1. Introduction

Solar concentration has the potential to lower the cost associated with solar cell materials. In concentration photovoltaics (CPV) solar cells are reduced in size, thus saving on expensive semi-conductor PV cell material. The receiving aperture is replaced by an optical system, forming the concentrator, which can be either of the imaging or non-imaging type [1, 2]. The amount of solar energy incident on the CPV system is determined by the aperture of the receiving concentrator optics. Current state-of-the-art concentrators most commonly use parabolic mirrors [3] or Fresnel lenses [4] to focus sunlight onto the solar cell. Regardless of the technology any CPV module is described by its acceptance angle (the part of the sky the concentrator is looking at) and its concentration factor (the ratio of incident aperture to exit aperture). There is a fundamental relation [5] between these two parameters as it is impossible to achieve both a high concentration factor and a high acceptance angle (see Eq. (1), where C is the geometric concentration, n is the refractive index of the concentrator medium and θ_max,in is the half angle of acceptance).

This tradeoff results in concentrator technologies for CPV that can be divided into three categories depending on the value of the concentration factor [Fig. 1]: 1. Low CPV (<10x), medium CPV (10x – 200x) and high CPV (200x – 1000x). The border between medium and high concentration however is not exactly defined. The second important difference of CPV compared to flat-panel photovoltaics is the need of a mechanical tracker that follows the sun during its daily and seasonal changes in order to keep the focal spot formed by the concentration optics on the solar cell.

 

Fig. 1 There is a trade-off between concentration factor and acceptance angle [Eq. (1)]. For any given acceptance angle, there is an upper limit of possible concentration (orange area, n = 1.5). Due to this the field of CPV technologies is divided into three categories: High, medium, and low CPV. Our approach has a concentration factor that is to the right of the curve [Eq. (1)] due to its self-tracking mechanism, capable of reaching 300x geometric concentration with ± 16° acceptance angle (dark spot).

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The acceptance angle of the concentration system has an impact on the precision of the solar trackers. High concentration (HCPV) systems have the need for the highest precision dual-axis trackers as they operate within very narrow acceptance angles (≤ 1°). Due to the cost of all the elements combined, including III-V multi-junction solar cells and high precision trackers, today’s high concentration systems are solely used with concentrations > 500x. Low concentration system (LCPV) have a much higher acceptance angle and require only very coarse or no tracking. Medium concentration (MCPV) is set just in between these two. For reasons explained below, MCPV has been in decline in recent years and there are only a few solutions operating in this range. Its main drawback is the requirement for precise tracking while not achieving high concentration values and hence not justifying the high cost and use of efficient III-V multi-junction cells (44.4% [6]). On the other hand, lower efficiency single junction silicon cells (with 25.6% and 27.6% world record efficiencies, respectively designed for 1-sun and 92-suns intensity [6]) does not justify the cost and use of a tracking system. This has been due to the steady decrease in the price of silicon and overall PV system manufacturing and installation costs during the last decades [7], showing a price reduction by a factor 10 over the last 23 years. Tracking is thus an impediment to MCPV systems. This paper proposes a solution for MCPV where active tracking is replaced by passive self-tracking for which the energy is provided by the sun itself.

In contrast to Fresnel or parabolic mirror solar concentration systems, planar solar concentrators use a waveguide in order to concentrate the light at one of its facets. They are categorized in the low to medium concentration range and have the advantage of a small form factor. However they suffer from either low concentration (2-4x, holographic concentrators [8]) or low efficiency (4-7%; luminescent concentrators [9–11]). Karp et al. [12] proposed the first efficient (90% - 82%), high concentration (73x-300x), planar concentrator. Lateral shifting of a lens array has been shown to be a viable option of increasing the acceptance angle [13]. By lateral shifting of either the lens array or the coupling feature, the initially low acceptance angle was increased to nearly ± 10° [14].

The proposed concept in this paper can theoretically achieve an effective concentration of 200x (C_geo = 400x, η = 50%), if the energy driving the actuator is not taken into account, and is therefore in the center of the MCPV range. The additional advantage of the system is its self-tracking feature, which significantly reduces the tracking requirement and complexity and can achieve an acceptance angle of 32° ( ± 16°). Self-tracking in general is less aimed at removing the tracking requirements entirely, but complementing it so that seasonal changes ( ± 20 degrees) can be tracked over the self-tracking axis, while at the same time increasing the tolerances for tracking on the other axis. This allows a coarse and inexpensive 1-dimensional tracker to cover the daily change and opens up the potential to economically operate in the MCPV range. If coupled with a passive tracker as proposed by Clifford et al. [15, 16], the gain in system efficiency (as compared to the use of an energy consuming tracker) might be even higher, as no electrical energy would be required for diurnal tracking. Self-tracking has been proposed by several research groups including ours via several light induced methods, including a refractive index change [17], the use of a self-aligning high index fluid [18], a phase-change of a hydrogel [19], the use of paraffin wax as a responsive switch [20] and vapor bubbles in a liquid waveguide [21, 22].

This paper focuses on the construction of a working demonstration device, by extending the work described in our previous work [23, 24] [Fig. 2].The proof-of-principle concept is extended from a single element to a device with an aperture of 53x53 mm². The actuation mechanism uses paraffin wax, a commonly used material for micro valves, micro actuators and MEMS devices [25, 26]. A dichroic membrane separates the solar spectrum into a reflected part (400 – 750 nm) and a transmitted part (> 750 nm). A 30° line prism array in the membrane reflects the visible part at an angle around 60°. The transmitted light is absorbed by black paraffin wax under the membrane. Consequently the paraffin wax heats up and undergoes a phase change at its melting temperature (48°C). Due to the phase change of the paraffin wax, its volume increases by up to 10%. The paraffin wax is constrained on all sides except the top side and thus the volume expands upward and presses the membrane against the waveguide situated above. With the removal of the air gap between waveguide and membrane, the reflected part of the light can now be efficiently coupled into the waveguide. The waveguide acts as a homogenizer and transports the light by total internal reflection (TIR) towards a solar cell situated at one of its facets.

 

Fig. 2 The three stages show the actuation and the self-tracking mechanism. In stage 1, the dichroic mirror splits the spectrum in two parts. The transmitted part (red; >750 nm) is transmitted and absorbed by the paraffin wax (black). In stage 2, the paraffin wax melts and expands upward, creating a coupling feature for the reflected light (yellow). As the sun moves throughout the day/season the focal spot changes and a different part of the actuator is activated (stage 3).

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2. System components and upscaling

This section describes the different parts of the concentrator as well as the improvements and adjustments necessary to scale up the size and concentration of a device. The concentrator has an aperture of 53 x 53 mm². This aperture is made from a 3 x 3 square lens array with individual lens apertures, 17.68 mm x 17.68 mm in size. The size of the waveguide and actuator are increased to fit the total lens array aperture. While the waveguide size increase is straightforward, the membrane process had to be adapted to the larger size.

Apart from the waveguide, which is a single element in the concentrator, the other components can be divided into units. Each unit, consists of a lens pair, an actuation element and a dichroic membrane. The waveguide itself is left out of these units and applied to the device as a single entity. Small area thin-film silicon photodiodes are deposited at one end of the waveguide. The purpose of those cells is to characterize the light intensity within the waveguide.

2.1. Lens design

The lens design consists of two lenses per cell. Both lenses are plastic (Zeonex E48R), one inch, aspheric lenses, purchased as off-the-shelf products (Lens 1: EFL = 40 mm, Lens 2: EFL = 25 mm). Together these two lenses provide an effective focal length of 36.7 mm and a numerical aperture of 0.44. The two lenses were selected so as to yield a flat Petzval field curvature over the full range of the desired acceptance angle ( ± 20°) [24], and to increase the telecentricity of the focus on the actuators. A flat Petzval field curvature is one of the important parameters of the optical system in order to keep the focus spot small over the entire spectrum of incoming angles. This is needed to achieve efficient coupling, as the intensity at the focal spot for every angle is responsible for the functionality of the actuator. The telecentricity of the lens combination is also important as it helps to constrain the range of ray angles reflected from the coupling facets, necessary for efficient coupling and TIR within the waveguide. The choice of a two lens system was also motivated because a single plano-convex lens has an angular range of only ± 5° [Fig. 3(a)].

 

Fig. 3 The combination of the two lenses yields a flat Petzval field curvature (blue) over the desired angular range in contrast to the use of a single plano-convex lens (a). The experimental results of the acceptance angle (b) agree with the simulation [Fig. 3(a)] corresponding to a reduction of the acceptance angle to from ± 23° to ± 16°.

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We chose to cut the lenses of each cell in a square shape since it maximizes fill factor in the array. The lens pair array was produced in house. The plastic lenses were milled to the biggest square (17.68 x 17.68 mm²). However, the edge cut lenses have a reduced angular acceptance due to the fraction of light exiting from the first lens which vignettes at the corresponding second lens [Fig. 4(a)].This reduces the acceptance angle of the optical system from ± 20° to ± 16° [Fig. 3(b)]. This value is below the angular range for seasonal tracking ( ± 23°), however it is sufficient for a demonstration of the system’s performance. Since the optical system is primarily responsible for the acceptance angle of the device, changing the optical system at a later stage to an optimized version capable of ± 23° acceptance angle, is expected to result in a working concentrator suitable for seasonal tracking.

 

Fig. 4 (a) The lens arrays were created from one inch off-the-shelf lenses by milling the outer parts and leaving the center square. (b) The pair of lens arrays use a custom holder to keep them at the desired separation. Simulations indicate a reduction of the acceptance angle down to ± 16°.

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The square lenses were then glued together using an epoxy. Care was taken especially to manage the tilt of the lenses. A custom holder for each of the lens arrays has reference pins so as to align the two lens arrays and keep them at the desired separation [Fig. 4(b)].

We measured the assembled lens arrays in terms of spot size and angular performance over the array and then compared the results to those obtained with Zemax raytracing simulations. Figure 3(a) shows the RMS of the spot size for the optical system using the AM1.5 spectrum and highlights the telecentricity of the system.

The focal spot of the combined optical system agrees with the simulation results for different light incident angles [Fig. 5].The spot size becomes distorted (ellipsoid shape) at angles different from normal incidence. The red dots corresponds to the beam profile measurements (FWHM) in x and y direction for a collimated input at 633 nm. The blue shapes are the results for different raytracing simulations around the focal spot, showing ray density. In summary the quality of the lens arrays is good enough to serve as the actuation system. To serve as the optical system for a seasonal tracking device however, a higher acceptance angle would be required.

 

Fig. 5 The experimental measurements (red) of the beam size at different positions around the focus and at different angles, are similar to the simulation results (blue) and indicate a good agreement between the actual fabricated lens arrays and the virtual model in Zemax.

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2.2. Waveguide

The main purpose of the waveguide is to transport the light from the coupling centers towards a single edge where a solar cell would be placed. Its second purpose is to act as a homogenizing element for the coupled modes. The waveguide is the single largest element in the demonstration device (52 x 80 mm²). For obvious reasons of efficiency and stability it was not divided into several parts and then included into the cells (consisting of optical system and actuator). The waveguide is made from fused silica, polished on all sides. A 100 µm protection chamfer runs along all edges to protect it from edge chipping during the polishing step. The waveguide is first cleaned in a standard piranha bath [27] and then coated with Aluminum (for reflectivity) and Chromium (as an oxidation protection) on all edges using an Alliance-Concept DP 650 sputtering machine. The process resulted in a reflectivity of around 90% at λ = 633 nm.

To characterize the system and measure its efficiency, micro-crystalline thin film photodiodes were custom deposited on the waveguide. This improvement from the proof-of-principle device, which used an external thermal sensor to measure the light coupled into the waveguide [24], increases the measurement accuracy by canceling most of the Fresnel losses present in the prior method.

The photodiodes were custom deposited on top of the waveguide instead of the exit facet. Because of the inter-electrode gap of the PECVD reactor constraints, deposition on the edge of the waveguide was not possible. Simulations show [Fig. 6] that a 2 mm wide photodiode deposited on top results in a system performance only 5% lower when compared to a photodiode deposited on the 1 mm edge.

 

Fig. 6 Left: relative efficiency curve. The baseline is given by the power detected by the photodiode positioned at the edge of the waveguide (see position (1) on right figure). The photodiodes can also be placed on top of the waveguide (pos. 2, pos. 3). A photodiode placed on the top of the waveguide, having a lateral dimension W > 2 mm shows a difference in collection efficiency less than 5%, with respect to a photodiode placed at the edge.

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Custom microcrystalline silicon (µc-Si) photodiodes of size 5x2 mm² were deposited on the top surface of the waveguide. This step also provided a qualification of the concept of integration of one long 52 mm cell on the top surface by thin-film deposition instead of having the photodiode as a separate component to be attached with optical glue at the edge of the waveguide. The fabrication of the photodiodes starts with the deposition of a transparent front contact layer made of as-grown rough boron-doped zinc oxide (ZnO) deposited by low pressure chemical deposition (LPCVD) from a mixture of diethylzinc, water vapor and diborane [26]. This is done through a hard mask, in order to deposit the 2 micron thick layer on an area of 52 x 5 mm² at the extremity of the top surface of the waveguide. Then the µc-Si thin-film p-i-n junction is deposited by plasma enhanced chemical deposition (PECVD) from a gas mixture of silane and hydrogen and the addition of trimethylboron and phosphine for the p-type and n-type doped layer, respectively. The back contact, also made of ZnO deposited through the same hard mask, is deposited by LPCVD after having delimited the size of the 8 photodiodes with ink in order to lift-off in acetone some ZnO and to dry etch the µc-Si material, where needed, by reactive ion etching in a plasma of sulfur hexafluoride and oxygen. The photograph of Fig. 7(b) shows the final result. The linearity of the short circuit current of the photodiode with intensity has been experimentally verified [Fig. 7(a)]. As the value of the short circuit current is used to infer the amount of concentration at the photodiode this ensures the validity of the results.

 

Fig. 7 (a) Response of the short circuit current of the photodiode to different intensity levels has been experimentally verified to ensure the validity of the results. (b) Photograph of the 52x80 mm² fused silica waveguide with Ag/Cr metallization at the edges and the front ZnO contact and µc-Si layers deposited by LPCVD and PECVD, respectively. Eight 2x5 mm² photodiodes integrated at the extremity of the waveguide after ZnO back contact deposition, lift-off and RIE processes. (c) Spectral response of a reference photodiodes.

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The choice of a single junction µc-Si device over amorphous silicon or any multi-junction architecture is driven by the aim to use the solar cell as a photodiode in order to experimentally access the light intensity inside the waveguide. Maximizing the electrical energy at the output of the system might require another choice. Also, the spectral response of the µc-Si photodiodes shown in Fig. 7(c) is matched to the spectral irradiance within the waveguide (illustrated in Fig. 8(b)).

 

Fig. 8 The actuator consists of the actuation array (a) filled with paraffin wax and the dichroic membrane on top that splits the spectrum in two parts (b).

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2.3. Actuator and dichroic membrane

The actuator is the active component of the system. It is essentially an array of pistons made from paraffin wax that push upwards where the sunlight is focused. It consists of three elements: 1. A metal array of holes, 2. A membrane to split the solar spectrum and couple light into the waveguide and 3. Blackened paraffin wax which absorbs the infrared part of sunlight and expands under phase change which provides the actuation.

The metallic hexagonal hole array consists of a single metal piece that houses nine regions, each with a diameter of 16 mm aligned with one lens pair. Its function is to constrain the paraffin wax in lateral dimensions so that upon heating it is only able to expand in the direction of the membrane and the waveguide. 510 µm holes have been laser cut in a hexagonal array from the metal element in each of these regions [Fig. 8(a)]. The thickness of the metal separating two paraffin cylinders is small compared to the focal spot of the optical system. Simultaneous actuation of two neighboring cylinders has been frequently seen experimentally.

The dichroic membrane splits the spectrum into two parts, mostly reflecting light below 750 nm, and mostly transmitting light above this transition wavelength [Fig. 8(b)]. A line prism array is imprinted into PDMS (Polydimethylsiloxan) from a master. The pitch between two prisms is 50 µm with a height of 15 µm, resulting in an angle of 30°. A 30° angle is superior to other designs as the shadowing is minimized [12]. Subsequently a stack of dielectric materials is deposited onto the line prism array by “Iridian Spectral Technologies” (Canada). Finally a 50 µm PDMS layer is spincoated on top of the dichroic prism, sealing it inside the membrane and providing a flat surface for efficient waveguide coupling. During fabrication of the actuator, a major hurdle was to seal the paraffin wax in the actuation holes. The initial assumption that the stack of dielectric material would seal the gas diffusive PDMS turned out wrong and as a result paraffin wax diffused through the membrane and condensed on top of the waveguide, clogging the air gap between waveguide and membrane. Blackened paraffin wax would in the process also dye the PDMS black and render the membrane useless. To prevent gas diffusion through the PDMS membrane, a 75 µm membrane of photopolymer NOA65 was attached on top of the metal array using a stamping technique, prior to attaching the dichroic PDMS membrane. Since NOA65 is non gas-diffusive, paraffin stays confined in the holes of the actuation array. To simplify fabrication, nine individual dichroic PDMS membranes are placed on each of the nine regions of the metal array.

Paraffin wax is a thermal phase change material. The material property used in this device and in similar applications (microactuators, microvalves, MEMS) is its high volume expansion (10%) upon the phase change from solid to liquid. In our system the paraffin wax is mixed with Sudan black B [27], a lysochrome commonly used to stain lipids and lipoproteins in life sciences. Mixing Sudan Black B with paraffin (5:95) under high temperature results in a black wax mixture. This mixtures is then flown into the holes by heating it to 55 °C under vacuum. After this, the backside of the actuator is sealed with a photoactive glue (NOA61) and a glass slide.

3. Performance of the demonstration device

We characterized the concentrator performance and compared these results to the expected simulation results, calculated with Lighttools, a raytracing program. We constructed a complete model of the experimental device so that reflection and absorption losses could be included [Fig. 9].The demonstration device currently has a geometric concentration of 27x ((53 x 53 mm²) / (2 x 52 mm²)) using a single 2 mm photodiode, placed on top of the waveguide. The optical-to-optical theoretical efficiency using the full AM 1.5G spectrum is 0.37. Of the remaining 63%, 29% is used to drive the actuator and approximately 20% is lost as Fresnel losses at the 5 interfaces. The remaining 14% is lost due to absorption and outcoupling from the waveguide. The effective concentration is thus theoretically 10x (0.37 x 27x). Reducing the width of the photodiodes size from 2 mm to 1 mm and placing it at the exit facet of the waveguide will increase the effective concentration factor from 10x to 20x. In the current waveguide, the scattering ZnO layer surrounding the photodiodes at the waveguide edge outcouples most of the light hitting this area. The ZnO layer approximately divides into 20% reflectance and 80% transmittance. Since 14% of the reflectance is diffusive and all of the transmission is scattered, only 6% is specularly reflected and can be taken into account. This negates the effect of the reflective aluminum coating on this side of the waveguide and leads to an inhomogeneous illumination of the photodiode.

 

Fig. 9 The experimental device (b) was based on the simulation model (a). The simulation is then adapted to incorporate the same materials as used in the demonstration device for a full understanding of the performance. The top view shows the actuator unit numbering and photodiode numbering used during the experiments (c).

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The single photodiode has been divided into eight 2 x 5 mm² photodiodes as outlined in section 2.2. During the experiments only the third photodiode from the left [Fig. 7(b), Fig. 9(c)] was used. Taking into account the ZnO layer and the reduced photodiode size (2 x 5 mm²), the effective concentration factor is then 7x, according to simulations.

To confirm the simulation results, a similar setup as in our previous work was used [Fig. 10] [24]. The main difference between the two setups is, that before we were turning the actuator in the beam of the solar simulator, while now the concentrator is fixed because of stability of the micro-positioners that read out the short-circuit current from the photodiodes. The setup features a motorized rotation stage and a motorized linear translation stage working together to adjust the position of the mirror in order to simulate incoming angles between ± 16°, perpendicular to the line prism array [Fig. 10]. Due to the telecentricity of the system and the fact, that the prisms are small compared to the focal spot, the response of the system is the same if moved parallel or perpendicular to the direction of the line prism array. An Ampere meter then records the short-circuit current I_SC of the photodiode. A hot mirror is placed in the beam path close to the exit of the solar simulator to simulate low intensity condition (it attenuates only the infrared portion of the spectrum). In the experiments, every single unit of the concentrator has been tested individually. If all units were to be tested at the same time, the exact response of a single unit would be unknown. For every unit, the response of the short-circuit current of a photodiode is recorded. This gives insight into the dynamics of every unit for every input angle. The sum of the responses of each unit then results in the overall response of the concentrator. Results of the concentrator simulation were then used to compare the experimental with theoretical values.

 

Fig. 10 The experimental setup uses a motorized rotation and linear stage to record the short-circuit current response to any input. The incoming light on the device was changed in angle from −16° (Start) to + 16° (End). Every single unit (lens pair + actuator) was analyzed on its own and the response of all nine units summed up.

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The experiment starts with the removal of the hot mirror and the recording of the current response to the actuation system. After t = 20 s, the hot mirror is inserted back into the beam path and the current response to the de-actuation is measured (since the infrared portion of the solar spectrum is blocked). This results in a maximum current value I_SC,max which corresponds to the actuated state, and a minimum value I_SC,min, which represents the non-actuated state [Fig. 11].

 

Fig. 11 a) The maximum (actuated state) and minimum (non-actuated state) values of ISC for the unit 5 show actuation over an angular range of 16° (green area) indicated by a large difference of the two values. A perfect unit would show this behavior over the angular range ± 16°. b) The actuation dynamics show a rise in measured current after removing the hot mirror and a decline towards the previous value after inserting the hot mirror into the beam.

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The dynamics for every angle have been recorded using a Fluke digital multi meter and two microprobes, measuring the short-circuit current between the ZnO and the photodiode. After an analysis of the dynamics themselves, the values are added up for all units to obtain the overall performance of the concentrator over the complete angular input range [Fig. 12].The simulations, as comparison, show an evenly distributed response over the whole actuation range [Fig. 12(b)]. Since in these measurements, only one actuator is working for a given time, the optical-to-optical efficiency is higher due to minimal outcoupling losses. Simulations show that this leads to an increase of the effective concentration from 7x, for the case of all actuators working at the same time, to 8x for summed up, single unit measurements.

 

Fig. 12 Measuring every unit on its own and adding the results up, shows an effective concentration just short of 4x (a). However, not all lenses participate actively. In comparison the added simulation results for the unit achieve close to 8x (b).

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Due to the non-center position of the custom photodiodes and the high outcoupling of the ZnO layer, units 7-9 [Fig. 9(c)] have a much smaller influence on the photodiode used (#3). All units were measured with the same photodiode, instead of switching to a different one. The theoretical maximum for a single photodiode of the size 2x5 mm² is 7x (when all actuators function at the same time), according to simulations, in contrast to the 10x the system would achieve with a minimal size ZnO layer and a single photodiode (52 x 2 mm²). The experimental results show an effective concentration of 3.5x (C_geo = 280x, η = 1.25%). The main cause for this difference is that not all units perform equally well or not at all over the whole angular range. This becomes clearer when we observe the difference between the maximal recorded short-circuit current I_SC and its minimum current, which represents a constant coupled value [Fig. 13].The constant coupled value stems from the membrane being locally attached to the waveguide, leading to a coupling independent of actuation. I_SC,max describes the performance of the device, taking into account actuation and constant coupling, only leaving out the units that do not participate at all. By using the difference (I_SC,max - I_SC,min), any constant coupling terms are taken out of the analysis and only the actuation terms become visible. In the current device this makes up about 50% of the performance.

 

Fig. 13 In contrast to Fig. 12 the erroneous terms due to constant coupling have been removed and the difference I_SC,max - I_SC,min plotted. Apart from unit 2, no unit performs over the desired angular range. However most perform well over a reduced angular ranges.

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Multiple reasons can lead to a unit that is not performing up to its expected simulation value. This can be from 1. A suboptimal paraffin mixture, such that the amount of light absorbed is not high enough 2. An air bubble either in the actuation chamber or in the membrane, or 3. A non-perfectly flat membrane surface, so that the distance between membrane and waveguide is too large for the actuation height.

In summary, the solar concentrator demonstrates self-tracking using a paraffin wax thermal actuator over an angular range of ± 16° [Fig. 14].Although effective concentration is a factor two short of the simulated value over the angular range for a single photodiode of this size, we expect that control over the flatness of the membrane will greatly improve the results. This will also minimize the effect of a local attachment of the membrane to the waveguide which allows the actuation to perform over the complete angular range.

 

Fig. 14 Photograph of the concentrator. The lens array is focuses on the actuator (not visible in the photograph) which couples light into the waveguide. Light hitting the scattering ZnO layer around the photodiodes is outcoupled and lost (reason this region is seen in the picture). Two micro-probes (front right) are used to measure the short-circuit current.

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4. Conclusion

Self-tracking for solar concentration addresses the need for precision mechanical tracking necessary in CPV. While it cannot eliminate the entire tracking device due to restrictions in the optical system, it enhances the tolerances and the angular acceptance of the system.

The work described in this paper shows a working demonstration of a concentrator that integrates a self-tracking system with an angular acceptance of 32° ( ± 16°) and a measured 3.5x effective concentration, compared to a simulated effective concentration of 8x (C_geo = 280x, η = 2.8%). This geometrical concentration factor however, is artificially high, while the efficiency is artificially low, due to the small size of the photodiode. Upscaling the photodiode to full size increases the effective concentration to 10x (C_geo = 27x, η = 37%). Moving the solar cell location from the top to the waveguide facet allows a reduction of the solar cell width to 1 mm and thus further increases the effective concentration to 20x (C_geo = 53x, η = 37%). All elements of the system have been upscaled from a former single-element proof-of-principle device. This includes the optical system, the waveguide and the actuation system itself. The addition of a photodiode to the waveguide has improved the measurement of the system efficiency. The custom micro-crystalline silicon photodiodes added to the waveguide features a spectral response that is matched to the reflection of the dichroic membrane. Overall the self-tracking system shows actuation over the desired acceptance angle. The efficiency of the concentrator, however, is half that expected from simulation. The main difficulties stemmed from the low actuation height (5-10 µm) of the paraffin wax which is not in accordance with previous results obtained (40 µm) and the challenge to maintain a 5-10 µm constant gap over the whole size of the actuator.

Future work will focus on improving the concentrator optical efficiency. Better materials for the actuator housing is expected to yield a higher actuation height. By using single element actuators instead of an actuation array, it facilitates the integration and also provides a better control of the gap between waveguide and actuator. A flatter membrane over the whole actuation array will contribute to increasing the optical efficiency by minimizing constant outcoupling centers and maximizing the coupling due to actuation.

Simulation show that the concept has the potential to achieve an effective concentration factor of 200x (C_geo = 400x, η = 50%), assuming reasonable dimensions (30 cm waveguide length, 1 mm waveguide thickness, 100% fill factor) and a matched spectrum to a solar cell.

Appendix

This section is aimed as an additional discussion to the dynamics observed during the actuation process. It highlights the different possible cases for a paraffin actuator as presented in this paper.

By looking at the result for a single unit (Fig 11(a)), it is possible to distinguish four possible scenarios (cases): 1. I_SC,min low, I_SC,max medium - high, 2. I_SC,min low, I_SC,max low, 3. I_SC,min medium, I_SC,max medium, and 4. I_SC,min med, I_SC,max medium - high. These cases correspond to different states of the waveguide/membrane interface. A fifth case is distinguishable from these four by looking at the dynamics, as it has a much later start in actuation. All of these cases are displayed in Fig. 15. In case 1, the actuation works as intended. The minimum value is close to zero and the minimal response of the photodiode corresponds to ambient light and minimal scattering at the waveguide interface. The second case corresponds to the case where either actuation is happening but the membrane never touches the waveguide or actuation is not happening at all. For case 2, no light is coupled into the waveguide.

 

Fig. 15 The five cases observable in the actuation results are displayed. Case 1-3 can be seen in Fig. 11(a) whereas case 5 only is visible in Fig. 11(b).

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The third case corresponds to the case, where the membrane partially touches the waveguide and no successful actuation is happening. This means that part of the incoming light is coupled into the waveguide, but no additional light enters the waveguide upon actuation. In case 4, the membrane is already partially touching the waveguide in the non-actuated state, similar to case three, but upon actuation the remaining area around the focal spot gets actuated and an increase in the photodiodes response becomes visible. The fifth case only becomes apparent by looking at the dynamics of the actuation. The usual response is a direct increase in the short-circuit current of the photodiode, after removal of the hot mirror. However in a few cases a much later onset of actuation has been observed, all of them with a much lower short-circuit current than expected [Fig. 11(b): 14°]. This case corresponds to a state, where the distance between waveguide and membrane is only slightly smaller than the maximum actuation height of the actuator. This results in light coupling into the waveguide only when the maximal actuation height is nearly reached. Since the membrane is attached to the metal honeycomb array, the shape of a single actuated paraffin piston can be described as the deformation of a disc, with a clamped circumference under a uniformly distributed load, which can be described by a quadratic function [23]. Due to the smaller coupling area of only the tip touching the waveguide, a much smaller amount of light is coupled into the waveguide.

Acknowledgment

The authors would like to acknowledge the support from the Swiss National Science Foundation: Nano-Tera project 20NA21_145936 “Solar integrated Nano Electrolyzer: SHINE.”

References and links

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