We investigated light absorption in various Si thin film solar absorbers and designed efficient input couplers using finite-difference time-domain simulation. In the simulation, a dielectric coating on Si thin film led to enhanced light absorption at near-ultraviolet to blue wavelengths, while the absorption peaks at longer wavelengths were nearly preserved. In a 300-nm-thick Si film with a 60-nm-thick Si3N4 top-coated layer, current density was augmented by ~35% compared to a bare Si film. For broadband absorption, we introduced two-dimensional square-lattice periodic patterns consisting of low-index dielectric materials, SiO2 or Si3N4, or high-index material, Si. The periodic pattern exhibited tunable and pronounced absorption peaks that are indentified as horizontally-propagating waveguide modes. The high absorption peaks were significantly amplified with increasing refractive index of the dielectric pattern. For a Si-patterned structure with a pitch size of 400 nm and a pattern depth of 80 nm, current density was achieved up to 17.0 mA/cm2, which is enhanced by a factor of 2.1 compared to the current density of bare Si film. Deep understanding of the light absorption in optical cavities with wavelength-scale thickness will be useful in the design of efficient thin film solar absorbers as well as novel nanophotonic elements.
© 2012 OSA
Over the past decade, photovoltaic solar cells have been considered as promising alternative sources of electricity . These electric devices harness pollution-free solar energy, but occupy only a small portion of the world energy market, which is currently dominated by fossil fuel and nuclear energy [1–3]. Both the power conversion efficiency and correlated efficiency-to-cost metric must be further increased [2,3]. The efficiency or efficiency-to-cost of solar cells was degraded partly due to carrier recombination determined by material defects and incomplete light absorption determined by reflection or transmission loss . Although the power conversion efficiency can be improved in wafer-based solar cells by diverse technologies that include purification of the wafer  together with anti-reflection coating [6,7] and surface texturing [8–15], the cost relative to efficiency remains a nontrivial issue.
Cost reduction could be achieved in solar cells based on thin film structures that are composed of binary/quaternary compound semiconductors or crystalline/amorphous silicon [16,17]. Unlike wafer-based solar cells, thin film solar cells with wavelength-scale thickness are regarded as multimode optical cavities wherein each optical mode exhibits a strong cavity effect . Numerous studies have introduced diverse structures for anti-reflection of sunlight, and have dealt with optimal design to maximize light absorption efficiency [6–15]. For example, measurements of the absorption  or reflection spectrum  from nano-patterned 1-μm-thick or wafer-thick crystalline Si structures have been reported. Numerical simulations also showed broadband light absorption in the patterned Si absorbers [8–15]. However, the mechanism of how the optical modes in submicron-thick film solar cells influence the anti-reflection of sunlight has not been investigated deeply.. In this paper, we quantitatively studied optical resonances in Si thin film solar absorbers and their interaction with input couplers for anti-reflection, using finite-difference time-domain (FDTD) simulation. Several rules were proposed for designing efficient input couplers particularly when strong cavity effects are taken into account, which can be extended to other thin film solar absorbers with different configurations or compositions. We introduced a low-index coating layer and/or a two-dimensional (2-D) periodic pattern on Si solar absorbers to maximize light absorption efficiency. Calculated absorption spectra and mode profiles revealed several design principles and their underlying physics related to anti-reflection and diffraction of light.
2. Anti-reflection coating on Si thin film
In a wafer-thick absorption structure, incident photons experience a single pass for light absorption inside the structure (top, Fig. 1(A) ). On the other hand, a thin film structure with a reflecting substrate sustains one-dimensional (1-D) oscillating optical resonances with different numbers of anti-nodes (bottom, Fig. 1(A)). To investigate resonance features of the thin film structure, we calculated absorption spectra using FDTD simulation (Fig. 1(B)). In the simulation, 300-nm-thick single-crystalline Si was used as an absorbing material, and the substrate was either a perfect absorber (solid black, Fig. 1(B)) or quartz (solid blue, Fig. 1(B)). In such a subwavelength-thick solar absorber, resonant modes can be discretized in the spectrum and absorption profiles can be localized spatially, as a result of a strong cavity effect. To describe the dispersion relation of the Si, the Drude-critical points model was incorporated into the FDTD simulation . The plasma and collision frequencies were obtained by fitting the tabulated refractive index and extinction coefficient of single-crystalline Si over the wavelength range of spectrum . For a normally incident plane wave, the absorption efficiency of a Si thin film solar absorber was obtained by integrating J·E at each grid points inside the Si layer, where J and E are the polarization current density and electric field, respectively. Comparison of both spectra reveals several key features related to the choice of substrate. First, the Si thin film structure with a quartz substrate shows several absorption peaks, while the structure with a perfect absorber has a featureless spectrum. Second, the absorption peaks in the structure with quartz substrate are assigned to 1-D Fabry-Perot modes with progressively increasing number of anti-nodes (inset, Fig. 1(B)). Third, the structure with quartz substrate has 1.5-2.0 fold enhanced amplitudes at the positions of the absorption peaks compared to the structure with a perfect absorber. Together, the thin film structure with a reflecting substrate shows strong cavity effects such as discrete resonant modes and accompanying absorption enhancement. Therefore, it is important to rationally design a thin film cavity to enhance or tune its resonant modes.
An anti-reflection dielectric coating is a conventional and common technique to increase light absorption in solar cells [6,7]. Using FDTD simulation, we investigated how dielectric coating influences the absorption spectra of Si thin film with a silver reflecting substrate (Fig. 1(C)). Figure 1(C) shows the absorption spectra of Si film with no coating layer (dashed green, Fig. 1(C)), a 20-nm-thick coating layer (solid pink, Fig. 1(C)), and a 40-nm-thick Si3N4 coating layer (solid brown, Fig. 1(C)). The simulation result illustrates that for the absorption peaks at λ<450 nm, the amplitudes are greatly enhanced due to the introduction of the dielectric coating, which exhibits the same effect as the anti-reflection coating in wafer-based solar cells. On the other hand, the amplitude and wavelength of the absorption peaks at λ>450 nm are nearly preserved. The wavelength of each peak is more red-shifted with increasing thickness of the Si3N4 coating layer, because the effective thickness (Si + dielectric coating) of the thin film cavity increases. This wavelength-dependent dielectric coating effect is distinguishable from the conventional anti-reflection coating, which is related to optical resonances . For a Si thin film cavity, incident photons at long wavelengths undergo multiple oscillations due to a low absorption coefficient of Si at these wavelengths. The strong optical feedback allows the generation of high-amplitude absorption peaks that are marginally affected by the dielectric coating, because the cavity modes already have an anti-reflection effect.
To quantify the dielectric coating effect in a Si thin film structure, we calculated current density while varying the thickness (t) of Si3N4 (n = 2.0) layer (Fig. 1(D)). The current density was calculated by integrating the absorption spectrum multiplied by the solar spectrum over λ = 280-1000 nm [22,23]. For simplicity, we assumed that the internal quantum efficiency is unity. The result shows that current density is augmented by up to 35% at t = 60 nm. This thickness, which provides the largest current density, agrees well with that obtained in the quarter-wavelength interference condition, if the central wavelength of incident light is ~450 nm. Consequently, the dielectric coating effect in a thin film solar absorber results in increased absorption at shorter wavelengths, and thus an efficient input coupler for broadband light absorption will be needed to further enhance the current density.
3. Two-dimensional SiO2 or Si3N4 periodic patterns on Si absorber
As another way of enhancing light absorption, a periodic pattern can be used in solar absorbers. We introduced a 2-D square-lattice periodic pattern on a Si thin film structure (Fig. 2(A) ). In the simulation model, the 200-nm-thick SiO2 (n = 1.45) or Si3N4 (n = 2.0) pillars with square cross-section were formed periodically on top of a 300-nm-thick Si thin film. For both dielectric materials, we assumed that the refractive indices are constant and the absorption coefficients are zero over the range of wavelengths . Figure 2(B) shows the absorption spectra of a Si film with patterned SiO2 (solid blue, Fig. 2(B)) or Si3N4 (solid pink, Fig. 2(B)) structures, where the pitch size of the pattern (a) and the diameter of the pattern were set to 400 nm and 200 nm, respectively. The simulation result highlights several key features to explain how a periodic pattern enhances light absorption. First, these structures with periodic patterns support several new absorption peaks, as compared to a planar structure shown in Fig. 1(C). The new peaks have relatively sharp bandwidths and high amplitudes. Second, the new absorption peaks have much higher amplitudes in the structure with the Si3N4 pattern. Third, the spectral features of the original peaks obey the same trend as those shown in a thin film with the top dielectric coating. The amplitudes of the peaks were enhanced at short wavelengths, while only marginally changed at long wavelengths. To understand the origin of these new absorption peaks in the dielectric-patterned structures, we obtained representative absorption mode profiles at several resonant wavelengths. Comparison of the mode profiles from the original absorption peaks (Fig. 2(C)) to those from the new absorption peaks (Fig. 2(D)) reveals important features. The original peaks correspond to 1-D Fabry-Perot modes with progressively increasing number of anti-nodes, similarly to the peaks that appeared in a thin film cavity without pattern as shown in the inset of Fig. 1(B). On the other hand, the new resonant peaks have additional anti-nodes along the horizontal direction. The wavelength of new peaks is red-shifted compared to the original peak with the same number of anti-nodes along the vertical direction. For example, the wavelength of the new peak with three anti-nodes is λ = 825 nm while that of the original peak is λ = 700 nm. We note that the spectral density of the new peaks is higher than that of the original peak since the peaks with more horizontal anti-nodes are also excited in the spectrum.
In general, a periodic pattern generates in-plane Bloch momentum that can be supplied to the initial momentum of photons at specific wavelengths . In the case of a thin film structure, normally incident photons can be converted into horizontally-propagating photons under an appropriate diffraction condition. The new absorption peaks, identified as waveguide modes, are generated due to the diffraction of the periodic pattern. Therefore, the absorption mode profiles with the transverse anti-nodes show a manifestation of the additional in-plane Bloch momentum. Each new absorption peak is assigned to a waveguide mode with a different diffraction order. Apparently, the horizontal propagation of the waveguide modes increases the photon life time in a thin film structure such that sharp and high-amplitude peaks emerge in the spectrum . Since the diffraction is enhanced by larger contrast of the refractive index (n) in the dielectric pattern , the amplitudes of the absorption peaks in the Si film structure with Si3N4 (n = 2.0) pattern are larger than those in the structure with the SiO2 (n = 1.45) pattern. On the other hand, for the original peaks resulting from normal cavity modes, the dielectric pattern is considered as a single layer with an average refractive index determined by the filling-factor of the pattern.
According to the diffraction theory related to periodic media, the magnitude of Bloch momentum is mainly dictated by the pitch size of the pattern, a . To understand how the pitch size influences the absorption spectrum of a thin film cavity, we calculated the absorption spectra with varying pitch size of the Si3N4 pattern (Fig. 3(A) ). First, we examined slightly different pitch sizes of a = 380 nm (solid black, Fig. 3(A)) and a = 420 nm (solid red, Fig. 3(A)). The simulation result shows that both spectra have nearly the same amplitude and wavelength at the absorption peaks assigned to normal cavity modes. However, for the waveguide modes (i.e. the peaks with wavelengths of λ = 720, 760, 815 nm at a = 380 nm and the peaks with wavelengths of λ = 750, 780, 835 nm at a = 420 nm), the wavelengths are red-shifted in the patterned structure with larger pitch size. Therefore, it is possible to tune the waveguide modes to specific wavelengths where the solar irradiance (dashed green, Fig. 3(A)) is the maximum, and thus the current density can be enhanced further [22,23].
Next, we calculated the current density of the Si3N4-patterend Si film structure over a wide range of pitch sizes (Fig. 3(B)). The result shows that current density plateaus at a = 600 nm with an enhancement factor of 1.68 or 1.24 as compared to a bare Si film or the optimized Si3N4-coated Si film structure as shown in Fig. 1(D), respectively. The optimum pitch size of ~600 nm agrees well with the values shown in previously reported works . For a high-refractive-index thin film structure with a dielectric pattern, light absorption is maximized at a pitch size similar to the wavelength of incident light . If a<<λ, there are only a few channels to meet the diffraction condition such that the number of waveguide modes excited by the periodic pattern is reduced. On the other hand, if a>>λ, the magnitude of Bloch momentum is too small, and thus only higher-order waveguide modes can be diffracted efficiently. Because the solar irradiance has a relatively high amplitude at λ = 450-700 nm, the optimum pitch size for the maximum light absorption lies in the middle of this wavelength range. Together, it is important to choose an appropriate pitch size of a dielectric pattern to achieve the maximum power conversion efficiency of a solar absorber.
4. Two-dimensional periodic pattern in Si absorber
We found that the amplitude of waveguide modes was highly enhanced with increasing the refractive index of a dielectric pattern. In this section, we introduce a 2-D square-lattice periodic pattern to a Si thin film absorber (Fig. 4(A) ). The absorption spectra calculated at different Si pattern depths (h) show that the Si-patterned structures excite several new absorption peaks (left, Fig. 4(B)). Significantly, the spectrum at h = 80 nm (solid purple, Fig. 4(B)) has higher amplitude than the spectrum at h = 20 nm (solid black, Fig. 4(B)), while both spectral densities are nearly the same. The mode profiles of the new absorption peaks show that the peaks are also assigned to the waveguide modes with anti-nodes in the horizontal direction (right, Fig. 4(B)). For λ<450 nm, the anti-reflection effect allows for the structure with h = 80 nm to yield higher absorption efficiency than the structure with h = 20 nm, because the Si pattern with larger depth can satisfy a quarter-wavelength interference condition. On the other hand, for λ>450 nm, because of the amplified waveguide modes, the structure with h = 80 nm shows greatly enhanced light absorption. We calculated the current density of the Si-patterned structure with varying h, and as a result, the maximum current density was 17.0 mA/cm2 at h = 80 nm (solid blue, Fig. 4(C)). This current density was augmented by a factor of 2.1 compared to a bare Si film structure as shown in Fig. 1(D). The current density is reduced for larger Si pattern depths, which implies that the diffraction strength is saturated at a pattern depth beyond the point at which the loss of absorbing volume becomes dominant.
To investigate an effect related to Si absorber thickness, we repeated the simulation for 600-nm-thick film absorbers with different pattern depths (h) (solid red, Fig. 4(C)). The overall current density of the thicker Si absorber is larger than that of the 300-nm-thick absorber and the enhancement factor over a bare Si film is maximized at h = 150 nm. However, the maximum enhancement factor in the 600-nm-thick absorber is reduced compared to the 300-nm-thick one, since the absorption efficiency becomes saturated at broad range of wavelengths with increasing thickness of a Si absorber. Lastly, we investigated the light absorption from a Si-patterned thin film structure coated conformally by a low-index dielectric material on the top (inset, Fig. 4(D)) . The absorption spectra of the Si-patterned structure with and without a 20-nm-thick Si3N4 coating layer were compared (Fig. 4D). The Si3N4 coating enhances the light absorption significantly at near-ultraviolet wavelengths, whereas the resonant peaks at longer wavelengths are slightly red-shifted, showing a small change in amplitude. The additional enhancement of ~5% in current density was achieved in the Si-patterned structure with a 60-nm-thick Si3N4 coating layer. Taken together, broadband light absorption can be achieved in a thin film absorber with a 2-D periodic pattern coated by a low-index material, due to the emergence of new waveguide modes as well as an anti-reflection effect.
In this study, we designed several anti-reflection structures in a Si thin film solar absorber. The dielectric coating layer with a quarter-wavelength thickness enhanced light absorption effectively near blue wavelengths, while the absorption modes at longer wavelengths were slightly red-shifted, showing a small change in amplitude. The 2-D periodic pattern composed of a dielectric material led to a conventional anti-reflection effect as well as excitation of new waveguide modes, and resulted in broadband light absorption. In a Si thin film absorber with patterned low-index material, current density increased with increasing refractive index of the patterned material. We calculated a maximum current density of 17.0 mA/cm2 in the Si-patterned structure with a total thickness of 300 nm. A tailored design (e.g. filling-factor, lattice type, pattern morphology) of a dielectric pattern can further enhance current density . We believe that our deep understanding of light absorption interplaying with optical resonances can be utilized to design diverse multifunctional photonic devices, including semiconductor solar absorbers.
S.-K.K and K.-D.S. contributed equally to this work. We thank R. W. Day for helpful discussions. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Grant No. 2012-0000242).
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