Two-dimensional VO2 photonic crystal selective emitter

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Two-dimensional VO2 photonic crystal selective emitter Hong Ye n, Hujun Wang, Qilin Cai Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China

a r t i c l e i n f o

abstract

Article history: Received 20 August 2014 Received in revised form 16 January 2015 Accepted 25 January 2015

The design and simulation of a two-dimensional (2D) photonic crystal (PhC) selective emitter made of vanadium dioxide (VO2), a type metal oxide with a high temperature resistance, are reported. Spectral emission characteristics of the 2D VO2 PhCs were investigated using the finite difference time domain (FDTD) method. The PhC consists of a periodic array of cylindrical air microcavities. The influences of the geometric characteristic parameters are discussed. The influences of the radius and depth on the emission of the 2D VO2 PhC can be explained based on the coupled-mode theory. The emissivities at wavelengths below the cut-off wavelength were enhanced by increasing the depth. When the depth was much larger than the radius, the cut-off wavelength increased with the radius. The effect of the period on the emissivity at wavelengths less than the period was highly influenced by the diffraction modes. The designed 2D VO2 PhC emitter exhibited a selective emission that was well-matched with InGaAs cells. The spectral emissivities within the convertible wavelength range of the InGaAs cells reached 0.95, and the emissivities for non-convertible wavelengths were less than 0.3. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Vanadium dioxide Photonic crystals Selective emitter FDTD

1. Introduction Thermophotovoltaic (TPV) technology can directly convert the infrared radiation of a high temperature heat source into electrical energy using TPV cells. Recent advancements in the field of low-bandgap photovoltaic cells have led to a renewed interest in the pursuit of high performance TPV systems [1–4]. Although low-bandgap TPV cells allow more efficient conversion of the emission from the heat source, the broadband thermal emission from the gray emitter comprises a significant portion of the non-convertible wavelengths of TPV cells. The key to achieving the high efficiency and power density predicted by theoretical studies is to develop selective emitters, which can emit photons in a certain spectral range that match well with a certain TPV cell. Photonic crystals (PhCs) n Corresponding author. Tel.: þ86 551 63607281; fax: þ86 551 63607281. E-mail address: [email protected] (H. Ye).

are a type of periodic micro/nanostructured material that can form photonic forbidden bands or pass bands in a wavelength range comparable to the geometric size of the structure. PhCs are promising for their use in the design of high-performance selective emitters through material selection and physical design. A great deal of work has been dedicated to the design and fabrication of high-performance PhC selective emitters. [5–7] It has been found that the emissivities of 1D PhCs are usually sensitive to emission direction and show restricted suitability for high temperature applications and that 3D PhCs are difficult to prepare [8]. Currently, 2D PhCs offer immense potential for use in high-performance selective emitters. The 2D PhCs consisting of periodic inverted pyramids [9] and rectangular or cylinder microcavities [9–18] have been intensively studied. These PhCs all exhibit spectral emissivities that match TPV cells. Considering the high operating temperatures and long run times required for energy conversion, high temperature thermal stability is a great challenge that cannot be

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Please cite this article as: Ye H, et al. Two-dimensional VO2 photonic crystal selective emitter. J Quant Spectrosc Radiat Transfer (2015), http://dx.doi.org/10.1016/j.jqsrt.2015.01.022i

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ignored. Therefore, refractory metals such as tantalum (Ta) and tungsten (W) are commonly adopted to fabricate microstructure emitters due to their high melting points and low vapor pressures. However, according to a study by Lee [19], the micro/nanostructures of selective emitters degrades or disappears due to grain growth, oxidation, surface diffusion and evaporation when the structures are subjected to high temperatures over certain durations of time. This result has also been shown by Rinnerbauer [14]. It is well known that metallic oxide usually exhibits high-temperature stability, and it may be an alternative material that can be used to overcome problems such as oxidation. Unlike metallic materials, the emissivities of the metallic oxides usually increase with wavelength from near infrared to far infrared. This indicates that the use of metallic oxides in the design of selective emitters must not only enhance the emissions within the convertible wavelength range but also decrease the emissions within non-convertible wavelengths. Fortunately, metal insulator transition (MIT) materials [20], one type of metallic oxide, can transform from a relatively infrared transparent state to a metallic and relatively infrared reflecting state when the temperature rises above the phase transition temperature. Hence, it is possible to design a high-performance PhC selective emitter using MIT materials. In this paper, vanadium dioxide (VO2), an MIT material, was used for the first time to design a 2D PhC emitter. Based on the optical constants of VO2 in the high temperature metal phase, the spectral emissivity of the 2D PhC was calculated using the finite difference time domain (FDTD) method. The influences of the geometric characteristic parameters on the emissivities of 2D PhC emitters are discussed. According to the analysis and optimization of the feature sizes, a high-performance 2D VO2 selective emitter was designed.

Here ε1 represents a constant contribution to the real part of the dielectric constant from high frequency electronic transitions, h is Planck’s constant, and c is the speed of light in a vacuum. The parameters Ej, Amj and Brj are the energy, amplitude, and dumping coefficient of the oscillator j, respectively. The values of the parameters are listed in Table 1. The optical constants of VO2 (metal phase) were obtained below 120 1C. To investigate the stability of VO2 at higher temperatures, X-ray diffraction (XRD) was used to characterize the lattice structures of VO2 at various temperatures. VO2 powder samples were used in the XRD measurement. The powders were prepared via the thermolysis of a vanadyl ethylene glycolate precursor in an atmosphere of air. [23] A D/MAX-TTR III X-ray diffractometer was used to characterize the lattice structures of the powders, and the results are shown in Fig. 1. Compared with the standard data of VO2 in the metal phase, as shown in Fig. 1e, the characteristic peaks remain approximately unchanged when the temperature was increased from 200 to 800 1C. The lattice structure of Table 1 Lorentz oscillator parameters of VO2 (metal phase) [22].

ε1 ¼ 5:0

Oscillator

1

2

3

Ej (eV) Amj (eV) Brj (eV)

3.15 23.20 0.90

2.60 0 0.45

0 17.50 0.90

2. Materials and methods VO2 is a thermochromic material with a phase transition temperature of approximately 68 1C and a melting point of 1542 1C [13]. Monoclinic VO2 (insulator phase) transforms to tetragonal rutile VO2 (metal phase) when its phase transition temperature is reached. This material exhibits prospects for use in broad applications due to changes in its optical, electrical, and magnetic properties and lattice structure after phase transition. Recently, Zhou et al. [21] reported that introducing a periodic porous structure into a VO2 film revealed a new avenue for achieving excellent thermochromic properties. Kakiuchida et al. [13,14] reported the optical constants of VO2 in the visible and near-infrared wavelength ranges at various temperatures between 25 and 120 1C. The results indicated that the optical constants minimally changed for temperatures above 100 1C. The optical constants of VO2 (metal phase) can be described by the Lorentz-oscillator formula [22], εðωÞ ¼ ε1 þ

3 X

Amj

2 2 j ¼ 1 Ej  ðhc=λÞ  iBrðhc=λÞ

ð1Þ Fig. 1. X-ray diffraction (XRD) results of VO2 at various temperatures.

Please cite this article as: Ye H, et al. Two-dimensional VO2 photonic crystal selective emitter. J Quant Spectrosc Radiat Transfer (2015), http://dx.doi.org/10.1016/j.jqsrt.2015.01.022i

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the metal phase of VO2 does not change with the increase in temperature. Because it is difficult to obtain the high temperature optical constants of VO2, as a first step of the estimation, it was assumed that the optical constants of the metal phase VO2 were temperature-insensitive. The optical constants of the metal phase VO2 at 120 1C were used to calculate the high temperature radiative properties of 2D PhC emitters in this study. The temperature dependence of the optical constants at higher temperature above 120 1C should be studied as a future work. Fig. 2 shows a schematic diagram of a 2D VO2 PhC selective emitter. The PhC consists of a periodic array of cylindrical air microcavities. The spectral reflectivity of the 2D VO2 PhC was calculated using the finite difference time domain (FDTD) method. The FDTD model is shown in Fig. 3. The recording plane is an infinite plane parallel to the section of the structure. VO2 resides in a relatively infrared transparent state of a monoclinic structure below the phase transition temperature and undergoes a structural transformation to a metallic and relatively infrared reflecting state of a tetragonal structure above the phase transition temperature. In this work, the thickness of the substrate was on the order of at least millimeters, which was much larger than the penetration depth of VO2. Therefore, the emitter could be considered opaque in the visible and near-infrared regions at high temperatures. According to Kirchhoff’s Law and the

3

radiative property of an opaque medium, ελ;θ ¼ αλ;θ ;

ð2Þ

and αλ;θ þ ρλ;θ ¼ 1;

ð3Þ

where, ελ;θ , αλ;θ and ρλ;θ correspond to the normal spectral emissivity, absorptivity and reflectivity, respectively. Thus, the normal spectral emissivity can be obtained by ελ;θ ¼ 1  ρλ;θ

ð4Þ

3. Theoretical model 3.1. The couple-mode theory For 2D microcavity-type metallic PhCs, it has been reported that the enhancement in emissivity is usually achieved by coupling the emission to resonant electromagnetic modes of the cavity, and the cut-off wavelength is determined by the fundamental mode of the cylindrical metallic cavity [6,13,24]. Based on the coupled-mode theory [14] and the assumption that the electromagnetic response characteristics of a one-end-open cylindrical cavity with depth d can be approximated by that of a completely enclosed cylinder cavity with a depth of 2d, the resonant frequencies can be approximated as [25] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   1 X mn 2 pπ 2 ðf r ÞTMmnp ¼ pffiffiffiffiffi ; ð5Þ þ 2π με 2d r and ðf r ÞTEmnp

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  0 2 1 X mn pπ ¼ pffiffiffiffiffi þð Þ2 ; 2π με 2d r

ð6Þ

where, Xnm is the nth root of the mth order Bessel function, X 0mn is the nth root of the mth order Bessel function derivative, d and r are the depth and radius of the cylinder, respectively (as defined in Fig. 2), μ and ε are the permeability and permittivity of the medium filled in the cavity, and m, n and p are integers. There exists a series of resonant modes, and the TE and TM modes with the lowest resonant frequency are the TM010 and TE111 modes, respectively. For the TM010 and TE111 modes, Fig. 2. A diagram of the 2D VO2 PhC.(characteristic parameters: period a, depth d and radius r).

X 01 ¼ 2:405; and 0

X 11 ¼ 1:841:

Recording plane Reflect light Light source

The resonance wavelengths of the TM010 and TE111 modes can be expressed as λTM010 ¼ 2:61r

ð7Þ

and

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λTE111 ¼ 3:413r= 1 þ2:912r 2 =ð2dÞ2 :

Incident lignt Microstructure Fig. 3. The FDTD model of the 2D VO2 PhC.

ð8Þ

As the resonance frequency of the fundamental mode, the cut-off frequency can be approximated by the smaller of the resonance frequencies of the TE111 and TM010 modes. Hence, the cut-off wavelength can be approximated by the larger of the resonance wavelengths in Eqs. (7) and (8).

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3.2. Simplified TPV model Here, a simplified TPV model shown in Fig. 4 is used to investigate the performance of the TPV system with the VO2 PhC selective emitter. It is assumed that the view factor from the emitter to the cells is 1, and there is no energy loss from the side surfaces of the selective emitter. The temperature of the cell is set as 323 K. The net power density of the emission from the emitter to the cells is defined as Z 1 P R;total ¼ εR ðλÞEλ;b ðλ; TÞdλ; ð9Þ 0

Here εR ðλÞ is the hemispherical spectral emissivity of the emitter, and it was approximated by the normal one predicted in this work. Eλ;b ðλ; TÞ is the spectral power density of the blackbody defined as Eλ;b ðλ; TÞ ¼

2πhc20

ð10Þ

λ5 ðexp½hc0 =ðλkT R Þ 1Þ

h is Plank’s constant, c0 is the light speed in a vacuum, and k is the Boltzmann constant. The radiant power output within the convertible wavelength range of the TPV cell can be defined as Z λg P R;inband ¼ εR ðλÞEλ;b ðλ; TÞdλ ð11Þ λ0

Here λg is the bandgap wavelength, and λ0 is the smallest wavelength that can be converted by the TPV cells. Radiative efficiency is defined as ηsp ¼ P R;in band =P R :

ð12Þ

where εR(λ) is the spectral emissivity of the emitter, Eλ,b(λ) is the spectral power density of blackbody, λ0 and λg are the TPV cell band edges, SPλ is the spectral response of TPV cells which can be calculated from SP λ ¼

Q Eext eλ ; hc

ð15Þ

QEext is the external quantum efficiency of the cells, c is the speed of light, h is Plank’s constant and e is the electron charge. The open-circuit voltage, Voc is given by [1] V oc ¼

nkT C lnðJ SC =J 0 Þ e

ð16Þ

where n is the diode ideality factor (taken as 1.0 here), TC is the temperature of the cell, k is the Boltzmann factor, and JSC and J0 are the short circuit current density and the saturation current density, respectively. The saturation current density is estimated using the expression J 0 ¼ 1:5  105 expð 

Eg Þ; k UT C

ð17Þ

here Eg is the energy bandgap of the TPV cells. The fill factor is given by FF ¼ β

v  lnðv þ 0:72Þ vþ1

ð18Þ

where v ¼ eV oc =kT C and β is the amendment coefficient. Finally, the far-field TPV conversion efficiency can be expressed as ηsys ¼

P el  100%: P R;total

ð19Þ

The output electric power density[27] can be defined as P el ¼ V oc J SC FF;

ð13Þ

where Voc, JSC and FF are the open-circuit voltage, the short-circuit current and the fill factor of the TPV cell, respectively. Here, the short-circuit current is determined by Z λg J SC ¼ εR ðλÞEλ;b ðλÞSP λ dλ ð14Þ λ0

4. Results and discussions 4.1. The influence of the radius From Eqs. 7 and 8, the cut-off wavelength is only influenced by r and d. First, the spectral emissivities of the 2D VO2 PhCs with various radii were calculated, and the results are shown in Fig. 5, where the depth and period are fixed at 6.00 μm and 1.30 μm, respectively. The emis-

Heat

Selective emitter

hv>Eg

TPV cells Fig. 4. The schematic diagram of the TPV system [26].

Fig. 5. Simulated spectral emissivities of 2D VO2 photonic crystals with various radii (other dimensions: a¼ 1.30 μm; d ¼ 6.00 μm).

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sivity of flat VO2 is also provided as a comparison. As shown in Fig. 5, the VO2 PhC exhibits remarkable selective emission properties, and the simulated cut-off wavelengths increases with the radius. This finding is in agreement with Eq. (8), i.e., the cut-off wavelength increases with the radius when the depth is fixed. Here, the simulated cut-off wavelength represented the largest wavelength where the emission peak was located. Based on the coupled-mode theory, the cut-off wavelength can be approximated by the resonance wavelength of the fundamental mode TE111 of the cylindrical cavity under these geometry conditions. The comparison of the cut-off wavelengths obtained from Eq. (8) and the simulated results are given in Table 2. The results are within a 6% margin of error. This shows that the couple-mode theory can also be used to explain the radiative properties

Table 2 Estimated and simulated cut-off wavelengths for the 2D PhC emitters. Case

r (μm)

d (μm)

a (μm)

λTE111 (μm)

λsim (μm)

I II III

0.50 0.55 0.60

1.30 1.30 1.30

6.00 6.00 6.00

1.70 1.87 2.04

1.67 1.80 1.92

5

of the metal phase VO2 PhCs. In addition, there exist multiple emission peaks below the cut-off wavelengths, as emissions at wavelengths below the cut-off wavelength can be enhanced by coupling to high frequency resonant electromagnetic modes of the cavity. To further understand the resonance characteristics, the local field distributions at a selection of wavelengths are given in Fig. 6. Fig. 6a shows the field distribution at the wavelength of 3 μm, which is larger than the cut-off wavelength. The electromagnetic wave at this wavelength can minimally propagate in the cavity. Therefore, the structure presents a high reflectivity at this wavelength. The field distributions at three peaks (1.67, 1.60 and 1.52 μm) are shown in Fig. 6(b–d), respectively. Unlike the result shown in Fig. 6a, the electromagnetic waves at these three wavelengths are able to propagate in the cavity. The number of the standing waves increases with decreasing wavelengths. The electromagnetic wave can couple with the electromagnetic modes of the cavity at these wavelengths. Thus, the absorption is enhanced, and enhanced emissivity is also achieved according to Kirchhoff's law. Notably, not all of the emission peaks can be predicted based on the couple-mode theory. For example, Case I listed in Table 3 compares the simulated results (λsim) and the resonance wavelengths (λ). The results show that the

Fig. 6. The normalized electric field intensity distributions at various wavelengths. (a. λ ¼ 3 μm; b. λ ¼ 1.67 μm; c. λ ¼1.60 μm; d. λ¼ 1.52 μm).

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Table 3 The resonance wavelengths and simulated results of Case I. λsim (μm)

λ (μm)

1.67 1.60 1.52 1.43 1.29 1.20 1.12

1.70 (TE111) – – – 1.31 (TM010) – –

Fig. 8. Simulated spectral emissivities of 2D VO2 photonic crystals with various periods (other dimensions: d ¼6.00 μm; r¼ 0.50 μm).

Fig. 7. Simulated spectral emissivities of 2D VO2 PhCs with various depths (other dimensions: a¼ 1.40 μm; r¼ 0.50 μm).

couple-mode theory cannot predict all of the emission peaks, which has also been shown in previously reported studies [6,14,17,18,28]. 4.2. The influence of depth The influence of depth on spectral emissivity was calculated when the radius and period were fixed at 0.50 μm and 1.40 μm, respectively, and the results are shown in Fig. 7. The cut-off wavelength appears insensitive to the depth. As previously mentioned, the cut-off wavelength can be evaluated using Eq. (8). When d is a constant, the resonance wavelength of the lowest TE mode decreases with increasing r, and vice versa. However, it 2 should be noted that 2:912ðr 2 =4d Þ{1 for the PhCs in Fig. 7, so the cut-off wavelength seems to be invariable with d. In addition, with increased d, the interaction time of light becomes longer and the light is able to be absorbed more efficiently. Therefore, the emissivities at wavelengths below the cut-off wavelength become larger. 4.3. The influence of the period The previous analysis showed that the influences of the radius and depth on the emission of 2D VO2 PhC can be explained with the coupled-mode theory. However, the period is not contained in Eq. (8). To discuss the influence of period, the spectral emissivities of PhCs with various

Fig. 9. Spectral emissivity (blue line) of the 2D VO2 PhC emitter matched with the InGaAs cells (r¼ 0.45 μm, d ¼6.00 μm, and a¼ 1.00 μm) and the quantum efficiency [31] of the InGaAs cell (black line).

periods were calculated, and the results are shown in Fig. 8. The cut-off wavelength remains nearly constant with the increased period. The emissivity at wavelengths below the period decreases significantly. This is in consistent with the results reported by Ghebrebrhan et al. [29]. In this wavelength region, diffracted plane-wave modes appear. As described by Chou et al. [30], the grating equation can be used to analyze the influence of diffraction on the radiative property of PhCs: aðsinθi þsinθm Þ ¼ mλ; m ¼ 7 1; 7 2; 73:::

ð15Þ

Here a is the period, θi is the incident angle of the light, θm is the diffractive angle of order m, and λ is the wavelength. The emissivity decreases due to diffractive reflection, according to Eq. (4). For normal incident light (θi ¼0), the diffraction at order m occurs when θm ¼901, which leads to a ¼mλ. Only light at wavelengths less than or equal to the period can couple to diffractive modes. For light at oblique angles, the diffraction occurs at a high order of m. This explains the decrease in emissivity identified for wavelengths less than the period, as shown in Fig. 8. Therefore, it is important to choose a small period for a fixed radius to achieve broadband emissivity enhancement.

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Table 4 The performances of the TPV systems with SiC and VO2 PhC emitters. The temperature of emitter (K)

Emitter

Effective power density (W cm  2)

Radiative efficiency (%)

1300

VO2 PhC SiC

2.32 2.57

41.57 19.28

8.44 5.38

1400

VO2 PhC SiC

3.96 4.30

48.20 23.75

10.45 6.88

1500

VO2 PhC SiC

6.36 6.80

54.11 28.24

12.37 8.43

In addition, the emission at wavelengths longer than the cut off wavelength is very low. Because there are no modes to couple for the radiation in this region, the emission is only influenced by the materials in this region. The emissivity approaches that of flat VO2 with a decreasing ratio of the radius to the period.

4.4. The performance of a TPV system with a matched VO2 PhC emitter InGaAs cells are some of the most commonly used lowbandgap (0.62 eV) TPV cells. In0.69Ga0.31As cell [20,31] was used to investigate the performance of the TPV system with the VO2 PhC selective emitter. Using the guidelines previously mentioned, a 2D PhC emitter matched with an InGaAs cell was designed. According to the previous analysis, the cut-off wavelength can be tailored by selecting the cylindrical radius and depth. The emissivity at wavelengths below the cut-off wavelength can be enhanced by increasing the depth, and the cut-off wavelength can be increased with the radius when the radius is much smaller than the depth. Small periods decrease the influence of the diffraction modes. Here, the depth of the cavity was set to 6.00 μm to enhance the emissivity at wavelengths below the cut-off wavelength, and the radius was set to 0.45 μm to ensure that the cut-off wavelength matched the bandgap of the InGaAs (0.62 eV) cell. The period was set to 1.00 μm to decrease the influence of the diffraction modes. The optimized results are shown in Fig. 9. Compared with the quantum efficiency of InGaAs cells, the average emissivity within the convertible wavelength range of the InGaAs cells reached 0.95, and the non-convertible emissivity was less than 0.3. In addition, selective emitters matched with various TPV cells can be designed by adjusting the specific sizes of the structure. Based on the simplified TPV system model introduced in Section 3.2, the performances of TPV systems with SiC (commonly used as the gray emitter) and VO2 PhC emitters were predicted. Because the power density of blackbody in the range of 0–0.6 μm accounts for a tiny proportion (0.17%) of the total radiative power density at 1500 K, the emission in the range of 0–0.6 μm could be ignored, and the smallest wavelength for the integration of the spectral radiative energy in Eqs. 9 is 0.6 μm. The results are listed in Table 4. The performance of the TPV system increases with the temperature. The radiative efficiency of the VO2 PhC emitter reached 54.11% at 1500 K. The efficiency of the TPV system with a VO2 PhC emitter

TPV efficiency (%)

increased by approximately 50% compared to the efficiency of the TPV system with an SiC emitter.

5. Conclusions VO2, a phase-change metal oxide, was used for the first time to design a 2D photonic crystal selective emitter. Based on the optical constants of VO2 in the metal phase, the spectral emissivity of the PhC consisting of a periodic array of cylindrical air microcavities was calculated using the FDTD method. The cut-off wavelength increased with the radius, the emissivity at wavelengths below the cut-off wavelength were enhanced with increased depths, and the emissivity at wavelengths less than the period was highly influenced by the diffraction modes. According to the analysis, a 2D PhC emitter matched with InGaAs cells was designed, the emissivity within the convertible wavelength range of InGaAs cells reached 0.95, and the emissivity at non-convertible wavelength was less than 0.3. The system efficiency of a TPV system with a VO2 PhC emitter is approximately 50% higher than that of a TPV system with an SiC emitter. References [1] Iles PA, Chu C, Linder E. The influence of bandgap on TPV converter efficiency. AIP Conf Proc 1996;358:446–57. [2] Fraas LM, Qiu K. Ceramic IR emitter with spectral match to GaSb PV cells for TPV. MRS Online Proc Libr 2013;1493:11–22. [3] Charache GW, Baldasaro PF, Danielson LR. InGaAsSb thermophotovoltaic diode physics evaluation. Conference: 40 electronic materials conference, Jun 24, Charlottesville, United States; 1998. [4] Fraas L, Minkin L. TPV history from 1990 to present & future trends. AIP Conf Proc 2007;890:17–23. [5] Zhao B, Wang L, Shuai Y, Zhang ZM. Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure. Int J Heat Mass Transf 2013;67:637–45. [6] Rinnerbauer V, Ndao S, Yeng YX, Chan WR, Senkevich JJ, Joannopoulos JD, et al. Recent developments in high-temperature photonic crystals for energy conversion. Energy Environ Sci 2012;5:8815–23. [7] Shemelya C, DeMeo DF, Vandervelde TE. Two dimensional metallic photonic crystals for light trapping and anti-reflective coatings in thermophotovoltaic applications. Appl Phys Lett 2014;104: 0211151–4. [8] Chen YB, Tan KH. The profile optimization of periodic nanostructures for wavelength-selective thermophotovoltaic emitters. Int J Heat Mass Transf 2010;53:5542–51. [9] Sai H, Kanamori Y, Yugami H. Tuning of the thermal radiation spectrum in the near-infrared region by metallic surface microstructures. J Micromech Microeng 2005;15:S243–9. [10] Hanamura K, Kameya Y. Spectral control of thermal radiation using rectangular micro-cavities on emitter-surface for thermophotovoltaic generation of electricity. J Therm Sci Tech-JPN 2008;3:33–44.

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[28]

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Please cite this article as: Ye H, et al. Two-dimensional VO2 photonic crystal selective emitter. J Quant Spectrosc Radiat Transfer (2015), http://dx.doi.org/10.1016/j.jqsrt.2015.01.022i