A III-V multi-junction tandem solar cell is the most efficient photovoltaic structure that offers an extremely high power conversion efficiency. Current mismatching between each subcell of the device, however, is a significant challenge that causes the experimental value of the power conversion efficiency to deviate from the theoretical value. In this work, we explore a promising strategy using CdSe quantum dots (QDs) to enhance the photocurrent of the limited subcell to match with those of the other subcells and to enhance the power conversion efficiency of InGaP/GaAs/Ge tandem solar cells. The underlying mechanism of the enhancement can be attributed to the QD’s unique capacity for photon conversion that tailors the incident spectrum of solar light; the enhanced efficiency of the device is therefore strongly dependent on the QD’s dimensions. As a result, by appropriately selecting and spreading 7 mg/mL of CdSe QDs with diameters of 4.2 nm upon the InGaP/GaAs/Ge solar cell, the power conversion efficiency shows an enhancement of 10.39% compared to the cell’s counterpart without integrating CdSe QDs.
© 2013 OSA
The past few years have witnessed an explosive growth in research that addresses different aspects of the use of semiconductor materials in varied configurations for photovoltaic applications [1–11]. Among them, III-V compound tandem solar cells, which take advantage of the bandgap tunability by elemental multi-junction compositions and of the high optical absorption by direct bandgap materials, have attracted increasing attention for their extremely high conversion efficiency [12–15]. Ideally, a calculated power conversion efficiency as high as η = 50.1% (under AM1.5G, 1000 sun) is achievable for a series-connected InGaP/GaAs/Ge triple-junction solar cell, which is far beyond the theoretical limit of a single-junction solar cell estimated by the Shockley-Queisser’s calculation scheme [16,17]. In practice, an appropriate alignment of the bandgap energy of multi-stacking layers that provides current matching between each subcell is the most challenging issue in this tandem architecture, which restricts the maximum power conversion efficiency of the device and the potential applications in the photovoltaic industry. More specifically, the GaAs middle subcell generally limits the overall photocurrent of a InGaP/GaAs/Ge tandem solar cell. To overcome the issue of current mismatching, several approaches, such as the use of a quaternary AlGaInP top subcell and the substitution of the middle subcell with an InGaAs material, have been widely investigated . However, an introduction of Al content into the InGaP top subcell causes a significant photocurrent droop due to the associated oxygen contamination on minority-carrier properties . In addition, the substitution of a fraction of the gallium atoms with indium in the middle subcell accompanies a lattice mismatch and requires a complicated growth scheme such as the graded buffer layers to avoid a large dislocation density that also reduces the photocurrent of the device . Hence, for InGaP/GaAs/Ge tandem solar cells, an approach that does not adversely affect the device’s performance and that is capable of resolving the current-mismatching issue is necessary. Recently, semiconductor nanoparticles, known as quantum dots (QDs), have been intensively studied and utilized to generate multiple carrier excitations from one incident photon by the so-called impact ionization [21–23]. Such a nonlinear phenomenon can cause a solar cell’s quantum efficiency to be greater than 100%, primarily due to the discrete carrier density of states and the strong quantum confinement effect . Additionally, as the electronic energy levels and the optical spectrum strongly depend on the QD’s dimension, its effective bandgap energy can be tunable. For the same reason, the semiconductor QDs are also adopted as downconverter materials to help harvest the ultraviolet regime of solar energy in silicon solar cells . In this study, we recognize the photon conversion aspect of nanocrystal QDs and explore a novel strategy using CdSe QDs to tailor the incident spectrum of solar light to enhance the photocurrent of a limited subcell in InGaP/GaAs/Ge tandem solar cells and to enhance the overall power conversion efficiency of the cell. We demonstrate the ability of CdSe QDs to enhance the performance of the device, not only by theoretical calculations based on the fundamental of material optics but also by directly measuring the device’s electrical characteristic. The device exhibits an enhancement of 10.39% in the power conversion efficiency compared to the device’s counterpart without integrating QDs. The theoretical and experimental results validate that the CdSe QDs have promising potential for efficient solar spectrum utilization in InGaP/GaAs/Ge tandem solar cells.
2. Experiment and simulation
Figure 1(a) shows a schematic configuration of the proposed structure. The three lattice-matched subcells of the triple-junction solar cell from top to bottom in order are the InGaP, GaAs, and Ge subcells, grown on the p-type Ge substrate by low-pressure metal-organic chemical vapor deposition (MOCVD). To form a QD suspension, CdSe QDs were dispersed onto the top AlInP-window layer by spin-casting that covered the metal electrode (further details of the CdSe QDs synthesis procedure is reported in our previous work ). Onto the sample was dropped a fixed volume (~125 μL) of colloid QDs at various concentrations in toluene solution; it was then spin-cast at 2500 r.p.m for 10s to disperse CdSe QDs uniformly. The sample was then placed under a fume hood, where it stood for one minute to evaporate off toluene to enable light J-V measurements to be made. Trimethyl sources of aluminum, gallium and indium were used as group-III precursors, and arsine and phosphine were used for the group-V reaction agents. Silane (SiH4) and diethylzinc (DEZn) were used as the n-type and p-type dopant sources, respectively. The InGaP and GaAs subcells are connected to each other by a p-AlGaAs (p = 4 × 1020 cm−3, 20 nm)/n-InGaP (n = 1 × 1020 cm−3, 20 nm) tunnel junction, whereas the GaAs middle subcell is connected to the Ge bottom subcell by a p-GaAs (p = 6 × 1019 cm−3, 30 nm)/n-GaAs (n = 1 × 1020 cm−3, 30 nm) tunnel junction. Silver was chosen as the metal electrodes for both the front and backside contacts. The chip size of the individual cell is designed to be 1 cm × 1 cm. The device’s performance was characterized by an Oriel Sol3A solar simulator. The current density vs. voltage (J-V) characteristic was obtained using a Keithley 2400 multi-meter in four-wire sensing mode to eliminate the resistance contribution from the probes and the contact resistances.
To systematically analyze the dependence of the QD’s dimension on the device’s efficiency, we developed a simple model based on the fundamentals of material optics that simulates the energy distribution of the solar spectrum converted by CdSe QDs on each individual subcell. As a result, the power conversion efficiency of the device with CdSe QDs of different sizes can be quantitatively determined and compared. The solar cell device [Fig. 1(a)] was simplified as an InGaP/GaAs/Ge multi-stacking layer to facilitate the optical calculation, as shown in Fig. 1(b). The p-type and n-type active regions are combined as a single layer, and the metal electrode on the top surface is neglected. The solar light was normally incident from the top surface down through the whole device. The optical dispersion is also considered by applying the wavelength-dependent refractive index and the extinction coefficient on each subcell [27, 28]. As the energy bandgap of the QDs is well known to be dominated by the diameters of the QDs, the incident spectrum and radiative intensity of the solar light inside the device can be tuned. In Fig. 1(b), the solar light is incident onto the CdSe QDs, and the solar light with high energy was partially absorbed by the QDs and re-emitted as radiation with photon energies that equaled the bandgap of the CdSe QDs. Hence, when CdSe QDs of the necessary diameters are applied to the top of a tandem solar cell, with the radiation of the CdSe QDs effectively generates more photocurrent that is supplied to the current-limiting subcell which has the lowest photocurrent of the three subcells, promoting the overall power conversion efficiency of the device. The formula for the incident intensity I0i and the transmitted light intensity I0t can be expressed as follows:29], and I0i and I0t indicate the intensity inside the CdSe QDs. The CdSe QDs’ absorbance can also be defined as follows:30] and nair and nQD are the refractive indices of the air and the CdSe QDs, respectively. Restated, the CdSe QDs absorb the high-energy regime of the incident solar light and re-emit radiation with an energy intensity IPL that is equivalent to the QDs’ band-gap energy, which can be directly acquired by the photoluminescence (PL) measurement. Therefore, by considering the optical conversion of the CdSe QDs and the optical reflection at the dot-InGaP interface, the incident intensity of the solar light inside the top surface of the InGaP subcell can be described as follows:Eqs. (3) and (5), the incident intensities I2i and I3i inside the top surface of the GaAs and Ge subcells can be written as follows:Eq. (3). α2 and L2 are the absorption coefficient and the cell thickness of the GaAs subcell, respectively. Consequently, the optical absorption of each subcell can be determined by the difference between the incident and transmitted light intensities inside the subcell:31]:
3. Results and discussion
Figure 2 shows the measured (a) absorbance and (b) PL spectra of CdSe QDs of different sizes in toluene. Accordingly, the reduced dimensionality of the CdSe QDs exhibits quantization of electronic energy levels, and consequently, a blue shift of the optical absorption edge occurs. The optical absorption edge shifts from ~700 nm to ~500 nm as the diameters of the CdSe QDs decrease from D = 6.6 nm to D = 2.1 nm. At a given diameter, the optical absorption increases as the emitting wavelength of the excitation source decreases. Similarly, the main peak of the CdSe QD emission is blue-shifted as the diameters of the CdSe QDs decrease. The main PL peaks of λpeak = 640 nm, λpeak = 610 nm, λpeak = 590 nm, λpeak = 560 nm, λpeak = 520 nm, and λpeak = 480 nm were observed at CdSe QD diameters of D = 6.6 nm, D = 5.0 nm, D = 4.2 nm, D = 3.3 nm, D = 2.5 nm, and D = 2.1 nm, respectively. Additionally,all of the PL intensity exhibits a similar full width at half maximum of FWHM = 32 nm. The above observations are direct evidence that CdSe QDs demonstrate wavelength conversion for incident photons and that the conversion interval is mainly dominated by the diameters of the QDs.
By substituting the absorbance and the PL intensity measured above into Eqs. (4)-(6), Fig. 3 plots the calculated light intensity of the solar spectrum I(1,2,3)i(λ) distributed on each individual subcell for the device (a) without and (b) with CdSe QDs with diameters of D = 2.1 nm. The quantum efficiency of each subcell QE(1,2,3)(λ) was also plotted in the figure and will be employed with I(1,2,3)i(λ) to derive the J-V characteristic of the device by Eq. (8). In this case, the CdSe QDs mainly convert the ultraviolet light into visible light, and hence, the peak intensity of I1i (λpeak = 480 nm) is even stronger than that of the original solar spectrum. Additionally, the InGaP subcell exhibits the highest QE response to the incident wavelength of ~500 nm. We therefore expect that applying CdSe QDs with diameters of D = 2.1 nm primarily enhances the photocurrent of the InGaP subcell. The light intensities of the solar spectra on the GaAs and Ge subcells are also enhanced because the CdSe QDs provide an additional functionality as an antireflection coating for light trapping of the solar light .
Figure 4 plots the calculated J-V characteristics of each subcell by Eq. (8) for the device (a) without and (b) with CdSe QDs with diameters of D = 2.1 nm. As expected, due to the unoptimized dimensions of the CdSe QDs, the enhancement of the photocurrent is mainly observed in the InGaP subcell. By applying CdSe QDs, the calculated short-circuit current density of the InGaP subcell is considerably enhanced from JSC = 9.60 mA to JSC = 12.01 mA. However, as in the previous discussion of Fig. 3, the enhancement of the solar intensity in the GaAs subcell is insufficient; therefore, the short-circuit current density of that subcell is only slightly boosted from JSC = 9.38 mA to JSC = 10.19 mA, and the overall power conversion efficiency of the device increases from η = 25.12% to η = 26.75% (blue dash-line). Restated, the enhanced photocurrents of the GaAs and Ge subcells are mainly attributed to the reduction of optical reflection because the CdSe QDs also serve as an antireflection coating for the long spectral regime.
Next, we are going to investigate the influence of the CdSe QDs’ dimensions on the device’s performance. The absorbance and PL spectra of the CdSe QDs of different dimensions measured in Fig. 2 are substituting into Eq. (8), and the results are summarized in Fig. 5. Figure 5 shows (a) the short-circuit current density of each subcell and (b) the power conversion efficiency of the device as a function of the CdSe QD’s diameter. Accordingly, the JSC of the Ge subcell is slightly boosted to JSC ~12.70 mA/cm2, and is barely affected by variations of the QD’s diameter, as the photon conversion effect of the CdSe QDs that is used in this study occurs mainly for solar light with an incident wavelength of λ<640nm, which falls outside the QE response regime (900nm<λ<1800nm) of the Ge subcell. As for the GaAs subcell, because the PL spectrum is red-shifted and gradually approaches its high QE response regime as the QD’s diameter increases, the corresponding JSC is significantly increased. However, the photocurrent of the InGaP subcell reaches the maximum value of JSC ~13.17 mA/cm2 for CdSe QDs with diameters of D = 4.2 nm and then reduces remarkably as the QDs’ diameters increase further. Again, the degree of overlap between the PL spectrum and the QE response dominates the photocurrent of the InGaP subcell. Consequently, as shown in the bottom of Fig. 5, the device’s overall power conversion efficiency is still determined by the GaAs subcell for small QD diameters of D≤5 nm and then becomes dominated by the InGaP subcell as the QDs’ diameters increase further. The maximum power conversion efficiency is estimated to be η = 29.87% for CdSe QDs with diameters of D = 4.2 nm, corresponding to an ~18.91% enhancement compared to the device without CdSe QDs. Ideally, a power conversion efficiency as high as η = 31.04% is achievable by choosing CdSe QDs with diameters of D = 5.3nm, in which the photocurrents of the InGaP and GaAs subcells are equal, i.e., a current-matching condition, and hence dramatically enhances the device’s efficiency by ~23.56%.
To examine the experimental characteristics of the device after the integration of CdSe QDs, the J-V curves are measured under AM1.5G normal illumination (100 mW/cm2, 1-sun) at room temperature. The QD’s diameter was selected to be D = 4.2 nm as this diameter exhibits the highest power conversion efficiency based on our calculation in reference to Fig. 5. Figure 6(a) plots the light J-V curves of the bare tandem solar cell, and of tandem solar cells with a traditional antireflection coating (ARC, 100 nm SiNx), CdSe QDs, and CdSe QDs on top of the SiNx ARC. The J-V curves in Fig. 6 were obtained as averages over five samples at each QD concentration. The J–V plots were found to be repeatable as two J–V characterizations of each sample deviated by less than 1%. Thus the JSC enhancement is mostly attributable to the incorporation of CdSe QDs, and is unaffected by the intensity fluctuation of the solar simulator that was used in the experiment. A photograph of the bare tandem solar cells with and without CdSe QDs is also inserted in the figure with dimensions of 1 cm × 1 cm. From the photograph of both devices, it is visually evident that CdSe QDs provide an additional benefit of serving as an antireflection layer. Accordingly, the SiNx ARC clearly increased the short-circuit current density and the power conversion efficiency from JSC = 11.04 ± 0.11mA/cm2 to JSC = 11.59 ± 0.19 mA/cm2 and from η = 23.66% to η = 24.89%, respectively. However, the cell with CdSe QDs on top of the SiNx ARC exhibited a poorer performance of JSC = 10.68 ± 0.31mA/cm2 and η = 22.51%, respectively because the effective refractive index and optical thickness of the CdSe QD layer do not match those of the SiNx ARC layer underneath, causing destructive interference of the incident light, reducing the Fresnel reflection. Most importantly, as compared to that of the bare tandem solar cell, the use of 7 mg/mL of CdSe QDs with diameters of D = 4.2 nm increased the short-circuit current density and power conversion efficiency to JSC = 12.12 ± 0.20 mA/cm2 and to η = 26.12%, respectively. Since the photogenerated carriers in the device drift under the influence of the internal electrical field, before being directly collected by the silver electrodes without passing through CdSe QDs, in principle, additional dispersing QDs do not disturb the energy-band profile of the device. Therefore, the addition of CdSe QDs does not influence the open-circuit voltage (VOC = 2.51V) and fill factor (FF = 85.4—85.9%) of the device. Note that the measurement and the comparison are conducted on the exact same solar cell before and after spreading the CdSe QDs to fairly validate our hypothesis. Figure 6(b) shows the J-V characteristics of the InGaP/GaAs/Ge solar cells with different concentrations of CdSe QDs (D = 4.2nm) to gauge the impact of the QDs on the device’s performance. A summary of JSC as a function of the QD concentration is also plotted and inserted into the figure. Cleary, the concentration of CdSe QDs significantly affects the J-V characteristics of the device, and the highest power conversion efficiency is observed on the concentration of 7 mg/mL.
To determine the possible effect of the concentration of CdSe QDs on the J-V characteristics of the device, measurements of reflectance were made on the devices with CdSe QDs at concentrations of 5 mg/mL, 7 mg/mL, and 9 mg/mL, and these are plotted in Fig. 7. The diameter of the CdSe QDs is maintained as D = 4.2nm. The reflectance of the bare tandem solar cell is also plotted in this figure. The CdSe QDs were dispersed uniformly on the device by the spin-casting method [inset in Fig. 6(a)], forming an optically homogeneous layer. The effective refractive index depended strongly on the concentration of the CdSe QDs, which substantially affected the measured reflectance of the device. Accordingly, the reflectance measured when CdSe QDs were spin-cast on the top of the devices, was much lower than that of the bare tandem solar cell, especially for incident wavelengths of 400nm<λ<1000nm, which are in the QE response regimes of InGaP and GaAs subcells. The measured JSC of the device with CdSe QDs is therefore enhanced, as presented in the inset in Fig. 6(b). The minimal reflectance is reached at a specific concentration of 7 mg/mL, at which the effective refractive index of the CdSe QDs matches that of the InGaP top subcell, serving as an optimal antireflection layer to eliminate the Fresnel reflection. As a result, most solar light is emitted into the device and is then converted by the CdSe QDs, yielding the highest power conversion efficiency herein of η = 26.12%.
In conclusion, we have demonstrated the use of CdSe QDs to tailor the incident spectrum of solar light and achieve efficient solar spectrum utilization in InGaP/GaAs/Ge tandem solar cells. We have also shown that the integration of CdSe QDs can significantly enhance the power conversion efficiency of an InGaP/GaAs/Ge tandem solar cell under AM1.5 illumination by both theory and experiment. Most importantly, because the fabrication and integration of CdSe QDs are simple, low cost, and compatible with the current manufacturing process of the photovoltaic industry, we believe that the proposed scheme is viable and highly promising for future generations of energy devices.
The authors gratefully acknowledge financial support from the National Science Council of Republic of China (ROC) in Taiwan (contract Nos. NSC–100–2112–M–003–006–MY3 and NSC–101–2221–E–182–056–MY2) and from the National Taiwan Normal University (NTNU100-D-01).
References and links
1. Y.-J. Lee, Y.-C. Yao, and C.-H. Yang, “Direct electrical contact of slanted ITO film on axial p-n junction silicon nanowire solar cells,” Opt. Express 21(S1Suppl 1), A7–A14 (2013). [CrossRef]
2. Y.-C. Yao, M.-T. Tsai, H.-C. Hsu, L.-W. She, C.-M. Cheng, Y.-C. Chen, C.-J. Wu, and Y.-J. Lee, “Use of two-dimensional nanorod arrays with slanted ITO film to enhance optical absorption for photovoltaic applications,” Opt. Express 20(4), 3479–3489 (2012). [CrossRef]
3. Y.-J. Lee, M.-H. Lee, C.-M. Cheng, and C.-H. Yang, “Enhanced conversion efficiency of InGaN multiple quantum well solar cells grown on patterned sapphire substrates,” Appl. Phys. Lett. 98(26), 263504 (2011). [CrossRef]
4. X. Yan, D. J. Poxson, J. Cho, R. E. Welser, A. K. Sood, J. K. Kim, and E. F. Schubert, “Enhanced omnidirectional photovoltaic performance of solar cells by multiple-discrete-layer tailored- and low- refractive-index anti-reflection coatings,” Adv. Funct. Mater. 23(5), 583–590 (2013). [CrossRef]
5. J. K. Sheu, C. C. Yang, S. J. Tu, K. H. Chang, M. L. Lee, W.-C. Lai, and L.-C. Peng, “Demonstration of GaN-based solar cells with GaN/InGaN superlattice absorption layers,” IEEE Electron Device Lett. 30(3), 225–227 (2009). [CrossRef]
6. M. C. Wei, S. J. Chang, C. Y. Tsia, C. H. Liu, and S. C. Chen, “SiNx deposited by in-line PECVD for multi-crystalline silicon solar cells,” Sol Energ Mat Sol C. 80(2), 215–219 (2006).
7. A. G. Bhuiyan, K. Sugita, A. Hashimoto, and A. Yamamoto, “InGaN Solar Cells: Present State of the Art and Important Challenges,” Photovoltaics, IEEE Journal of 2(3), 276–293 (2012). [CrossRef]
8. R. R. King, D. C. Law, K. M. Edmondson, C. M. Fetzer, G. S. Kinsey, H. Yoon, R. A. Sherif, and N. H. Karam, “40% efficient metamorphic GaInP/GaInAs/Ge multijunction solar cells,” Appl. Phys. Lett. 90(18), 183516 (2007). [CrossRef]
9. S. W. Boettcher, J. M. Spurgeon, M. C. Putnam, E. L. Warren, D. B. Turner-Evans, M. D. Kelzenberg, J. R. Maiolo, H. A. Atwater, and N. S. Lewis, “Energy-conversion properties of vapor-liquid-solid-grown silicon wire-array photocathodes,” Science 327(5962), 185–187 (2010). [CrossRef]
10. J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, and M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013). [CrossRef]
11. F. Hetsch, X. Xu, H. Wang, S. V. Kershaw, and A. L. Rohach, “Semiconductor nanocrystal quantum dots as solar cell components and photosensitizers: material, charge transfer, and separation aspects of some device toplogies,” J. Phys. Chem. Lett. 2(15), 1879–1887 (2011). [CrossRef]
12. M. S. Leite, R. L. Woo, J. N. Munday, W. D. Hong, S. Mesropian, D. C. Law, and H. A. Atwater, “Towards an optimized all lattice-matched InAlAs/InGaAsP/InGaAs multijunction solar cell with efficiency >50%,” Appl. Phys. Lett. 102(3), 033901 (2013). [CrossRef]
13. Sharp Develops Concentrator Solar Cell with World's Highest Conversion Efficiency of 44.4%,” http://sharp-world.com/corporate/news/130614.html (2013)
14. J. Geisz, D. Friedman, J. Ward, A. Duda, W. Olavarria, T. Moriarty, J. Kiehl, M. Romero, A. Norman, and K. Jones, “40.8% efficient inverted triple-junction solar cell with two independently metamorphic junctions,” Appl. Phys. Lett. 93(12), 123505 (2008). [CrossRef]
15. K. Tanabe, “A review of ultrahigh efficiency III-V semiconductor compound solar cells: multijunction tandem, lower dimensional, photonic up/down conversion and plasmonic nanometallic structures,” Energies 2(3), 504–530 (2009). [CrossRef]
16. L. A. Kosyachenko, Solar Cells-Silicon Wafer-Based Technologies (InTech, Rijeka, Croatia, 2011), p. 335–337.
17. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510 (1961). [CrossRef]
18. M. W. Wanlass, S. P. Ahrenkiel, R. K. Ahrenkiel, D. S. Albin, J. J. Carapella, A. Duda, J. F. Geisz, S. Kurtz, T. Moriarty, R. J. Wehrer, and B. Wernsman, “Lattice-mismatched approaches for high-performance, III-V photovoltaic energy converters,” in Proceedings of the 31th IEEE Photovoltaic Specialists Conference (Institute of Electrical and Electronics Engineers, New York, 2005), pp. 530–535. [CrossRef]
19. R. R. King, M. Haddad, T. Isshiki, P. Colter, J. Ermer, H. Yoon, D. E. Joslin, and N. H. Karam, “Next-generation, high-efficiency III-V multijunction solar cells,” in Proceedings of the 28th IEEE Photovoltaic Specialists Conference (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 998–1001. [CrossRef]
20. F. Dimroth, U. Schubert, and A. W. Bett, “25.5% efficient Ga0.35In0.65P/Ga0.83In0.17 as tandem solar cells grown on GaAs substrates,” IEEE Electron Dev. 21(5), 209–211 (2000). [CrossRef]
21. A. J. Nozik, “Quantum dot solar cells,” Physica E 14(1–2), 115–120 (2002). [CrossRef]
22. R. D. Schaller and V. I. Klimov, “High efficiency carrier multiplication in PbSe nanocrystals: implications for solar energy conversion,” Phys. Rev. Lett. 92(18), 186601 (2004). [CrossRef]
24. M. Wolf, R. Brendel, J. H. Werner, and H. J. Queisser, “Solar cell efficiency and carrier multiplication in Si1-xGex alloys,” J. Appl. Phys. 83(8), 4213–4221 (1998). [CrossRef]
25. C.-Y. Huang, D.-Y. Wang, C.-H. Wang, Y.-T. Chen, Y.-T. Wang, Y.-T. Jiang, Y.-J. Yang, C.-C. Chen, and Y.-F. Chen, “Efficient light harvesting by photon downconversion and light trapping in hybrid ZnS nanoparticles/Si nanotips solar cells,” ACS Nano 4(10), 5849–5854 (2010). [CrossRef]
26. Y.-J. Lee, C.-J. Lee, and C.-M. Cheng, “Enhancing the conversion efficiency of red emission by spin-coating CdSe quantum dots on the green nanorod light-emitting diode,” Opt. Express 18(S4), A554–A561 (2010). [CrossRef]
27. H. Kato, S. Adachi, H. Nakanishi, and K. Ohtsuka, “Optical properties of (AlxGa1-x)0.5In0.5P quaternary alloys,” Jpn. J. Appl. Phys. 33(1A), 186–192 (1994).
28. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. V. Stryland, Handbook of Optics, Third Edition Volume IV: Optical Properties of Materials, Nonlinear Optics, Quantum Optics (set) (McGraw Hill Professional, New York, 2009).
29. D. Souri and K. Shomalian, “Band gap determination by absorption spectrum fitting method (ASF) and structural properties of different compositions of (60−x) V2O5–40TeO2–xSb2O3 glasses,” J. Non-Cryst. Solids 355(31–33), 1597–1601 (2009). [CrossRef]
30. ASTMG173–03, Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37 degree Tilted Surface (ASTM International, West Conshohocken, Pennsylvania, 2005).
31. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef]