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Energy Express

  • Editor: Christian Seassal
  • Vol. 21, Iss. S6 — Nov. 4, 2013
  • pp: A1035–A1051
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Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems

Yi Xiang Yeng, Walker R. Chan, Veronika Rinnerbauer, John D. Joannopoulos, Marin Soljačić, and Ivan Celanovic  »View Author Affiliations


Optics Express, Vol. 21, Issue S6, pp. A1035-A1051 (2013)
http://dx.doi.org/10.1364/OE.21.0A1035


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Abstract

One of the keys towards high efficiency thermophotovoltaic (TPV) energy conversion systems lies in spectral control. Here, we present detailed performance predictions of realistic TPV systems incorporating experimentally demonstrated advanced spectral control components. Compared to the blackbody emitter, the optimized two-dimensional (2D) tantalum (Ta) photonic crystal (PhC) selective emitter enables up to 100% improvement in system efficiency. When combined with the well characterized cold side tandem filter and the latest InGaAs TPV cells, a TPV energy conversion system with radiant heat-to-electricity efficiency of 25% and power density of 0.68 W cm−2 is achievable today even at a relatively low temperature of 1320 K. The efficiency could be increased to ∼ 40% (the theoretical 0.62 eV single bandgap TPV thermodynamic limit at 1320 K is 55%) as future implementation of more optimized TPV cells approach their theoretical thermodynamic limit.

© 2013 OSA

1. Introduction

Recent advancements in the field of low bandgap photovoltaic (PV) cells [1

1. C. A. Wang, H. K. Choi, S. L. Ransom, G. W. Charache, L. R. Danielson, and D. M. Depoy, “High-quantum-efficiency 0.5 eV GaInAsSb/GaSb thermophotovoltaic devices,” Appl. Phys. Lett. 75, 1305–1307 (1999). [CrossRef]

4

4. M. W. Dashiell, J. F. Beausang, H. Ehsani, G. J. Nichols, D. M. Depoy, L. R. Danielson, P. Talamo, K. D. Rahner, E. J. Brown, S. R. Burger, P. M. Fourspring, W. F. Topper Jr., P. F. Baldasaro, C. A. Wang, R. K. Huang, M. K. Connors, G. W. Turner, Z. A. Shellenbarger, G. Taylor, J. Li, R. Martinelli, D. Donetski, S. Anikeev, G. L. Belenky, and S. Luryi, “Quaternary InGaAsSb thermophotovoltaic diodes,” IEEE Trans. Electron. Dev. 53, 2879–2891 (2006). [CrossRef]

] has led to renewed interest in developing high efficiency and high power density thermophotovoltaic (TPV) energy conversion systems, whereby direct conversion of thermal radiation to electricity is achieved via the PV effect [5

5. H. H. Kolm, “Solar-battery Power Source,” Tech. Rep., MIT Lincoln Laboratory. Quarterly Progress Report, Group 35, pp. 13 (1956).

7

7. T. J. Coutts, “A review of progress in thermophotovoltaic generation of electricity,” Renew. Sust. Energ. Rev. 3, 77–184 (1999). [CrossRef]

]. Compared to solar PV conversion, the heat source is sig-nificantly closer to the PV cell, resulting in photon flux and power density that is orders of magnitude higher. However, due to the much lower temperatures achievable in practical TPV systems (< 2000 K), the majority of emitted photons lie in the near- to mid-infrared spectrum, hence the importance of high quality low bandgap PV cells in developing high efficiency TPV systems. TPV systems offer many advantages, including the promise of highly versatile and compact high power density energy conversion systems that have no moving parts, leading to quiet and robust operation. Virtually any high grade heat source can be utilized, including waste heat [7

7. T. J. Coutts, “A review of progress in thermophotovoltaic generation of electricity,” Renew. Sust. Energ. Rev. 3, 77–184 (1999). [CrossRef]

], fossil fuels [8

8. M. Zenker, A. Heinzel, G. Stollwerck, J. Ferber, and J. Luther, “Efficiency and power density potential of combustion-driven thermophotovoltaic systems using GaSb photovoltaic cells,” IEEE Trans. Electron. Dev. 48, 367–376 (2001). [CrossRef]

], radioisotopes [9

9. B. Wernsman, R. G. Mahorter, R. R. Siergiej, S. D. Link, R. J. Wehrer, S. J. Belanger, P. M. Fourspring, S. Murray, F. Newman, D. Taylor, and T. Rahmlow, “Advanced thermophotovoltaic devices for space nuclear power systems,” in AIP Conference Proceedings: Space Technology and Applications International Forum (AIP, 2005), pp. 1441–1448. [CrossRef]

, 10

10. R. W. Kaszeta, Y. X. Yeng, M. Ghebrebrhan, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Advanced radiative emitters for radioisotope thermophotovoltaic power systems,” in 5th World Conference on Photovoltaic Energy Conversion / Ninth Thermophotovoltaic World Conference (2010).

], and solar energy [11

11. N. P. Harder and P. Wurfel, “Theoretical limits of thermophotovoltaic solar energy conversion,” Semicond. Sci. Technol. 18, S151–S157 (2003). [CrossRef]

, 12

12. V. M. Andreev, A. S. Vlasov, V. P. Khvostikov, O. A. Khvostikova, P. Y. Gazaryan, S. V. Sorokina, and N. A. Sadchikov, “Solar thermophotovoltaic converters based on tungsten emitters,” J. Sol. Ener. Eng. 129, 298–303 (2007). [CrossRef]

].

Even though low bandgap PV cells allow more efficient use of the emitted radiation, the broadband nature of thermal emission at the relatively low temperatures considered results in significant emission of below bandgap photons. For instance, only 28% of the radiant exitance of a blackbody at 1500 K with peak radiation at a wavelength of 1.93 μm lies below 2 μm, which is approximately the bandgap of InGaAs PV cells [3

3. R. R. Siergiej, B. Wernsman, S. A. Derry, R. G. Mahorter, R. J. Wehrer, S. D. Link, M. N. Palmisiano, R. L. Messham, S. Murray, C. S. Murray, F. Newman, J. Hills, and D. Taylor, “20% efficient InGaAs/InPAs TPV cells,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 5th Conference (AIP, 2003), pp. 414–423. [CrossRef]

,13

13. C. S. Murray, C. J. Crowley, S. Murray, N. A. Elkouh, R. W. Hill, and D. E. Chubb, “Thermophotovoltaic converter design for radioisotope power systems,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 123–132.

]. The remaining non-convertible photons emitted result in parasitic heat losses, which would also lead to highly undesirable elevated PV cell operating temperatures. Hence, spectral control is critical in achieving higher TPV system efficiencies.

Spectral control can be achieved firstly via the use of selective emitters to preferentially emit convertible photons. To date, various selective emitters have been investigated; from rare-earth oxides [14

14. R. A. Lowe, D. L. Chubb, S. C. Farmer, and B. S. Good, “Rare-earth garnet selective emitter,” Appl. Phys. Lett. 64, 3551–3553 (1994). [CrossRef]

17

17. B. Bitnar, W. Durisch, J.-C. Mayor, H. Sigg, and H. Tschudi, “Characterisation of rare earth selective emitters for thermophotovoltaic applications,” Sol. Ener. Mater. Sol. Cells 73, 221–234 (2002). [CrossRef]

], to 1D [18

18. A. Narayanaswamy and G. Chen, “Thermal emission control with one-dimensional metallodielectric photonic crystals,” Phys. Rev. B 70, 125101 (2004). [CrossRef]

, 19

19. D. L. C. Chan, M. Soljačić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E 74, 016609 (2006). [CrossRef]

], 2D [20

20. A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).

25

25. R. Biswas, D. Zhou, I. Puscasu, E. Johnson, A. Taylor, and W. Zhao, “Sharp thermal emission and absorption from conformally coated metallic photonic crystal with triangular lattice,” Appl. Phys. Lett. 93, 063307 (2008). [CrossRef]

], and 3D photonic crystals (PhCs) [26

26. S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic power generation,” Appl. Phys. Lett. 83, 380–382 (2003). [CrossRef]

, 27

27. D. L. C. Chan, M. Soljačić, and J. D. Joannopoulos, “Direct calculation of thermal emission for three-dimensionally periodic photonic crystal slabs,” Phys. Rev. E 74, 036615 (2006). [CrossRef]

]. Another spectral control approach relies on recuperating non-convertible photons using front surface reflectors [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

31

31. T. D. Rahmlow, D. M. Depoy, P. M. Fourspring, H. Ehsani, J. E. Lazo-Wasem, and E. J. Gratrix, “Development of front surface, spectral control filters with greater temperature stability for thermophotovoltaic energy conversion,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 7th Conference (AIP, 2007), pp. 59–67.

] and back surface reflectors [32

32. G. W. Charache, D. M. DePoy, P. F. Baldasaro, and B. C. Campbell, “Thermophotovoltaic devices utilizing a back surface reflector for spectral control,” AIP Conf. Proc. 358, 339–350 (1996). [CrossRef]

34

34. L. B. Karlina, M. M. Kulagina, N. K. Timoshina, A. S. Vlasov, and V. M. Andreev, “In0.53Ga0.47As/InP conventional and inverted thermophotovoltaic cells with back surface reflector,” AIP Conf. Proc. 890, 182–189 (2007). [CrossRef]

] on the PV cell. A TPV system including both aspects of spectral control is shown in Fig. 1(b).

Fig. 1 (a) Conventional thermophotovoltaic (TPV) energy conversion system without spectral control. (b) TPV system with 2D photonic crystal (PhC) selective emitter and cold side filter. Spectral control enables performance enhancement of up to 400% over the conventional TPV system.

Following recent efforts on the design, fabrication, characterization, and optimization of spectral control devices for TPV applications, many studies have attempted to estimate the enhancement in TPV system performance [8

8. M. Zenker, A. Heinzel, G. Stollwerck, J. Ferber, and J. Luther, “Efficiency and power density potential of combustion-driven thermophotovoltaic systems using GaSb photovoltaic cells,” IEEE Trans. Electron. Dev. 48, 367–376 (2001). [CrossRef]

,35

35. P. F. Baldasaro, J. E. Raynolds, G. W. Charache, D. M. Depoy, C. T. Ballinger, T. Donovan, and J. M. Borrego, “Thermodynamic analysis of thermophotovoltaic efficiency and power density tradeoffs,” J. Appl. Phys. 89, 3319–3327 (2001). [CrossRef]

37

37. P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010). [CrossRef] [PubMed]

]. In this investigation, we focus on obtaining estimates of TPV system performance using spectral control components that have recently been demonstrated experimentally while taking into account high temperature and angular dispersion properties to ensure realistic estimates. In particular, we focus on 2D tantalum (Ta) PhCs as the selective emitter; this design enables a sharp emittance cutoff that is easily shifted and optimized [24

24. I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008). [CrossRef]

,38

38. M. Ghebrebrhan, P. Bermel, Y. X. Yeng, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Tailoring thermal emission via Q-matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011). [CrossRef]

,39

39. Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. Joannopoulos, M. Soljačić, and I. Čelanović, “Enabling high temperature nanophotonics for energy applications,” Proc. Natl. Acad. Sci. USA 109, 2280 (2011). [CrossRef]

], is scalable to large areas [40

40. M. Araghchini, Y. X. Yeng, N. Jovanovic, P. Bermel, L. A. Kolodziejski, M. Soljačić, I. Celanovic, and J. D. Joannopoulos, “Fabrication of two-dimensional tungsten photonic crystals for high-temperature applications,” J. Vac. Sci. Technol. B 29, 061402 (2011). [CrossRef]

,41

41. V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljačić, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013). [CrossRef]

], and has been proven to be thermally stable at high temperatures in high vacuum conditions [42

42. V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013). [CrossRef] [PubMed]

]. The performance of this emitter is evaluated with or without a cold side tandem filter [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

,31

31. T. D. Rahmlow, D. M. Depoy, P. M. Fourspring, H. Ehsani, J. E. Lazo-Wasem, and E. J. Gratrix, “Development of front surface, spectral control filters with greater temperature stability for thermophotovoltaic energy conversion,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 7th Conference (AIP, 2007), pp. 59–67.

], which to date is widely regarded as one of the more promising experimentally realized reflective spectral control device [29

29. R. T. Kristensen, J. F. Beausang, and D. M. Depoy, “Frequency selective surfaces as near-infrared electromagnetic filters for thermophotovoltaic spectral control,” J. Appl. Phys. 95, 4845–4851 (2004). [CrossRef]

,43

43. B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, C. S. Murray, F. Newman, D. Taylor, D. M. Depoy, and T. Rahmlow, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004). [CrossRef]

,44

44. C. J. Crowley, N. A. Elkouh, S. Murray, and D. L. Chubb, “Thermophotovoltaic converter performance for radioisotope power systems,” in AIP Conference Proceedings: Space Technology and Applications International Forum (AIP, 2005), pp. 601–614. [CrossRef]

].

In the following section, we discuss the numerical model used to obtain detailed performance predictions of TPV systems. Inputs to the model include key physical properties of each component that constitute the TPV system; optical properties are captured by the absorptance, reflectance, and transmittance of the emitter, cold side filter, and PV cell; electrical power generating properties are captured by the quantum efficiency, dark current, parasitic resistances, and ideality factor of the PV cell. Methods to obtain optimized 2D Ta PhC selective emitter and cold side tandem filter designs are also discussed. In section 3, TPV modeling results of various emitter and cold side filter combinations are presented. In addition, we analyze the performance of 3 different current state-of-the-art low bandgap TPV cells using key physical properties that have been experimentally measured from fabricated cells; GaSb [2

2. O. V. Sulima and A. W. Bett, “Fabrication and simulation of GaSb thermophotovoltaic cells,” Sol. Ener. Mater. Sol. Cells 66, 533–540 (2001). [CrossRef]

, 45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

], InGaAs [3

3. R. R. Siergiej, B. Wernsman, S. A. Derry, R. G. Mahorter, R. J. Wehrer, S. D. Link, M. N. Palmisiano, R. L. Messham, S. Murray, C. S. Murray, F. Newman, J. Hills, and D. Taylor, “20% efficient InGaAs/InPAs TPV cells,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 5th Conference (AIP, 2003), pp. 414–423. [CrossRef]

, 13

13. C. S. Murray, C. J. Crowley, S. Murray, N. A. Elkouh, R. W. Hill, and D. E. Chubb, “Thermophotovoltaic converter design for radioisotope power systems,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 123–132.

], and InGaAsSb [1

1. C. A. Wang, H. K. Choi, S. L. Ransom, G. W. Charache, L. R. Danielson, and D. M. Depoy, “High-quantum-efficiency 0.5 eV GaInAsSb/GaSb thermophotovoltaic devices,” Appl. Phys. Lett. 75, 1305–1307 (1999). [CrossRef]

, 4

4. M. W. Dashiell, J. F. Beausang, H. Ehsani, G. J. Nichols, D. M. Depoy, L. R. Danielson, P. Talamo, K. D. Rahner, E. J. Brown, S. R. Burger, P. M. Fourspring, W. F. Topper Jr., P. F. Baldasaro, C. A. Wang, R. K. Huang, M. K. Connors, G. W. Turner, Z. A. Shellenbarger, G. Taylor, J. Li, R. Martinelli, D. Donetski, S. Anikeev, G. L. Belenky, and S. Luryi, “Quaternary InGaAsSb thermophotovoltaic diodes,” IEEE Trans. Electron. Dev. 53, 2879–2891 (2006). [CrossRef]

, 45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

]. The results using experimentally realizable components are benchmarked against idealized components to identify areas that require improvement. We conclude by summarizing our findings in section 4.

2. Numerical model

2.1. Thermophotovoltaic (TPV) system

To obtain the short circuit current Isc generated, the net irradiance incident on the PV cell is calculated following a ray tracing approach. We begin with the definition of the spectral radiance of a blackbody iBB:
iBB(λ,t)=2hc2λ5[exp(hcλkT)1]
(1)
where λ is the wavelength, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, and T is the temperature of the blackbody. The total radiant power emitted Pem by an emitter of area A1 with angular dependent emittance ε(λ, θ1, ϕ1) at temperature T is then given by:
Pem=0dλ0π2dθ102πdϕ1A1dA1[iBB(λ,T)ε(λ,θ1,ϕ1)cosθ1sinθ1]
(2)
where θ1 is the polar angle and ϕ1 is the azimuthal angle.

The fraction of Pem reaching the PV cell can be evaluated by first considering the differential radiant power incident on the PV cell of infinitesimal area dA2 from an emitter of infinitesimal area dA1:
dQdA1dA2=iBB(λ,T)ε(λ,θ1,ϕ1)dA1dF2
(3)
dF2 is the differential view factor, which is defined as the fraction of radiant energy emitted by dA1 incident on dA2:
dF2=cosθ1cosθ2s2dA2
(4)
where θ2 is the angle between the straight line connecting the two infinitesimal areas and the normal vector for dA2, and s is the distance between dA1 and dA2.

In a TPV system, it is important to take into account the multiple reflections taking place between the emitter and the PV cell. It is thus convenient to define the differential view factor dFl for dAl, a differential virtual surface area constructed at a distance sl from the initial emitter dA1 to properly take into account the lth order reflection [46

46. E. R. G. Eckert and E. M. Sparrow, “Radiative heat exchange between surfaces with specular reflection,” Int. J. Heat Mass Trans. 3, 42–54 (1961). [CrossRef]

]:
dFl=cosθ1cosθlsl2dAl
(5)
Even values of l represent reflections to the PV cell, while odd values represent reflections back to the emitter. Thus, the radiant power reabsorbed Pre by the emitter can be evaluated by integrating Eq. (3) and summing over the odd values of l:
Pre=p=1dλdF2p+1dA1[iBB(λ)R2pR1p1(1R1)ε(λ,θ2p+1,ϕ2p+1)]
(6)
where R1 and R2 are the angular dependent reflectance of the emitter and the PV cell respectively. The terms R2pR1p1 and 1 − R1 respectively captures the multiple reflections and final absorption events. For a parallel plate TPV system configuration considered in this investigation, Eq. (6) can be further simplified to the following:
Pre=p=1dλdA2p+1dA1[iBB(λ)R2pR1p1(1R1)ε(λ,θ2p+1,ϕ2p+1)cos2θ2p+1s2p+12]
(7)
Similarly, the useful radiant power incident on the PV cell Pcell, and Isc can be obtained by summing over the even values of l:
Pcell=p=10λgdλdA2pdA1[iBB(R1R2)p1(1R2)ε(λ,θ2p,ϕ2p)cos2θ2ps2p2]
(8)
Isc=2qcp=1IQE(λ)dλλ4[exp(hcλkT)1]dA2pdA1[(R1R2)p1(1R2)ε(λ,θ2p,ϕ2p)cos2θ2ps2p2]
(9)
where IQE(λ) and λg are respectively the internal quantum efficiency and bandgap of the PV cell. Equation (9) is then used to evaluate the total output current I as a function of applied voltage V at the output terminals of the PV cell according to:
I=IscIoexp[q(V+IRs)mkTc]V+IRsRsh
(10)
where m, Io, Rs, Rsh, and Tc are respectively the ideality factor, dark current, series resistance, shunt resistance, and temperature of the PV cell, and q is the elementary electronic charge [47

47. J. Nelson, The Physics of Solar Cells (Imperial College Press, 2003). [CrossRef]

]. The output electrical maximum power point Pelec,max is then obtained by maximizing Pelec = IV by setting d(IV)/dV = 0. The radiant heat-to-electricity TPV efficiency ηTPV is then given as follows:
ηTPV=Pelec,maxPemPre
(11)
ηTPV can further be broken down into the overall spectral efficiency when TPV cavity effects are taken into account ηCav–Spec, and the PV cell efficiency ηCell:
ηCavSpec=PcellPemPre
(12)
ηCell=Pelec,maxPcell
(13)
Note that the evaluation of Eqs. (7)(9) can be computationally intensive, especially in obtaining estimates for optimization purposes. Thus, it is interesting to consider the simplification of capturing the angular dependence via the spectral hemispherical emittance εH(λ):
εH(λ)=1π0π2dθ102πdϕ1[ε(λ,θ1,ϕ1)cosθ1sinθ1]
(14)
Using this, the problem simplifies into radiation exchange between two general surfaces of total area A1 and A2, thereby not requiring the intensive numerical integration over all differential areas. Indeed, we have verified that both the full ray tracing method and the spectral hemispherical approximation produce results that agree very well. This is expected given the very high view factors (> 0.85) involved in practical parallel plate TPV systems that are considered in this investigation, whereby most emission up to θ1 = 85° is incident on the PV cell.

2.2. Two-dimensional (2D) tantalum (Ta) photonic crystals (PhCs) as selective emitters

To achieve a highly efficient TPV system, the emitter should exhibit maximum emission at wavelengths below the cutoff of the PV cell, whilst simultaneously suppressing emission in the non-convertible range. In addition, the emitter has to survive high temperature operation of up to 1500 K over extended periods of time, thus limiting the materials and architectures that can be used in these systems.

To overcome these critical issues, we select a material platform consisting of single element, broadband tunable spectrally selective infrared emitters comprised of a 2D square array of cylindrical cavities with period a, radius r, and depth d etched into a large area metallic surface as shown in the inset of Fig. 2. This relatively simple design allows one to simultaneously achieve near-blackbody emittance at short wavelengths as well as emittance almost as low as a polished metal at long wavelengths, with a sharp cutoff separating the two regimes, which is critical for high efficiency TPV energy conversion. Of the various refractory metals available, tantalum (Ta) is an excellent choice given its low vapor pressure, high melting point, machinability and weldability. To date, the 2D Ta PhC emitter has been demonstrated to be thermally stable at high temperatures in high vacuum environments [42

42. V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013). [CrossRef] [PubMed]

], and the fabrication process is scalable to large areas [40

40. M. Araghchini, Y. X. Yeng, N. Jovanovic, P. Bermel, L. A. Kolodziejski, M. Soljačić, I. Celanovic, and J. D. Joannopoulos, “Fabrication of two-dimensional tungsten photonic crystals for high-temperature applications,” J. Vac. Sci. Technol. B 29, 061402 (2011). [CrossRef]

, 41

41. V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljačić, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013). [CrossRef]

], both of which are essential for practical large scale adoption.

Fig. 2 Simulated high temperature (T = 1478 K) normal spectral emittance of flat Ta and 2D Ta PhCs optimized for GaSb (Design I: r = 0.43 μm, d = 8.00 μm, a = 0.95 μm), InGaAs (Design II: r = 0.51 μm, d = 8.00 μm, a = 1.11 μm), and InGaAsSb (Design III: r = 0.57 μm, d = 8.00 μm, a = 1.23 μm). As can be seen, the cutoff is easily shifted by modifying the dimensions of the PhC.

In general, the enhancement in emission is achieved by coupling into resonant cavity electromagnetic modes, whereby the cutoff wavelength is approximately given by the fundamental mode of the cylindrical metallic cavity [22

22. H. Sai and H. Yugami, “Thermophotovoltaic generation with selective radiators based on tungsten surface gratings,” Appl. Phys. Lett. 85, 3399–3401 (2004). [CrossRef]

24

24. I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008). [CrossRef]

]. Hence, the cutoff wavelength is mainly affected by r, with d playing only a secondary role for the aspect ratios considered. To further enhance the selective emitter’s performance, the appropriate r, d and a are selected such that the radiative and absorptive rates of the metallic cavities are matched, i.e. satisfying the Q-matching condition [38

38. M. Ghebrebrhan, P. Bermel, Y. X. Yeng, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Tailoring thermal emission via Q-matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011). [CrossRef]

]. This allows the PhC to exhibit emittance peaks that approach the theoretical blackbody in the vicinity of the fundamental mode.

While Q-matching of the fundamental mode allows quick identification of near-optimal designs for TPV systems, it is not the global optimum as it is difficult to simultaneously achieve Q-matching for higher order modes, which is important in broadening the bandwidth for maximum emittance. Hence, global optimization using numerical methods is employed [37

37. P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010). [CrossRef] [PubMed]

], with the design provided by Q-matching of the fundamental mode used as the initial estimate.

The emittance ε(λ, θ1, ϕ1) of the 2D Ta PhC can easily be determined via finite-difference time-domain (FDTD) numerical methods [48

48. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

] coupled with the Lorentz–Drude model fitted to elevated temperature emittance [42

42. V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” Opt. Express 21, 11482–11491 (2013). [CrossRef] [PubMed]

] to capture the optical dispersion of Ta. However, the high memory requirements and slow computational speed of FDTD methods limit its application in determining the globally optimum design for a TPV system. Thus, to obtain quicker estimates, we utilize the mode matching formalism described in [49

49. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93, 227401 (2004). [CrossRef] [PubMed]

] by Bravo-Abad et al., of which we have confirmed to match very well with FDTD methods. In essence, the reflectance is calculated by matching the radiation fields at the boundary of free space and the cylindrical cavities via expansion of the cavity modes for shorter wavelengths and utilizing a surface area weighted impedance for longer wavelengths.

The calculated ε(λ, θ1, ϕ1) can then be used to obtain ηTPV and the maximum power density Jelec,max = Pelec,max/A1 as described in Section 2.1. For optimization purposes, we define the figure of merit FOM as follows:
FOM=xηTPV+(1+x)Jelec,maxPhCJelec,maxBB
(15)
where Jelec,maxPhC/Jelec,maxBB captures the TPV system power density performance of the 2D Ta PhC emitter compared to a blackbody, and x is the weighting given to ηTPV in the optimization routine, which could be modified depending on design goals. In this investigation, we are mainly concerned in obtaining the highest ηTPV possible, thus x = 0.9 is used. Using this, 3 different designs optimized for GaSb [2

2. O. V. Sulima and A. W. Bett, “Fabrication and simulation of GaSb thermophotovoltaic cells,” Sol. Ener. Mater. Sol. Cells 66, 533–540 (2001). [CrossRef]

, 45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

], InGaAs [3

3. R. R. Siergiej, B. Wernsman, S. A. Derry, R. G. Mahorter, R. J. Wehrer, S. D. Link, M. N. Palmisiano, R. L. Messham, S. Murray, C. S. Murray, F. Newman, J. Hills, and D. Taylor, “20% efficient InGaAs/InPAs TPV cells,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 5th Conference (AIP, 2003), pp. 414–423. [CrossRef]

, 13

13. C. S. Murray, C. J. Crowley, S. Murray, N. A. Elkouh, R. W. Hill, and D. E. Chubb, “Thermophotovoltaic converter design for radioisotope power systems,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 123–132.

], and InGaAsSb [1

1. C. A. Wang, H. K. Choi, S. L. Ransom, G. W. Charache, L. R. Danielson, and D. M. Depoy, “High-quantum-efficiency 0.5 eV GaInAsSb/GaSb thermophotovoltaic devices,” Appl. Phys. Lett. 75, 1305–1307 (1999). [CrossRef]

, 4

4. M. W. Dashiell, J. F. Beausang, H. Ehsani, G. J. Nichols, D. M. Depoy, L. R. Danielson, P. Talamo, K. D. Rahner, E. J. Brown, S. R. Burger, P. M. Fourspring, W. F. Topper Jr., P. F. Baldasaro, C. A. Wang, R. K. Huang, M. K. Connors, G. W. Turner, Z. A. Shellenbarger, G. Taylor, J. Li, R. Martinelli, D. Donetski, S. Anikeev, G. L. Belenky, and S. Luryi, “Quaternary InGaAsSb thermophotovoltaic diodes,” IEEE Trans. Electron. Dev. 53, 2879–2891 (2006). [CrossRef]

, 45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

] cells are obtained. As can be seen in Fig. 2, the normal incidence spectral emittance of the optimized 2D Ta PhCs is high at wavelengths below the bandgap of the respective TPV cells, and low in the non-convertible wavelength range. Note that in the optimization routine, we assume an approximate operating T of 1500 K and a fixed view factor F = 0.99, which is realistically achievable using a 10 cm × 10 cm flat plate geometry with separation s = 500 μm. Regardless, the exact operating T and F of the final optimal TPV system is relatively unimportant as long as they are reasonably close. This is due to the fact that the optimization routine indirectly searches for the design with the best selective normal and hemispherical emittance. Note that we have also limited d to 8.00 μm for ease of fabrication [41

41. V. Rinnerbauer, S. Ndao, Y. X. Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljačić, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” J. Vac. Sci. Technol. B 31, 011802 (2013). [CrossRef]

].

2.3. Plasma-dielectric stacks as cold side bandpass filters

Recent TPV system experiments demonstrating record ηTPV of 19% employed a greybody-like graphite emitter with a cold side tandem filter [44

44. C. J. Crowley, N. A. Elkouh, S. Murray, and D. L. Chubb, “Thermophotovoltaic converter performance for radioisotope power systems,” in AIP Conference Proceedings: Space Technology and Applications International Forum (AIP, 2005), pp. 601–614. [CrossRef]

]. It is thus instructive to compare the TPV system performance using 2D Ta PhCs as the emitter, with or without the tandem filter.

The tandem filter consists of bi-material multilayer dielectric stack terminated with a plasma filter [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

,31

31. T. D. Rahmlow, D. M. Depoy, P. M. Fourspring, H. Ehsani, J. E. Lazo-Wasem, and E. J. Gratrix, “Development of front surface, spectral control filters with greater temperature stability for thermophotovoltaic energy conversion,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 7th Conference (AIP, 2007), pp. 59–67.

]. The dielectric stack exhibits high transmission for photons within the convertible range yet simultaneously providing high reflection in the mid-infrared range (λ ∼ 2–6 μm). A plasma filter consisting of a highly doped semiconductor placed at the end of the multilayer dielectric stack extends the bandwidth of high reflection beyond λ = 6 μm. The cutoff can be shifted by modifying the thicknesses of the dielectric stack layers, and further optimized for particular TPV cells using the optimization technique described in [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

] by Rahmlow et al. The measured normal incidence transmittance of two particular designs optimized for 0.5 eV and 0.6 eV cutoffs are shown in Fig. 3. The filters are fabricated by Rugate Technologies, Inc. using antimony selenide (Sb2Se3) and yttrium fluoride (YF3) as the multilayer dielectric stack, and a heavily doped indium phosphide arsenide (InPAs) layer as the plasma filter.

Fig. 3 Measured normal incidence transmittance of tandem filters optimized for 0.5 eV and 0.6 eV TPV cells. The tandem filters consist of dielectric stacks of antimony selenide (Sb2Se3) and yttrium fluoride (YF3), terminated with a 1 μm thick heavily doped indium phosphide arsenide (InPAs) layer as the plasma filter. The tandem filters are sourced from Rugate Technologies, Inc.

3. Results and discussion

3.1. Optimized InGaAsSb TPV system

Figure 4 presents the measured external quantum efficiency (EQE) of the fabricated InGaAsSb cells [45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

], together with the normal (ε) and hemispherical emittance (εH) of the optimized 2D Ta PhC. As can be seen, the cutoff of the emittance matches well with the EQE of the InGaAsSb TPV cell. Although the performance is excellent at normal incidence, εH is significantly lower in the region of high EQE, which would negatively impact both ηTPV and Jelec,max since typical TPV systems are operated at high view factors.

The intrinsic angular selectivity of the 2D Ta PhC arises from the constancy of the resonant peaks and the decreasing diffraction threshold as a function of incident polar angle. At wavelengths below the diffraction threshold, absorptance decreases because there are more channels to reflect back to and the radiative Q decreases, thus destroying Q-matching. Therefore, at larger incident polar angles, the in-band absorption region decreases and has a lower average absorptance (see Fig. 4). Nevertheless, εH still approaches the long wavelength limit determined by the volume fraction of air to Ta, thus maintaining some degree of spectral selectivity.

Fig. 4 Relevant optical properties for optimized components in an InGaAsSb TPV system. The normal incidence emittance ε and hemispherical emittance εH of the optimized 2D Ta PhC emitter, and 45° reflectance Rθ=45° of the 0.53 eV tandem filter is shown to match the external quantum efficiency (EQE) of InGaAsSb. An ideal cutoff emitter is included in the analysis to elucidate the effect of non-ideal spectral emittance of the optimized 2D Ta PhC.

The tandem filter also suffers from angular dispersion detrimental to TPV systems. However, variations in the magnitude of transmittance for wavelengths smaller than the cutoff and reflectance for wavelengths larger than the cutoff are less severe compared to the optimized 2D Ta PhCs. As θ increases, the cutoff shifts to smaller wavelengths; selectivity only starts degrading above θ = 60° [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

]. Hence, the spectral hemispherical reflectance of the tandem filter is closely approximated by θ = 45° reflectance, Rθ= 45°. Since spectral hemispherical reflectance measurements of optimized filters are not available, shifted versions of measured normal incidence transmittance of filters shown in Fig. 3 are used as an estimate for Rθ= 45° in order to obtain estimates of ηTPV for systems employing the tandem filter. This is reasonable given that the cutoff of the filter is easily shifted within the wavelength range of interest in TPV by altering the layers’ thicknesses, Rθ= 45° closely approximates normal incidence reflectance, and the filter exhibits absorptance close to zero for λ = 1–9 μm [28

28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, and D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.

]. The estimated Rθ= 45° for a 0.53 eV tandem filter optimized for InGaAsSb TPV cells is shown in Fig. 4.

For TPV systems without the optimized tandem filter, the reflectance of the bare InGaAsSb cell becomes critical. Hence, reflectance of the InGaAsSb cells are included whenever possible, i.e. extracted from data published in literature [45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

]. Nevertheless, due to the limited wavelength range where reflectance data is available, we assume zero reflectance at wavelengths where data is unavailable to ensure conservative ηTPV estimates. We also assume a constant reflectance for the TPV cells over all angles as published literature data for experimentally fabricated cells are limited to near normal incidence. Regardless, these approximations do not prevent us from exposing critical spectral control requirements necessary in engineering efficient TPV systems, which is the main objective of this investigation.

3.2. Effect of temperature and view factor

Using the numerical model presented in Section 2, ηTPV can be estimated for InGaAsSb TPV systems comprising the ideal cutoff selective emitter, 2D Ta PhC selective emitter, or greybody emitter (ε= 0.9), with or without the optimized tandem filter. First, we consider a system with a fixed F = 0.99. As shown in Fig. 5(a), there exists an optimum operating T for each of the combinations considered; if T is too low, the emission peak is located at wavelengths smaller than the bandgap of the TPV cell as indicated by sub-optimal ηCav–Spec and ηCell shown in Figs. 5(b) & (c); if T is too high, the TPV cell’s series resistance losses dominate as indicated by the reduction in ηCell shown in Fig. 5(c).

At the optimum T, highest ηTPV is achieved by including the optimized 0.53 eV tandem filter; coupling the filter with the greybody and 2D Ta PhC emitter results in a maximum efficiency ηTPV,max of 23.5% and 23.7% respectively, which is extremely close to the performance of the ideal cutoff emitter of ηTPV,max = 24.3%. The optimum operating temperatures are 1260 K, 1230 K, and 1210 K for the 2D TaPhC, greybody, and ideal cutoff emitter respectively, when coupled with the tandem filter. For all three cases, power density is approximately 0.62 W cm−2. The results however indicate that in a high F system, the use of a selective emitter is not critical if an optimized tandem filter is present. This is mainly due to the tandem filter’s steep cutoff and high reflectance below the bandgap. Nevertheless, if implementation of the filter is not possible, the optimized 2D Ta PhC emitter offers > 70% improvement in ηTPV,max over the greybody emitter.

Fig. 5 (a) Radiant heat-to-electricity ηTPV for various emitters with or without an optimized tandem filter in combination with InGaAsSb TPV cell at fixed view factor F = 0.99 (10 cm × 10 cm flat plate geometry with separation s = 500 μm). An optimum temperature T exist for each combination. Due to considerable emission below the bandgap of the In-GaAsSb TPV cell for the emitters considered, significant improvement is seen with the use of the tandem filter. (b) Overall spectral efficiency when TPV cavity effects are included, ηCav–Spec. When F = 0.99, use of a selective emitter is not critical if an optimized tandem filter is present. (c) TPV cell efficiency ηCell. For T > 1200 K, degradation of ηCell is seen due to larger series resistance losses from high carrier injection.

To further study the effect of F, we consider each of the combinations at their optimum T. As shown in Fig. 6 the greybody performs as well as the optimized 2D Ta PhC when coupled with the optimized tandem filter at F > 0.97 (10 cm × 10 cm flat plate geometry with separation s < 1.7 mm). If F < 0.97, significant improvement is seen with the optimized 2D Ta PhC over the greybody as the efficiency of photon recycling using the tandem filter deteriorates. Note also that in practical systems, F is limited by the reduction in active cell area due to front side metallization requirements of the TPV cells.

Fig. 6 With T fixed at the optimum, the most efficient combination depends on the experimentally achievable F. For F > 0.97 (10 cm × 10 cm flat plate geometry with separation s < 1.7 mm), the use of the optimized tandem filter allows the greybody to slightly outperform the optimized 2D Ta PhC selective emitter. In contrast, it is important to restrict below bandgap emission via selective emitters in TPV systems with smaller view factors.

3.3. Effect of non-ideal selective emitter

As can be seen in Fig. 5, a selective emitter is critical for TPV systems without the optimized tandem filter. It is also observed that the optimized 2D Ta PhC emitter does not come close to achieving the performance of the ideal cutoff emitter. This is primarily due to long wavelength emittance that is larger by a factor of two compared to the ideal cutoff emitter, which is inevitable even with a low emissivity polished metal given that intrinsic free electron damping losses significantly increase with the rise of temperature [50

50. Y. S. Touloukian and D. P. DeWitt, “Thermal Radiative Properties: Metallic Elements and Alloys,” in Thermo-physical Properties of Matter Volume 7(IFI/PLENUM, 1970).

]. The question now lies as to how much improvement can be seen if the long wavelength emission can be suppressed to hypothetical levels in future selective emitter development. To study this, we compare the performance of a greybody emitter to an ideal cutoff selective emitter, with above bandgap hemispherical emittance εsw = 0.9, and a varying below bandgap hemispherical emittance εlw. Estimates of ηTPV for both emitters at T = 1250 K (which is approximately the optimum for InGaAsSb TPV) with or without the 0.53 eV optimized tandem filter are presented in Figs. 7(a) and 7(b) for F = 0.99 and F = 0.97 respectively.

Fig. 7 ηTPV for an InGaAsSb TPV system including an ideal cutoff emitter with varying below bandgap hemispherical emittance εlw with or without a 0.53 eV optimized tandem filter at a fixed temperature T of 1250 K. (a) F = 0.99. To outperform the greybody - optimized tandem filter combination, εlw must be smaller than 0.03, to a point where addition of the tandem filter is detrimental given the larger reduction in power density for a small improvement in ηTPV. (b) F = 0.97. To outperform the greybody - optimized tandem filter combination, εlw must be smaller than 0.08. As F is reduced, both aspects of spectral control become important.

As can be seen, use of a selective emitter results in markedly increased ηTPV over a grey-body if the optimized tandem filter is absent. Notice that a larger relative improvement in ηTPV is seen compared to the relative reduction in εlw. However, for a TPV system using only the ideal cutoff emitter for spectral control, εlw must be smaller than 0.03 to outperform the grey-body – optimized tandem filter combination. Thus, effective spectral control is more readily attainable using the cold side optimized tandem filter compared to the hot side selective emitter in high F TPV systems. If F < 0.97, both aspects of spectral control become important; a relative improvement > 10% over the greybody emitter is realized for εlw < 0.1 when used in combination with the optimized tandem filter.

3.4. Effect of non-ideal TPV cells

From 1975 to 2000, efficiencies of silicon PV cells under AM1.5G solar irradiance have more than doubled from 13% to 25% [51

51. NREL, “Best Research-Cell Efficiencies Chart,” http://www.nrel.gov/ncpv/images/efficiency_chart.jpg.

]. In fact, the latest state of the art silicon PV cells approach ∼ 85% of their theoretical thermodynamic limit [52

52. C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51, 4494–4500 (1980). [CrossRef]

], a feat made even more impressive given that silicon has an indirect bandgap. It is thus reasonable to envision a similar path followed by direct low bandgap TPV cells if similar research efforts are undertaken, upon which would lead to significantly higher ηTPV.

To quantify the possible increase in ηTPV, we consider TPV cells limited only by thermalization losses and radiative recombination, i.e. the Shockley-Queisser limit [53

53. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32, 510–519 (1961). [CrossRef]

]. This is easily implemented in the model described in Section 2.1 by setting Rs = 0, Rsh = ∞, and m = 1 in Eq. 10. In addition, Io is set to the thermodynamic limit determined solely by radiative recombination [52

52. C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51, 4494–4500 (1980). [CrossRef]

]:
Io=A2q(n2+1)Eg2kTc4π2h¯3c2exp(Eg/kTc)
(16)
where n is the refractive index of the TPV semiconductor region, Eg is the energy gap of the TPV cell, and = h/2π. Lastly, the ideal TPV cell is assumed to possess an EQE(λ) of 1 for wavelengths smaller than the bandgap and 0 for wavelengths larger than the bandgap. Using this, predicted ηTPV for all emitter-filter-TPV cell combinations are obtained and are presented in Table 1. Note that the 2D Ta PhC selective emitters, tandem filter, and T indicated in brackets are optimized for current state of the art low bandgap TPV cells (GaSb [45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

], InGaAs [3

3. R. R. Siergiej, B. Wernsman, S. A. Derry, R. G. Mahorter, R. J. Wehrer, S. D. Link, M. N. Palmisiano, R. L. Messham, S. Murray, C. S. Murray, F. Newman, J. Hills, and D. Taylor, “20% efficient InGaAs/InPAs TPV cells,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 5th Conference (AIP, 2003), pp. 414–423. [CrossRef]

], and InGaAsSb [45

45. W. Chan, R. Huang, C. A. Wang, J. Kassakian, J. D. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Sol. Ener. Mater. Sol. Cells 94, 509–514 (2010). [CrossRef]

]). In this analysis, we have also neglected the contribution of reabsorption of photons generated by radiative recombination in the TPV cells by the emitter, since it is much smaller than Pem, and that typical maximum power operation extracts > 90% of the photocurrent generated. If this contribution is included, we expect < 5% relative increase in ηTPV estimates for the ideal cell.

Table 1. Predicted ηTPV,max for three different TPV cells utilizing experimentally realizable spectral control components at fixed F = 0.99. Optimum temperature indicated in brackets is determined for each TPV system combination using fabricated and characterized TPV cells (GaSb [45], InGaAs [3], and InGaAsSb [45]). Results indicate that current state of the art fabricated TPV cells are ∼ 50% as efficient as their thermodynamically ideal counterparts. It is also interesting to note that spectral control via the optimized 2D Ta PhC and tandem filter enables TPV cells with larger bandgaps (GaSb) to perform as well as TPV cells with smaller bandgaps (InGaAsSb). However, the use of smaller bandgap TPV cells would result in lower optimum temperatures.

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As can be seen in Table 1, current state of the art fabricated TPV cells are ∼ 50% as efficient as their thermodynamically ideal counterparts. For the InGaAsSb TPV system utilizing the optimized tandem filter and the optimized 2D Ta PhC selective emitter at the optimum operating T = 1260 K, ∼ 12%, ∼ 28%, and ∼ 13% of the losses are attributable to non-ideal EQE, non-radiative recombination mechanisms, and series resistance respectively. Series resistance is also the main cause of lower optimum operating T. As T approaches 1800 K, the proportion of losses attributable to series resistance increases to ∼ 40%.

The most efficient TPV system that can be assembled today consists of the experimentally demonstrated InGaAs TPV cells in combination with an optimized 2D Ta PhC selective emitter and an optimized cold side tandem filter. This system exhibits ηTPV = 25% and Jelec,max = 0.68 W cm−2 at realistic T = 1320 K and F = 0.99. ηTPV for this configuration is ∼ 55% of the ideal TPV cell limit shown in Table 1. If TPV cells are to follow a similar research path witnessed by silicon PV cells (reaching ∼ 85% of their theoretical thermodynamic limit), ηTPV for this system could reach ∼ 40%. Note that the theoretical 0.62 eV single bandgap TPV thermodynamic efficiency limit (with ideal TPV cell and ideal spectral control, which is analogous to the Shockley-Queisser limit for silicon PV), and the theoretical infinite bandgaps TPV thermodynamic efficiency limit (i.e. the Carnot efficiency limit) are respectively 55% and 77% at T = 1320 K and Tc = 300 K.

3.5. Comparisons with notable TPV experimental efforts

To the best of our knowledge, the highest radiant heat-to-electricity efficiency reported to date is 23.6% with Jelec,max = 0.79 W cm−2 at T = 1312 K using InGaAs cells attached with a similar cold side bandpass filter described in Section 2.3, and a greybody-like SiC emitter [43

43. B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, C. S. Murray, F. Newman, D. Taylor, D. M. Depoy, and T. Rahmlow, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004). [CrossRef]

]. Note, however, that this measurement does not include optical cavity losses. If optical cavity losses are included, our numerical model predicts ηTPV = 19.9% and Jelec,max = 0.80 W cm−2, which is in good agreement with the reported results. A similar experiment, albeit with modifications to include optical cavity losses, and using a greybody-like graphite emitter instead, resulted with ηTPV = 19.1% and Jelec,max = 0.66 W cm−2 at T = 1350 K [44

44. C. J. Crowley, N. A. Elkouh, S. Murray, and D. L. Chubb, “Thermophotovoltaic converter performance for radioisotope power systems,” in AIP Conference Proceedings: Space Technology and Applications International Forum (AIP, 2005), pp. 601–614. [CrossRef]

]. Our numerical model, which does not include cell array losses, predicts ηTPV = 20.4% and Jelec,max = 0.73 W cm−2. If the greybody-like graphite emitter is substituted with an optimized 2D Ta PhC, the TPV system can achieve ηTPV = 20.6% and Jelec,max = 0.76 W cm−2. Due to the marginal improvements, a greybody-like emitter would be a better choice in a high F system if an optimized tandem filter is present. This result also highlights the need for developing selective emitters that approach the ideal cutoff emitter, possess ultra low εlw, and maintain selectivity over all angles, in order to maintain its relevance in advancing the performance of TPV systems.

For GaSb based TPV systems, the highest radiant heat-to-electricity efficiency reported to date is 21.5% (does not include optical cavity losses) with Jelec,max = 1.50 W cm−2 at T = 1548 K using an anti-reflection coated tungsten emitter with a dielectric filter that transmits useful photons with wavelengths below 1.8 μm while reflecting over 95% the photons in the wavelength range 1.8–3.5 μm [54

54. L. M. Fraas and L. Minkin, “TPV history from 1990 to present & future trends,” AIP Conf. Proc. 890, 17–23 (2007). [CrossRef]

]. This is consistent with the results presented in Table 1. These results also reveal another interesting aspect; spectral control is a great equalizer between different TPV cell technologies. Hence, the simpler, cheaper, and more robust GaSb cells might be the future way forward for practical TPV systems.

4. Conclusion

Spectral control via selective emitters and/or cold side filters is vital towards achieving higher TPV efficiencies. Amongst experimentally demonstrated selective emitters, 2D Ta PhC’s hold great promise due to ease of design, large area fabrication, system integration, and ability to withstand extended operation at high temperatures. Most importantly, the selectivity enables up to 100% improvement over a greybody emitter. Substantial improvements in performance can be achieved if further selective emitter development that reduces both long wavelength emittance and angular dispersion is undertaken.

The optimum spectral control approach depends on the achievable view factor, F. For F > 0.97 (10 cm × 10 cm flat plate geometry with separation s < 1.7 mm), the greybody emitter outperforms the 2D Ta PhC emitter when coupled with an optimized cold side tandem filter. This is due to high photon recycling efficiency at large F. However, as F < 0.97, use of both the selective emitter and the cold side filter becomes necessary for maximum TPV efficiencies.

By combining an optimized 2D Ta PhC selective emitter with an optimized cold side tandem filter, a TPV energy conversion system with radiant heat-to-electricity efficiency of 25% and power density of 0.68 W cm−2 can be achieved using experimentally demonstrated InGaAs TPV cells at realistic emitter temperatures of 1320 K and F = 0.99 (10 cm × 10 cm flat plate geometry with s = 500 μm). The efficiency could be increased to ∼ 40% (the theoretical 0.62 eV single bandgap TPV and infinite bandgaps TPV thermodynamic limit at emitter temperature of 1320 K and cell temperature of 300 K are 55% and 77% respectively) if TPV cells are to follow a similar research path witnessed by silicon PV cells, thus paving the way towards widespread adoption of what may be a promising highly efficient, portable, and reliable energy conversion system.

Acknowledgments

The authors would like to thank Peter Bermel and Michael Ghebrebrhan for valuable discussions. We would also like to thank Christine Wang of Lincoln Laboratory for providing us with the InGaAsSb TPV cells in this work. This work was partially supported by the Army Research Office through the Institute for Soldier Nanotechnologies under Contract No. W911NF-13-D-0001. Y. X. Y., W. R. C., and M. S. were partially supported by the MIT S3TEC Energy Research Frontier Center of the Department of Energy under Grant No. DE-SC0001299. V. R. gratefully acknowledges funding by the Austrian Science Fund (FWF): J3161-N20.

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T. D. Rahmlow, D. M. Depoy, P. M. Fourspring, H. Ehsani, J. E. Lazo-Wasem, and E. J. Gratrix, “Development of front surface, spectral control filters with greater temperature stability for thermophotovoltaic energy conversion,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 7th Conference (AIP, 2007), pp. 59–67.

32.

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R. K. Huang, C. A. Wang, M. K. Connors, G. W. Turner, and M. W. Dashiell, “Hybrid back surface reflector GaInAsSb thermophotovoltaic devices,” AIP Conf. Proc. 738, 329–336 (2004). [CrossRef]

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P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010). [CrossRef] [PubMed]

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M. Ghebrebrhan, P. Bermel, Y. X. Yeng, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Tailoring thermal emission via Q-matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011). [CrossRef]

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OCIS Codes
(260.2160) Physical optics : Energy transfer
(050.5298) Diffraction and gratings : Photonic crystals
(290.6815) Scattering : Thermal emission

ToC Category:
Thermophotovoltaics

History
Original Manuscript: August 6, 2013
Revised Manuscript: September 30, 2013
Manuscript Accepted: October 1, 2013
Published: October 17, 2013

Citation
Yi Xiang Yeng, Walker R. Chan, Veronika Rinnerbauer, John D. Joannopoulos, Marin Soljačić, and Ivan Celanovic, "Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems," Opt. Express 21, A1035-A1051 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S6-A1035


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References

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  2. O. V. Sulima, A. W. Bett, “Fabrication and simulation of GaSb thermophotovoltaic cells,” Sol. Ener. Mater. Sol. Cells 66, 533–540 (2001). [CrossRef]
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  8. M. Zenker, A. Heinzel, G. Stollwerck, J. Ferber, J. Luther, “Efficiency and power density potential of combustion-driven thermophotovoltaic systems using GaSb photovoltaic cells,” IEEE Trans. Electron. Dev. 48, 367–376 (2001). [CrossRef]
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  12. V. M. Andreev, A. S. Vlasov, V. P. Khvostikov, O. A. Khvostikova, P. Y. Gazaryan, S. V. Sorokina, N. A. Sadchikov, “Solar thermophotovoltaic converters based on tungsten emitters,” J. Sol. Ener. Eng. 129, 298–303 (2007). [CrossRef]
  13. C. S. Murray, C. J. Crowley, S. Murray, N. A. Elkouh, R. W. Hill, D. E. Chubb, “Thermophotovoltaic converter design for radioisotope power systems,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 123–132.
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  15. H. Yugami, H. Sai, K. Nakamura, N. Nakagawa, H. Ohtsubo, “Solar thermophotovoltaic using Al2O3/Er3Al5O12eutectic composite selective emitter,” in Conference Record of the Twenty Eigth IEEE Photovoltaic Specialists Conference (IEEE, 2000), pp. 1214–1217. [CrossRef]
  16. L. Ferguson, F. Dogan, “A highly efficient NiO-Doped MgO matched emitter for thermophotovoltaic energy conversion,” Mat. Sci. Eng. B 83, 35–41 (2001). [CrossRef]
  17. B. Bitnar, W. Durisch, J.-C. Mayor, H. Sigg, H. Tschudi, “Characterisation of rare earth selective emitters for thermophotovoltaic applications,” Sol. Ener. Mater. Sol. Cells 73, 221–234 (2002). [CrossRef]
  18. A. Narayanaswamy, G. Chen, “Thermal emission control with one-dimensional metallodielectric photonic crystals,” Phys. Rev. B 70, 125101 (2004). [CrossRef]
  19. D. L. C. Chan, M. Soljačić, J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Phys. Rev. E 74, 016609 (2006). [CrossRef]
  20. A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
  21. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, R. Biswas, “Photonic crystal enhanced narrow-band infrared emitters,” Appl. Phys. Lett. 81, 4685–4687 (2002). [CrossRef]
  22. H. Sai, H. Yugami, “Thermophotovoltaic generation with selective radiators based on tungsten surface gratings,” Appl. Phys. Lett. 85, 3399–3401 (2004). [CrossRef]
  23. D. L. C. Chan, M. Soljačić, J. D. Joannopoulos, “Thermal emission and design in 2D-periodic metallic photonic crystal slabs,” Opt. Express 14, 8785–8796 (2006). [CrossRef] [PubMed]
  24. I. Celanovic, N. Jovanovic, J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008). [CrossRef]
  25. R. Biswas, D. Zhou, I. Puscasu, E. Johnson, A. Taylor, W. Zhao, “Sharp thermal emission and absorption from conformally coated metallic photonic crystal with triangular lattice,” Appl. Phys. Lett. 93, 063307 (2008). [CrossRef]
  26. S. Y. Lin, J. Moreno, J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic power generation,” Appl. Phys. Lett. 83, 380–382 (2003). [CrossRef]
  27. D. L. C. Chan, M. Soljačić, J. D. Joannopoulos, “Direct calculation of thermal emission for three-dimensionally periodic photonic crystal slabs,” Phys. Rev. E 74, 036615 (2006). [CrossRef]
  28. T. D. Rahmlow, J. E. Lazo-wasem, E. J. Gratrix, P. M. Fourspring, D. M. Depoy, “New performance levels for TPV front surface filters,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 6th Conference (AIP, 2004), pp. 180–188.
  29. R. T. Kristensen, J. F. Beausang, D. M. Depoy, “Frequency selective surfaces as near-infrared electromagnetic filters for thermophotovoltaic spectral control,” J. Appl. Phys. 95, 4845–4851 (2004). [CrossRef]
  30. F. O’Sullivan, I. Celanovic, N. Jovanovic, J. Kassakian, S. Akiyama, K. Wada, “Optical characteristics of one-dimensional Si/SiO2photonic crystals for thermophotovoltaic applications,” J. Appl. Phys. 97, 033529 (2005). [CrossRef]
  31. T. D. Rahmlow, D. M. Depoy, P. M. Fourspring, H. Ehsani, J. E. Lazo-Wasem, E. J. Gratrix, “Development of front surface, spectral control filters with greater temperature stability for thermophotovoltaic energy conversion,” in AIP Conference Proceedings: Thermophotovoltaic Generation of Electricity 7th Conference (AIP, 2007), pp. 59–67.
  32. G. W. Charache, D. M. DePoy, P. F. Baldasaro, B. C. Campbell, “Thermophotovoltaic devices utilizing a back surface reflector for spectral control,” AIP Conf. Proc. 358, 339–350 (1996). [CrossRef]
  33. R. K. Huang, C. A. Wang, M. K. Connors, G. W. Turner, M. W. Dashiell, “Hybrid back surface reflector GaInAsSb thermophotovoltaic devices,” AIP Conf. Proc. 738, 329–336 (2004). [CrossRef]
  34. L. B. Karlina, M. M. Kulagina, N. K. Timoshina, A. S. Vlasov, V. M. Andreev, “In0.53Ga0.47As/InP conventional and inverted thermophotovoltaic cells with back surface reflector,” AIP Conf. Proc. 890, 182–189 (2007). [CrossRef]
  35. P. F. Baldasaro, J. E. Raynolds, G. W. Charache, D. M. Depoy, C. T. Ballinger, T. Donovan, J. M. Borrego, “Thermodynamic analysis of thermophotovoltaic efficiency and power density tradeoffs,” J. Appl. Phys. 89, 3319–3327 (2001). [CrossRef]
  36. T. A. Walsh, S. Y. Lin, “Power density and efficiency of thermophotovoltaic energy conversion using a photonic-crystal emitter and a 2-D metal-grid filter,” IEEE Trans. Electron. Dev. 55, 1101–1108 (2008). [CrossRef]
  37. P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010). [CrossRef] [PubMed]
  38. M. Ghebrebrhan, P. Bermel, Y. X. Yeng, J. D. Joannopoulos, M. Soljačić, I. Celanovic, “Tailoring thermal emission via Q-matching of photonic crystal resonances,” Phys. Rev. A 83, 033810 (2011). [CrossRef]
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