Application of perovskite quantum dots in carrier redistribution in III-V multijunction solar cells with luminescent coupling effect

Abstract. The luminescent coupling effect in a multijunction solar cell is known to help achieve current matching among subcells through carrier redistribution. We demonstrate the carrier redistribution in III-V multijunction solar cell devices using a moisture-resistant, all-inorganic perovskite quantum dot (PQD) film. This hydrophobic PQD film was applied on a full III-V multijunction solar cell device. This successfully demonstrated current redistribution vertically, shown by the increased current collection in the lower bandgap subcells, and laterally, as observed from improved current collection homogeneity in the lower bandgap subcell adjacent to the higher bandgap subcell where the luminescence originated.


Introduction
The III-V multi-junction solar cells (MJSCs) currently hold the best research cell efficiency record of 47.1% under concentrated sunlight. 1 To further increase this, the current produced among its subcells should be as matched as possible. In experimental devices, current matching among series-constrained III-V MJSC subcells can be naturally achieved through the luminescent coupling (LC) effect. The LC effect is known as the reabsorption of photons emitted from a higher bandgap subcell to a lower bandgap subcell. [2][3][4][5] Previous studies have reported that when this effect is made stronger through controlled external irradiation upon a higher bandgap subcell, larger current can be produced in the lower bandgap subcell. [6][7][8][9][10][11][12][13][14][15] However, the LC efficiency was found to saturate within 60% to 70% of radiative emission in the higher bandgap subcell. 16 The use of metal halide perovskite quantum dots (PQDs) could be a cost-effective way to enhance photon emission toward the current-limiting cell. Recently, composition-tunable metal halide PQDs were reported as candidate materials for producing high-efficiency photovoltaic devices. 17,18 In particular, all-inorganic cesium lead halide (CsPbX 3 ) PQDs were observed to have higher absorption coefficients, narrower emission wavelengths, higher photoluminescence (PL) quantum yields, and better oxidation resistance than methylammonium lead halide (CH 3 NH 3 PbX 3 ) PQDs. [19][20][21][22][23][24][25][26][27][28][29] The goal of this work was to demonstrate current matching among III-V MJ subcells using moisture-stable CsPbX 3 PQDs applied on full III-V MJSC devices limited by a lower bandgap subcell. When current matching among MJ subcells is achieved, the MJSC conversion efficiency can be increased further. This approach was also an attempt to enhance the LC effect homogeneity in a current-limiting subcell through photopassivation by the PQD layer. Attaining this could help maximize the lifespan of MJSCs. 11 2 Methodology

Perovskite Quantum Dot Synthesis
CsPbX 3 (X = Br and I) PQDs were synthesized using the methods reported in Refs. 25 and 26. The same process reported in Ref. 27 was used to prepare the cesium (Cs)-oleate precursor solution and for synthesis in the reaction flask (RF). The synthesis temperature was set at 170°C to produce ∼8-nm 25 to 9.5-nm 26 PQD nanocrystals. The synthesized PQDs were diluted in hexane to achieve a 5-mg∕mL CsPbI 2.5 Br 0.5 PQD solution. The detailed procedure of the CsPbI 2.5 Br 0.5 PQD solution preparation can be found in Appendix A.

Perovskite Quantum Dot-Cyclic Olefin Copolymer Solution
Perovskite materials, by themselves, are known to be easily degraded by moisture; hence, their performance as photonic materials easily decline over a short period of time, from a few weeks to a few minutes under typical atmospheric conditions. [30][31][32][33][34][35][36][37][38] To protect the PQDs from humidity, polymer matrices can be used. Polymer matrices can be made from one or a combination of materials from the group consisting of polystyrene (PS), polycarbonate (PC), cellulose acetate (CA), polyvinyl chloride (PVC), polyvinylidene fluoride (PVDF), polyurethane (PU), polymethyl methacrylate (PMMA), polyvinyl alcohol (PVA), polyethylene oxide (PEO), polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), polymaleic anhydride-alt-1-octadecene (PMA), and polynitriles. [39][40][41][42][43][44] Aside from these, amorphous thermoplastics such as cyclic olefin copolymers (COCs) are known to be moisture-resistant 45,46 and are transparent to wavelengths beyond 300 nm 47,48 for about 88%, as shown in Fig. 1(a). Figure 1(a) shows the light transmission spectrum of the COC film as found in the manufacturer's datasheet. 48 Experimentally, COC was found to be transparent to wavelengths between 200 and 1000 nm by 91%, as shown in Fig. 1(b). This was derived from the reflectance measurements of COC on a quartz substrate. The reflectance measurements were obtained using a commercial ultraviolet (UV)-visible light spectrophotometer. It also has a refractive index of 1.5, making it optically compatible with III-V optoelectronic materials used in solar cell fabrication. Solar cell devices are designed to absorb UV, visible, and infrared (IR) wavelengths from the sun and are made of III-V semiconductors typically with refractive indices of more than 2.0 for III-V materials and more than 1.5 for II-VI materials. 49 Because of its suitable optical properties and its capability to protect perovskite materials from moisture, this amorphous thermoplastic film was used as the CsPbI 2.5 Br 0.5 PQD encapsulant by mixing.
COC pellets dissolved in cyclohexane (C 6 H 12 ) were added to the synthesized CsPbI 2.5 Br 0.5 PQD solution before substrate dip coating. In this work, about 50-mg∕mL COC dissolved in C 6 H 12 by ultrasonic bath were mixed with at least 10-mg∕mL CsPbI 2.5 Br 0.5 PQDs dispersed in hexane (C 6 H 14 ) to form moisture-robust PQD films on a target substrate. Considering C 6 H 12 and C 6 H 14 volatilities, only a rough estimate of the solution concentration at the time of preparation can be made, based on the measured masses of the pure COCs and CsPbI 2.5 Br 0.5 PQDs and the injected volumes of C 6 H 12 and C 6 H 14 , respectively. The COC in C 6 H 12 and PQD in C 6 H 14 solutions were mixed at a 1:1 proportion before dip coating the III-V MJSC samples. Hence, the approximate concentrations of each solution in the mixture were effectively halved. Concentrations of COC in C 6 H 12 and PQD in C 6 H 14 became 25 and 5 mg∕mL, respectively. The MJSCs dipped into the PQD-COC solution were commercial, third-generation, terrestrial grade 0.31 cm 2 InGaP/GaAs/Ge 3JSCs samples. These samples were mounted on copper plate and were partially encapsulated. Each of the samples is connected to a bypass diode.
In the past, it was found that the optimal withdrawal speed of GaAs, a III-V material, to produce optically smooth and emissive films was 5 mm∕s, where the values tested were between 1 and 20 mm∕s. 27 In dip coating, the withdrawal speed is the most critical parameter that affects both the film thickness and its quality. 50,51 On the other hand, the number of dipping cycles was fixed at 5 times.

Electro-optical Characterization
The dip-coated MJSC samples were evaluated through a laser beam induced current (LBIC) mapping method at room temperature. Here each subcell was made current limiting and subjected to either LC effect excitation or direct laser irradiation. 8 These measurements were validated through external quantum efficiency (EQE) and current-voltage (J − V) characteristics measurements.

Laser beam induced current mapping
To acquire the spatial distribution profile of photocurrent produced in subcells at the various conditions listed in Table 1, the 3JSC samples were subjected to the LBIC mapping method. Here continuous LED biases were used to make a specific 3JSC subcell current limiting. This was done to ensure that there would be no change of current-limiting subcell during the LBIC measurements.
The InGaP photocurrent collection maps were acquired by switching on continuous 780-, 970-, and 1550-nm LEDs at the same time. Their intensities are summarized in Table 1, condition 1. In this condition, a 450-nm pulsed laser was used to excite the InGaP top cell. Then the GaAs LC current collection maps were obtained by switching on continuous 440-, 970-, and 1550-nm LEDs (condition 2), while a 450-nm modulated laser excited InGaP. Since there was no light bias exciting GaAs, its LC current collection was measured. Then through direct laser excitation, the GaAs photocurrent collection maps were acquired by switching on continuous 440-, 970-, and 1550-nm LEDs (condition 3). With these LEDs, a 785-nm pulsed laser was activated to excite GaAs. As for the bottom cell, the Ge LC current collection maps were obtained by switching on continuous 440-and 660-nm LEDs simultaneously (condition 4). Then a 785-nm pulsed laser was also activated to excite GaAs. Since there was no light bias exciting Ge, its LC current collection was measured. Finally, by direct 1064-nm laser excitation, the Ge photocurrent collection maps were acquired by switching on continuous 440-and 660-nm LEDs (condition 5). The specifications of the modulated lasers used in LBIC mapping are summarized in Table 2.
The lasers have a duty cycle of 50%, a switching frequency of 2000 Hz, and a scanning frequency of 2 Hz. For performance stability, the temperature of the lasers was kept at 20°C.

External quantum efficiency
To determine the number of incident photons successfully converted into electrons, subcell EQE measurements were performed on the III-V based MJSC samples. First, an external voltage was applied across the 3JSC sample. Then the evaluated subcell was made current-limiting using continuous LED settings as listed in Table 1. Next, continuous light from a white lamp source with a global air mass 1.5 (AM 1.5G) filter was passed through a monochromator and a chopper to produce an optical AC signal with different wavelengths. The generated AC signal response was then measured using a lock-in amplifier. Finally, the EQE signal generated was recorded in a desktop computer connected to the setup components.

Current-voltage (J-V) characteristics measurement
The DC J-V characteristics measurements were obtained under global air mass 1.5 (AM 1.5G) sunlight conditions from InGaP/GaAs/Ge 3JSC samples before and after PQD-COC film application. For these measurements, an AM 1.5G filtered white lamp was used and precalibrated using a 0.1-cm 2 crystalline silicon photodiode detector with known current production at 1 sun.

Integrated current density at AM 1.5G
The reference spectrum for the EQE measurements used was the AM 1.5G standard. From the subcell EQE measurements, the equivalent AM 1.5G current density at an applied terminal voltage V, J AM1.5G ðVÞ, was calculated by integrating the solar irradiance within the absorption range of a certain subcell. This is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 1 6 2 J AM1.5G ðVÞ ¼ q hc Here EQEðλ; VÞ is the subcell EQE response to incident wavelength λ at V, I AM1.5G ðλÞ is the reference AM 1.5G solar spectrum irradiance at each wavelength based on the ASTM G173-03 standard, 52 λ i−1;UL and λ i−1;LL are the upper and the lower limits of the subcell absorption range, respectively, and the remaining variables are commonly known constants. The absorption ranges of the InGaP/GaAs/Ge 3JSC subcells were determined from the EQE measurements obtained.

Standard deviation of the current collection
From the LBIC measurements, the standard deviation of the current collection σ x given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 6 6 2 was calculated to quantify the spatial uniformity of current production by inducing the LC effect 12,15 or by direct single-wavelength excitation on the current-limiting cell of the 3JSC samples before and after PQD film deposition. In this equation, the subscript x refers to the direct subcell (x: DS) or to the LC effect (x: LC) excitation, N is the total number of points in an LBIC map, J l is the current collected at a spot l, and J is the average subcell current obtained at all points on the map. Better current distribution uniformity is indicated by a lower value of σ x .

Percent differences
To compare the samples before and after PQD-COC dip coating of 3JSCs, the percent difference of a parameter Y, %ΔY x , was calculated. Here Y can be the average current production J x;ave or the standard deviations of the current collection σ x described in Eq. (2). %ΔY x was calculated using the following relation: ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 4 4 7 This was obtained to quantify the change in Y before ½Y xðbeforeÞ and after PQD-COC film deposition ½Y xðafterÞ on the MJSC front surface. The following results indicate performance improvement after deposition: a positive %ΔJ x;ave denotes an increase in the current collection, whereas a negative %Δσ x is interpreted as current homogeneity improvement.

Preliminary PQD-COC Deposition on a III-V Substrate
Before application on full III-V MJSC devices, PQD-COC was first deposited on semi-insulated, undoped GaAs substrates. From the single-layer samples, the following were obtained: (1) the PL spectrum, from which the peak emission wavelength was acquired, (2) the qualitative PL under 365-nm UV light to augment the PL spectroscopy results, (3) the surface roughness, and (4) the thickness of PQD-COC films. The PL spectrum of the CsPbI 2.5 Br 0.5 PQD without and with COC are shown in Figs. 7(a) and 7(b) (Appendix B), respectively. As shown in these images, the peak emission wavelength of the PQD on GaAs is about 680 nm. In a span of 2 months, the PQD-COC on the GaAs sample exhibited less PL intensity degradation. This suggests that the COC preserved the PL properties of the CsPbI 2.5 Br 0.5 PQDs under ambient air conditions. Moreover, the UV PL from the PQD-COC film on GaAs was observed to be more emissive than the sample without COC. The PQD films without (left) and with COC (right) under white room light and under 365-nm UV PL are shown in Figs. 9(a) and 9(b) (Appendix B), respectively.
The surface roughness of the CsPbI 2.5 Br 0.5 PQD on GaAs without and with COC was obtained through atomic force microscopy (AFM) imaging, as shown in Fig. 10. The measurements of the surface roughness of the samples without and with COC were 9.79 and 1.33 nm, respectively. Meanwhile, the average thicknesses of the PQD film on GaAs without and with COC were found to be 1.021 and 1.089 μm, respectively. These values were obtained through the stylus profilometer measurements shown in Fig. 11 (Appendix B).
More details on the optical and surface characterization of PQD-COC on GaAs can be found in Appendix B.

Current Collection and Homogeneity
To determine the effect of adding PQD-COC on InGaP/GaAs/Ge 3JSCs, the LBIC maps were acquired from each subcell before and after dip coating 5 times, with GaAs being the limiting subcell in some cases. 53,54 Figure 2 shows the simplified illustration of the 3J sample with PQD-COC film on the front surface. The series of LBIC maps before and after PQD-COC DC are shown in Fig. 3. Also the J x;ave and σ x values together with their percent differences before and after PQD-COC DC are summarized in Tables 3 and 4, respectively.
Comparing the LBIC maps acquired through direct InGaP excitation before [ Fig. 3(a)] and after [ Fig. 3(b)] dip coating the 3J sample into the PQD-COC solution, the current collection in InGaP decreased after dip coating by 13.5%, based on the J InGaP;ave values calculated from LBIC maps acquired. Furthermore, σ InGaP increased after dip coating by 11.4%, indicating spatial current uniformity degradation. This suggests that the PQD-COC film was able to absorb some portion of the incident light before it reached the top cell.
As for the GaAs LC and direct 785-nm laser excitation, 12.3% and 7.5% increases in the current collection were observed after dip coating Meanwhile, 6.6% and 20.2% current collection increases and 5.54% and 5.66% current homogeneity improvements were observed from Ge LC and direct 1064-nm laser excitation, respectively. Because the light absorption in the GaAs middle cell was enhanced by the light emitted from the deposited PQD-COC film, the LC effect between GaAs and Ge subcells became stronger. This was reported in past literature that specifically tackled the LC effect between these subcells in InGaP/GaAs/Ge 3JSC devices. [7][8][9]14,15 Collectively, the results from the LBIC measurements suggest that dip coating PQD on full III-V MJSCs is a potential solution for both current matching and homogenizing subcell current collection.

Subcell EQE Measurements
The trend observed from the LBIC measurements shown in Fig. 3 was investigated further by comparing the subcell EQE measurements before and after PQD-COC dip coating. These measurements are shown in Fig. 4. Although the InGaP EQE decreased, some increase in the longer  wavelength region of GaAs and an increase in Ge EQE were observed. The decrease of the InGaP EQE is inferred as the decrease in InGaP current density. On the other hand, the increases in both GaAs and Ge EQE measurements after PQD-COC dip coating indicate an increase in GaAs and Ge current densities. These were numerically confirmed by the calculations of J AM1.5G;i from the subcell EQE measurements using Eq. (1). These are summarized in Table 5. Before dip coating, the current-limiting cell was found to be the GaAs middle cell, having the lowest current density value of 10.3 mA∕cm 2 among the subcells. After dip coating the InGaP/ GaAs/Ge 3JSCs into the 680-nm PQD-COC solution, EQE measurement and J AM1.5G;i calculations revealed that photon re-emission from the PQD-COC film toward the middle cell occurred. These results then confirm that controlling current matching among subcells is possible through PQD-COC film deposition on full III-V MJSCs. On the other hand, the EQE increase in the Ge bottom cell further suggests that the increased absorption in the GaAs middle cell has led to a stronger LC effect between GaAs and Ge subcells.

Impact on the 1-sun J-V Characteristics
To determine the impact of adding CsPbX 3 PQDs with the moisture encapsulant on the net performance of the MJSCs, J-V characteristics were obtained across the sample terminals before and after PQD-COC deposition on full InGaP/GaAs/Ge 3JSC devices at 1 sun. The J-V characteristics measurement at AM 1.5G, 1 sun condition, showed a decrease [ Fig. 5], confirming further that InGaP became the current limiting cell. This decrease, which corresponds to its EQE and J AM1.5G;InGaP decreases, implies that the thickness of the PQD film is not yet optimum. Hence, optimizing the PQD-COC film thickness to be applied on current-mismatched MJSC devices could be a step closer to improved MJSC conversion efficiency in the bigger picture.

PQD-COC Deposition as an Additional Step in III-V MJSC Device Fabrication
Reflectance measurements of PQD on GaAs samples with and without COC solution added to the CsPbX 3 PQD solution were obtained. This was done to determine if the refractive indices n of the films are larger or smaller than those of the III-V materials typically used as solar cell absorbers. Details on how to qualitatively determine n can be found in Appendix C. Figure 6 shows the reflectivity spectra of a GaAs substrate dipped 5 times on a PQD-COC solution, together with those of HCl-treated, bare GaAs substrate and those from the published Fig. 6 Reflectivity spectra derived from GaAs substrates dip coated 5 times on PQD solutions with and without COC added. These are plotted together with the reflectivity of InGaP, 55 GaAs, 56 and SiN x , 57 derived from optical constants, n and k . Plots with * on their labels were obtained from previous literature, while plots with ** were acquired experimentally. spectrally resolved n and extinction coefficient k values of InGaP 55 and GaAs. 56 The spectra were calculated using Eq. (6). The PQD-COC film had a larger R, and therefore a larger n, than silicon nitride (SiN x ). SiN x is typically used as an antireflection coating (ARC) for solar cells, with n value being less than those of the III-V materials. Considering light refraction, the active layers of an MJSC should be stacked from the lowest refractive index to the highest, following the direction of the incident light. Hence, it can be inferred from Fig. 6 that the PQD-COC film can be deposited after growing the III-V stack but before the deposition of an ARC such as SiN x . 57 Alternately, if the MJSC is already fabricated, the limiting subcell current should be determined first. Then an optimum PQD-COC film thickness should be fabricated, as recommended earlier.

Conclusion
A pathway to possibly homogenize and increase current collection in a limiting cell of a III-V MJSC device is through the application of a PQD-amorphous thermoplastic film. The PQD-COC on a full III-V MJSC device successfully demonstrated current redistribution from the top cell and improved current homogeneity in the lower subcells-either by direct light re-emission from the PQD-COC layer or by consequently enhancing the LC effect between adjacent lower bandgap subcells. Thus for enhanced MJSC current matching, the use of a photoassistive layer like PQD, encapsulated with COC or other hydrophobic, amorphous thermoplastic films is recommended.   PL spectroscopy measurements were obtained for CsPbI 2.5 Br 0.5 PQDs on GaAs substrates between 500 and 950 nm. In the PL measurement setup, a continuous 532-nm laser was used to excite the PQDs on GaAs samples, having it pass through an IR-absorbing filter, a transmission filter, and a series of mirrors and a beam splitter. The output power of the laser before it passes through the mentioned optical elements ranges from 60 to 70 mW. The spot size of the 532-nm laser is about 100 μm. The transmissivity of the filter used was 10% and the exposure time of the charge-coupled device camera detector was fixed at 20 ms. These settings were used such that PL intensities of the samples would not saturate the detector. Also the grating and the slit width of the photodetector were fixed at 150 gratings∕500 nm and 50 μm, respectively. To compare the PL emission spectra appropriately, the samples were mounted alongside each other such that the mount was only moved along one axis. Then each sample was excited approximately at its center.
PL emission spectra were obtained at different times after dip coating GaAs substrates five times into CsPbI 2.5 Br 0.5 PQD solutions without [ Fig. 7(a)] and with COC [ Fig. 7(b)], simultaneously. It was observed that the PL emission intensities were larger in samples with no COC than those from substrates with COC within 48 h after dip coating. In this instance, the samples had experienced an average of 60% humidity. The larger PL from samples without COC may be attributed to the lower volatility of the PQD-COC solution than the PQD solution without COC, that is, the latter's solvent evaporated faster than that of the PQD-COC. As a result, the PQD solution without COC may have had a larger effective concentration than the PQD-COC solution, which then could have allowed a larger number of PQDs to be deposited on the GaAs substrates. Hence, a higher PL was observed within the spot area of the 532-nm excitation laser of the PQD on the GaAs sample. However, after a week to 2 months of experiencing average humidity between 56% and 57%, the PQD-COC on the GaAs sample exhibited less variation in PL emission, whereas the PQD on the GaAs sample showed a decrease in PL emission over time. From these results, it may be inferred that the COC was able to protect the PQDs from ambient moisture, and without COC, the PQD film oxidized overtime under ambient humidity. Hence, COC, a hydrophobic material, can act as a moisture barrier that may preserve the desired optical properties of the CsPbX 3 PQDs.
The addition of the COC solution to the PQD solution before substrate dip coating did not alter the peak emission wavelength λ peak;1 , which was around 680 nm [ Table 6]; hence, the COC did not cause regressive effects on the λ peak of the PQDs. On the other hand, a blue shift of about 10 nm was observed from λ peak;1 of the PQD sample without COC after 2 months. This could be due to the oxidation of the film, leading to film volume reduction as observed in quantum dots intended for live cells. 58 The expected PQD sizes D PQD were calculated using an empirical formula 59 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 3 1 1 where λ peak is the CsPbX 3 PQD peak emission wavelength obtained from PL spectroscopy. Based on the measured λ peak;1 values corresponding to peak 1 in Fig. 7 as listed in Table 6,   Table 7.
Although it was not expected, a weak secondary peak emission, λ peak;2 , appeared between 760 and 840 nm wavelengths in all logarithmic PL spectra plots measured from both samples, as shown in Fig. 7. This could be attributed to the PQDs that formed aggregates during dip coating, making the effective dot size in some areas of the substrate be about 20 nm. The sizes of the PQD aggregates based on the measured λ peak;2 (D PQD;2 ) are summarized in Table 7. These were confirmed by scanning electron microscopy (SEM) imaging of CsPbI 2.5 Br 0.5 PQDs on the GaAs substrate shown in Fig. 8. During the counting, the SEM image was partitioned into 4 × 6 parts or a total of 400 × 600 nm 2 . A box plot of the number of dots per area was provided [ Fig. 8(c)].
Here the dots were clustered as either having a diameter of ∼10 or 20 nm.
PL peak emission from the GaAs regime of all samples λ peak;3 was observed between 800 and 900 nm. This was weak compared with the λ peak;1 because there was no carrier confinement structure 60 or a passivation layer 61-70 that may assist absorption or emission grown on the GaAs  substrate. Hence, improving the interface between the PQD film and the GaAs substrate 71 may increase the PL intensity in the latter.
To further investigate the PL observations, the samples were subjected to 365-nm UV irradiation in a dark room within 48 h after DC. Figures 9(a) and 9(b) show the PQD films without and with COC under white room light and under a 365-nm UV lamp, respectively. Upon exposing the samples under the 365-nm UV lamp at room temperature with 49% humidity on the day of dip coating (December 6, 2019), the PL emission from the PQD-COC films were observed to be much stronger as compared with samples having PQD films only. Comparing with the PL spectra obtained through 532-nm laser excitation within 48 h after dip coating, the UV-PL images suggest that the PL emission strength of PQD films have an excitation wavelength dependence. Nevertheless, the UV-PL images confirm the effectiveness of COC in protecting the optical performance of CsPbI 2.5 Br 0.5 PQDs under an environment with high-humidity and high-light energy exposure.

Surface Morphology
The surface morphology of CsPbI 2.5 Br 0.5 PQDs deposited on GaAs substrates was evaluated through AFM imaging. During imaging, a 3 μm × 3 μm surface approximately within the center of the sample was observed. From these measurements, the root-mean-square values of the PQD film surface roughness S q were obtained. This parameter was interpreted depending on the expected PQD nanocrystal size D PQD , which can be predicted using Eq. (4). If the S q value acquired was less than or equal to D PQD , the deposited film was considered optically smooth. Also a lower S q value indicates better PQD deposition uniformity.
To compare the surface morphologies of the samples with and without the COC solution added to the PQD solution, AFM images were obtained from PQD films without and with COC on GaAs. These images are shown in Figs. 10(a) and 10(b), respectively. The one with COC garnered a lower S q of 1.33 nm; hence, it is optically smoother than the one without COC (S q ¼ 9.79 nm). In this aspect, PQD films with COC are more desirable than those without COC.

Film Thickness Measurement
The thicknesses of CsPbI 2.5 Br 0.5 PQD films on GaAs substrates were measured using a stylus profilometer. These were measured at a scanning resolution of 0.167 μm using a 12.5-μm-radius stylus set to 2-mg scanning force. The average thicknesses of the PQD film on GaAs without and with COC were 1.021 and 1.089 μm, respectively. The average values were acquired from the height profile shown in Fig. 11 after a leveling correction was applied. These measurements were obtained 3 days after dip coating.
where Ref Ag is the measured reference silver mirror reflectance, Ref bg is the background reflectance, and Ref sample is the measured reflectance of the sample. From the published wavelengthresolved optical constants, which are the refractive index nðλÞ and the extinction coefficient kðλÞ, the reflectivity can be calculated as well. It is given as 72 Fig. 11 Height profiles of CsPbI 2.5 Br 0.5 PQD on GaAs (dotted line) and CsPbI 2.5 Br 0.5 PQD-COC on GaAs (solid line) after DC 5 times and being kept under an average (ambient) humidity of 56% to 60% acquired through stylus profilometry. These profiles were obtained 3 days after DC. R ¼ ð1 − nÞ 2 þ k 2 ð1 þ nÞ 2 þ k 2 : Here a larger set of R values relative to others implies a larger refractive index. The published optical constants of InGaP, 55 GaAs, 56 and SiN x , 57 commonly used as the ARC for solar cells, were used for reflectivity calculations, in comparison with those derived from measured reflectance of PQD on GaAs samples with and without COC.
Nazmul Ahsan received his BE degree in electrical and electronic information engineering from Toyohashi University of Technology, Japan, in 1997 and his MS degree and PhD in electronic engineering from the University of Tokyo (UT), Japan, in 1999 and 2002, respectively. He then held a Japan Science and Technology Agency research fellowship at UT and worked on light and electric field control of ferromagnetism using III-V heterostructures. He is currently a project associate professor at the Research Center for Advanced Science and Technology (RCAST), Utah, USA. His research interests include ultra-high-efficiency photovoltaic devices, spintronic devices, and molecular beam epitaxy of compound semiconductors. His articles have more than 1000 citations (Google Scholar).