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  • Editor: Bernard Kippelen
  • Vol. 20, Iss. S1 — Jan. 2, 2012
  • pp: A141–A156
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Transmission line equivalent circuit model applied to a plasmonic grating nanosurface for light trapping

Alessia Polemi and Kevin L. Shuford  »View Author Affiliations


Optics Express, Vol. 20, Issue S1, pp. A141-A156 (2012)
http://dx.doi.org/10.1364/OE.20.00A141


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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 OSA

1. Introduction

Light trapping is an optical phenomenon that many photovoltaic cells employ to increase performance. The design and fabrication of novel optical components that can improve light trapping capability is essential to achieve higher efficiencies in photovoltaic devices [1

1. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010). [CrossRef]

]. In recent years, researchers have investigated several architectures to accomplish this goal including the use of different semiconductor materials, such as cadmium telluride and copper indium gallium arsenide, which have produced record efficiencies [2

2. A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl. 9, 211–215 (2001). [CrossRef]

, 3

3. A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl. 12, 93–111 (2004). [CrossRef]

]. Unfortunately, these materials are scarce in nature; thus, the dominant commercial solar material, silicon (Si), is still most relevant. Silicon is a weak absorber in much of the optical regime, requiring at least 200–300μm of material thickness to completely absorb incident sunlight [4

4. W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

, 5

5. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010). [CrossRef] [PubMed]

]. For crystalline Si, 50% of the cell cost is due to the cost of material itself [4

4. W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

], which suggests the film could be made thinner to substantially decrease cost. However, the energy trapped and converted into photocurrent is in fact proportional to the number of cavity modes supported by the semiconductor film [6

6. P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17, 975–20, (2009). [CrossRef]

, 7

7. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8, 4391–4397 (2008). [CrossRef]

]. As a general guideline, the higher the number of modes, the higher the absorption of the incident light in the semiconductor. The number of modes is dictated primarily by the thickness of the semiconductor layer. In particular, the number of modes supported increases with the thickness of the film, which implies higher material costs. Also, for thick films, due to the long path length of the photonic modes, the electron-hole recombination rate increases [3

3. A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl. 12, 93–111 (2004). [CrossRef]

]. As a consequence, the photocurrent available for conversion decreases, diminishing the solar cell efficiency. For these reasons, the tradeoff between keeping the cost of semiconductors low and providing a high degree of absorption must be achieved in a different way.

The paper is organized as follows. In Section 2, we apply the transmission line model to the simple case of a flat, Ag-Si cell and demonstrate how to calculate the absorption through the circuit theory. Also, we show the dispersion diagram of the solar cell, obtained by means of the relevant Green’s function, emphasizing the number of cavity (photonic) modes and the TM-plasmonic mode. In Section 3, we apply the same model to the 1-D grating nanosurface, characterizing both TE and TM polarization. We show how to modify the model by applying the circuit theory based on the conservation of the tangential components of the electromagnetic field at the junction between the ridge zone and the flat zone of the grating. This leads to a shunt connection for TE fields and to a series connection for TM fields. Also, we demonstrate how to include an extra load in the circuit, which represents the plasmonic near field accumulation around the ridge of the grating. The absorption coefficient is calculated and compared with a full wave simulation using CST Microwave Studio [23

23. www.cst.com (2011 CST Computer Simulation Technology AG).

]. The model is also applied to the same structure covered by an antireflecting coating of TiO2. In Section 4, we present the absorption enhancement with respect to a flat metallic film solar cell. In particular, we demonstrate how the circuit theory allows us to interpret the peaks in the absorption spectrum in terms of an equivalent open circuit condition at the air-Si interface, which can be used as a guideline to design more efficient structures.

2. Plasmonic modes and photonic modes

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

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

The overall absorption of the solar cell can be calculated as
Ap(λ)=1|Γp(λ)|2p=TM,TE
(6)
where Γ(λ) is the reflection coefficient at the air-Si interface. The transmission coefficient is neglected because it is negligibly small for these thicknesses. The reflection coefficient can be expressed via the equivalent impedance at the same interface as
Γp(λ)=ZintpZ0pZintp+Z0pp=TM,TE
(7)
where Z0p is the TM or TE free space impedance. The calculated absorption is shown in Fig. 3(a) and compared with a full wave simulation performed using CST. The light is impinging normally to the surface, i.e. kt = k0 sinθ = 0 (see Fig. 1), which implies that the two polarizations are equivalent. The structure, in fact, is totally symmetrical. The agreement between the calculated solution from the transmission line model and the full wave result is excellent. We also want to emphasize the spectral nature of the interface impedance, Zint, shown in Fig. 3(b). It is easy to verify that the peaks of absorption occur when the real part of the impedance at the air-Si interface assumes large values and the imaginary part crosses the zero line. This corresponds to an open circuit condition, which implies a peak of the voltage in the equivalent circuit. From the electromagnetic point of view, this behavior reflects a quasi-PMC condition at the interface, justifying a maximum in the tangential electric field, which in turn maximizes penetration inside the Si slab. The peaks shift in the spectrum when the angle of incidence is varied from normal, but the general concepts still hold.

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).

3. Transmission line model of the 1-D grating nanosurface

In this section, we show how to apply the same equivalent transmission line model to a 1-D grating nanosurface. An example of the grating nanosurface is shown in Fig. 4. The ridges have width w, height r, and are in a periodic configuration of period d. The Si has height h. The conventional TM and TE polarization reference is taken and defined with respect to the plane crossing the grating (xz plane). The presence of the ridges introduces additional scattering inside the Si slab, which results in an increase of the photonic and plasmonic path length. A qualitative description of the scattering phenomena is depicted in the top of Fig. 5. The cavity modes are primarily dictated by the reflection of the electromagnetic wave on the metal surface or the ridges of the grating. Furthermore, because of the plasmonic nature of Ag, the light impinging on the edges of the ridge creates an accumulation of positive and negative charge resulting in a dipole-like behavior on each ridge, which is only present for TM polarization. If the ridges are not closely packed, this effect is stronger than the coupling between adjacent ridges. For TE polarization, the electric field is oriented along the edge of the ridges and does not undergo diffraction. This behavior is clear from Fig. 5(a) and (b), where the electric field distribution is shown for both polarizations. In the TM case, the dipole-like electric field appears around the ridge of the grating, while in the TE case, the field distribution is affected just by the reflection mechanism.

Fig. 4 Reference geometry for the grating nanosurface
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.

The above mentioned phenomena can be interpreted in terms of a transmission line model, as was done for the flat film in Section 2. This leads to an approximate, closed form expression for the total reflection coefficient in Eq. (7), which can be used to calculate the overall absorption from Eq. (6). Although a closed form expression of the absorption coefficient is difficult to obtain for complicated structures, this simple examination of the grating nanosurface is insightful for understanding the basic phenomena. As a first step, we need to calculate the interface impedance, Zint. We use an equivalent transmission line model, which is shown in Fig. 6 and 8 for TE and TM polarizations, respectively. Each unit cell of the grating nanosurface is subdivided into two zones. At the interface between Zone 1 and Zone 2, the tangent component of the electric or magnetic field is continuous. Depending on the polarization, we will use this information to connect the two zones according to the circuit theory.

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 ZintTE 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.
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 ZintTM 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.

3.1. Transverse electric excitation

We start with the TE case for simplicity. From Zone 1, we expect to retrieve an equivalent impedance at the interface that can be calculated as in Eq. (2), where here kt = k0 sinθ and θ is the angle of incidence of the incoming light. We write the transmission line expression again for convenience:
Z1TE=ZSiTEZAgTE+jZSiTEtan(hkSi2k02sin2θ)ZSiTE+jZAgTEtan(hkSi2k02sin2θ).
(8)
For Zone 2, we calculate an equivalent impedance Z2TE analogous to Z1TE in Eq. (8), but where the Ag load impedance, ZAgTE, is moved to the interface by the distance hr instead of h. For TE polarization, at the junction between Zone 1 and Zone 2, the tangent electric field (tangent to the plane separating the two zones) is always continuous for any angle of incidence (see Fig 6). From a circuit theory point of view, this means that the electric potential difference at the nodes of the two impedances is constant, and the connection between the two loads is then a shunt connection. When dealing with shunt connections, it is easier to express the loads in terms of admittances Y1,2TE=1/Z1,2TE, since the total admittance is simply the sum of the two. To take into account the actual size of Zone 1 and 2 with respect to the unit cell, we weight the two admittances according to unit cell filling factors. In particular, Y1TE is weighted by a factor f1 = w/d and Y2TE by f2 = (d – w)/d. Thus, the equivalent interface impedance to be used in Eq. (7) can be written as
ZintTE=1Y1TEf1+Y2TEf2
(9)
and the absorption can be calculated using Eq. (6). The result for normal incidence (θ = 0) is shown in Fig. 7(a) (red line) along with the full wave CST simulation of the grating nanosurface. The agreement is good overall except for some small discrepancies, which are likely due to higher order effects that are not considered in the model.

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.

3.2. Transverse magnetic excitation

As was done for the TE case, we calculate the equivalent impedance at the air-Si interface from Zone 1 and Zone 2. For Zone 1, we rewrite the Ag load impedance, ZAgTM, at the interface using the usual transmission line formula (Eq. (8)) applied for TM polarization
Z1TM=ZSiTMZAgTM+jZSiTMtan(hkSi2k02sin2θ)ZSiTM+jZAgTMtan(hkSi2k02sin2θ).
(10)
For Zone 2, we need to consider two different phenomena. As for Zone 1, there is a Ag load impedance ZAgTM; however, we must also account for the extra dipole-like contribution due to the TM field diffraction. The latter is dominated by positive and negative charge accumulation at the edge of the ridge, which can be represented as an extra capacitive load in a shunt connection with the Ag load as shown in Fig. 8. We approximate the capacitive impedance associated with this charge accumulation, ZC, as the series of a capacitance and a resistance (Si has losses)
ZC=1jωC+RC,
(11)
with C = Re(εSi)w and RC = Im(εSi)w. Then, the impedance Z2TM is calculated as the parallel of ZC and ZAgTM moved to the air-Si interface through the formula in Eq. (10), where ZAgTM is substituted by the shunt of ZAgTM||ZC. Moreover, for TM polarization at the junction between Zone 1 and Zone 2, the tangent magnetic field (tangent to the plane separating the two zones) is continuous for any angle of incidence (see Fig 8). From a circuit theory point of view, this means that the current flowing through the two impedances is constant, and the connection between the two loads is then a series connection. The total load is the sum of the two impedances weighted according to the unit cell filling factors, i.e. Z1TM is weighted by f1 = w/d and Z2TM by f2 = (dw)/d. Thus, the equivalent interface impedance to be used in Eq. (7) can be written as
ZintTM=Z1TMf1+Z2TMf2
(12)
and then the absorption can be calculated through Eq. (6). The result for normal incidence (θ = 0) is shown in Fig. 7(b) (blue line) and compared with a full wave CST simulation. Despite the degree of approximation of the equivalent impedances calculated above, which only account for the largest first order effects, the results show that the global physical mechanism is captured by the model. Also, we show the absorption for the same structure without accounting for the impedance ZC in the model (dotted line). This result is important because it demonstrates how the plasmonic nature amplifies the diffraction at the ridges of the grating. The calculated absorption without ZC still agrees with the full wave solution, except in the range of the spectrum where the SPP is strongly excited (see dispersion diagram in Fig. 2).

3.3. Inclusion of an antireflective coating

In most cases, photovoltaic cells are covered by an antireflection (AR) coating (see Fig. 9(a)). The AR coating is a thin layer of dielectric material, whose interference effects cause the wave reflected from the top surface to be out of phase with the wave reflected from the Si surface. These out of phase reflected waves destructively interfere, resulting in zero net reflected energy. This ideal zero-reflection occurs only at the specific frequency and angle of incidence for which its thickness hAR = λ/(4nAR cosθ), where nAR is the refractive index of the material used as AR coating. We use here TiO2 with refractive index nAR = 2.5 [5

5. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010). [CrossRef] [PubMed]

] (the material is assumed to be lossless) and set hAR = 60nm. We apply the transmission line equivalent circuit model for both TE and TM polarizations, as shown in Fig. 9(b). The equivalent impedance utilized in Section 3.1 for TE and Section 3.2 for TM needs to be transformed by an extra piece of transmission line of length hAR and characterized by a characteristic impedance as in Eq. (1), where X = AR. The new Zint impedance is then calculated at the air-AR coating interface using the usual transmission line formula as in Eq. (8) for TE and in Eq. (10) for TM. This result is then plugged into Eq. (7) to evaluate the absorption coefficient analytically via Eq. (6). The calculated result is compared with a CST simulation in Fig. 10 for both polarizations. The agreement is extremely good throughout the optical spectrum.

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.
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.

4. Absorption enhancement

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.

5. Conclusions

We have shown how light absorption in a plasmonic grating nanosurface can be calculated approximately by means of a simple analytical model based on a transmission line equivalent circuit. The geometry investigated here is a 1-D grating realized on a Ag metal back film covered by a Si slab. The transmission line model is specified for both TE and TM polarizations of the incident light. We have shown how to apply the circuit theory based on the conservation of the tangential components of the electromagnetic field at the junction between the ridge zone and the flat zone of the grating. This has lead to two different connections of elements for TE and TM fields, in particular a shunt connection for the first and a series connection for the second. Also, for the TM polarization, we have included the effect of charge accumulation at the grating ridges by adding an extra capacitive impedance in the circuit to account for plasmon excitation. Under the assumption that the adjacent ridges are not strongly coupled, we have shown that the approximate closed form expression of the reflection coefficient at the air-Si interface can be used to evaluate the light absorption of the solar cell. Moreover, we have demonstrated the utility of the circuit theory as an interpretive tool for understanding peaks in the absorption coefficient and relating these to resonances of the equivalent transmission line model. The weak-coupling assumption employed here is valid if the grating structure is not closely packed and the impinging light is close to normal incidence. We have empirically determined that for the structure under investigation, an angle of incidence beyond 20° from the normal is sufficient to induce higher order couplings, which are not included in the present form of the model. Expanding the model to incorporate higher order effects is under investigation currently. We note in closing that the transmission line model is not meant to substitute for full wave simulations, which are essential for complex nanostructures, but it provides physical insight for understanding the resonances that are responsible for the light trapping mechanism at a fraction of the cost.

Acknowledgments

This material is based upon work supported by the Department of Energy under Award Number DE-SC0006922.

References and links

1.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010). [CrossRef]

2.

A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl. 9, 211–215 (2001). [CrossRef]

3.

A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl. 12, 93–111 (2004). [CrossRef]

4.

W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).

5.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010). [CrossRef] [PubMed]

6.

P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express 17, 975–20, (2009). [CrossRef]

7.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8, 4391–4397 (2008). [CrossRef]

8.

M. Green, Third generation photovoltaics: advanced solar energy conversion, Springer series in photonics (Springer, 2003). URL http://books.google.com/books?id=TimK46htCMoC.

9.

D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express 19, 95–107 (2011). [CrossRef]

10.

R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009). [CrossRef]

11.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett. 98, 104–107 (2011). [CrossRef]

12.

C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl. 14, 629–641 (2006). [CrossRef]

13.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]

14.

T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Electron. Commun. 31, 116–120 (1977).

15.

N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices 54, 1926–1933 (2007). [CrossRef]

16.

J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun. 283, 5236–5244 (2010). [CrossRef]

17.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A 71, 811–818 (1981). [CrossRef]

18.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996). [CrossRef]

19.

A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78, 023,825 (2008). [CrossRef]

20.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18, 366–380 (2010). [CrossRef]

21.

I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys. 104, 502–034, (2008).

22.

L. Felsen and N. Markuvitz, Radiation and scattering of waves, 1st ed. (Prentice-Hall, Englewood Cliffs, NJ, 1973).

23.

www.cst.com (2011 CST Computer Simulation Technology AG).

24.

E. Palik, Handbook of optical constants of solids, 1st ed. (Academic Press, Orlando, 1985).

25.

A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag. 49, 1667–1677 (2001). [CrossRef]

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B. Davies, “Locating the zeros of an analytic function,” J. Comput. Phys. 66, 36–49 (1986). [CrossRef]

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(160.4760) Materials : Optical properties
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Plasmonics

History
Original Manuscript: October 28, 2011
Revised Manuscript: December 13, 2011
Manuscript Accepted: December 16, 2011
Published: January 2, 2012

Citation
Alessia Polemi and Kevin L. Shuford, "Transmission line equivalent circuit model applied to a plasmonic grating nanosurface for light trapping," Opt. Express 20, A141-A156 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S1-A141


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References

  1. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010). [CrossRef]
  2. A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001). [CrossRef]
  3. A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004). [CrossRef]
  4. W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).
  5. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010). [CrossRef] [PubMed]
  6. P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009). [CrossRef]
  7. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008). [CrossRef]
  8. M. Green, Third generation photovoltaics: advanced solar energy conversion, Springer series in photonics (Springer, 2003). URL http://books.google.com/books?id=TimK46htCMoC .
  9. D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011). [CrossRef]
  10. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009). [CrossRef]
  11. A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011). [CrossRef]
  12. C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl.14, 629–641 (2006). [CrossRef]
  13. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966). [CrossRef]
  14. T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Electron. Commun.31, 116–120 (1977).
  15. N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007). [CrossRef]
  16. J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun.283, 5236–5244 (2010). [CrossRef]
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