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基于CaF2/W多层膜人工双曲介质的近场热光伏器件

杜玮 尹格 马云贵

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基于CaF2/W多层膜人工双曲介质的近场热光伏器件

杜玮, 尹格, 马云贵

High-performance near-field thermophotovoltaic device with CaF2/W multilayer hyperbolic metamaterial emitter

Du Wei, Yin Ge, Ma Yun-Gui
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  • 基于近场热辐射的热光伏器件是一种极具应用前景的热电转换器件. 近场下由于倏逝波的隧穿作用, 可以获得远超黑体辐射的热流及热电功率, 此时辐射表面光子态密度是个关键因素. 本文提出了一种具有高表面态密度的CaF2/W多层膜人工双曲介质作为辐射器, 可以针对有限温度热源获得高效热电转化效果. 采用禁带宽度为0.17 eV的锑化铟p-n结作为接收端, 在200 K温度差和50 nm近场间隙下, 理论上计算获得了超过1 kW/m的高发电功率, 热电转化效率在11%以上, 显著高于热电材料的能量转换效率. 与纯钨热源情形相比, 双曲介质具有更高的倏逝波态密度, 有助于显著增强辐射热流与能量利用率. 进一步研究发现, 当多层膜双曲介质厚度超过140 nm时, 基底的影响已经可以忽略, 这对器件的实际制作非常有益. 相对于纳米线阵列或自然双曲介质, 本文提出的多层膜结构在制作和带宽上具有明显优势, 研究结果为近场热光伏的发展起到了促进作用.
    Thermophotovoltaic (TPV) device is a thermoelectric conversion method with great application prospects. In the far-field regime, the thermoelectric power is usually small due to the Planck blackbody radiation limit, but can be substantially enhanced in the near-field regime where evanescent waves will participate in the heat transfer by tunneling. In this aspect, the surface optical density of state is a key factor that will determine the transfer conversion of thermal photons. Plasmonic or phononic resonance materials have been discussed in the literature to acquire large heat flux. Besides, metamaterial is another way to pursue the design freedoms for the same purpose. In this work, we propose a [CaF2/W]n multilayer based infrared hyperbolic metamaterial (HMM) with high surface density of states as an emitter of a high-performance TPV cell made of an InSb p-n junction (energy bandgap = 0.17 eV). The effective medium theory (EMT) is utilized to describe the electromagnetic behavior of the HMM. The near-field heat flux is calculated based on electrodynamic wave theory and Green's function method, and the photocurrent of thermophotovoltaic device is derived using diffusion equation for semiconductor. For comparison, we design three different radiators, i.e. tungsten film (W), [GaF2/W]n multilayer hyperbolic metamaterial (HMM), and tungsten-grounded HMM (WHMM). Compared with the pure tungsten radiator, the artificial structure exhibits the hyperbolic dispersion characteristic in a wide frequency range, which gives rise to a higher local density of states, in particular in the hyperbolic-to-elliptic spectral transition region. As a result, the radiation power and the energy conversion efficiency are greatly enhanced, which are more easily realized by a matched emission band achieved by the structural design. We find that the thermophotovoltaic device with WHMM radiator has a similar power and conversion efficiency to that with the HMM radiator. The influence of the substrate can be ignored when the hyperbolic metamaterial is thicker than 140 nm, very beneficial to the actual fabrication of the device. By our system, with multilayer hyperbolic metamaterial (HMM) radiator, a high electric power >1 W/m2 and a conversion efficiency about 11% can be obtained at a bias temperature of 200 K and a 100 nm vacuum gap. Compared with nanowire arrays or natural hyperbolic material, the multilayer structure proposed in this paper has obvious advantages in bandwidth and manufacturing and may find important applications in near-field thermophotovoltaic device and other relevant areas.
      通信作者: 马云贵, yungui@zju.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61775195)和浙江省自然科学基金(批准号: LR15F050001, LZ17A040001)资助的课题
      Corresponding author: Ma Yun-Gui, yungui@zju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61775195) and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LR15F050001, LZ17A040001)
    [1]

    Hoffert M I, Caldeira K, Jain A K, Haites E F, Harvey L D D, Potter S D, Schlesinger M E, Schneider S H, Watts R G, Wigley T M L, Wuebbles D J 1998 Nature 395 881Google Scholar

    [2]

    BCS, Inc 2008 Waste Heat Recovery. Technology and Opportunities in U.S. Industry (Hinsdale: BCS) pp6–19

    [3]

    Liu W S, Jie Q, Kim H S, Ren Z F 2015 Acta Mater. 87 357Google Scholar

    [4]

    Alam H, Ramakrishna S 2013 Nano Energy 2 190Google Scholar

    [5]

    Chan W R, Bermel P, Pilawa-Podgurski R C N, Marton C H, Jensen K F, Senkevich J J, Joannopoulos J D, Soljacic M, Celanovic I 2013 PNAS 110 5309Google Scholar

    [6]

    Bierman D M, Lenert A, Chan W R, Bhatia B, Celanovic I, Soljacic M, Wang E N 2016 Nat. Energy 1 16068Google Scholar

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    Whale M D, Cravalho E G 2002 IEEE Trans. Energy Convers. 17 130Google Scholar

    [8]

    Yang J, Du W, Su Y, Fu Y, Gong S, He S, Ma Y 2018 Nat. Commun. 9 4033Google Scholar

    [9]

    Thomas N H, Sherrott M C, Broulliet J, Atwater H A, Minnich A J 2019 Nano Lett. 19 3898Google Scholar

    [10]

    Zhao B, Guizal B, Zhang Z M, Fan S, Antezza M 2017 Phys. Rev. B 95 245437Google Scholar

    [11]

    Zwol P J, Thiele S, Berger C, Heer W A, Chevrier J 2012 Phys. Rev. Lett. 109 264301Google Scholar

    [12]

    Liu B, Shen S 2013 Phys. Rev. B 87 115403Google Scholar

    [13]

    Jin S, Lim M, Lee S S, Lee B J 2016 Opt. Express 24 A635Google Scholar

    [14]

    Shi J, Liu B, Li P, Ng L Y, Shen S 2015 Nano Lett. 15 1217Google Scholar

    [15]

    Park K, Basu S, King W P, Zhang Z M 2008 J. Quant. Spectrosc. Radiat. Transfer 109 305Google Scholar

    [16]

    于海童, 刘东, 杨震, 段远源 2018 物理学报 67 024209Google Scholar

    Yu H T, Liu D, Yang Z, Duan Y Y 2018 Acta Phys. Sin. 67 024209Google Scholar

    [17]

    Zhao B, Santhanam P, Chen K, Buddhiraju S, Fan S 2018 Nano Lett. 18 5224Google Scholar

    [18]

    Fiorino A, Zhu L, Thompson D, Mittapally R, Reddy P, Meyhofer E 2018 Nat. Nanotechnol. 13 806Google Scholar

    [19]

    Papadakis G T, Buddhiraju S, Zhao Z, Zhao B, Fan S 2020 Nano Lett. 20 1654Google Scholar

    [20]

    Datas A, Vaillon R 2019 Appl. Phys. Lett. 114 133501Google Scholar

    [21]

    Malitson I H 1963 Appl. Opt. 2 1103Google Scholar

    [22]

    Liu X L, Zhang R Z, Zhang Z M 2014 Int. J. Heat Mass Transfer 73 389Google Scholar

    [23]

    Biehs S A, Tschikin M, Messina R, Ben-Abdallah P 2013 Appl. Phys. Lett. 102 131106Google Scholar

    [24]

    Lim M K, Jin S K, Lee S S, Lee B J 2015 Opt. Express 23 A240Google Scholar

    [25]

    Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 958Google Scholar

    [26]

    Liu X L, Bright T J, Zhang Z M 2014 J. Heat Transfer 136 092703Google Scholar

    [27]

    Zhang R Z, Zhang Z M 2017 J. Quant. Spectrosc. Radiat. Transfer 197 132Google Scholar

    [28]

    Volokitin A I, Persson B N J 2007 Rev. Mod. Phys. 79 1291Google Scholar

    [29]

    Volokitin A I, Persson B N J 1999 J. Phys. Condens. Matter 11 345Google Scholar

    [30]

    Vaillon R, Robin L, Muresan C, Ménézo C 2006 Int. J. Heat Mass Transfer 49 4454Google Scholar

    [31]

    Guo Y, Newman W, Cortes C L, Jacob Z 2012 ADOP 2012 1

    [32]

    Francoeur M, Vaillon R, Mengüç M P 2011 IEEE Trans. Energy Convers. 26 686Google Scholar

    [33]

    Lang S, Tschikin M, Biehs S A, Petrov A Y, Eich M 2014 Appl. Phys. Lett. 104 121903Google Scholar

    [34]

    Laroche M, Carminati R, Greffet J 2006 J. Appl. Phys. 100 063704Google Scholar

    [35]

    Baldasaro P F, Raynolds J E, Charache G W, DePoy D M, Ballinger C T, Donovan T, Borrego J M 2001 J. Appl. Phys. 89 3319Google Scholar

    [36]

    Bright T J, Wang L P, Zhang Z M 2014 J. Heat Transfer 136 062701Google Scholar

  • 图 1  p-n结型热光伏器件示意图

    Fig. 1.  Schematic of the near-field TPV system with a p-n junction.

    图 2  (a)钨和CaF2组成的人工介质材料的介电系数; (b)半导体锑化铟的介电系数谱

    Fig. 2.  (a) Effective dielectric function of the HMM emitter; (b) permittivity of InSb.

    图 3  距离为50 nm时的透射几率τp的分布 (a), (b), (c) 对应的源的结构分别是W, WHMM, HMM时的情形; (d) 间距为50 nm时的热传输谱

    Fig. 3.  p-polarization transmission possibility τp(ω, kx) with the emitter (a) W, (b) WHMM, (c) HMM; (d) thermal radiation spectrum.

    图 4  (a)不同源结构下热能传输谱$ {h}_{\omega } $的分布; (b), (c)和(d)分别是在p-n结内的p区区域的热能分布hz (z, ω), 其中源的结构分别是(b) W, (c) WHMM, (d) HMM

    Fig. 4.  (a) Heat flux density spectrum with the emitter of W, WHMM and HMM; and heat flux density in the p-region with the emitter of (b) W, (c) WHMM, and (d) HMM.

    图 5  间距为d = 50 nm时的电流谱 (a) p区$ {j}_{\mathrm{e}}\left(\omega \right) $; (b) n区$ {j}_{\mathrm{h}}\left(\omega \right) $; (c) 耗尽层内$ {j}_{\mathrm{d}\mathrm{p}}\left(\omega \right) $; (d) p-n结内的总电流大小$ {j}_{\mathrm{t}} $随间距的变化

    Fig. 5.  Current density spectrum in the (a) p-region, (b) n-region, and (c) depletion region; (d) total current with respect to the vacuum gap width.

    图 6  (a)不同结构作为源时的辐射热流h随间距的变化; (b)热光伏器件的总输出功率PE与热能转换效率η随间距的变化

    Fig. 6.  (a) Total heat flux density and (b) net power and conversion efficiency of the proposed system as a function of the vacuum gap width.

    表 1  InSb半导体的参数[24]

    Table 1.  Electric parameters of InSb[24].

    参数p 区n 区
    载流子浓度/cm–3NA = 1019 ND = 1019
    扩散系数/cm2·s–1De = 186Dh = 5.21
    弛豫时间/nsτe = 1.45τh = 1.81
    复合速率/m·s–1up =104un = 0
    区域长度/μmLp = 0.4Ln = 10
    下载: 导出CSV
  • [1]

    Hoffert M I, Caldeira K, Jain A K, Haites E F, Harvey L D D, Potter S D, Schlesinger M E, Schneider S H, Watts R G, Wigley T M L, Wuebbles D J 1998 Nature 395 881Google Scholar

    [2]

    BCS, Inc 2008 Waste Heat Recovery. Technology and Opportunities in U.S. Industry (Hinsdale: BCS) pp6–19

    [3]

    Liu W S, Jie Q, Kim H S, Ren Z F 2015 Acta Mater. 87 357Google Scholar

    [4]

    Alam H, Ramakrishna S 2013 Nano Energy 2 190Google Scholar

    [5]

    Chan W R, Bermel P, Pilawa-Podgurski R C N, Marton C H, Jensen K F, Senkevich J J, Joannopoulos J D, Soljacic M, Celanovic I 2013 PNAS 110 5309Google Scholar

    [6]

    Bierman D M, Lenert A, Chan W R, Bhatia B, Celanovic I, Soljacic M, Wang E N 2016 Nat. Energy 1 16068Google Scholar

    [7]

    Whale M D, Cravalho E G 2002 IEEE Trans. Energy Convers. 17 130Google Scholar

    [8]

    Yang J, Du W, Su Y, Fu Y, Gong S, He S, Ma Y 2018 Nat. Commun. 9 4033Google Scholar

    [9]

    Thomas N H, Sherrott M C, Broulliet J, Atwater H A, Minnich A J 2019 Nano Lett. 19 3898Google Scholar

    [10]

    Zhao B, Guizal B, Zhang Z M, Fan S, Antezza M 2017 Phys. Rev. B 95 245437Google Scholar

    [11]

    Zwol P J, Thiele S, Berger C, Heer W A, Chevrier J 2012 Phys. Rev. Lett. 109 264301Google Scholar

    [12]

    Liu B, Shen S 2013 Phys. Rev. B 87 115403Google Scholar

    [13]

    Jin S, Lim M, Lee S S, Lee B J 2016 Opt. Express 24 A635Google Scholar

    [14]

    Shi J, Liu B, Li P, Ng L Y, Shen S 2015 Nano Lett. 15 1217Google Scholar

    [15]

    Park K, Basu S, King W P, Zhang Z M 2008 J. Quant. Spectrosc. Radiat. Transfer 109 305Google Scholar

    [16]

    于海童, 刘东, 杨震, 段远源 2018 物理学报 67 024209Google Scholar

    Yu H T, Liu D, Yang Z, Duan Y Y 2018 Acta Phys. Sin. 67 024209Google Scholar

    [17]

    Zhao B, Santhanam P, Chen K, Buddhiraju S, Fan S 2018 Nano Lett. 18 5224Google Scholar

    [18]

    Fiorino A, Zhu L, Thompson D, Mittapally R, Reddy P, Meyhofer E 2018 Nat. Nanotechnol. 13 806Google Scholar

    [19]

    Papadakis G T, Buddhiraju S, Zhao Z, Zhao B, Fan S 2020 Nano Lett. 20 1654Google Scholar

    [20]

    Datas A, Vaillon R 2019 Appl. Phys. Lett. 114 133501Google Scholar

    [21]

    Malitson I H 1963 Appl. Opt. 2 1103Google Scholar

    [22]

    Liu X L, Zhang R Z, Zhang Z M 2014 Int. J. Heat Mass Transfer 73 389Google Scholar

    [23]

    Biehs S A, Tschikin M, Messina R, Ben-Abdallah P 2013 Appl. Phys. Lett. 102 131106Google Scholar

    [24]

    Lim M K, Jin S K, Lee S S, Lee B J 2015 Opt. Express 23 A240Google Scholar

    [25]

    Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 958Google Scholar

    [26]

    Liu X L, Bright T J, Zhang Z M 2014 J. Heat Transfer 136 092703Google Scholar

    [27]

    Zhang R Z, Zhang Z M 2017 J. Quant. Spectrosc. Radiat. Transfer 197 132Google Scholar

    [28]

    Volokitin A I, Persson B N J 2007 Rev. Mod. Phys. 79 1291Google Scholar

    [29]

    Volokitin A I, Persson B N J 1999 J. Phys. Condens. Matter 11 345Google Scholar

    [30]

    Vaillon R, Robin L, Muresan C, Ménézo C 2006 Int. J. Heat Mass Transfer 49 4454Google Scholar

    [31]

    Guo Y, Newman W, Cortes C L, Jacob Z 2012 ADOP 2012 1

    [32]

    Francoeur M, Vaillon R, Mengüç M P 2011 IEEE Trans. Energy Convers. 26 686Google Scholar

    [33]

    Lang S, Tschikin M, Biehs S A, Petrov A Y, Eich M 2014 Appl. Phys. Lett. 104 121903Google Scholar

    [34]

    Laroche M, Carminati R, Greffet J 2006 J. Appl. Phys. 100 063704Google Scholar

    [35]

    Baldasaro P F, Raynolds J E, Charache G W, DePoy D M, Ballinger C T, Donovan T, Borrego J M 2001 J. Appl. Phys. 89 3319Google Scholar

    [36]

    Bright T J, Wang L P, Zhang Z M 2014 J. Heat Transfer 136 062701Google Scholar

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出版历程
  • 收稿日期:  2020-06-11
  • 修回日期:  2020-06-30
  • 上网日期:  2020-10-14
  • 刊出日期:  2020-10-20

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