GaAs quantum dot solar cells attributed to quantum dot size effects

GaAs quantum dot solar cells attributed to quantum dot size effects

Solar Energy Materials & Solar Cells 155 (2016) 70–78 Contents lists available at ScienceDirect Solar Energy Materials & Solar Cells journal homepag...

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Solar Energy Materials & Solar Cells 155 (2016) 70–78

Contents lists available at ScienceDirect

Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat

Efficiency limit of InAs/GaAs quantum dot solar cells attributed to quantum dot size effects Im Sik Han a, Ryan P. Smith b, Jong Su Kim a,n, Sam Kyu Noh c, Sang Jun Lee c,n, Chang-Lyoul Lee d, Jae-Young Leem e a

Department of Physics, Yeungnam University, Gyeongsan 712-749, Korea Department of Physics, California State University - East Bay, Hayward, CA 94542, USA c Division of Convergence Technology, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea d Advanced Photonics Research Institute, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea e School of Nano Engineering, Center for Nano Manufacturing, Inje University, Gimhae 621-749, Korea b

art ic l e i nf o

a b s t r a c t

Article history: Received 12 September 2015 Received in revised form 19 March 2016 Accepted 26 April 2016

The effects of quantum dot (QD) size on the optical and electrical properties of InAs/GaAs QD solar cells (QDSCs) were investigated. QDSCs with varying InAs QD size were fabricated by controlling the total InAs deposition thickness (θ) from 0 to 3.0 mono-layers (ML). The optical and electrical properties of the QDSCs were investigated using photoluminescence (PL), time-resolved PL (TRPL), photoreflectance (PR) spectroscopy, capacitance-voltage (C-V), and current-voltage (J-V) measurements. The QD size effects on the p-n junction electric fields (Fpn) and the efficiencies (η) of the QDSCs were revealed. The QDSCs had a maximum η of 21.17% for θ ¼2.0 ML (the efficiency is enhanced by 17.4% over the reference GaAs-SC) and minimized Fpn (113 kV/cm) by an enhanced photovoltaic effect caused by improved carrier generation. We find that these optimal properties result from a balance between carrier generation and exhaustion processes through trapping and re-capturing by defects and relatively large QDs. & 2016 Elsevier B.V. All rights reserved.

1. Introduction Quantum dot solar cells (QDSCs) based on compound semiconductors have attracted much attention over the past several years [1–7]. One approach to improving the efficiency (η) of QDSCs is introducing strain-based InAs/GaAs QDs to extend the absorption wavelength into the near-infrared (NIR) region of the solar spectrum [6]. Many methods have been proposed to achieve highly efficient QDSCs, such as the enhancement of the photocarrier generation and collection and suppression of carrier losses by re-capturing and trapping carriers in larger QDs and defect states [1–7]. To realize high-efficiency QDSCs, strain compensation layers (SCLs) were introduced to reduce strain-induced defects; examples of such layers include GaP and GaNAs thin layers for InAs/ GaAs-based QDs, and incorporation of group-III ions with different sizes into II-VI host materials for InGaN/ZnO QDs [2–5]. Highdensity QD growth techniques have been proposed to improve carrier generation in the NIR region [6]. Moreover, to extend the absorption wavelength of an InAs/GaAs QDSC to the NIR region, n

Corresponding authors. E-mail addresses: [email protected] (J.S. Kim), [email protected] (S.J. Lee).

http://dx.doi.org/10.1016/j.solmat.2016.04.045 0927-0248/& 2016 Elsevier B.V. All rights reserved.

the QD size distribution should be controlled since the absorption wavelength is related to the size of the InAs QDs. In general, increasing the QD size, the absorption wavelength is shifted to a longer wavelength. However, the stain-related defects caused by interface strain between InAs and GaAs cannot be avoided. Furthermore, the photo-generated carriers can be re-captured easily by large QDs during carrier transport. Photo-generated carrier loss could be increased by trapping and re-capturing carriers at the strain-related defects and QD states, respectively [7]. The trapped and re-captured carriers are exhausted by radiative and nonradiative recombination processes. The carrier re-capturing probability should increase when increasing the QD size while the absorption wavelength is shifted to a longer wavelength. The defect generation is related to the QD size due to the stain near the QD interface and the capping materials. Therefore, to understand the contribution of the QD size effect to the η of QDSCs, it is necessary to consider the carrier trapping and re-capturing by the defects and QD states based on the QD size. The present work revealed the QD size effects on η and p-n junction electric fields (Fpn). To study this, various QD sizes were embedded in GaAs p-n junction QDSC structures. The effects of QD size on the optical and electrical properties were investigated by photoluminescence (PL), time-resolved PL (TRPL), photoreflectance

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(PR), capacitance-voltage (C-V), current-voltage (J-V), and solar simulator measurements.

was adjusted with a Si reference cell (Fraunhofer ISE, certificate No. C-ISE269) with a one-sun light intensity of 100 mW/cm2.

2. Experiment

3. Results and discussion

Five solar cell samples were fabricated with various QD sizes using molecular beam epitaxy (MBE). The QD sizes were controlled by supplying various deposition thicknesses of InAs (θ ¼0, 1.7, 2.0, 2.5, and 3.0 mono-layers (ML). Fig. 1 shows a schematic of the InAs/GaAs QDSCs and an atomic force microscopy (AFM) image of 2 ML InAs QDs embedded in the p-n junction. Each QDSC contains eight InAs QD layers located in the n-GaAs (2.8  1017/ cm3) absorption layer region of a p þ -n-n þ junction grown on n þ GaAs (100) substrates. Each QD layer is separated by a 40 nm-thick n-GaAs space layer, repeated eight times for a total thickness of 320 nm for the QD structure. The doping concentration of n-GaAs absorption layer (2.8  1017/cm3) was selected to optimize SC efficiency (the absorption layer doping levels were varied from 2  1015/cm3 to 6  1017/cm3) in solar simulator measurements. The reference GaAs p þ -n-n þ junction solar cell (as a reference SC; θ ¼0 ML) consists of a 300 nm n þ -GaAs layer (2  1018/cm3), a 1.5 mm n-GaAs absorption layer, and a 0.6 mm p þ -GaAs layer (2  1018/cm3), followed by a 50 nm p þ -Al0.9Ga0.1As window and 10 nm p þ -GaAs layer for Ohmic contact. During the growth of QDSCs, the growth temperature was kept at 580 °C for all structures except the InAs QDs and the n-GaAs space layer (470 °C). A 320 nm n-GaAs layer grown at low temperature (470 °C) was inserted in the reference GaAs-SC to investigate only the QD size effect without the growth temperature effect. To enhance the photon recycling effect, the position of the QD layers were placed bottom of the n-GaAs absorption layer from the p þ -n interface. With this structure, relatively higher energy photons ( 41.42 eV) are absorbed by n-GaAs absorption layer closer to the surface while NIR photons are absorbed by the InAs QD layers near the n-nþinterface. These additional NIR photo-carriers contribute the photo-current because of the n-n þ interface electric field. The optical and electrical properties of the QDSCs were investigated by low-temperature PL, TRPL, room-temperature PR, C-V and J-V measurements. J-V measurements of the QDSCs were performed in the dark and under simulated AM1.5 G white light illumination using a Hewlett-Packard 4155A semiconductor parameter analyzer and a solar simulator (Polaronix K201 Lab50, McScience). The AM1.5 G white light was produced by a solar simulator based on a filtered Xe lamp (Oriel, 91,193). Its intensity

The AFM results indicate that the average diameters of the 1.7, 2.0, 2.5, and 3.0 ML InAs QDs were 21.5, 24.0, 40.6, and 53.5 nm, respectively, while the heights were 1.5, 2.5, 5.5, and 6.7 nm. The InAs QD size increased with increasing θ on the GaAs surface [8,9]. The density for the samples changed from  1010 to  109/cm2. The QD densities of the 1.7, 2.0, 2.5, and 3.0 ML QDs were 4.3  1010, 5.0  1010, 3.6  1010, and 5.2  109/cm2, respectively. To investigate the effects of the QD size on optical properties such as the emission wavelength, PL spectra were measured with various QD sizes, as shown in Fig. 2(a). With increasing θ, the emission wavelengths shifted to the longer wavelength due to the QD size effect. However, the integrated PL intensities decreased with increasing θ with more than 2.5 ML. The full width at half maximum (FWHM) also increased, as shown in Fig. 2(b). The increased FWHM is attributed to the change in the QD size distribution with increasing θ. The small increase of the integrated PL intensity of the QDs between 1.7 ML and 2.0 ML can be explained by the QD density effect. However, the reduced intensity beyond 2.5 ML is predominately caused by increasing the defect densities because of the strain-induced defect generation in the S-K growth mode [9,10]. TRPL measurement was performed to investigate the formation of defects with increasing QD size and their role in the optical properties. Fig. 3(a) shows the low-temperature TRPL spectra with various θ, and Fig. 3(b) summarizes the PL intensity decay time as a function of θ. With increasing θ, the radiative carrier lifetimes (τR ) drastically decreased, as shown in Fig. 3(b). Generally, τR increases with the QD size due to the reduced oscillation strength [11]. However, the decreasing τR is caused by the introduction of the non-radiative recombination process through the defect states. Therefore, the reduction of τR can be explained by the formation of defects with increasing QD size. Based on the PL and TRPL results, we find that the optical properties of InAs QDs predominately depend on the formation of strain-induced defects with increasing QD size. To study the exhaustion of photo-generated carriers through trapping and re-capturing, the photovoltaic effect was investigated by PR measurements [12]. The PR spectra are sensitive to the interface electric fields such as the p þ -n junction (Fpn) and surface (Fs) fields. In the high electric field regime, Franz-Keldysh

Fig. 1. Schematic of InAs/GaAs quantum dot solar cell (QDSC) and atomic force microscopy (AFM) image of 2 ML InAs QD embedded in the GaAs p-n junction.

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Fig. 2. (a) Low-temperature photoluminescence (PL) spectra of InAs QDs with various deposition thickness of InAs (θ ML) and (b) summary of integrated PL intensity and full width at half maximum (FWHM) as a function of θ.

oscillations (FKOs) appear in the PR spectrum for energies above the bulk band gap. When Fpn is affected by the carrier density variation, the change of Fpn is reflected in the PR spectra, especially FKOs, because the FKO period is directly related to interface electric field strengths in a sample [12]. Generally, the photovoltaic effect in a p-n junction SC is caused by field screening. In steady state, when the photo-carriers continuously generate under light illumination on the SC, the strength of Fpn at the p-n interface can be reduced because the carriers accumulated near p-n junction side screen Fpn. This effect, known as field screening effect [12], is enhanced by an increase in photogenerated carriers from due to InAs QDs, leading to an additional reduction of Fpn. On the other hand, as increasing the probability of carrier trap or re-capture, the number net carriers are decreased, thereby reducing the field screening effect and leading to a recovery in Fpn. Overall the net carrier density is reduced by a carrier exhaustion process such as carrier recombination through the defects and QD states, the screening effect can be reduced. Therefore, an increase of Fpn is evidence of carriers vanishing through the defects and QD states. Moreover, a SC can exhibit good device performance characteristics such as high efficiency when the number of photo-generated carriers increases. Therefore, the reduction of Fpn implies an enhancement of carrier generation, resulting in an increase of SC efficiency. PR analysis was done to explore the effects of QD size on Fpn resulting from the exhaustion of photo-generated carriers due to radiative and non-radiative recombination for the InAs QDSCs. Fig. 4(a) and (b) show the room-temperature PR spectrum and fast Fourier Transform (FFT) results of the reference GaAs-SC. The PR spectrum contains three main features contributed by the GaAs inter-band (Eg ¼1.42 eV) transition, spin orbital split

Fig. 3. (a) Low temperature time-resolved photoluminescence (TRPL) spectra with various θ and (b) summary of PL decay time as a function of θ.

(Eg þ Δo ¼1.76 eV) transition, and FKOs. The room-temperature PR spectrum clearly exhibits an oscillatory feature related to the FKOs above the GaAs band gap energy due to the Fs and Fpn, as shown in Fig. 4(a). To distinguish the FKO components in the frequency domain (eV  3/2), FFT was performed on the PR spectrum, as shown in Fig. 4(b). The strength of the electric fields in the interfaces of GaAs can be evaluated from the FFT frequency (f) of the FKOs [13]. The interface electric field strengths Fi of the i-th interface such as the p-n junction and surface are related to the oscillation frequency of the FKOs (f) [14]:   1=2 1 2 2μ ; ð1Þ f¼ 3π eℏF i where μ is the reduced effective mass in the direction of Fi. In Eq. (1), μ is an important parameter because GaAs has two possible reduced effective masses due to the electron-heavy hole (e-hh) reduced effective mass (μhh) and electron-light hole (e-lh) reduced effective mass (μlh). Therefore, when there is a single electric field in bulk GaAs, two FKO frequency components are expected in the PR spectrum due to the e-hh and e-lh transitions [15]. The PR spectrum is composed of contributions from both the e-hh transition and the e-lh transition [15]. In Eq. (1), the ratio of the square root of the reduced effect masses (μlh1/2/μhh1/2) is equal to the frequency ratio of the e-hh and e-lh transitions (flh/fhh). In the case of GaAs, flh/fhh is 0.7915, and the amplitude of the oscillator of e-hh is much larger than that of the e-lh transition [15,16]. The FFT power spectrum of the reference GaAs-SC exhibits two distinct peaks with broad frequency bands, as shown in Fig. 4(b). Because the ratio of the two

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Fig. 4. (a) Room-temperature photoreflectance (PR) and (b) fast Fourier transform (FFT) result of PR spectrum for GaAs p-n junction reference solar cell.

frequencies is not close to 0.7915, we decided that the two frequencies fs-hh and fpn-hh originated from two different electric fields that are primarily related to Fs and Fpn corresponding to the dominant e-hh transitions. In addition, the broadening of the FFT spectrum is caused by the broad electric field distributions at the p-n junction interfaces of the sample due to the unintentional diffusion of doping material and the overlapping of e-hh and e-lh transition frequency components. For the reference GaAs-SC (θ ¼0 ML), the evaluated electric field strengths from the FKO frequencies fs-hh and fpn-hh are  395 and 134 kV/cm, respectively. To determine the origin of the two dominant electric fields in the reference GaAs-SC, the experimental results were compared to the simulation of the sample structure using the one-dimensional Poisson equation. In the simulation, there were two electric fields at the surface and the p-n junction interface [17]. The calculated maximum electric field strength at the surface and the p-n junction interfaces are 755 kV/cm and 257 kV/cm, respectively. These calculated electric fields are higher than those extracted from the PR measurement since the measurement includes the effects such surface states which can reduce Fs, and photovoltaic which can reduce Fpn via photo-generated carriers induced field screening at high excitation intensity (17 mW/cm2) [17]. Comparing the experimental electric fields with the simulation results suggests that the fields of  395 kV/cm and 134 kV/cm correspond to the fields at the surface and p-n junction, respectively. In addition, the tail of the high-energy part of the FKO oscillatory features caused by the Fs is penetrating and overlapping with Eg þ Δo transitions in the PR spectrum, so fs-hh could be shifted from the original

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frequency. It is hard to evaluate Fs with high accuracy from fs-hh in the FFT results, so in further investigations, only Fpn corresponding to fpn-hh was considered. To investigate the effect of QD size on Fpn, room-temperature PR measurements, and FFT were performed for InAs QDSCs with various θ. Fig. 5(a) through (c) respectively show the FKO, the FFT spectra for the QDSCs with various θ, and a summary of the Fpn of QDSCs as a function of θ. The oscillatory features of FKO are not simple and strongly affected by changing θ, as shown in Fig. 5(a). Due to the degeneracy of the valence band and its splitting caused by strain in InAs/GaAs QDs, the PR spectra also show heavy- and light-hole splitting features near GaAs band edge [18]. However, in the QDSC samples we did not observe the splitting of hh and lh transitions in the PR spectra. This absence can be explained by broadened PR spectra around the GaAs bandgap (  1.42 eV) from the doping effect [17]. To distinguish the FKO frequencies of the oscillatory features, FFT results are shown in Fig. 5(b). The dominant frequencies (fpn-hh) shift from that of the reference GaAs-SC (yellow trend lines). Fpn corresponding to fpn-hh is plotted as a function of θ in Fig. 5(c). Fpn gradually decreased with increasing θ from 0 to 2.0 ML. This behavior can be explained by the enhancement of carrier screening due to the increase of photo-generated carriers from the QD states. These results indicate that the InAs QD layers efficiently generated more photo-carriers by the enhancement of NIR absorption compared to the reference GaAs-SC. As a result, the photovoltaic effect is improved via the enhancement of carrier screening, leading to a decrease in the net strength of Fpn. For θ Z 2.5 ML, however, Fpn gradually increased with increasing θ. For such large θ, we attribute three effects to the observed increase of Fpn. First, the larger QD sizes introduce strain-induced defects through lattice mismatch in which the photo-carriers can be trapped [19]. These defect states contribute to trapping and subsequent exhaustion of the carriers through non-radiative recombination processes. Secondly, a decrease in the QD density leads to a reduction in the generation of photo-carriers, which subsequently reduces the photovoltaic effect in Fpn, leading a recovery in the field strength. Lastly, enhanced size-effect carrier recapturing in QD states can similarly reduce the photovoltaic effect in Fpn. Since the carrier re-capturing rate of QDs increases with the size of QDs [20], photo-generated carrier re-capturing is more efficient for larger QD size, leading to subsequent exhaustion through radiative recombination processes. These combined effects contribute to a screening effect causing Fpn to recover to the value of the reference GaAs-SC, as shown in Fig. 5(c). By varying QD size, we explore the balance between carrier generation and exhaustion processes affecting the net carrier density, which affects the photovoltaic effect. Further details of carrier generation and exhaustion factors contributing to the current will be discussed in J-V measurement parts. To investigate the QD size effect on background carrier concentrations (Nd) and depletion layer width (W) of n-GaAs absorber layer, we performed a room-temperature C-V measurement. Fig. 6 show (a) the C-V curves of QDSCs under reverse bias with various θ and (b) summary of Nd (open circle) and W (solid circle) as a function of θ. In Fig. 6(a), the capacitance of QDSCs drastically decreased compared with the GaAs SC. Since the sample capacitance scales as the square root of Nd [21], the degradation of capacitance is mainly attributed to the introduction of QDs caused by such carrier quantum confinement and/or defect passivation effects. To understand these changes in Nd as a function of QD size, we suggest two contributing effects: defect passivation and carrier confinement due to the quantum confinement effect. It is well known that the Nd in n-GaAs layer is correlated with defect passivation. As inserting QD in n-GaAs region the defect density could be

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Fig. 5. (a) Franz-Keldysh oscillations (FKOs), (b) FFT spectra of FKOs for various θ and (c) summary of the p-n junction electric field (Fpn) of QDSCs as a function of θ. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

increased caused by strain induce defect generation as shown in PL and TRPL results. Moreover since number of confined carriers related to QD density Nd is also affected by QD size effect. Therefore, in Fig. 6(b) the drastic change in Nd observed at 1.7 ML compared with the reference GaAs SC could be affected by not only defects passivation but also quantum confinement effects. In Fig. 6(c), as increasing QD size up to 2.0 ML the QD density increase about 16% from that of the 1.7 ML QD and the Nd only decrease 4.6%. Moreover, between 2.0 ML and 3.0 ML the QD densities decrease up-to 87% while the Nd recovered about 60% as shown in Fig. 6(d). From this consideration we suggest that the residual carrier losses could be involved by carrier passivation process through strain-induced defect states. Therefore, the change of the Nd could be affected by not only QD density via quantum confinement effects but also from defects as a function of θ. Moreover, the depletion width (W) of QDSCs was drastically increased compared to the GaAs SC as shown in Fig. 6(b). Ideally, Nd in n-GaAs absorption layer depends on the defects passivation

and carrier confinement in QD states. Since W is inversely proportional to the square root of Nd [21,22], the increment of W with increased QD layers arises mainly from carrier confinement in QDs and the passivation of defect states. Therefore, in the QDSCs, W is changing with increasing θ because of the change of QD and defect densities. To understand the effects of QD sizes on the electrical properties of QDSCs, the J-V characteristics were measured for various θ. The measured η and other parameters are shown in Table 1. Fig. 7 (a) shows the J-V characteristic curves illuminated by 1 sun (AM1.5 G ¼100 mW/cm2) for various θ, and Fig. 7(b) shows the deviations of the solar cell parameters (Voc and Jsc) from the values of the reference GaAs-SC (θ ¼ 0 ML) as a function of θ. The 1.7 and 2.0 ML QDSCs show a marginal increase of the open-circuit voltage (Voc) compared with the reference GaAs-SC. The lower Voc of the GaAs-SC can be explained by defects effects. The defects were introduced during the low-temperature growth process (470 °C) of the 320 nm thick GaAs absorption layer for the reference GaAs-SC.

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Fig. 6. (a) Room-temperature C-V curves for various ML thickness samples. (b) Summary of depletion layer thickness (W) and background doping concentration (Nd). (c) Relation between QD density and Nd. (d) Deviation of Nd and QD density as a function of θ. Table 1 Open-circuit voltage (Voc), short-circuit current density (Jsc), fill factor (FF), efficiency (η), and dark J-V characteristics (saturation current density; Jo, and ideal factor; n) for QDSCs with various θ. θ (ML) 0 1.7 2.0 2.5 3.0

Voc (V) 0.973 1.003 1.000 0.943 0.852

Jsc (mA/cm2) 20.44 20.52 20.80 19.88 19.78

FF (%) 78.25 79.83 81.72 74.70 59.43

η (AR) (%) 15.56 (18.03) 16.43 17.00 (21.17) 14.00 10.02

J0 (A/cm2)  11

6.23  10 2.79  10  11 1.12  10  11 6.36  10  9 5.49  10  4

n 1.92 2.36 2.40 2.35 5.13

With low-temperature growth, defect formation in the GaAs crystal cannot be avoided. However, Voc for the 2.5 and 3.0 ML QDSCs decreased by 3.1% and 12.4%, respectively. The degradation of Voc could be connected to the strain-induced defect generation from the larger QDs [2]. The short-circuit current densities (Jsc) with 1.7 and 2.0 ML QDSCs also increased compared to that of the reference GaAs-SC. These improvements in Jsc are related to the additional photo-carrier generation in NIR region with the insertion of QDs. However, the decrease in Jsc for the larger QDs (θ Z2.5 ML) is caused by not only carrier trapping in the defect states but also the re-capturing of carriers in larger QDs during the carriers transport. In our previous work [23], to understand the role of the QD size in carrier transportation we reported the external quantum efficiency (EQE) results with various θ. In the EQE spectra, the EQE of the 2.0 ML QDSC is enhanced over the whole spectral range above the GaAs band gap energy. This result shows that the 2.0 ML QDSC efficiently absorbs not only near-infrared photons but also photons with energies above the GaAs band gap energy. In contrast, the asymmetric EQE reduction behavior in the 2.5 and the 3.0 ML QDSCs can be explained by the hot-carrier effect, which is

evidence for the carrier re-capturing in relatively larger QDs as demonstrated by the J-V results. To investigate the effect of QD size on the current transportation of QDSCs more precisely, the dark J-V characteristics were examined and revealed an effect on the fill factor (FF) of the QDSCs. Fig. 8(a) shows a summary of the reverse saturation current density (J0) and the ideality factor (n) of the diode structures. Fig. 8(b) shows the FF of QDSCs as a function of θ. J0 with 1.7 and 2.0 ML was reduced compared to that of the reference GaAs-SC because the reference GaAs-SC has defects induced by lowtemperature growth. These phenomena could be explained by the reduced defect states during the InAs deposition. For θ Z2.5 ML, however, the drastic increase of J0 could be related to the increase of strain-induced defects caused by relatively lager QD formation. On the other hand, n increases a little with increasing θ below 2.5 ML. This reflects that the carrier recombination processes are enhanced by the radiative process due to the re-capturing of the carriers in the larger QDs. Particularly, the higher n at 3.0 ML is predominantly affected by the defects near the bigger QDs. FF was slightly increased until θ ¼ 2.0 ML and drastically decreased over 2.5 ML, as shown in Fig. 8(b). Generally, FF is dependent on J0, Voc and n [24,25]. Our experimental results demonstrate that the change of FF is strongly correlated with the trend of both J0 and Voc. Moreover, Voc is related to the carrier losses such as recombination processes, which increase with decreasing J0. The high FF (81.72%) of the QDSC (θ ¼2.0 ML) is attributed to improved crystal quality as evidenced by the increased both Voc and Jsc and the reduced J0 as shown in Figs. 7 and 8. The degradation of FF in the 2.5 ML QDSC is primarily caused by high J0 and low Voc. Therefore, FF of the QDSCs predominantly depends on the carrier loss process due to the change of defects and re-capturing caused by the QD size effect. In addition, the degradation of FF in QDSCs with larger QDs (θ Z2.5 ML)

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Fig. 7. (a) Room-temperature current-voltage (J-V) characteristic curves illuminated by 1 sun (AM1.5 G ¼100 mW/cm2) for various θ and (b) deviations of the solar cell parameters (Voc and Jsc) from the values of reference GaAs-SC (θ ¼ 0 ML) as a function of θ.

is principally due to both the high J0 and the high ideality factor (n 4 4 2).These results suggest that the higher n and J0 are attributed to the increase of defect and re-capturing states caused by the larger QDs. Also, the dramatic reduction in Voc for the 3.0 ML QDSC is evidence of increasing density of the defect states in the QDSC due to strain. Overall as θ is increased, since the variation of FF is affected by carrier loss process introduced by defects and re-capturing related to the QD size the SC efficiency relate to FF. The data above suggest additional carriers generated from the QD layers and carrier-exhaustion processes through recombination in defects and QD states. To quantitatively understand this phenomenon, we consider simple model for total carrier processes in the bulk GaAs SC and the QDSC layers. The carrier density ðN carrier  SC Þ which includes current through the photo-carrier generation ðNGaAs  G Þ and carrier losses at defects ρt ðNdef ect  GaAs Þ in the GaAs absorber layer can be described by N carrier  SC ¼ N GaAs  G  ρt ðN def ect  GaAs Þ

ð2Þ

where N GaAs  G , Ndef ect  GaAs and ρt are photo-generated carrier density, defect density and carrier trapping probability at GaAs absorber layer, respectively. In the case of the QDSC, the carrier density (Ncarrier  Q DSC ) which contributes to current, can be modeled by N carrier  Q DSC ¼ N GaAs  G þ N Q D  G  ρt ðN def act  GaAs þ Ndef act  Q D Þ  ðρre  ρesc ÞNQ D ;

ð3Þ

Fig. 8. (a) Summary of the reverse saturation current density (Jo) and the ideality factor (n) of the diode structures and (b) fill factor (FF) of QDSCs as a function of the θ.

where N Q D  G , N def ect  Q D , N Q D , ρre and ρesc are photo-generated carrier density from QDs, defect density caused by QDs, QD density, the probability of carrier re-capturing and the carrier escaping probability at QD states, respectively. The carrier re-capturing and escaping probabilities relation ðρre  ρesc Þ can be simplified by an effective probability of carrier confinement ðρc ¼ ρre  ρesc Þ because we only consider carrier loss processes through carrier recombination in QD states. N def ect  Q D is also simplified by using αNQ D , since QD related defect density is proportional to the QD density, where α is a defect generation coefficient due to the QD size effect caused by strain. Therefore Eq. (3) can be re-written as Ncarrier  Q DSC ¼ N GaAs  G þN Q D  G  ρt N def act  GaAs  ðαρt þ ρc ÞN Q D ð4Þ From the Eq. (2) and Eq. (4), if we consider the only increment of carrier density which contributes to current by QD, the net carrier density from QD is given by Ncarrier  Q DSC  N carrier  SC ¼ N Q D  G  ðαρt þ ρc ÞNQ D :

ð5Þ

Finally we assume that N Q D  G is proportional to the QD density ðN Q D  G ¼ ρG N Q D Þ, Eq. (5) can be simply filed as a function of NQ D ; Ncarrier  Q D ¼ ðρG  αρt  ρc ÞN Q D ;

ð6Þ

where ρG is the photo-carrier generation probability in the QD states. Eq. (6) implies that the number of carriers contributing to the current from QDs is determined by a balance between the generation and exhaustion due to ρG and ðαρt þ ρc Þ, respectively. The carrier exhaustion process is composed of carrier trapping and recombination probabilities. In Fig. 7(b), 1.7 and 2.0 ML QDSCs show the increment of photocurrent from QD contributions. In this case the increased carrier generation process competes with the

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Fig. 9. (a) Radiative carrier recombination densities per unit time corresponding to recombination rate. (b) Carrier loss factors in radiative and non-radiative recombination processes as a function of θ.

Fig. 10. (a) Deviation of Fpn from that of the reference GaAs-SC and the solar cell efficiency (η)as a function of θ, and (b) η as a function of Fpn.

exhaustion processes such as trapping. However, 2.5 and 3.0 ML QD shows the decrease of current, which imply that the carrier exhaustion process is dominate than the carrier generation. To investigate the carrier exhaustion process through radiative and non-radiative process, we consider the TRPL results. The effective carriers re-capturing ρc and trapping ρt probabilities are strongly related to the radiative and non-radiative process. In the case of radiative process, the carrier capturing in QD state could exhaust radiative recombination process. The carrier exhaustion density per unit time through radiative recombination process can be described by N Q D =τR as shown in Fig. 9(a), where τR is radiative recombination life time taken from TRPL in Fig. 3(b). As the QD size increases between 1.7 and 2.0 ML the carrier loss through radiative recombination increases because of the QDs density and then for 2.5 and 3.0 ML, the QDSC decreases in carrier losses through radiative recombination. Because this result has opposite tendency compared to the photocurrent results, the non-radiative carrier loss process should be considered. From the TRPL results, we note that as the QD size increases, reduction of the radiative life time implies that the defect density can be increased by strain effects. In Eq. (6), α is related to the ratio of defect density which increases with QD size. Moreover, in Fig. 8(a), the ideality factor n also implies the recombination processes which include radiative and non-radiative recombination. From consideration of n as a function of QD size, we computed the contribution factors to carrier loss processes such non-radiative and radiative through the defects and QD states as shown in Fig. 9(b). In the case of nonradiative carrier loss, 2.0 ML QDSC has lowest non-radiative carrier loss factor which implies a high crystal quality of QDs. However, as the QD size is further increased, the non-radiative loss factor drastically increases by a factor of 8 at 3.0 ML from that of 2.0 ML.

From these considerations, we find that the carrier contribution in QDSCs performance to be related to the balance between the carrier generation and exhaustion processes through the nonradiative and radiative recombinations. We compared η and Fpn to determine their relationship. In Fig. 10, η is compared with the deviation of Fpn from that of the reference GaAs-SC as a function of θ and Fpn. The change of η has an opposite tendency to Fpn, as shown in Fig. 10(a). As Fpn increases, η decreases, as shown in Fig. 10(b). The relation between Fpn and η could be explained as follows. The change of Fpn is mainly due to the variation of the photo-voltaic effect by the varying carrier density. The carrier density can be changed by the generation and recombination processes as discussed in Fig. 9. In the InAs QDSCs, we expect an additional increase of photogenerated carriers from QD states due to NIR absorption. However, there should be unintentional carrier exhaustion process such as radiative and non-radiative recombination by re-capturing and trapping carriers in the QDs and defect states, respectively. When the photons are injected in the solar cell structure they can generate carriers that screen Fpn. This is called the photo-voltaic effect. If QD states can generate additional carriers, Fpn should be reduced proportionally to the generated carrier density. Moreover, when the carriers are re-captured and trapped in the QDs and defect states, Fpn should recover to its initial value. When QDs are embedded in the p-n SC, the QD states can generate additional carriers that improve η. With increasing QD size, the QD and defect states can exhaust the carriers mostly through radiative and non-radiative recombination, and η should degrade. In the cases of 1.7 and 2.0 ML QDSCs, the increase of photogenerated carriers improves η and reduces Fpn, as shown in Fig. 10 (b). However, with the relatively large QDs in the 2.5 and 3.0 ML

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QDSCs, η is lower and Fpn is larger than that of the 2.0 ML QDSC. These results could be explained by the carrier exhaustion effect predominantly due to the increase of the strain-induced defect states with larger QDs. The change of Fpn in various QDSCs is explained by the results of the photo-voltaic effect due to the balance between carrier production and exhaustion from the QD and defect states. The 2.0 ML QDSC presented an optimal η of 21.17% due to the balance between the carrier generation and exhaustion.

4. Conclusion The QD size effects on the optical and electrical properties of QDSCs were investigated using PL, TRPL, PR spectroscopy, C-V and J-V measurements. The GaAs p-n junction based QDSC structures were grown by MBE. The various QD sizes were formed by varying the total InAs deposition thickness (θ). The sizes and densities of QDs were confirmed by AFM measurements. The average diameters of θ ¼ 1.7, 2.0, 2.5, and 3.0 ML InAs QDs were 21.5, 24.0, 40.6, and 53.5 nm, respectively. The density for the samples changed from 1010 to  109/cm2. From the PL results, with increasing θ, the emission wavelengths shifted to the longer wavelengths because of the QD size effect. The reduction of integrated PL intensity with increasing θ implies a rise in defect densities predominately from strain due to lattice mismatch. TRPL showed that the decreasing radiative recombination lifetime is caused by the introduction of the non-radiative recombination process through the defect states. In PR results, Fpn changed from that of the reference GaAs-SC due to the photo-voltaic effect caused by the balance between carrier generation and exhaustion. At 2.0 ML QDSC, the reduction of Fpn facilitates the enhancement of carrier generation. From the C-V results, we conclude that Nd is affected by not only defect passivation but also QD states due to the quantum confinement effects. The J-V results considered with other optical and electrical properties reflect that the carrier recombination processes are enhanced by radiative processes via re-capturing of the carriers in the larger QDs. Particularly, the higher n at 3.0 ML is predominantly affected by defects near the bigger QDs. To explain our observations from complex mixed effects when changing ML thickness, we suggest a simple total carrier processes model in GaAs SC and QDSC that includes additional carriers generated in the QD layers and a carrier exhaustion process through recombination such defects and QD states. Overall the QD size effects on Fpn and η of the QDSCs were revealed. We achieved QDSCs with η of 21.17% for θ ¼2.0 ML. The 2.0 ML QDSC had lowest Fpn due to the enhanced photovoltaic effect caused by the improved carrier generation. The QD size affects optical and electronic properties due to the balance between the carrier generation and exhaustion processes through trapping and re-capturing by defects and relatively large QDs.

Acknowledgments This work was supported in part by a National Research Foundation of Korea grant funded by the Korean Government (NRF2009–0093259, NRF-2011–00111728 and NRF-2013K2A2A2000881).

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