Optical characteristics of surface plasmon resonance based on ZnO and metallic nano-grating structures

Doo Gun Kim, Seon Hoon Kim, Hyun Chul Ki, Hyo Jin Kim, Hang Ju Ko, Myung-Soo Han,

Swook Hann, Tae Un Kim, and Hwe Jong Kim, Photonics Device Team, Korea Photonics Technology Institute, WolChul-dong, Buk-go,

Gwangju 500-779, Korea, Phone: +82-62-605-9214, Fax: +82-62-605-9229, Email: emblemdo@kopti.re.kr

Geum-Yoon Oh and Young Wan Choi,

School of Electronic and Electrical Engineering, Chung-Ang University, 221 Heuksuk-Dong, Dongjak-ku, Seoul, 156-756, Korea

ABSTRACT

We proposed the grating coupled surface plasmon resonance (GC-SPR) sensors using ZnO and metallic nano-

grating structures to enhance the sensitivity of an SPR sensor. The GC-SPR sensors were analyzed using the finite-

difference time-domain method. The optimum resonance angles of 49 and 55.5 degrees are obtained in the 150 nm wide

grating structure with a period of 300 nm for the ZnO thickness of 30 and 50 nm, respectively. Here, an enhanced

evanescent field is obtained due to the surface plasmon on the edge of the bandgap when the ZnO and metallic grating

structures are used to excite the surface palsmon.

Keywords : Surface plasmon resonance, ZnO, Metallic nano-grating, Sensor

1. INTRODUCTION

Recently, biosensors using optical properties have gained increasing interest. Optical biosensors convert biological

interactions to measurable quantities of optical signal. This signal delivers the information of biological events such as

the presence of a specific biomolecule and the amount of biological pathogen in a medium of interest. For reliable and

accurate detection of trace amounts of them, highly sensitive techniques are essential. As of good example, surface

plasmon resonance (SPR) sensor [1] and fluorescence biosensors have been reported. The SPR biosensor is preferred to

fluorescence biosensor which is required to take the labeling process reacting a specific biological pathogen. For

example, the use of SPR for gas detection and biosensing was demonstrated by Nylander and Lienberg in 1982 [2].

Then, applications as a real-time monitor of surface interactions (e.g., the Pharmacia BIAcoreTM system) [3] was found,

and is being extensively studied for other chemical or biological sensing applications. It has many advantages, such as

real time detection, non-labeling, and high sensitivity. Here, the electromagnetic surface wave between metal and

dielectric interface, called surface plasmon wave (SPW), was demonstrated in 1950’s [4]. The excitation of SPW by

Quantum Sensing and Nanophotonic Devices VII, edited by Manijeh Razeghi, Rengarajan Sudharsanan, Gail J. Brown,Proc. of SPIE Vol. 7608, 76081H · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.841444

Proc. of SPIE Vol. 7608 76081H-1

light was introduced by Otto in 1968 [5] and Kretschmann-configuration was developed in the same year. In Otto-

configuration air gap is existed between a prism and a thin-metal film on substrate. However, Kretschmann-

configuration is coated with a thin-metal film on the prism interface directly [6]. In general, the phenomenon of SPR

shows optical properties on attenuated total reflection (ATR) mirror. The SPR can be observed when a p-polarized light

is incident through a prism onto a thin-film metal, such as silver, gold or aluminum. The SPR is a charge density

oscillation that may exist at the interface of two media with dielectric constants of opposite signs. The wave vector of

the surface plasmon wave is described by the following equation:

2

2

2 m ssp

m s

nkn

επλ ε

=+

, (1)

where εm is the dielectric constant of metal, and ns is the refractive index of the mirror block. The resonance condition

occurs in a particular wavelength when the wave vector of the incident light which parallel to the interface, kx, equals to

ksp. Under this resonance condition, incident light gets highly absorbed and loses a fair amount of its energy, which

results in a dip in the intensity profile of the reflected light. In this case, the required electric-field components to excite

the SPW have to be p-polarized light because this particular polarization has the electric-field vector oscillating normal

to the plane that contains the metal film. Though commercialized SPR sensors are readily available, there are increases

in development of other types of biosensors which are comparable to or better than the conventional SPR sensors in

terms of sensitivity. Then, the application with a grating structure was developed to enhance the sensitivity of the

conventional SPR sensors [7-9]. The nano-grating structure can be utilized to perturb the propagation of the surface

plasmon. The grating structure with dielectric grating on the metal film can be studied [10]. The ZnO material has good

properties of direct wide bandgap and high excitation binding energy at room temperature. Then, sensors based on ZnO

material can be developed due to many advantages such as the chemical sensitivity to volatile and other radical gases,

high chemical stability, non-toxicity, and low cost [11].

In this paper, we propose and analyze the grating coupled surface plasmon resonance (GC-SPR) sensors using ZnO

and metallic nano-grating structures to enhance the sensitivity of an SPR surface. This configuration was calculated

using the finite-difference time-domain method (FDTD) method. Here, the frequency dependent function of thin-

metal film was approximated by a Drude model in the FDTD method [12]. First, the properties such as the optimum

gold thickness and a resonance angle for the conventional SPR sensor were calculated. Then, we also have optimized

the GC-SPR sensors using FDTD method for the width, thickness, and period of the ZnO and metallic grating structures.

The following section gives the conventional SPR structure. This is followed by the dielectric and metallic grating

structure. Finally, conclusions are given.

Proc. of SPIE Vol. 7608 76081H-2

2. CONVENTIONAL SPR STRUCTURE

The FDTD method, originally proposed by Yee [13], is one of the most successful algorithms for the integration of

the time dependent form of Maxwell’s equations. However, Yee’s original formulation only described isotropic

materials with a static permittivity. In addition, the values of the negative permittivity make the standard time iteration

scheme unstable. Two main methods have been proposed for including dispersive materials in the FDTD method: the

recursive method and the auxiliary differential equation (ADE) method. We used ADE method to implement a

formulation of the FDTD scheme to describe the optical response of metals. In the ADE method, the electric flux

density is described by a differential equation in the time domain by means of a pole residue model of the dielectric

susceptibility function in the frequency domain [14]. Especially, for analysis of thin-metal film on the prism, optical

properties can be numerically presented. The understanding of optical properties of metal requires both electrodynamics

and solid state theory. The theory of electrodynamics developed by Maxwell in the 19th century very successfully

describes the relations of magnetic and electric fields and their propagation in free space. The internal structure of solids

was largely unknown until the beginning of the 20th century, when the discovery of the electron, the crystal lattice

structure and the advent of quantum mechanics provided the background for the description of the interaction of light

with matter. The extended electrodynamical theory includes the interaction with matter. Although it describes correctly

the reaction of matter to electric and magnetic fields, some material properties (for example, the complex dielectric

function ε) enter as input parameters. Thus, important optical effects such as light induced transmission or luminescence

are implicitly excluded if time-independent and field-independent material properties are used [15]. A simple model was

developed by Drude for noble metals, based on the kinetic gas theory. It assumes that the electrons with a common

relaxation time were independent and free. This free-electron model was later modified to include a minor correction for

the band-structure of matter (effective mass) and termed the quasi-electron model. This Drude model describes the

characteristics of metals well, despite its drastic assumptions. Optical properties described by the frequency dependent

dielectric function ε(ω) are predicted by:

2 2 20

2 30

( )( )

p p pii

ω ω γ ωε ω ε ε

ω ω γ ω ω∞ ∞= − ≈ − ++ , (2)

where pω is the plasma frequency and 0γ is the electron relaxation rate. The frequency dependent dielectric

permittivity for gold is shown in Fig. 1, where the real and imaginary values of the permittivity is given as a function of

light frequency by P.B. Johnson and R. W. Christy’s experimental results [16].

Proc. of SPIE Vol. 7608 76081H-3

0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2

-180

-150

-120

-90

-60

-30

0

R

e(e)

Photon energy [eV]

Experimental data(JC) Drude model

0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.20

5

10

15

20

25

Im(e

)

Photon energy [eV]

Experimental data(JC) Drude model

(a) (b)

Fig. 1. (a) Real and (b) imaginary values of the permittivity of gold

The complex dielectric permittivity of gold using the Drude model was fitted with a plasma frequency of 8.63 eV, a

collision rate of 109 meV, and a static permittivity ( ε∞ ) of 9.84. These fitted results by the Drude model agreed well

with the experimental data obtained at a wavelength of 632.8 nm. The limiting case for Maxwell’s equations can be

expressed as [17]:

1( , , , ) [ ( , , , ) ( , , , )] ,( , , , )eff

E x y z t H x y z t J x y z tt x y z tε∂

= ∇× −∂

(3)

0

1( , , , ) ( , , , ) ,H x y z t E x y z tt μ∂

= − ∇×∂

(4)

and 0( , , , ) ( ) .eff rx y z tε ε ε= ∞ (5)

Here, current-density vector J is initially at zero in the regions of free space and having some dielectric material with a

real dielectric constant. However, pω , 0γ , and ε∞ have some values in metallic regions as seen in the Drude model.

Therefore, the current-density vector can be represented by:

20 0 .pJ J E

tγ ε ω∂

+ =∂

(6)

Figure 2 shows the FDTD simulation results compared with conventional theory. For p-polarized light, the reflected

intensity as a function of angle of incident light was shown in Fig. 2. Since the gold thickness is directly related to the

amount of free electron charge, it influences significantly the peak mode attenuation, shape of the SPR dip as well as its

position. The resonance angle to generate surface plasmon wave is about 44.4 degrees. The parameters used are a

wavelength of 632.8 nm and the prism block effective index of 1.515. The thickness and the complex permittivity of the

gold film are 50 nm and εm= -10.66 + i1.374, respectively.

Proc. of SPIE Vol. 7608 76081H-4

42 45 48 51 540.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ance

Angle [deg]

FDTD Results SPR Theory

Damping radiation

Fig. 2. Reflectance as a function of incident angle for p-polarized light

3. DIELECTRIC AND METALLIC GRATING STRUCTURE

The configuration of ZnO and metallic grating structure is shown in Fig. 3. The gold film of 50 nm is coated

on a prism block and can generate the excitation of surface plasmons. ZnO gratings with a period Λ are regularly

patterned on an Au thin film. The 150 nm wide grating structure has a period of 300 nm. When the light is launched

into a prism mirror block, the evanescent field interacts with the free electrons of the gold layer. Therefore, the

evanescent wave gets absorbed by the metal’s free electrons, and electron charge density waves or SPW are generated.

θ

Light In Light Out

Au(ε m)

ZnO(ε z)

Prism (ε p)

Λ

Fig. 3. Configuration of ZnO and metallic grating structure

The reflectance and the optical-mode propagations as a function of incident angle are calculated by using the

FDTD method and are shown in Fig. 4. The parameters used here are a wavelength of 632.8 nm and the ZnO refractive

index of 1.989. The complex permittivity of the 50 nm gold film is mε = -10.66 + i1.374 and refractive index of sensing

area is 1.0. The optimum resonance angles of 49 degrees are obtained in the 150 nm wide grating structure with a period

Proc. of SPIE Vol. 7608 76081H-5

of 300 nm for the ZnO thickness of 30 nm. Under this resonance condition, incident light gets highly absorbed and loses

a fair amount of its energy, which results in a dip in the intensity profile of the reflected light. In this case, the required

electric-field components to excite the SPW have to be p-polarized light because this particular polarization has the

electric-field vector oscillating normal to the plane that contains the metal film. The optical-mode propagations at the

resonance angle of 49 degrees and the reflected angle of 55 degrees are shown in the inset of Fig. 4. The enhanced

evanescent field on the resonance angle is shown in Fig. 5. The generated SPW is confined around the grating pattern of

the ZnO. Here, an enhanced evanescent field is obtained due to the surface plasmon on the edge of the bandgap when

the ZnO and metallic grating structures are used to excite the surface palsmon.

40 42 44 46 48 50 52 54 56 58 60

0.60

0.65

0.70

0.75

0.80

Ref

lect

ance

Angle [deg]Surface plasmon wave

[49˚]

[55˚]

Fig. 4. Reflectance and the optical-mode propagations as a function of incident angle using FDTD method

Fig. 5. Enhanced evanescent field on the resonance angle using FDTD simulation.

We also calculated the different grating structure with 150 nm wide grating pattern with a period of 300 nm for

the ZnO thickness of 50 nm. The reflectance and the optical-mode propagations as a function of incident angle are

calculated by using the FDTD method and are shown in Fig. 6. The parameters used here is in the same conditions of

Fig. 4. The resonance angles of 55.5 degrees are achieved in the 150 nm wide grating structure with a period of 300 nm

Proc. of SPIE Vol. 7608 76081H-6

for the ZnO thickness of 50 nm. The optical-mode propagations at the resonance angle of 55.5 degrees and the reflected

angle of 61 degrees are shown in the inset of Fig. 6. In that case, the enhanced evanescent field on the resonance angle is

shown in Fig. 7. The generated SPW is confined around the grating pattern of the ZnO.

50 52 54 56 58 60 620.48

0.52

0.56

0.60

0.64

Ref

lect

ance

Angle [deg]Surface plasmon wave

[55.5˚]

[61˚]

Fig. 6. Reflectance and the optical-mode propagations as a function of incident angle using FDTD method

Fig. 7. Enhanced evanescent field on the resonance angle using FDTD simulation.

4. CONCLUSIONS

We have proposed and analyzed the GC-SPR sensors using ZnO and metallic nano-grating structures to enhance the

sensitivity of an SPR sensor. The GC-SPR sensors were analyzed using the FDTD method. Here, the frequency

dependent function of thin-metal film was approximated by a Drude model in the FDTD method. First, the properties

such as the optimum gold thickness and a resonance angle for the conventional SPR sensor were calculated. Then, we

also have optimized the GC-SPR sensors using FDTD method for the width, thickness, and period of the ZnO and

metallic grating structures. The optimum resonance angles of 49 and 55.5 degrees are obtained in the 150 nm wide

grating structure with a period of 300 nm for the ZnO thickness of 30 and 50 nm, respectively. Here, an enhanced

Proc. of SPIE Vol. 7608 76081H-7

evanescent field is obtained due to the surface plasmon on the edge of the bandgap when the ZnO and metallic grating

structures are used to excite the surface palsmon. Then, sensor system based on ZnO grating can offer many applications

due to many advantages such as the chemical sensitivity to volatile and other radical gases, high chemical stability, non-

toxicity, and low cost.

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