQD PL have been acquired as described in the method section and fitted by mono exponential fits. For all three cQD-graphen photodetecting structures studied, transients were recorded as a function of the gate voltage, respectively. The plots shown in Fig. SI.3 include monoexponential fits to the transients used to extract the radiative lifetime.