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Quantum Well Solar Cells and Quantum Dot Concentrators
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Nanostructured Materials for Solar Energy Conversion T. Soga (editor) © 2006 Elsevier B.V. All rights reserved.
Chapter 16
Quantum Well Solar Cells and Quantum Dot Concentrators K.W.J. Barnhama, I. Ballarda, A. Bessièrea, A.J. Chattena, J.P. Connollya, N.J. Ekins-Daukesa, D.C. Johnsona, M.C. Lyncha, M. Mazzera,d, T.N.D. Tibbitsa, G. Hillb, J.S. Robertsb and M.A. Malikc a
Blackett Laboratory, Physics Department, Imperial College London, London, SW7 2BW, UK b EPSRC National Centre for III-V Technologies, Sheffield S1 3JD, UK c Chemistry Department, University of Manchester, Manchester M13 9PL, UK d CNR-IMM, University Campus Lecce, Italy 1. INTRODUCTION This chapter reviews the development over the past half a decade of the quantum well solar cell (QWSC) and the quantum dot concentrator (QDC). The study of nanostructures such as quantum wells (QWs) and quantum dots (QDs) has dominated opto-electronic research and development for the past two decades. Photovoltaic (PV) applications of these nanostructures have been less extensively studied. Our group has pioneered the study of both QWs and QDs for PV applications. Others groups have made significant contributions, particularly to the study of lattice matched QWSCs and the theory of the cells, particularly in the ideal limit. These earlier contributions have been acknowledged in the two reviews, which were written at the turn of the new century [1,2]. In this chapter we will review recent advances since then, concentrating in particular on studies of the strain-balanced quantum well solar cell (SB-QWSC) as a concentrator cell [3] and the thermodynamic modelling of the QDC [4]. The SB-QWSC offers a way to extend the spectral range of the highest efficiency single-junction cell, the GaAs cell. We will discuss how this can in principle lead to higher efficiency in both single-junction and multi-junction cells and offers particular advantages in high-concentration systems. The high efficiency, wide spectral range and small cell size make these systems
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particularly attractive for high concentration, building-integrated applications using direct sunlight. The QDC is a novel, non-tracking concentrator. It is a promising approach for concentrating diffuse sunlight and is therefore complementary to the SB-QWSC in building integrated concentrator photovoltaics (BICPV).
2. STRAIN-BALANCED QUANTUM WELL SOLAR CELLS The highest efficiency single-junction solar cells under both 1-sun conditions and concentration are GaAs cells. Both single-junction records have held for a decade and a half [5]. The GaAs bandgap (1.42 eV) is, however, rather high as optimal efficiency requires a bandgap around 1.1 eV at both 1 sun and high concentration [6]. Since those records were established, the main effort to raise efficiency has gone into developing tandem cells, which can now achieve 37.4%. These have a high-bandgap GaInP top cell grown lattice matched to the GaAs bottom cell with electrical connection between the cells provided by a tunnel junction. As the cells are in series, the same current passes through both cells and is limited by the current generated in the poorer cell. This turns out to be the GaAs bottom cell in most spectra, again because of the relatively high GaAs bandgap. The utility of the tandem approach has yet to be demonstrated at the very high-concentration levels required for cost reduction and in the varied spectral conditions of building-integrated applications. A tandem or multi-junction cell can achieve high efficiencies when optimised at the series current level of specific spectral conditions and temperature. In the varying spectral conditions of BICPV, with the cell temperature varying, plus the difficulty of maintaining good tunnel junction performance at high-current levels, a highly efficient, single-junction cell with wide spectral range may well, over a year, harvest comparable electrical energy to a tandem cell with nominally higher efficiency. In summary, for terrestrial concentrator applications of “Third Generation” GaAs-based cells, either single- or multi-junction, it is important to be able to lower the bandgap of the conventional GaAs cell. The problem in doing so, which III–V cell designers have had to face for at least two decades, is that though there are higher-bandgap alloys such as GaInP and AlGaAs that can be grown lattice matched to GaAs, there is no lattice matched binary or ternary III–V compound with lower-bandgap than GaAs. To extend the GaInP/GaAs tandem cell efficiency, considerable effort is going into studying the quaternary GaInNAs which can be grown lattice matched to GaAs, but demonstrates poor minority carrier lifetimes resulting in insufficient current to avoid limiting the multi-junction performance [7].
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The addition of lattice-matched QWs to AlGaAs, InP and GaAsP cells has been shown to extend the spectral range and enhance the efficiency [1,2], but when it comes to enhancing the GaAs cell, the QW approach also suffers from the absence of a lattice matched lower-bandgap ternary alloy. A number
Fig. 1. (a) Schematic of SB-QWSC with compressively strained InxGa1⫺xAs wells and tensile-strained GaAs1⫺yPy barriers. (b) Energy band-edge diagram of p–i–n SB-QWSC. Note that the GaAs1⫺yPy barriers in the i-region are higher than the bulk GaAs in p and n regions.
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of strained InGaAs wells with lower-bandgap than GaAs and larger lattice constant can be grown compressively strained to GaAs. However, only a limited number of wells can be grown before relaxation occurs and these give insufficient current enhancement to overcome the loss of voltage [8]. In SB-QWSC, illustrated schematically in Fig. 1a, the low-bandgap, higher-lattice-constant (a2) alloy InxGa1–xAs wells (In composition x ⬃ 0.1–0.2) are compressively strained. The higher-bandgap, lower-lattice-constant (a1) alloy GaAs1–yPy barriers (P composition y ⬃ 0.1) are in tensile strain [3]. Of the many possible balance conditions we find that the zero-stress gives the best material quality [9] and enables at least 65 wells to be grown without relaxation [10]. Fig. 2 shows the spectral response of a 50 shallow well SB-QWSC. The cell is a p–i–n diode with an i-region containing 50 QWs 7 nm wide of compressively strained InxGa1–xAs with x ⬃ 0.1 inserted into tensile strained GaAs1–yPy barrier regions. The QWs extend absorption from bulk bandgap Eg to threshold energy Ea determined by the confinement energy as in Fig. 1b, giving the extra absorption and wider spectral response demonstrated in Fig. 2.
Fig. 2. Spectral response (external quantum efficiency at zero bias) of a 50-well SBQWSC. The fit shows separate contributions of p, i and n regions as discussed in the text.
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Alternative approaches to lowering the GaAs involve the growth of InGaAs on a relaxed virtual substrate [11, 12]. However, this approach inevitably results in material with a residual dislocation density. Dislocations are completely absent in a SB-QWSC [3]. This is important if the recombination is to be minimal, as discussed in the next section. It should be noted in Fig. 1 that the GaAsP barriers in the i-region have higher-bandgaps than GaAs, which also helps reduce the unwanted recombination.
3. IDEAL DARK-CURRENT BEHAVIOUR AT CONCENTRATOR CURRENT LEVELS An important observation has been made when studying the dark currents of a range of SB-QWSC with differing well number and depth. We observe that, at current levels corresponding to 200⫻ concentration and above, the dark currents of SB-QWSCs have ideality n ⫽ 1 as observed for the best GaAs p–n cells. The importance of this observation is that one can expect minimum recombination and maximum efficiency at high concentration. Concentration levels ⬃400⫻ are generally accepted to be necessary if GaAs cells are to be cost competitive in terrestrial systems. When we studied a range of SB-QWSCs with different well numbers and depth we observed a further, in this case unexpected, result. The reverse bias saturation current of the n ⫽ 1 contribution does not show the absorption threshold energy dependence expected of an ideal Shockley diode. We explain this behaviour in terms of two contributions to the n ⫽ 1 current as discussed below. A range of SB-QWSCs were grown by metal-organic vapour phase epitaxy (MOVPE) at the EPSRC National Centre for III–V Technologies, Sheffield. Further growth details can be found in Refs. [3, 13]. Growth included a series of structures with P fraction y ⫽ 0.08 and a varying number (10–65) of shallow 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). Details of the characterisation can be found in Refs. [5, 11]. Dark currents were measured at 25⬚C on fully metallised test diodes. A typical result is shown in Fig. 3. At currents corresponding to 200⫻ concentration and above the ideality n ⫽ 1 contribution dominates. We have measured the dark-current densities of between 8 and 18 fully metallised devices for each wafer and have fitted with two exponentials, one with ideality n ⬃ 2 and the other with ideality n fixed at 1.
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Fig. 3. Measured dark currents at 25⬚C of the device in Fig. 2 compared in the n ⬃ 2 region and the n ⫽ 1 region with the models discussed in the text.
J d ⫽ J 01 (eeV/kT ⫺1) ⫹ J 02 (eeV/nkT ⫺1)
(1)
The reverse bias saturation current density of the n ⫽ 1 contribution (J01), which we estimate from the zero bias intercept of the ideality n ⫽ 1 fit, is plotted in Fig. 4 against the threshold energy Ea. The latter we take to be the energy of the e1–h1 exciton for the SB-QWSCs and the GaAs bulk bandedge for the homostructure p–i–n control cell. For each wafer in Fig. 4 we show the extrapolated intercept for the device with lowest dark current. In Ref. [4] we argue that the lowest dark current is the one most representative of the structure. The experimental increase in intercept with well number at fixed band edge is not very marked, as discussed later. The absorption edge dependence of the intercept J01 of the n ⫽ 1 contribution is expected to be determined by the square of the intrinsic carrier density and therefore to vary exponentially with band edge as indicated by the line based on the control homostructure p–i–n cell. In fact, the trend of the data is significantly below this expectation, particularly as the wells get deeper.
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1E-12 Ex p(-E g/ kT )
GaAs p-i-n control Intercept Jo of n = 1 Am-2
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Lowest Jo Data trend
1E-14
1E-15
1E-16 1.25
1.3
1.35 1.4 Absorption Edge (eV)
1.45
Fig. 4. Reverse bias saturation current density (J01) from the intercept of the ideality n ⫽ 1 fits to the lowest measured dark current, plotted against exciton position.
4. MODELLING THE n ⬃2 AND n ⴝ 1 DARK-CURRENT BEHAVIOUR To explain this unexpected behaviour, as the wells get deeper, we describe the data in the n ⬃ 2 region with a model we have developed for QWSCs in two lattice-matched material systems [14, 15]. 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 [16]. This requires the non-radiative lifetimes of the carriers. The evidence suggests we can equate the electron and hole lifetimes [14] so we are left with two parameters which depend on material quality, the carrier lifetimes tB and tW in the barrier and well, respectively. For lattice-matched QWSCs, we determine these two parameters by fitting homostructure or double heterostructure controls which have i-regions formed from the material of the barrier or the well, respectively. In the case of SB-QWSC, bulk material of
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comparable bandgap to the QW and of similar material quality does not exist. We assume that, for these low P and In fractions, the well and barrier quality are sufficiently similar, “so that the lifetimes can be considered to be equal” (i.e., tB ⫽ tW ⫽ t). We find reasonable fits can be obtained to the n ⬃ 2 region of the dark current of these variable well samples with the single parameter t. We anticipate that there are two distinct contributions to the n ⫽ 1 current. Firstly the standard, ideal Shockley diode current [17]. 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 field-free regions. This contribution depends in a standard way on the minority-carrier diffusion lengths, doping levels and the surface recombination in the neutral regions [17]. We can estimate this current from the minority-carrier parameters obtained when fitting the spectral response in the neutral regions as in Fig. 2. Further examples are given in Ref. [15] where details can be found including the effect of strain on QW depth and barrier height. 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. This relates the photons absorbed to the photons radiated, as discussed in Ref. [18] and references cited therein. The radiated spectrum as a function of photon energy E in an electrostatic field F, L(E,F) dE, is determined by the generalised Planck equation: L ( E , F ) dE ⫽
2pn2 LW a( E , F )E 2 dE h3c 2 e( E⫺⌬EF ) /kBT ⫺1
(2)
We integrate this spectrum over the energy and the cell geometry as described in Ref. [18] to give a total radiative current. This will depend on the quasi-Fermi level separation ⌬EF and the absorption coefficient a(E,F) as a function of energy and field. For this study, we assume that ⌬EF ⫽ eV where V is the diode bias. In Section 5, we discuss evidence from singleand 5-well SB-QWSCs that ⌬EF ⬍ eV though we have yet to observe this effect in the high well-number samples reported here [19].
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1.00E-13
Intercept Jo1 Am-2
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Model - deep wells Data - deep wells Model - shallow wells Data - shallow wells
1.00E-14
1.00E-15 5
10 15 20 25 30 35 40 45 50 55 60 65 70 Well Number
Fig. 5. Mean of measurements of the intercept of the n ⫽ 1 dark current from fits to 8–18 devices with n ⬃ 2 and n ⫽ 1 exponential terms. Data are plotted against number of wells and compared with the radiative plus ideal model described in the text.
The absorption coefficient a(E,F) is calculated from first principles [18] 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. 2. The sum of the two n ⫽ 1 terms is compared with the typical data in Fig. 3. In Fig. 5 the measured mean intercept from the experimental double-exponential fits is compared with the sum of the Shockley ideal and QW-radiative terms. Reasonable agreement is observed even though there are essentially no free parameters for the model. Note also that for a given well depth the intercept is only weakly dependent on the well number. Fig. 6 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. 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. We conclude that at concentrator current levels the ideality n ⫽ 1 behaviour becomes increasingly dominated by radiative recombination in the wells
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1 Radiative Fraction
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1.28
1.3 1.32 1.34 Absorption Edge (eV)
1.36
1.38
Fig. 6. Ratio of QW-radiative well current to sum of QW-radiative current plus ideal Shockley current against QW absorption edge given by first exciton position.
rather than non-radiative and radiative recombination in the GaAs p and n regions as the wells get deeper. This is important not only because deeper wells take the cell to absorption edges corresponding to higher efficiency [6] but also because the recombination can be further reduced by photon recycling techniques to be discussed in Section 6. However, to get PV power form these devices we must first consider if this low-recombination behaviour persists under light illumination as will be discussed in the next section.
5. TESTING ADDITIVITY IN SB-QWSCS In the last section the dark current Jd behaviour of SB-QWSC, described by Eq. (1), was discussed at some length. Under illumination, the current–voltage curve J(V) of the highest efficiency III–V cells can generally be described by J (V ) ⫽ J sc ⫺ J d
(3)
where Jsc ⫽ J(0) is the short-circuit current density. It is important to check if the additivity condition in Eq. (3) holds in SB-QWSCs for three reasons: (i) The ideal dark-current behaviour discussed in the last section will only translate into high efficiency if it does hold.
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(ii) There are theoretical claims based on a thermodynamic model that the suppressed radiative recombination we have observed in the dark in low well number QWSCs [18,19] will result in increased recombination in the light [20]. (iii) QWSCs are p–i–n devices and the built-in field must be maintained across the i-region at the operating bias to ensure efficient collection of photo-generated carriers. Background doping in the i-region or the build-up of one or other of the charge carriers in the wells could lead to the failure of additivity and a resulting loss of efficiency. We have tested additivity for the 1-, 5- and 10-well samples used to confirm that the suppressed radiative recombination observed in low-well number strained and lattice-matched QWSCs also occurs in the SB devices [19]. The SB-QWSCs were light-biased to the zero-current, open-circuit voltage Voc by illumination with a laser exciting on the continuum in the QW and the photoluminescence (PL) spectrum measured with a spectrometer and charged coupled device (CCD) system. The laser intensity is equivalent to around 1 sun. The PL spectrum is then compared with the electroluminescence spectrum (EL) obtained when the laser is turned off and the cell biased externally to the same voltage (0.88 V in the example in Fig. 7) at the same temperature. Significant radiative recombination suppression is observed in the 1- and 5-well SB-QWSC, consistent with the earlier strained- and lattice-matched QWSCs [19]. The suppression is smaller in the 5-well devices, consistent with the zero suppression observed in the 10-well case. However, in the 1-, 5and 10-well samples the PL and EL spectra are virtually identical, as can be seen for the single-well example in Fig. 7. At Voc the J(V) in Eq. (3) is zero and the equality of the PL and EL spectra suggest that the photo-generated recombination (PL) and the radiative-dark current (EL) cancel. This result is not consistent with the model in Ref. [20]. It is important to extend these tests to higher-current levels corresponding to the high concentrations in which these cells must operate for cost-effective terrestrial applications and to current levels where good dark-current performance is observed. Here the main problem becomes the challenge of contact fabrication such that resistance effects are minimised. We are currently limited by device processing. This can be seen in Fig. 8 where we show the efficiency of a 50-well SB-QWSC as a function of concentration. The cell parameters were measured in a 3000 K black-body spectrum in a shuttered measurement system. The 1-sun intensity was set by calculating the shortcircuit current level Isc to be expected by integrating the measured spectral response of the cell over an AM1.5D spectrum. The cell was then moved
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100000 EL PL
Intensity (a.u)
10000
1000
100 1.28
1.32
1.36 1.40 Energy (eV)
1.44
1.48
1.52
Fig. 7. Photo-luminescence (full line) and electroluminescence (scattered points) spectra at 290.9 K of the single-well SB-QWSC biased at ⫹0.88 V. Data points in the filter window have been removed.
28 26 Efficiency (%)
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22
Data for QT1628 Predicted for QT1628 Data for p-n cell
20
Predicted for p-n cell World Record
18 1
10
100
1000
Log (No. of Suns)
Fig. 8. Efficiency of 50-well SB-QWSC measured in a shuttered concentrator system compared with p–n control cell. The full lines show the predictions of additivity. If additivity holds at high concentration, the QW cell could achieve an efficiency close to the World single-junction record [5].
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closer to the illumination with its temperature maintained by a Peltier control system. The cell position was optimised at each distance, and the effective concentration was assumed to be proportional to Isc. The first observation to be noted from Fig. 8 is that the 50 shallow-well SB-QWSC has a significantly higher efficiency than that of the p–n cell, which has comparable material quality. The prediction of additivity in Eq. (3) is shown for both cells by the full lines. These were generated assuming Jd was given by fits to the measured dark current, which included the cell series resistance measured in the dark. The data fall significantly below this prediction at ⬃200 suns. This could be the result of an extra resistive term under light-generation or the failure of additivity at high concentration. We believe the former explanation at present as the effect is also observed in the p–n cell, which has no i-region. Furthermore, EL studies indicate that the deviation from additivity is accompanied by non-uniform current behaviour. We are currently studying improvements to our masks and contacting procedures in order to extend the additivity studies to higher-concentration levels and to challenge the World single-junction efficiency limit.
6. PHOTON RECYCLING IN SB-QWSCs As mentioned in Section 5, the dominance of radiative recombination at high-current levels suggests that the dark current could be further reduced by photon recycling schemes. The analysis presented there indicated that radiative recombination in the wells dominates over radiative and nonradiative recombination in the GaAs regions. A SB-QWSC is ideal therefore to observe photon recycling effects as the generalised-Planck equation in Eq. (2) favours the emission of photons well below the GaAs bandgap energy that can be reflected by a distributed Bragg reflector (DBR) at the back of the cell. These will only be re-absorbed in the QWs rather than regions of the cell where non-radiative recombination dominates as occurs in conventional homostructure cells. A number of 50-well SB-QWSCs have been grown at the EPSRC National Centre for III–V Technologies in the Quantax reactor, which will take two substrates. One, the upstream wafer (U) was a conventional GaAs wafer. The second, GaAs substrate, the downstream one (D), had a 20.5 period DBR optimised for high reflectivity within the QW wavelengths, which had been grown in an earlier run. A SB-QWSC was then grown on both wafers so that the overgrown device was as similar as possible and comparison of the U and D wafer would enable the effect of the DBR to be extracted.
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Fig. 9. (a) Typical dark current of a 50-well SB-QWSC control (squares) and DBR (circles) cell showing the ideality n ⫽ 1 (solid) and ideality n ⬃ 2 (dotted) dark-current components. (b) High-bias results plotted separately for the 20 devices in each case. Ideality n ⫽ 1 dark currents for QT1910 control devices (broken lines) and DBR devices (full lines) clearly have different reverse saturation currents J01.
The wafers were first processed as fully metallised diodes to minimise resistive effects such as those discussed in the last section. The dark currents of 20 different devices were measured from both the DBR (D) and control (U) wafers. Typical dark currents for a wafer QT1910 with 50 relatively deep (In ⬃ 0.17) wells are shown in Fig. 9a. The ideality n ⬃ 2 and n ⫽ 1 components from a fit of the dark current to Eq. (1) are also shown. The dark currents of all the QT1910 devices shown in Fig. 9b clearly display a separation between the DBR and non-DBR devices at high voltage when radiative recombination dominates. On the other hand, the Shockley–Read–Hall ideality n ⬃ 2 dark-current component is not significantly changed between the DBR and non-DBR devices. The average overall DBR devices of the intercepts J01 of the n ⫽ 1 component is (6.7⫾0.1) ⫻ 10⫺21 Am⫺2, which is significantly less than that of the control devices (8.9 ⫾ 0.3) ⫻ 10⫺21 Am⫺2. This reduction is consistent with the expectations of a model for the electroluminescence based on Eq. (1) as described in Ref. [21]. We believe this is the first direct observation of the effect of photon recycling on the dark current of a solar cell.
7. QWSCs FOR TANDEM AND THERMOPHOTOVOLTAIC APPLICATIONS The ability to tailor the bandgap of a GaAs-based cell without introduction of dislocations gives the SB-QWSC an advantage as the lower cell in a
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0.39 Current matching in bluer spectrum
0.38 0.37 Predicted efficiency
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0.32 0.31 0.30 1.0
1.5
2.0
2.5
Air Mass
Fig. 10. The predicted performance of tandem cells of GaInP/SB-QWSC and GaInP/GaAs tandems using measured dark currents at 300 and 800 suns.
GaInP/GaAs monolithic tandem-cell arrangement, where it is well known that the bottom GaAs cell limits the series current in most solar spectra. This advantage has been demonstrated theoretically and a typical result is shown in Fig. 10 [22]. The Quantax reactor has been unable to grow the GaInP top cell but its replacement, a Thomas Swan reactor, will have this facility and be able to grow tandem cells based on SB-QWSCs. The QWSC approach can be used in the GaInAsP/InP system and both lattice-matched and SB-QW cells have been demonstrated. The ability to tailor the bandgap and to operate at a higher voltage for a given output power has advantages for thermophotovoltaics, particularly in the case of narrow-band, rare-earth, radiant emitters. There is insufficient space in this chapter to discuss this work, but this application is extensively discussed in Ref. [23].
8. THE QUANTUM DOT CONCENTRATOR The luminescent concentrator was originally proposed in the late 1970s [24]. It consisted of a transparent sheet (thickness, D) doped with appropriate organic dyes. Sunlight incident on the top surface of the sheet (width, W, and length, L) is absorbed by the dye and then re-radiated isotropically. Ideally the luminescence has high quantum efficiency (QE) and much of the flux is trapped in the sheet by total internal reflection. The luminescence propagates
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by waveguide action along the length (L) of the waveguide to a cell (area ⫽ D·W) mounted at the edge of the sheet. This gives an upper limit to the concentration ratio of L/D if all the light is absorbed in the depth (D) and no luminescence is lost through the escape-cone or re-absorption. A stack of sheets doped with different dyes can separate the light, and solar cells can be chosen to match the different luminescent wavelengths to convert the trapped light at the edge of the module. The advantages over geometric concentrators include that solar tracking is unnecessary and that both direct and diffuse radiation can be collected. However, the development of this promising concentrator was limited by the stringent requirements on the luminescent dyes, particularly suitable red-shifts and stability under illumination [25]. The QDC is an updated version of the luminescent concentrator in which the dyes are replaced by QDs [4]. The first advantage of the QDs over dyes is the ability to tune the absorption threshold simply by choice of dot diameter. Secondly, since they are composed of crystalline semiconductor, the dots should be inherently more stable than dyes. Thirdly, the red-shift may be tuned by the choice of spread of QD sizes [4]. We have developed a series of thermodynamic models for single concentrator slabs and modules [26–28], which are comprised of a slab with a solar cell bonded to one edge. The models were developed by applying detailed balance arguments to relate the absorbed light to the spontaneous emission using self-consistent three-dimensional (3D) fluxes. The models were derived by applying the method of Schwarzschild and Milne [29], in which the angular dependence of the radiative intensity described by Chandrasekhar’s [30] general three dimensional transfer equation is ignored and the radiation is considered as consisting simply of forward (⫹) and backward (⫺) streams. We have extended this approach to streams parallel to the x, y and z axes of a concentrator slab and apply appropriate reflection boundary conditions to the radiation depending on whether it falls within the escape cone or the solid angle of total internal reflection. In addition to the forward and backward radiation streams in each co-ordinate direction, we also distinguish what happens when the direction of propagation, u is greater or less than the critical angle uc. Escaping photons with u⬍uc and trapped photons with u⬎uc are treated as separate streams [26–28]. The models allow for: (i) a significant fraction of the incident flux to be absorbed by the concentrator
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(ii) spectral overlap of the incident radiation with the luminescence (iii) re-absorption of radiation emitted into the escape cone (iv) losses due to absorption in the host material, all of which could not be accounted for in earlier models [31]. The model has recently been extended [28] to stacks of slabs doped with QD of different diameters so as to achieve higher efficiency matching slabs of different absorption thresholds to cells of appropriate bandgaps, as envisaged for the original dye-doped approach [25]. Full details of all the thermodynamic models can be found in Refs [26–28]. Here we will report some typical comparisons of the model with data. The detailed balance condition ensures that the trapped flux depends crucially on the absorption coefficient of the dots near threshold. This is analogous to the importance of the QW absorption coefficient a(E,F) in Eq. (3). However, the problem is more complex as the photon chemical potential m(x,y,z) varies much more strongly with position in the slab than the equivalent quasi-Fermi level separation ⌬EF in Eq. (3). For QDs with d-function density of states and Gaussian distributed diameters the dependence of the QD absorption near threshold a(Eg) is expected to be Gaussian in the photon energy Eg. The experimental absorption can often be fitted by a Gaussian down to threshold and this was the situation with the CdSe/CdS core-shell QDs in acrylic studied in Fig. 11. Given this a(Eg) the special variation of m(x,y,z) is fitted with a Newton–Raphson approach. Following convergence the fluxes escaping the surfaces of the slab can be calculated as shown in Fig. 11. The calculation agrees well with the shape and position of the flux collected by a solar cell mounted at the right surface. The figure also shows the gain in escaping flux at the edge compared with the flux escaping from the top surface. The luminescence in the flux at the edge is red-shifted due to re-absorption when compared to the flux escaping the top. This is also reproduced by the models. Short-circuit currents, Jsc, resulting from the radiation escaping the right surfaces of various slabs and modules were measured and are compared with the predicted values in Table 1. These measurements were performed on a slab of CdSe/CdS QDs in acrylic, a slab of red dye in Perspex, a mirrored slab of red dye in Perspex and a module comprising a slab of red dye in Perspex. In each case Jsc was measured using silicon solar cells, one of which was bonded to the edge of a slab of red dye in Perspex with sil-gel to form the module. The mirrored slab had aluminium evaporated onto the left, near, far and bottom surfaces.
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light incident on the top surface (AM1.5) average flux escaping the top surface
2.5 Flux/107 photons m-2 s-1
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2 1.5 1 0.5 0 1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
E/eV
Fig. 11. Predicted average fluxes escaping the top and right surfaces together with the normalised observed luminescence escaping the right surface for a L ⫻ W ⫻ D ⫽ 42 ⫻ 10 ⫻ 5 mm slab of CdSe/CdS QDs with QE ⫽ 0.5 in acrylic. The slab has perfect mirrors on the bottom, near, far and left surfaces and is illuminated by AM1.5 at normal incidence.
Table 1 Comparison of short-circuit currents with predictions of Thermodynamic Model Slab/module
CdSe/CdS QD slab Red dye slab Mirrored red dye slab Red dye module
Slab size (mm)
42 ⫻ 10 ⫻ 5 40 ⫻ 15 ⫻ 3 40 ⫻ 15 ⫻ 3 40 ⫻ 15 ⫻ 3
QE
0.50 0.95 0.95 0.95
Jsc/mA m⫺2 at x ⫽ L Exp
Pred
11.1 ⫾ 2.0 20.1 ⫾ 2.0 26.0 ⫾ 2.0 31.1 ⫾ 2.0
10.0 ⫾ 1.4 22.1 ⫾ 1.7 26.2 ⫾ 2.6 29.3 ⫾ 2.8
The slabs and module were positioned on a matt black stage with a matt black background to avoid unwanted reflections and were illuminated at normal incidence by a calibrated tungsten halogen lamp. The uncertainty in the measurements is due to current generated by coupling of the incident light into the edges of the solar cell. Allowance has been made for this by background measurements. The uncertainty in the predictions is mainly due to uncertainty in the low-absorption coefficient of the host material. In these calculations, we assumed that the reflectivity of the evaporated Al mirrors was 0.9 and that the Si concentrator cell, which has an anti-reflection coating
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and a textured surface, gives a reflectivity of 0.05 for the slab/sil-gel/cell interface in the module. It is encouraging for the 3D thermodynamic model that the measurements in Fig. 11 and Table 1 agree well with the predictions, in particular given that the materials have very different losses owing to the high QE of the dyes and relatively low QE of the QDs. Our confidence in the models is also increased by the agreement with experiment for the slab with mirrored surfaces and the further agreement for the module, which has a solar cell bonded to the exit face.
9. CONCLUSION We have demonstrated the performance of the SB-QWSC that makes it a good candidate for use in terrestrial high-concentration systems, particularly in the varying spectral conditions of a BICPV system. The advantages are: (i) Higher efficiency than comparable homostructure GaAs cells. (ii) Lower bandgap than GaAs, without dislocations, suitable for concentrator and multi-junction applications. (iii) Wider-spectral range than single-junction GaAs cells. (iv) Radiative-recombination dominated dark current for deep wells at concentrator current levels. (v) Dark currents reduced by photon-recycling demonstrated for the first time. We have also demonstrated a 3D thermodynamic model capable of describing the performance of dye-doped and QD-doped slabs of luminescent concentrators. The model is a powerful tool for analysing the performance of the luminescent concentrators. The fits show that concentrator performance is currently limited by the QE of the QDs dispersed in the plastics.
ACKNOWLEDGMENTS We have benefited from the financial support of the EPSRC, EU Framework VI, Ashden Trust and Imperial BP Strategic Alliance.
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K.W.J. Barnham, P. Abbott, I. Ballard, D.B. Bushnell, A.J. Chatten, J.P. Connolly, N.J. Ekins-Daukes, B.G. Kluftinger, J. Nelson, C. Rohr, M. Mazzer, G. Hill, J.S. Roberts, M.A. Malik and P. O’Brien, Electrochemical Society Proc., 2001–10 (2001) 31–45.
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K.W.J. Barnham, I. Ballard, J.P. Connolly, N.J. Ekins-Daukes, B.G. Kluftinger J. Nelson and C. Rohr, J. Mater. Sci.: Mater. Electron., 11 (2000) 531–536. N.J. Ekins-Daukes, K.W.J. Barnham, J.G. Connolly, J.S. Roberts, J.C. Clark, G. Hill and M. Mazzer, Appl. Phys. Lett., 75 (1999) 4195–4198. K. Barnham, J.L. Marques, J. Hassard and P. O’Brien, Appl. Phys. Lett., 76 (2000) 1197–1200. M.A. Green, K. Emery, D.L. King, S. Igori and W. Warta, Prog. Photovolt.: Res. Appl., 13 (2005) 387–392. J.S. Ward, M.W. Wanlass, K.A. Emery and T.J. Coutts, Proc. 23rd IEEE Photovoltaic Specialists Conf., pp. 650–654, Louisville, IEEE, 1993. D.J. Friedman, J.F. Geisz, S.R. Kurtz and J.M. Olson, 2nd World Conference and Exhibition on Photovoltaic Energy Conversion, pp. 3–7, Vienna, 1998. P.R. Griffin, J. Barnes, K.W.J. Barnham, G. Haarpaintner, M. Mazzer, C. Zanotti-Fregonara, E. Grunbaum, C. Olson, C. Rohr, J.P.R. David, J.S. Roberts, R. Grey and M.A. Pate, J. Appl. Phys., 80 (1996) 5815–5820. N.J. Ekins-Daukes, K. Kawaguchi and J. Zhang, Cryst. Growth Des., 2 (2002) 287–292. 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 and M. Mazzer, J. Mater. Sci., 40 (2005) 1445–1449. F. Dimroth, P. Lanyi, U. Schubert and A.W. Bett, J. Electron. Mater., 29 (2000) 42–46. R.R. King, C.M. Fetzer, P.C. Colter, K.M. Edmondson, D.C. Law, A.P. Stavrides, H. Yoon, G.S. Kinsey, H.L. Cotal, J.H. Ermer, R.A. Sherif, K. Emery, W. Metzger, R.K. Ahrenkiel and N.H. Karam, Proc. 3rd World Conf. Photovoltaic Energy Conversion, pp. 622–625, Osaka, 2003. D.B. Bushnell, K.W.J. Barnham, J.P. Connolly, M. Mazzer, N.J. Ekins-Daukes, J.S. Roberts, G. Hill, R. Airey and L. Nasi, J. Appl. Phys., 97 (2005) 124908. J.P. Connolly, J. Nelson, I. Ballard, K.W.J. Barnham, C. Rohr, C. Button, J.S. Roberts and C.T. Foxon, Proc. 17th European Photovoltaic Solar Energy Conf., Munich, Germany, pp. 204–207, 2001. J.P. Connolly, I.M. Ballard, K.W.J. Barnham, D.B. Bushnell, T.N.D. Tibbits and J.S. Roberts, Proc. 19th European Photovoltaic Solar Energy Conf., pp. 355–358, Paris, 2004. W. Shockley and W.T. Read, Phys. Rev., 87 (1952) 835; R.N. Hall, Phys. Rev., 87 (1952) 387. W.T. Shockley, Bell Syst. Tech. J., 28 (1949) 435. J. Nelson, J. Barnes, N. Ekins-Daukes, B. Kluftinger, E. Tsui, K. Barnham, C.T. Foxon, T. Cheng and J.S. Roberts, J. Appl. Phys., 82 (1997) 6240. A. Bessière, J.P. Connolly, K.W.J. Barnham, I.M. Ballard, D.C. Johnson, M. Mazzer and G. Hill, J.S. Roberts, Proc. 31st IEEE Photovoltaic Specialists Conf., pp. 679–683, Orlando, IEEE, 2005. A. Luque, A. Marti and L. Cuadra, IEEE Trans. Elect. Devices, 48 (2001) 2118–2124. D.C. Johnson, I.M. Ballard, K.W.J. Barnham, A. Bessière, D.B. Bushnell, J.P. Connolly, J.S. Roberts, G. Hill, C. Calder, Proc. 31st IEEE Photovoltaic Specialists Conf., Orlando, pp. 699–703, IEEE, 2005.
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[22] T.N. Tibbits, I.M. Ballard, K.W.J. Barnham, D.B. Bushnell, N.J. Ekins-Daukes, R. Airey, G. Hill and J.S. Roberts, Proc. 3rd World Conf. Photovoltaic Energy Conversion, pp. 2718–2721, Osaka, 2003. [23] J.P. Connolly and C. Rohr, Semicon. Sci. Technol., 18 (2003) 216–220. [24] A. Goetzberger and W. Greubel, Appl. Phys., 14 (1977) 123–139. [25] A. Goetzberger, W. Stahl and V. Wittwer, Proc. 6th European Photovoltaic Solar Energy Conf., pp. 209–215, Reidel, Dordrecht, 1985. [26] A.J. Chatten, K.W.J. Barnham, B.F. Buxton, N.J. Ekins-Daukes and M.A. Malik, Proc. 3rd World Conf. Photovoltaic Energy Conversion, pp. 2657–2660, Osaka, 2003. [27] A.J. Chatten, K.W.J. Barnham, B.F. Buxton, N.J. Ekins-Daukes and M.A. Malik, Proc. 19th European Photovoltaic Solar Energy Conf. Exhibition, pp. 109–112, Paris, (2004) 82–85. [28] A.J. Chatten, D. Farrell, C. Jermyn, P. Thomas, B.F. Buxton, A. Büchtemann, R. Danz and K.W.J. Barnham, Proc. 31st IEEE Photovoltaic Specialists Conf., Orlando, IEEE, 2005. [29] E.A. Milne, Monthly Notices Roy. Astron. Soc. Lond., 81 (1921) 361. [30] S. Chandrasekhar, Radiative Transfer, Clarendon, Oxford, UK, 1950. [31] E. Yablonovitch, J. Opt. Soc. Am., 70 (1980), p. 1362.
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Chapter 16
Quantum Well Solar Cells and Quantum Dot Concentrators K.W.J. Barnhama, I. Ballarda, A. Bessièrea, A.J. Chattena, J.P. Connollya, N.J. Ekins-Daukesa, D.C. Johnsona, M.C. Lyncha, M. Mazzera,d, T.N.D. Tibbitsa, G. Hillb, J.S. Robertsb and M.A. Malikc a
Blackett Laboratory, Physics Department, Imperial College London, London, SW7 2BW, UK b EPSRC National Centre for III-V Technologies, Sheffield S1 3JD, UK c Chemistry Department, University of Manchester, Manchester M13 9PL, UK d CNR-IMM, University Campus Lecce, Italy 1. INTRODUCTION This chapter reviews the development over the past half a decade of the quantum well solar cell (QWSC) and the quantum dot concentrator (QDC). The study of nanostructures such as quantum wells (QWs) and quantum dots (QDs) has dominated opto-electronic research and development for the past two decades. Photovoltaic (PV) applications of these nanostructures have been less extensively studied. Our group has pioneered the study of both QWs and QDs for PV applications. Others groups have made significant contributions, particularly to the study of lattice matched QWSCs and the theory of the cells, particularly in the ideal limit. These earlier contributions have been acknowledged in the two reviews, which were written at the turn of the new century [1,2]. In this chapter we will review recent advances since then, concentrating in particular on studies of the strain-balanced quantum well solar cell (SB-QWSC) as a concentrator cell [3] and the thermodynamic modelling of the QDC [4]. The SB-QWSC offers a way to extend the spectral range of the highest efficiency single-junction cell, the GaAs cell. We will discuss how this can in principle lead to higher efficiency in both single-junction and multi-junction cells and offers particular advantages in high-concentration systems. The high efficiency, wide spectral range and small cell size make these systems
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particularly attractive for high concentration, building-integrated applications using direct sunlight. The QDC is a novel, non-tracking concentrator. It is a promising approach for concentrating diffuse sunlight and is therefore complementary to the SB-QWSC in building integrated concentrator photovoltaics (BICPV).
2. STRAIN-BALANCED QUANTUM WELL SOLAR CELLS The highest efficiency single-junction solar cells under both 1-sun conditions and concentration are GaAs cells. Both single-junction records have held for a decade and a half [5]. The GaAs bandgap (1.42 eV) is, however, rather high as optimal efficiency requires a bandgap around 1.1 eV at both 1 sun and high concentration [6]. Since those records were established, the main effort to raise efficiency has gone into developing tandem cells, which can now achieve 37.4%. These have a high-bandgap GaInP top cell grown lattice matched to the GaAs bottom cell with electrical connection between the cells provided by a tunnel junction. As the cells are in series, the same current passes through both cells and is limited by the current generated in the poorer cell. This turns out to be the GaAs bottom cell in most spectra, again because of the relatively high GaAs bandgap. The utility of the tandem approach has yet to be demonstrated at the very high-concentration levels required for cost reduction and in the varied spectral conditions of building-integrated applications. A tandem or multi-junction cell can achieve high efficiencies when optimised at the series current level of specific spectral conditions and temperature. In the varying spectral conditions of BICPV, with the cell temperature varying, plus the difficulty of maintaining good tunnel junction performance at high-current levels, a highly efficient, single-junction cell with wide spectral range may well, over a year, harvest comparable electrical energy to a tandem cell with nominally higher efficiency. In summary, for terrestrial concentrator applications of “Third Generation” GaAs-based cells, either single- or multi-junction, it is important to be able to lower the bandgap of the conventional GaAs cell. The problem in doing so, which III–V cell designers have had to face for at least two decades, is that though there are higher-bandgap alloys such as GaInP and AlGaAs that can be grown lattice matched to GaAs, there is no lattice matched binary or ternary III–V compound with lower-bandgap than GaAs. To extend the GaInP/GaAs tandem cell efficiency, considerable effort is going into studying the quaternary GaInNAs which can be grown lattice matched to GaAs, but demonstrates poor minority carrier lifetimes resulting in insufficient current to avoid limiting the multi-junction performance [7].
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The addition of lattice-matched QWs to AlGaAs, InP and GaAsP cells has been shown to extend the spectral range and enhance the efficiency [1,2], but when it comes to enhancing the GaAs cell, the QW approach also suffers from the absence of a lattice matched lower-bandgap ternary alloy. A number
Fig. 1. (a) Schematic of SB-QWSC with compressively strained InxGa1⫺xAs wells and tensile-strained GaAs1⫺yPy barriers. (b) Energy band-edge diagram of p–i–n SB-QWSC. Note that the GaAs1⫺yPy barriers in the i-region are higher than the bulk GaAs in p and n regions.
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of strained InGaAs wells with lower-bandgap than GaAs and larger lattice constant can be grown compressively strained to GaAs. However, only a limited number of wells can be grown before relaxation occurs and these give insufficient current enhancement to overcome the loss of voltage [8]. In SB-QWSC, illustrated schematically in Fig. 1a, the low-bandgap, higher-lattice-constant (a2) alloy InxGa1–xAs wells (In composition x ⬃ 0.1–0.2) are compressively strained. The higher-bandgap, lower-lattice-constant (a1) alloy GaAs1–yPy barriers (P composition y ⬃ 0.1) are in tensile strain [3]. Of the many possible balance conditions we find that the zero-stress gives the best material quality [9] and enables at least 65 wells to be grown without relaxation [10]. Fig. 2 shows the spectral response of a 50 shallow well SB-QWSC. The cell is a p–i–n diode with an i-region containing 50 QWs 7 nm wide of compressively strained InxGa1–xAs with x ⬃ 0.1 inserted into tensile strained GaAs1–yPy barrier regions. The QWs extend absorption from bulk bandgap Eg to threshold energy Ea determined by the confinement energy as in Fig. 1b, giving the extra absorption and wider spectral response demonstrated in Fig. 2.
Fig. 2. Spectral response (external quantum efficiency at zero bias) of a 50-well SBQWSC. The fit shows separate contributions of p, i and n regions as discussed in the text.
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Alternative approaches to lowering the GaAs involve the growth of InGaAs on a relaxed virtual substrate [11, 12]. However, this approach inevitably results in material with a residual dislocation density. Dislocations are completely absent in a SB-QWSC [3]. This is important if the recombination is to be minimal, as discussed in the next section. It should be noted in Fig. 1 that the GaAsP barriers in the i-region have higher-bandgaps than GaAs, which also helps reduce the unwanted recombination.
3. IDEAL DARK-CURRENT BEHAVIOUR AT CONCENTRATOR CURRENT LEVELS An important observation has been made when studying the dark currents of a range of SB-QWSC with differing well number and depth. We observe that, at current levels corresponding to 200⫻ concentration and above, the dark currents of SB-QWSCs have ideality n ⫽ 1 as observed for the best GaAs p–n cells. The importance of this observation is that one can expect minimum recombination and maximum efficiency at high concentration. Concentration levels ⬃400⫻ are generally accepted to be necessary if GaAs cells are to be cost competitive in terrestrial systems. When we studied a range of SB-QWSCs with different well numbers and depth we observed a further, in this case unexpected, result. The reverse bias saturation current of the n ⫽ 1 contribution does not show the absorption threshold energy dependence expected of an ideal Shockley diode. We explain this behaviour in terms of two contributions to the n ⫽ 1 current as discussed below. A range of SB-QWSCs were grown by metal-organic vapour phase epitaxy (MOVPE) at the EPSRC National Centre for III–V Technologies, Sheffield. Further growth details can be found in Refs. [3, 13]. Growth included a series of structures with P fraction y ⫽ 0.08 and a varying number (10–65) of shallow 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). Details of the characterisation can be found in Refs. [5, 11]. Dark currents were measured at 25⬚C on fully metallised test diodes. A typical result is shown in Fig. 3. At currents corresponding to 200⫻ concentration and above the ideality n ⫽ 1 contribution dominates. We have measured the dark-current densities of between 8 and 18 fully metallised devices for each wafer and have fitted with two exponentials, one with ideality n ⬃ 2 and the other with ideality n fixed at 1.
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Fig. 3. Measured dark currents at 25⬚C of the device in Fig. 2 compared in the n ⬃ 2 region and the n ⫽ 1 region with the models discussed in the text.
J d ⫽ J 01 (eeV/kT ⫺1) ⫹ J 02 (eeV/nkT ⫺1)
(1)
The reverse bias saturation current density of the n ⫽ 1 contribution (J01), which we estimate from the zero bias intercept of the ideality n ⫽ 1 fit, is plotted in Fig. 4 against the threshold energy Ea. The latter we take to be the energy of the e1–h1 exciton for the SB-QWSCs and the GaAs bulk bandedge for the homostructure p–i–n control cell. For each wafer in Fig. 4 we show the extrapolated intercept for the device with lowest dark current. In Ref. [4] we argue that the lowest dark current is the one most representative of the structure. The experimental increase in intercept with well number at fixed band edge is not very marked, as discussed later. The absorption edge dependence of the intercept J01 of the n ⫽ 1 contribution is expected to be determined by the square of the intrinsic carrier density and therefore to vary exponentially with band edge as indicated by the line based on the control homostructure p–i–n cell. In fact, the trend of the data is significantly below this expectation, particularly as the wells get deeper.
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GaAs p-i-n control Intercept Jo of n = 1 Am-2
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Lowest Jo Data trend
1E-14
1E-15
1E-16 1.25
1.3
1.35 1.4 Absorption Edge (eV)
1.45
Fig. 4. Reverse bias saturation current density (J01) from the intercept of the ideality n ⫽ 1 fits to the lowest measured dark current, plotted against exciton position.
4. MODELLING THE n ⬃2 AND n ⴝ 1 DARK-CURRENT BEHAVIOUR To explain this unexpected behaviour, as the wells get deeper, we describe the data in the n ⬃ 2 region with a model we have developed for QWSCs in two lattice-matched material systems [14, 15]. 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 [16]. This requires the non-radiative lifetimes of the carriers. The evidence suggests we can equate the electron and hole lifetimes [14] so we are left with two parameters which depend on material quality, the carrier lifetimes tB and tW in the barrier and well, respectively. For lattice-matched QWSCs, we determine these two parameters by fitting homostructure or double heterostructure controls which have i-regions formed from the material of the barrier or the well, respectively. In the case of SB-QWSC, bulk material of
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comparable bandgap to the QW and of similar material quality does not exist. We assume that, for these low P and In fractions, the well and barrier quality are sufficiently similar, “so that the lifetimes can be considered to be equal” (i.e., tB ⫽ tW ⫽ t). We find reasonable fits can be obtained to the n ⬃ 2 region of the dark current of these variable well samples with the single parameter t. We anticipate that there are two distinct contributions to the n ⫽ 1 current. Firstly the standard, ideal Shockley diode current [17]. 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 field-free regions. This contribution depends in a standard way on the minority-carrier diffusion lengths, doping levels and the surface recombination in the neutral regions [17]. We can estimate this current from the minority-carrier parameters obtained when fitting the spectral response in the neutral regions as in Fig. 2. Further examples are given in Ref. [15] where details can be found including the effect of strain on QW depth and barrier height. 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. This relates the photons absorbed to the photons radiated, as discussed in Ref. [18] and references cited therein. The radiated spectrum as a function of photon energy E in an electrostatic field F, L(E,F) dE, is determined by the generalised Planck equation: L ( E , F ) dE ⫽
2pn2 LW a( E , F )E 2 dE h3c 2 e( E⫺⌬EF ) /kBT ⫺1
(2)
We integrate this spectrum over the energy and the cell geometry as described in Ref. [18] to give a total radiative current. This will depend on the quasi-Fermi level separation ⌬EF and the absorption coefficient a(E,F) as a function of energy and field. For this study, we assume that ⌬EF ⫽ eV where V is the diode bias. In Section 5, we discuss evidence from singleand 5-well SB-QWSCs that ⌬EF ⬍ eV though we have yet to observe this effect in the high well-number samples reported here [19].
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1.00E-13
Intercept Jo1 Am-2
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Model - deep wells Data - deep wells Model - shallow wells Data - shallow wells
1.00E-14
1.00E-15 5
10 15 20 25 30 35 40 45 50 55 60 65 70 Well Number
Fig. 5. Mean of measurements of the intercept of the n ⫽ 1 dark current from fits to 8–18 devices with n ⬃ 2 and n ⫽ 1 exponential terms. Data are plotted against number of wells and compared with the radiative plus ideal model described in the text.
The absorption coefficient a(E,F) is calculated from first principles [18] 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. 2. The sum of the two n ⫽ 1 terms is compared with the typical data in Fig. 3. In Fig. 5 the measured mean intercept from the experimental double-exponential fits is compared with the sum of the Shockley ideal and QW-radiative terms. Reasonable agreement is observed even though there are essentially no free parameters for the model. Note also that for a given well depth the intercept is only weakly dependent on the well number. Fig. 6 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. 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. We conclude that at concentrator current levels the ideality n ⫽ 1 behaviour becomes increasingly dominated by radiative recombination in the wells
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1 Radiative Fraction
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1.28
1.3 1.32 1.34 Absorption Edge (eV)
1.36
1.38
Fig. 6. Ratio of QW-radiative well current to sum of QW-radiative current plus ideal Shockley current against QW absorption edge given by first exciton position.
rather than non-radiative and radiative recombination in the GaAs p and n regions as the wells get deeper. This is important not only because deeper wells take the cell to absorption edges corresponding to higher efficiency [6] but also because the recombination can be further reduced by photon recycling techniques to be discussed in Section 6. However, to get PV power form these devices we must first consider if this low-recombination behaviour persists under light illumination as will be discussed in the next section.
5. TESTING ADDITIVITY IN SB-QWSCS In the last section the dark current Jd behaviour of SB-QWSC, described by Eq. (1), was discussed at some length. Under illumination, the current–voltage curve J(V) of the highest efficiency III–V cells can generally be described by J (V ) ⫽ J sc ⫺ J d
(3)
where Jsc ⫽ J(0) is the short-circuit current density. It is important to check if the additivity condition in Eq. (3) holds in SB-QWSCs for three reasons: (i) The ideal dark-current behaviour discussed in the last section will only translate into high efficiency if it does hold.
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(ii) There are theoretical claims based on a thermodynamic model that the suppressed radiative recombination we have observed in the dark in low well number QWSCs [18,19] will result in increased recombination in the light [20]. (iii) QWSCs are p–i–n devices and the built-in field must be maintained across the i-region at the operating bias to ensure efficient collection of photo-generated carriers. Background doping in the i-region or the build-up of one or other of the charge carriers in the wells could lead to the failure of additivity and a resulting loss of efficiency. We have tested additivity for the 1-, 5- and 10-well samples used to confirm that the suppressed radiative recombination observed in low-well number strained and lattice-matched QWSCs also occurs in the SB devices [19]. The SB-QWSCs were light-biased to the zero-current, open-circuit voltage Voc by illumination with a laser exciting on the continuum in the QW and the photoluminescence (PL) spectrum measured with a spectrometer and charged coupled device (CCD) system. The laser intensity is equivalent to around 1 sun. The PL spectrum is then compared with the electroluminescence spectrum (EL) obtained when the laser is turned off and the cell biased externally to the same voltage (0.88 V in the example in Fig. 7) at the same temperature. Significant radiative recombination suppression is observed in the 1- and 5-well SB-QWSC, consistent with the earlier strained- and lattice-matched QWSCs [19]. The suppression is smaller in the 5-well devices, consistent with the zero suppression observed in the 10-well case. However, in the 1-, 5and 10-well samples the PL and EL spectra are virtually identical, as can be seen for the single-well example in Fig. 7. At Voc the J(V) in Eq. (3) is zero and the equality of the PL and EL spectra suggest that the photo-generated recombination (PL) and the radiative-dark current (EL) cancel. This result is not consistent with the model in Ref. [20]. It is important to extend these tests to higher-current levels corresponding to the high concentrations in which these cells must operate for cost-effective terrestrial applications and to current levels where good dark-current performance is observed. Here the main problem becomes the challenge of contact fabrication such that resistance effects are minimised. We are currently limited by device processing. This can be seen in Fig. 8 where we show the efficiency of a 50-well SB-QWSC as a function of concentration. The cell parameters were measured in a 3000 K black-body spectrum in a shuttered measurement system. The 1-sun intensity was set by calculating the shortcircuit current level Isc to be expected by integrating the measured spectral response of the cell over an AM1.5D spectrum. The cell was then moved
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100000 EL PL
Intensity (a.u)
10000
1000
100 1.28
1.32
1.36 1.40 Energy (eV)
1.44
1.48
1.52
Fig. 7. Photo-luminescence (full line) and electroluminescence (scattered points) spectra at 290.9 K of the single-well SB-QWSC biased at ⫹0.88 V. Data points in the filter window have been removed.
28 26 Efficiency (%)
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22
Data for QT1628 Predicted for QT1628 Data for p-n cell
20
Predicted for p-n cell World Record
18 1
10
100
1000
Log (No. of Suns)
Fig. 8. Efficiency of 50-well SB-QWSC measured in a shuttered concentrator system compared with p–n control cell. The full lines show the predictions of additivity. If additivity holds at high concentration, the QW cell could achieve an efficiency close to the World single-junction record [5].
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closer to the illumination with its temperature maintained by a Peltier control system. The cell position was optimised at each distance, and the effective concentration was assumed to be proportional to Isc. The first observation to be noted from Fig. 8 is that the 50 shallow-well SB-QWSC has a significantly higher efficiency than that of the p–n cell, which has comparable material quality. The prediction of additivity in Eq. (3) is shown for both cells by the full lines. These were generated assuming Jd was given by fits to the measured dark current, which included the cell series resistance measured in the dark. The data fall significantly below this prediction at ⬃200 suns. This could be the result of an extra resistive term under light-generation or the failure of additivity at high concentration. We believe the former explanation at present as the effect is also observed in the p–n cell, which has no i-region. Furthermore, EL studies indicate that the deviation from additivity is accompanied by non-uniform current behaviour. We are currently studying improvements to our masks and contacting procedures in order to extend the additivity studies to higher-concentration levels and to challenge the World single-junction efficiency limit.
6. PHOTON RECYCLING IN SB-QWSCs As mentioned in Section 5, the dominance of radiative recombination at high-current levels suggests that the dark current could be further reduced by photon recycling schemes. The analysis presented there indicated that radiative recombination in the wells dominates over radiative and nonradiative recombination in the GaAs regions. A SB-QWSC is ideal therefore to observe photon recycling effects as the generalised-Planck equation in Eq. (2) favours the emission of photons well below the GaAs bandgap energy that can be reflected by a distributed Bragg reflector (DBR) at the back of the cell. These will only be re-absorbed in the QWs rather than regions of the cell where non-radiative recombination dominates as occurs in conventional homostructure cells. A number of 50-well SB-QWSCs have been grown at the EPSRC National Centre for III–V Technologies in the Quantax reactor, which will take two substrates. One, the upstream wafer (U) was a conventional GaAs wafer. The second, GaAs substrate, the downstream one (D), had a 20.5 period DBR optimised for high reflectivity within the QW wavelengths, which had been grown in an earlier run. A SB-QWSC was then grown on both wafers so that the overgrown device was as similar as possible and comparison of the U and D wafer would enable the effect of the DBR to be extracted.
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Fig. 9. (a) Typical dark current of a 50-well SB-QWSC control (squares) and DBR (circles) cell showing the ideality n ⫽ 1 (solid) and ideality n ⬃ 2 (dotted) dark-current components. (b) High-bias results plotted separately for the 20 devices in each case. Ideality n ⫽ 1 dark currents for QT1910 control devices (broken lines) and DBR devices (full lines) clearly have different reverse saturation currents J01.
The wafers were first processed as fully metallised diodes to minimise resistive effects such as those discussed in the last section. The dark currents of 20 different devices were measured from both the DBR (D) and control (U) wafers. Typical dark currents for a wafer QT1910 with 50 relatively deep (In ⬃ 0.17) wells are shown in Fig. 9a. The ideality n ⬃ 2 and n ⫽ 1 components from a fit of the dark current to Eq. (1) are also shown. The dark currents of all the QT1910 devices shown in Fig. 9b clearly display a separation between the DBR and non-DBR devices at high voltage when radiative recombination dominates. On the other hand, the Shockley–Read–Hall ideality n ⬃ 2 dark-current component is not significantly changed between the DBR and non-DBR devices. The average overall DBR devices of the intercepts J01 of the n ⫽ 1 component is (6.7⫾0.1) ⫻ 10⫺21 Am⫺2, which is significantly less than that of the control devices (8.9 ⫾ 0.3) ⫻ 10⫺21 Am⫺2. This reduction is consistent with the expectations of a model for the electroluminescence based on Eq. (1) as described in Ref. [21]. We believe this is the first direct observation of the effect of photon recycling on the dark current of a solar cell.
7. QWSCs FOR TANDEM AND THERMOPHOTOVOLTAIC APPLICATIONS The ability to tailor the bandgap of a GaAs-based cell without introduction of dislocations gives the SB-QWSC an advantage as the lower cell in a
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0.39 Current matching in bluer spectrum
0.38 0.37 Predicted efficiency
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0.36 0.35 0.34 0.33 QT1405R 300 suns (p-n) QT1405R 800 suns (p-n) QT1744 800 suns (MQW) QT1744 300 suns (MQW)
0.32 0.31 0.30 1.0
1.5
2.0
2.5
Air Mass
Fig. 10. The predicted performance of tandem cells of GaInP/SB-QWSC and GaInP/GaAs tandems using measured dark currents at 300 and 800 suns.
GaInP/GaAs monolithic tandem-cell arrangement, where it is well known that the bottom GaAs cell limits the series current in most solar spectra. This advantage has been demonstrated theoretically and a typical result is shown in Fig. 10 [22]. The Quantax reactor has been unable to grow the GaInP top cell but its replacement, a Thomas Swan reactor, will have this facility and be able to grow tandem cells based on SB-QWSCs. The QWSC approach can be used in the GaInAsP/InP system and both lattice-matched and SB-QW cells have been demonstrated. The ability to tailor the bandgap and to operate at a higher voltage for a given output power has advantages for thermophotovoltaics, particularly in the case of narrow-band, rare-earth, radiant emitters. There is insufficient space in this chapter to discuss this work, but this application is extensively discussed in Ref. [23].
8. THE QUANTUM DOT CONCENTRATOR The luminescent concentrator was originally proposed in the late 1970s [24]. It consisted of a transparent sheet (thickness, D) doped with appropriate organic dyes. Sunlight incident on the top surface of the sheet (width, W, and length, L) is absorbed by the dye and then re-radiated isotropically. Ideally the luminescence has high quantum efficiency (QE) and much of the flux is trapped in the sheet by total internal reflection. The luminescence propagates
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by waveguide action along the length (L) of the waveguide to a cell (area ⫽ D·W) mounted at the edge of the sheet. This gives an upper limit to the concentration ratio of L/D if all the light is absorbed in the depth (D) and no luminescence is lost through the escape-cone or re-absorption. A stack of sheets doped with different dyes can separate the light, and solar cells can be chosen to match the different luminescent wavelengths to convert the trapped light at the edge of the module. The advantages over geometric concentrators include that solar tracking is unnecessary and that both direct and diffuse radiation can be collected. However, the development of this promising concentrator was limited by the stringent requirements on the luminescent dyes, particularly suitable red-shifts and stability under illumination [25]. The QDC is an updated version of the luminescent concentrator in which the dyes are replaced by QDs [4]. The first advantage of the QDs over dyes is the ability to tune the absorption threshold simply by choice of dot diameter. Secondly, since they are composed of crystalline semiconductor, the dots should be inherently more stable than dyes. Thirdly, the red-shift may be tuned by the choice of spread of QD sizes [4]. We have developed a series of thermodynamic models for single concentrator slabs and modules [26–28], which are comprised of a slab with a solar cell bonded to one edge. The models were developed by applying detailed balance arguments to relate the absorbed light to the spontaneous emission using self-consistent three-dimensional (3D) fluxes. The models were derived by applying the method of Schwarzschild and Milne [29], in which the angular dependence of the radiative intensity described by Chandrasekhar’s [30] general three dimensional transfer equation is ignored and the radiation is considered as consisting simply of forward (⫹) and backward (⫺) streams. We have extended this approach to streams parallel to the x, y and z axes of a concentrator slab and apply appropriate reflection boundary conditions to the radiation depending on whether it falls within the escape cone or the solid angle of total internal reflection. In addition to the forward and backward radiation streams in each co-ordinate direction, we also distinguish what happens when the direction of propagation, u is greater or less than the critical angle uc. Escaping photons with u⬍uc and trapped photons with u⬎uc are treated as separate streams [26–28]. The models allow for: (i) a significant fraction of the incident flux to be absorbed by the concentrator
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(ii) spectral overlap of the incident radiation with the luminescence (iii) re-absorption of radiation emitted into the escape cone (iv) losses due to absorption in the host material, all of which could not be accounted for in earlier models [31]. The model has recently been extended [28] to stacks of slabs doped with QD of different diameters so as to achieve higher efficiency matching slabs of different absorption thresholds to cells of appropriate bandgaps, as envisaged for the original dye-doped approach [25]. Full details of all the thermodynamic models can be found in Refs [26–28]. Here we will report some typical comparisons of the model with data. The detailed balance condition ensures that the trapped flux depends crucially on the absorption coefficient of the dots near threshold. This is analogous to the importance of the QW absorption coefficient a(E,F) in Eq. (3). However, the problem is more complex as the photon chemical potential m(x,y,z) varies much more strongly with position in the slab than the equivalent quasi-Fermi level separation ⌬EF in Eq. (3). For QDs with d-function density of states and Gaussian distributed diameters the dependence of the QD absorption near threshold a(Eg) is expected to be Gaussian in the photon energy Eg. The experimental absorption can often be fitted by a Gaussian down to threshold and this was the situation with the CdSe/CdS core-shell QDs in acrylic studied in Fig. 11. Given this a(Eg) the special variation of m(x,y,z) is fitted with a Newton–Raphson approach. Following convergence the fluxes escaping the surfaces of the slab can be calculated as shown in Fig. 11. The calculation agrees well with the shape and position of the flux collected by a solar cell mounted at the right surface. The figure also shows the gain in escaping flux at the edge compared with the flux escaping from the top surface. The luminescence in the flux at the edge is red-shifted due to re-absorption when compared to the flux escaping the top. This is also reproduced by the models. Short-circuit currents, Jsc, resulting from the radiation escaping the right surfaces of various slabs and modules were measured and are compared with the predicted values in Table 1. These measurements were performed on a slab of CdSe/CdS QDs in acrylic, a slab of red dye in Perspex, a mirrored slab of red dye in Perspex and a module comprising a slab of red dye in Perspex. In each case Jsc was measured using silicon solar cells, one of which was bonded to the edge of a slab of red dye in Perspex with sil-gel to form the module. The mirrored slab had aluminium evaporated onto the left, near, far and bottom surfaces.
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3
light incident on the top surface (AM1.5) average flux escaping the top surface
2.5 Flux/107 photons m-2 s-1
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average flux escaping the right surface observed luminescence escaping the right surface
2 1.5 1 0.5 0 1.65
1.75
1.85
1.95
2.05
2.15
2.25
2.35
2.45
2.55
E/eV
Fig. 11. Predicted average fluxes escaping the top and right surfaces together with the normalised observed luminescence escaping the right surface for a L ⫻ W ⫻ D ⫽ 42 ⫻ 10 ⫻ 5 mm slab of CdSe/CdS QDs with QE ⫽ 0.5 in acrylic. The slab has perfect mirrors on the bottom, near, far and left surfaces and is illuminated by AM1.5 at normal incidence.
Table 1 Comparison of short-circuit currents with predictions of Thermodynamic Model Slab/module
CdSe/CdS QD slab Red dye slab Mirrored red dye slab Red dye module
Slab size (mm)
42 ⫻ 10 ⫻ 5 40 ⫻ 15 ⫻ 3 40 ⫻ 15 ⫻ 3 40 ⫻ 15 ⫻ 3
QE
0.50 0.95 0.95 0.95
Jsc/mA m⫺2 at x ⫽ L Exp
Pred
11.1 ⫾ 2.0 20.1 ⫾ 2.0 26.0 ⫾ 2.0 31.1 ⫾ 2.0
10.0 ⫾ 1.4 22.1 ⫾ 1.7 26.2 ⫾ 2.6 29.3 ⫾ 2.8
The slabs and module were positioned on a matt black stage with a matt black background to avoid unwanted reflections and were illuminated at normal incidence by a calibrated tungsten halogen lamp. The uncertainty in the measurements is due to current generated by coupling of the incident light into the edges of the solar cell. Allowance has been made for this by background measurements. The uncertainty in the predictions is mainly due to uncertainty in the low-absorption coefficient of the host material. In these calculations, we assumed that the reflectivity of the evaporated Al mirrors was 0.9 and that the Si concentrator cell, which has an anti-reflection coating
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and a textured surface, gives a reflectivity of 0.05 for the slab/sil-gel/cell interface in the module. It is encouraging for the 3D thermodynamic model that the measurements in Fig. 11 and Table 1 agree well with the predictions, in particular given that the materials have very different losses owing to the high QE of the dyes and relatively low QE of the QDs. Our confidence in the models is also increased by the agreement with experiment for the slab with mirrored surfaces and the further agreement for the module, which has a solar cell bonded to the exit face.
9. CONCLUSION We have demonstrated the performance of the SB-QWSC that makes it a good candidate for use in terrestrial high-concentration systems, particularly in the varying spectral conditions of a BICPV system. The advantages are: (i) Higher efficiency than comparable homostructure GaAs cells. (ii) Lower bandgap than GaAs, without dislocations, suitable for concentrator and multi-junction applications. (iii) Wider-spectral range than single-junction GaAs cells. (iv) Radiative-recombination dominated dark current for deep wells at concentrator current levels. (v) Dark currents reduced by photon-recycling demonstrated for the first time. We have also demonstrated a 3D thermodynamic model capable of describing the performance of dye-doped and QD-doped slabs of luminescent concentrators. The model is a powerful tool for analysing the performance of the luminescent concentrators. The fits show that concentrator performance is currently limited by the QE of the QDs dispersed in the plastics.
ACKNOWLEDGMENTS We have benefited from the financial support of the EPSRC, EU Framework VI, Ashden Trust and Imperial BP Strategic Alliance.
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