Enhanced light trapping in solar cells with a meta-mirror following generalized Snell’s law

M. Ryyan Khan; Xufeng Wang; Peter Bermel; Muhammad A. Alam

doi:10.1364/OE.22.00A973

Optics Express
Vol. 22,
Issue S3,
pp. A973-A985
(2014)
•https://doi.org/10.1364/OE.22.00A973

Enhanced light trapping in solar cells with a meta-mirror following generalized Snell’s law

M. Ryyan Khan, Xufeng Wang, Peter Bermel, and Muhammad A. Alam

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M. Ryyan Khan, Xufeng Wang, Peter Bermel, and Muhammad A. Alam, "Enhanced light trapping in solar cells with a meta-mirror following generalized Snell’s law," Opt. Express 22, A973-A985 (2014)

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Table of Contents Category
- Light Trapping for Photovoltaics
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About this Article
History
- Original Manuscript: February 18, 2014
- Revised Manuscript: March 28, 2014
- Manuscript Accepted: March 31, 2014
- Published: April 23, 2014

Abstract

As the performance of photovoltaic cells approaches the Shockley-Queisser limit, appropriate schemes are needed to minimize the losses without compromising the current performance. In this paper we propose a planar absorber-mirror light trapping structure where a conventional mirror is replaced by a meta-mirror with asymmetric light scattering properties. The meta-mirror is tailored to have reflection in asymmetric modes that stay outside the escape cone of the dielectric, hence trapping light with unit probability. Ideally, the meta-mirror can be designed to have such light trapping for any angle of incidence onto the absorber-mirror structure. We illustrate the concept by using a simple gap-plasmon meta-mirror. Even though the response of the mirror is non-ideal with the unwanted scattering modes reducing the light absorption, we observe an order of magnitude enhancement compared to single pass absorption in the absorber. The bandwidth of the enhancement can be matched with the range of wavelengths close to the solar cell absorber band-edge where improved light absorption is required.

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Fig. 1 (a) The concept of light trapping is shown. A dielectric with refractive index

n

is placed on top of a meta-mirror which follows the generalized Snell’s law of reflection. The meta-mirror is shown here as a combination of a perfect mirror and a gradient phase adding interface layer. The ideal path for the light ray is shown. (b) The red line shows the law of reflection at the back meta-mirror. The black line represents specular reflection for total internal reflection at the top dielectric-air interface. The shaded region represents the escape cone angles. The blue circles are the incident angles at the meta-mirror after multiple bounces for the example illustrated in (a).

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Fig. 2 (a) The meta-surface mirror configuration embedded in the dielectric. (b) Scattered

H_{y}

field profile for: (top)

θ_{i} = 0, λ = 600 nm

, (middle)

θ_{i} = 15^{\circ}, λ = 600 nm

, and (bottom)

θ_{i} = 0, λ = 700 nm

. (c) The transfer characteristics (

θ_{r}

vs.

θ_{i}

) are shown as a spectrum of scattered

H_{y}

field amplitudes at

λ = 600

nm. (d) The scattered

H_{y}

field amplitudes for different

θ_{r}

as a function of

λ

is shown (at

θ_{i} = 0

). Here, the mode marked ( + 1) corresponds to the generalized Snell’s law of reflection.

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Fig. 3 (a) The light trapping scheme for thin film solar cell is shown using the meta-surface mirror. (b) The black line represents the absorption in the structure with a conventional mirror at the back. The blue line in (b) shows the absorption in the absorber layer for structures in (a).

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Fig. 4 (a) The graded index mirror configuration embedded in the dielectric. (b) The transfer characteristics (

θ_{r}

vs.

θ_{i}

) are shown as a spectrum of scattered

H_{y}

field amplitudes at

λ = 600

nm. (c) The scattered

H_{y}

field amplitudes for different

θ_{r}

as a function of

λ

is shown (at

θ_{i} = 0

). Here, the mode marked ( + 1) corresponds to the generalized Snell’s law of reflection.

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Fig. 5 (a) The light trapping scheme for thin film solar cell is shown using the graded index mirror. The ARC layer on top of the dielectric is used to minimize reflection of the incident light. (b) The black line shows the absorption in the structure with a conventional mirror at the back. The blue line show the absorption in the absorber layer for structures in (a).

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Fig. 6 (a) Sub-cell of the meta-mirror periodic structure. The various lengths have been defined here. Varying metal strip widths

W

are used to form the supercell (single period) of the meta-mirror. (b) The phase added by super-cells as a function of

W

at normal incidence (blue solid line). 10 components/sub-cells are used in a supercell (red circles). These components have

W

values as listed in the table (bottom). (c) The 10 sub-cells create a linearly varying (relative) phase profile for normal incidence (

θ_{i} = 0

), which is shown for two periods as red circles. However, for

θ_{i} = 40^{\circ}

, the linearity of the phase profile is disrupted (see blue crosses).

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Tables (1)

Table 1 Design parameters for the graded index mirror structure.

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Equations (9)

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k_{x (r)} = k_{x (i)} + Δ k_{x} .

k_{0} n \sin θ_{r} = k_{0} n \sin θ_{i} + Δ k_{x}

or, θ_{r} = \sin^{- 1} (\sin θ_{i} + \frac{Δ k_{x}}{k_{0} n}) = \sin^{- 1} (\sin θ_{i} + δ)

\begin{array}{l} \sin θ_{r 1} = \sin θ_{i 1} + δ \geq \sin θ_{C} \\ or, - \sin θ_{C} + δ \geq \sin θ_{C} \\ or, δ \geq 2 \sin θ_{C} \end{array}

Γ_{x} = \frac{2 π}{Δ k_{x}} = \frac{2 π}{k_{0} n δ} \leq \frac{λ_{0}}{2}

θ_{r}^{(+ 1)} = \sin^{- 1} (δ) = \sin^{- 1} (\frac{Δ k_{x}}{n k}) = \sin^{- 1} (\frac{2 π / Γ_{x}}{n 2 π / λ}) = \sin^{- 1} (\frac{λ / n}{Γ_{x}}) .

(Δ n N_{S}) \times t_{G I} \times 2 = λ_{0} .

Δ n = \frac{λ_{0}}{2 t_{G I}} \times \frac{1}{N_{S}},

n_{G I} = n_{L} + β Δ n .

Parameter	Value / expressions
$λ_{0}$	$600$ nm
$Γ_{x}$	$550$ nm
$n_{L}$	$= 1.5 \times n$
$t_{G I}$	$= \frac{1}{n_{L}} \times \frac{7 λ_{0}}{4} \times \frac{1}{2}$
$N_{S}$	$5$
$Δ n$	$= \frac{λ_{0}}{2 t_{G I}} \times \frac{1}{N_{S}}$
$n_{m a t c h i n g}$	$= \sqrt{n_{L} n}$
$t_{m a t c h i n g}$	$= \frac{1}{n_{m a t c h i n g}} \times \frac{5 λ_{0}}{4}$

Abstract

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Tables (1)

Equations (9)

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