An approach of enhanced light-trapping in a thin-film silicon solar cell by adding a two-filling-factor asymmetric binary grating on it is proposed for the wavelength of near-infrared. Such a grating-on-thin-film structure forms a guided-mode resonance notch filter to couple energy diffracted from an incident wave to a leakage mode of the guided layer in the solar cell. The resonance wave coupled between two-filling-factor gratings would laterally extend the optical power and induce multiple bounces within the active layer. The resonance effect traps light in the cell enhancing its absorption probability. A dynamic light-trapping behaviour in solar cells is observed. A photon dwelling time is proposed for the first time to quantify the light-trapping effect. Moreover, the light absorption probability is also quantified. As compared the grating-on-thin-film structure with the one of planar silicon thin film, simulation results reveal that it is 3-fold enhancement in the light absorption within a spectral range of 920–1040 nm. Moreover, such an enhancement can be maintained even the incident angle of near-IR broadband light wave varies up to ±40°.
© 2008 Optical Society of America
The thin-film silicon (TF-Si) solar cell is a promising low-cost approach due to less consumption of silicon material than that in bulk silicon solar cells. It also offers reduced bulk recombination leading to lower dark current, higher open-circuit voltage and higher filling factor of the device . However, TF-Si solar cells suffer from a sever problem of insufficient absorption of long wavelength photons due to relatively low absorption of the indirect band gap, leading to the absorption length in the infrared spectrum should be as large as 10 µm to 3 mm . For solving poor light absorption in TF-Si solar cells at higher wavelengths, the improvement in light trapping can be realized by two effects simultaneously, including (1) light diffraction (or refraction) by surface textures with random pyramids [3, 4], periodic pyramids [5, 6], and binary gratings [7, 8] to increase optical path length and (2) enhancement of internal reflection that confines light within cells by metal reflectors [7–9] and distributed Bragg reflectors . In general, the feature size of random pyramids is in the range of several microns, and thus their use with thin-film cells is limited. By using dry-etching processes, it is possible to fabricate regular submicron textures such as periodic pyramids or binary gratings in a Si surface. The period of regular textures in common is designed at a specific wavelength. As the incident wavelength is away from it, the effect of energy coupling from incident wave to diffracted ones by textures will decay. Therefore, the optical path length of a broadband light source in cells can’t be effectively elongated by surface textures due to the limited diffraction angles. Moreover, the cell thickness can’t satisfy the constructive interference condition for all incident wavelengths. As the diffracted wave is reflected by the rear-side metal and impinges the front-side textures again, a part of wave will evanesce from the surface textures and can’t bounce in the cell again. Therefore, the light-trapping effect occurring in thin-film solar cells is a result of spatial resonance of optical wave as both conditions of diffraction by textures and reflection by reflectors are met simultaneously within narrow bandwidths and limited incident angles.
If solar cells are designed as broadband micro-resonators for the omni-directionally incident wave, their light-trapping capability will be significantly improved. Optical micro-resonators including micro-rings, coupled-resonator optical waveguides (CROW), and guided mode resonance (GMR) devices [10–13] have been widely utilized in various applications of slow light propagation. Such a phenomenon of slow light propagation would elongate the optical path length to enhance light trapping in solar cells. Among these optical resonators, the GMR structure associated with asymmetric binary grating of two filling factors in one period  has been experimentally demonstrated as an wide-angle and broadband notch filter with a suppressed transmittance as low as -20 dB in a spectral range of 1175–1265 nm and a high immunity for the angular deviation up to ±20°[15, 16]. In this paper, a GMR TF-Si solar cell combined with broadband micro-resonators based on the GMR effect is proposed to enhance light trapping in cells. Such a grating-on-thin-film structure forms a guided-mode resonance filter to couple energy diffracted from an incident wave to a leakage mode of the guided layer in the solar cell. In order to realize the flattened broadband performance for a micro-resonator in near-IR wavelengths of 920–1040 nm under oblique incidence up to ±40°, the strongly modulated grating with two filling factors is adopted in GMR structure. By using the finite difference time domain (FDTD) method, the resonance behavior of near-IR wave in the proposed GMR TF-Si solar cell is observed. A parameter of photon dwelling time is proposed for the first time to quantify the dynamic variations of photons trapped in TF-Si solar cells of the proposed GMR type and the planar type. Moreover, the enhancement factors of corresponding light-absorption probability in cells for various wavelengths and incident angles are also quantified for the first time.
2. Spectral response of proposed GMR TF-Si solar cell
As shown in Fig. 1, the proposed GMR TF-Si solar cell consists of a one-dimensional diffraction grating and a planar waveguide layer in a poly-silicon film deposited on a quartz (or glass) substrate. The incoming near-IR wave with an incident wave vector Ki directly impinges upon the grating layer. Its incident angle θ corresponding normal incidence is applied to define the effective incidence vector K equal to Kisinθ. The p-i-n active region of cell is defined in the whole GMR structure to confine the diffracted light. The sum of 0.5 for two distinct filling factors of f1 and f2 in one grating period Λ is adopted. The refractive indices of poly-silicon and quartz are assumed to be npoly-Si of 3.48 and nQuartz of 1.46, respectively. The other structure parameters are denoted as follows, including the grating period Λ=0.56 µm, the grating depth dg=0.32 µm, and the waveguide thickness dw=0.08 µm. The two filling factors f1 and f2 are chosen as 0.12 and 0.38 to achieve the flattened broadband characteristic.
By using the rigorous coupled-wave analysis (RCWA), Fig. 2 demonstrates the dispersion relation for the transmission efficiency of proposed GMR TF-Si solar cell corresponding to the incident wavelength and the incident angle under TE polarization. The transmission efficiency is a parameter used to normalize the power emitting from the rear side of quartz substrate corresponding to the incident power. As shown in this figure, there is an eye-like region of low transmittance within the incident wavelengths of 920–1040 nm and the incident angles of -30°-+30°. The low emitting power from the rear side of quartz substrate means that the GMR structure can effectively prevent the incident power from penetrating into the quartz substrate for a broad wavelength range of 120 nm under inclined illumination of incident angles up to ±30°.
3. Light trapping due to guided mode resonance
In order to understand the phenomenon of light trapping due to guided mode resonance, the dynamic behaviour of resonant wave in proposed GMR TF-Si solar cell is demonstrated by using the FDTD method. The dynamic behaviour of resonant wave is described in Figs. 3(a)–3(d) by using four typical time-varying energy distributions in the structure. As shown in Fig. 3(a), under normal incidence, the TE-polarized finite-width planar wave with the wavelength of 1 µm is assumed to impinge upon the GMR structure from a starting position of z=-0.2 µm. The wavefront width of 0.56 µm equal to the grating period is chosen for clearly observing the resonance wave coupling between adjacent grating periods. For providing a good time resolution in dynamic resonances, the incident wave is assumed as a pulse signal with a duration time of 10 femto-seconds. In the initial stage of power penetrating into the GMR structure, the incident wave tends to concentrate in the wider grating and further diffracts into the waveguide layer. It is notable that the waveguide layer prevents the diffracted wave from further penetrating into the quartz substrate. In the second stage illustrated in Fig. 3(b), the optical power constrained in the waveguide layer forms a leakage mode and couples into neighbouring gratings. As demonstrated in Figs. 3(b)–3(c), owing to the assistance of thinner gratings, the optical power tends to couple into gratings in the left side. The stable stage shown in Fig. 3(d) reveals that the incident power is periodically extended in the GMR structure and finally converts into a spatial resonance mode following a saw-toothed route. Therefore, the GMR effect indeed traps light in the cell and elongates the optical path length.
4. Photon dwelling time for quantifying dynamic light-trapping
With the assistance of the time-variant energy distribution in cells obtained by the FDTD analysis, the dynamic variation of photon number trapped in silicon layers is calculated. As illustrated in Figs. 4(a) and 4(b), time-variant photon numbers corresponding to the wavelength of 1 µm under various incident angles are demonstrated for the planar type and the proposed GMR type of TF-Si solar cells with and without considering material absorption coefficient α. The same thickness of silicon thin film is assumed for both types in the simulation. As shown in these figures, for all incident angles, total photon numbers trapped in both types increase gradually until the pulse signal is turned off. As compared with the planar type under various incident angles, maximum photon numbers of the proposed GMR type increase by 1.3 times for the cases without considering material absorption and 1.17 times for the cases with considering material absorption. It means much more photons can be coupled into the proposed GMR structure than the planar one.
After the pulse signal is turned off, photons in the planar TF-Si structure drop down quickly due to parts of photons penetrating into the quartz substrate or escaping into the air again. However, photon numbers in the proposed types will decay slowly even the incident angle up to 40°. The strongly lateral coupling effect caused by the two-filling-factor GMR structure prevents photons from penetrating into the quartz substrate as predicted in Fig. 3(d). In order to quantify the dynamic light-trapping behaviour, the dwelling time Tdw is introduced as a time constant of photons trapped in cells by using the exponential function to fit curves of photon decay. The dwelling time Tdw is defined as a time that the photon number decays from the peak value to its exp(-1). The dwelling times of photons in proposed GMR solar cells are 20 nano-seconds for the incident pulse signal with a duration time of 10 femto-seconds. As compared with the planar type, it is 6-fold enhancement in the dwelling time in an incident-angle range of 0–40 degrees. The larger dwelling time means that the optical length of trapped photon would be effectively enhanced and the probability of light absorption in solar cells would increase. It also reveals that two-filling-factor gratings can effectively reduce the Fresnel lose of the front-side interface. It must be noted, however, that the dependence of the polarization versus the grating arrangement is considerable. Indeed, the arrangement of grating can be modified to the mesh-type for non-polarized light source such as the sun light.
In the interfaces of solar cell, photons penetrate into the quartz substrate or escape into the air would degrade its light-trapping effect. In order to quantify such dynamic behaviours, the reflection and transmission of photons in the interfaces of solar cell are simulated by the FDTD analysis. Figure 5 shows the reflectance and the transmittance of photons corresponding to the wavelength of 1 µm in three different interfaces of solar cell, including air-to-silicon, silicon-to-quartz, and quartz-to-air for both of the planar type and the proposed GMR type. The insets indicate the locations of monitoring photon numbers. As shown in Fig. 5(a), the first peaks occurring at C×t less than 2 µm indicate the reflectance of incident wave in the air-to-silicon interface of both types. It demonstrates that the proposed GMR structure possesses better performance in anti-reflection. The second peaks occurring at C×t of around 4 µm indicate almost the same number of photons escaping into the air again. As shown in Fig. 5(b), the photons penetrating into the quartz substrate of the proposed GMR type is less than that of the planar type. For the proposed GMR type, Fig. 5(c) demonstrates that only a small part of photons can further penetrate into air in the rear side of quartz. In means that photons penetrate into the quartz of proposed GMR type can turn back into the silicon layer.
5. Enhancement factor of light-absorption probability
The photon dwelling time clear quantifies the dynamic light-trapping behaviour in solar cells. However, the probability of light absorption in a solar cell is a more important parameter related to its quantum efficiency. In this paper, an enhancement factor Γ of light-absorption probability of the GMR solar cell corresponding to the planar type is proposed and defined as below,
where tdw is the photon dwelling time and NGMR and NPlanar are photon numbers trapped in the GMR and planar types, respectively. As shown in Fig. 2(a), there is a low-transmittance region within the incident wavelengths of 920–1040 nm and the incident angles of -40°-+40° for the proposed GMR solar cell. Therefore, its enhancement factor Γ of light-absorption probability is calculated for the low-transmittance region. As shown in Fig. 6, corresponding to the planar solar cell, the enhancement factor Γ of light-absorption probability of the proposed GMR one is maintained within 3.1-2.9 for the incident wavelengths of 920–1040 nm. This figure demonstrates the broadband spectral response of the proposed GMR structure with two filling-factor gratings. In Fig. 7, corresponding to the planar solar cell, the enhancement factor Γ of light-absorption probability of the proposed GMR one is kept within 2.95–2.75 for the incident angles of 0°-+40° as the wavelength is assumed as 1 µm. The enhancement factor Γ descends slowly with a decay rate of 4.5×10-3 per degree as the incident angles raise up to 40°. It demonstrates the high angular endurance of the proposed GMR structure with two filling-factor gratings.
In this paper, the GMR effect is applied for to the application of TF-Si solar cells by using asymmetric binary gratings with two filling factors. The broadband resonance with a high angular endurance results from the proposed GMR structure provides solar cells a new design concept to enhance the light absorption. By using the FDTD analysis, a dynamic light-trapping behaviour in solar cells is observed. A new parameter of photon dwelling time is proposed to quantify the light-trapping effect. Moreover, an enhancement factor of light absorption probability is also applied to quantify the light absorption in cells. As compared the proposed GMR cell with the one of planar type, simulation results reveal that it is 3-fold enhancement in the light absorption within a spectral range of 920–1040 nm. Such an enhancement can be maintained even the incident angle of near-IR broadband light wave varies up to ±40°
This work was supported by National Science Council of the Republic of China under Grant number NSC96-2221-E-008-109.
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