Progress in quantum well solar cells

Progress in quantum well solar cells

Thin Solid Films 511 – 512 (2006) 76 – 83 www.elsevier.com/locate/tsf Progress in quantum well solar cells M. Mazzer a,*, K.W.J. Barnham b, I.M. Ball...

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Thin Solid Films 511 – 512 (2006) 76 – 83 www.elsevier.com/locate/tsf

Progress in quantum well solar cells M. Mazzer a,*, K.W.J. Barnham b, I.M. Ballard b, A. Bessiere b, A. Ioannides b, D.C. Johnson b, M.C. Lynch b, T.N.D. Tibbits b, J.S. Roberts c, G. Hill c, C. Calder c a

CNR-IMM, University Campus Lecce, Italy and Experimental Solid State Physics, Blackett Laboratory, Imperial College of Science, Technology and Medicine, London SW7 2BW, UK b Experimental Solid State Physics, Blackett Laboratory, Imperial College of Science, Technology and Medicine, London SW7 2BW, UK c EPSRC III-V Facility, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK Available online 2 February 2006

Abstract A quantum well solar cell is a special multiple-band gap device with intermediate properties between heterojunction cells (sum of the currents generated in the different materials but voltage controlled by the lowest of the two band gaps) and tandem cells (sum of the voltages but current determined by the worst of the two sub-cells). Strain-balanced GaAsP/InGaAs multi-quantum wells move the absorption edge of GaAs solar cells closer to the optimum value for single junction cells with no need for any partially relaxed buffer layer to accommodate lattice mismatch between the absorbing layers and the substrate. Covering a large spectral range in a single-junction cell has the benefit that the cell remains close to optimal efficiency in the varying spectral conditions of a typical terrestrial concentrator. Though monolithic multi-junction cells have significantly higher efficiency, the series-current constraint means that some of this advantage is lost as the illuminating spectra and the cell temperature change from the values at which the tandem was optimised. The good material quality which can be achieved with these structures makes the cell dark current at the typical operating conditions expected under moderate sunlight concentration (¨200), increasingly dominated by radiative processes the deeper the quantum wells. We will report on high concentration measurements of strain-balanced quantum well solar cells with and without Bragg-stack reflectors and discuss the ‘‘additivity’’ between the short-circuit current and the dark-current. We discuss a 50 shallow well cell with measured AM1.5d efficiency of (26 T 1)% at around 200 concentration. This is approximately 2% higher than a comparable p – n cell with comparable material quality. The good material quality is also responsible for another effect previously observed in single quantum wells becoming measurable in structures with 5 and 10 wells, that is the suppression of carrier recombination in quantum wells with respect to expectations assuming that the quasi-Fermi level separation in the depletion region is equal to the cell output voltage throughout the active region. The latest results are presented together with possible explanations for this effect both in the dark and under illumination. Finally a brief discussion about the potential applications of quantum well solar cells completes the paper. D 2005 Elsevier B.V. All rights reserved. Keywords: Photovoltaic; Quantum well; III-V semiconductors; Solar concentrators

1. Introduction The Quantum Photovoltaic Group (QPV) at Imperial has pioneered the application of low-dimensional systems [1] such as quantum wells [2] and quantum dots [3] in photovoltaics (PV). The strain-balanced quantum well solar cell (SB-QWSC)

* Corresponding author. E-mail address: [email protected] (M. Mazzer). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.12.120

was introduced as a way to extend the spectral range of high efficiency GaAs cells. We have demonstrated that the extended spectral range can be achieved and the SB-QWSCs can be grown with zero dislocations in the active region, in contrast to the alternative approach using virtual substrates [2]. The SB-QWSC can achieve optimal band-gaps for the highest single-junction efficiencies due to the tunability of the quantum well thickness and composition. Moreover, although tandem cells can achieve significantly higher efficiencies under standard AM 1.5 solar spectra, the series current constraint of a

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monolithic, multi-junction cell results in some of this advantage being lost in the varying spectral conditions of a typical urban environment. This spectral sensitivity is also likely to mean the efficiency of multi-junction cell is more dependent on cell temperature, which is particularly important under high concentration. Furthermore, tunnel junction performance is more problematic at concentrator current levels. The absence of dislocations and radiative dominance at high current levels in the SB-QWSC means that the dark-current is minimal at the optimum band-gap [4]. Furthermore radiative recombination dominance means that photon recycling can be used to reduce the dark-current further [5]. We report on our latest measurements of SB-QWSC performance under concentrated light and in particular the test of additivity up to 200 concentration. Finally, the most recent data on the behaviour of the quasi-Fermi level separation in multiple-quantum well solar cells are reviewed and discussed with reference to our earlier results in single quantum well devices. 2. The strain-balanced quantum well solar cell The AM1.5d efficiency variation with band-gap of a single junction cell in a concentrator system is well known to peak below the band-gap of GaAs. It is also well known that there is no binary or ternary III – V alloy lattice matched to GaAs with lower band-gap. Hence, to achieve optimum efficiencies, tandem cells are often grown on relaxed or ‘‘virtual-substrates’’ which necessarily involve dislocations [6,7]. The GaInNAs quaternary alloy is being considered for multi-junction cells though its bulk and QW material properties are currently poor. The band-gap of the SB-QWSC is represented schematically in Fig. 1. It consists of a p –i – n diode with an i-region containing a number (up to 65) of approximately 7 nm wide quantum wells (QWs) of compressively strained Inx Ga1x As inserted into tensile strained GaAs1y Py barrier regions. The crystal structure is represented in Fig. 2. The alloy compositions and well and barrier thicknesses are adjusted to minimise the

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Fig. 2. Schematic of the crystal structure of the strain-balanced quantum well solar cell.

formation of dislocations. The stress – balance condition ensures that when the structure in Fig. 2 is grown epitaxially with the same lattice constant as the substrate, there is essential zero stress between the thin alloy layers. The critical thickness of the overall structure is well above 1 Am. This constraint means that the GaAs1y Py barriers have higher band-gap than the bulk GaAs in the p and n regions and this helps to reduce the dark-current. The QWs extend absorption from bulk band-gap E g to threshold energy E a determined by the confinement energy as in Fig. 1. For 7 nm wells and GaAs1y Py barrier alloys with y¨0.1 (barrier band-gap¨1.5 eV) the threshold energies that can be achieved are E a¨1.34 eV for In fractions x¨0.1 and E a¨1.28 eV for x¨0.17. The extra absorption is demonstrated for a 50 well sample in Fig. 3, which shows the experimental spectral response (external quantum efficiency at zero bias) and the fit described in Ref. [4]. Fig. 3 also demonstrates a sharp exciton feature in the QW which is a good indication of material quality. 3. Dark current behaviour at concentrator current levels A range of SB-QWSCs has been grown by metal-organic vapour phase epitaxy (MOVPE). Further growth details can be found in Ref. [1]. These include a series of structures with P fraction y = 0.08 and a varying number (10 to 65) of shallow

Fig. 1. Schematic of a SB-QWSC with compressively strained Inx Ga1x As wells and tensile strained GaAs1y Py barriers higher than the bulk GaAs in p and n regions.

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Fig. 3. Spectral response of a 50 well SB-QWSC. The fit shows the separate contributions of the p, i and n regions and is discussed in Ref. [4].

wells (x = 0.1), a 50 QW device with P fraction y = 0.08 and an intermediate depth well of In (x = 0.13) and a second series with P fraction y = 0.08 and 20, 30 or 40 deeper wells (x = 0.17). Further sample details can be found in Ref. [4]. Dark-currents were measured at 25 -C on fully-metallised test structures. A typical result is shown in Fig. 4. At currents corresponding to 200 concentration and above the ideality n = 1 contribution dominates. We measure the dark-currents of ¨10– 20 fully-metallised devices for each wafer and have fit with two exponentials, one with ideality n¨2 and the other with ideality n fixed at 1.  eV   eV  Jd ¼ J01 e kT  1 þ J02 e nkT  1 : We can describe the data in the n¨2 region with a model we have developed for QWSCs in two lattice matched material systems [8]. The model solves for the variation in the carrier distributions n(x) and p(x) with position x through the i-region using the known QW density of states, assuming the depletion approximation holds. This approach gives similar results to an exact self-consistent calculation up to the voltages at which the n = 1 contribution dominates. From carrier densities a recombination rate is determined assuming the Shockley – Hall – Read (SHR) approach [8]. A typical one-parameter fit is shown in Fig. 4. We anticipate that there are two distinct contributions to the n = 1 current [9]. Firstly the standard, ideal Shockley diode current. This assumes no recombination in the depletion region but does assume the radiative and non-radiative recombination of injected minority carriers with majority carriers in the fieldfree regions. This contribution depends in a standard way on the minority carrier diffusion lengths, doping levels and the surface recombination in the neutral regions. We can estimate this current from the minority carrier parameters obtained when fitting the spectral response in the n and p regions as in Fig. 4.

The second contribution to the n = 1 current results from the recombination of carriers injected into the QWs and barriers in the depletion region. Like the ideal Shockley current this is expected to have both radiative and non-radiative contributions. However, we assume that the non-radiative contribution in the i-region is described by the SHR n¨2 model discussed above. The radiative contribution to the QW recombination can be estimated by a detailed balance argument [10]. This relates the photons absorbed to the photons radiated and depends on the absorption coefficient a(E, F) as a function of energy E and field F and is calculated from first principles [10] in the programme used to fit the spectral response of the QWs assuming unity quantum efficiency for escape from the wells. It should be noted that the important parameters for both the ideal Shockley (minority carrier diffusion lengths) and the QW radiative current levels (absorption coefficient a(E, F)) are therefore determined by the spectral response fits in the bulk and QW regions, respectively, as in Fig. 3. The model for the n = 1 region is therefore a zero-parameter prediction that agrees well compared with the data of Fig. 4. Other examples of the comparison of this model with data are presented in Ref. [4]. Fig. 5 shows the absorption threshold energy dependence of the ratio of the QW radiative current intercept to the sum of the intercepts of the ideal Shockley and the QW radiative currents for shallow and deep InGaAs wells. It can be clearly seen that the dark-current is becoming increasingly radiatively dominated as the threshold moves to lower energies and the wells get deeper. For a given absorption edge the ratio is not strongly dependent on the number of wells. The dominance of radiative recombination at concentrator current levels is important as it suggests that the recombination is at the minimum value to be expected from detailed balance and that the efficiencies will therefore be a maximum. In addition one might hope to benefit from a further dark-current reduction due to the effect of photon recycling. To investigate such photonic effects we have grown pairs of wafers in the MOVPE reactor, in which the same SB-QWSC structure is grown on two adjacent wafers, one up-stream the other down-

Fig. 4. Measured dark-currents of the device in Fig. 3 at 25 -C compared in the n¨2 region and the n = 1 region with the models discussed in the text.

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1 0.9 0.8 0.7 0.6 0.5 0.4 1.26

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Absorption threshold (eV) Fig. 5. Ratio of QW radiative current to total ideality n = 1 current plotted against QW absorption threshold given by first exciton position.

stream. The up-stream wafer is grown on a GaAs substrate. Downstream the overgrowth is on a wafer which already has a distributed Bragg reflector (DBR) optimised for the radiative recombination wavelength comparable with the first exciton in the well (see Fig. 3). Comparison of dark-current measurements on fully metallised diodes [5] shows that the intercept J 01 of the ideality n = 1 dark current in the SB-QWSC grown on the Bragg stack reflector is significantly lower than in a identical cell without the DBR, which suggests that photon recycling is occurring (see Fig. 6). Hence, though a Bragg stack is an extra complexity in growth, it carries a dual advantage, reducing the dark-current at concentrator current levels by photon recycling and very significantly increasing the absorption in the quantum wells [5] above that demonstrated in Fig. 3. 4. Test of additivity and efficiency enhancement

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demonstrates that additivity holds at concentrator current levels, i.e., that the light IV can be represented by the difference between the short-circuit current and the dark current. This has been observed to hold at one-sun illumination for i-regions containing up to 65 QWs [11]. To test additivity under concentrated illumination we have processed the wafers with appropriate grid-structure with low series resistance. The measurements were made in a 3000 K spectrum with a triggered shutter arrangement. Typical measurements shown in Fig. 7 demonstrate that additivity holds reasonably well in a 50 shallow well SBQWSC up to 190 concentration. An alternative test for additivity, which eliminates the effect of series resistance, is to plot the measured short-circuit current I sc against Voc at different concentrations as in Fig. 8. At Voc no current flows as the light-generated current is exactly cancelled by the dark-current and hence the series resistance should not affect the voltage. The dark current in the absence of series resistance can be estimated by taking the fit to the measured dark current (dark full line in Fig. 8), from which a series resistance has been fitted and assuming that this resistance is zero, giving the light full line in Fig. 9. Additivity predicts that

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Bias (V) Fig. 6. Dark currents of between 10 and 20 fully metallised diodes from a shallow 50 well SB-QWSC (In fraction x = 0.17) overgrown on a GaAs substrate (control) and a GaAs substrate plus a 20 period distributed Bragg reflector (DBR) measured in the concentrator current regime.

Fig. 7. Light IV measurement at 190 concentration of a 50 shallow well SBQWSC processed as a concentrator cell (full line). The broken line is the prediction assuming that additivity holds, i.e., the light IV is the difference between the short-circuit current and the measured dark current. The measured fill factor is 84% compared with a prediction from additivity of 87%.

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0.6 1.0E+00

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Bias (V) Fig. 8. Measurements of I sc plotted against Voc for a 50 shallow well SB-QWSC processed as a concentrator cell, compared with the extrapolation of a fit to the dark-current data assuming zero series resistance. The highest data point corresponds to 190 concentration.

this zero resistance dark current at the Voc point will cancel the I sc and hence the data points will fall on the R = 0 dark-current. This is observed at low voltages but at the highest voltage, corresponding to 190 concentration, the data point falls above the zero resistance line. This is consistent with the small displacement of the experimental intercept from the theoretical one on the voltage axis of Fig. 7. To calculate a standard efficiency from the 3000 K source measurements, corrections were made to AM1.5d with the measured SR and assuming 5% metallisation. The curves in Fig. 9 are the predictions of additivity assuming the series resistance measured in the dark and a concentration given by the ratio of measured J sc to one-sun J sc. The data falls below additivity around 100 suns. However, this also occurs for the p –n control cell, suggesting a problem such as non-uniform illumination or spreading resistance in the light that affects both cells. The concentration data confirm the 1-sun observation that this 50 well QWSC has significantly higher efficiency than the p –n control cell which has similar material quality. If we could solve the problems responsible for the failure of additivity, efficiencies near the World single-junction record would result. Though these results have yet to be confirmed by independent measurements at a calibration laboratory we believe that the measurement of (26 T 1)% AM1.5d efficiency at ¨200 concentration in a SB-QWSC is a significant achievement.

p – i –n junction and in particular no difference should be detected between quantum wells and barriers. In fact a thorough experimental analysis of the radiative components of the dark recombination current in strained single quantum well (SQW) devices and in a lattice matched double quantum well (DQW) devices [14,15] showed evidence of reduced radiative recombination in quantum wells with respect to level predicted by the generalised detailed balance model. More recently the study has been extended to strainbalanced multiple quantum-well solar cells by measuring and modelling the electroluminescence (EL) and photoluminescence (PL) response of GaAsP/GaAs/InGaAs strain-balanced devices in the dark. The comparison between the EL measurements and the theoretical limits in three SB-QWSCs with 1, 5 and 10 quantum wells gives evidence of a suppressed radiative recombination in the wells in all the devices although the magnitude of the reduction appears to decrease as the number of wells increases (see Fig. 10). For the sake of presenting the experimental results, the suppression of non-radiative recombination is described in terms of reduced Quasi-Fermi Level Separation (QFLS) in the wells with respect to the barriers. However the discrepancy between the experimental results and the model might be an indication that the actual carrier population in the well could be significantly different from that which can be described by a generalised-Plank distribution and a single temperature for the carriers and the crystal lattice [16]. One of the possible explanations for these discrepancies is that an additional thermodynamic force enhances carrier extraction from the wells and sustains a non-zero QFLS gradient throughout the active region of the device in forward bias condition. In fact a temperature variation of just a few degrees between crystal lattice and charge carriers in the wells (hot carriers) could account for the observed QFLS variation in the dark [16]. Extensive tests have also been carried out to verify that the suppression of radiative recombination in the wells is not cancelled or reversed under illumination [17]. The single-well device presented above was illuminated by a laser at 915 nm, 29

5. Suppression of radiative recombination in quantum wells Efficiency (%)

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Although practical efficiency enhancement of multi quantum well cells over identically grown control structures without wells has been demonstrated [11], the fundamental question about whether the efficiency of quantum well solar cells can exceed the theoretical limit expected for ideal single band-gap devices is still open. Theoretical analyses based on detailed balance and thermodynamic models [12,13] were proposed to address this issue. On the basis of these models no efficiency enhancement over an ideal single band-gap cell is possible. However, these models assume that in the radiative limit, the quasi Fermi level separation is constant throughout the high field region in the

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Energy (eV) Fig. 10. Electroluminescence spectra (scattered points) taken at room temperature of the single well (a), 5 well (b), and 10 well (c) SB-QWSCs biased at +0.98V compared to model predictions for DE F = Vapplied (full lines) or a reduced DE F (dotted lines).

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Intensity (a.u)

that is below the absorption edge of both the GaAs p and n regions and the GaAsP barriers but above the absorption edge of the InGaAs quantum well. The room temperature EL spectrum obtained under an applied forward bias of about + 0.88 V, i.e., close to the open circuit voltage generated by the cell under 1-sun illumination, is plotted in Fig. 11 together with the PL spectrum obtained in the same experimental conditions by adjusting the laser intensity to obtain the same open circuit voltage. The two spectra are almost indistinguishable demonstrating that at such an illumination level, the escape of photoinduced charges from the wells is ideal. This indicates that the QFLS reduction observed in the dark in strain-balanced structures is unchanged under illumination as originally observed in a strained SQW device [17]. If hot carriers are responsible for the QFLS reduction, a stronger effect should be observed under light concentration when energy dissipation is larger due to carrier thermalisation, and transferred less efficiently to the lattice due to phonon confinement [16]. Work is in progress to test this hypothesis.

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Energy (eV) Fig. 11. Photoluminescence (full line) and electroluminescence (scattered points) spectra at 290.9 K of the single well SB-QWSC biased at +0.88V.

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M. Mazzer et al. / Thin Solid Films 511 – 512 (2006) 76 – 83 QWSC Single-Junction

Third-generation cells could have an important part to play if deployed in high concentration systems to reduce costs below those of first and second generation cells. Having approximately twice the efficiency of the latter [18], third generation cells can also cope with the inevitable losses that result from non-optimal module orientation in a building integrated environment. Also transparent concentrator systems allow the diffuse light through for efficient interior illumination. First and second generation cells must be either thinned or deployed with spaces between cells to achieve this objective. For such application the cells must be small¨mm in size and provide high PV conversion efficiency under a wide range of solar spectra. In fact, very high efficiency cells based on multi-junction devices have AM1.5 efficiencies ¨34 –36%. Though this is a much higher efficiency than our 26% singlejunction SB-QWSC (Fig. 9), the series-current constraint means that the efficiency of a monolithic multi-junction cell is more sensitive to spectral variation and band-gap change with temperature. We demonstrate this effect in Fig. 12 by considering the spectral changes of sunlight during the day and over a year comparing a tandem cell which has 15% higher (relative) efficiency than a SB-QWSC at AM1.5. However, over a whole year of operation the energy harvested by the multi-junction cell is less than 10% (relative) above that harvested by the SB-QWSC. In addition, one would anticipate that cell temperature variation will be important for building integrated concentrators. Again the series current constraint will make the multi-junction cell sensitive to the consequent band-gap variation. We have not quantified this effect as we have yet to determine the temperature coefficients of our cell. These effects together with the absence of any tunnel junction, which limits the accepted solar concentration to a maximum of about 500 suns in current multi-junction cells, makes the SB-QWSC an attractive option for future generations of solar concentrators for building integrated applications. 7. Conclusions We believe that the GaAsP/GaInAs SB-QWSC is an appropriate cell for the small, high concentration systems which will be used in high-efficiency building integrated photovoltaics. SB-QWSCs extend the spectral range of the GaAs cell. In Fig. 9 we demonstrate a SB-QWSC with efficiency under AM1.5d at ¨200 concentration of (26 T 1)%. This is approximately 2% higher than a GaAs cell of comparable material quality. The dark-currents of SB-QWSCs show ideality n = 1 behaviour at current levels corresponding to 200 concentration and above. The data in this region can be described in terms of ideal Shockley behaviour and also a radiative recombination term, which is dominated by the recombination in the quantum wells. The latter contribution becomes increasingly important as the wells deepen, suggesting that radiative recombination in the QWs dominates the dark-current at high concentration levels. This not only means that recombination will be minimal but also that the dark-

Energy/(kWh/m2)

6. Applications

Tandem Cell

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 28 56 84 112 140 168 196 224 252 280 308 336 364

Day Fig. 12. Calculated electric energy delivered by a photovoltaic concentrator system for a typical building integrated configuration based on a III – V tandem cell (solid line) and on a quantum well solar cell (broken line). The tandem cell has 15% higher efficiency at AM1.5 relative to the SB-QWSC but the overall energy delivered by the two systems over one year differs by less than 10%.

current can be further reduced by photon-recycling effects we have already demonstrated in fully metallised devices. Finally, the observed suppression of radiative recombination in quantum wells with respect to limits predicted by the current thermodynamic models may be exploited in the future to further enhance the efficiency of SB-QWSCs under high concentration. Acknowledgements We wish to acknowledge financial support from the U.K. Engineering and Physical Sciences Research Council (EPSRC), Ashden Trust and the Imperial College London– B.P. Strategic Alliance. References1 [1] K.W.J. Barnham, P. Abbott, I. Ballard, D.B. Bushnell, A.J. Chatten, P. Connolly, N.J. Ekins-Daukes, B.G. Kluftinger, J. Nelson, C. Rohr, M. Mazzer, G. Hill, J.S. Roberts, M.A. Malik, P. O’Brien, Future Applications of Low Dimensional Structures in Photovoltaics, Photovoltaics for the 21st Century II, Electrochemical Society Proc., vol. 2001-10, 2001, p. 30. [2] N.J. Ekins-Daukes, K.W.J. Barnham, J.P. Connolly, J.S. Roberts, J.C. Clark, G. Hill, M. Mazzer, Appl. Phys. Lett. 75 (1999) 4195. [3] K.W.J. Barnham, J.L. Marques, J. Hassard, P. O’Brien, Appl. Phys. Lett. 76 (2000) 1197. [4] K.W.J. Barnham, I.M. Ballard, D.B. Bushnell, J.P. Connolly, R. Day, N.J. Ekins-Daukes, D.C. Johnson, C. Lim, M. Lynch, M. Mazzer, T.N.D. Tibbits, C. Calder, G. Hill, J.S. Roberts, Proc. 19th European Photovoltaic Solar Energy Conference, Paris, 2004, p. 328. [5] D.C. Johnson, I. Ballard, K.W.J. Barnham, A. Bessiere, D.B. Bushnell, J.P. Connolly, M. Mazzer, C. Calder, G. Hill, J.S. Roberts, Dark-current suppression due to photon recycling in distributed Bragg Reflector Strainbalanced Quantum Well Solar Cells, Conference Record IEEE Photovoltaic Specialists Conference, Orlando, USA, 2005, p. 699 (January 31). [6] A.W. Bett, C. Baur, F. Dimroth, et al., in: Proc. 3rd World Conference on Photovoltaic Energy Conversion, Osaka, vol. 634, 2003. [7] R.R. King, C.M. Fetzer, P.C. Colter, et al., 3rd World Conference on Photovoltaic Energy Conversion, 2003, p. 622.

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Preprints available from http://www.sc.ic.ac.uk/¨q_pv.

M. Mazzer et al. / Thin Solid Films 511 – 512 (2006) 76 – 83 [8] J.P. Connolly, J. Nelson, I. Ballard, et al., Proc. 17th European Photovoltaic Solar Energy Conf., 2001, p. 204. [9] J.P. Connolly, et al., Proc. 19th European Photovoltaic Solar Energy Conference, Paris, 2004, p. 355. [10] J. Nelson, J. Barnes, N.J. Ekins-Daukes, et al., J. Appl. Phys. 82 (1997) 6240. [11] M.C. Lynch, I.M. Ballard, D.B. Bushnell, J.P. Connolly, D.C. Johnson, T.N.D. Tibbits, K.W.J. Barnham, N.J. Ekins-Daukes, J.S. Roberts, G. Hill, R. Airey, M. Mazzer, J. Mater. Sci. 40 (2005) 1445. [12] G.L. Araujo, A. Marti, Sol. Energy Mater. Sol. Cells 33 (1994) 213. [13] A. Luque, A. Marti, L. Cuadra, IEEE Trans. Electron Devices 48 (2001) 2118.

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[14] J. Nelson, J. Barnes, N.J. Ekins-Daukes, B. Kluftinger, et al., J. Appl. Phys. 82 (1997) 6240. [15] B. Kluftinger, K.W.J. Barnham, J. Nelson, et al., Microelectron. Eng. 51 – 52 (2000) 265. [16] M. Mazzer, et al., Proc. 3rd World Conf. on Photo-voltaic Energy Conversion, WCPEC-3, Osaka, 2003, pp. 2661. [17] N.J. Ekins-Daukes, et al., Proc. 3rd World Conf. on Photovoltaic Energy Conversion, Osaka, Japan, 2003, p. 262. [18] M.A. Green, Future Applications of Low Dimensional Structures in Photovoltaics, Photovoltaics for the 21st Century II, Electrochemical Society Proc., vol. 2001-10, 2001, p. 1.