## 3 Results  
Figure 1 depicts the morphology, size and structure of the PbS QD nanocrystals, which were measured using TEM and the high-resolution TEM technique. Figure 1a shows the size of the QD in the range of 3-8 nm; it is spherical of shape and very uniform. Figure 1b is the size distribution histogram of more than 100 nanoparticles of PbS, which demonstrates that the nanoparticles are highly monodisperse and high purity, with an average diameter of 4.2 \(\pm\) 0.3 nm. The high-resolution TEM image (Figure 1c--inset) of one nanoparticle reveals that the material is highly crystalline with lattice spacing of 0.295 nm. The diffraction rings in the selected-area electron diffraction pattern of the nanoparticles (Figure 1d) show the corresponding cubic rock-salt structure of bulk PbS. The pattern shows the clear planes of (111), (200), (220), (311) and (222) of PbS. This result matches well with the X-ray diffraction result in our previous work [13]. Furthermore, Figure 2a-d shows the transmission electron microscopy images of rGO. From Figure 2a, it is observed that rGO is a transparent thin sheet-layered structure, which is prepared from graphene oxide [17]. Figure 2b shows the selected area electron diffraction  
Figure 1: (**a**) Transmission electron microscopy (TEM) image of PbS nanoparticles, (**b**) size histogram of PbS nanoparticles, (**c**) high-resolution TEM image a PbS nanocrystal and (**d**) selected area electron diffraction pattern of PbS nanocrystal. (SAED) pattern of the rGO, which has two rings. The outer ring is indicated by the (0001) face, whereas the inner ring is assigned to the (1100) face. The X-ray diffraction pattern of rGO is displayed in Figure 2c. There are two diffraction peaks: the first peak at the position of 20 = 23.5\({}^{\circ}\) confirms that the GO was completely transformed into rGO by hydrazine solution [18] and the second peak at the position of 20 = 43\({}^{\circ}\) confirms the (100) plane of the hexagonal carbon structure [19]. The surface morphology of rGO film on the glass substrates was measured using AFM technique with 5 \(\upmu\)m \(\times\) 5 \(\upmu\)m as scan area, as shown in Figure 2d. We observed that the surface roughness of the film is \(\sim\) 3 nm. The device performance of the VFQPH solar cells was fabricated and characterized using solar simulation under AM 1.5 illumination at 100 mW/cm\({}^{2}\). The solar cell responses of the devices with the structure of ITO/PEDOT:PSS/PbS:PCBM/E-GaIn, ITO/rGO/PbS:PCBM/E-GaIn and ITO/rGO/PEDOT:PSS/PbS:PCBM/E-GaIn are displayed in Figure 3i,a and Table 1. The device with PEDOT:PSS as a hole transport buffer layer shows a short-circuit current, \(J_{\text{sc}}\) = 3.41 mA/cm\({}^{2}\), open-circuit voltage, \(V_{\text{oc}}\) = 0.67 V and fill factor, FF = 62%; however, the cell's power conversion efficiency (PCE) is affected by low fill factor and current density leading to a PCE of about 1.52%. The device with rGO as a hole transport buffer layer displays a short-circuit current, \(J_{\text{sc}}\) = 4.58 mA/cm\({}^{2}\), open-circuit voltage, \(V_{\text{oc}}\) = 0.7 V, fill factor, FF = 67% and PCE of about 2.14%. The highest power conversion efficiency, PCE = 3.27%, short-circuit current, \(J_{\text{sc}}\) = 6.69 mA/cm\({}^{2}\), open-circuit voltage, \(V_{\text{oc}}\) = 0.7 V and fill factor, FF = 70% for the device with rGO/PEDOT:PSS was inserted as a hole transport buffer layer. Figure 2: (**a**) Transmission electron microscopy (TEM) image of rGO, (**b**) selected area electron diffraction pattern of rGO, (**c**) X-ray diffraction pattern of rGO and (**d**) surface morphology of rGO film on the glass substrate. To study the electric contact properties in the interface between the electrode and the active layer, the material's resistivity, such as shunt resistance (Rsh) and series resistance (Rs), should be measured to further evaluate device performance. A good solar cells device should have low series resistance and high shunt resistance.