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How to assess light trapping structures versus a Lambertian Scatterer for solar cells?

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Abstract

We propose a new figure of merit to assess the performance of light trapping nanostructures for solar cells, which we call the light trapping efficiency (LTE). The LTE has a target value of unity to represent the performance of an ideal Lambertian scatterer, although this is not an absolute limit but rather a benchmark value. Since the LTE aims to assess the nanostructure itself, it is, in principle, independent of the material, fabrication method or technology used. We use the LTE to compare numerous proposals in the literature and to identify the most promising light trapping strategies. We find that different types of photonic structures allow approaching the Lambertian limit, which shows that the light trapping problem can be approached from multiple directions. The LTE of theoretical structures significantly exceeds that of experimental structures, which highlights the need for theoretical descriptions to be more comprehensive and to take all relevant electro-optic effects into account.

© 2014 Optical Society of America

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Figures (4)

Fig. 1
Fig. 1 Short-circuit currents as a function of the absorber thickness. The JMB and Jmin graphs correspond to currents generated by a double pass traversal of light in the absorber layer with (blue solid) and without (black dotted) perfect anti-reflection coating, respectively. The JLL refers to devices textured with an ideal Lambertian scatterer and perfect anti-reflection coating (red-dashed line). All devices have a perfect mirror on the back.
Fig. 2
Fig. 2 The performance of a scatterer relies on the refractive index contrast and thus on the materials between the structures. Therefore, the LTE is defined for the total thickness ttot of the absorber material that includes the scattering layer.
Fig. 3
Fig. 3 The calculated light trapping efficiency (LTE) of proposed c-Si structures in literature. All µc-Si:H data points were also qualitatively assessed with the optical constants of c-Si [17]. While the LTE is, in principle, independent of absorber thickness, we note that the highest performing structures operate in the 1µm - 5µm range, which we believe is motivated by the fact that the benefit of light trapping is maximum in this thickness range. We also note that solar cells with the highest efficiency (e.g. the PERL cell of [18]) are not necessarily the best light trapping structures, which highlights the difference between the LTE and the absolute efficiency as well as the importance of anti-reflection coating, as already shown in Fig. 1.
Fig. 4
Fig. 4 When randomization of light at the scattering layer allows to neglect coherent effects, the propagation of an average light ray in a lossy waveguide is described by the external reflection Rext, the internal effective reflectances Rf and Rb and the attenuated transmissions T+ and T respective to a single-pass traversal Tsp.

Tables (3)

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Table 1 Experimental structures using c-Si.

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Table 2 Experimental structures using µc-Si:H (qualitatively assessed with c-Si [17]).

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Table 3 Numerical structures using c-Si (considering the best proposal in each reference).

Equations (9)

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J LL ( t tot )= J sun e hc 300nm 1200nm λ 1+ n 2 ( 1 T r 2 T r 2 ) d I sun dλ dλ.
T r ( t tot )=exp( α eff t tot )=2 0 π/2 cosθexp(α t tot /cosθ) sinθdθ.
J MB ( t tot )= J sun e hc 300nm 1200nm λ d I sun dλ exp(2α t tot )dλ .
J min ( t tot )= J sun e hc 300nm 1200nm ( n1 n+1 ) 2 λ d I sun dλ exp(2α t tot )dλ.
LTE= J max J ref J LL J MB .
η C a r n o t = T a b s T 0 T a b s 0 ,
A=1RT =1[ R ext +(1 R ext )(1 R f ) R b T T + m=0 ( R b R f T T + ) m ] [ (1 R ext )(1 R b )T m=0 ( R b R f T T + ) m ] =(1 R ext ) (1T)+ R b T[ 1 T + + R f ( 1 T /T ) T + ] 1 R b R f T T +
A = ( 1 R ext ) ( 1 T r )( 1+ R b T r ) 1 R b R f T r 2 .                 
A=(1 R ext ) 1 T r 2 + T r 2 / n 2 T r 2 / n 2 1(11/ n 2 ) T r 2 =1 1 1+ (1 T r 2 ) T r 2 n 2 .
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