Fund Project: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)
Received Date:11 June 2020
Accepted Date:30 June 2020
Available Online:14 October 2020
Published Online:20 October 2020
Abstract: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. Keywords:near-field thermal radiation/ hyperbolic metamaterial/ thermophotovoltaic cell/ heat recycling
将源的温度设置为500 K, 受光子能量分布谱$ \varTheta \left(\omega, T\right) $的影响, 热能传输谱$ {h}_{\omega } $与图3(d)中热传输谱$ {H}_{\omega } $的分布有了较大的差别, $ {h}_{\omega } $高频部分的幅值大幅降低, 三种热光伏器件的热能传输谱$ {h}_{\omega } $分布如图4(a)所示. 图4(b)—图4(d)是三种不同源下的热流传输谱在p区的分布$ hz(\omega, z) $, 图中虚线表示InSb禁带宽度的对应频率$ {\omega }_{\rm{g}} $. 当$ \omega <{\omega }_{\rm{g}} $时, InSb的介电系数虚部为0, 对这个频率范围内的光子没有吸收作用, 所以$ hz $不会衰减, 然而实际情况中一部分光子会在接收端被消耗转化为热能影响器件性能, 故可在接收端使用金属背板反射这部分光子[36]. 当频率大于$ {\omega }_{\rm{g}} $时, hz会随着在接收端深度z的增加而衰减, 由(6a)式和(7)式可知, 此时会产生光生载流子. 图 4 (a)不同源结构下热能传输谱$ {h}_{\omega } $的分布; (b), (c)和(d)分别是在p-n结内的p区区域的热能分布hz (z, ω), 其中源的结构分别是(b) W, (c) WHMM, (d) HMM Figure4. (a) Heat flux density spectrum with the emitter of W, WHMM and HMM; and heat flux density in the p-region with the emitter of (b) W, (c) WHMM, and (d) HMM.
当$ \omega \!<\! {\omega }_{\rm{g}} $时, 接收端中的热传输分布谱hz(z, ω)不会随其深度z变化, 没有光生载流子的产生, 光生电流值为0. p区、n区和耗尽层三个区的厚度分别为400 nm, 10 μm和100 nm. 图5(a)—图5(c)分别给出了p区、n区和耗尽层内的电流谱, 在所设定的源温度500 K下, $ {\omega }_{\rm{g}} $附近有最大的光生电流密度, p区的光生电流$ {j}_{\mathrm{e}} $最大, 这是因为电子的迁移率远大于空穴[24]. 图5(d)是光生电流随间隙d的变化, 可以看到, HMM结构与W结构相比在50 nm间隙下可以使器件光生电流值有5倍的提高. 图 5 间距为d = 50 nm时的电流谱 (a) p区$ {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 Figure5. 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.
这三种源结构下的总辐射热流与间隙的关系如图6(a)所示. 可以看到, HMM结构相比W结构, 器件的辐射热流有大幅度的提高. 对比图6(a)和图5(d), 光生电流近似与热辐射功率呈正比关系, 这表明光生电流大小主要由热辐射传输功率决定. 由(12)式和(14)式可以得到这三种热光伏器件的热电功率PE和转换效率η随间隙d的变化分别如图6(b)中的实线和虚线所示, PE和η随d的增加而减小, 在50 nm时, 使用纯钨热源的器件功率为141.4 W/m2, 转换效率为6.36%, 使用HMM结构分别提高了8倍和0.78倍, 功率可达1.2768 kW/m2, 效率可达11.35%, 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; 实际源WHMM模型与理想源HMM模型器件性能差别不大, 这表明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. 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 Figure6. (a) Total heat flux density and (b) net power and conversion efficiency of the proposed system as a function of the vacuum gap width.