Optoelectronic response of hybrid PbS-QD/graphene photodetectors

Quantum dots (QDs) are semiconducting optoelectronic nanoparticles that offer significant advantages over their bulk versions due to quantum confinement.^1,2 QDs have shown very high extinction coefficient³ and tunable bandgap.⁴ They have been used as active materials in solar cells,^2,5 light-emitting diodes,⁶ and photodetectors in both electronic and medical applications.⁷ In particular, lead sulfide (PbS) QDs have been widely used due to their high absorption coefficient, direct bandgap, wide spectral range, chemical stability, and affordable synthesis using the hot-injection method.^8–11 PbS QDs have been used for both photodetection and luminescence in the infrared range.^4,12 PbS QDs have also been used for high-resolution ex vivo and in vitro bioimaging, allowing for the acquisition of deep imaging inside biological tissues.^13,14 PbS QDs have been utilized as active materials in solar cells because of their high visible (vis)-IR light absorption and high chemical stability.^10,15 The power conversion efficiency of PbS QD solar cells has gradually increased to surpass 10%.^16–18 

Recently, hybrid photodetectors combining PbS QDs with single layer graphene (SLG) showed excellent performance reaching a high responsivity (>10⁷ A/W).^19,20 This system combines and compensates the advantages and limitations of both nanomaterials. QDs have strong and size tunable light absorption with direct bandgap resulting in high carrier photogeneration, but their charge confinement and nanoparticle composition results in films with very poor conductivity, strongly limiting charge collection and transport.^21–25 On the other hand, graphene has the highest mobility and excellent electrical conductivity, but its one-atom thickness severely limits its light absorption and practical application as an active material in solar cells or photodetectors. The hybrid Gr/QD configuration allows a synergy between materials, using QDs for light absorption to generate photocarriers that are then transferred to graphene for efficient charge transport and photocurrent generation. The Gr/QD device and operation is shown in Fig. 1. The operational principle is that under illumination, PbS QDs transfer photoexcited holes to the Gr channel, which leads to an increase in the hole density of typically p-type graphene on the SiO₂/Si substrate, leading to an increase in conductivity.²⁶ 

In this work, we present a systematic study on how the two main tunable parameters of QD size and QD film thickness affect the spectral response, responsivity, and time response of hybrid PbS QDs and graphene (Gr) photodetectors. Previous reports have focused on maximizing the photoresponse; however, the effect of QD size and film thickness has been not studied in detail. This information is critical to understand and optimize the operation of hybrid Gr/QD photodetectors. We study QD sizes from d = 2.65 nm (λ = 805 nm) to 4.96 nm (λ = 1350 nm), covering a broad spectral response from the visible to the near IR and analyzing how the QD size affects the photoresponsivity of the devices.²⁵ We describe the synthesis of QDs of different sizes, their structural and optical properties, and the fabrication of hybrid Gr/QD devices. We study the spectral and time response as well as the effect of power density. Finally, we also study the effect of thickness on the photoresponse, which provides an alternative way to tune the spectral response of Gr/QD devices.

PbS QDs synthesis: 0.94 g of lead oxide (PbO) was dissolved in 25 ml of 1-octadecene (ODE) with different concentrations of oleic acid (2.98, 7.45, 11.92, 19.37, and 35.76 ml) to achieve various sizes of PbS QDs.²⁹ After that, it was degassed under vacuum at 90 °C for 2 h to be dissolved. When the color of the solution becomes clear, 420 μl of bis(trimethylsilyl) sulfide dissolved in 12.8 ml of ODE was injected into the solution. Next, we waited for 30 s for the reaction to be done and then cooled down by placing the flask in water. The PbS QDs were separated from the raw solution by centrifugation, followed by cleaning with toluene and acetone, and then dissolved in toluene. The PbS QD solution was filtered with a 0.25 μm pore size filter.

Graphene transfer: Single layer graphene on copper coated with poly-methyl methacrylate (PMMA) was purchased from Graphenea (Spain) and transferred by the wet method using PMMA as the supporting layer.³⁰ The copper layer was removed by wet etching using an ammonium persulfate solution. After the copper layer was completely etched, the transparent PMMA/graphene layer was transferred to deionized (DI) water to remove Cu etching residues. Then, the graphene layer was transferred onto an Au patterned electrode SiO₂/Si substrate and dried for 2 h at room temperature. Finally, PMMA was removed by acetone and cleaned with isopropyl alcohol and DI water.

Material characterization: The absorption and transmission of PbS QDs were measured by UV-vis spectroscopy (UH4150, Hitachi). The crystallographic phase of PbS quantum dots was investigated by X-ray diffraction (XRD) (Smartlab, Rigaku) equipped with Cu Kα radiation. The refractive index and extinction coefficient of PbS quantum dots were analyzed by an ellipsometer (M-2000D, J. A. Woollam). The size of PbS QDs was analyzed by transmission electron microscopy (TEM), and the images were recorded on a field emission gun JEOL-2800 at 200 kV with the Gaten OneView Camera, installed at the UC Irvine Materials Research Institute (IMRI). The average diameter of the particle size was analyzed using Image J software.

Device fabrication: PbS quantum dot films were prepared by a spin coating method. 0.1 ml of PbS quantum dots in toluene was deposited on the substrate by spin coating at 2500 rpm for 10 s. Next, 0.03M tetrabutylammonium iodide (TBAI) solution in methanol was added for ligand exchange by incubation for 30 s and followed by cleaning in methanol. The concentration of PbS QD solutions for spin coating was 60, 50, 50, 40, and 30 mg/ml for QD sizes of d = 2.65, 3.16, 3.62, 3.9, and 4.96 nm, respectively. The SEM cross sections of the QD films are shown in Fig. S1 of the supplementary material. Their respective thickness for a single coating layer was 30, 30, 30, 17, and 14 nm measured by the ellipsometry. For Gr/QD photodetectors, QDs were deposited on Gr layers on Si/SiO₂ chips with the prepatterned Au electrodes. The active area of the photodetectors is defined by the area between electrodes, which have a width of 500 μm and are separated by 100 μm. The optical images of the Gr/QD devices are shown in Fig. S2 of the supplementary material.

Optoelectronic characterization: The light power of a 635 nm laser diode (CPS635R, Thorlabs) was measured with a standard silicon photodetector (S120VC, Thorlabs). The power intensity of the 635 nm laser diode was achieved by absorptive neutral density filters (NE503A, NE510A, NE520A, and NE530A, Thorlabs). Current vs voltage and current vs time data were measured using a Keithley 2400 source meter. The spectral response was measured using a Keithley 2400 source meter under a xenon lamp and filters (66485-500HX-R1, USFW-100, Newport) with a monochromator (CS260-RG-3-FH-D, Newport).

We synthesized PbS QDs with the ratio of PbO to oleic acid (PbO:OA) of 1:2, 1:5, 1:8, 1:13, and 1:24, resulting in QD sizes of d = 2.65, 3.16, 3.62, 3.90, and 4.96 nm, respectively. The TEM images and their PbO:OA ratios are shown in Fig. 2(a). Histograms with the size distributions of QDs are shown in Fig. S3 of the supplementary material. Figure 2(b) shows the relation between the PbO:OA ratio and the resulting size of the QDs. In addition to the PbO:OA ratio, previous reports show that the injection temperature can also be used to control the size and dispersity of PbS QDs.^29,31 X-ray diffraction (XRD) spectra shown in Fig. 2(c) show the crystallographic phase of the QDs. The peaks are well matched with a cubic PbS structure in accordance with previous reports.³² The broad peaks of the (111), (200), and (220) planes suggest that the size of PbS quantum dots is in the nanometer scale. The full-width-at-half maximum (FWHM) of the diffraction peaks increases as the size of the PbS QDs decreases as shown in Fig. 2(d). For nanocrystal particles, the Scherrer equation below allows us to estimate the particle size from the FWHM,³³ 

where d is the particle size, λ is the wavelength of the radiation, θ is the Bragg angle, β is the FWHM on a 2θ scale, and K is a dimensionless shape factor. By correlating the QD size extracted from TEM with d from the Scherrer equation, we can extract a shape factor of K = 1.05 to predict the size of the QDs from the FWHM of XRD data as shown in Fig. 2(e).

Figure 3(a) shows a series of absorption spectra for the PbS QDs of different sizes, showing a clear shift in absorption and its first exciton peak from λ = 805 nm for d = 2.65 nm to λ = 1350 nm for d = 4.96 nm. As expected from quantum confinement, the first exciton goes to a shorter wavelength (higher energy) as the size of the QD decreases. UV/vis transmission through QD films with varying thicknesses was performed to extract their absorption coefficients shown in Fig. 3(b). The full set of absorption curves as a function of thickness and wavelength is shown in Fig. S4 of the supplementary material, showing clearly the decrease in absorption as the thickness decreases and as the wavelength increases. The absorption coefficient was calculated by the Beer-Lambert law equation,³⁴ 

where I(λ) is the wavelength-dependent transmittance, I_o is the reference transmittance without the absorption film, α(λ) is the wavelength-dependent absorption coefficient, and t is the thickness of the absorption film. The absorption coefficients obtained and shown in Fig. 3(b) reach more than 10⁵ cm⁻¹ in the visible range, in good agreement with previous reports.³ The absorption coefficients also show a peak due to the first exciton level. From ellipsometry measurements, we extracted the refractive index and the extinction coefficient (n, k) of PbS QDs in the visible range. The (n, k) values for d = 3.62 nm QDs are shown in Fig. 3(c), and the full set of (n, k) for the rest of QD sizes is shown in Fig. S5 of the supplementary material. The extinction coefficient (k) from ellipsometry provides a second way to extract the absorption coefficient from the following expression:³⁵ 

The absorption coefficient values from ellipsometry and UV-vis absorption are shown in Fig. 3(d) for d = 2.65 nm, showing similar behavior in the vis range. The absorption coefficients from UV/vis absorption and from k (ellipsometry) for the rest of the QDs are shown in Fig. S6 of the supplementary material, which also show similar behavior in the vis range. The penetration depths extracted from UV-vis absorption coefficients are shown in Fig. 3(e). In the visible range (400–700 nm), the absorption levels are very similar for different QD sizes, showing that the most visible light has a penetration depth of <400 nm. However, for longer wavelengths in the IR (λ > 700 nm), the penetration depths increase drastically. IR photons have much larger penetration depths in smaller QDs since photons with large wavelengths do not have enough energy to be absorbed by smaller QDs with higher bandgaps. The penetration depths show a minimum at the first exciton level, which dominates the light absorption in the IR. The bandgap of PbS quantum dots is calculated from the following equation:³⁶ 

where α is the absorption coefficient, h is Planck’s constant, v is the photon’s frequency, and E_g is the bandgap. The value of the exponent denotes the nature of the electronic transition. PbS is the direct allowed transition, so r = 1/2 is used for the calculation. The bandgaps of PbS quantum dots shown are Eg = 1.39, 1.14, 1.07, 0.96, and 0.86 eV for PbS QDs with respective d = 2.65, 3.16, 3.62, 3.9, and 4.96 nm, as shown in Fig. 3(f).

Hybrid photodetectors were fabricated by spin coating PbS QDs on single layer Gr to investigate the hybrid Gr/QD photoresponse performance. PbS QDs of different sizes were coated on a graphene monolayer to reach a thickness of 150 nm. The photocurrent normalized for different sizes of QDs as a function of light wavelength is shown in Fig. 4(a) using a Xe lamp with a monochromator. The photocurrent is normalized to the highest photoresponse for each QD. The photocurrent shifts toward the IR and has a peak closely matching the absorption exciton peak. This behavior resembles the absorption spectrum behavior, proving the role of QDs absorbing light and generating photocarriers. After the photoresponse exciton peak, the photocurrent drops since longer wavelengths are not able to excite photocarriers. Figure 4(b) shows the photoresponsivity of 150 nm thick films with different sizes as a function of QD size under a λ = 635 nm laser excitation. The photoresponse clearly decreases as the size of the QDs increases. This can be related to a higher filling factor, i.e., more packed QDs, with smaller QDs. This higher filling factor will result in more QDs absorbing light with the same thickness. In addition, better packed QDs can result in easier transport of photoexcited holes through the QDs in their path to the bottom graphene. A lower response for larger QDs has also been observed in previous reports.¹⁹ The time response of Gr/QD photodetectors was also investigated, as shown in Fig. 4(c). The devices with different QD sizes show similar time responses in the time scale of the experiments, in all cases showing subsecond modulation, with rising times of ∼10 to 50 ms and slower recovery times of 50–100 ms. Time fittings are shown in Fig. S7 of the supplementary material. The recovery process also has a slower component >1 s, which has also been reported in previous hybrid Gr/QD reports associated with traps in the QDs.^19,26 However, Fig. 4(c) shows that subsecond modulation is possible with different quantum sizes and, therefore, with a broad spectral range. The time responses in Fig. 4(c) also confirm the higher photoresponse for smaller QDs. We also measured the effect of light intensity on photoresponse, showing a decrease in photoresponsivity as the light intensity decreases as shown in Fig. 4(d). The plot also confirms higher responsivity for smaller QDs. The decrease in responsivity with the light intensity is due to saturation in traps in QDs, higher recombination rate, and lower transfer of photocarriers from QDs to Gr.^20,26 Small QDs d = 2.65 nm can reach a photoresponsivity >10⁷ A/W. Overall, photoresponsivity is affected by QD size, bias voltage, power, and wavelength, with clear trends showing higher photoresponsivity for smaller QDs and under low incident power.

An important design parameter for QD photodetectors is the thickness. For correct operation, there is a lower limit to the film thickness set by the penetration depth, which is wavelength dependent. Films thinner than the penetration depth would rapidly collect less than 63% of light at the wavelength of interest, drastically reducing its photoresponse. Thickness also has an upper limit set by the diffusion length, which sets the maximum length that photocarriers can travel before they recombine. Due to the poor mobility of QD films, the diffusion length is typically below 200 nm.²⁷ This compromise in thickness is illustrated in Fig. 5(a). We study the photoresponse of hybrid Gr/QD devices as a function of thickness using the smallest PbS QDs (d = 2.65 nm). Figure 5(b) shows the photocurrent vs wavelength with various thicknesses of 2.65 nm PbS QDs. Thin layers show higher responsivity in the vis range (∼400 to 600 nm). As the thickness increases, their photoresponse improves toward the infrared. Figure 5(c) shows that for visible light (λ = 500 nm), the maximum photoresponse is at t = 360 nm, but for thicker films, the responsivity rapidly decreases. For near IR light (λ = 800 nm), the maximum photoresponsivity is at t = 1250 nm, followed by a decrease as t increases. Thin films absorb visible light efficiently due to its short penetration depth while also collecting photocarriers efficiently since they are thinner than their diffusion length. However, thin films collect IR light poorly, resulting in a low photoresponse. For thick films, such as t = 1200 nm, visible light is effectively absorbed in the top 500 nm layers, but the charges recombine before reaching the bottom graphene charge collector. For IR light, as the wavelength increases, it gets absorbed deeper into the QD film and closer to the graphene collector, increasing the photoresponse as the wavelength increases until reaching the bandgap edge. Figure 5(d) shows the wavelength detection window vs thickness. The long wavelength limit (low energy) is determined by the size (bandgap) of the PbS QDs, and the bottom limit (high energy) of the window is set by the thickness of PbS QDs. The window was set as the full-width at half maximum of the spectral response from Fig. 5(b). Above t = 700 nm, high energy photons absorbed at the top cannot reach the graphene layer and only longer wavelengths penetrate deep enough to produce photocarriers near the graphene layer. As t increases, the response window narrows down toward the infrared. In cases in which the graphene collector would be on top, these trends would reverse. Recently, it was shown that intercalated layers inside the QD film can overcome the limitations of the short diffusion length on the thickness of hybrid Gr/QD photodetectors.²⁷ Figure 5(e) shows the time response for different thicknesses under λ = 635 nm. The photoresponse is higher for thin films and decreases as the films get thicker. In all cases, we observe fast modulation below the subsecond scale. These results show that in addition to the QD size, the thickness can also be used to tune the spectral response of hybrid Gr/QD photodetectors keeping subsecond time modulation capabilities.

In summary, we report on the optical properties of PbS QDs and the effect of QD size and film thickness on the photoresponse of novel hybrid PbS QD on graphene photodetectors. The size of PbS QDs is controlled by the ratio of PbO and oleic acid. The size allows controlling the absorption spectrum, shifting the absorption peak due to the first exciton peak to longer wavelengths as the QD size increases. The absorption coefficient of PbS QDs reaches values of 10⁵ to 10⁴ cm⁻¹ in the visible region with little variations with the QD size. In IR, the absorption coefficients are size dependent as the first exciton peak shifts. The photoresponse of hybrid Gr/QD photodetectors has a high responsivity (>10⁷ A/W), with a response time of ∼50 ms and a recovery time of ∼100 ms for varying QD sizes and film thicknesses. As expected, as the QD size increases, the spectral photoresponsivity is shifted toward the IR. For a fixed thickness, the responsivity decreases as the QD size increases, which can be due to a lower packing factor as the QD size increases; however, further analysis is required. The thickness also allows us to tune the spectral response of the QDs, with thin (t < 400 nm) films having stronger photoresponse in the visible and thicker films enhancing the response toward the IR. The results herein provide valuable information to design the QD size and film thickness for a high response and tunable spectrum hybrid QD/Gr photodetector.

See the supplementary material for SEM cross sections of QD films (Fig. S1), optical images of devices (Fig. S2), size histogram from TEM images (Fig. S3), transmission spectra (Fig. S4), refractive index (n, k) (Fig. S5), absorption coefficient: UV/vis vs ellipsometry (Fig. S6), fitting for response and recovery time (Fig. S7), and I/V curves as a function of power intensity for different QD sizes (Fig. S8).

This work was supported by the National Science Foundation under Award No. 1710472. This work was performed in part at the San Diego Nanotechnology Infrastructure (SDNI) of UCSD, NANO3, a member of the National Nanotechnology Coordinated Infrastructure, which was supported by the National Science Foundation (Grant No. ECCS-1542148). S.A. was supported by the Kwanjeong Fellowship from the Kwanjeong Educational Foundation.