Thermophotovoltaic (TPV) devices: introduction and modelling

4 Thermophotovoltaic (TPV) devices: introduction and modelling R. J. NICHOLAS and R. S. TULEY, University of Oxford, UK

Abstract: An introduction is given to thermophotovoltaic (TPV) systems which are used to convert radiant energy from hot bodies directly into electricity, together with a review of current photovoltaic device performance. Detailed modelling of the devices is described for a variety of sources and spectral control systems, varying the bandgap of the devices to determine the optimum configuration for different systems. Key words: thermophotovoltaic (TPV) devices, spectral control, photovoltaic device modelling, tandem TPVs, indium gallium arsenide TPV cells.

4.1

Introduction to thermophotovoltaics (TPVs)

The basic principle of a thermophotovoltaic (TPV) system is that it uses the thermal radiation emitted from a hot body which is not the sun to generate electricity using the sample principles as a conventional photovoltaic (PV) cell. Due to the lower temperature the peak emission wavelength is longer and this means that it is necessary to use materials with a lower bandgap, which makes it more difficult to achieve high efficiency. A typical TPV system consists of four main components: a radiative heat source, normally in the range 1000–1800 K; a selective emitter and filters for spectral control; a PV cell; and a cooling system. An outline of such a system is shown in Fig. 4.1. The main differences between TPV and conventional solar cells are the lower temperature sources found in a TPV system and the much closer proximity of cell to the source (∼1–10 cm in TPV compared to 1.5 × 1010 m to the Sun), resulting in much higher power densities (5–60 compared with 0.1 Wcm−2). These power densities are comparable to those reached by a concentrating solar system. These high power densities make more expensive, higher efficiency cells an attractive option, both for TPV and solar concentrator applications. In addition, unlike solar systems, TPV systems allow control of the emitter, including reflection or suppression of the emission of photons which cannot be harnessed efficiently by the cell, thus increasing the system efficiency. This also results in reduced demands on cell cooling and a reduced input energy (fuel) to heat the emitter. 67 © Woodhead Publishing Limited, 2012

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Heat energy input

Selective emitter spectrum

Radiation re-emitted backwards or in waste combustion gases

Filtered spectrum

Filter reflection

Emitter

Spectral filter

Electrical energy

Heat energy via cell cooling

Cell reflection

TPV cells

4.1 The outline of a TPV system, showing the main components, the energy input and outputs and the internal radiative transfers.

TPV systems have been proposed both as power sources on their own – for example, for portable electricity generation and in applications where the heat output can also be usefully used, as in combined heat and power (CHP) generation systems. Advantages of TPV systems include: high power densities (>1 Wcm−2), potentially allowing them to be lightweight; versatile fuel usage; quiet operation with no moving parts (and so low maintenance); and controllability, allowing supply and demand to be in phase. A simple TPV power conversion system was first demonstrated by Kolm in 1956, but interest in the field only grew significantly after lectures by P. Aigrain at MIT in 1960–1961 (Nelson, 2003). The continuing development of high-efficiency, low-bandgap cells has renewed interest in this field. A brief discussion of various energy sources, spectral control schemes and TPV cells which have been reported now follows. A more detailed introduction to the field of TPV can be found in Coutts (1999), Krier (2006) and Chubb (2007).

4.1.1 Energy sources for TPV The required heat energy input can be from a wide range of sources, including: combustion of gas (Kushch et al., 1997; Durisch et al., 2003; Fraas et al., 2003) or wood (Broman and Marks, 1994) for combined heat and power production in boiler systems or in off-grid locations; diesel combustion (Horne et al., 2003) for mobile power sources; radioisotope decay (Schock et al., 1995; Wilt et al., 2007) for deep-space missions; high-temperature waste heat such as in the glass industry (Bauer, 2003); or even from the Sun itself (see Section 4.5). These heat sources generally result in a source temperature of 1000–1800 K (Coutts, 1999; Nagpal et al., 2008). As will be seen later, lower temperatures than this make it increasingly difficult to achieve reasonable efficiencies, while higher combustion temperatures lead to NOx

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emissions which exceed safe limits. In a CHP system the waste heat energy – from cooling the cells and in the waste combustion gases – is an important part of the system and is used, for example to pre-heat hot water in a boiler system (Kushch et al., 1997), or provide room heating (Fraas et al., 1999). This increases the useful energy output, and puts less stringent demands on the spectral control as the cell electrical output is not the sole determining factor. The largest potential market is for CHP boilers which, based on a 1 kW electrical output per system, would suggest a potential total market in a country the size of the UK of the order of 20 GW for TPV cells. Such systems would need to compete against mechanical systems based on Stirling engines or the Rankine cycle but have the intrinsic advantage of a lack of moving parts.

4.1.2 Spectral control Spectral control improves the system performance substantially by suppressing the large quantity of long-wavelength, sub-bandgap photons present in the blackbody spectrum. Spectral control can be achieved by the use of either a selective emitter which has a reduced emissivity in the unwanted parts of the spectrum, or by the use of a filter system which can return unusable photons back to the source, or by a combination of the two. This leads to a higher cell efficiency, as the incident power density has fallen without the electrical output power changing. A higher efficiency is necessary to decrease the running costs of the system (less fuel), to enable easier heat management of the cells, and potentially to allow higher emitter temperatures, as less total radiation is emitted. It should be noted, however, that the absolute power output per unit of cell area is not increased as the spectral control is only removing unusable photons. Generally, a selective emitter or single filter alone is not sufficient to fully control the spectral properties of the system, so a combination of several control mechanisms is often used. By using several components, the requirements for any one individual part are relaxed, so that photon suppression can be achieved with both a sharp turn-on and a broad response range. For typical TPV sources this means that the optimum part of the spectrum is the range 1–2 µm. A variety of selective emitters have been proposed, and a few practical implementations are shown in Fig. 4.2. Selective emitters can either be broadband, mainly suppressing the sub-bandgap photons, such as NiOdoped ceramic (Ferguson and Dogan, 2001) or the AR-tungsten (Fraas et al., 2000), or act like a bandpass filter, such as the erbium mantle (Bitnar et al., 2002), which also reduces significantly above-bandgap photons which experience large thermalization losses. However, a bandpass system reduces

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Spectral energy density (Wm–3sr–1)

LM InGaAs bandgap Blackbody Erbium mantle AR tungsten with filter NiO doped ceramic

4.0 × 1010 3.0 × 1010

2.0 × 1010 1.0 × 1010

0.0 1000

2000

3000

4000

5000

Wavelength (nm)

4.2 The large long-wavelength tail at 1600 K cannot be used by a 0.74 eV lattice-matched InGaAs cell, so spectral control is required to suppress this emission. The example spectral control schemes shown here have been taken from measured emissitivities in the literature. (Source: Bitnar et al., 2002; Fraas et al., 2000; Ferguson and Dogan, 2001.)

the power output available, so to produce a net improvement in efficiency, the suppression of out of band radiation must be very good (Section 4.6.3). Additionally, since the cost of the cells is often a significant fraction of the capital cost of the system (Fraas et al., 2003; Palfinger et al., 2003), a high output power density is required in order to achieve a low capital cost for the same system power. Other spectral control systems have been demonstrated, including dielectric stacks combined with plasma filters (Rahmlow et al., 2007), resonant antenna arrays (Horne et al., 2005), photonic crystals (Mao and Ye, 2010) and tungsten lattices (Seager et al., 2005). The highest efficiency system reported to date (>23%), which was developed for a space application (Wernsman et al., 2004) combines a dielectric stack and plasma filter with the additional step of utilizing back-reflectance from the back of the PV cell’s substrate. Another interesting approach is to use near-field effects – by reducing the gap between emitter and cells to less than the wavelength, which allows the total radiative energy transfer to exceed the Stefan–Bolzmann law for the far-field. The power transfer increase is related to the square of the smaller of the refractive indices of the emitter and cell (Pan et al., 2000). This could produce a large increase in the photocurrent without having a significant impact on the dark current (Whale and Cravalho, 2002; Laroche et al., 2006). Experimentally, increases of 3–15 times have been observed (DiMatteo et al., 2001), but so far only with low emitter temperatures (up to 1100 K), limiting the total power transferred.

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Further discussion of potential spectral control schemes can be found in Coutts (1999) and Licciulli et al. (2003), while the effect of a range of different spectral control schemes is modelled in Section 4.6.3.

4.2

Practical TPV cell performance

Several PV cell types have been used in TPV systems, and are reviewed in this section. Initial work used silicon solar cells developed for solar photovoltaics, and these are still investigated for high-temperature sources with selective emitters (Durisch et al., 2003), as they can offer cost savings. However, silicon has a rather high bandgap (1.1 eV) for most TPV work (Coutts, 1999 and Section 4.6.3), so electrical efficiencies have only reached ∼2% (Durisch et al., 2003). Germanium cells with bandgap 0.66 eV have also been developed (Andreev, 2003, and references within), but due to the larger electron effective mass (and so higher intrinsic carrier concentration) and difficulties passivating the germanium surface (Coutts, 1999; Khvostikov et al., 2007), the open-circuit voltage Voc is generally lower than can be achieved in other materials. Germanium cells have a cost advantage however, and cells have been produced which will give efficiencies of order 10% if the back surface reflection efficiency is 85%. The majority of work has focused therefore on GaSb (0.73 eV) based materials or In1−xGaxAs on InP substrates (bandgap of 0.74 eV when lattice matched, lower when lattice mismatched). GaSb cells have been produced with high Voc and high efficiencies at high current densities (Fraas et al., 1997; Andreev, 2003; Bett and Sulima, 2003 and references within). GaSb cells have demonstrated slightly inferior performance compared to InGaAs cells in a system (Fraas et al., 2003), but based on dark currents the performance is comparable (Charache, 1999). Currently, GaSb substrates are more expensive than InP substrates (although this disparity is partly due to the lower volume of GaSb produced (Fraas et al., 2003)). JXCrystals have commercialized a basic TPV system using GaSb cells (the Midnight Sun) (Fraas et al., 2003) which operate at an output level of order 2.5 W/cm2. Other materials can be grown on GaSb, such as GaxIn1−xAsySb1−y, lattice matched to GaSb with 0.29 ≤ Eg ≤ 0.73 (Mauk and Andreev, 2003). This system however has a miscibility gap, in which alloys are metastable and prone to decomposition, which limits the lowest practical bandgap to 0.53 eV, but high-quality cells can be produced down to this value (Charache et al., 1999; Mauk and Andreev, 2003; Dashiell et al., 2006). High-quality InGaAs TPV cells have been developed by a number of authors, with both lattice-matched 0.74 eV InGaAs cells (Wilt et al., 1994, 2004; Wanlass et al., 1996; Hudait et al., 2002; Karlina et al., 2007) and mismatched cells produced. Output levels of up to 3.5 W/cm2 at 15% efficiency have been reported for lattice-matched cells with high temperature

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(∼1800 K) illumination. The majority of the lattice-mismatched work has concentrated on 0.6 eV (Hudait et al., 2003, 2009; Wernsman et al., 2004; Newman et al., 2006; Su et al., 2007; Cederberg et al., 2008) with some work at bandgaps down to 0.5 eV (Wojtczuk et al., 1996; Wehrer et al., 2004). A significant driver for work on this material has been for space applications with a radioisotope heat source (Schock et al., 1995; Wilt et al., 2007). In this case the significant factors become weight and reliability, rather than cost, and efficiencies of up to ∼20% and power generation of 12 W/kg have been reported (Wilt et al., 2007). Replacing the standard planar junction with a dot junction (Sinharoy et al., 2005) has also been considered, but no experimental improvement over planar cells has currently been demonstrated. Table 4.1 shows a summary of some of the best results for the InGaAsP system, with values for Voc as calculated from the modelling Table 4.1 Comparison of reported cell performance for different material band gaps Eg in the InGaAsP system at the literature reported Jsc and the source blackbody temperature or solar spectrum (AM0) illumination conditions Voc (V) Reference Wehrer et al., 2004 Wojtczuk et al., 1996 Wernsman et al., 2004 Newsman et al., 2006 Su et al., 2007 Hudait et al., 2003 Cederberg et al., 2008 Wanlass et al., 1996 Wilt et al., 1994 Wanlass et al., 1991 Dharmarasu et al., 2001 Steiner et al., 2009 Steiner et al., 2009

Eg (eV)

Source T (°K)

Jsc (A cm−2)

Measured

Model

Efficiency %

0.52

1300

1.64

0.283

0.295

0.55

1300

1.2

0.307

0.311

0.6

1039

2.84

0.417

0.391

0.6

3200

1.15

0.385

0.373

0.6 0.6

AM0 2050

1.06 1.18

0.365 0.357

0.364 0.367

0.6

3000

1.7

0.348

0.367

0.74

AM0

0.06

0.402

0.421

12.8

0.74

AM0

0.057

0.376

0.420

11.2

0.95

50 × AM0

0.532

0.658

0.668

9.4

0.95

AM0

0.053

0.578

0.559

16.5

0.98

AM0

0.018

0.598

0.603

8.2

0.98

45 × AM0

0.82

0.70

0.703

9.5

23.6

7.8

Note: A comparison is made for the predicted and the best measured data reported for Voc calculated using the model described in Section 4.3.

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described below. As can be seen it is difficult to make comparisons of the absolute efficiency due to the widely differing illumination conditions used in the literature. Significantly lower bandgap cells (0.3 eV), especially useful for lowtemperature sources, have also been demonstrated, including InAsSbP on InAs (Mauk et al., 2003; Gevorkyan et al., 2008), InAsSb on GaSb and even the penternary alloy GaInAsSbP (lattice matched to either GaSb or InAs) (Carrington et al., 2010). InGaAs and InGaAsP quantum well cells for TPV applications have also been produced (Rohr et al., 2006), and showed an increase in performance over a p-i-n bulk cell. However, it is unclear if their performance is better than more conventional abrupt p–n junction cells.

4.2.1 Solar thermophotovoltaics (STPVs) Solar thermophotovoltaics (STPVs) have also been proposed, where the solar energy is used to heat an intermediate emitter coupled to a TPV cell to produce electrical power. These have a high theoretical limiting efficiency of 85% (Harder and Würfel, 2003), which has yet to be realized in practice, with only efficiencies of ≤10% so far demonstrated (Andreev et al., 2005). This large difference is due to practical limitations, such as achievable absorber and emitter area ratios, and small but nonzero sub-bandgap losses. Theoretical models which include these loss effects (Andreev et al., 2007; Datas and Algora, 2009) suggest that a realistic system is likely to be limited to an efficiency of 15−30%. Therefore it seems unlikely that this will soon be able to rival the >40% efficiency currently demonstrated with conventional solar concentrator cells.

4.3

Modelling TPV cells

The results described earlier demonstrate the difficulty in making comparisons between different cells and system. In order to make an effective comparison of the results we now model the best performance that can be expected from realistic systems taking account of different possible spectral conditions, illumination conditions, working temperatures and other practical considerations such as series resistance effects. The modelling described here (Tuley and Nicholas, 2010) is based on realistic material parameters including Auger recombination. These effects all tend to increase the energy of the optimum bandgap when compared with simple thermodynamic estimates. Our modelling does not necessarily aim to find a single optimum bandgap for a TPV device, but rather to explore what considerations should be taken into account when considering an optimum bandgap for a particular system and its application. Previous modelling of TPV cells with a range of bandgaps and incident spectra have approached the problem

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either empirically or from the fundamental thermodynamic limits. Previous empirical models (Woolf, 1986; Coutts, 1999) have used dark-current expressions which have been extrapolated from higher bandgap devices – for example, Coutts (1999) extrapolates from the range 0.75–1.93 eV (Wanlass et al., 1991) – and have not considered the full range of spectral control or temperatures possible. Thermodynamic models (Gray and El-Husseini, 1996; Cody, 1999; Coutts, 1999; Baldasaro et al., 2001) have considered radiative recombination as the only limiting factor (the detailed balance limit – Shockley and Queisser, 1961). Neither of these modelling approaches has fully examined the effect of Auger recombination, which will become significant in low-bandgap devices, or thoroughly considered the influence of series resistances and cell temperatures. In order to produce numerical results, the mature InP-based material system is chosen as there exists significant literature on the relevant material parameters. A range of bandgaps has been investigated: 0.5–0.74 eV with lattice-mismatched InGaAs and 0.74–1.0 eV with lattice-matched InGaAsP. Higher bandgaps were excluded due to decreasing power densities and efficiencies, whereas lower bandgaps require such a substantial mismatch that growth of high-quality devices becomes difficult. Modelling the fundamental physical processes in a practical device architecture allows us to see how to make improvements towards the thermodynamic limit. The TPV cells were modelled using PC1D (Clugston and Basore, 1997), which provides a one-dimensional (1D) numerical solution of the semiconductor transport equations and absorption processes. The material parameters required for the InGaAs and InGaAsP materials were extracted from the best-quality material reported in a wide range of literature sources and averaged and interpolated where necessary (Tuley and Nicholas, 2010). Minority carrier lifetimes are all found to be within the range 50–120 ns across the whole 0.5–1.0 eV bandgap range at a 1 × 1017 cm−3 doping level. The majority of this carrier recombination is radiative. A simple n-p structure was simulated, producing similar results to previous work by Emziane and Nicholas (2007b), although a more comprehensive set of doping-dependent material parameters was used here. A practical optimized cell design limited to a maximum total thickness of 4 µm was used, and was shown to have a performance of ∼98% of a cell with no thickness limitations for a 1400 K spectrum. We do not include back surface mirror effects which would decrease this difference further. The modelling suggests an approximate optimum structure for all bandgap combinations consisting of a 0.5 µm, 1 × 1017 cm−3 n-doped emitter/3.5 µm, 1 × 1017 cm−3 p-doped base (Tuley and Nicholas, 2010). Alternative structures can produce similar performances however; for example in 0.74 eV cells, a more commonly used thin, highly doped emitter was found to give 98% of the performance of this optimum, and may help reduce lateral spreading resistances in an actual device.

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4.3.1 Comparison with previous empirical and thermodynamic models The results discussed here are compared to previous empirical and thermodynamic approaches. A comparison under a 1800 K source is given in Fig. 4.3. The performance of the model is higher than Coutts’s empirical model (Coutts, 1999). This is likely to be due to the development and improvement of the material used in real cells in recent years, as Coutts’s model is derived from reported cell dark currents with bandgaps 0.75–1.93 eV from 1991 (Wanlass et al., 1991). The performance improvement seen in this model over Coutts’s model produces a smaller relative improvement at lower bandgaps partly due to the inclusion of previously neglected Auger recombination effects. The thermodynamic limit is still significantly higher than the model results here, especially at lower bandgaps. This is predominantly due to a higher Voc and correspondingly higher fill factor, as shown in Fig. 4.3b. It can be seen that the predicted Voc is consistently ≤0.1 V lower than the thermodynamic limit, independent of bandgap, and so has a larger effect at lower bandgaps. The thermodynamic model considers the only recombination to be radiative, and calculates the minimum radiative recombination as that emitted from the surface, thus assuming perfect photon recycling, infinite mobility and infinite thickness, leading to a limiting dark current (Martí et al., 1997). Any increase in mobility has little effect in a device of the thickness discussed here, as it is already much smaller than the diffusion length (e.g., 3.5 µm compared with 47 µm in the base for 0.74 eV cells). The advantage of increasing thickness is to ensure complete absorption, but over 95% of the energy which would be absorbed in an infinite thickness cell with a 1800 K spectrum has already been absorbed in a 4 µm thick cell, so does not account (b)

20

0.9

Thermodynamic limit (Cody) This work Previous empirical work (Coutts)

18 16 14 12

0.8 Voc (V)

Power (Wcm–2)

(a)

10 8

0.7 0.6 0.5

6 4 2 0 0.5

Thermodynamic limit This work

0.4

0.6

0.7

0.8

0.9

0.3 0.5

0.6

Bandgap (eV)

0.7

0.8

0.9

Bandgap (eV)

4.3 (a) Power output under a 1800 K blackbody source compared to thermodynamic modelling by Cody (1999) and previous empirical modelling by Coutts (1999) with cell temperature Tcell = 300 K. (b) The corresponding Voc from this work is compared with the thermodynamic limit (Baldasaro et al., 2001). (Source: Tuley and Nicholas, 2010.)

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for the large difference observed. Therefore the thermodynamic limit must be significantly higher due to photon recycling. Although the model includes Auger recombination which influences low-bandgap results, the minority carrier lifetimes are still predominantly radiatively limited across the bandgap range (the Auger recombination rate is comparable to the radiative recombination rate only for Eg < 0.6 eV). If the model was changed so that the lifetime was solely determined by radiative recombination with perfect photon recycling, then the lifetime for all bandgaps would increase by a large, very approximately constant, recycling factor (Asbeck, 1977) as their thicknesses, refractive indices and absorption coefficient shapes are similar. A constant multiplicative increase in lifetime leads approximately to a multiplicative decrease in dark current and thus the constant additive change in Voc required to reach the thermodynamic limit. Therefore, in order to achieve very high performance low-bandgap cells, photon recycling must be maximized. To achieve the large improvement in device performance predicted thermodynamically, a significant increase in the lifetime is required. Photon recycling factors calculated for specific 0.74 eV InGaAs structures are only in the range 3–6 (Parks et al., 1997; Gfroerer et al., 1998; Gfroerer et al., 2003), even including a back surface reflector. The resulting lifetime increase produces <5% improvement in Voc. This is only a modest improvement due to the non-radiative recombination limiting the potential increase in lifetime, with the Auger recombination being the dominant mechanism. Auger recombination is more significant for lower-bandgap devices, so will limit photon recycling, and therefore limit progress towards the thermodynamic limit, unless different materials or structures can be developed.

4.3.2 Comparison with previous experimental results The validity of the model was tested by comparison with reported data, but since there are no set TPV standards, the model was calculated for the cell temperatures at which the cells were experimentally tested, with an illumination intensity set to give a short-circuit current Jsc which matches the experimental cells. The predicted open-circuit voltage Voc was used, as unlike the fill factor, or power output, it will not be significantly affected by series resistance effects. The measured devices were compared to the modelled optimum, with the assumption that the best reported devices must have a reasonably well optimized structure. The comparison showed that the predicted values are within 10% of the observed values, with the majority within 5% (Tuley and Nicholas, 2010). Since the reported results may have a lower Voc due to non-optimized structures, lower-quality material with increased Shockley–Read–Hall recombination, additional shunt paths, or non-uniform illumination (Dhariwal and Mathur, 1987), the agreement

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was considered to be good. Some 0.6 eV devices were found to exceed the model’s predictions – possibly due to high (>95%) back-reflectance (Fatemi et al., 1997) allowing thinner optimized devices with a higher Voc or good photon recycling which reduces effective radiative recombination.

4.3.3 TPV cells for different sources Typical TPV source temperatures of 1000–1800 K were modelled. The cells were assumed to be cooled to just above room temperature (303 K). The incident power on the cells was assumed to be that emitted from a planar blackbody source, which will be achieved in a planar geometry system (e.g., see Fraas et al., 2003) or a mirror system that focuses the emitted light onto the cells with a 1:1 ratio. The power output of the cells under a range of blackbody sources is shown in Fig. 4.4, demonstrating that the output power can be significantly increased by both increasing the source temperature which results in a higher overall incident power (≥T4), and by lowering the cell bandgap which allows more of the spectrum to be absorbed, which more than compensates for the increased thermalization losses. Control over the incident spectrum can be used to increase the efficiency of the devices. This is necessary to decrease the running costs of the system (less fuel), to enable easier heat management of the cells, and potentially to allow higher emitter temperatures as less total radiation is emitted. A spectral control scheme must suppress photons which cannot be efficiently harnessed by the cell, so is bandgap dependent, with the result that the total incident power on the cell will also be bandgap dependent. An ideal TPV Source temperature: 1800 K 1600 K 1400 K 1200 K 1000 K

Power from cell (Wcm–2)

10

1

0.1

0.01 0.5

0.6

0.7 0.8 Bandgap (eV)

0.9

1.0

4.4 Power output for modelled cells with a range of bandgaps under illumination by 1000–1800 K blackbody source temperatures. (Source: After Tuley and Nicholas (2010).)

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system will therefore exhibit both a high output power density and a high efficiency. However, in practice the balance between these depends on the details of the system, and the cost of the components. There are a variety of potential spectral control mechanisms, such as selective emitters, filters and back surface reflectors (see e.g., Coutts, 1999 and references within), but these are often dependent on specific materials and systems. Here we wish to compare efficiencies between ideal systems and so a simplified spectral control scheme was used to describe the radiation entering the cell, with an emittance of one at energies above the bandgap, and ∊BBG ≤ 1 below the bandgap. Any reflection from the cell was assumed to be included in this spectral control scheme. The use of a selective emitter with these characteristics should not affect the electrical power output, as emittance is one above bandgap, so the power output is almost unchanged from the case of a blackbody shown in Fig. 4.4. The low emittance below the bandgap suppresses the radiation that cannot be used, decreasing the incident power on the cell and increasing the electrical efficiency. The efficiency therefore increases as ∊BBG decreases as shown in Fig. 4.5a. As ∊BBG decreases, the peak efficiency also moves towards higher bandgaps, as when the loss from below-bandgap photons is minimized, then higher bandgaps are favoured to both reduce thermalization losses and reduce the higher inherent losses in low-bandgap cells (Section 4.6.1). A different

Efficiency (%)

(c)

∈BBC

40

35 30

30 20

25 20 15 10

10

5 (d)

0

∈BBC = 0.1

0 40

1800 K 1600 K 1400 K 1200 K 1000 K

35

10

30 Efficiency (%)

Thermal power dissipated (Wcm–2)

(b)

1800 K 1600 K 1400 K 1200 K 1000 K

40

0 0.05 0.1 0.25 1

50

Efficiency (%)

(a) 60

∈BBC 1

0 0.05 0.1 0.25 1

25 20 15 10 5

∈BBC = 0.05

0 0.5

0.6

0.7

0.8

Bandgap (eV)

0.9

1.0

0.5

0.6

0.7

0.8

0.9

1.0

Bandgap (eV)

4.5 (a) Efficiency and (b) thermal power dissipated as a function of bandgap with a 1400 K source with selective emitters with different below-bandgap emissitivities ∊BBG. The slight kink between 0.74 and 0.8 eV is due to the separate interpolations of the material parameters to 0.74 eV. (c) and (d) show efficiency as a function of bandgap with source temperatures 1000–1800 K with below-bandgap emissitivity ∊BBG for (c) 0.1, (d) 0.05. (Source: Tuley and Nicholas, 2010.)

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selective emitter scheme which additionally reduces the emission of significantly above-bandgap photons would decrease the thermalization losses, but would reduce the output power density, and for ∊BBG ≥ 0.05 does not lead to a significant gain in efficiency. The efficiency gain from a reduction in ∊BBG is very sensitive to its precise value when close to zero, especially at high bandgaps, due to the large proportion of the energy below the bandgap in the blackbody spectrum. It is important to note that the optimum efficiency generally does not occur at the same bandgap as the optimum output power density. Lower-bandgap cells with this selective emitter scheme result in higher incident power densities on the cell than in an equivalent higher bandgap system, so although higher electrical output power densities can be produced, the thermal power to be extracted from the cell is significantly higher – see Fig. 4.5b. This is especially true for high-quality spectral control (low ∊BBG) as the efficiency is higher for higher bandgaps, and so leads to a large difference in the thermal management required. Therefore, if the same cooling is used for all these cells, lower bandgaps will run at higher temperatures, thus reducing the power output and efficiencies from those described here. Further discussion of cell temperature effects is given in Section 4.6.4. The effect of a selective emitter for a range of source temperatures is shown in Fig. 4.5. This emphasizes the shift in peak efficiency towards higher bandgaps, both as selective emitter quality is improved, and when source temperature increases. This shows that for high-temperature sources, a higher bandgap than the conventional optimum (Coutts, 1999) of ∼0.5–0.6 eV may be required, as efficiency can be more important when high power densities make cell cooling more difficult. Therefore, lattice-matched (0.74 eV) InGaAs or even InGaAsP with a good selective emitter could be a better choice in this case.

4.3.4 Temperature effects Any real TPV system is likely to run the cells at elevated temperatures to reduce the cooling requirements, which can have an effect on the optimum bandgaps. Temperature effects were examined by two approaches: either a constant elevated cell temperature was assumed for all bandgaps or the cell cooling was fixed with a constant thermal resistance of 3 K W−1 cm2 for a water-cooled system (Royne et al., 2005), assuming that the cooling water was at 25°C. This cooling mechanism must remove both absorbed below-bandgap photons and losses in the conversion of radiative to electrical power. The results for a representative ∊BBG = 0.1 are shown in Fig. 4.6. This demonstrates that increasing the cell temperature decreases the power output, with a slightly larger decrease for lower bandgaps, but the cells still have acceptable efficiencies even at 100°C. Fixing the cell cooling at the value given above results in only a small change in cell temperature as a function of bandgap for low-temperature sources, but has a large effect on

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4.6 (a) Power and (b) efficiency of the modelled cells for different fixed cell temperatures and when the thermal resistance (i.e., cooling mechanism) is fixed (∊BBG = 0.1). (c) Power and (d) efficiency of the modelled cells for different values of the series resistance (∊BBG = 0.1). (Source: Tuley and Nicholas, 2010.)

high-temperature sources. Therefore, lower bandgaps are still favoured to maximize power densities for all but a high-temperature source (1800 K) with a constant thermal resistance. For a 1800 K source with a constant thermal resistance, the power density actually passes through a maximum at 0.6 eV. The efficiency also correspondingly drops when cell temperature is raised to a fixed value, with only a slight shift in the peak towards higher bandgaps. If, however, the thermal resistance is fixed, then for a 1800 K source there is a more pronounced shift towards higher bandgaps for an optimum efficiency. Therefore, temperature considerations show the advantage of higher bandgap systems, both for higher efficiencies and potentially even as a result of power density considerations. The choice of cooling system can thus impact on the choice of cell for a well optimized system.

4.3.5 Series resistance effects A practical TPV cell will have a finite resistance, due to lateral current spreading to the contact grid, metal-to-semiconductor contact resistance,

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grid resistance and rear contact resistance. This can be problematic for the very high current densities involved. Typical resistances of measured devices can be in the range 15–60 mΩ cm2, even when using multiple small interconnected devices in a monolithically integrated module (MIM) (Wojtczuk, 1997; Chubb, 2007; Su et al., 2007). The significance of this issue can be judged by the fact that the best TPV performances reported to date have been using MIM structures, where the losses due to the formation of nonactive interconnects are more than balanced by the gains due to the reduction in Joule heating produced by series connection of smaller area devices. The effect of a 10 and a 25 mΩ cm2 series resistance on both the power and the efficiency is shown in Fig. 4.6. These results demonstrate that series resistance effects can have a very large impact on performance at high source temperatures (high power densities) and low bandgaps. This leads to both the highest power densities and highest efficiencies moving to larger bandgaps. Higher source temperatures can even result in lower efficiencies (but higher power densities) if there is a large series resistance effect. There is no significant fundamental lower limit on series resistance, but practically it is limited due to an increase in grid shadowing (a loss mechanism neglected here) when increasing metallization of the front surface or practical limitations in fabrication (Gessert and Coutts, 1992). It is clear that for a high-temperature source, minimization of the series resistance will be crucial to producing efficient devices, and the use of larger bandgaps can mitigate the effect. An alternative approach to reduce the impact of series resistance would be to move to a tandem device, where the voltage output is higher and the current output lower.

4.3.6 TPV cell summary TPV cells have been successfully optimized using material parameters interpolated from the literature. These show good agreement with the literature data on measured cell performance. Cell power densities and efficiencies have been examined under a range of selective emitters, source temperatures and cell temperatures and the large significance of series resistance has been examined. This modelling demonstrates that there is no clear optimum bandgap for TPV cells, as the choice depends on the application; the two main factors affecting its choice are source temperature and the required balance between power density and efficiency of the cell, with efficiency strongly dependent on the likely quality of selective emitter. The inclusion of Auger recombination, considerations of cell temperature and cell thermal management, and series resistance, all effects generally not examined in detail in previous models, have been shown to bias the ideal cell bandgap towards a higher value than the conventional ∼0.5−0.6 eV.

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4.4

Tandem TPV cells

A potential route to improve the efficiency and reduce series resistance effects under high illumination levels is to use a series-connected two-junction tandem cell (Martí and Arajo, 1996). This requires the top and bottom cells to be current matched, ideally at their maximum power points (Kurtz et al., 1990), which generally occurs close to matching the currents at short circuit, although with slightly higher short-circuit currents in the bottom cell (Kurtz et al., 1990; Wanlass and Albin, 2004). Unfortunately, the range of different potential sources means that different bandgap combinations are needed in each case. Similar calculations to those described in the previous section have been used to model two examples in order to give a qualitative idea of the potential performance gains. The first device considered is purely lattice matched, with the minimum possible bottom cell bandgap of 0.74 eV, and an upper InGaAsP cell with a bandgap chosen to current match the bottom cell for the specific source used. The minimum bandgap for the bottom cell is used to maximize the power density output for a lattice-matched configuration. The second device consists of a lattice-matched 0.74 eV top cell, and a lattice-mismatched bottom cell with a bandgap again chosen to allow current matching. This design could be grown in an inverted configuration and illuminated through a semi-insulating substrate (Wehrer et al., 2002). Results for 1600 and 1800 K are shown in Table 4.2. This shows that the use of a tandem cell rather than a single junction with the bandgap of the bottom cell (same incident spectrum) results in an absolute efficiency increase of 4–5%, with a corresponding power increase. Although this is only a modest improvement, such a device will have Jsc tandem <1/2 Jsc single and Voc tandem >2Voc single so that the series resistance effects are much smaller (by a factor Table 4.2 The performance of a selection of tandem, series-connected thermophotovoltaic devices, compared to a single-junction cell with a bandgap equal to the bottom cell of the tandem

Source temperature (K) 1600

1800

EBG

Top cell bandgap (eV)

0.1 0.05 0.1 0.05 0.1 0.05 0.1 0.05

0.9 0.9 0.74 0.74 0.93 0.93 0.74 0.74

Efficiency Bottom single cell Power bandgap output Efficiency junction (%) (%) (eV) (Wcm−2) 0.74 0.74 0.58 0.58 0.74 0.74 0.55 0.55

3.9 3.9 6.0 6.0 8.7 8.7 12.2 12.2

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36.5 42.4 37.5 40.5 41.2 45.8 37.7 39.6

32.5 37.7 32.2 34.8 36.5 40.6 33.0 34.6

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of ≤4). For example, the 0.93 eV/0.74 eV tandem under a 1800 K source (ϵBG = 0.1) only suffers an absolute 2.9% efficiency drop if Rs = 10 mΩcm2, whereas a 0.74 eV single-junction cell suffers a 11.5% drop. An alternative approach would be to use a tandem cell with lattice-mismatched In1−xGaxAsyP1−y, where the top and the bottom cell have the same mismatch to the InP substrate (Siergiej et al., 2004; Newman et al., 2006), allowing a wider range of bandgap pairs. Only a few double-junction TPV cells have been investigated in practice, such as the lattice-mismatched In1−xGaxAsyP1−y/In1−xGaxAs pair (Siergiej et al., 2004; Newman et al., 2006). Lattice-matched (0.74 eV) material has also been combined with lattice-mismatched In1−xGaxAs cell – for example, 0.63 eV (Wilt et al., 2004) or 0.5 eV (Wehrer et al., 2002). A tandem has also been produced using the GaSb material system, GaSb/InGaAsSb (Andreev et al., 1997). In general, these tandem cells have not performed as well as the combination of the performance of the cells grown individually, and so have not produced the performance enhancement expected so far. An alternative approach is to use a three-terminal cell, in which each junction can be contacted independently. This approach has the advantage that the same cell can be used to provide improved performance from a variety of sources, but comes at the cost of increased complexity of manufacture and additional shading losses due to the need for a second currentcollecting grid. The potential efficiencies for such devices are good, as has been shown theoretically by Emziane and Nicholas (2007a). There have been a few reports of three-terminal double-junction cell results for cells designed for solar PV applications (Flores, 1983; Lewis et al., 1988; Soga et al., 1996), including two reports on InP-based materials (Wanlass et al., 1991; Steiner et al., 2009), but no significant improvements in real devices have been reported to date.

4.5

Conclusions

TPV cell structures have been reviewed and modelled for a variety of spectral configurations and show good agreement with the literature data on measured cell performance. They show a performance improvement from previous (Coutts, 1999) estimates of empirical cell performance. A comparison to the thermodynamic limit has shown that significant improvements are theoretically possible, especially at lower bandgaps. In practice, these will be hard to achieve as they require large improvements in photon recycling, which requires suppression of Auger recombination. To date, practical applications of TPV structures have been limited to specialist applications such as space systems or remote power generation but they have the potential for significant use in CHP systems. Current production costs of around £10 cm−2 mean that power output levels of a few

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Wcm−2 make CHP systems uneconomic, but with significant investment it is realistic to expect mass production costs being reduced to levels of order £1 per watt of electricity produced which would make them economic as components of CHP systems.

4.6

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