Ray optical light trapping in silicon microwires: exceeding the 2n2 intensity limit

Abstract

Abstract:We develop a ray optics model of a silicon wire array geometry in an attempt to understand the very strong absorption previously observed experimentally in these arrays. Our model successfully reproduces the n 2 ergodic limit for wire arrays in free space. Applying this model to a wire array on a Lambertian back reflector, we find an asymptotic increase in light trapping for low filling fractions. In this case, the Lambertian back reflector is acting as a wide acceptance angle concentrator, allowing the array to exceed the ergodic limit in the ray optics regime. While this leads to increased power per volume of silicon, it gives reduced power per unit area of wire array, owing to reduced silicon volume at low filling fractions. Upon comparison with silicon microwire experimental data, our ray optics model gives reasonable agreement with large wire arrays (4 μm radius), but poor agreement with small wire arrays (1 μm radius). This suggests that the very strong absorption observed in small wire arrays, which is not observed in large wire arrays, may be significantly due to wave optical effects. for photovoltaic applications," Nano Lett. 7, 3249-3252 (2007). 14. E. Yablonovitch, "Statistical ray optics," J. Opt. Soc. Am. 72(7), 899-907 (1982 , 1999). 17. We find our model very slightly exceeds the ergodic limit across all aspect ratios for the smallest filling fraction. This is observed across aspect ratios, with no trend with increasing aspect ratios. The maximum amount by which the ergodic limit is exceeded is approximately 1% and is likely due to small inaccuracies in the model. 18. This should not be confused with the areal filling fraction of the wire array. In solar cells, the power can be calculated by multiplying the short circuit current, the open circuit voltage, and the fill factor, where the fill factor accounts for the fact that the current-voltage curve is not square in the power-producing region.

Modal analysis of enhanced absorption in silicon nanowire arrays

“…This contrasts a statistical approach pioneered by Yablonovitch [23], and applied to SiNW arrays by Kosten et al [24]. In their approach the reflection of light at interfaces is assumed to be Lambertian, so that the direction of the light inside the structure is random, whereas its further propagation follows from geometrical optics.…”

Single-nanowire solar cells beyond the Shockley–Queisser limit

“…Interestingly, when these arrays stand on a Lambertian back-reflector, an asymptotic increase in light trapping for low filling factors (FFs) is predicted 19 . This is advantageous for improvement of the efficiency-to-cost ratio of solar cells and has led to the demonstration of microwire arrays exhibiting higher absorption than in the equivalent thickness of textured film 19,21,22 . The case for nanowires is quite different.…”

“…In low-absorbing microwire arrays, such as those composed of silicon, light absorption is understood via ray optics or by calculation of the integrated local density of optical states of the nanowire film 19,20 . Interestingly, when these arrays stand on a Lambertian back-reflector, an asymptotic increase in light trapping for low filling factors (FFs) is predicted 19 .…”

“…In low-absorbing microwire arrays, such as those composed of silicon, light absorption is understood via ray optics or by calculation of the integrated local density of optical states of the nanowire film 19,20 . Interestingly, when these arrays stand on a Lambertian back-reflector, an asymptotic increase in light trapping for low filling factors (FFs) is predicted 19 . This is advantageous for improvement of the efficiency-to-cost ratio of solar cells and has led to the demonstration of microwire arrays exhibiting higher absorption than in the equivalent thickness of textured film 19,21,22 .…”

Hybrid Materials for Integrated Photonics

“…Recently, new concepts of solar cells based on arrays of microwires demonstrate large improvement in the photovoltaic cell performance. In particular higher absorption compared to that obtained in similarly textured films was demonstrated [52,53]. The main limit of these proposals relies on the limited total absorption rate, even in the case of arrays of highly absorbing nanowires [54].…”