Browsing by Author "Lin, Albert"
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Item type:Item, A flatter gallium profile for high-efficiency Cu(In,Ga)(Se,S)(2) solar cell and improved robustness against sulfur-gradient variation(2016-09-07) ;Huang, Chien-Yao ;Lee, Wen-Chin ;Lin, Albert ;電子工程學系及電子研究所Department of Electronics Engineering and Institute of ElectronicsCo-optimization of the gallium and sulfur profiles in penternary Cu(In,Ga)(Se, S)(2) thin film solar cell and its impacts on device performance and variability are investigated in this work. An absorber formation method to modulate the gallium profiling under low sulfur-incorporation is disclosed, which solves the problem of Ga-segregation in selenization. Flatter Ga-profiles, which lack of experimental investigations to date, are explored and an optimal Ga-profile achieving 17.1% conversion efficiency on a 30 cm x 30 cm sub-module without anti-reflection coating is presented. Flatter Ga-profile gives rise to the higher V-oc x J(sc) by improved bandgap matching to solar spectrum, which is hard to be achieved by the case of Ga-accumulation. However, voltage-induced carrier collection loss is found, as evident from the measured voltage-dependent photocurrent characteristics based on a small-signal circuit model. The simulation results reveal that the loss is attributed to the synergistic effect of the detrimental gallium and sulfur gradients, which can deteriorate the carrier collection especially in quasi-neutral region (QNR). Furthermore, the underlying physics is presented, and it provides a clear physical picture to the empirical trends of device performance, I-V characteristics, and voltage-dependent photocurrent, which cannot be explained by the standard solar circuit model. The parameter "FGa" and front sulfur-gradient are found to play critical roles on the trade-off between space charge region (SCR) recombination and QNR carrier collection. The co-optimized gallium and sulfur gradients are investigated, and the corresponding process modification for further efficiency-enhancement is proposed. In addition, the performance impact of sulfur-gradient variation is studied, and a gallium design for suppressing the sulfur-induced variability is proposed. Device performances of varied Ga-profiles with front sulfur-gradients are simulated based on a compact device model. Finally, an exploratory path toward 20% high-efficiency Ga-profile with robustness against sulfur-induced performance variability is presented. Published by AIP Publishing.Item type:Item, A fully functionalized metamaterial perfect absorber with simple design and implementation(2016-10-26) ;Fu, Sze Ming ;Zhong, Yan Kai ;Tu, Ming Hsiang ;Chen, Bo RueiLin, AlbertBroadband perfect metamaterial absorbers have been drawing significant attention in recent years. A close-to-unity absorption over a broad spectral range is established and this facilitates many photonic applications. A more challenging goal is to construct a broadband absorber with a tailored spectral absorption. The spectral absorption control and spectral shaping are very critical in many applications, such as thermal-photovoltaic, thermal emitters, spectrum imaging system, biomedical and extraterrestrial sensing, and refractive index sensor. In this work, one-dimensional (1D) planar stacking structure is designed to achieve the ultimate goal of a functionalized absorber with a fully tailorable spectral absorption. The lithography and etching process are totally eliminated in this proposed structure, and the fabrication is fully compatible with the regular silicon IC processing. By using similar to 2 nm ultra-thin metallic layers with a 10-pair (10X) SiO2/Si3N4 integrated dielectric filter, we can achieve decent spectral response shaping. The planar configuration of the ultra-thin-metal metamaterial perfect absorber (MPA) is the key to the easy design/integration of the dielectric filters on top of the MPA. Specifically, band-rejected, high-pass, low-pass and band-pass structure are constructed successfully. Finally, experimental evidence to support our simulation result is also provided, which proves the feasibility of our proposal.Item type:Item, A Multimetal Broadband Metamaterial Perfect Absorber With Compact Dimension(2016-04-01) ;Zhong, Yan Kai ;Fu, Sze Ming ;Tu, Ming-Hsiang ;Chen, Bo-RueiLin, AlbertWe propose an extremely simple multiple-metal metamaterial perfect absorber (MPA). The dimension of our proposed design is only 221 nm for the visible wavelength range from 400 to 700 nm. This is comparable with past efforts on MPAs using plasmonics at the same wavelength range, whereas the plasmonic excitation is absent in our proposal. A unity broadband absorption can be achieved with ultrathin metallic films. In addition, the wavelength scalability is possible using our design, and the fully planar simple configuration facilitates large-area photonic design without the need for lithography and etching. The physics is the field penetration and the field absorption for the photons at different wavelength ranges using different metallic layers. We also show that the adjustment of the individual layer thickness is critical to attaining a perfect wave impedance matching to vacuum. The titanium (Ti), nickel (Ni), and aluminum (Al) triple-metal configuration is used to demonstrate the concept experimentally, and a close match to the theoretical result is observed. The absorption band can be further widened with more stacking layers with various metals. We believe that the proposed design is very promising in the aspects of simple processing and scalable for large-area broadband unity absorption. It thus improves the future implementation of MPAs and facilitates a wide range of relevant applications.Item type:Item, A path-finding toward high-efficiency penternary Cu(In,Ga)(Se,S)(2) thin film solar module(2019-01-01) ;Huang, Chien-Yao ;Parashar, Parag ;Chou, Hao-Ming ;Lin, Yi-ShivanLin, AlbertThe optimal p-n junction structure in a state-of-the-art Cu(In,Ga)(Se,S)(2) thin-film solar module technology is investigated. For co-optimization design and path-finding, a TCAD model is developed with experimental samples. The engineerable parameters, i.e., F-Ga, GGI(avg), and CdS thickness, are demonstrated to play a critical role in determining the p-n junction properties such as dark current characteristics J(dark)(V), voltage-dependent photocurrent, localized carrier collection efficiency, and interface carrier transportation. We show the optimal Ga-grading is determined by a trade-off between the recombination loss in space charge region and the photo carrier collection in quasi-neutral region. The optimal CdS thickness is determined by a trade-off between carrier collection efficiency, short-circuit current (J(SC)) loss, and J(dark)(V), which depends on varied Ga-profiles. Overall, thin CdS (<= 10 nm) is preferred to reduce the J(SC) loss in accumulated Ga-profiles, while thicker CdS is preferred to enhance the carrier collection efficiency in flatter Ga-profiles. The band alignment effect on varied Cu(In,Ga)(Se,S)(2)/CdS junctions is also investigated. It is found sulfur-incorporation can suppress the V-OC saturation behavior at wide bandgap. For CIGSeS absorber with SS = 20% and D-p = 15%, the maximum V-OC of 780 mV can be achieved by co-optimized Ga-profile. Furthermore, varied Ga-profiles and CdS buffer layers are explored for pathfinding. An optimal p-n junction structure shows a relative + 40% efficiency improvement from 15.5% to 21.9%. This work shows the efficiency headroom of reported CIGSeS thin-film solar module technology through co-optimized CIGSeS composition gradient and buffer layer.Item type:Item, A Planarized Thermophotovoltaic Emitter With Idealized Selective Emission(2016-08-01) ;Fu, Sze Ming ;Zhong, Yan Kai ;Tu, Ming Hsiang ;Chen, Bo RueiLin, AlbertCompared with conventional solar cells, thermophotovoltaics (TPV) can be more efficient and, thus, exceeds the detailed balance efficiency limit. In particular, the emitter of TPV is a critical design since it determines whether the thermalization loss can be reduced and whether the sub-band-gap radiation can be suppressed, as far as the photovoltaic (PV) process is concerned. In this paper, we propose a selective planar emitter composed of alternating ultrathin metal and dielectric layers. An aperiodic dielectric stacking is designed to tailor the emission spectrum by shaping the emission peak and by adjusting the emission wavelength. We show that the peak emission wavelength (lambda(emission)) is adjustable from lambda = 1500 nm to lambda = 2500 nm. Furthermore, the long-wavelength cutoff is very sharp for our proposed emitter structure, and the absorption is suppressed to 0.1 beyond the cutoff. The preliminary experiment is also conducted to fulfill the concept of a fully planar ultrathin refractory metal emitter design, and the result is similar to the calculated ones. We believe that the planar thermal emitter based on ultrathin metals and aperiodic dielectric stacking is very promising for future thermal emission applications since it requires no lithography and etching, provides strong peak emission power, and possesses wide wavelength scalability.Item type:Item, An electrophoretic-deposited low-cost carbon nanotube (CNT) thermophotovoltaic emitter(2018-01-01) ;Lin, Albert ;Parashar, Parag ;Yang, Chien-Chih ;Hao-MingChouLin, Yi-ShiuanWe use electrophoresis technique to deposit a low-cost carbon nanotube (CNT) film on tantalum (Ta) for thermophotovoltaic (TPV) emitters. The initial thermal measurement of the EPD-CNT film from 200 degrees C-800 degrees C is conducted. The elimination of high-temperature CVD deposition facilitates the commercialization of TPV devices. The UV-VIS-NIR spectrum and high-temperature FTIR measurement are reported to assess the feasibility of EPD-CNT as a TPV emitter candidate. The planarized nature of the proposed emitter can be easily integrated with dielectric multi-layer filter for spectral shaping depending on applications.Item type:Item, An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles(2013-01-14) ;Lin, Albert ;Fu, Sze-Ming ;Chung, Yen-Kai ;Lai, Shih-yunTseng, Chi-WeiSurface plasmon enhancement has been proposed as a way to achieve higher absorption for thin-film photovoltaics, where surface plasmon polariton(SPP) and localized surface plasmon (LSP) are shown to provide dense near field and far field light scattering. Here it is shown that controlled far-field light scattering can be achieved using successive coupling between surface plasmonic (SP) nano-particles. Through genetic algorithm (GA) optimization, energy transfer between discrete nano-particles (ETDNP) is identified, which enhances solar cell efficiency. The optimized energy transfer structure acts like lumped-element transmission line and can properly alter the direction of photon flow. Increased in-plane component of wavevector is thus achieved and photon path length is extended. In addition, Wood-Rayleigh anomaly, at which transmission minimum occurs, is avoided through GA optimization. Optimized energy transfer structure provides 46.95% improvement over baseline planar cell. It achieves larger angular scattering capability compared to conventional surface plasmon polariton back reflector structure and index-guided structure due to SP energy transfer through mode coupling. Via SP mediated energy transfer, an alternative way to control the light flow inside thin- film is proposed, which can be more efficient than conventional index-guided mode using total internal reflection (TIR). (C)2012 Optical Society of AmericaItem type:Item, An ultra-compact blackbody using electrophoretic deposited carbon nanotube films(2018-01-01) ;Lin, Albert ;Yang, Chien-Chih ;Parashar, Parag ;Lin, Chien-YungJian, Ding RungCarbon nanotubes (CNTs) possesses decent optical properties and thus can be considered as a candidate for perfect absorbers due to their close-to-air refractive index and minimal extinction. However, weak absorption in porous materials, due to the low extinction coefficients, requires an inevitably thick absorption layer (similar to 100 mu m) for the perfect opaque absorbers. Thus, the requirement of large thicknesses of CNTs prohibits them from being used as miniaturized integrated photonic devices. Here, we propose an electrophoretic deposited (EPD) CNT resonant cavity structure on tantalum (Ta) to enhance optical absorption. Efficient random light scattering along with the resonant cavity structure using Ti/SiO2 stacking enhances the absorption in our proposed EPD-CNT film while maintaining the total device thickness to <1 mu m. The experiment results reveal that the absorption band covers the entire UV-VIS-NIR spectrum (lambda = 0.3-2.6 mu m), using resonant-cavity EPD-CNT design. The EPD deposition process is done at relatively low temperature < 120 degrees C. We believe that this proposal is very promising for sensing, antenna, and thermophotovoltaics (TPV), in terms of bandwidth, compactness and cost.Item type:Item, An ultra-efficient energy transfer beyond plasmonic light scattering(2014-11-14) ;Fu, Sze-Ming ;Zhong, Yan-Kai ;Lin, Albert ;電子工程學系及電子研究所Department of Electronics Engineering and Institute of ElectronicsThe energy transfer between nano-particles is of great importance for, solar cells, light-emitting diodes, nano-particle waveguides, and other photonic devices. This study shows through novel design and algorithm optimization, the energy transfer efficiency between plasmonic and dielectric nano-particles can be greatly improved. Using versatile designs including core-shell wrapping, supercells and dielectric mediated plasmonic scattering, 0.05 dB/mu m attenuation can be achieved, which is 20-fold reduction over the baseline plasmonic nano-particle chain, and 8-fold reduction over the baseline dielectric nano-particle chain. In addition, it is also found that the dielectric nanoparticle chains can actually be more efficient than the plasmonic ones, at their respective optimized geometry. The underlying physics is that although plasmonic nano-particles provide stronger coupling and field emission, the effect of plasmonic absorption loss is actually more dominant resulting in high attenuation. Finally, the group velocity for all design schemes proposed in this work is shown to be maintained above 0.4c, and it is found that the geometry optimization for transmission also boosts the group velocity. (C) 2014 AIP Publishing LLC.Item type:Item, Aperiodic and randomized dielectric mirrors: alternatives to metallic back reflectors for solar cells(2014-05-05) ;Lin, Albert ;Zhong, Yan-Kai ;Fu, Sze-Ming ;Tseng, Chi WeiYan, Sheng LunDielectric mirrors have recently emerged for solar cells due to the advantages of lower cost, lower temperature processing, higher throughput, and zero plasmonic absorption as compared to conventional metallic counterparts. Nonetheless, in the past, efforts for incorporating dielectric mirrors into photovoltaics were not successful due to limited bandwidth and insufficient light scattering that prevented their wide usage. In this work, it is shown that the key for ultra-broadband dielectric mirrors is aperiodicity, or randomization. In addition, it has been proven that dielectric mirrors can be widely applicable to thin-film and thick wafer-based solar cells to provide for light trapping comparable to conventional metallic back reflectors at their respective optimal geometries. Finally, the near-field angular emission plot of Poynting vectors is conducted, and it further confirms the superior light-scattering property of dielectric mirrors, especially for diffuse medium reflectors, despite the absence of surface plasmon excitation. The preliminary experimental results also confirm the high feasibility of dielectric mirrors for photovoltaics. (C)2014 Optical Society of AmericaItem type:Item, Approaching conversion limit with all-dielectric solar cell reflectors(2015-02-09) ;Fu, Sze Ming ;Lai, Yi-Chun ;Tseng, Chi Wei ;Yan, Sheng LunZhong, Yan KaiMetallic back reflectors has been used for thin-film and wafer-based solar cells for very long time. Nonetheless, the metallic mirrors might not be the best choices for photovoltaics. In this work, we show that solar cells with all-dielectric reflectors can surpass the best-configured metal-backed devices. Theoretical and experimental results all show that superior large-angle light scattering capability can be achieved by the diffuse medium reflectors, and the solar cell J-V enhancement is higher for solar cells using all-dielectric reflectors. Specifically, the measured diffused scattering efficiency (D.S.E.) of a diffuse medium reflector is >0.8 for the light trapping spectral range (600nm-1000nm), and the measured reflectance of a diffuse medium can be as high as silver if the geometry of embedded titanium oxide(TiO2) nanoparticles is optimized. Moreover, the diffuse medium reflectors have the additional advantage of room-temperature processing, low cost, and very high throughput. We believe that using all-dielectric solar cell reflectors is a way to approach the thermodynamic conversion limit by completely excluding metallic dissipation. (C) 2015 Optical Society of AmericaItem type:Item, Arbitrarily-Wide-Band Dielectric Mirrors and Their Applications to SiGe Solar Cells(2015-08-01) ;Zhong, Yan Kai ;Fu, Sze Ming ;Yan, Sheng Lun ;Chen, Po YuLin, AlbertThe dielectric mirror is an important optical component for optoelectronic devices, passive photonic devices, and solar cells. Unfortunately, the reflection bandwidth of distributed Bragg reflectors (DBRs) and high-index contrast mirrors (HCGs) are limited by the index contrast of the material system used. Here, an aperiodic design for dielectric mirrors is proposed, and it is shown that for a fixed index contrast, the bandwidth of the reflection band can be arbitrarily widened by simply incorporating more dielectric layers. This is pronouncedly different from the fixed bandwidth of HCGs and DBRs. The physics behind the broadband reflection for the aperiodic stacking is identified as the photonic bandgap widening due to the annihilation of the quasi-guided modes in nonperiodic structures. This observation applies very well to aperiodic auto-cloned 3-D photonic crystal reflectors, to aperiodic DBRs, and even to diffuse dielectric mirrors that have recently emerged to be very promising for solar cells due to their zero plasmonic absorption nature. Experimentally, the white paint diffuse medium reflectors are applied to SiGe solar cells to confirm their high reflectance and the feasibility of enhancing solar cell efficiency.Item type:Item, Back-Contacted Thin-Film GaAs Solar Cells(2016-01-01) ;Hong, Chung-Yu ;Lin, Yu-Chen ;Ho, Kuan-Ying ;Tsai, Jia-LingChien, Zhan-TienIn this work, we present a thin-film GaAs solar cell employing via contacts for forming a back-contacted solar cell to eliminate light blocking effects and enhance photon recycling at the same time. The fabrication procedure and the characterization of the fabricated devices are discussed in this paper. From our measurement, a conversion efficiency of 6.5%, open circuit voltage of 0.95 V, and a current density of 8.6mA/cm(2) under one-sun illumination were obtained in a 5x5 mm cell.Item type:Item, Broadband Polarization-Insensitive Metamaterial Perfect Absorbers Using Topology Optimization(2016-10-01) ;Fu, Sze Ming ;Zhong, Yan Kai ;Ju, Nyan Ping ;Tu, Ming-HsiangChen, Bo-RueiA novel scheme for a perfect hyperbolic metamaterial (HMM) absorber is proposed, and experimental verification is provided. It has been shown previously that tapered HMM stacks can provide adiabatic waveguiding over a wide spectral range and thus are an ideal opaque absorber. Here, nontapered shape-optimized HMM absorbers are proposed, which facilitates the fabrication and promotes the large-area applications such as thermophotovoltaics (TPV). In the synthesis of the optimal patterns, we use 5-harmonic rigorously coupled wave analysis (RCWA) and experimental trials to shorten the trial-and-error time. The best pattern provides an averaged broadband experimental absorption of 88.38% over lambda = 1 mu m to lambda = 2 mu m, which is comparable to the state-of-the-art experimental effort using tapered HMM. The nontapered nature can be easier to fabricate from the semiconductor processing viewpoint. The physics behind the pattern-optimized HMM cavity is the broadband light coupling by the air-cavity and the unbounded photonic density of the states (PDOS) associated with the HMM. The topology optimized air cavity effectively couples the incident photons into the metal-dielectric stacking, eliminating the need of sidewall tapers. We believe the proposed topology-optimization methodology benefits the future design of compact metamaterial perfect absorbers (MPA), sensors, antenna, and thermophotovoltaic emitters, and absorbers.Item type:Item, Comparison of nano-structured solar cell anti-reflection coating based on graded-index or mode coupling approach(2014-11-01) ;Lin, Albert ;Zhong, Yan-Kai ;Fu, Sze-Ming ;電子工程學系及電子研究所Department of Electronics Engineering and Institute of ElectronicsSolar cell nano-structured anti-reflection coatings based on graded index (GI) and mode coupling are all proposed to significantly reduce the reflection from semiconductor-air interface. In this work, it is shown that purely graded index approach can lead to degradation of long wavelength absorption by eliminating quasi-guided mode excitation. The reason is that the physically graded layer not only provides low reflectance path from air to semiconductor, but also from semiconductor to air, leading to photon escape. This results in out-coupling of photons from the semiconductor to air. On the other hand, anti-reflection coating based on mode coupling does not suffer from degraded long wavelength absorption and it is capable of acting as one-way photon pass coating. It is found that the sidewall thickness of mode coupling anti-reflection coating has significant impact on its effectiveness for antireflection, and therefore the selection of process methods is critical for its low reflectance. It is proposed that the purely graded index coating is more suitable for wafer-based photovoltaics where full absorption is possible by two photon traces. The mode coupling coating is suitable for both wafer-based photovoltaics and thin-film photovoltaics since it provides not only low reflectance but also long wavelength quasi-guided mode excitations. In the end, new types of anti-reflection coating and light trapping structure are proposed to further enhance the performance. (C) 2014 Elsevier B.V. All rights reserved.Item type:Item, Cultural politics of Techno music in Taiwan: Shining 3 girls(2007) ;Lin, Albert ;交大名義發表National Chiao Tung UniversityItem type:Item, Decoupling Spectral Overlap of Intermediate Band Solar Cells using Low-High State Filling(2012) ;Lin, Albert ;Phillips, Jamie ;電子工程學系及電子研究所Department of Electronics Engineering and Institute of ElectronicsThe high efficiency predicted for solar cells based on multi-photon processes relies on the assumption of optical transitions with non-overlapping spectral bands. Spectral overlap reduces the conversion efficiency due to energy loss associated with improper usage of higher energy photons for lower energy optical transitions. In this study, device structures with non-uniform occupation of intermediate electronic states are proposed to reduce the dependence of conversion efficiency on spectral overlap. Solar cell conversion efficiencies are calculated for structures where absorption bands are spatially decoupled due to defined occupation of intermediate states. Conversion efficiencies for a two section and three section device with spectral overlap of 4 eV are determined to be 52.8 % and 61.5 %, respectively, and are significantly larger than the calculated efficiency of 35.1% for the case of a standard multi-photon cell with uniform half-filled intermediate states The spectrally-decoupled device provides a means to achieve high theoretical efficiency independent of spectral overlap that approaches the detailed balance efficiency limit of 63.2 % for intermediate state devices without spectral overlap and 63.8 % for unconstrained triple-junction tandem cells.Item type:Item, Experimentally-implemented genetic algorithm (Exp-GA): toward fully optimal photovoltaics(2015-09-21) ;Zhong, Yan Kai ;Fu, Sze Ming ;Ju, Nyan Ping ;Chen, Po YuLin, AlbertThe geometry and dimension design is the most critical part for the success in nano-photonic devices. The choices of the geometrical parameters dramatically affect the device performance. Most of the time, simulation is conducted to locate the suitable geometry, but in many cases simulation can be ineffective. The most pronounced examples are large-area randomized patterns for solar cells, light emitting diode (LED), and thermophtovoltaics (TPV). The large random pattern is nearly impossible to calculate and optimize due to the extended CPU runtime and the memory limitation. Other scenarios that numerical simulations become ineffective include three-dimensional complex structures with anisotropic dielectric response. This leads to extended simulation time especially for the repeated runs during its geometry optimization. In this paper, we show that by incorporating genetic algorithm (GA) into real-world experiments, shortened trial-and-error time can be achieved. More importantly, this scheme can be used for many photonic design problems that are unsuitable for simulation-based optimizations. Moreover, the experimentally implemented genetic algorithm (Exp-GA) has the additional advantage that the resultant objective value is a real one rather than a theoretical one. This prevents the gaps between the modeling and the fabrication due to the process variation or inaccurate numerical models. Using TPV emitters as an example, 22% enhancement in the mean objective value is achieved. (C) 2015 Optical Society of AmericaItem type:Item, Fully Planarized Perfect Metamaterial Absorbers With No Photonic Nanostructures(2016-02-01) ;Zhong, Yan Kai ;Fu, Sze Ming ;Ju, Nyan Ping ;Tu, Ming-HsiangChen, Bo-RueiIn the past, perfect metamaterial absorbers (PMAs) have required nanolitho-graphy patterning to boost broadband absoprtion. Tapered structures, in particular, are shown to achieve close-to-unity absorption over broadband using adiabatic light coupling. A nontapered PMA is desirable due to the fact that it is easier to fabricate using regular lithography techniques. This facilitates the scalability to large-area photonic applications such as thermophotovoltaics. In this work, we propose a fully planarized design with ultrathin metallic films for broadband PMAs. The design provides close-to-unity absorbance over a wide spectral range and is wavelength scalable from middle ultraviolet to long wavelength infrared. The planarized design is extremely easy to fabricate, and it requires no lithography nor etching. The design can be used with different moderate-extinction metals such as tungsten, titanium, tantalum, and nickel. The physics is that the thin layer of the moderate-extinction metal allows photons to penetrate through itself. The insertion of the dielectric between thin metal layers is necessary to spatially separate the ultrathin metallic thin film to boost the effect of thin-film absorption. As far as the bandwidth normalized to center wavelength is concerned, we believe that the experimental result demonstrated here shows the broadest bandwidth to date.Item type:Item, HIT Solar Cell Performance Enhancement with Luminescent Down Shifting Phenomenon(2018-01-01) ;Lin, Albert ;Huang, Chien-Yao ;Parashar, Parag ;Chou, Hao-MingLin, Yi-ShiuanLuminescent down-shifting (LDS) phenomenon has been employed to enhance the HIT solar cell efficiency. The efficiency and J(SC) are increased by 2.3% and 11.5% respectively. External quantum efficiency (EQE) data supports our claim.