An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles

Albert Lin; Sze-Ming Fu; Yen-Kai Chung; Shih-yun Lai; Chi-Wei Tseng

doi:10.1364/OE.21.00A131

Optics Express
Vol. 21,
Issue S1,
pp. A131-A145
(2013)
•https://doi.org/10.1364/OE.21.00A131

An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles

Albert Lin, Sze-Ming Fu, Yen-Kai Chung, Shih-yun Lai, and Chi-Wei Tseng

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Albert Lin, Sze-Ming Fu, Yen-Kai Chung, Shih-yun Lai, and Chi-Wei Tseng, "An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles," Opt. Express 21, A131-A145 (2013)

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Abstract

Surface plasmon enhancement has been proposed as a way to achieve higher absorption for thin-film photovoltaics, where surface plasmon polariton(SPP) and localized surface plasmon (LSP) are shown to provide dense near field and far field light scattering. Here it is shown that controlled far-field light scattering can be achieved using successive coupling between surface plasmonic (SP) nano-particles. Through genetic algorithm (GA) optimization, energy transfer between discrete nano-particles (ETDNP) is identified, which enhances solar cell efficiency. The optimized energy transfer structure acts like lumped-element transmission line and can properly alter the direction of photon flow. Increased in-plane component of wavevector is thus achieved and photon path length is extended. In addition, Wood-Rayleigh anomaly, at which transmission minimum occurs, is avoided through GA optimization. Optimized energy transfer structure provides 46.95% improvement over baseline planar cell. It achieves larger angular scattering capability compared to conventional surface plasmon polariton back reflector structure and index-guided structure due to SP energy transfer through mode coupling. Via SP mediated energy transfer, an alternative way to control the light flow inside thin-film is proposed, which can be more efficient than conventional index-guided mode using total internal reflection (TIR).

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Fig. 1 Illustration of SP mode coupling between discrete metallic nano-particles.

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Fig. 2 The first attempt of SP energy transfer structure and its parameters to be optimized.

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Fig. 3 Spectral response for initial attempt of optimized SP energy transfer structure.

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Fig. 4 The second SP energy transfer structure and its parameters to be optimized.

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Fig. 5 Spectral response for the Optimized second evolutionary structure with more closely spaced bottom Ag grating

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Fig. 6 Genetic algorithm statistics for the second evolutionary structure.

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Fig. 7 Electric field profile of optimized energy transfer structure at λ = 642.4nm (a) for scattering problem (b) for corresponding eigen mode (c) successive mode coupling between adjacent nano-particles.

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Fig. 8 (a) Vector field plot of Poynting vector for optimized energy transfer structure at λ = 642.4nm. (b) lateral component of Poynting vector at λ = 642.4nm.

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Fig. 9 (a) Spectral response, (b) angular distribution of Poynting vector, and (c) electric field profile for energy transfer between discrete nano-particles (ETDNP) at λ = 642nm.

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Fig. 10 (a) Spectral response, (b) angular distribution of Poynting vector, and (c) electric field profile for surface plasmon polariton (SPP) enhancement at λ = 812nm.

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Fig. 11 (a)Spectral response, (b)angular distribution of Poynting vector, and (c) electric field profile for index-guided (IG) enhancement at λ = 606nm.

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Tables (1)

Table 1 Comparison of Silicon Absorbance and Metallic Loss for Various Schemes

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Equations (11)

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\begin{array}{l} {\overset{⇀}{Ρ}}_{poynintg} = \overset{⇀}{E} (\overset{⇀}{r}) \times \overset{⇀}{H} (\overset{⇀}{r}) \\ Ρ_{absorption} = \overset{⇀}{E} (\overset{⇀}{r}) \cdot \overset{⇀}{J} (\overset{⇀}{r}) = \overset{⇀}{E} (\overset{⇀}{r}) \cdot σ (λ) \overset{⇀}{E} (\overset{⇀}{r}) \end{array}

\begin{array}{l} {\overset{⇀}{P}}_{poynting, avg} = P_{poynting, avg, x} {\hat{a}}_{x} + P_{poynting, avg, y} {\hat{a}}_{y} \\ = \frac{1}{2} Re {E_{y} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})} {\hat{a}}_{x} - \frac{1}{2} Re {E_{x} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})} {\hat{a}}_{y} \end{array}

\frac{\partial Ε_{EMW,avg}}{\partial t} = 0

\int_{V} P_{Loss, avg} d V + \oint_{S} {\overset{⇀}{P}}_{poynting, avg} \cdot d \overset{⇀}{S} = 0

\begin{array}{l} \frac{1}{2} \int_{V} Re {\overset{⇀}{E} (\overset{⇀}{r}) \cdot \overset{⇀}{J}^{*} (\overset{⇀}{r})} d v + \frac{1}{2} \oint_{S} Re {\overset{⇀}{E} (\overset{⇀}{r}) \times {\overset{⇀}{H}}^{*} (\overset{⇀}{r})} \cdot d \overset{⇀}{S} \\ = \frac{1}{2} \int_{V} \overset{⇀}{E} (\overset{⇀}{r}) \cdot σ (λ) {\overset{⇀}{E}}^{*} (\overset{⇀}{r}) d v + \frac{1}{2} \oint_{S} Re {\overset{⇀}{E} (\overset{⇀}{r}) \times {\overset{⇀}{H}}^{*} (\overset{⇀}{r})} \cdot d \overset{⇀}{S} \\ = 0 \end{array}

θ = \tan^{- 1} \frac{P_{poynting, avg, x}}{P_{poynting, avg, y}} = \tan^{- 1} \frac{Re {E_{y} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})}}{- Re {E_{x} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})}}

\begin{array}{l} θ_{a v g} = \frac{\sum_{θ = 0}^{2 π} | modulus (θ, π) - \frac{π}{2} | \times ‖ {\overset{⇀}{P}}_{poynting, avg} (θ) ‖}{\sum_{θ = 0}^{2 π} ‖ {\overset{⇀}{P}}_{poynting, avg} (θ) ‖} \\ = \frac{\sum_{θ = 0}^{π} | θ - \frac{π}{2} | \times ‖ {\overset{⇀}{P}}_{poynting, avg} (θ) ‖ + \sum_{θ = π}^{2 π} | θ - \frac{3 π}{2} | \times ‖ {\overset{⇀}{P}}_{poynting, avg} (θ) ‖}{\sum_{θ = 0}^{2 π} ‖ {\overset{⇀}{P}}_{poynting, avg} (θ) ‖} \end{array}

\overset{⇀}{E} (\overset{⇀}{r}) = \overset{⇀}{u} (\overset{⇀}{r}) \exp (i {\overset{⇀}{k}}_{InPlane} \cdot \overset{⇀}{r})

k_{x} = k'_{x} + i k "_{x} = \frac{ω}{c} {(\frac{ε_{m} ε_{d}}{ε_{m} + ε_{d}})}^{1 / 2}

k_{z, m} = k'_{z, m} + i k "_{z, m} = \frac{ω}{c} {(\frac{ε_{m}^{2}}{ε_{m} + ε_{d}})}^{1 / 2}

\begin{array}{l} \nabla^{2} E (x, z) + ω^{2} μ ε E (x, z) \\ = \nabla^{2} [\sum_{i} b_{i} (z) e x p (j k_{x, i} x)] \\ + ω^{2} μ ε \sum_{i} b_{i} (z) e x p (j k_{x, i} x) = 0 \end{array}

	Only bottom Ag grating in Si (no back reflector)	Only top Ag grating (no back reflector)	Planar Si slab	ETDNP	SPP	IG
Integrated Silicon Absorbance	0.2006	0.1558	0.1461	0.2147	0.2859	0.2691
Integrated Metal Absorbance	0.2153	0.0546	0	0.2492	0.2807	0.1568

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Tables (1)

Equations (11)

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