Light-trapping is important for photovoltaic solar cells whenever the material of which they are made has an indirect gap. This prevents the complete absorption of the part of the solar spectrum whose energy is close above the bandgap. Obviously, this problem applies to crystalline silicon, the most commonly used material for photovoltaic solar cells. If a reflecting mirror exists at the rear side of the cell, then light will escape at the front face of the cell for those wavelength for which the absorption constant K of the material is not significantly larger than 1/2t, where t stands for the thickness of the solar cell. However, if the reflecting mirror is replaced by a diffraction grating, the light arriving at the rear side of the cell can be diffracted into a higher order mode whose angle of propagation can be very large, leading to an optical path length which will be much larger than 2t, and, if the grating constant is appropriately chosen, the angle of propagation can be tuned to 90 degrees, such that the light travels parallel to the silicon sheet, i.e. the optical path becomes macroscopic, limited only by the lateral extent of the solar cell, not by its thickness. The absorption can thus be increased significantly precisely in the spectral range where the optical absorption length 1/K diverges, i.e. close to the bandgap. This consideration shows how well suited diffraction gratings are for dealing with indirect bandgap semiconductors, as the optical path length of the higher order mode diverges in a manner very similar to the divergence of the absorption length.
This idea is based on the assumption that it is possible to diffract the incoming light into the desired higher order mode with unit amplitude. That this will be possible at least in a very limited spectral range, and for polarized light, is quite plausible. If and how it is possible in a practical way for unpolarized light and for a sufficiently large spectral range, has to be explored by means of rigorous calculations Morf(1995). First accounts of these investigations were published by Morf et al.(1989) and by Heine et al (1995).
At this point, the following results of our rigorous calculations are worth mentioning:

1. One-dimensional (linear) gratings can be designed to trap light of both polarizations, although they represent a compromise. For polarized light, more effective light-trapping is possible.
2. Symmetric gratings may not be the most effective structures for light-trapping: By symmetry, both right- and left-moving diffracted waves are generated by the grating with equal magnitude. As a result, a diffracted wave will, after total reflection, impinge again on the grating, though reduced in intensity by absorption in the silicon. In the same way that such a wave is generated by an incoming zeroth-order wave, according to the reciprocity theorem, it will couple to an outgoing zeroth-order wave. This limits light-trapping by symmetric structures.

Nonsymmetric structures or blazed gratings do not suffer from this limitation, as is illustrated in Fig. 1. Indeed, it is possible to design a structure for which the reflected waves of order zero, as well as left moving orders are very small in amplitude. So, ideally, one is left with only right-moving diffracted waves. When such a wave, after total reflection at the front surface, impinges on the grating, there is no a priori reason that a zero-order outgoing wave will be generated. Therefore, perfect light-trapping should become possible in principle, at least for some selected wavelengths. How useful such non-symmetric gratings can be in practice, only rigorous calculations can tell. In particular, one may worry that such structures might produce efficient light-trapping for one polarization, only. Furthermore, it might be expected that the asymmetry of the grating will lead to more efficient light trapping for positive angles of incidence only, while the average over angles might not benefit.

Figure 1 The blazed grating structure is optimized such that the zeroth-order incident wave generates only right-moving diffracted waves of order one or two.Very efficient light-trapping is achieved if the strongly excited right-moving diffracted wave couples only weakly to the zero-order outgoing wave.  

In spite of these considerations, we have undertaken a systematic numerical study of blazed gratings and found them significantly more efficient, also for unpolarized and uncollimated light. In order to simplify the calculations, staircase approximations of blazed gratings were investigated instead of the saw-tooth gratings of Fig. 1 [cf. Heine et al. (1996)].

Figure 2 Theoretical results for the absorption of sunlight in silicon cells as a function of their thickness. The reflector at the rear surface is: (1) a planar silver mirror (circles), (2) a rectangular silver-coated grating (squares), and (3) a blazed silver-coated grating (triangles). A 20 micrometer thick silicon sheet with rectangular grating has about the same absorption as a 4 times thicker, 80 micrometer, silicon cell with planar mirror. For a blazed grating, the effective optical thickness is even more enhanced: A 5 micrometer cell with a staircase grating has about the same absorption, about 89%, as a 20 times thicker cell with planar reflector. For an infinite substrate, the reflection loss with a two layer AR-coating amounts to 2.4%, which sets the upper limit of absorption to 97.6%, as indicated. The superior light-trapping performance of the blazed grating is evident, in particular for very thin cells (< 10 micrometer thickness).  

The calculated absorption of sunlight at normal incidence for cells with planar silver reflector, with rectangular and blazed silver coated gratings are shown in Fig. 2 as a function of the thickness of the silicon solar cell. The gain in ligh-trapping efficiency by use of blazed gratings is conspicuous. Indeed, a 5 micrometer thick cell with blazed grating exhibits the same absorption as a 80-100 micrometer cell with a planar reflector at the back. Thus, the effective optical thickness is increased by close to a factor 20. By contrast, the optimized rectangular grating yields an effective optical thickness that is only about a factor of 4 larger than that of the cell with planar reflector. In Figure 3, we show the scanning electron micrograph of such a blazed grating fabricated in silicon by means of lithography and ion-beam etching.

Figure 3 Example of saw-tooth grating in silicon fabricated with lithography and ion beam etching. The ion-beam was oriented at 35 degrees to the horizontal plane of the wafer.  

References

Heine, C. and Morf, R.H. (1995) "Submicron gratings for solar applications", Appl. Opt. 34, 2476-2482.

Heine, C., Morf, R.H., and Gale, M.T. (1996) "Coated submicron gratings for broadband antireflection in solar energy applications", J. Mod. Opt. 43, 1371-1377.

Morf, R.H. and Kiess, H. (1989) "Submicron gratings for light trapping ins silicon solar cells: a theoretical study", Proc. of the 9th Photovoltaic Solar Energy Conf., Freiburg, 313-315.

Morf, R.H. (1995), "Exponentially convergent numerically efficient solution of Maxwell's equations for lamellar gratings", J. Opt. Soc. Am. A, 12, 1043-1056.

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