Near-field thermophotovoltaics

Thermophotovoltaic (TPV) systems are energy conversion units that generate electric power directly from thermal radiation. TPV systems operate on the principle of photovoltaic effect, in which photons whose energy is greater than the band gap of a semiconductor generate electron–hole pairs. Thus two key components in TPV energy conversion are a high-temperature thermal emitter and a TPV cell, a p-n junction semiconductor that converts the radiative energy to electric power using the photogeneration of electron-hole pairs. The main advantages of TPV systems over other energy conversion devices are the versatility of the heat source and the absence of moving parts. Wasted heat from other systems, such as furnace or engines, could be used as an energy source in TPV, leading to considerable energy savings. Having no moving parts allows quiet and reliable operations in harsh environments, making TPV ideal in military or space applications [1]. However, two serious drawbacks that prevent further adoption of TPV devices are their low energy conversion efficiency and low throughput due to a large amount of unusable radiation [2]. To address these challenges and further advance the TPV technology, a new type of TPV system has been recently proposed by utilizing the principle of near-field thermal radiation, i.e., near-field TPV.

Near-field TPV takes advantage of the tremendous enhancement of radiative energy transport by photon tunneling when placing a thermal emitter in the proximity of a TPV cell. The feasibility of the near-field TPV system has been investigated by several research groups [3-7]. Pan et al. [8] were the first to analyze the performance of near-field TPV systems. However, they used the same dielectric material for both the emitter and TPV cell to calculate the near-field energy enhancement, which is not only overly simplified but also impractical. Whale and Cravalho [9] considered a more realistic system by using a fictitious Drude material with a low conductivity and InGaAs for the emitter and the TPV cell, respectively. Narayanaswamy and Chen [10] theoretically demonstrated the effect of surface polaritons in improving the performance of near-field TPV systems. However, their work focused only on the thermal radiation enhancement, leaving questions on the near-field effect on the photocurrent generation unanswered. Laroche et al. [11] provided an analysis on the performance and efficiency of near-field TPV systems based on the assumption of 100% quantum efficiency in calculating the photocurrent generation; this may result in an overestimation of the TPV system performance. Park et al. [12] performed a more realistic analysis of the power generation in a near-field TPV system by calculating the photocurrent generation in different regions of the TPV cell. Francoeur et al. [13] developed a coupled near-field thermal radiation and the charge and heat transfer model within the cell and stressed the thermal management issues in near-field TPV systems.

A near-field TPV energy conversion system consists of a TPV cell and the thermal source that are separated with a very small vacuum gap. Figure 17 illustrates a near-field TPV device studied in this review: the thermal source is assumed to be made of tungsten and maintained at TH = 2000 K, so that the characteristic wavelength of thermal emission is 1.5 μm [12]. As for the TPV cell, In0.18Ga0.82Sb, an alloy of InSb and GaSb, is chosen because its energy bandgap of 0.56 eV is sufficiently low for the thermophotovoltaic energy conversion. Figure 1 also schematically depicts a TPV cell with a p-on-n configuration. Doping concentration of the p-layer is typically set to 1019 cm-3 whilst the tellurium-doped n-layer has a doping concentration of 1017 cm-3. The concentration gradient of the majority carriers across the p-n junction diffuses electrons from the n- to p-region and vice versa for the holes. As a result, the depletion region having only ionized dopants is formed at the junction. The depletion region width estimated to be 0.1 μm from the given doping concentrations [13]. The thicknesses of the p and n- layers are set to 0.4 and 10 μm, respectively, for the computation. For the analysis, the TPV cell is assumed to be maintained at TC = 300 K.

Figure 1. Schematic of a near-field TPV system, where In0.18Ga0.82Sb is used as the TPV cell material and plain tungsten is used as the emitter. Both the emitter and the cell material are modeled as semi-infinite media. The minority carrier diffusion lengths and depletion region in a p-n junction are also illustrated.

The whole TPV system is configured with N+1 layers. The first and second layers are respectively the semi-infinite tungsten emitter and the vacuum gap, and the last layer is the semi-infinite In0.18Ga0.82Sb substrate. The intermediate region, i.e., the p-n junction part of the TPV cell, is divided into N-2 layers. Dividing the TPV cell into discrete thin layers enables one to calculate the generation of electron-hole pairs due to absorption of radiative power in each layer and the diffusion of electrons and holes to the depletion region. The radiative power absorption in each layer of the TPV cell is calculated using the fluctuation-dissipation theorem and the dyadic Green’s function of Maxwell’s equations for a multilayered structure which have been discussed earlier. When thermal radiation is absorbed in the lth layer of the TPV cell, photons whose energy is greater than the band gap Eg will generate electron-hole pairs inside the TPV cell. The photogeneration rate of electron-hole pairs in the lth layer can be written as

$g_l(\lambda)=\frac{ Q_{\lambda,l} }{ d_l (hc / \lambda )}$, with $\frac {hc}{ {\lambda} } \ge E_g$

(1)

Here, dl is the thickness of layer l, and Qλ,l is the absorbed spectral radiative power. If the photon energy is higher than the band gap, the number of generated electron-hole pairs equals the number of absorbed photons. However, photogenerated electron-hole pairs experience recombination while they are collected to electrodes, generating photocurrents with the quantum efficiency having less than 100%: Details about the photocurrent can be obtained from Park et al. [12]. The spectral photocurrent can be divided to

Jλ(λ) = Je(λ) + Jh(λ) + Jdp(λ)

(2)

where Je(λ), Jh(λ) and Jdp(λ) are the currents generated in the p-doped, n-doped, and depletion region of the TPV cell, respectively. The performance of a TPV system can be evaluated through two efficiencies: the quantum efficiency ηq and the conversion efficiency η. The quantum efficiency is the ratio of the number of generated electron-hole pairs that can be used for photocurrent generation to the number of photons absorbed. The conversion efficiency is the ratio of the electric power generated from a TPV cell to the absorbed radiative power.

Figure 2(a) shows the spectral distribution of the thermal radiation propagating into the TPV cell when the vacuum gap width d is set to 10 nm. The spectral power has a peak around 1.5 μm, which is the characteristic wavelength of thermal radiation at 2000 K. At shorter wavelengths, the net Poynting vector decays exponentially inside the cell due to the strong absorption of In0.18Ga0.82Sb, having a short penetration depth. However, the penetration depth of the radiation inside the TPV cell increases with the wavelength, almost non-absorptive at wavelengths longer than the bandgap wavelength of the cell (i.e., λg 2.22 μm for In0.18Ga0.82Sb). Besides being spectrally dependent, the penetration depth strongly depends on the vacuum gap between the thermal emitter and the TPV cell. Figure 2(b) shows the spectral and gap-dependence of the penetration depth inside the considered TPV cell and operation condition, demonstrating that the penetration depth becomes smaller for a short wavelength and a small vacuum gap.

Figure 2. (a) Spectral distribution of the incident radiative power when the vacuum gap width d = 10 nm. Beyond λg = 2.22 μm, there is very little absorption. (b) Spectral distribution of the penetration depth for different gap widths. Notice that beyond λg = 2.22 μm, the penetration depth is very large due to the small absorption coefficient of the cell material [12].

The spectral and gap-dependence of the penetration depth makes a significant effect on the performance of the near-field TPV system, as shown in Fig. 3. Figure 3(a) shows the total photocurrents as a function of the vacuum gap width. In general, Jh is greater than Je due to the larger thickness of the n-region. However, when the vacuum gap is very small, i.e., d < 4 nm, Je becomes greater than Jh because a significant amount of the near-field thermal radiation is absorbed very close to the surface. As a result, as shown in Fig. 3(b), both the raditive power absorption and resultant photocurrent generation tremendously increase as the vacuum gap decreases. The amount of electric power generation at d = 10 nm is predicted to be 1 MW/m2, suggesting that a TPV device having a 25 cm2 cell area could generate approximately 2.5 kW, which is enough to meet the electricity demand per household in the United States [14]. However, the short penetration depth provides an adverse effect to the conversion efficiency, as shown in Fig. 3(c). When compared to the 100% quantum efficiency case, the conversion efficiency calculated by considering diffusion and recombination is significantly lower than the ideal case and experiences a reduction as the vacuum gap decreases below 10 nm. At small vacuum gaps, most of the photon energy is absorbed close to the surface of the cell, more vulnerable to the recombination of electron-hole pairs. This tendency leads to lower quantum efficiency, resulting in the decrease of the conversion efficiency at smaller vacuum gaps. The reduced conversion efficiency is the combination of decreasing quantum efficiency and increasing thermal radiation absorption. Thus, despite the remarkable enhancement of the electrical power generation, reducing the vacuum gap does not always increase the efficiency of a near-field TPV system.

Figure 3a. The effect of vacuum gap width d on the local current generation.
Figure 3b. The effect of vacuum gap width d on the absorbed radiative power and electrical power generation.

Figure 3c. The effect of vacuum gap width d on the conversion efficiency. The conversion efficiency for ηq = 100% is also plotted for comparison [12].

The relatively low conversion efficiency is a technical challenge to be overcome in further development of near-field TPV systems. To make it worse, a thermal emitter with a high temperature, like the case considered above, would further deteriorate the conversion efficiency due to the temperature increase of the TPV cell. While the TPV system from low to moderate temperature (from about 800 K to 1500 K) is desired, the lack of resonant photon tunneling of near-field thermal radiation across the vacuum gap within this temperature range would make the development of near-field TPV more challenging. One possible approach to address these challenges of near-field TPV would be to place a wavelength-selective filter on the emitter to tailor the spectrum of the near-field thermal radiation to become quasi-monochromatic slightly above the bandgap of the TPV cell. Although not developed yet, recent development of various nanostructures, such as coherent thermal emission structures discussed in the consecutive section for example, will realize the so-called near-field TPV filter in the near future.

Another challenge in near-field TPV lies in the difficulty of its design and fabrication. In particular, it remains extremely challenging to realize a sub-100-nm vacuum gap having a large area with good parallelism. Although near-field radiation has been experimentally verified, as discussed in Sec. 3.6, only near-field thermal radiation between a sphere and flat substrate has been successfully measured near room temperature at nanometer distances [15-18]. Nanoscale thermal radiation between two flat surfaces has not been experimentally demonstrated despite several attempts in the past [19-22]. When considering that the sphere-to-substrate case is not the adequate geometry for the near-field TPV system, parallelism between two flat surfaces with a small gap distance must be realized for the development of the near-field TPV system. Recently, Ottens et al. [23] demonstrated near-field effect on the heat flux between flat sapphire plates separated at a distance as small as 1-2 μm. DiMatteo et al. [24] suggested using tubular spacers between the emitter and TPV cell to realize a sub-micron vacuum gap and also to prevent parasitic conduction heat transfer between the thermal emitter and the TPV cell. They achieved an about 120 nm vacuum gap and demonstrated that less than 3% of total radiation (far field) is transferred through the tubular spacers, which is one order of magnitude improved from their previous spacer design [25]. Based on previous research results, their concept is in the phase of commercialization (http://www.mtpvcorp.com): the first generation module that generates the current density of 1 W/cm2 has been developed, being anticipated to advance it to 40 – 50 W/cm2 within two years.

References

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