## Abstract

We use a rigorous electromagnetic approach to analyze the fundamental limit of light-trapping enhancement in grating structures. This limit can exceed the bulk limit of 4*n*
^{2}, but has significant angular dependency. We explicitly show that 2D gratings provide more enhancement than 1D gratings. We also show the effects of the grating profile’s symmetry on the absorption enhancement limit. Numerical simulations are applied to support the theory. Our findings provide general guidance for the design of grating structures for light-trapping solar cells.

©2010 Optical Society of America

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### Equations (17)

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(1)
$$\frac{d}{dt}a=(j{\omega}_{0}-\frac{N{\gamma}_{e}+{\gamma}_{i}}{2})a+j\sqrt{{\gamma}_{e}}S$$
(2)
$$A(\omega )=\frac{{\gamma}_{i}{\gamma}_{e}}{{(\omega -{\omega}_{0})}^{2}+{({\gamma}_{i}+N{\gamma}_{e})}^{2}/4}$$
(3)
$$\sigma ={\displaystyle {\int}_{-\infty}^{\infty}A(\omega )d\omega}$$
(4)
$$\sigma =2\pi \frac{{\gamma}_{i}}{N+{\gamma}_{i}/{\gamma}_{e}}$$
(5)
$${\sigma}_{\mathrm{max}}=\frac{2\pi {\gamma}_{i}}{N}$$
(6)
$$A=\frac{{\displaystyle \sum {\sigma}_{\mathrm{max}}}}{\Delta \omega}=\frac{2\pi {\gamma}_{i}}{\Delta \omega}\frac{M}{N}$$
(7)
$$F=\frac{A}{\alpha d}=\frac{2\pi {\gamma}_{i}}{\alpha d\Delta \omega}\frac{M}{N}$$
(8)
$$N=\frac{2{k}_{0}}{2\pi /L}=\frac{2L}{\lambda}$$
(9)
$$M=\frac{2{n}^{2}\pi \omega}{{c}^{2}}\left(\frac{L}{2\pi}\right)\left(\frac{d}{2\pi}\right)\Delta \omega $$
(10)
$$F=\frac{A}{d\alpha}=\pi n$$
(11)
$$N=2\lfloor \frac{{k}_{0}}{2\pi /L}\rfloor +1=2\lfloor \frac{L}{\lambda}\rfloor +1$$
(12)
$$\begin{array}{l}L>>\lambda /n\\ d>>\lambda /n\end{array}$$
(14)
$$\begin{array}{l}{S}_{even}=\frac{1}{\sqrt{2}}({S}_{{k}_{//}}+{S}_{-{k}_{//}})\\ {S}_{odd}=\frac{1}{\sqrt{2}}({S}_{{k}_{//}}-{S}_{-{k}_{//}})\end{array}$$
(15)
$$M=\frac{8\pi {n}^{3}{\omega}^{2}}{{c}^{3}}{\left(\frac{L}{2\pi}\right)}^{2}\left(\frac{d}{2\pi}\right)\Delta \omega .$$
(16)
$${G}_{m,n}=m\frac{2\pi}{L}\widehat{x}+n\frac{2\pi}{L}\widehat{y},$$
(17)
$$k={k}_{//}+{G}_{m,n}\text{},$$