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 NO_x 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 sup pressing 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 NiO- doped 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 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.

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.

4.2.1 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.

4.3.1 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 V_oc and correspondingly higher fill factor, as shown in Fig. 4.3b. It can be seen that the predicted V_oc 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 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 band- gap range (the Auger recombination rate is comparable to the radiative recombination rate only for E_g < 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 V_oc 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 result- ing lifetime increase produces < 5% improvement in V_oc. 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 thermo- dynamic 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 J_sc which matches the experimental cells. The predicted open-circuit voltage V_oc 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 V_oc 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 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 V_oc 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 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 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 e_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 func- tion of bandgap for low-temperature sources, but has a large effect on 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, 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 m cm², eVen when using multiple small inter- connected 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 m 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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