Tailoring silicon radiative properties

Optics Communications 250 (2005) 316–320 www.elsevier.com/locate/optcom

Tailoring silicon radiative properties M. Laroche *, F. Marquier, R. Carminati, J.-J. Greffet Laboratoire dÕE´nerge´tique Mole´culaire et Macroscopique; Combustion, E´cole Centrale Paris, Centre National de la Recherche Scientifique, Grande Voie des Vignes, 92295 Chaˆtenay-Malabry Cedex, France Received 9 December 2004; received in revised form 9 February 2005; accepted 10 February 2005

Abstract We study several schemes to enhance the emission of radiation of silicon surfaces in the infrared. First, we investigate the emission pattern of microscale lamellar gratings ruled on doped silicon which is substantially modified due to the excitation of surface plasmons. In addition to their remarkable spectral selectivity, those sources emit 50% more than a plane interface of bulk doped silicon. An interferential antireflection system similar to a Salisbury screen is also considered. This broadband emitter allows a significant enhancement of the total emitted power compared to the plane interface. These results may have broad applications in sensing and radiative cooling.
2005 Elsevier B.V. All rights reserved. PACS: 78.20.Ci; 44.40.+a; 78.66.
w; 73.20.Mf Keywords: Silicon; Radiative properties; Emissivity

Because of its technological importance, emission of radiation by silicon is particularly interesting. Absorption and emission in the infrared is virtually null for undoped silicon. Yet, previous studies have shown that microstructured-doped silicon can have a large emission [1]. It was suggested in [1] that the emission may be enhanced by organ pipes modes in a grating structure ruled *

Corresponding author. Tel.: +33 141 131 078; fax: +33 147 028 035. E-mail address: [email protected] (M. Laroche).

on the surface. A recent work [2] has shown that optimizing the grating parameters and using heavily doped silicon could drastically modify its emission properties in p-polarization. The key role of surface polaritons has been demonstrated in [2,3]. In particular, the spatial coherence properties of thermal sources were discussed and demonstrated in [3,4]. The grating allows the coupling of the surface polariton with a propagating wave. If the design of the grating is optimum the emissivity reaches unity. Two different kinds of sources have been designed [2]. The first one displays highly

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2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.02.041

M. Laroche et al. / Optics Communications 250 (2005) 316–320

directional emissivity, the wavelength of the maximum of emission changing with the emission angle. The second one is a quasi-isotropic source with a maximum of emissivity related to the plasma frequency. These surfaces can be used as selective emitter and could also find applications for thermophotovoltaics, spectroscopy and sensing applications. Tailoring radiative properties of microstructured materials has also been achieved without using surface waves. Microroughness plays an important role in the modification of surface emissivity [5,6]. Cavity modes allow the design of selective absorbers for solar applications [7]. The same mechanism has been applied for spectrally selective and angle independent emission [8–10]. The potential of 3D photonic crystal to modify silicon emissivity has also been explored recently [11,12]. Simpler systems based on interferences have been considered. Kollyukh et al. [13,14] have studied the properties of a thin silicon film. Planar multilayers systems (or 1D photonic crystals) have also been recently investigated [15–17]. A particular system, that combines interferences and absorption by a thin metallic film, the Salisbury screen [18] has been extensively studied first as broadband absorber in microwaves and then in the infrared, for applications to thermal or pyroelectric sensors [19–21]. Yet, these solutions have not been used to enhance emission so far. In this paper, we explore different solutions to increase silicon emissivity in the infrared. The first approach is based on the use of surface plasmons that can be excited on doped silicon [2]. We calculate the total emitted power integrated over all frequencies and all angles. This is of interest for radiative cooling applications. The second approach relies on the use of a structure similar to the Salisbury screen [18]. All the systems studied here are made of heavily p-doped silicon with a carrier concentration N = 2.5 · 1020 cm
3. The first system is a lamellar grating shown in Fig. 1(a). The directional source is produced with the following parameters: period K = 6.3 lm, filling factor F = 0.4 and depth h = 0.6 lm. The quasi-isotropic source has different parameters: period K = 2.5 lm, filling factor F = 0.8 and depth h = 0.6 lm.

317

Fig. 1. Geometry of (a) the lamellar grating with period K, filling factor F and depth h and (b) the Salisbury screen with medium 1 of thickness d and medium 2 of thickness e, deposited above a reflector.

In Fig. 1(b), the second system mimics the Salisbury screen and consists in a thin absorbing film, usually a metal film (medium 1) placed above a reflector with a transparent dielectric layer (medium 2) in between. The field above a perfect reflector is a standing wave with a maximum at a quarter of wavelength for normal incidence. If a thin absorbing film is deposited at this distance, it has been shown that the absorption of the system could reach 100% for a particular value of the film thickness [20]. This type of antireflection system is optimized for a given wavelength and a given incidence to have 100% absorption and hence by KirchhoffÕs law [22], 100% emission. In our case, both the reflector and the thin absorbing film are made of doped silicon. The medium in between is transparent and has a refractive index equal to 1.5 which is assumed to be constant in the range of wavelengths considered here (for example, ThF4). This system is optimized to have an emissivity peak coinciding with the maximum of PlanckÕs function at 100 C, which is k = 7.8 lm. Thus, the film must have a thickness d = 3.67 · 10
8 m and must be placed at a distance e = 1.68 · 10
6 m. An alternative solution would be to use an interferential antireflection coating deposited on top of a bulk of doped silicon. Yet, the calculation showed that the coating should have a thickness of 520 nm and a refractive index of 8.73 which does not correspond to any real material. Now, we compare the emissivity of those systems versus the wavelength and the emission angle. With a rigourous coupled wave analysis (RCWA) [23], the emissivity is calculated in a plane perpendicular to the grating lines using

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for the dielectric constant of p-doped silicon the same formula as in [2]. Figs. 2(a) and (b) show the emissivity of the directional and quasi-isotropic sources, respectively. The emissivity of a plane surface of the same material is plotted in Fig. 2(c). In the near infrared (k < 4.2 lm), the emissivity is high for the flat surface as seen in Fig. 2(c). In fact, this high emissivity is due to the dielectric behaviour of doped silicon for wavelengths lower than the plasma wavelength which is 4.2 lm for N = 2.5 · 1020 cm
3. In the region above this wavelength, doped silicon behaves as a metal and hence, the emissivity of a flat surface is very low (high reflectivity). However, by ruling

a grating on the surface, the emissivity can be significantly increased. In Fig. 2(a) (directional source), we clearly see the directional peak of emission which changes with the angle. It corresponds to the bright line (emissivity of 1) beginning from k = 6.62 lm at normal incidence and ending at k = 12.22 lm for angle of 70 with the normal direction. In Fig. 2(b) (quasi-isotropic source), we observe a wider peak at 5.7 lm which remains unchanged, with emissivity unity when the angle of emission changes. The physical mechanism [3,24,4] lies on the thermal excitation of surface-plasmon polaritons at the interface air-doped silicon. In the presence of the grating,

Fig. 2. Emission pattern in p-polarization of p-doped silicon gratings with N = 2.5 · 1020 cm
3 (the corresponding plasma wavelength is 4.2 lm), (a) directional source with parameters K = 6.3 lm, F = 0.4, h = 0.6 lm, and (b) quasi-isotropic source with parameters K = 2.5 lm, F = 0.8, h = 0.6 lm. (c) Emission pattern of the plane interface of p-doped silicon with N = 2.5 · 1020 cm
3.

M. Laroche et al. / Optics Communications 250 (2005) 316–320

319

Table 1 Hemispherical total emissivity at T = 100 C p-polarisation

s-polarisation

Plane interface

Directional source

Isotropic source

Salisbury screen

Plane interface

Salisbury screen

0.24

0.29

0.376

0.583

0.114

0.699

the surface mode becomes a leaky mode so that it radiates in the far field. Depending on the period of the grating [4], the structure will be directional (large period), or quasi-isotropic (small period). From those observations, we can expect that the emitted flux integrated on the range of wavelength and angle will be higher for the isotropic source than the directional source because the larger the zone where the emissivity is high, the higher the emitted flux. Let us now consider the emissivity of the Salisbury screen made of doped silicon. Both polarizations are considered. As it is a system based on interferences, we expect the emission peak to be broadband and relatively independent of the angle. This is observed in Fig. 3. We can see that the maximum of emission is around k = 7.8 lm. As this system is optimized for s-polarization (because of continuity of the field across the thin film), the zone where the emissivity is high is larger in Fig. 3(b) than in Fig. 3(a).

For a temperature of 100 C, we evaluate for each system the total hemispherical emissivity
(T) defined by the ratio of the hemispherical emitted flux with the emitted flux of the blackbody at the same temperature T: Z Z 1 1
ðT Þ ¼ 4
ðX; kÞI 0k ðT Þ dX dk; rT X¼2pst 0 where
(X, k) is the emissivity of the surface for a given wavelength k and in a given solid angle X, I 0k ðT Þ is the PlanckÕs function and r is StefanÕs constant. For the grating sources, the calculation has been made in a plane perpendicular to the grating lines. To first approximation we assume that the emissivity is the same in 2p steradians. Table 1 summarizes the results and compares the values of the total hemispherical emissivity of our devices with that of a plane interface. As expected, in ppolarization, the isotropic source has a higher emitted flux than the directional source and both of them emit about 50% more radiation than the

Fig. 3. Salisbury screen emission pattern with medium 1: p-doped silicon film with N = 2.5 · 1020 cm
3 and of thickness d = 3.67 · 10
8 m, medium 2: dielectric layer of refractive index 1.5 and of thickness e = 1.68 · 10
6 m for (a) p-polarization and (b) spolarization.

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plane interface. The interest of those sources is their spectral selectivity for the isotropic source and their directivity for the directional source. The most efficient source is the Salisbury screen because of its broadband emissivity spectrum and the quasi-isotropic emission pattern of the device. For p-polarization, the device emits more than twice as much as the plane interface (Fig. 2(c)), and for s-polarization it reaches an enhancement of six times compared to the plane interface. In summary, we have shown that thanks to efficient coupling of the surface-plasmon polaritons to propagating waves, we could enhance the radiated flux emitted by a device of heavily doped silicon. We also demonstrated that a Salisbury screen could be used as an efficient broadband emitter. Moreover, because of its low absorptivity in the visible and its high emissivity in a large range of infrared wavelengths, this latter could be used for radiative cooling [25].

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