pubs.acs.org/NanoLett
Optical Absorption Enhancement in Silicon Nanohole Arrays for Solar Photovoltaics Sang Eon Han and Gang Chen* Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ABSTRACT We investigate silicon nanohole arrays as light absorbing structures for solar photovoltaics via simulation. To obtain the same ultimate efficiency as a standard 300 µm crystalline silicon wafer, we find that nanohole arrays require twelve times less silicon by mass. Moreover, our calculations show that nanohole arrays have an efficiency superior to nanorod arrays for practical thicknesses. With well-established fabrication techniques, nanohole arrays have great potential for efficient solar photovoltaics. KEYWORDS Nanohole, nanorod, photonic crystal, optical absorption, photovoltaics
P
oor infrared absorption of crystalline silicon (c-Si) resulting from its indirect band gap poses a challenge to its use in solar photovoltaics. Currently, commercial solar cells have 200-300 µm c-Si active layers that absorb light efficiently. This thickness accounts for ∼40% of the total cost and needs to be reduced to several micrometers.1 A thinner active layer has the added advantage of efficient charge-carrier transport. Thus, an effective technique for light trapping in thin active layers needs to be developed.2-9 While various structures employing randomly2 or periodically3-5 structured surfaces, nanoparticles6-8 or other plasmonic structures9 to increase absorption in thin film photovoltaics have been widely investigated, an alternative strategy is to structure the active layer itself. For example, vertically aligned nanorod or nanocone arrays of active layers have been considered.10-14 Theoretical studies have shown that these structures can improve light absorption15-17 and carrier collection,18 leading to higher efficiency. For nanorod arrays, one can construct a p-n or a p-i-n junction in the radial direction of each nanorod to shorten the carrier diffusion length. These structures have been successfully fabricated using various methods such as the vapor-liquid-solid process.11-14 While past theoretical and experimental studies have mostly focused on nanorod arrays, an alternative structure for photovoltaics would be nanohole arrays that can be produced using different fabrication techniques. In a wellestablished technique, highly ordered holes are produced on a c-Si wafer by lithography and subsequent etching in acid.19-22 Dielectric nanohole arrays have been studied primarily in the context of photonic crystals. Light propagation perpendicular to the hole axis has been the chief focus of these studies. However, they have neither been thoroughly studied for light absorption in the direction of the hole
axis, nor have they been considered for photovoltaic applications.23 We report in this paper the light trapping characteristics of nanohole arrays for photovoltaics and compare them to that of nanorod arrays. We find that nanohole arrays are comparable to or even better than nanorod arrays in terms of light absorption. To evaluate the absorption performance of solar cells, we calculate the ultimate efficiency, η, which is defined as the efficiency of a photovoltaic cell as the temperature approaches 0 K when each photon with energy greater than the band gap produces one electron-hole pair24 g
η)
∫0∞ I(λ)dλ
(1)
where I is the solar intensity per wavelength interval, A is the absorptance, λ is the wavelength, and λg is the wavelength corresponding to the band gap. For the solar intensity, we use the Air Mass 1.5 spectrum.25 Equation 1 shows that for a given absorption and solar radiation spectrum λ/λg can be regarded as a weighting factor for integration. As the wavelength decreases from the band gap, the contribution of the absorbed solar energy to the ultimate efficiency decreases because the excess energy of photons above the band gap is wasted. Thus, while the solar Air Mass 1.5 spectrum peaks around 500 nm, the most important contribution to the ultimate efficiency of a c-Si solar cell comes from wavelengths around 670 nm. We investigate the coupling between this 670 nm light and the structures. Light is assumed to be incident along the hole/rod axis (see Figure 1a). As the wavelength is comparable to the lattice constant, we expect strong optical diffraction. If a single eigenmode were excited inside the structures, we could use the impedance model to calculate reflectance for an infinitely thick structure.26-28 However, as will be shown later, many modes can be excited and this
* To whom correspondence should be addressed. E-mail:
[email protected]. Received for review: 12/17/2009 Published on Web: 02/08/2010 © 2010 American Chemical Society
∫0λ I(λ)A(λ) λλg dλ
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FIGURE 2. Calculated absorptance spectra for the nanohole and the nanorod array structures when the thickness d is 2.33 µm and 1.193 mm. The c-Si filling fraction and the lattice constant are 0.5 and 500 nm, respectively. A moving average of the spectra has been taken to smooth out narrow peaks.
Figure 1c. The wavevector k is in the direction of the nanohole axis and normalized by the lattice constant (a ) 500 nm) in the plane perpendicular to the direction. We make three important observations on the band structure. First, many bands are formed above the Si band gap of 1.1 eV. This is because the waveguide cutoff for the fundamental mode is located at low frequencies and many higher modes are excited in the frequency ranges of interest. Second, the bands shift to lower frequencies as the filling fraction increases because the frequencies of waveguide modes decrease as the size of the waveguide (Si) increases. This implies that, at a specific frequency, light propagation becomes more complicated for higher filling fractions because a greater number of modes will be available. Third, the group velocities of the bands are mostly lower than those of the light line for a homogeneous Si (gray dashed line in Figure 1c). The combination of a large number of bands and the relatively small group velocities implies a higher density of states of photons and hence larger absorption above that for a homogeneous film. These three features were found also for nanorod arrays. Guided by the calculations in Figure 1, we choose the parameters a ) 500 nm and f ) 0.5 to calculate the absorption spectra for the nanohole and the nanorod array. Figure 2 gives the results when the thickness d of the structures is 1.193 mm and 2.33 µm. In both cases, absorption is higher for the nanohole array when λ is less than approximately 750 nm. When d ) 1.193 mm, the nanohole array gives a slightly higher ultimate efficiency of 42.6% compared to 41.2% for the nanorod array. However, when d ) 2.33 µm, the efficiency is 27.7 and 24.0% for the nanohole and the nanorod array, respectively, giving a larger difference between the two structures. This implies that light trapping in the small volume is more efficient for the nanohole array. Indeed, even when 750 nm < λ < 1 µm where absorption in the thick structure (1.193 mm) is lower for the nanohole array, the thin nanohole array (2.33 µm) absorbs more strongly than the nanorod array.
FIGURE 1. (a) Schematic illustrations of nanohole and nanorod arrays. Light is incident from above. (b) Calculated absorptance at λ ) 670 nm as a function of c-Si filling fraction for the nanohole and the nanorod array structures occupying a half space. (c) Dispersion relation for the nanohole array structures for different c-Si filling fractions in the direction of the hole axis. Gray dashed lines are dispersion relations for homogeneous c-Si. The lattice constant a is 500 nm for both (b) and (c).
model is not available in our case. Instead, we directly calculate the normal absorptance for infinite thickness by varying the c-Si filling fraction f. For calculations, we use the transfer matrix method29 with the dielectric functions in ref 30 and select the lattice constant to be 500 nm. A lattice constant of 500 nm is close to the optimum ultimate efficiency condition found in previous studies for nanorod arrays.15,16 Figure 1b shows that absorption increases as the filling fraction decreases in both nanohole and nanorod arrays as a result of the smaller optical density, which creates antireflection effect.15,17 Over the entire range of the investigated filling fraction, nanohole arrays show better light coupling than nanorod arrays. For nanohole arrays, absorption drops rather quickly when the filling fraction exceeds 0.5. Since absorption will not be efficient for thin structures if the filling fraction is too small, we expect that the optimum filling fraction for a finite structure will be close to 0.5. The propagation of light inside nanohole arrays can be investigated by using the photonic band structure shown in © 2010 American Chemical Society
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FIGURE 3. Calculated ultimate efficiency as a function of the lattice constant of the nanohole and the nanorod array structures for various filling fractions when the thickness is 2.33 µm.
FIGURE 4. Calculated ultimate efficiency as a function of the thickness of the nanohole array, the nanorod array, and the homogeneous c-Si film (a) with and (b) without a Si3N4 antireflection (AR) coating. The AR coating thicknesses are optimized for a c-Si thickness of 2.33 µm and are 58, 62, and 62 nm for the nanohole array, nanorod array, and the homogeneous film, respectively. The filling fraction and the lattice constant are 0.5 and 500 nm for the nanohole array, and 0.6 and 600 nm for the nanorod array, respectively. These geometries correspond to the maximum ultimate efficiency for a thickness of 2.33 µm.
To determine whether nanohole arrays have a higher efficiency than nanorod arrays given other structural parameters, we calculate the efficiency for various lattice constants and filling fractions when d ) 2.33 µm as shown in Figure 3. Nanohole arrays show a higher efficiency in most cases and the optimum efficiency found in the range of parameters investigated is also higher for nanohole arrays. The optimum efficiency is found to be 27.7% for nanohole arrays of the same structure as in Figure 2 and 26.3% for nanorod arrays of a ) 600 nm and f ) 0.6. The optimum structural parameters for the nanorod array agree with ref 15 but the efficiency might increase further by increasing the lattice constant. We did not pursue this range because the calculation accuracy becomes poorer at large lattice constants and quantitative investigations will not be accurate. The general trend that the efficiency increases as the lattice constant becomes larger also agrees with ref 15 where such an effect was attributed to the increasing number of waveguide modes. More precisely, the coupling of light to the waveguide modes should also be considered. For the optimum lattice constant and filling fraction found for d ) 2.33 µm, we calculate the thickness dependence of the efficiency for both the nanohole and the nanorod array as shown in Figure 4a. In both cases, the efficiency is higher than a homogeneous c-Si film, which has not been achieved for small lattice constants.17 The nanohole array shows higher efficiencies than the nanorod array for the practical cases where efficiencies above 25% are desired. The maximum efficiency of 31.4% for a homogeneous film is achieved for nanohole arrays with the thickness of only around 7 µm and for nanorod arrays of over 9 µm. However, the efficiency of a homogeneous © 2010 American Chemical Society
film can also be improved by an antireflection (AR) coating. For example, a silicon nitride (Si3N4) AR coating can improve the efficiency significantly. Using the dielectric function of Si3N4 given in ref 30, the optimum thicknesses of the coatings are found to be 58, 62, and 62 nm for the nanohole array, the nanorod array, and the homogeneous film, respectively, when the c-Si layer thickness is 2.33 µm. The efficiency improves with these AR coatings in each case, as shown in Figure 4b. The difference in efficiency between the nanohole and the nanorod array becomes very small with the AR coatings. Our results indicate that a nanohole array without an AR coating yields a higher efficiency than the AR coated homogeneous film except at very large thicknesses. For example, the efficiency for the 2.33 µm nanohole array can be achieved with the AR coated homogeneous c-Si thickness of 6 µm. This result is the consequence of the larger photonic density of states for the nanohole array shown in Figure 1c. Since the thickness of c-Si in commercial solar cells is around 300 µm, we can estimate, from Figure 4b, the nanohole array thickness that is required to give the same ultimate efficiency as the c-Si thickness of commercial solar cells. A 300 µm thick homogeneous film with the AR coating specified earlier has an efficiency of 40.5%. The AR-coated nanohole array of 50 µm thickness gives an identical efficiency. Therefore, the nanohole array requires one-sixth the thickness of a comparable crystalline wafer and, because the 1014
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Si nanohole arrays can be fabricated with well-established techniques, experimental studies can follow directly. When we fabricate nanohole arrays with processes different than those for nanorod arrays, the quality of the structure and the carrier dynamics may be different. Further experimental investigations should follow to address these points. Acknowledgment. We thank A. Mavrokefalos for helpful discussions on experiments. This work was supported by NSF through UC Berkeley SINAM and Center for Clean Water and Clean Energy at MIT and KFUPM. REFERENCES AND NOTES (1) (2) (3) (4) (5) (6) (7) (8)
FIGURE 5. Calculated ultimate efficiency for the nanohole and the nanorod array as a function of the angle from the surface normal for transverse-electric and transverse-magnetic polarizations. The structural parameters are the same as in Figure 4 and the angle is in the ΓX direction.
(9) (10) (11)
filling fraction is 0.5, twelve times less c-Si by mass. Note that this estimate is conservative because the nanohole array structure and its AR coating have not been optimized at this thickness. The maximum efficiency of 46.8% for the AR coated nanohole array is not far from the blackbody limit of 49.5% for a band gap of 1.1 eV. This result shows that our nanohole array couples well to incident sunlight. As the incidence angle of sunlight can deviate from the surface normal, we calculate the angular dependence of efficiency for the nanohole and nanorod structures. Figure 5 suggests that for both structures the transverse-electric (TE) polarization has a stronger dependence on the angle of incidence than the transverse-magnetic (TM) polarization. The nanohole array is more absorptive than the nanorod array when the angle is less than 40 degrees. Larger angles are less important than smaller ones because the amount of light incident on a given area of solar cells decreases as the angle increases. To summarize, we have presented the results of our investigation of the optical properties of c-Si nanohole array structures for solar photovoltaic applications and found that their absorption is better than nanorod arrays. Our calculations indicate that a nanohole array structure requiring onetwelfth the c-Si mass and one-sixth the thickness of a standard 300 µm Si wafer will have an equivalent ultimate efficiency. The strong optical absorption is attributed to both effective optical coupling between the array and the incident sunlight as well as the large density of waveguide modes. Since © 2010 American Chemical Society
(12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23)
(24) (25) (26) (27) (28) (29) (30)
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