Dual layer ultrathin film optics II: experimental studies

1

Dual-layer ultrathin film optics II: experimental studies and

designs

Kim Peng Lim and Qian Wang

Data Storage Institute, A*STAR (Agency for Science, Technology and Research), DSI building, 5

Engineering Drive 1, Singapore 117608

Email: [email protected]

Abstract

This paper presents an experimental study of using dual-layer ultrathin films with a high refractive index and

low refractive index to approximate a single-layer thin film with an equivalent intermediate refractive index,

which is the basis of the functional graded refractive index thin film stack using dual-layer ultrathin films. Using

ion beam deposition, five sets of ultrathin films of titanium dioxide (TiO2) and aluminium oxide (Al2O3) are

deposited on silicon with different volume fractions and characterized by spectroscopic ellipsometer for the

ordinary/extraordinary refractive index and by spectrophotometer for the reflectance. By designing the

sequence of TiO2 and Al2O3 ultrathin films, the measured results show a good agreement between the

experiments and simulation of the equivalent birefringent thin film. An application example of using the TiO2

and Al2O3 dual-layer ultrathin films to approximate a single-layer antireflection coating for silicon is presented.

Keywords: dual-layer ultrathin film, ion-beam assisted deposition, antireflection

1. Introduction

Today, most optical thin films for e.g., antireflection (AR) coating, high-reflection or

wavelength filtering are based on the optimization of quarter-wavelength (λ/4) film stack by adjusting

the layer thickness and adding film layers, while restricting to the existing available refractive index

of materials. Alternative to this approach, thin films with ”continuous” refractive index profile are

considered attractive and for material systems in integrated photonic circuits, solar cells, light emitting

diodes, lens coupler and other optoelectronic devices [1-4]. Recent progress in the graded refractive

index (GRIN) thin film technology has led to encouraging achievement to approximate the desired

2

refractive index such as the use of composite films [5], nanostructured arrays such as nanorods or

nanocylinders [6-8] and dual-layer ultrathin films [9, 10].

Out of all the aforementioned approaches, the most straightforward method to achieve the

desired refractive index is the use of dual-layer ultrathin film of high (nH) and low index (nL)

materials. According to the Herpin equivalent method [11], this ultrathin alternate layer structure can

exhibit a similar spectral response to that of a single optical thickness of λ/4 coating layer when the

thickness of each layer is much smaller than the wavelength of interest. By simply changing the

relative thickness of these index layers, any desired refractive index in between (nL<n<nH) can be

obtained [12]. At present, theoretical studies employing effective medium theory [13, 14] have

suggested that dual-layer ultrathin film can approximate an effective birefringent material with the

effective refractive index dependent on the volume fraction of the nH material but without revealing

the influence of thickness of dual-layer thin films, the incidence angle and desired refractive index of

the birefringent film on the approximation. In our companion theoretical work, we further derive the

detailed formulations of using dual-layer ultrathin films to approximate a single thin film layer for s-

polarized and p-polarized light under arbitrary incidence angle. A comprehensive analysis of the

effect of film thickness and the incidence angle for both s-polarized light and p-polarized light on the

equivalence approximation is also given [15]. Unlike any other work, in this paper, we conduct the

experimental study of dual-layer ultrathin film optics. As both TiO2 and Al2O3 materials are finding

an increasing use in the nanophotonic devices due to their good thermal and mechanical stability, the

dual-layer ultrathin films based on TiO2 and Al2O3 deposited by ion beam deposition (IBD) are thus

chosen in this work to approximate a single-layer birefringent film.

IBD is a thin film deposition technique that combines the concurrent use of a low energy

assisted ion beam source with the physical sputtering of material targets by a primary ion beam source

in order to improve the properties of the deposited coating. Such difference from other ultrathin film

deposition techniques such as chemical vapour deposition and atomic layer deposition permits control

over film adhesion, intrinsic stress of the film and morphology. Applying such ion-assisted beam

processes thus offers the ability to grow very dense, high quality and stable films with minimum

3

moisture absorption. Characterization tools such as ellipsometry and spectrophotometry are used to

extract the effective refractive index of the ultrathin discrete bilayers with its equivalent birefringent

thin film. The measured results show a good agreement with the simulated results of the equivalent

birefringent thin film.

Building from the dual-layer thin films’ concept, we further demonstrate a design example of

a simple three-layer TiO2/Al2O3/TiO2 ultrathin film to approximate a single layer for silicon (Si)

antireflection coating. The flexibility in designing the dual-layer ultrathin film stack is demonstrated.

Our work requires only three layers while retaining an excellent agreement indicated by both the

theoretical and experimental results, instead of using 60 layers of Al2O3 and TiO2 films by atomic

layer deposition (ALD) for Si AR coating [16, 17]. The present experimental work can be further

extended to a functional GRIN thin-film stack such as broadband omnidirectional antireflection

coating, wavelength bandpass filter and integrated GRIN lens for the light coupling into a

nanowaveguide.

2. Ultrathin TiO2/Al2O3 layers: Experimental details

The growth of TiO2/Al2O3 ultrathin films is carried out using IBD (Oxford Instrument

Optofab3000) at room temperature with low background pressure of ~6 x 10-6

Torr. This two-material

thin film stack deposition is achieved by rotating and sputtering at the respective 4” dielectric target

materials of TiO2 and Al2O3 installed in the chamber. A mixture of argon and oxygen ions is used to

provide a stable assist which helps to densify the films at reduced substrate temperature. We prepared

five different sets of dual-layer ultrathin TiO2/Al2O3 films on Si substrate. The total thickness of the

dual-layer thin films is chosen to be 50 nm. The volume fractions of the TiO2 layer, 𝒇𝑯 =𝒉𝑯

𝒉𝑳+𝒉𝑯,

where hH and hL is the thickness of TiO2 and Al2O3 film, respectively, for these five sets samples are

0.18, 0.32, 0.5, 0.6 and 0.8.

4

2.1 Characterization by ellipsometer: Effective Refractive index of single equivalent anisotropic film

For the deposited films, a variable angle spectroscopic ellipsometer (VASE) is employed to

give the refractive index with dispersion over the wavelength range and thickness. Ellipsometry is

known to measure the change in polarization of light reflected or transmitted from the surface of a

sample. The change in polarization is represented by both an amplitude ratio, Ψ, and phase difference,

∆. These values are related to the ratio of Fresnel reflection coefficient Rp and Rs for p-polarized and

s-polarized light, respectively and are written as 𝑅𝑝

𝑅𝑠= tan(𝜓) 𝑒𝑖∆. Hence the spectral acquisition

range and the variable angles of incidence in the VASE can be optimized for the determination of

layer thickness or the optical constants of the film. Each single TiO2 layer film and Al2O3 layer film

and the dual-layer thin film are first characterized using the isotropic Cauchy model. The dual-layer

thin film is then characterized incorporating the anisotropic Bruggeman effective medium

approximation (EMA) model which treat both layers as an optical continuum to fit the measured (Ψ,

∆) curves [18]. We note that this model is valid for only ultrathin films (one tenth of the optical

wavelength). The model mixes the isotropic optical constants of the measured single layer TiO2 and

Al2O3 and the void volume fractions in the anisotropic EMA model are assumed from the varying

thickness of the two-layer TiO2 and Al2O3.

We use one of the film sets with a volume fraction fH=0.18 where the thickness of TiO2 film

is 9 nm and Al2O3 film is 41 nm as an example. Figure 1(a) and figure 1(b) compared the fitting

results of Ψ and ∆ parameters from the anisotropic Bruggeman EMA model against the measured

homogeneous dual-layer films at three incident angles, 65, 70 and 75o. The results indicate a

reasonable quality fit indicating for both the isotropic dual-layer model and single equivalent

anisotropic film model. The mean squared error (MSE) which is used to quantify the difference

between these curves is ~25. Figure 2 shows the resultant nxx and nyy and nzz of the single birefringent

anisotropic film and the refractive index of the dual-layer TiO2/Al2O3 film. The single anisotropic film

has a refractive index in between the refractive index of single TiO2 film and single Al2O3 film.

5

(a)

(b)

Figure 1. The comparison of the ellipsometric parameter (a) Ψ and (b) ∆ of the anisotropic

Bruggeman EMA with the dual-layer model for 9nm TiO2/ 41nm Al2O3 two- layer film at three

incident angles, 65, 70 and 75o.

400 600 800 1000 1200 1400 160010

15

20

25

30

35

40

45

50

(

deg

rees)

Wavelength (nm)

Anisotropic model 65o



Dual layer model 65o



400 600 800 1000 1200 1400 160050

60

70

80

90

100

110

120

130

140

150

160

Wavelength (nm)

(

deg

rees)







6

Figure 2. Plot of the resultant nxx and nyy and nzz of the single birefringent anisotropic film and the

refractive index of the dual-layer TiO2/Al2O3 film.

Figure 3. Plot of the corresponding effective nxx and nyy and nzz calculated and measured at 1000 nm

wavelength against the volume fraction fH.

400 600 800 1000 1200 1400 1600

1.6

1.7

1.8

2.24

2.26

2.28

nzz

nxx

=nyy

nAl2O3

nTiO2

nAl2O3

nTiO2

Refr

acti

ve in

dex

Wavelength (nm)

0.0 0.2 0.4 0.6 0.8 1.01.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

E

ffecti

ve in

dex, n

zz

Eff

ecti

ve in

dex, n

xx=

nyy

Volume fraction, fH

Calculated nxx

, nyy

Measured nxx

, nyy

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

Calculated nzz

Measured nzz

nxx

nyy nzz

7

2.2 Characterization by spectrophotometer: Comparison of dual-layer structure and birefringent film

For the TiO2/Al2O3 dual-layer thin films, Figure 3 gives the corresponding effective nxx and

nyy and nzz calculated and measured at 1000 nm wavelength against the volume fraction fH (different

thickness of TiO2 film) where 𝑛𝑥𝑥 = 𝑛𝑦𝑦 = √𝑛𝐻2 ℎ𝐻+𝑛𝐿

2ℎ𝐿

ℎ𝐻+ℎ𝐿 and

1

𝑛𝑧𝑧= √

1

𝑛𝐻2 ℎ𝐻+

1

𝑛𝐿2ℎ𝐿

ℎ𝐻+ℎ𝐿, nH and nL is the

refractive index of TiO2 and Al2O3, respectively. The circle and triangle marks are the respective

ordinary and extraordinary refractive index measured via the spectroscopic ellipsometer. Open circles

represent the measured results in nxx=nyy direction whereas the closed triangles represent the measured

results in nzz direction. The MSE for these five film sets is ~25, 38, 47, 43 and 29. The measured data

show a good agreement with the theoretical calculation. The measured results agree well with the

calculated results except for the sample with fH = 0.8 (40 nm TiO2/ 10 nm Al2O3). This may be

contributed by the high porosity of the 10 nm deposited layer Al2O3 which has a measured low

refractive index of ~1.53 since thicker Al2O3 layer exhibits higher refractive index of ~1.64. This

“effective” birefringence is an inherent property of dual-layer ultrathin film stack. Therefore, in our

numerical calculation and design of dual-layer ultrathin film based devices, we take account of this

“effective” birefringence using the equivalent anisotropic thin film modal for the accuracy of the

design. The comparison between the isotropic and anisotropic equivalent thin-film models shows that

there is some difference in terms of the device’s performance but it is not significant due to the

orientation of extraordinary axis. However, when using this dual layer ultrathin film stack as graded

refractive indexes lens for nanowaveguide collimating as proposed recently, this birefringent property

introduces different focusing length between the s-polarized and p-polarized light [19].

Following the refractive index characterization of these dual-layer thin films, we seek to study

the reflectance results. The reflectance measurement is conducted and compared with the numerical

simulations based on the real dual-layer thin films structure and equivalent birefringent film. A UV-

VIS-NIR spectrophotometer (UV-3600) with the integrating sphere compartment (MPC-3100) is used

to carry out the reflectance measurement. The spectrophotometer is equipped with three detectors

such as a PMT (photomultiplier tube), InGaAs (indium gallium arsenide), and PbS (lead sulfide)

8

detector which ensures high sensitivity across the entire measured wavelength range from 240 to 2600

nm. In addition, the compartment can accommodate large samples and allows the installation of

absolute specular reflectance attachment of 5 and 45 degrees. Using the TiO2/Al2O3 set with a volume

fraction of fH=0.18 where the thickness of TiO2 film is 9 nm and Al2O3 film is 41 nm as an example,

figure 4 compared the measured and simulated reflectance spectra with a reflection angle of 5.

Except for the bumps at around 720 and 850 nm which are due to the wavelength grating switch

during the reflectance analysis, the experimental results agreed well with the calculated results based

on the original dual-layer thin films (the dashed line). However the simulation results based on the

usual one effective birefringent layer vary away from the two layers and it is more severe at the short

wavelength end. As pointed out in our theoretical paper, the thickness of the dual-layer film is

required to be less than 1/10 wavelength in the media in order for a good agreement between the

equivalent birefringent film and dual-layer thin film. However, the ellipsometer measurement above

still gives a good approximation. This is because the ellipsometer measurement used a much larger

incident angles (65 to 75o) than the presented spectrophotometer results in this section and it was

pointed out in our theoretical paper, that a large incidence angle has a better tolerance to the thin film

thickness as compared to the case of small incidence angle.

400 500 600 700 800 900 1000 1100 0

0.1

0.2

0.3

0.4

0.5

0.6

Wavelength (nm)

Ref

lect

ance

Measured data

Calculated results based on TiO2/Al2O3

Calculated results based on single birefringent

film

9

Figure 4. Comparison of the measured and simulated reflectance spectra of dual-layer film with a

reflection angle of 5.

Figure 5. Division of a single Al2O3 layer to two thinner layers to form a top birefringent TiO2/Al2O3

layer.

Figure 6. Comparison of the measured and simulated reflectance spectra of the hybrid thin film with a

reflection angle of 5.

Al2O3

TiO2 Single birefringent layer

TiO2

Al2O3

Al2O3

Top birefringent layer

400 500 600 700 800 900 1000 1100

0.1

0.2

0.3

0.4

0.5

0.6

Wavelength (nm)

Ref

lect

ance

Measured data

Calculated results based on TiO2/Al2O3

Calculated results based on top birefringent

film/Al2O3

10

To improve the approximation accuracy, we sub-divide the Al2O3 layer into two layers

artificially as shown in figure 5. The top Al2O3 layer is combined with the TiO2 layer to form the dual-

layer ultrathin films and the bottom Al2O3 layer is retained. Therefore, the original dual-layer thin

films now turns into a ultrathin isotropic Al2O3 layer with a birefringent layer on top and the

birefringent layer has a corresponding nxx = nyy and nzz of 1.76 and 1.69 respectively. For such hybrid

thin films, the reflectance for this new approximated thin film layers is shown in figure 6. As

compared to the results of single equivalent birefringent layer, this design of thin films gives a

significant better agreement with the experimental data. This also implies that we can apply such

hybrid thin-film stack, i.e., a combination of ultra-thin films based birefringent films with the

isotropic thin film structure in practical coating applications as shown in the next paragraph.

3. Demonstration of TiO2/Al2O3 ultrathin films as one single layer antireflection coating

Here, using the above concept of the hybrid dual-layer TiO2 and Al2O3 ultrathin films, we

demonstrate the use of such thin films to experimentally approximate a single antireflection coating

for Si. This choice is made only for simplicity and is not limited to any applications. In Reference

[16], the authors demonstrated using 60 layers of Al2O3 and TiO2 films by ALD for Si AR coating.

However for comparison, our dual-layer AR coating presented in this paper only requires three layers

as shown below while retaining an excellent agreement with the desired single layer.

11

Figure 7. Design of the dual-layer ultrathin film stack for AR coating.

Figure 7 illustrates the design procedure starting from (a) to (d). Figure 7(a) is the original

single layer antireflection film. Using the refractive index of silicon at 500 nm measured as design

example, the corresponding refractive index and thickness of the single-layer antireflection film are

2.072 and 60.32 nm. According to the above example, the individual thickness of the film will be

quite thick if we use just a single pair of TiO2 and Al2O3 films directly to approximate the

antireflection film. Therefore, in our design, we first split the antireflection layer film into two thinner

layers and thickness of each layer is now 30.16 nm (dashed box in figure 7(a)). Next, two pairs of

TiO2/Al2O3 films is used to approximate them as shown in figure 7(b) and the thickness of the TiO2

and Al2O3 is 16.9 nm and 13.25 nm, respectively.

A useful property for such dual-layer ultrathin films is that its performance is independence of

the sequence of the two thin films. Hence it is possible to switch the sequence of the bottom

TiO2/Al2O3 films from figure 7(b) to figure 7(c) and the two Al2O3 thin films can be simply merged

into one single thicker layer as shown in figure 7(d). Based on this new design, a three layer of thin

TiO2/ thicker Al2O3/ thin TiO2 is formed to approximate the single antireflection layer and the

thickness of the three layers is 16.9 nm, 26.7 nm and 16.9 nm, respectively. This three layer sequence

has lesser number of steps in the fabrication process. In the fabrication process, the first layer of TiO2

thin film is deposited on the Si substrate using IBD with 850 W of RF power to the 4 inch TiO2 target

TiO2

Al2O3

Al2O3

Single layer AR coating with

thickness of ~60 nm

TiO2

Al2O3

TiO2

Al2O3

(a) (b)

(c) (d)

TiO2 Al2O3

12

at 1.5 SCCM (standard cubic centimetre per minute) of Ar gas and 0.9 SCCM of O2 gas for ~7

minutes. The second layer of Al2O3 is also deposited using 880 W of RF power to the 4 inch Al2O3

target at 3 SCCM of Ar gas and with 0.2 SCCM of O2 flowing into the chamber for ~8 minutes. The

growth process is then completed with the final deposition of TiO2 layer for 7 minutes.

Optical measurement is then carried for three cases: 1) light with incidence angle of 5o (no

obvious difference between s-polarized and p-polarized light at this small angle); 2) s-polarized light

with an incidence angle of 45o and 3) p-polarized light under an incidence angle of 45

o. The measured

reflectance from bare silicon substrate is also presented in each figure. To have a comparison between

the experimental data and theoretical design, the calculated reflectance from the single antireflection

layer and TiO2/Al2O3/TiO2 three-layer thin film stack for these three cases are presented. The

corresponding results for these three cases are given in figure 8(a), figure 8(b) and figure 8(c),

respectively. The considered wavelength range is from 400 nm to 1100 nm. First, the results of the

three cases show the significant reflection reduction as compared to bare Si due to the effect of the

TiO2/Al2O3/TiO2 film stack and also the calculation has a very good agreement with the measured

data, which means the designed TiO2/Al2O3/TiO2 has a very good approximation to the single-layer

thin film for either s-polarized or p-polarized light under various incidence angles. Hence our current

work requires only three layers to approximate a Si AR coating while retaining an excellent

agreement indicated by both the theoretical and experimental results.

13

(a)

(b)

400 500 600 700 800 900 100 1100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ref

lect

ance

Wavelength (nm)

Measured reflectance from silicon substrate

Measured reflectance from TiO2/Al

2O

3/TiO

2 stack

Calculated reflectance from TiO2/Al

2O

3/TiO

2 stack

Calculated reflectance from the single AR layer

Incidence light angle 5

400 500 600 700 800 900 1000 1100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ref

lect

ance

Wavelength (nm)



2O

3/TiO

2 stack


2O

3/TiO

2 stack


S-polarized incidence light angle 45

14

(c)

Figure 8. Measured and simulated reflectance spectra of TiO2/Al2O3/TiO2 stack at (a) s-polarized

light with incident angle of 5o (b) s-polarized light with incidence angle of 45

o (c) p-polarized light

with incidence angle of 45o.

4. Conclusion

We have demonstrated the use of dual-layer ultrathin films with a high refractive index nH and low

refractive index nL to approximate a single-layer thin film. With IBD deposition, a set of ultrathin

films of TiO2 and Al2O3 have been deposited on Si with different volume fractions and characterized

by spectroscopic ellipsometer for the ordinary/extraordinary refractive index and by

spectrophotometer for the reflectance, respectively. The measured results have shown a good

agreement between the experiments and simulation of the equivalent birefringent thin film by

designing the sequence of TiO2 and Al2O3 layers. As an application example, our design and

experimental demonstration of using TiO2 and Al2O3 to approximate a single-layer antireflection for

silicon agrees very well with the theoretical simulations. This experimental study of the dual-layer

ultrathin films is useful for the development of graded-refractive index thin film stack based devices.

400 500 600 700 800 900 1000 1100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ref

lect

ance

Wavelength (nm)



2O

3/ TiO

2 stack


2O

3/TiO

2 stack


P-polarized incidence light angle 45

15

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Dual layer ultrathin film optics II: experimental studies