**2. Experimental procedure**

140 Advances in Unconventional Lithography

Recently, the emitting efficiency of light emitting diodes (LEDs) has improved; thus, they are used in lighting devices. To this end, miniaturizing the LEDs for smaller lighting devices and controlling the luminosity of LEDs are required. The conventional oval lamp-type LEDs cannot realize these requirements because the lens height of such LEDs is approximately 5 mm and its distribution of luminosity is determined by its shape. In this study, instead of the oval lamp-type lens, we used the diffractive lens on the optical films, as shown in Fig. 1. If the diffractive lens with short focal length (order of micrometer) can be fabricated, miniaturization of the lens system and consequently the LED lighting devices can be achieved. In order to realize the refractive lenses with the short focal length, large curvature radius is needed, thus making it difficult to realize it easily. Therefore, the diffractive lenses are suitable for realizing the short focal length lenses. Furthermore, by modifying the structure of the diffractive lens, it is easy to control the luminosity of the LEDs and the farfield pattern. Therefore, in this study, we focused on the diffractive lens because it enabled us to reduce the thickness of the lens, control the luminosity distribution of LEDs, and

facilitate the realization of the binary structure.

Yamada et al., 2004).

Fig. 1. Schematic representation of diffractive lens on the optical film

achromatized diffractive lenses were reported (Kleemann et al., 2008).

The zone plate was the first diffractive lens invented by I. L. Solet in 1875. To improve light efficiency, kinoform was invented by J. A. Jordan (Jordan et al., 1970). Recently, binary optics technology was developed using CAD design and VLSI technology (Swason and Veldkamp, 1989). The diffractive optical elements with multi-level grating having step-like cross-section have been developed. By controlling thestructure of the multi-level gratings, an optical effect almost same as that of the kinoform can be obtained (Orihara et al., 2001 &

On the other hand, subwavelength structures (SWSs), which are equivalent to a blazed structure, were suggested by P. Lalanne (Lalanne et al., 1999 & Mait et al., 1999). These structures are fabricated binary SWSs converted from Fresnel lenses. These structures are fabricated easily than those of the multi-level gratings because they can be fabricated by electron beam lithography (EBL) or nanoimprint lithography (NIL). Furthermore, in the case of photolithography, combining some masks is not necessary. By using these structures,

We aim to realize a highly effective short focal length diffractive lens using the binary diffractive lens fabricated by EBL, and expect the equivalent effect with the diffractive lens of the saw-like structure. NIL or photolithography can easily fabricate these structures at In this section, the methods of design, fabrication, and characterization of the binary diffractive lens are described.

#### **2.1 Basic optical characteristics of materials related to binary diffractive lens**

The binary diffractive lenses, on which this study is focused, were fabricated on the poly(ethylene terephthalate) (PET) films. The PET films are often used as optical sheets for liquid crystal displays. There are many types of optical films such as polycarbonate (PC) and poly(methyl methacrylate) (PMMA). In this study, the EBL process was used for fabricating the binary diffractive lenses; this process required the optical films to endure high temperature and chemicals, making them more suitable than PC or PMMA.

In this study, the binary diffractive lens was fabricated by developing the resist for EBL (ZEP-520A, ZEON Co.) on the PET films (Teijin® Tetoron® Film, Teijin DuPont Films, Japan). If the refractive indexes of both materials are almost same, the binary diffractive lens can be fabricated by developing the resist instead of etching the PET films. Therefore, the refractive indexes of the PET films and the resist are evaluated by ellipsometry (M-2000DI, J.A. Woollam Co., Inc.). Fig. 2 shows the wavelength dispersion of the PET film and the resist on the PET film, including the data from the catalog of ZEP-520A. D2 and halogen lamps were used for this measurement. The refractive index of the PET film is relatively

Fig. 2. Wavelength dispersion of the PET film and the resist on the PET film, including the data from the catalog of ZEP-520A

Fabrication of Binary Diffractive Lens on Optical Films by Electron Beam Lithography 143

*hmax*

N=1

N=2

N=4

Fig. 4. Structure of the binary diffractive lens, (a) the conversion of the step-like structure to

The 125-μm-thick PET films were used as the substrate. Fig. 5 shows the procedure for the fabrication of the binary diffractive lens on the optical films by EBL. Before spin coating the EB resist, hexamethyldisilazane (HDMS) was spin coated on the surface of the PET film to improve the adherence between the PET film and the EB resist (Fig. 5 (a)). The surface was spin coated with an EB positive resist followed by pre-baking (Fig. 5 (b)). Then, the charge-

The EBL system (Crestec CABL-8000) was equipped with a ZrO/W thermal field emission cathode. The acceleration voltage was 30 kV; the electrons accelerated by this voltage were able to penetrate the resist (Fig. 5 (d)). After exposure, the resist was developed and the binary diffractive lens could be obtained from these procedures (Fig. 5 (e)). The size of the

The optimum results obtained using the diffractive lenses fabricated by EBL, such as period, width, and height of the fabricated binary diffractive lenses, are useful for fabricating the

the binary structure, (b) the examples of the structures, (c) the complete structure

patterns for the binary diffractive lens ranged from 100 × 100 μm2 to 2 × 2 mm2.

**2.3 Fabrication of binary diffractive lens on optical films by EBL** 

up prevention was spin coated on the EB resist (Fig. 5 (c)).

molds of the thermal-type nanoimprint.

Step-like structure

Binary structure

Duty ratio *ti* = 1 − *h <sup>i</sup>*( *x <sup>i</sup>*) / *h* max

2 levels (n=2) <sup>d</sup> <sup>d</sup>

g *hmax*

hi (xi )

4 levels (n=4)

(b)

(c)

(a)

6 levels (n=6)

g

higher than that of the resist; however, in the visible region, their refractive indexes are between 1.58 and 1.60. Thus, in this study, these values are considered to be almost same. Furthermore, by using ellipsometry, the thickness of the resist is estimated using the multilayer model. Fig. 3 shows the relationship between the thickness of the resist and the number of rotations of the spin coater. The thickness of the resist varies from 760 to 460 nm and increases with the number of rotations. Thus, in this study, the binary diffractive lens structures of the electron beam (EB) resist were fabricated by developing an EB resist on the PET films. The development of the EB resist can be regarded as processing the surface of a PET film. The thickness of the resist is equivalent to the height of the binary diffractive lens.

Fig. 3. Relationship between the thickness of the resist and the number of rotations of the spin coater

## **2.2 Design of diffractive lens**

The fabricated binary diffractive lens was based on the micro-Fresnel lens. In this study, a part of two-level zone plates with a pattern of lines and spaces was fabricated. Radius of the mth zone rm is

$$\mathbf{r}\_{\rm m} = 2\mathbf{m}\mathbf{f}\lambda + (\mathbf{m}\lambda)^2,\tag{1}$$

where f is the focal length of the designed lens and λ is the dominant wavelength. Equation 1 is based on the imaging theory of the diffractive lens (Buralli et al., 1989).

Then, mth period of this lens dm is determined by rm − rm−1. In period dm, the blazed structure is approximated to a step-like structure with n steps and then the step-like structures is converted to the relief structures by duty ratio of height *t*i = 1 – *h*(*x*i)/*h*max in each interval *g*, as shown in Fig. 4 (a). In the interval, the width of the air part is given by *g*\**t*i. In the binary diffractive lens, *N* is the number of the relief structures in a period. Examples of the structures are shown in Fig. 4 (b) and the complete structure of this lens is shown in Fig. 4 (c).

higher than that of the resist; however, in the visible region, their refractive indexes are between 1.58 and 1.60. Thus, in this study, these values are considered to be almost same. Furthermore, by using ellipsometry, the thickness of the resist is estimated using the multilayer model. Fig. 3 shows the relationship between the thickness of the resist and the number of rotations of the spin coater. The thickness of the resist varies from 760 to 460 nm and increases with the number of rotations. Thus, in this study, the binary diffractive lens structures of the electron beam (EB) resist were fabricated by developing an EB resist on the PET films. The development of the EB resist can be regarded as processing the surface of a PET film. The thickness of the resist is equivalent to the height of the binary

1000 1500 2000 2500 3000

The number of rotations (rpm)

Fig. 3. Relationship between the thickness of the resist and the number of rotations of the

The fabricated binary diffractive lens was based on the micro-Fresnel lens. In this study, a part of two-level zone plates with a pattern of lines and spaces was fabricated. Radius of the

 rm = 2mfλ + (mλ)2, (1) where f is the focal length of the designed lens and λ is the dominant wavelength. Equation

Then, mth period of this lens dm is determined by rm − rm−1. In period dm, the blazed structure is approximated to a step-like structure with n steps and then the step-like structures is converted to the relief structures by duty ratio of height *t*i = 1 – *h*(*x*i)/*h*max in each interval *g*, as shown in Fig. 4 (a). In the interval, the width of the air part is given by *g*\**t*i. In the binary diffractive lens, *N* is the number of the relief structures in a period. Examples of the structures are shown in Fig. 4 (b) and the complete structure of this lens is

1 is based on the imaging theory of the diffractive lens (Buralli et al., 1989).

diffractive lens.

spin coater

mth zone rm is

shown in Fig. 4 (c).

450

**2.2 Design of diffractive lens** 

500

550

600

The thickness of the resist (nm)

650

700

750

800

Fig. 4. Structure of the binary diffractive lens, (a) the conversion of the step-like structure to the binary structure, (b) the examples of the structures, (c) the complete structure

## **2.3 Fabrication of binary diffractive lens on optical films by EBL**

The 125-μm-thick PET films were used as the substrate. Fig. 5 shows the procedure for the fabrication of the binary diffractive lens on the optical films by EBL. Before spin coating the EB resist, hexamethyldisilazane (HDMS) was spin coated on the surface of the PET film to improve the adherence between the PET film and the EB resist (Fig. 5 (a)). The surface was spin coated with an EB positive resist followed by pre-baking (Fig. 5 (b)). Then, the chargeup prevention was spin coated on the EB resist (Fig. 5 (c)).

The EBL system (Crestec CABL-8000) was equipped with a ZrO/W thermal field emission cathode. The acceleration voltage was 30 kV; the electrons accelerated by this voltage were able to penetrate the resist (Fig. 5 (d)). After exposure, the resist was developed and the binary diffractive lens could be obtained from these procedures (Fig. 5 (e)). The size of the patterns for the binary diffractive lens ranged from 100 × 100 μm2 to 2 × 2 mm2.

The optimum results obtained using the diffractive lenses fabricated by EBL, such as period, width, and height of the fabricated binary diffractive lenses, are useful for fabricating the molds of the thermal-type nanoimprint.

Fabrication of Binary Diffractive Lens on Optical Films by Electron Beam Lithography 145

fabricated binary diffractive lens. From these results, it is clear that the luminous intensity

Fig. 6. SEM image of the fabricated binary diffractive convex lens with 2-mm focal length on

Spectral Irradiance (μW/m2

)

50 μm

(b)


With binary diffractive lens

lens

Without binary diffractive

Angle (deg.)

distribution can be controlled using this type of lens.

the PET film.

300



330


lens (a)

0

270 90

30

With binary diffractive lens

30o

60

**3.2 Binary diffractive convex lens with 150-**μ**m focal length** 

designed the binary diffractive convex lens with 150-μm focal length.

60o

Without binary diffractive

90o

Fig.7 Ddistribution of the irradiance. (a) Angle dependence of normalized spectral irradiance. (b) Angle dependence of the absolute value of spectral irradiance

Although the binary diffractive lens was effective in controlling the luminous intensity, diffraction efficiency was reduced when the diffraction angle was decreased (Lalanne et al., 1999; Kleemann et al., 2008). Furthermore, the focal length of the fabricated binary diffractive lens is 2 mm. In order to realize a thin LED light source, the focal length has to be shorter. In this section, to improve the diffraction efficiency and shorten the focal length, we

In this study, a binary diffractive lens with a focal length of approximately 150 μm was designed and light propagation of the plane wave was simulated by the finite domain time difference (FDTD) method. Fig. 8 shows the field intensity distributions for TE polarization of the binary diffractive lens. The simulation parameters were λ = 632 nm, n = 1.575 (refractive index of the PET film), and n0 = 1.0 (refractive index of air). The value of the period in part of the fringe was smaller than that in the center. The designed lens was placed along the x-axis (z = 0). The light was incident from z = 0 to the +z direction, resulting in the light being focused at x = 0 μm and z = 140 μm. After focusing, the light was spread with

Fig. 5. Procedure for the fabrication of the binary diffractive lens on optical films by EBL, (a) spin coating HMDS, (b) spin coating EB resist and pre-baking, (c) spin coating charge-up prevention, (d) exposing e− beam, (e) developing the resist and obtaining the binary diffractive lens
