Amorphous Silicon Photovoltaic Solar Cells Inexpensive, High- Yield Optical Designs

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1 M. Gollares-Pereira Departamento de Energias Renovaveis, L.N.E.T.I., Azinhaga dos Lameriros, 1600 Lisboa, Portugal J. M. Gordon 1 Applied Solar Calculations Unit, Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84993, Israel Amorphous Silicon Photovoltaic Solar Cells Inexpensive, High- Yield Optical Designs We propose a new method for manufacturing and deploying amorphous silicon solar cells which is based on creating an effectively "bifacial"photovoltaic device by utilizing part of the glazing of a CPC-type nonimaging concentrator as active absorber. This solar collector could enhance the yearly energy delivery of amorphous silicon solar cells by about 100 percent if the cells are manufactured so as to exploit illumination on both cells sides. 1 Introduction Two generic types of photovoltaic (PV) solar cells are manufactured today: the "monofacial" PV, where one side only is illuminated; and the "bifacial" PV, where both sides of the device are illuminated and are active absorbers. These bifacial cells, however, typically have higher materials and circuitry requirements than corresponding monofacial cells. With the advent of amorphous silicon PV production technology, a new possibility arises. Thin films of amorphous silicon can be deposited on conducting glass and covered with transparent electrodes. Hence, by using properly designed circuitry, bifacial cells can be produced with the same amount of PV material required for monofacial cells. Such cells are, in fact, already in commercial production [1]. Three methods have been proposed thus far for maximally exploiting both sides of a bifacial PV. Two of these methods essentially use the ground, or the immediate environment of the PV modules, as diffuse reflector [2-4]. Since the ground is typically a rather low-reflectance surface, this method offers poor utilization of the "underside" of the bifacial cell, as well as possible power losses due to resistance effects associated with the unequal illumination of the two sides of the solar cell. Placing the PV system near white surfaces which act as diffuse reflectors (walls, floors, etc.) improves utilization of the "underside" of the bifacial PV provided the dimensions of the diffuse reflector are, as proposed in [2], ten times larger than the dimensions of the PV panel. However, degradation of the reflectance of exposed outdoor surfaces with time (due to dust and/or other environmental factors) will usually render a solution of this type as valuable for a relatively short period of time if left without adequate maintenance. Furthermore, as will be noted, inexpensive, alternative optical boosting for bifacial PV's can yield around 50 percent more yearly energy than diffuse reflector configurations. A third method proposed is use of a low concentration ratio, nonimaging, Compound Parabolic Concentrator (CPC)-type collector. CPC-type concentrators offer the advantages of being fully stationary for sufficiently low concentration ratio (ratio of aperture to absorber area), and ensuring maximal illumination of both sides of the bifacial PV cell (Fig. 1), [5-6]. Furthermore, CPC-type concentrators can achieve the highest concentration ratio permitted by nature for a fixed acceptance angle (field of view) [7-8]. For «o«imaging, as opposed to focusing, concentrators, optical performance is rather tolerant to small errors in reflector slope. In many cases, and for the idea proposed herein, the "non- PV" components of the concentrator are very inexpensive. Also at the Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva, Israel. Contributed by the Solar Energy Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received by the Solar Energy Division, September 1988; final revision, December Fig. 1 Ideal CPC-type concentrator, with aperture AB, for bifacial absorber CD. Acceptance half angle, 0 3 = deg and AB/(2 CD) = /Vol. 111, MAY 1989 Copyright 1989 by ASME

2 AB / CD - 2 Fig. 3 Ideal CPC-type concentrator of the type in Fig. 2, with aperture AB for bifacial absorber CD. Acceptance half angle, 0, = 90 deg. C = AB/CD = 2. Fig. 2 A second type of ideal CPC-type concentrator, with aperture AB, for bifacial absorber CD. Acceptance half angle, 9 a =41.81 deg and AB/(2CD) = 1.5. For example, they may consist of simple, properly bent or molded aluminum sheet, or reflector film on extruded polyurethane. Based on production experience for CPC-type solar thermal collectors, the nonabsorber components of the device, including labor, cost of the order of $20/m 2 of aperture [9]. Such costs are considerably less than even optimistic cost projections for amorphous silicon PV's. They are also markedly less than the non-pv costs of high concentration, focusing, continuous tracking PV's. Therefore, even for relatively inexpensive bifacial amorphous silicon PV's, there should, in principle, be an economically optimal geometric concentration ratio. Due to the relatively low cost of amorphous silicon PV's (or for the potential thereof) and the economic desirability of totally stationary collectors, optimal concentration ratios will be relatively low. This is the reason for the limited range of designs considered next. We stress that the idea proposed, and the associated economic incentive, pertains to bifacial, as opposed to monofacial, amorphous silicon solar cells. The idea of using CPC-type concentrators for bifacial PV cells was first proposed for bifacial crystalline silicon solar cells [3]. The specific proposal of [3] was to use the design of Fig. 1 with the concentrator trough being filled with a dielectric such as mineral oil. This serves two purposes: (a) it enhances concentration due to the index of refraction of the dielectric; and (b) it enhances convective heat loss from the collector for liquid dielectrics. However, this step is expensive and incurs increased reliability and safety problems. A second possible configuration for bifacial absorbers in CPC-type concentrators is illustrated in Fig. 2 a configuration that has been considered for solar thermal applications [10]. The drawbacks of using the CPC-type concentrators of Figs. 1-2 for bifacial PV cells in the manner just described are: (a) effective double-glazing (aperture plus solar cell encapsulant) and the associated optical losses; (b) possibly nonuniform illumination on either or both sides of the solar cell for particular incidence angles and high beam fractions of solar radiation (with the associated power losses and the danger of large reverse bias voltages); and (c) low heat losses relative to flat-plate configurations, with the associated efficiency penalty. Journal of Solar Energy Engineering Fig. 4 CPC-type concentrator of the type in Fig. 2, with aperture AB, for bifacial absorber CD. The concentrator is truncated with acceptance half angle, 0 a = 30 deg and extreme edge ray angle, 0, = 90 deg. C = AB/CD = The aperture glazing would be necessary even were the concentrator trough not filled with a dielectric such as oil, but rather filled with air, since degradation of the reflector by natural outdoor conditions would destroy most of the value of this type of solar collector. Our idea is based on using a specifically well-suited, CPCtype concentrator design for bifacial amorphous silicon PV cells. This idea has already been tested experimentally with the bifacial crystalline silicon PV cells of Isofoton Corp. (Malaga, Spain). These results [11-12] show that a bifacial PV CPCtype optical booster can deliver around 50 percent more annual energy than the corresponding white diffuse reflector configuration as proposed in [2-4]. The advantages of our proposed device are that it: (a) exploits new production techniques for amorphous silicon solar cells so as to create a bifacial PV cell from a nominally monofacial device, [1]; (b) does not suffer from all the optical losses of effective double-glazing; (c) does not suffer from significantly lower heat loss than flat-plate configurations; and (d) can avoid "hot spots" (nonuniform illumination) on both sides of the bifacial PV cell. 2 Bifacial Photovoltaic Cell Incorporated Into a CPC- Type Concentrator We suggest using both sides of only the central part of the aperture glazing of a CPC-type concentrator as active absorber. This limits us to the general configuration of Fig. 2 with one key constraint, specifically, that the absorber and aperture surfaces effectively be coincident, as in Figs This can be achieved either with an "ideal" concentrator of acceptance angle 180 deg as in Fig. 3 (in which case AB/CD MAY 1989, Vol. 111/113

3 achieves its minimal value of 2), or by truncating a concentrator of smaller acceptance angle so that its extreme ray angle is 90 deg as in Fig. 4. The geometry of the problem places an upper limit of 3 on AB/CD [10]. The active bifacial absorber area is then formed by depositing one thin film only in "sandwich" form between two transparent outer layers, the upper of which is the concentrator's glazing. A transparent lower conducting layer and appropriate circuitry would ensure proper operation of the bifacial cell. Production of the active PV absorber could then become part of the process for manufacturing the glazing for the concentrator, with absorber deposition on a fraction of the glazing (that fraction depending on the concentration ratio desired) so as to create an effectively bifacial solar cell. (It is possible that coating only part of the aperture glazing with amorphous silicon may be more expensive than current production technologies in which entire glass sheets are coated. However, in today's economic scenario where, due to mechanized production facilities, materials are a relatively expensive component, this possibility is doubtful.) Toward minimizing the possibility of "hot spots" or nonuniform illumination on the solar cell, the concentrator glazing material could be made of translucent glass. This type of glazing forward scatters incoming solar radiation while introducing negligible attenuation compared to clear transparent glass. The translucent glazing is well suited to CPC-type concentrators because these concentrators take incoming isotropic radiation (i.e., uniformly distributed over its acceptance angle at the aperture) and produce an isotropic radiation distribution at the absorber [7-8]. Finally, Figs. 3-4 represent symmetric concentrators. Asymmetric concentrators are also possible, however, but offer inferior yearly energy delivery compared to their symmetric counterparts [11-12]. 3 Yearly Energy Delivery We now present an illustrative calculation for yearly energy delivery of the specific type of bifacial amorphous silicon PV cell proposed here. We consider the general configuration of Fig. 4 with arbitrary acceptance half angle 6 a, O<0 a <9O deg. The concentrator is constrained to have an extreme edge ray angle of 90 deg (i.e., absorber and aperture are effectively coincident), which fixes the concentration ratio C for a given acceptance angle (2<C<3). The definition of concentration ratio must be qualified. The conventional definition for concentration ratio for the bifacial devices of our figures is C = AB/(2 CD). This definition is based on a bifacial device usually requiring twice as much absorber material as the monofacial case. However, we have here a bifacial amorphous silicon material requirement that is the same as for the monofacial case. Hence, one could equally well define concentration ratio as twice the value noted, namely C = AB/CD. We select this latter definition. The optical and collectible energy elements of our calculation are detailed in [10, 13]. In addition, for our illustrative calculation, for specificity, we consider the following system and site details: (1) Site: Bet Dagan, Israel; latitude = 32 deg N; yearly average clearness index (ratio of horizontal global to horizontal extraterrestrial -solar radiation) = (2) PV cells are operated at maximum power point, and all electricity produced is utilized. (3) Totally stationary collectors at tilt = latitude and zero azimuth, and concentrator axis-oriented east-west to maximize yearly collectible energy [14]. (For a particular site and/or seasonally-peaked application, the optimal orientation may be different. Our calculation is for illustrative purposes.) (4) We neglect power losses associated with nonidentical illumination of the two sides of the bifacial PV cell. (5) Optical efficiency at normal incidence. JJ = 0.85 for 114/Vol. 111, MAY 1989 the corresponding flat-plate, monofacial configuration. For the total bifacial cell in the CPC-type concentrator. 7] = 0.85p <n>, where p is the reflector reflectivity (assumed here to be 0.87, which is typical for inexpensive, commercially available reflector films [9, 15]), and <n> is the average number of reflections, which can be calculated analytically [26]. (The seemingly high optical efficiency assumed for the bifacial concentrator is based on the assumption of very small optical losses in the transparent underside of the bifacial cell, and of part of the solar radiation that is not fully absorbed in one half of the bifacial cell being partly absorbed in its complement.) (6) A linearized heat-loss coefficient, U, (for passive cooling) of 30 W/(K-m 2 ) for the flat-plate configuration, and of 20 W/(K-m 2 of aperture) for the concentrator [27]. (7) We assume either no degradation of the PV cells or equal degradation in both the concentrator and flat-plate configurations. Toward modelling the dependence of PV efficiency on solar cell temperature, T c, and collectible insolation on the collector aperture, 7 coll, we proceed as follows. For crystalline and polycrystalline PV's one can, to a very good approximation, express PV efficiency, -q, in two equivalent forms [16-18]: V = n R (l-p(.t c -T R )) and (1) r, = r, -U(T c -T a )/I coll, (2) where: r] R and T R = PV efficiency and solar cell temperature, respectively, at specified reference conditions; /3 = PV temperature coefficient (in 1/K); T a = ambient temperature; and 7 coll includes all incidence angle losses (in W/m 2 of aperture). Eliminating T c and taking advantage of the relative magnitudes of the parameters cited above, we obtain a linear efficiency equation in T a and 7 cou [16-18]: V=r,Al+l3T R -l3t a ~(3(r, n -r lr )I con /U). (3) The parameters in equation (3) can be measured directly or estimated from related known PV properties [18]. For our illustrative example here, we select: /3 = (1/K); r) R =0.05; and T R = 25 C; which are typical for amorphous silicon PV's [19-21]. Yearly average power output per unit aperture area, <P>, can then be well approximated by [18]: <P>= VR <I con >(l+pt R -l3<t a > ~l3(r, -r, R )<f co n>/(u<i coll >)) (4) where the brackets < > denote yearly average values, and the radiation statistic, <7 2 0, > / </ co n >»is calculated analytically as delineated in [18]. An assumption inherent in the above treatment is that, at fixed T c, PV efficiency can be approximated as independent of 7 coll (i.e., in equation (1), rj is independent of 7 con ). This indeed has proven to be the case for commercial crystalline and polycrystalline PV's [22], particularly for calculations of monthly or yearly energy delivery. One qualification here is that at very low insolation levels, typically, 7 coll < 100 W/m 2, PV efficiency decreases noticeably as / coll decreases, due to the logarithmic dependence of open-circuit voltage on 7 col ]. However, for monthly or yearly energy delivery calculations, these lower efficiencies are weighted not only by the lowest insolation levels that occur, but also by the fact that they tend to occur with relatively low statistical weight. Hence, the error incurred by ignoring this effect turns out to be negligible [18, 22]. For amorphous silicon PV's, however, -q R may not be well approximated as independent of 7 col]. Amorphous silicon PV's tend to exhibit significantly higher effective series resistance than their crystalline or polycrystalline counterparts [23, 24].

4 9 _ / "\^ Differences in the type of amorphous silicon PV material used (e.g., value of series resistance) and climate, for example, will slightly shift the location of the energetic optimum of Fig. 5. However, the "allowed" range of geometric concentration ratio is small (2<C<3), and the optimum in Fig. 5 is rather broad. B y 7 I I I I I I I 1 L CONCENTRATION RATIO Fig. 5 Ratio of yearly electrical energy delivery of the bifacial PV concentrator (Q(CONC)) to that of the corresponding monofacial flat-plate PV (Q(FLAT PLATE)), versus concentration ratio. Note that the x-axis is limited to the range 1.7 to 2.0. This is the primary source of the relatively low fill factors characteristic of amorphous silicon PV's. In addition, high series resistance can result in a nonnegligible dependence of i) R on 7 coll for the range 7 coll < 2 suns, the range which will be experienced by the CPC-type concentrators proposed here. Published data on commercial amorphous silicon PV's indicate that, for the range 7 coll < 2 suns, in some cases the dependence of efficiency on I con is as negligible as for crystalline and polycrystalline silicon PV's, while in other cases efficiency can vary by as much as ±10 percent about its yearly average value [23-24]. In the following illustrative calculations, we have assumed a negligible dependence of i; R on 7 cou because: (a) there appears to be no generalizable behavior observed thus far for amorphous silicon PV's, with one important class of amorphous silicon PV's indeed exhibiting q R approximately independent of 7 coll [23-24]; and (6) the amorphous silicon PV's of the future will assumedly be higher efficiency devices with relatively small series resistance and the associated negligible dependence of ij R on f co n for the range of insolation values of importance. It is possible, however, that our calculations for yearly energy delivery could vary by as much as ± 10 percent based on the extreme behavior of certain high series resistance samples of amorphous silicon PV's. Our results are presented in Fig. 5, a plot of the ratio of yearly electrical energy delivery of the bifacial PV concentrator (Q(conc)) to that of the corresponding monofacial PV flat-plate (Q(flat-plate)) versus concentration ratio. The results summarized in Fig. 5 are consistent with the experimental findings of [11-12] for bifacial crystalline silicon PV CPCtype concentrators. For our specific illustrative example, the concentrator configuration with C = 2.34 (6 a = 30 deg, Fig. 4) maximizes yearly energy delivery per square meter of absorber, delivering close to 100 percent more yearly energy than the corresponding monofacial flat-plate configuration, and about 10 percent more yearly energy than the C = 2 (0 = 90 deg) configuration (Fig. 3). The C = 2 concentrator minimizes collector (aperture) and reflector area, and will likely minimize production costs. In this specific illustrative case, the economically optimal configuration will depend on the relative costs of concentrator assembly and delivered energy. The optimum must fall between the configuration that maximizes yearly energy delivery (in this case, C = 2.34, Fig. 4) and the configuration that minimizes material needs and production costs (C = 2, Fig. 3). 4 Summary The type of fully-illuminated, bifacial amorphous silicon PV solar cell CPC-type concentrator we are proposing would overcome the key problems associated with bifacial PV cell deployment, be it in concentrators or otherwise, since: (1) less active absorber material is required for the same energy delivery or, equivalently, more energy is produced for the same amount of active absorber; (2) manufacture of the bifacial PV cell would become part of the manufacture process for the concentrator glazing; (3) the need for at least half (and typically more) of the effective second glazing of other concentrators would be obviated; (4) the efficiency penalty due to increased PV cell temperatures would be comparable to (although slightly in excess of) conventional flat-plate configurations; and (5) problems associated with "hot spots" could be alleviated at negligible sacrifice in collectible energy. The concentrators we propose should deliver close to 100 percent more yearly electrical energy than the corresponding monofacial amorphous silicon PV cell. Such devices are particularly attractive for a technology where a bifacial PV is noticeably less expensive than two monofacial PV's of the same active absorber area. All the PV concentrators we have considered are totally stationary. A further advantage is that a technology for manufacturing the non-pv concentrator components has already been developed industrially for solar thermal collectors [15, 25]. Acknowledgment The authors thank David Faiman and Ari Rabl for stimulating discussions. 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