Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Transmission line equivalent circuit model applied to a plasmonic grating nanosurface for light trapping

Alessia Polemi and Kevin L. Shuford

Open Access Open Access

Abstract

In this paper, we show how light absorption in a plasmonic grating nanosurface can be calculated by means of a simple, analytical model based on a transmission line equivalent circuit. The nanosurface is a one-dimensional grating etched into a silver metal film covered by a silicon slab. The transmission line model is specified for both transverse electric and transverse magnetic polarizations of the incident light, and it incorporates the effect of the plasmonic modes diffracted by the ridges of the grating. Under the assumption that the adjacent ridges are weakly interacting in terms of diffracted waves, we show that the approximate, closed form expression for the reflection coefficient at the air-silicon interface can be used to evaluate light absorption of the solar cell. The weak-coupling assumption is valid if the grating structure is not closely packed and the excitation direction is close to normal incidence. Also, we show the utility of the circuit theory for understanding how the peaks in the absorption coefficient are related to the resonances of the equivalent transmission model and how this can help in designing more efficient structures.

© 2011 Optical Society of America

Full Article  |  PDF Article
More Like This
Modified transmission line model for grating solar cells

Niloufar Anvarhaghighi and Amir Habibzadeh-Sharif
Opt. Express 31(10) 16315-16329 (2023)

Light trapping limits in plasmonic solar cells: an analytical investigation

Xing Sheng, Juejun Hu, Jurgen Michel, and Lionel C. Kimerling
Opt. Express 20(S4) A496-A501 (2012)

Combined front and back diffraction gratings for broad band light trapping in thin film solar cell

Xianqin Meng, Emmanuel Drouard, Guillaume Gomard, Romain Peretti, Alain Fave, and Christian Seassal
Opt. Express 20(S5) A560-A571 (2012)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)
Fig. 1
Fig. 1 (a) Reference geometry for a flat metallic film solar cell. (b) Equivalent transmission line (p=TM,TE)

Download Full Size | PDF

Fig. 2
Fig. 2 Dispersion diagram of the flat Ag-Si solar cell. The Si slab has height h = 200nm.

Download Full Size | PDF

Fig. 3
Fig. 3 (a) Calculated absorption compared with a full wave CST simulation for a Si substrate of height h = 200nm. The light is impinging normal to the surface, implying that the two polarizations coincide. (b) Equivalent impedance Zint at the air-Si interface calculated through Eq. (2).

Download Full Size | PDF

Fig. 4
Fig. 4 Reference geometry for the grating nanosurface

Download Full Size | PDF

Fig. 5
Fig. 5 Qualitative depiction of the scattering process induced by the grating nanosurface (top of the figure). Electric field distribution for normal incidence at λ = 857 nm: (a) TM polarization; (b) TE polarization.

Download Full Size | PDF

Fig. 6
Fig. 6 (left) The unit cell is divided into two main zones, one relevant to the ridge and one relevant to its complementary region. For the TE polarization, the electric field tangent to the junction between the two regions is continuous. This implies that the electric potential difference across the two equivalent loads retrieved at the interface is constant, and the connection is in parallel. (right) TE circuit. The equivalent impedance Z int TE at the interface can be calculated by means of two equivalent admittances at the air-Si interface in a shunt connection weighted by the unit cell filling factors.

Download Full Size | PDF

Fig. 8
Fig. 8 (left) The unit cell is divided into two main zones, one relevant to the ridge and one relevant to its complementary region. For TM polarization, the magnetic field tangent to the junction between the two regions is continuous. This implies that the current flowing through the two equivalent loads retrieved at the interface is constant, and the connection is in series. (right) TM circuit. The equivalent impedance Z int TM at the interface can be calculated by means of two equivalent impedances at the air-Si interface in a series connection weighted by the unit cell filling factors.

Download Full Size | PDF

Fig. 7
Fig. 7 Comparison of the CST full wave result and absorption calculated with the model for (a) TM and (b) TE excitation for a grating nanosurface with h = 200nm, d = 300nm, w = 100nm, r = 50nm.

Download Full Size | PDF

Fig. 9
Fig. 9 (a) Reference geometry of the grating nanosurface with a top cover of AR coating. (b) Modification of the transmission line equivalent circuit to account for the extra AR coating.

Download Full Size | PDF

Fig. 10
Fig. 10 Comparison of the CST full wave result and absorption calculated with the model for (a) TM and (b) TE excitation for a grating nanosurface with an AR coating of TiO2. (hAR = 60nm, h = 200nm, d = 300nm, w = 100nm, r = 50nm.

Download Full Size | PDF

Fig. 11
Fig. 11 (a) Absorption gain of the 1-D grating nanostructure over the flat film solar cell for TM and TE polarizations. (b) Real and (c) imaginary part of the equivalent impedance at the air-Si interface for the grating nanosurface and for the flat case.

Download Full Size | PDF

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Z X TM ( k t ) = ξ X k X 2 − k t 2 k X
Z X TE ( k t ) = ξ 0 k 0 k X 2 − k t 2
Z int p = Z Si p Z Ag p + jZ Si p tan ( h k Si 2 − k t 2 ) Z Si p + j Z Ag p tan ( h k Si 2 − k t 2 )
GF p = I g p Z 0 p Z int p Z 0 p + Z int p
GF p = Z 0 p Z Si p [ Z Ag p + jZ Si p tan ( h k Si 2 − k t 2 ) ] [ Z Si p ( Z 0 p + Z Ag p ) + j ( Z 0 p Z Ag p + Z Si p 2 ) tan ( h k Si 2 − k t 2 ) ]                     p = TM , TE
k t = k 0 ε Si ε Ag ε Si + ε Ag
A p ( λ ) = 1 − | Γ p ( λ ) | 2                   p = TM , TE
Γ p ( λ ) = Z int p − Z 0 p Z int p + Z 0 p                 p = TM , TE
Z 1 TE = Z Si TE Z Ag TE + j Z Si TE tan ( h k Si 2 − k 0 2 sin 2 θ ) Z Si TE + jZ Ag TE tan ( h k Si 2 − k 0 2 sin 2 θ ) .
Z int TE = 1 Y 1 TE f 1 + Y 2 TE f 2
Z 1 TM = Z Si TM Z Ag TM + j Z Si TM tan ( h k Si 2 − k 0 2 sin 2 θ ) Z Si TM + j Z Ag TM tan ( h k Si 2 − k 0 2 sin 2 θ ) .
Z C = 1 j ω C + R C ,
Z int TM = Z 1 TM f 1 + Z 2 TM f 2
G p ( λ ) = A grating p ( λ ) / A flat p ( λ )                   p = TM , TE
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use