A theoretical study on optical field distribution and absorption of stacked thin films supported by a reflective back layer

Vy, Nguyen Duy; Pham, Vinh N. T.; Dat, Le Tri

doi:10.1063/5.0198937

The stacked thin films have recently been of great interest for enhancing the optical and thermal absorption of the system via their specific optical properties depending on the optical wavelength and layer thickness. Here, by using Maxwell’s equation for the electromagnetic fields penetrating thin films, we simulated in detail the absorption of the nanometer-thick thin film of several materials, such as Au, Ag, Cu, and Al, and figured out the optimal thickness range for the outer layers exposed to incoming field to optimize the energy harvesting. In particular, the absorption of the film supported by a totally reflective layer at the back of the structure could be significantly enhanced, and the maximal absorption happens at a layer much thinner than that in the case of the film solely irradiated by the field. These results could help suitably choosing of detailed thickness for the structure to optimize the field effect on a specific layer.

I. INTRODUCTION

Stacked thin films with high absorption layers have been attracting the community for decades for its wide application in electronics and energy harvesting devices.^1–5 Several complicated materials with modern combined/embedded techniques have been adopted to enhance the absorption of THz to visible range electromagnetic waves, such as the iron oxide over metallic thin films,^6–9 lossy thin films fabricated over reflective substrates,¹⁰ nanoparticles on the surface or inside the solar cell,^11,12 graphene,¹³ or nanogratings.¹⁴ The thermal–optical materials are used when the heat is needed to create electric currents. Meanwhile, opto-electrical materials rely on the absorption of photons, the electromagnetic quanta of energy, to excite the electrons in the materials to make currents or to release other light quanta subsequently.¹⁵ In all methods, the absorption of coating materials is of crucial importance because it determines the fraction of the irradiated field that could penetrate the inner films. Therefore, having a system with a high absorption ratio as well as high stability with environmental corrosion is of crucial interest.

Using the metallic thin film as part of solar energy harvester has recently been of interest due to the high plasmonic and mobility properties of these materials. The metallic thin film could play the role of the semi-transparent layer, the partially absorptive layer, or the conductive part as the anode of the solar cell.¹⁶ For example, Qian et al.¹⁶ showed that, when used as an ITO-free transparent conductive electrode, Ag metallic films in the multilayer structure present a comparable device performance or even better than that of those fabricated from the ITO electrode. Surya Prakasarao et al.¹⁷ examined ultra-thin Au–Ag–Au tri-layer film layers as a transparent conducting electrode and obtained a higher transmittance together with Hall effect measurements that show high conductivity and carrier concentration. Furthermore, Yamben et al.¹⁸ used Au as the material for anode and obtained an increase in efficiency to 49% when the transmittance of the Au film is increased from 38% to 54%. Therefore, besides the electrical properties, the optical properties are of crucial importance and many factors contributed to the efficiency of a solar cell are still open to question.

In this study, we model a system of stacked layers of metallic thin films, as shown in Fig. 1, and use Maxwell’s equations to examine the field distribution and absorption (P_abs) of the system. The change of P_abs vs the optical wavelength, film thickness, and cavity length (the distance between reflective layers) will be clarified. We first obtained the field distribution in every layer of the system and then calculated the optical absorption when the wavelength is tuned to search for the maximal absorption. In particular, an optimal structure to maximize the absorption is proposed. This result could guide the experimentalist in the fabrication of an effective system for electronic and solar cell applications.

FIG. 1.

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A model describing a simplified structure for enhancing the electromagnetic (em) field in the solar cell. The first metallic thin film lets the electromagnetic field partly penetrate the inside part with active and supported films. When the distance between the first and second metallic films matches a number of half wavelengths (nλ/2), the resonance exists and a very high field intensity between the two films is obtained.

II. THEORETICAL MODEL AND BACKGROUND

A complex stacked thin film could be modeled by a system of layers that are arranged in parallel. Each layer i has a thickness of d_i − d_i−1, as shown in Fig. 2 (left panel). The electromagnetic field exerted on the system is assumed to travel from left to right (z-direction). The field components inside these layers are usually obtained by using the transfer matrix method. However, we have also figured out that a matrix equation containing all field components of the system could be established and solved.¹⁹ In this study, we assume that the first layer is a metallic thin film and there is only one middle layer that is transparent to light. The back layer is used to support the absorption on the first layer by partially or totally reflecting the light. The distance between the two metallic layers is chosen to be approximately a number of half-optical wavelengths. The simplified model is shown in Fig. 2 (right panel), where δ is usually called the cavity length and the incoming light is perpendicular to the film surface. The case of an oblique irradiation (with incident angle θ) will be examined elsewhere; however, the current study (θ = 0) still holds the universal formalism for the other cases. In this study, Au, Cu, Ag, and Al are examined as typical materials for the solar cell. The parameters for the dielectric functions are extracted from Ref. 20.

FIG. 2.

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Model of a multi-layer system arranged in parallel. The electromagnetic components of the ith layer are presented as $E_{i}^{+}$ and $E_{i}^{-}$ for the incoming and outgoing fields, respectively. The gap between any two metallic layers could become an optical cavity if the gap width is equal to a number of half-optical wavelengths.

A. Absorption of a metallic layer

The reflective layer located behind the thin film plays the role of an enhancement factor via partly or totally reflecting the light to the film. The absorption of a metallic layer of thickness d is calculated as follows:

P_{abs} = \int_{0}^{d} d z {|E (z)|}^{2} I m [1 - ϵ (ω)] \frac{ω}{c},

(1)

where E(z) is the electric field inside the metal film, ϵ(ω) is the complex optical dielectric function with optical frequency, ω = 2πc/λ, and the integration is taken over the film thickness [0, d] as shown in Fig. 2 (right). We use the Lorentz–Drude model^22,23 for the dielectric function of the metallic layer,

ϵ_{L D} (ω) = ϵ_{b} (ω) + ϵ_{f} (ω),

(2)

where

ϵ_{f} (ω) = 1 - \frac{f_{0} ω_{p}^{2}}{ω^{2} + i Γ_{0} ω}

is related to the intraband part and

ϵ_{b} (ω) = \sum_{j = 1}^{K} \frac{f_{j} ω_{p}^{2}}{(ω_{j}^{2} - ω^{2}) + i Γ_{j} ω}

describes the interband part of dielectric function. The complex optical dielectric function is

ϵ (ω) = ϵ_{L D}^{1} - i ϵ_{L D}^{2}

⁠. The electric field inside a layer is presented as follows:

E = E^{+} e^{ikz} + E^{-} e^{- i k z},

(3)

where, E⁺ is the incident field, E⁻ is reflected field, and k is wave number. The electric and magnetic fields are written as follows:

E = E^{+} e^{ikz} + E^{-} e^{- i k z},

(4)

H = H^{+} e^{ikz} + H^{-} e^{- i k z},

(5)

where E⁺ and H⁺ are the incident fields, E⁻ and H⁻ are the reflected fields, and

k = \sqrt{ϵ} ω / c

is the wave number. Considering a position d_j that was a joint between two layers, we obtained a pair of equations at that point,

E_{j}^{+} e^{i k_{j} d_{j}} + E_{j}^{-} e^{- i k_{j} d_{j}} = E_{j + 1}^{+} e^{i k_{j + 1} d_{j}} + E_{j + 1}^{-} e^{- i k_{j + 1} d_{j}},

(6)

H_{j}^{+} e^{i k_{j} d_{j}} + H_{j}^{-} e^{- i k_{j} d_{j}} = H_{j + 1}^{+} e^{i k_{j + 1} d_{j}} + H_{j + 1}^{-} e^{- i k_{j + 1} d_{j}} .

(7)

In this study, we assumed

\vec{k} ‖ \vec{z}

⁠, so

| \vec{k} | = k_{z} = k

⁠. One has 2(N − 1) equations for N different layers. However, to calculate conveniently, we converted them to a matrix equation with the size M × M, where M equals 2(N − 1) as used in Ref. 19. The first equation is rearranged in the following form:

E_{j}^{-} e^{- i k_{j} d_{j}} - E_{j + 1}^{+} e^{i k_{j + 1} d_{j}} - E_{j + 1}^{-} e^{- i k_{j + 1} d_{j}} = - E_{j}^{+} e^{i k_{j} d_{j}} .

(8)

Furthermore, the magnitude of the incoming field is assumed as

E_{0}^{+}

= 1 and that of the outgoing field of the last boundary is assumed as

E_{N}^{-}

= 0. In the following matrix, only the equations for the first and the last boundaries are shown for brevity. The matrix has the following form:

[\begin{matrix} e^{- i k_{0} d_{0}} & - e^{i k_{1} d_{0}} & - e^{- i k_{1} d_{0}} & \dots & 0 \\ - e^{- i k_{0} d_{0}} & - \frac{k_{1}}{k_{0}} e^{i k_{1} d_{0}} & \frac{k_{1}}{k_{0}} e^{- i k_{1} d_{0}} & \dots & 0 \\ \dots & \dots & \dots & \dots & \dots \\ 0 & \dots & e^{i k_{N - 1} d_{N - 1}} & e^{- i k_{N - 1} d_{N - 1}} & - e^{i k_{N} d_{N - 1}} \\ 0 & \dots & e^{i k_{N - 1} d_{N - 1}} & - e^{- i k_{N - 1} d_{N - 1}} & - \frac{k_{N}}{k_{N - 1}} e^{i k_{N} d_{N - 1}} \end{matrix}] [\begin{matrix} E_{0}^{-} \\ E_{1}^{+} \\ E_{1}^{-} \\ . \\ . \\ . \\ E_{N}^{+} \end{matrix}] = [\begin{matrix} - 1 \\ - 1 \\ 0 \\ . \\ . \\ . \\ 0 \end{matrix}] .

(9)

One can solve Eq. (9) and obtain these fields for each layer.

B. Absorption of a metallic layer with a reflective layer

Now, we assumed that the reflective layer lies right side of the metal [Fig. 2 (right panel)] and split a space distance δ = d₂ − d₁. This reflective layer creates an empty optical cavity of length L_C = δ and could enhance the electric field stored inside the cavity up to several factors.^24,25 To figure out the electric fields, a matrix equation was written out as follows:

[\begin{matrix} 1 & - 1 & - 1 & 0 \\ - 1 & - \frac{k_{1}}{k_{0}} & \frac{k_{1}}{k_{0}} & 0 \\ 0 & e^{i k_{1} d} & e^{- i k_{1} d} & - e^{i k_{2} d} (1 + e^{i 2 k_{2} δ}) \\ 0 & e^{i k_{1} d} & - e^{- i k_{1} d} & - \frac{k_{2}}{k_{1}} e^{i k_{2} d} (1 - e^{i 2 k_{2} δ}) \end{matrix}] [\begin{matrix} E_{0}^{-} \\ E_{1}^{+} \\ E_{1}^{-} \\ E_{2}^{+} \end{matrix}] = [\begin{matrix} - 1 \\ - 1 \\ 0 \\ 0 \end{matrix}] .

(10)

Here, at the position z = d + δ, the field is assumed

E_{2}^{-} = E_{2}^{+} e^{i2k(d+δ)}

with L_C = δ to obtain the total reflection.

III. RESULTS AND DISCUSSION

A. The electric field distribution in an optical microcavity with the reflective layer

The normalized magnitude of the electromagnetic field (|E|²) inside and outside the system is shown in Fig. 3 assuming four different materials, such as Au, Ag, Cu, and Al. Here, the optical wavelength of the laser is λ = 633 nm, the cavity length is L_C = λ, and the thickness of the metallic layer is 30 nm. The peaks are located in the center of the cavity and could reach around 60 for Ag, 25 for Cu, and 18 for Au. However, in the case of Cu, the resonator does not appear because, with a 30 nm thickness, only a small amount of the fields passes through the film, and this reduces the interference between the incoming and the backward fields inside the cavity.

FIG. 3.

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Field distribution in various regions of the system normalized to the incoming field. The first metallic thin film (green) together with the second (violet) gives rise to an optical microcavity and the constructive/destructive pattern inside the cavity. The wavelength of the input laser is λ = 633 nm, and the cavity length is δ = λ.

When investigating the distribution of the electric fields using different optical wavelengths and for a fixed cavity length, e.g., L_C = 633 nm, the field with wavelength longer than LC will be more off-resonant and the reflection is higher. This gives rise to higher peaks for λ = 700–800 nm in comparison with that of 600 nm. The position of reflective peaks is about an odd number of half-wavelengths. Therefore, the peaks in the region z < 0 shift back far from z = 0 for increasing wavelength, as shown in Fig. 4. In addition, this corresponds to a reduction in the stored field inside the cavity (z > 0).

FIG. 4.

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Field distribution vs incoming lights for various metals. Au (a) and Cu (c) present a more sensitive with wavelength than Ag (b) and Al (d). The field intensity greatly changes with the wavelength λ for a fixed cavity length L_C. For L_C = 633 nm, the fields of longer wavelength are more reflected and higher peaks on the left of z = 0 are seen.

In general, for the Al thin film, we do not see the resonance inside the cavity [see Fig. 4(d)]. Meanwhile, Au, Ag, and Cu films enhance the fields inside the cavity and increase the peak heights of the electric fields when the wavelengths increase [see Figs. 4(a)–4(c)]. This arises from the optical nature of Al from its dielectric function. Moreover, the results also imply that the Al layer could reflect the incoming light more stable in comparison with other layers.

B. Absorption of a single film

To examine the maximal absorption that the metallic film could be obtained, we use some wavelengths from 600 to 750 nm and explore in a wide range of film thickness up to 100 nm [see Fig. 5]. It could be seen that toward the short wavelength, the maximal absorption, P_abs/P₀, where P₀ is the input power, could reach nearly 20% in the case of Au and Cu. Ag, however, just reaches 7% most cases. Al is special for its different absorption [Fig. 5(d)] with other three metals by an inverted behavior that the shorter wavelength is less absorbed than the longer is. However, the maximum absorption using these wavelengths could reach $>$ 30%, a higher value compared to other materials. We could see that there exists a thickness t_m that maximizes absorption, and, in general, this thickness reduces with wavelength. Furthermore, the absorption increases when the wavelength decreases, as shown by the red dashed-dotted line for 750 nm and the blue solid line for 600 nm.

FIG. 5.

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Absorption of the metallic thin film of various thicknesses. There exists a thickness t_m that could maximize the absorption, and the value t_m is dependent on the optical wavelength, e.g., t_m ≃ 25 nm for Au at 600 nm (a), ≃ 20 nm for Ag (b), 10--20 nm for Cu (c) and an extremely small ≃ 5 nm for Al (d).

C. Absorption in case the totally reflective layer exists

Examining the role of the reflective layer on the absorption, we see that the absorption has been greatly increased, as shown in Fig. 6. The reflective layer put behind the metallic layer not only increases twice the absorption via the total reflection, but also creates interference inside the film if the film thickness matches a number of λ/2; therefore, the absorption could be increased more than twice. If the reflective layer is thinner than just partially reflecting light, the absorption in the first thin film will be smaller and the optimal thickness will be greater, as seen in a previous study.²⁵ In the current study with the totally reflective layer, the maximum absorption reaches 52% for the Au case [see Fig. 6(a)]. In particular, the optimal thickness t_mr in this case appears to have a thickness lower than that of the single film, i.e., t_mr < t_m. In particular, t_mr = 2 nm, the size of a few atomic layer, for the Al case, reflects the limitation of the current calculation method.

FIG. 6.

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Absorption when a totally reflective layer is available. (a) Au: up to $>$ 52% at λ = 600 nm (red solid line) and optimal thickness t_mr ≃ 15 nm. (b) and (c) Peaks appear at thinner thicknesses compared with gold, 8 nm for Ag and 9 nm for Cu, respectively. (d) Peak at 2 nm for Al case reflects the limitation of the calculation method. Here, δ = 632.32 nm.

In conventional experiments, a thickness of t_mr = 30–100 nm is usually used.²⁶ Therefore, we examine the practical absorption for t_mr = 50 nm as a typical case. Figure 7 shows that Au, Ag, and Cu could present a very high absorption. Meanwhile, Al has extremely low absorption. The maximal absorption is also obtained for the cavity length (δ) of a multiple of half-wavelength the cavity is resonant, i.e., the cavity length is equal to a number of half-wavelengths taking into account a penetration depth around 34 nm.¹⁹

FIG. 7.

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Absorption on a thin film examines a wide range of the cavity length δ. The absorption could reach unity at certain parameters for the optical wavelength λ = 632.82 nm when the resonance exists. Here, the thickness of the metallic layers was proposed with d = 50 nm.

Therefore, at every length L = δ = L₀ + nλ/2, we will see a peak in the absorption, where L₀ is the minimum length and n is an integer. The difference in the dielectric functions of the metals gives rise to the difference in the peak widths and shapes. The peak width is wider for Au and thinner for Al.

IV. DISCUSSION AND CONCLUSIONS

We have examined the optimal optical absorption on thin films toward the application in the solar cell by using a system of a semi-transparent thin film and a reflective layer embedded on a substrate. It has been shown that for metallic materials such as Au, Ag, Cu, and Al, the maximal absorption could be significantly enhanced thanks to reflection from the second layer. The optimal absorption happens at small thickness below 25 nm, and these thicknesses depend on the optical wavelength. An enhancement of more than twice the optical absorption of a single thin film has been obtained, from 20% to $>$ 52% for the case of Au and similar for other materials. This presents an important role for the reflective layer in enhancing the total absorption of the active metallic layer. The system could be fabricated with other modern two-dimensional materials, such as nanoparticles (NPs)^11,12 or NPs combined with organic materials²⁷ to exploit the plasmonic coupling, graphene¹³ to enhance the opto-electrical interaction, or nanogratings¹⁴ on thin films themselves, or even recently to increase absorption. Therefore, the results in this study could provide fruitful information for selecting suitable parameters for the system toward optimized absorption on the surface layer, or any layer in the middle as a host for the modified structure, to enhance its energy harvesting functions.

ACKNOWLEDGMENTS

N. D. Vy acknowledges the Van Lang University.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Nguyen Duy Vy: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Vinh N. T. Pham: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Le Tri Dat: Data curation (equal); Funding acquisition (equal); Software (equal); Writing – original draft (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES

1

M. A.

Kats

and

F.

Capasso

, “

Optical absorbers based on strong interference in ultra-thin films

,”

Laser Photonics Rev.

10

(

5

),

735

–

749

(

2016

).

https://doi.org/10.1002/lpor.201600098

Google Scholar

Crossref

2

A.

Pahuja

,

M. S.

Parihar

, and

V. D.

Kumar

, “

Performance enhancement of thin-film solar cell using Yagi–Uda nanoantenna array embedded inside the anti-reflection coating

,”

Appl. Phys. A

126

(

1

),

70

(

2020

).

https://doi.org/10.1007/s00339-019-3250-0

Google Scholar

Crossref

3

X.

Li

,

P.

Li

,

Z.

Wu

,

D.

Luo

,

H.-Y.

Yu

, and

Z.-H.

Lu

, “

Review and perspective of materials for flexible solar cells

,”

Mater. Rep.: Energy

1

(

1

),

100001

(

2021

).

https://doi.org/10.1016/j.matre.2020.09.001

Google Scholar

Crossref

4

B.

Liu

,

C.

Wang

,

S.

Bazri

,

I. A.

Badruddin

,

Y.

Orooji

,

S.

Saeidi

,

S.

Wongwises

, and

O.

Mahian

,

Optical properties and thermal stability evaluation of solar absorbers enhanced by nanostructured selective coating films

,

Powder Technol.

377

,

939

–

957

(

2021

).

https://doi.org/10.1016/j.powtec.2020.09.040

Google Scholar

Crossref

5

M.

Girtan

and

B.

Negulescu

, “

A review on oxide/metal/oxide thin films on flexible substrates as electrodes for organic and perovskite solar cells

,”

Opt. Mater.: X

13

,

100122

(

2022

).

https://doi.org/10.1016/j.omx.2021.100122

Google Scholar

Crossref

6

H.

Dotan

,

O.

Kfir

,

E.

Sharlin

,

O.

Blank

,

M.

Gross

,

I.

Dumchin

,

G.

Ankonina

, and

A.

Rothschild

, “

Resonant light trapping in ultrathin films for water splitting

,”

Nat. Mater.

12

(

2

),

158

–

164

(

2012

).

https://doi.org/10.1038/nmat3477

Google Scholar

Crossref

PubMed

7

M. A.

Kats

and

F.

Capasso

, “

Ultra-thin optical interference coatings on rough and flexible substrates

,”

Appl. Phys. Lett.

105

(

13

),

131108

(

2014

).

https://doi.org/10.1063/1.4896527

Google Scholar

Crossref

8

J.

Park

,

S. J.

Kim

, and

M. L.

Brongersma

, “

Condition for unity absorption in an ultrathin and highly lossy film in a Gires–Tournois interferometer configuration

,”

Opt. Lett.

40

(

9

),

1960

(

2015

).

https://doi.org/10.1364/ol.40.001960

Google Scholar

Crossref

PubMed

9

Y.

Zhu

,

Y.

Zhou

,

B.

Qin

,

R.

Qin

,

M.

Qiu

, and

Q.

Li

, “

Night-time radiative warming using the atmosphere

,”

Light: Sci. Appl.

12

(

1

),

268

(

2023

).

https://doi.org/10.1038/s41377-023-01315-y

Google Scholar

Crossref

PubMed

10

M. A.

Kats

,

R.

Blanchard

,

S.

Ramanathan

, and

F.

Capasso

, “

Thin-film interference in lossy, ultra-thin layers

,”

Opt. Photonics News

25

(

1

),

40

(

2014

).

https://doi.org/10.1364/opn.25.1.000040

Google Scholar

Crossref

11

J.-Y.

Lee

and

P.

Peumans

, “

The origin of enhanced optical absorption in solar cells with metal nanoparticles embedded in the active layer

,”

Opt. Express

18

(

10

),

10078

–

10087

(

2010

).

https://doi.org/10.1364/OE.18.010078

Google Scholar

Crossref

PubMed

12

P.

Spinelli

,

V. E.

Ferry

,

J.

van de Groep

,

M.

van Lare

,

M. A.

Verschuuren

,

R. E. I.

Schropp

,

H. A.

Atwater

, and

A.

Polman

, “

Plasmonic light trapping in thin-film Si solar cells

,”

J. Opt.

14

(

2

),

024002

(

2012

).

https://doi.org/10.1088/2040-8978/14/2/024002

Google Scholar

Crossref

13

M.

Jabeen

and

S.

Haxha

, “

Increased optical absorption and light–matter interaction in Silicon thin-film solar cell nanostructure using graphene and 2-D Au/Ag nanograting

,”

IEEE J. Quantum Electron.

54

(

6

),

1

–

12

(

2018

).

https://doi.org/10.1109/jqe.2018.2877185

Google Scholar

Crossref

14

F. E.

Subhan

,

A. D.

Khan

,

F. E.

Hilal

,

A. D.

Khan

,

S. D.

Khan

,

R.

Ullah

,

M.

Imran

, and

M.

Noman

, “

Efficient broadband light absorption in thin-film a-si solar cell based on double sided hybrid bi-metallic nanogratings

,”

RSC Adv.

10

(

20

),

11836

–

11842

(

2020

).

https://doi.org/10.1039/c9ra10232a

Google Scholar

Crossref

PubMed

15

E.

Bucher

, “

Solar cell materials and their basic parameters

,”

Appl. Phys.

17

(

1

),

1

–

26

(

1978

).

https://doi.org/10.1007/bf00885025

Google Scholar

Crossref

16

R.

Qian

,

J.

Liao

,

G.

Luo

, and

H.

Wu

, “

Ito-free organic solar cells with oxide/metal/oxide multilayer structure cathode

,”

Org. Electron.

108

,

106614

(

2022

).

https://doi.org/10.1016/j.orgel.2022.106614

Google Scholar

Crossref

17

C.

Surya Prakasarao

,

P.

Hazarika

,

S. D.

DSouza

,

J. M.

Fernandes

,

M.

Kovendhan

,

R.

Arockia Kumar

, and

D.

Paul Joseph

,

Investigation of ultra-thin and flexible Au–Ag–Au transparent conducting electrode

,

Curr. Appl. Phys.

20

(

10

),

1118

–

1124

(

2020

).

https://doi.org/10.1016/j.cap.2020.06.016

Google Scholar

Crossref

18

S. D.

Yambem

,

A.

Haldar

,

K.-S.

Liao

,

E. P.

Dillon

,

A. R.

Barron

, and

S. A.

Curran

, “

Optimization of organic solar cells with thin film au as anode

,”

Sol. Energy Mater. Sol. Cells

95

(

8

),

2424

–

2430

(

2011

).

https://doi.org/10.1016/j.solmat.2011.04.019

Google Scholar

Crossref

19

L. T.

Dat

,

S. H.

Luong

,

V. N.

Pham

,

N. D.

Vy

, and

T.

Iida

, “

Radiation pressure on a graphene layer inserted inside an optical microcavity

,”

Opt. Commun.

520

,

128478

(

2022

).

https://doi.org/10.1016/j.optcom.2022.128478

Google Scholar

Crossref

20

A. D.

Rakić

,

A. B.

Djurišić

,

J. M.

Elazar

, and

M. L.

Majewski

, “

Optical properties of metallic films for vertical-cavity optoelectronic devices

,”

Appl. Opt.

37

(

22

),

5271

–

5283

(

1998

).

https://doi.org/10.1364/AO.37.005271

Google Scholar

Crossref

PubMed

21

A.

Vial

,

A.-S.

Grimault

,

D.

Macías

,

D.

Barchiesi

, and

M. L.

de la Chapelle

, “

Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method

,”

Phys. Rev. B

71

(

8

),

085416

(

2005

).

https://doi.org/10.1103/physrevb.71.085416

Google Scholar

Crossref

22

A.

Vial

,

T.

Laroche

,

M.

Dridi

, and

L.

Le Cunff

, “

A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method

,”

Appl. Phys. A

103

(

3

),

849

–

853

(

2011

).

https://doi.org/10.1007/s00339-010-6224-9

Google Scholar

Crossref

23

N.

Duy Vy

and

T.

Iida

, “

Ambient-dependent optomechanical control of cantilever with mechanical nonlinearity by cavity-induced radiation force

,”

Appl. Phys. Lett.

102

(

9

),

091101

(

2013

).

https://doi.org/10.1063/1.4794060

Google Scholar

Crossref

24

N. D.

Vy

and

T.

Iida

, “

Enhancing thermally induced effects on atomic force microscope cantilevers using optical microcavities

,”

Appl. Phys. Express

9

(

12

),

126601

(

2016

).

https://doi.org/10.7567/apex.9.126601

Google Scholar

Crossref

25

C. M.

Hoang

,

T.

Iida

,

L. T.

Dat

,

H. T.

Huy

, and

N. D.

Vy

, “

Optimal coating thickness for enhancement of optical effects in optical multilayer-based metrologies

,”

Opt. Commun.

403

,

150

–

154

(

2017

).

https://doi.org/10.1016/j.optcom.2017.07.023

Google Scholar

Crossref

26

K.

Pydzińska-Białek

,

G.

Nowaczyk

, and

M.

Ziółek

, “

Complete perovskite solar cells with gold electrodes studied in the visible and near-infrared ranges

,”

Chem. Mater.

34

(

14

),

6355

–

6366

(

2022

).

https://doi.org/10.1021/acs.chemmater.2c00845

Google Scholar

Crossref

27

A. G.

Waketola

,

F. G.

Hone

,

G. T.

Mola

,

S. O.

Oseni

,

H.

Ogutu

, and

N. A.

Tegegne

, “

Hybrid silver/silver-oxide nanoparticles doped hole transport layer for efficient photon harvesting in organic solar cells

,”

Appl. Phys. A

129

(

2

),

96

(

2023

).

https://doi.org/10.1007/s00339-022-06349-4

Google Scholar

Crossref

A theoretical study on optical field distribution and absorption of stacked thin films supported by a reflective back layer

I. INTRODUCTION

II. THEORETICAL MODEL AND BACKGROUND

A. Absorption of a metallic layer

B. Absorption of a metallic layer with a reflective layer

III. RESULTS AND DISCUSSION

A. The electric field distribution in an optical microcavity with the reflective layer

B. Absorption of a single film

C. Absorption in case the totally reflective layer exists

IV. DISCUSSION AND CONCLUSIONS

ACKNOWLEDGMENTS

AUTHOR DECLARATIONS

Conflict of Interest

Author Contributions

DATA AVAILABILITY

REFERENCES

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A theoretical study on optical field distribution and absorption of stacked thin films supported by a reflective back layer Open Access

I. INTRODUCTION

II. THEORETICAL MODEL AND BACKGROUND

A. Absorption of a metallic layer

B. Absorption of a metallic layer with a reflective layer

III. RESULTS AND DISCUSSION

A. The electric field distribution in an optical microcavity with the reflective layer

B. Absorption of a single film

C. Absorption in case the totally reflective layer exists

IV. DISCUSSION AND CONCLUSIONS

ACKNOWLEDGMENTS

AUTHOR DECLARATIONS

Conflict of Interest

Author Contributions

DATA AVAILABILITY

REFERENCES

Citing articles via

Submit your article

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Related Content

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A theoretical study on optical field distribution and absorption of stacked thin films supported by a reflective back layer