HIGH EFFICIENCY 2D PHOTONIC CRYSTAL SILICON SOLAR CELL ARCHITECTURE Alongkarn Chutinan1, Nazir P. Kherani1,2,*, and Stefan Zukotynski1 1 Department of Electrical and Computer Engineering, University of Toronto 10 King's College Road, Toronto, Ontario, M5S 3G4, Canada 2 Department of Materials Science and Engineering, University of Toronto 184 College Street, Toronto, Ontario, M5S 3E4, Canada * Phone: +1 (416) 946-7372, Fax: +1 (416) 971-2326, Email:
[email protected] ABSTRACT Attaining high energy conversion efficiency in thin silicon solar cells continues to be an equally appealing and elusive prospect. The absorption of light in thin silicon (order of 1-10µm) is prohibitively small compared to that of the conventional thick-cell design (order of 150-200µm), especially in the near infra-red regime. In order to improve light absorption in thin silicon solar cells, an efficient light trapping scheme is indispensable. In this paper, we theoretically demonstrate significant enhancement in efficiency of thin crystalline silicon solar cells by using photonic crystals as the light absorbing layer. Particularly, we obtain an increase of 11.15% and 3.87% in energy conversion efficiency compared to the optimized conventional design for 2µm and 10µm thick silicon, respectively.
INTRODUCTION In recent years, interests in sustainable energy technologies such as photovoltaic cells have created rapidly increasing demand and price for silicon (Münzer el al., 1999). This has motivated a trend of thinning down the silicon wafers for photovoltaic cells in order to obtain more wafers and the larger total surface area from a bulk silicon ingot. The absorption of light in thin crystalline silicon (c-Si) solar cell is, however, prohibitively small compared to that of the conventional thick-cell design, especially in the near infra-red regime. Therefore, in order to improve light absorption in thin solar cells an efficient light trapping scheme is indispensable. In this work, we investigate light trapping schemes using photonic crystals (PC) as the light absorbing layer. Photonic crystals are a class of optical materials whose refractive index is periodically modulated at the optical wavelength scale (Yablonovitch, 1987 and John, 1987). In solid-state physics, electrons travelling inside semiconductors experience a periodic energy potential due to an atomic lattice. This gives rise to Bragg scattering of electronic waves and the interference results in a propagation characteristic of electrons that is different from when they travel in vacuum. The dispersion relation between the propagation constant and energy of electrons in semiconductor is known as an electronic band structure. Although electrons can possess any energy value in vacuum, Bragg scattering inside semiconductor crystals can result in destructive interference and therefore prohibit propagation of electrons in all directions for a certain range of electron energy. This range of energy is called a forbidden band or a band gap. A similar analogy applies for photons or electromagnetic waves. In this case, the corresponding potential is created by periodic modulation of the refractive index of materials. An artificial crystal for photons, or a photonic crystal, exhibits a characteristic dispersion relation between the propagation constant and the photon energy (corresponding to frequency) called a photonic band structure. Commonly, photonic crystals are fabricated by using two materials with different refractive index, e.g., silicon and air. While an electronic band gap can generally be found in any type of semiconductor, formation of a photonic band gap requires a strong refractive index contrast between the two materials and a rather specific geometry. The ratio of the two refractive indices has to be larger than 2 for a formation of a small band gap and a ratio greater then 3 is generally necessary for a large band gap. Furthermore, among various types of the three-dimensional (3D) lattices, only the diamond or diamond-like structures have been found to exhibit a large photonic band gap in 3D. This difference between electronic and photonic band gaps is a result of the difference between the scalar wave equation of electrons and the vectorial wave equation of photons. In principle, photonic crystals can enhance light absorption in a certain wavelength range by using high photon density of states at the photonic band edge (Gee, 2002 and Bermel et al., 2007). It has been shown by Yablonovitch and Cody that in a weak optical absorption regime, the enhancement of optical absorption in textured solar cells is, on
average, equal to 4n2, where n is the refractive index of the absorbing medium (Yablonovitch et al., 1982). The derivation of the above results consists of two steps. In the first step, the average intensity enhancement is derived based on two different approaches: statistical mechanics and geometrical optics. Statistical mechanically, at equilibrium an electromagnetic energy density inside a uniform material with a refractive index n radiated by an external black body (isotropic radiation) is proportional to n2. This is, in fact, proportional to the photon density of states of such material. It is further argued that the outcome would be the same if the external black body radiation were replaced by a collimated light and at the same time the surface is textured with the Lambertian scattering property (which disbututes light uniformly to all propagating directions). In the geometrical optical approach, assuming that light entered the medium has a uniform distribution over propagating angles due to Lambertian scattering, light is trapped and enhanced inside the medium by total internal reflection. The fraction of light inside the medium that could escape total internal reflection is that with a propagating angle smaller than the critical angle θc (which satisfies n sin θc = 1). In 3D, this fraction corresponds to 1/n2 times light intensity inside the medium. Since at steady state, the electromagnetic energy entering and leaving the medium must be equal, it is derived that the intensity of trapped light is n2 times that of the external light. In the second step, the absorption enhancement is calculated using geometrical optics by simply integrating the absorption over all propagating angles. The resulting absorption enhancement factor is 2n2 and 4n2 for structures without and with a back mirror, respectively. From the above, the derivation based on statistcal mechanics is particularly interesting because it implies possibility of further absorption enhancement by using a material with a large photon density of states (Gee, 2002). This can be obtained in a photonic crystal in a frequency range close to the band gap (called a photonic band edge). Similar to the regime of heavy electrons or heavy holes in semiconductors, the frequency ranges adjacent to the photonic band gap possess larger density of states than distant frequency ranges. Hence, it is expected that photonic crystals may provide more efficient light trapping for enhanced optical absorption in solar cells. However, it has been a challenge to design a solar cell with improved efficiency using photonic crystals so far. While an enhancement greater than 4n2 for certain bandwidths has been reported (Zeng et al., 2006, Feng et al., 2007, Bermel et al., 2007, and Zhou et al., 2008), it seems that such enhancement over a broader bandwidth is required to achieve improved solar cell efficiency. In our recent report (Chutinan et al., 2009), by investigating the use of photonic crystals as the light absorbing layer we theoretically demonstrate significant solar cell efficiency improvement over conventional design. Specifically, the question we address is “Given a certain amount of c-Si, which can be rearranged into any physical structure with unlimited addition of a non-absorbing material, what structure yields the highest energy conversion efficiency over a wavelength range of 300-1,100nm under AM1.5 solar radiation?” We also assume a perfect back mirror in all cases in order to eliminate differences in reflectivity at the back surfaces of different solar cell architectures. We show that a photonic crystal structure can be designed to yield a solar cell with greater energy conversion efficiency than an optimized non photonic crystal structure.
METHOD OF CALCULATION For simplicity, we consider 2D systems in this work. Figure 1 shows a schematic of conventional solar cells comprising an anti-reflective (AR) coating, a uniform c-Si layer, a back scatterer (grating), and a back reflector. We consider S-polarization, where the electric field vector is perpendicular to the page. The optical absorption in the solar cells is calculated using the scattering matrix method (Whittaker et al., 1999). The procedure for obtaining the energy conversion efficiency is as follows. First, the optical absorption of normally incident light impinging onto the front surface of the solar cell is calculated for the wavelength range 280-1,107nm. In our calculations, the number of calculated sampling (wavelength) points is 1,000. The number of absorbed photons is then calculated using the ASTM AM1.5 (Global tilt) solar spectrum (ASTMG173-03, 2005). Assuming each absorbed photon with energy greater than the c-Si band gap energy (1.12eV) generates an electron-hole pair that contributes to the photocurrent, the photo-induced current density Jph can be calculated by taking an integral of the number of photo-generated electron-hole pairs at each wavelength over a range of wavelengths above the c-Si band gap. Following Henry, 1980, this photo current is substituted into a standard diode I-V equation. Finally, the energy conversion efficiency is obtained by finding the ratio of the maximum power point and the incident solar radiation power (~1kW/m2). Again, these calculations assume complete, loss-less charge collection.
CONVENTIONAL DESIGN A schematic of the conventional solar cell architecture with a grating scatterer is shown in Figure 1. It consists of an anti-reflective (AR) coating, a uniform c-Si layer, a back scatterer (grating), and a back reflector. As mentioned above,
the back reflector is assumed to be a perfect mirror. We optimize the structure by iteratively scanning all the structural parameters: 1) the AR coating thickness (tAR), 2) the grating periodicity (a), 3) the grating depth (tg), and 4) the grating duty cycle (dc). In the process, the total amount of c-Si is kept equal to that of an untextured, uniform cell with a certain thickness. The optimization is performed for two different cell thicknesses of 2µm and 10µm.
(a)
H
(b)
E incident light
anti-reflective coating
anti-reflective coating
c-Si
c-Si
back reflector grating
back reflector grating
Figure 1. Schematic for conventional solar cell architecture consisting of an anti-reflective coating, a uniform c-Si layer, a back scatterer (a rectangular/triangular shape grating is shown in (a)/(b)), and a back reflector. The back reflector is assumed to be a perfect mirror. First, we use gratings with a rectangular shape as shown in Figure 1(a). For the cell thickness of 2µm, the optimized cell efficiency of 16.76% is obtained when tAR=70nm, a=620nm, tg=180nm, and dc=0.5. For the cell thickness of 10µm, the optimized cell efficiency of 22.24% is obtained when tAR=76nm, a=720nm, tg=220nm, and dc=0.5. Next, we use gratings with triangular shape as shown in Figure 1(b). It is expected that light scattering is improved since the triangular shape represents a gradual change from the uniform layer (at its base) to the periodic structure (at the apex) (see Figure 1(b)), compared to an abrupt change from the uniform layer to the periodic structure as in the rectangular grating (Figure 1(a)). This allows for an adiabatic coupling between the normal-incident light to the laterally scattered light. The optimized cell parameters for the 2µm thickness are tAR=72nm, a=750nm, and tg=260nm. The triangular grating yields an efficiency of 18.82%, which is plus 2 percentage points over the rectangular grating. For the 10µm thickness, the optimized cell efficiency of 23.24% is achieved when tAR=77nm, a=860nm, and tg=310nm, an expectedly smaller gain of plus 1 percentage point.
PHOTONIC CRYSTAL DESIGN We explore a solar cell design using PCs as an absorbing layer. A photonic crystal used in this work is a square lattice of square dielectric rods in an air background. We investigate solar cell designs with various lattice constants and find a design with a small lattice constant of ~160nm to yield high total absorption. The details are reported elsewhere (Chutinan et al., 2009). A grating with a larger periodicity (than the PC) is used to scatter light into off-normal directions. For simplicity, the periodicity of grating is chosen to be an integer multiple of the PC lattice constant. A large increase in efficiency is observed when the grating periodicity is 6 times the PC lattice constant. We show in Figure 2(a) a schematic of our photonic crystal solar cell design. Note that the shape of triangular grating at the back surface is inverted compared to Figure 1 to avoid abrupt changes in the dielectric structure. An AR coating and a coupler are required to efficiently couple light from free space into the photonic crystal absorbing layer. Figure 2(b) shows our design of the coupler. As in the conventional design, the topmost surface is covered with a uniform AR coating. To provide an adiabatic change from the uniform layer into the discrete structure of a PC, we use the following approach. For an adiabatic change in the lateral direction, a tapered 1D grating gradually connects the uniform AR layer to the square PC (lateral coupler). In the longitudinal direction, the initially connected square dielectric rods are gradually isolated to form the PC as shown in Figure 2(b) (longitudinal coupler). For the longitudinal coupler with nlc layers of square dielectric rods, the spacing between the ith and (i+1)th rods is given by i/nlc times the spacing in the regular PC region.
Similar to the previous section, we optimize the structure by iteratively scanning all the structural parameters; 1) the AR coating thickness (tAR), 2) the back grating periodicity (a) (the ratio between the back grating periodicity and the PC lattice constant is maintained at 6), 3) the grating depth (tg), 4) the lateral coupler thickness (tlc), and 5) the number of layers in the longitudinal coupler region (nlc). In the process, the total amount of c-Si is kept equal to that of an untextured, uniform cell with a certain thickness. The optimization is performed for two different cell thicknesses of 2µm and 10µm. For the cell thickness of 2µm, the optimized cell efficiency of 20.92% is obtained when tAR=74nm, a=708nm, tg=75nm, tlc=90nm, and nlc=9. There is a significant enhancement of plus 2 percentage points over the conventional design. We note that a good coupler is of critical importance in achieving high energy conversion efficiency. In fact, the same design without the longitudinal coupler only yields an efficiency of 18.62%. For the cell thickness of 10µm, the optimized cell efficiency of 24.21% is obtained when tAR=81nm, a=780nm, tg=85nm, tlc=290nm, and nlc=10, an expectedly smaller gain with increasing thickness. The above results are summarized in Table 1.
(a)
(b)
anti-reflective coating coupler
anti-reflective coating coupler region PC region
back reflector grating
air
c-Si
Figure 2. Schematic for photonic crystal solar cells showing (a) the entire structure and (b) the front coupler region. Table 1 Comparison of the energy conversion efficiency of solar cells with the conventional design and the photonic crystal design for two different cell thicknesses. The short circuit current is indicated in the parenthesis. In all cases shown, the open circuit voltage Voc~0.80V and the fill factor FF~0.86. Cells thickness 2µm
10µm
Conventional design
Photonic crystal design
18.82%
20.92% 2
(Jsc=27.4mA/cm )
(Jsc=30.4mA/cm2)
23.24%
24.21% 2
(Jsc=33.6mA/cm )
(Jsc=35.0mA/cm2)
CONCLUSION In conclusion, by using photonic crystals as an absorbing layer we have theoretically shown a crystalline-siliconbased solar cell architecture with significant improvement in optical absorption and accordingly attainment of enhanced energy conversion efficiency. The relative increase of 11.15% and 3.87% compared to the conventional design is achieved for 2µm and 10µm thicknesses, respectively. With the trend toward continual wafer thinning, this implies potential for applications in very thin cells, whereas the significance of photonic crystal designs may be less pronounced for thicker cells (50-200µm). While the improved efficiency has been shown only for specific
polarization in 2D systems, we expect that the results can be extended to the 3D cases as well as for materials other than crystalline silicon.
ACKNOWLEDGMENT This work was supported through funding from the Natural Sciences and Engineering Research Council of Canada, the Ontario Research Fund – Research Excellence, and Arise Technologies Corporation.
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