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Enhancement of photovoltaic cell performance using periodic triangular gratings Evgueni Bordatchev Mohammed Tauhiduzzaman Rajat Dey Downloaded From: http://photonicsforenergy.spiedigitallibrary.org/ on 04/17/2014 Terms of Use: http://spiedl.org/terms

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Page 1: Bordatchev, Tauhiduzzaman, Dey 2014 (JPE)

Enhancement of photovoltaic cellperformance using periodic triangulargratings

Evgueni BordatchevMohammed TauhiduzzamanRajat Dey

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Enhancement of photovoltaic cell performance usingperiodic triangular gratings

Evgueni Bordatchev,* Mohammed Tauhiduzzaman, andRajat Dey

National Research Council of Canada, London, Ontario N6G 4X8, Canada

Abstract. The solar energy industry strives to produce more efficient and yet cost effective solarpanels each consisting of an array of photovoltaic (PV) cells. The goal of this study was toenhance the performance of PV cells through increasing the cells’ optical efficiency definedas a percentage of surface incident light that reaches the PV material. This was achieved throughthe reduction of waveguide decoupling loss and Fresnel reflection losses by integrating specificnonimaging micro-optical structures on the top surface of existing PV cells. Due to this inte-gration, optical efficiency and performance were increased through the enhancement of lighttrapping, light guiding, and in-coupling functionalities. Periodic triangular gratings (PTGs)were designed, nonsequentially modeled, optimized, and fabricated in polydimethylsiloxaneas proposed micro-optical structures. Then the performance of PV cells with and without inte-grated PTGs was evaluated and compared. Initial optical simulation results show that an originalPV cell (without PTG) exhibits an average optical efficiency of 32.7% over a range of incidentlight angles between 15 and 90 deg. Integration of the PTG allows the capture of incomingsunlight by total internal reflection (TIR), whence it is reflected back onto the PV cell for multi-ple consecutive chances for absorption and PV conversion. Geometry of the PTG was optimizedwith respect to an angle of light incidence of {15, 30, 45, 60, 75, 90} deg. Optical efficiency ofthe geometrically optimized PTGs was then analyzed under the same set of incident light anglesand a maximum optical efficiency of 54.1% was observed for a PV cell with integrated PTGoptimized at 90 deg. This is a 53.3% relative improvement in optical performance when com-pared to an original PV cell. Functional PTG prototypes were then fabricated with optical surfacequality (below 10 nm Ra) and integrated with PV cells demonstrating an increase in maximumpower by 1.08 mW∕cm2 (7.6% improvement in PV performance) and in short circuit current by2.39 mA∕cm2 (6.4% improvement). © 2014 Society of Photo-Optical Instrumentation Engineers(SPIE) [DOI: 10.1117/1.JPE.4.044599]

Keywords: photovoltaic cell; optical efficiency; triangular grating; nonsequential optical mod-eling; micromachining; photovoltaic performance evaluation.

Paper 13020P received Aug. 4, 2013; revised manuscript received Mar. 3, 2014; accepted forpublication Mar. 5, 2014; published online Apr. 2, 2014.

1 Introduction

There is a growing interest in renewable energy in today’s market, a prominent form of which issolar power, and consequently there is an increasing demand for more efficient solar cells andpanels. There are two main ways to boost the efficiency of solar cells—enhancing the photo-voltaic (PV) effect and enhancing the optical performance by delivering more light energy ontothe PV material. The enhancement of the PV effect is based primarily on new chemical com-positions and combinations of materials and alloys, while improvements in optical performancetarget the maximum possible delivery of solar energy despite weather conditions and the positionof the sun. Improvements in optical performance are based on the integration of special opticalstructures (e.g., periodic textures, gratings, light/waveguides, optical filters retro-reflecting

*Address all correspondence to: Evgueni Bordatchev, E-mail: [email protected]

0091-3286/2014/$25.00 © 2014 SPIE

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elements, and other micro-optical features) directly onto a glass substrate coated with PVmaterial(s).1–5 Alternatively, these optical structures can be made from plastics or glass andplaced on the top of the PV panels.6,7 Each of these approaches has its own advantages anddisadvantages, although the second approach may pose fewer technological challenges duringmass production where well established large area replication technologies such as hotembossing and injection molding can be used. Additional advantages of using top surfacemounted optical structures are ease of placement, replacement and retrofitting, low maintenancecost, geometry customization for desired optical functionality, and the ability to be producedand/or placed on a free-form surface.

In particular, Chen et al.1 have developed and numerically modeled a metal square-waveperiodic grating as a back reflector in solar cells. These functions to enhance light scatteringand diffract light at oblique angles, which are larger than the critical angle for total internalreflection (TIR) of silicon (Si), thus increasing the photon path length within the absorberlayer for further absorption. The influence of a pyramid surface texture and its profile dimen-sions (i.e., period and height of pyramids) on the quantum efficiency and short circuit currentof microcrystalline Si solar cells with different absorber thicknesses was investigatedby Dewan et al.2 Their results have identified the key optical losses (unavoidable absorptionand reflection) in the solar cell structure and derived potential strategies to minimizethem.

Raymond et al.6–9 have developed the so-called “fusion” surface technology comprised ofgeometrical optical microstructures (essentially lenses) incorporated into the surface of a PVpanel. The structures are specifically designed to increase path length and/or TIR and todecrease surface reflection for a selected set of incoming ray angles, thereby improvingthe net efficiency of a PV panel. Recent testing of “fusion” has demonstrated a clearimprovement of 10% to 12.5% in short-circuit current ISC. This approach is a logical con-sequence of previous studies where the top surface of Si solar panels was textured withpyramids and different shaped grooves for enhancing light trapping and antireflectionperformances.10,11

Another approach for developing light-trapping capabilities was patented by Slager,12

where so-called “inverted cube” retro-reflecting optical elements (which have been knownfor decades in automotive lighting) were used to provide the TIR effect on the top surfaceof PV panels.

In addition to light trapping functionalities, submicron-range diffractive gratings with differ-ent cross-section shapes (e.g., triangular with sharp/rounded edges, rectangular, stair type, andsaw-tooth) can be used effectively as a broadband antireflection coupler achieving a couplingefficiency of 99% for triangular and ∼50% for saw-tooth gratings, respectively.13

This work continues the development of top surface mounted optical structures for enhanc-ing light-trapping capabilities and improving overall performance of PV cells using cost effec-tive plastic thin films.14,15 Innovation in this work with respect to (wrt) the aforementionedstudies consists in the full cycle (i.e., design, modeling, optimization, fabrication, and perfor-mance testing) of periodic triangular grating (PTG) development taking into account the day-time sunlight orientation. The PTGs are specifically designed to increase the optical pathlength and TIR effect as well as to reduce the loss due to surface reflection of light for aselected set of incoming angles, thereby improving the net optical efficiency of PV cells inte-grated into a PV panel. Initially, the PTGs are optimized for a specific incident sunlight anglein order to understand the initial optical performance of the PTGs. Subsequently, optical per-formance of optimized PTGs is numerically simulated for different values of sunlight orien-tation angle, which changes over the course of a day. It is necessary to note that numericalsimulation results were used in this study for subjective justification and verification of theselection and fabrication of optimized PTGs only and not for comparison of simulation andexperimental results. Functional prototypes of the PV cell with integrated PTGs were fabri-cated in two steps. Initially, dies with PTG geometry were fabricated from aluminum alloy6061 using micromachining technology and their surface quality was measured and evaluated.Further, PTGs were fabricated from polydimethylsiloxane (PDMS) and integrated with a PVcell. Electrical performance of integrated PV cells was evaluated using a sun simulator andmeasuring the I–V curve.

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2 Numerical Simulation of PV Cell Optical Performance

2.1 Optical Designs of Original and PTG Integrated PV Cells

The primary aim of numerical simulation of PTG optical performance was to analyze the abilityof the PTG to trap the sunlight within a waveguide, redirecting light back toward the PV materialsurface through TIR. There are several different strategies known to improve the light absorbingefficiency of PV panels, such as implementing antireflection coatings, optical filters, opticalconcentrators, and highly reflective back contacts.4–6,13,16–18 The use of micro-optical elementsand structures is an advanced knowledge-based approach to improve the optical and electricalefficiency of the PV panels. These micro-optical elements and structures modify (usuallyincrease) the optical path length of incident light, causing it to bounce, and travel within a wave-guide along the PV material surface for efficient absorption without changing the PV cell designitself. The use of micro-optics helps to trap the sunlight reflected from the PV cell surfaces withina waveguide which is located between the PTG and PV material. Normally, for flat PV cells andpanels, a certain portion of the sunlight reflected from the PV material surface is lost for PVenergy generation. By redirecting the reflected light back onto the PV material, progressive pos-sibilities for absorption and conversion into electricity arise. The entrapment and redirection oflight are achieved through the use of the well-known TIR effect, in which light is totally reflectedback into a medium with higher refractive index whenever the angle of incidence exceeds thecritical angle. In addition, the micro-optical elements (e.g., PTGs) located on the top surface ofthe PV cells help to enhance sunlight capture angles across the 180 deg horizon travel andretransmit light onto the PV cells with incident angles suitable for more efficient energygeneration.

In this study, the PV cell is considered as a complex opto-PV system constructed from (inbottom to top order) an absorber, PV material, glass cover sheet (waveguide), and PTG madefrom polymethyl methacrylate (PMMA) for enhancing overall performance through effectivelight collection and trapping capabilities. PMMAwas chosen as a material with proven excellentoptical properties (e.g., light transmission capability), durability, lightweight, low cost, and aswell suitability for cost-effective mass-scale production using injection molding and hotembossing technologies. The choice of optical materials is critical to opto-PV system perfor-mance. In addition to highly critical optical properties (e.g., refractive index, transmission,etc.), materials must be compatible with environmental factors such as daily and seasonalchanges in temperature and humidity, abrasive erosion, long-term exposure to solar flux,and other factors. In the present study, the PTG is made from a thin plastic sheet in order tominimize the optical path within the acrylic. Thus, optical transmission is reduced having asmaller impact on total light transmission over the lifetime of the PTG.

Figure 1 shows the schematic design of an original PV cell [Fig. 1(a)] and a PV cell withintegrated PTG [Fig. 1(b)] and their components. Based on a literature review and authors’ pre-liminary study,14 an initial geometry of PTGs was selected with a grating period of 112 μm and adepth of 25.0 μm giving equal left and right inclination angles (α) of triangular cross section of24.1 deg. These designs were used for optical modeling in the LightTools® software environ-ment, featuring an integration of the PMMA PTGs followed by a 4-mm thick waveguide (e.g.,BK7 glass, refractive index n ¼ 1.51872 at 546.1 nm), the PV material (0.005-mm thick Si), and

glass plate

PV material

absorber

PMMA-based PTG

period depth (b)

glass plate

PV material

absorber

(a)

Fig. 1 Schematic design of original photovoltaic (PV) cell (a) and PV cell with integrated periodictriangular gratings (PTG) (b) (not to scale).

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an absorber layer. It was also assumed that there are no air gaps between these optical elements(PTG, glass waveguide, and PV material). This is an ideal and desired condition for PV panelfabrication. The presence of air gaps and pockets significantly reduces the overall optical andtherefore PV performance of solar panels.

Functionally, the PTG is a typical nonimaging micro-optical structure comprising a set ofadjacent equilateral triangles; however, the triangles can be nonequilateral depending on specificfunctionality. When the PTG is attached to a stationary (no sunlight tracking) flat PV cell, it ishighly desirable that the PTG assumes dual functionality. First, the PTG should function asa light collector enhancing the capability of capturing light under varying azimuth orientations.In this case, the need for precision tracking mechanisms may be eliminated. Second, the PTGshould act as a micro-TIR structure that traps the light reflected from the top surface of the PVmaterial because TIR is lossless for highly specular surfaces. TIR forces light to bounce betweenthe PTG-air interface and the top surface of the PV material. This second functionality shouldensure that a maximum number (in an ideal case—all) of light rays will be eventually absorbedby the PV material. In this study, equilateral PTGs are selected due to their ease of fabricationthrough single point diamond cutting using a triangular cutting tool. This technology is highlyefficient in producing both tooling and functional prototypes of PTGs with optical surfacequality.15,19

2.2 Overall Optical Performance of Original and IntegratedWith PTG PV Cells

Optical performances of an original PV cell and PV cells with integrated PTGs were simulatednumerically using LightTools® element-based optical modeling and simulation software for per-forming nonsequential ray tracing. A typical ray-tracing model consists of a source(s), opticalsystem, and receivers. The source defines the illumination conditions applied to an opticalelement, specifying the light size, position, orientation, spectrum, and divergence. For solarsimulation applications, the solar spectrum is typically defined by the ASTM 1.5G173 spectralstandard below the lowest bandgap of the PV material used. The bandgap defines a bandwidth,where PV material is capable of converting photons into electricity. In this study, silicon waschosen as the PV material; and since it possesses a bandgap of 1100 nm (1.1 eV), the solarspectrum was, therefore, truncated at wavelengths greater than 1100 nm. For our opticalsimulation, the source was chosen as an area with uniform irradiance at an input plane witha defined angular acceptance region. For our model, a flat source was chosen with an artificialinput power of 1 W.

The receiver is an artificial optical sensor that virtually measures and records incident rays atthe target plane. LightTools® provides several optical performance characteristics, such as totalincident power (TIP), irradiance distributions, intensity (angular) distributions, and spectralinformation. In our model, the receiver can also be associated with an absorber and therefore,from the optical properties perspective, it was not necessary to specify the material of theabsorber layer. The absorber was modeled only as an optical element that cancels (fully absorbs)all the back reflections of light that pass through the PV material. Also, an additional flat receiverwas placed in front of the glass cover sheet.

A typical optical system consists of optical elements, such as lenses, gratings, apertures,lightguides, etc. Each optical element has specific properties attributed to the surface, material,and optical interface. In this study, the optical system of the original PV cell has three elements,each of rectangular volume: a glass plate (waveguide) made from BK7 glass material; the PVmaterial, made of silicon; and an absorber. The optical model of the PV cell with integrated PTGis based on this model of the original PV cell with added volumetric triangles made of PMMA ontop of the glass waveguide. It was assumed that both the front and back surfaces of the glasswaveguide have 80% transmission and 20% reflection, respectively. The same ratio of trans-mission to reflection was also applied for the air-PTG interface.

Two LightTools® ray trace models for an original PV cell and a PV cell with integrated PTGwere numerically simulated and analyzed. Initially, it was necessary to understand how rays ofsunlight enter, where they exit and how they are transmitted by the optical system. This analysishas been done by the visualization of optical paths tracing the rays as they travel through the

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system and interact with the various optical surfaces. For both models, it was assumed that thephysical features of the PTG and glass waveguide are large enough to avoid physical optics anddiffractive effects.

For the purposes of comparison, ray tracing diagrams demonstrating typical optical perfor-mance of the original PV cell and PV cell with integrated PTG with an angle of light incidence of60 deg are shown in Fig. 2. In general, Fig. 2 depicts how light has been captured by the specificoptical system as well as how it propagates within and travels along the waveguide deviating bythe law of reflection and TIR phenomena. Overall, the light trapping capability is evaluatedthrough the analysis of the optical path length and a number of occurrences of a light ray hittingthe PV material before escaping the optical system or being fully absorbed.

It can be observed that the main issue of the original PV cell [Fig. 2(a)] is the reflection ofrays from the glass cover plate and from the top surface of the PV material [points P1a and P2a inFig. 2(a)]. When light is not orthogonally incident on the glass cover sheet of the solar panel, asignificant portion of the light is reflected from this surface and the rest of the light is refractedtoward the top surface of the solar cell. As a result, some light rays are transmitted through theglass cover and absorbed by the PV material. Some light rays bounce off the top surface of thesolar cell at large angles of incidence wrt the surface normal. In this case, the projected area ofthe sun’s energy on the PV material surface becomes much smaller as the sun approachesthe horizon. Therefore, significantly less solar energy (up to 50%) will be absorbed by thePV material. This phenomenon is known as “cosine fall off.” In this case, the incoming raysare coming from different angles depending on the time of day as well as the season of theyear such that an undesirably small fraction of incident sun rays may be able to be absorbedby the PV absorbing material of the solar cell. Additionally, improper orientation of the solarpanel with regards to the azimuth of the sun may also contribute to the production of less solarenergy. As a result, the optical path within an original PV cell has only three distinguishedpoints: where a ray enters (P1a), where the ray is partially absorbed by the PV material(P2a), and where the ray escapes the optical system (P3a). As such, the ray has only one pos-sibility of interacting with the PV material. This is obviously not a preferable way for deliveringfull sunlight energy into the PV material.

Therefore to improve the light absorbing capability of the solar panels through efficient lighttrapping, it is proposed that the PTG be placed on the top surface of the glass cover sheet asshown in Fig. 2(b). It can be seen that the optical path within a PV cell with integrated PTG issignificantly more complicated but also more efficient wrt delivering sunlight energy into the PVmaterial. In particular, one input ray has been split into three rays that reach the PV material atpoints P5b, P6b, and P9b resulting in an overall longer path length and a threefold increase inlight absorption capability. This is achieved though the full utilization of the TIR effect enabledby PTG geometry, e.g., at points P3b, P4b, P7b, and P8b. Typical ray tracing results presented inFig. 2(b) clearly emphasize the presence of more TIR actions and less refraction behavior ofthe light reflected from the PV material.

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Fig. 2 Ray tracing diagrams demonstrating typical optical performance of original PV cell (a) andPV cell with integrated PTG (b) with an angle of light incidence of 60 deg.

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Also, Fig. 2(b) clearly demonstrates the dual functionality (collection and entrapment) ofthe PTG described in Sec. 2.1. First, significantly fewer light rays reflect off the top surfacewith PTGs than with the original PV cell. This can be seen by visually comparing Figs. 2(a)and 2(b). Second, it is shown that the TIR phenomenon reflects the rays back down towardthe PV material. When light is incident on the surface with micro-optical elements, the raystravel unencumbered through these elements and effortlessly reach the PV material. Howeverin reality, some portion of the light is still reflected back from the surface of the PV materialwhile trying to escape from the PTG. Further, these reflected light rays hit the TIR interfacebetween micro-optical elements because the refractive index of air is less than the refractiveindex of PMMA and they are reflected back toward the PV material. This effect may occurseveral times until each ray is either fully absorbed by the PV material or exits the PTGhaving an angle of incidence less than the TIR critical angle. As a result, the use ofPMMA-based micro-optical elements with a PV cell does not insure the absorption ofeach ray, but it does increase the probability of absorption by giving a portion of the unab-sorbed rays another chance to be absorbed by reflecting them back to the PV material atdifferent incident angles.

In addition to a visual analysis of the optical paths, the optical efficiency of both systems(original PV cell and PV cell with integrated PTG) was estimated as the percentage of lightpower entering the optical system (set as 1 W) that reaches the PV material. The results calcu-lated during numerical simulation (e.g., TIP) taken into account the Fresnel reflection losses,material absorption, and light “rejected” by an optical system (e.g., light rays that had enteredthe optical system but had not yet reached the PV material). It is also necessary to note thatnumerical simulations were performed with five million rays to ensure accuracy, precision,and reliability of the calculated results.

The results obtained have shown that an original PV cell inefficiently receives incident powerirrespective of the light incident angle, generating a total optical incident power of 0.229 W(which corresponds to 22.9% optical efficiency). It means that 77% of the incoming poweris reflected away from the solar panel light receiving surface, significantly reducing the PV effi-ciency and performance. In contrast, the PV cell with attached PTG acquires a higher incidentpower of 0.319 and 0.312 W for 15 and 60 deg sunlight orientation, respectively. Therefore, byplacing a PTG on top of the PV cells, the TIP is significantly increased (e.g., by 39.3% and36.2% for 15 and 60 deg sunlight orientation, respectively) due to the repeated redirectionof reflected light back to the PV material, thereby increasing the utilization rate of the incominglight.

3 Impact of Incident Sunlight Orientation

In this study, an additional focus is placed on the analysis of how PTGs optimized wrt the inci-dent sunlight orientation perform under different lighting conditions throughout the day.Therefore, the first step in this study was to optimize the PTGs geometry (e.g., depth and incli-nation angle) assuming a constant angle of the sunlight orientation at 15, 30, 45, 60, 75, and90 deg, respectively. LightTools® automatically optimizes the PTGs geometry with its built-inoptimization routine. The second portion of this study uses the optimized PTGs to numericallysimulate their optical performance over morning-noon-evening sunlight orientations, i.e., a rangeof {15, 30, 45, 60, 75, 90} deg.

The maximization of TIP delivered to a flat PV material was chosen as the objective functionfor the optimization of PTGs geometry parameters. As in general, the design of PTGs as equi-lateral triangles is based on only two geometrical parameters (symmetrical inclination angle anddepth); the optimized values of inclination angle corresponding to the maximum TIP were deter-mined by a sequential optimization method built into the LightTools® software. In this pro-cedure, the PTGs depth was fixed at 25 μm and inclination angle was a variable parameterallowed to be varied between 1 and 80 deg with a step of 1 deg. The PTG depth was selectedbased on the authors’ extensive microfabrication experience,20,19 a preliminary literature reviewand the authors’ initial study.14 An upper limit of 80 deg was selected based on the limitations ofthe micromachining process and by cutting tool availability.

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The sequential optimization procedure was performed for each angle of sunlight orientation(15, 30, 45, 60, 75, and 90 deg) through iterative simulations using different values of inclinationangle in a range of 1 to 80 deg. For each selected inclination angle value, the TIP was calculated.The inclination angle that provided the maximum TIP was designated as an optimized for acertain sunlight orientation angle. Further, the TIP was calculated for a PV cell with unoptimizedPTGs and PV cells with PTGs optimized at specific sunlight orientation angles when light isincident at 90 deg. As a result, their optical performances were compared wrt the TIP received byan original PV cell (without PTGs). The results from this first step of analysis are show inTable 1.

It can be noted (see Table 1) that our first approximation of PTGs without optimization(α ¼ 24 deg) was not suitable for enhancing the incident optical power delivered to the PVmaterial [e.g., 0.353 W for an original (with no PTGs) PV cell versus 0.296 W for PVpanel with unoptimized PTGs]. PTGs optimized for 15, 30, and 45 deg incident angles alsodid not enhance the optical performance when the light incident is 90 deg. Only when the actualincident angle is equal to or close to the incident sunlight orientation used to optimize the opticalperformance of the PV cells with optimized PTGs, an increase in the amount of TIP delivered tothe PV material is seen. For example, only PTGs optimized for 60, 75, and 90 deg incidentsunlight orientations outperformed the original PV cell (by 26.63%, 43.34%, and 53.26%,respectively) under the condition of orthogonally incident light. The enhancement of opticalperformance was calculated using the following formula:

enhancementð%Þ ¼ ðTIPwithPTGs − TIPorginalÞ∕TIPorginal: (1)

During the second step, the original PV cell and PV cells with optimized PTGs were analyzedfor daylight conditions when sunlight orientation changes from 1 to 180 deg wrt the top surfaceof PV material. The results are shown in Fig. 3, which is only half of the symmetrical pattern andindicates that each optimized PTG performs differently in daylight conditions having differentangular acceptance. This causes the PV cell with PTG to optically outperform or underperforman original PV cell. For example, the PTGs optimized for 60, 75, and 90 deg incident sunlighthave an acceptance angle from 30 to 45 deg that is more than twice as wider as an acceptanceangle of 15 deg for the PTG optimized for 15 deg incident sunlight. Yet each optimized PTG hasa certain angular acceptance and not all of them can outperform the original PV panel over anentire day. Average incident power was calculated by averaging TIPs from 15 to 90 deg of inci-dent light angle. It was found that PTGs optimized for 15 and 30 deg outperformed an originalPV cell by 4.59% (0.342 W versus 0.327 W) and 2.45% (0.335 W versus 0.327 W), respectively,over an entire day of incident sunlight. The PTGs optimized for other angles of incident light,

Table 1 Optimized geometries of PTGs and their performance wrt an original PV cell at 90 degincident light orientation.

PV cell configuration

Geometry (depth 25 μm)

Optical efficiencyat 90 deg (%)

Enhancement(%)α (deg) Period (μm)

Original (with no PTGs) – – 35.3 –

With unoptimized PTGs 24.0 112.0 29.6 −16.2

With PTGs optimized at 15 deg 60.0 112.0 34.3 −2.8

With PTGs optimized at 30 deg 70.0 108.5 34.4 −2.6

With PTGs optimized at 45 deg 15.0 333.6 34.8 −1.4

With PTGs optimized at 60 deg 33.0 133.1 44.7 26.6

With PTGs optimized at 75 deg 38.0 80.0 50.6 43.3

With PTGs optimized at 90 deg 39.0 117.6 54.1 53.3

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e.g., 45, 60, 75, and 90 deg, generated an average incident power less than that of an original PVcell, e.g., 0.274, 0.277, 0.260, and 0.278 W, respectively, at acute angles of light incident(≤45 deg) during a given day. It is important to note that in the simulation, the cross-sectionalarea of the PV system was 50 × 50 mm2. TIP represents the overall optical performance of thePV cell. This parameter does not uncover a mechanism and physical meaning of how and whyexactly the optical performance of PV system is changing over daylight conditions. Therefore,another optical performance parameter, radiance (W∕sr), should be used to describe the angulardistribution of the light intensity incident on the PV material. More specifically, the radiant inten-sity distribution describes how the light incident on the PTG changes its orientation and what thenew primary light orientation incident on the PV material will be. In other words, the radiantintensity distribution shows how the incoming light path and orientation were modified bythe PTG.

Figure 4 shows the results of numerical simulation of the radiant intensity (W∕sr) of the PVcells with and without optimized PTGs over daylight conditions, i.e., with sunlight orientationangles of {15, 30, 45, 60, 75, 90 deg}.

In the case when there are no PTGs (i.e., an original PV cell), the top surface of the PV cellreceives the incoming light at the same angle of incidence [see Fig. 4(a)]. However, this does notoccur consistently over the entire range of incoming light and it is different for each optimizedPTG. It can be clearly observed from the results obtained [see Figs. 4(b) and 4(c)] that the initialorientation is significantly changed by the PTGs geometry, associated optical effects (e.g., trap-ping) and the TIR phenomenon. When the ray reflected from the glass or PV material strikesthe PTGs face at an angle greater than 42 deg (PMMA/air critical angle), the TIR effect occurs.In this situation, the ray is redirected back onto the PV material for one or more chances to beabsorbed. However, this does not occur consistently over the entire range of incident angles asany internally reflected rays must satisfy the condition of TIR at the PMMA/air interface. In thisway, the PTG increases the total power incident on the PV material as compared to the intensityon the original PV cell. Figure 4(b) shows that the incoming sunlight oriented at 15 deg is deliv-ered mainly to the PV material through the PTG at 105 deg with a significantly higher radiantintensity of 8.04 W∕sr. This increases the efficiency of sunlight delivery to the PV material by111.58% [3.80 W∕sr, see Fig. 4(a) versus 8.04 W∕sr, see Fig. 4(b)].

A different signature of radiant intensity distribution is observed for the PTG optimized forthe incoming 90 deg oriented sunlight. In this case, the radiant intensity has two maxima located18 deg symmetrically about 90 deg (i.e., 108 and 72 deg) with values around 4.72 and

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(%)

Angle of light incident ( )

Flat Surface Unoptimized PTG Optimized at 15º Optmized at 30ºOptmized at 45º Optmized at 60º Optmized at 75º Optmized at 90º

angular acceptance for 90º opt’ed PTG angular acceptance for 15º opt’ed PTG

Fig. 3 Optical efficiency of original PV cell, PV cell with unoptimized PTG and PV cells with opti-mized at {15, 30, 45, 60, 75, 90 deg} PTGs wrt the different angles of sunlight incident.

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4.43 W∕sr, meaning that the incoming 90 deg oriented sunlight does not completely passthrough the PTG [see Fig. 4(c)]. Incoming sunlight sees a change in orientation from onearray of 90 deg incident rays into two major streams of rays with 90� 18 deg angles resultingin a total radiance of ð4.72þ 4.43Þ ¼ 9.15 W∕sr, which is much greater (by 60.8%) thanthe original cell in Fig. 4(a) which is only 5.69 W∕sr at a 90 deg light incident angle. In general,the results from numerical simulations of the optical performance of optimized PTGs laya foundation for the design and fabrication of functional PTG prototypes.

4 Fabrication of PV Cell Prototypes With Integrated PTGs

The fabrication of PV cell functional prototypes with integrated PTGs was performed in thefollowing steps:

(a) original PV cell

(b) PV cell with integrated PTG optimized for 15 deg

(c) PV cell with integrated PTG optimized for 90 deg

0

1

2

3

4

5

6

7

-180 -150 -120 -90 -60 -30 0

radi

ant i

nten

sity

(W

/sr)

Angle of incident on the PV cell (º)

15º 30º 45º 60º 75º 90º

90° 75° 60° 45° 30°

15°

0

1

2

3

4

5

6

7

8

9

-180 -150 -120 -90 -60 -30 0

radi

ant i

nten

sity

(W

/sr)

angle of incident on the PV cell (º)

15º 30º 45º 60º 75º 90º

90°

15°

105°

30°

45° 75°

60° 90°

0

1

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3

4

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-180 -150 -120 -90 -60 -30 0

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(W

/sr)

Angle of incident on the PV cell (º)

15º 30º 45º60º 75º 90º

90° 90°

15°

60°

108º 72º 50.4º 36º

Fig. 4 Radiant intensity distribution of the original PV cell (a) and PV cells with integrated PTGsoptimized for 15 deg (b) and 90 deg (c) wrt the incoming light incident at 15, 30, 45, 60, 75, and90 deg.

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a. fabrication of a master insert having the desired PTG geometry using micro-cuttingtechnology;

b. laser cutting of a small area PV cell sample from an industrial grade PV cell;c. soldering of top and bottom contacts on the small area PV cell sample;d. simultaneous fabrication in PDMS using a micromachined master insert and the integration

of a PTG on top of an original PV cell.

4.1 Fabrication of PTG Master Inserts

Fabrication of PTG master inserts was performed in this study on a modular multifunctionalmicromachining system MICROGANTRY nano5X by Kugler GmbH (Salem, Germany).This system integrates several micromachining technologies along with measurement instrumen-tation. The micromachining technologies are micromilling with a maximum 180,000 rpm spin-dle, fly cutting with a maximum 2000 rpm spindle and micromachining with a picosecond laser.A Renishaw™ touch probe with a measurement accuracy of �500 nm is used for measuringworkpiece geometry before and after machining as well as during alignment. The system is alsoequipped with a Blum™ laser tool setting sensor for measuring actual cutting tool geometry(e.g., diameter and overhang length), having a measurement repeatability of 100 nm� 2σ.The motion stages of this system are fitted with air bearings having an actual position measuringresolution of 10 nm and with a positioning accuracy within �250 nm in the X-Y-directions and�500 nm in the Z-direction. Straightness is within �800 nm per 100 mm travel for all linearaxes. The system is also equipped with an automatic tool changer able to accommodate up to 60cutting tools. The MICROGANTRY nano5X system and its components are shown in Fig. 5.

The integration of several micromachining processes with measurement capabilities opens anew direction in the development of modern microfabrication systems. Modularity and multi-functionality of the system are interrelated and provide three unique advantages—reconfigur-ability of the system kinematics from three (linear) to four (additional C-rotary) and to five(additional turn/swivel unit) motion axes; reconfigurability of the micromachining processusing independently or consecutively the laser micromachining, micromilling and fly cuttingprocesses; and hybridization of the micromachining processes for the development of newadvanced micromachining processes, e.g., laser assisted micromilling21 and laser polishing.22

In general, micromachining technologies, such as micromilling, laser micromachining, andfly cutting, bring significant benefits to the fabrication of micro/nano-scale optical parts, struc-tures and geometries. These benefits are based on the ability to fabricate both functional partprototypes and tooling (e.g., inserts, molds, dies, stamps, electrodes, etc.) with optical surfacequality (e.g., Ra below 10 nm) and with a very high aspect ratio (e.g., 1∶280 between wall widthand height).19 The direct fabrication of functional optical prototypes from plastics gives an

tilt/swivel unit

spindle

Renishaw probe

tool changer

laser beam

delivery

Fig. 5 Modular multifunctional micromachining system MICROGANTRY nano5X and itscomponents.

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opportunity to significantly reduce the cost of prototyping. In this case, there is no need forsignificant investments in the fabrication of tooling in order to verify the optical performanceof the initial design prototypes. The second benefit comes from the ability to fabricate toolingwith optical surface quality, thereby eliminating final polishing processes which are usuallymanual and typically constitute about 40% of the tooling total cost. With respect to the machin-ing of PTGs, micromilling and fly cutting are capable of producing extremely fine groovingwhich is unobtainable using photolithography, etching or ion-beam cutting,23 and with opticalsurface quality right from the machine, which is imperative since such geometries cannot bepolished.

The MICROGANTRY nano5X system described at the beginning of this section was usedfor the microfabrication of two PTG inserts having unoptimized and optimized geometry. Aphotograph of one of the fabricated inserts (with unoptimized geometry) and its geometric qual-ity characteristics such as three-dimensional geometry, dimensional accuracy and surface qualityare shown in Fig. 6. The unoptimized PTG insert has a grating period of 112.0 μm, includedangle of 48 deg, and a height (depth) of 25.0 μm. The master insert, having an area of30 × 30 mm2, was fabricated from 6061 aluminum alloy. A dimensional accuracy of lessthan �1 μm was achieved for a fabricated grating period of 112.2 μm and depth of25.4 μm [see Fig. 6(c)]. In order to achieve the desired optical performance of replicatedPTGs, the insert was fabricated with optical quality surface, e.g., a surface roughness Ra of6.03 nm and a peak-to-valley Rt of 43.5 nm [see Fig. 6(d)].

4.2 Integration of PDMS-Based PTG Thin Films With PV Cell Sample

Initially, four small PV cell samples having an area of 50 × 30 mm2 were cut using laser cuttingtechnology from commercially available original PV cells having approximate dimensions of150 × 150 mm2. A sample length of 50-mm length was chosen as it is the distance betweentwo adjacent electrical busses (connectors) and the width of 30 mm was based on the fabricatedmaster insert. Two wires were soldered to the electrical busses of each side of a small PV sampleafter the PV sample was placed and fixed on the top of a glass plate for proper handling anddielectric isolation.

Fig. 6 Photograph of the microfabricated insert with unoptimized geometry (a) and its geometricquality characteristics (b)–(d): (a) Inset for PDMS replication of functional PTG, (b) 3-D geometry,(c) distance along X -Y cross section, and (d) distance along Y -Y cross section.

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PDMS material was chosen for replicating PTGs instead of PMMA due to the poor adhesionof PMMA thin films without adhesives and because of the presence of large air bubbles whichare difficult to remove. In addition, PDMS has a refractive index of 1.42 at 633 nm, which is veryclose to the refractive index of PMMA of 1.49. The micro-optical PTG structures were replicatedin PDMS by baking Sylgard 184 base and curing agent mixed at 10∶1 ratio. The mixed solutionwas then poured into a frame with a pocket depth of 400 um and the master insert was placedinside forming the PTG geometry. This assembly was then degassed and baked at 100°C for20 min. Afterward, the fabricated PDMS-based PTG thin film was peeled off and attachedto the top face of the PV sample. Finally, a 30 × 30 mm2 area on the small PV cell samplewas exposed, and the rest of the area of the PV cell covered, to test it under a sun simulatorat different conditions. Figure 7 shows the photograph of the procedure described above.

5 Experimental Methodology and Setup for PV Performance Testing

The main challenge in the development of an experimental methodology for evaluating PV per-formance of small PV cell samples was in how to provide identical surface areas of two PV cellfunctional prototypes (original and integrated with PTG) for accurate and assertive comparison.One way of solving this challenge was to fabricate two sets of samples with and without inte-grated micro-optical PTG structures and compare them using measurable characteristics, e.g.,a current-voltage I–V curve. However, our experience has shown that no absolutely identicalsamples can be produced and assembled with our fabrication capabilities. Therefore, in order toavoid uncertainty in using semi-identical samples, it was decided to evaluate the relative changesin performance characteristics. This was achieved by first measuring the performance character-istics of each small PV sample, then integrating micro-optical PTGs on these samples and meas-uring the performance characteristics of the now integrated samples. In this case, characteristicsof the same sample are comparatively evaluated and analyzed in relative units, e.g., percentage ofimprovement or degradation of functional performance. This approach required half the numberof samples. In total, four samples were experimentally tested.

The performance testing experiments were conducted using a computer-based measuringsystem which includes a Class A sun simulator (by ScienceTech, Inc., London, Ontario,Canada) and a Keithley 2400 SourceMeter® instrument (by Keithley Instruments, Inc.,Cleveland, Ohio). Figure 8 shows a schematic diagram and photograph of the experimentalsetup for performance evaluation of PV samples. During the testing, the PV samples (withand without integrated PTGs) were initially connected in series to the Keithley 2400SourceMeter® following the “2-wire connection” configuration. Then the samples were placedunder light radiation produced by a sun simulator set to a 1 sun condition with an AM1.5G filter

50 mm × 30 mm

30 mm × 30 mm

electrical busses

glass plate connecting wires

(a) (b) (c)

Fig. 7 Fabrication of an integrated PV cell: (a) original PV cell; (b) 50 × 30 mm2 PV cell sample;and (c) integrated PV cell sample with a functional area of 30 × 30 mm2.

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generating natural light conditions, where 1 sun equals 100 mW∕cm2 at the point of arrival. TheSourceMeter’s GPIB interface was connected to a personal computer using an Agilent 82357AGPIB/USB cable. The Keithley 2400 SourceMeter® performing dual functions—it sends a volt-age V to the PV cell, sweeping across a voltage range from 0 to 0.6 V, and simultaneouslymeasures the actual current I in the electric circuit. These two functions are controlled bya publicly available LabVIEW driver named “Keithley 24XX Sweep and AcquireMeasurments.vi”24 which records both voltage V and electric current I values, deliveringlight IðVÞ characteristic having 100 data points in each sample data set. Each performance test-ing experiment was recorded five times for each sample with 1-h interval between each meas-urement in a temperature controlled (25°C) room. Each IðVÞ characteristic was recorded by acomputer functioning as a data acquisition system while the PV cell was being illuminated.

A typical acquired light IðVÞ characteristic is shown in Fig. 9(a) and has a distinct “waterfall” signature. In general, the light IðVÞ characteristic has four main parameters: open circuitvoltage VOC when I ¼ 0; short circuit current ISC when V ¼ 0; fill factor FF ¼ Pmax∕ISCVOC;and energy conversion efficiency η ¼ Pmax∕Pin, where Pmax is the maximum power generated bya PV cell under input power Pin (e.g., 100 mW∕cm2). It is necessary to point out that thesecharacteristics correlate linearly with incident irradiance. Also, VOC depends on the bandgapof the PV semiconductor, the quality of the PV cell, and the actual temperature. The IðVÞ char-acteristic allows the calculation of power-voltage characteristic PðVÞ, as PðVÞ ¼ V × IðVÞ, andtherefore these characteristics are interdependent. The PðVÞ characteristic always has a maxi-mum Pmax when a PV cell delivers maximum electrical energy, with corresponding Imax andVmax. All of these characteristics and parameters can be used for evaluation and comparisonof PV cell performance. In order to provide more universal evaluation of PV cell performance,these characteristics and parameters are normalized by controlling the area of a PV cell. Figure 9shows typical IðVÞ and PðVÞ characteristics and their interdependence and parameters. It is alsonecessary to point out the areal (two-dimensional) scaling of measured electrical characteristics[e.g., PðW∕cm2Þ and IðA∕cm2Þ] and it is not a density per se. This is a typical procedure inPV performance measurement in order to take into account the overall dimensions of a PV cellunder testing.

6 Experimental Results and Analysis

The objectives of the experimental analysis were the evaluation and comparison of the functionalperformance of PV cell samples with and without integrated micro-optical PTG thin-film

(a) (b)

Sun simulator

computer-based data acquisition

system power source

sample PV sell

Keithley 2400

SourceMeter

Keithley 2400 SourceMeter

reflector

V

filter 1.5G

Ilight

housing

LabViewdriver

test bed

computer-based data acquisition system

sample cell

GPIB interface

Agilent 82357A GPIB/USB cable

Fig. 8 Schematic diagram (a) and photograph (b) of the experimental setup for performanceevaluation of PV samples.

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Fig. 9 Typical IðV Þ and PðV Þ characteristics and their interdependence and parameters.

Fig. 10 Comparison of PV performance of original (without optics) and integrated (with unopti-mized PTG micro-optics) cells using IðV Þ (a) and PðV Þ (b) characteristics and their parameters.

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structures. This was achieved through the calculation and comparison of IðVÞ and PðVÞ char-acteristics and their parameters, e.g., Pmax, ISC, and η. For relative comparison purposes, thepercentage of improvement was always used because the individual performance of eachcell was different due to slight differences in area.

Figure 10 shows a comparison of PV performance of original (without optics) and integrated(with unoptimized PTG micro-optics) cells using IðVÞ [Fig. 10(a)] and PðVÞ [Fig. 10(b)] char-acteristics and their parameters. Unoptimized PTGs were fabricated from PDMS with anincluded angle of 48 deg (α ¼ β ¼ 24 deg), a depth of 25 μm and a thickness of ∼400 μm.The experimental results show an improvement in Pmax of 5.12% (from 14.738 to15.492 mW∕cm2, 0.754 mW∕cm2 increment), improvement in ISC of 4.12% (from 37.36 to38.90 mA∕cm2, 1.54 mA∕cm2 increment), improvement in η of 5.44% (from 0.147 to 0.155),and improvement in FF of 0.30% (from 0.666 to 0.668), when such an optical grating is used.Results achieved contradict the numerical simulation results for unoptimized PTGs, which weresupposed to decrease performance of a PV cell by 16.1% wrt to an original PV cell (see Table 1).However, our early numerical simulation results14 demonstrated an improvement of the opticalperformance by 32.00% increasing TIP from 0.25 W for an original PV cell to 0.33 W for a PVcell with identical unoptimized PTGs under 90 deg light incident. More detailed thoroughnumerical simulations are required to clarify the achieved results.

Figure 11 shows a comparison of PV performance of original (without PTG) and integrated(with optimized PTG) cells using IðVÞ [Fig. 11(a)] and PðVÞ [Fig. 11(b)] characteristics andtheir parameters. Optimized PTGs were fabricated from PDMS with an included angle of76 deg (α ¼ β ¼ 38 deg), a depth of 48 μm and a thickness of ∼450 μm. Experimental resultsobtained show an improvement in Pmax of 7.60% (from 14.200 to 15.279 mW∕cm2, 1.079 mW∕cm2 increment), an improvement in ISC of 6.40% (from 37.33 to 39.72 mA∕cm2, 2.39 mA∕cm2

increment), an improvement in η of 7.75% (from 0.142 to 0.153), and a reduction in FF of−1.07% (from 0.653 to 0.646), when such an optical grating is used. These improvements

Fig. 11 Comparison of PV performance of original (without optics) and integrated (with optimizedPTG micro-optics) cells using IðV Þ (a) and PðV Þ (b) characteristics and their parameters.

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are supported by our initial simulation results (see Table 1) and believed to be because of theincrease in an incidental light power of 53.3% wrt an original PV cell and 60.8% improvement inradiant intensity [see comparison of Figs. 4(a) and 4(c)]. It is necessary to note that PV perfor-mance was evaluated in relative units (e.g., % of improvement). It means that the effect ofPTGs on PV cell performance was identified and the results are independent of the particularPV cell used.

7 Summary and Conclusions

In this paper, triangular periodic gratings were studied as a possible cost-efficient solution forenhancing the performance of PV solar panels. Designs of the PTGs were optimized wrt theincident sunlight orientation and optical performance of the optimized PTGs was simulatednumerically over daylight conditions. Several functional prototypes of original PV cells andPV cells integrated with both unoptimized and optimized PTGs were fabricated and theirPV performance was evaluated using IðVÞ and PðVÞ characteristics and their parameters.From the results obtained, the following main conclusions can be drawn:

1. The PTGs integrated with PV cells have significant potential for improving the deliv-ery of sunlight and therefore increasing the total power incident on the PV material andenhancing the overall optical and PV performance. As a result, PTGs optimized for45, 75, and 90 deg incident sunlight orientations outperformed an original PV cell by26.6%, 43.3%, and 53.3%, respectively, in terms of TIP at 90 deg sunlight orientation.This was achieved by the trapping of light using the TIR effect and through theredirection of reflected light onto the PV material to allow additional chances forabsorption.

2. The radiant intensity distribution was studied to describe how the incoming light path ismodified by the PTG and what the new primary light orientation incident on the PVmaterial will be. It was found that PTGs significantly change the initial orientation,acceptance angle, and angular distribution of rays incident on the PV material. For exam-ple, for PTGs optimized for a 15 deg angle of incidence, incoming 15 deg orientedsunlight is mainly delivered to the PV material at 105 deg with a 110.5% higher radiantintensity of 8.04 W∕sr. Also, for PTGs optimized for a 90 deg angle of incidence,incoming sunlight orientation is changed from one array of 90 deg rays into twomajor streams of rays with 90� 18 deg angles, resulting in a total radiance of9.15 W∕sr which is 60.8% greater than the original cell (5.69 W∕sr) at a light incidenceangle of 90 deg.

3. Functional PTG prototypes were fabricated through replication of a master insertwith PTG geometry into PDMS. The capabilities of micromachining technologies inmicrofabrication of micro-optical structures, such as V-grooves and gratings, weredemonstrated through the fabrication of master PTG inserts from Al alloy 6061 witha dimensional accuracy within �1 μm. Additionally, surfaces of optical quality wereachieved, i.e., with a surface roughness Ra of 6.03 nm and a peak-to-valley amplitudeRt of 43.5 nm. During prototyping stages, such micromachining technologies (e.g.,micromilling and single point cutting) can be used for machining optical micro/nano-structures directly from plastics (e.g., PMMA) with optical surface quality withoutusing tooling and mass-scale replication processes (e.g., hot embossing and injectionmolding).

4. Both unoptimized and optimized PTGs fabricated from PDMS were integrated withoriginal PV cells and their PV performance was evaluated at an incident sunlight ori-entation of 90 deg. It was found that by adding PTGs optimized for an incident sunlightorientation of 90 deg, actual maximum irradiance was increased by 1.08 mW∕cm2

(7.6% improvement) and short circuit current was elevated by 2.39 mA∕cm2 (6.4%improvement). Such results confirm the practical applicability of PTGs for enhancingthe ability of PV cells to convert the maximum obtainable amounts of solar energythrough the integration of specific micro/nano-optical structures on the top surface ofthe PV cells through enhancing light trapping and in-coupling functionalities.

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5. The knowledge generated in this study lays the basis for the development of furtheradvanced micro/nano-optical structures for enhancing solar panels optical and PV per-formance. Therefore, our future work will be focused on micro/nano-fabrication of PTGsand the verification of their actual optical performance and the performance of integratedPV cells.

Acknowledgments

The authors would like to thank Mr. Hugo Reshef, Mr. Michael Chow and Mr. Mike Meinertfrom National ResearchCouncil of Canada (NRC) for their technical support in this work. Theauthors also gratefullyacknowledge the financial support provided by the Natural ResourcesCanada (NRCan)EcoEnergy Fund and by NRC.Authors also thankMr. V. Lyubchenko, CEOof Solgate Solar, Inc. (Woodbridge, Ontario, Canada) and Mr. B. Singh, President ofSunpetra Solar Energy Inc. (Mississauga, Ontario, Canada) for providing samples of PV cells.

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24. Driver “Keithley 24XX Sweep and Acquire Measurments.vi,” http://sine.ni.com/apps/utf8/niid_web_display.download_page?p_id_guid=25B255F3AA83660EE0440003BA7CCD71(26 January 2012).

Evgueni Bordatchev is a senior research officer at the National Research Council of Canada, inLondon, Ontario, since 1998. He is an expert in laser-based high-precision fabrication, micro-machining, surface texturing and polishing of miniature functional components, micro-opto-electro-mechanical systems/sensors, and micro-moulds/dies. He has authored/co-authoredover 180 papers in refereed journals and conference proceedings and holds 7 patents and patentapplications. He is an adjunct professor at the Western University, London, Ontario, Canadasince year 2000.

Mohammed Tauhiduzzaman obtained his BSc and MEngg in mechanical engineering fromBangladesh (BUET) and Singapore (NUS) in 2001 and 2005 respectively. He obtained hisdoctorate in 2011 from McMaster University, with a thesis related to surface generation indiamond turning. He worked for NRC, Canada from 2011 to 2012 as a research associate.Currently, he is working as a researcher at McMaster Manufacturing Research Institute. Hisresearch interests involve precision and ultra-precision machining.

Rajat Dey received his PhD in photonics from University of Western Ontario, Canada, ME inmicroelectronics from Royal Melbourne Institute of Technology (RMIT), Australia and BE inelectronics from Nagpur University, India. His research interest lies in the areas of optical systemdesign, illumination optics, optoelectronics devices, and silicon photonics. Currently he is work-ing as an optical engineer in GEM System Inc., Canada.

Bordatchev, Tauhiduzzaman, and Dey: Enhancement of photovoltaic cell performance using. . .

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