**2. SR lithography**

This section outlines the LIGA process, the fabrication mechanism of SR lithography, and optimum experimental conditions. To achieve high-accuracy microfabrication, optimum exposure and development conditions were determined using both experimental and theoretical values. Energy distribution, etching rate, control of processing depth, and microloading effects are described.

#### **2.1 LIGA process**

The LIGA process fabricates microstructures as components of MEMS (Figure 1). As shown in Figure 1, resist materials are first exposed using a soft X-ray source from an SR light through the mask, and the exposed resists are then developed. The exposure and development processes are discussed in more detail in Sections 2.2 and 2.3. Next, metallic moulds, such as Ni, are fabricated using an electroforming technique. Resist is then removed from the metallic moulds. In this process, it is possible to remove the resist under pressure as well as dissolve the resist using wet etching. Finally, microstructures of various materials are fabricated by moulding. The LIGA process can be applied to a wide range of materials, including plastics, metal, and ceramics, when the electroforming technique and moulding process are utilized.

This technology was developed in the 1980s by a group of researchers led by Becker and Ehrfeld of the Kernforschungszentrum Karlsruhe (KfK). LIGA is a German acronym consisting of the initial letters of three processes: lithographie (lithography), galvanoformung (electroforming), and abformung (moulding).

Fig. 1. Process flow of the LIGA process; (A) SR lithography; (B) electroforming; (C) removal resist; and (D) moulding

Next, we describe the characteristics of the LIGA process. Because SR light is highly directional, it is possible to fabricate a structure with a thickness of several hundred to one thousand micrometers. Moreover, because SR light contains X-ray (short wavelength) regions, it is possible to transfer patterns that are ≤ 1 m (diffraction during exposure does not occur readily). Therefore, SR lithography has been used as a fabrication technology for high-aspect-ratio microstructures. Fabrication of Ni structures with a line width of 2 m and an aspect ratio of 100 or a line width of 0.2 m and an aspect ratio of 75 have been reported (Kato et al., 2007; Kondo et al., 2000; Ueno et al., 2000). Although it is also possible to transfer patterns that are ≤ 1 m using electron beam lithography, it has the disadvantage of a long exposure time. On the other hand, because the production of large volumes is possible using electroforming and moulding in the LIGA process, it is a superior technology in terms of time and cost.

#### **2.2 Exposure**

316 Recent Advances in Nanofabrication Techniques and Applications

expectations regarding its application in various devices. PTFE fabrication by SR ablation is

This section outlines the LIGA process, the fabrication mechanism of SR lithography, and optimum experimental conditions. To achieve high-accuracy microfabrication, optimum exposure and development conditions were determined using both experimental and theoretical values. Energy distribution, etching rate, control of processing depth, and micro-

The LIGA process fabricates microstructures as components of MEMS (Figure 1). As shown in Figure 1, resist materials are first exposed using a soft X-ray source from an SR light through the mask, and the exposed resists are then developed. The exposure and development processes are discussed in more detail in Sections 2.2 and 2.3. Next, metallic moulds, such as Ni, are fabricated using an electroforming technique. Resist is then removed from the metallic moulds. In this process, it is possible to remove the resist under pressure as well as dissolve the resist using wet etching. Finally, microstructures of various materials are fabricated by moulding. The LIGA process can be applied to a wide range of materials, including plastics, metal, and ceramics, when the electroforming technique and moulding

This technology was developed in the 1980s by a group of researchers led by Becker and Ehrfeld of the Kernforschungszentrum Karlsruhe (KfK). LIGA is a German acronym consisting of the initial letters of three processes: lithographie (lithography),

Fig. 1. Process flow of the LIGA process; (A) SR lithography; (B) electroforming; (C) removal

Next, we describe the characteristics of the LIGA process. Because SR light is highly directional, it is possible to fabricate a structure with a thickness of several hundred to one thousand micrometers. Moreover, because SR light contains X-ray (short wavelength)

galvanoformung (electroforming), and abformung (moulding).

discussed in detail in Chapter 4.

loading effects are described.

**2. SR lithography** 

**2.1 LIGA process** 

process are utilized.

resist; and (D) moulding

#### **2.2.1 Light source**

In SR lithography, the use of ultra-bright and highly directional SR light sources provides perfect conditions for fabricating structures with the required thickness. Although SR light is spectrally continuous and includes a wide wavelength range, wavelengths of 0.2 to 0.5 nm are most suitable for SR lithography because they reduce the spread of light by Fresnel diffraction in the long-wavelength domain and the generation of secondary electrons inside resists in the short-wavelength domain, enhancing resolution.

Experiments described in this article utilized the superconductivity compact SR source "AURORA" at the SR Centre of Ritsumeikan University in Japan (Figure 2). The properties of SR at AURORA include a wavelength range from 0.15 nm to visible light and an applied electron energy and maximum storage current of 575 MeV and 300 mA, respectively. This light source was adapted for our studies; there are 16 beam lines, 4 of which are used in SR lithography. The light from AURORA penetrates two 200-m beryllium (Be) windows and, within the exposure chamber, uses light with a 0.15- to 0.95-nm wavelength domain. The outline of the beam line is shown in Figure 3. For beam line number 13 (Bl-13), the distance from the light source to the sample is 3.388 m. The exposure environment in the chamber was helium (He) gas at 1 atm to prevent the attenuation of X-rays by N2 or O2 gases and to prevent damage to the mask or resist by heat generated during exposure. Figure 4 shows the wavelength and photon density after penetration of the two 200-m Be windows; the peak wavelength was 0.37 nm.

Fig. 2. Superconductivity compact SR source "AURORA" at the SR Centre of Ritsumeikan University in Japan

Fabrication of 3-D Structures Utilizing Synchrotron Radiation Lithography 319

processing accuracy, and (4) the ability to fabricate high-aspect-ratio structures. To meet these requirements, heavy metals such as Au, Cu, W, and Ta are typically used as X-ray absorber materials. In general, X-ray absorptance increases with increasing atomic number. Additionally, it is possible to fabricate Au or Cu using electroforming. Because the absorptance of Cu in the X-ray region is lower than that of Au, a Cu absorber must be thicker and have a higher aspect ratio to achieve the same contrast. Therefore, fabrication of

Experiments described in this article utilized an X-ray mask consisting of a polyimide membrane with a thickness of 50 m and an Au absorber with a thickness of 3 m. The Xray mask was from Optnics Precision Co., Ltd. The linear expansion coefficient of polyimide is very low compared with other organic compounds and is close to that of metals; therefore, thermal expansion produces low strain when polyimide combines with a metal

Cu is difficult. On the other hand, it is possible to pattern W or Ta using RIE.

(A) (B)

which exposed areas are not dissolved after development.

polymethylmethacrylate (PMMA) is typically used as the X-ray resist.

Fig. 5. X-ray mask; (A) typical structure of an X-ray mask; and (B) the mask contrast indicates the ratio of energy through the "membrane only" to energy through the

When some types of polymer materials are exposed to light, the exposed areas undergo a photochemical reaction, and molecular structures are changed. There are three primary types of photochemical reactions: cross-linking, polarity change, and main-chain breaking. It is possible to design a wide variety of resist materials using these various reaction mechanisms. Additionally, there are two major classes of resist materials: positive resists, in which non-exposed areas are not dissolved after development, and negative resists, in

In general, polymer materials that have high sensitivity and X-ray resolution are suitable as X-ray resists. Most polymer materials used as electron beam resists are not exposed to visible or ultraviolet (UV) light. Therefore, X-ray resists are often used as electron beam resists. Further requirements of X-ray resists include a lack of exposure to small amounts of X-rays through the absorber for fabricating high-aspect-ratio structures and high mechanical strength to endure prolonged exposure and electroforming. To meet these requirements,

absorber.

"membrane and absorber"

**2.2.3 Resist** 

Fig. 3. The outline of the beam line; since wavelengths of 0.2 to 0.5 nm are most suitable for SR lithography, the light from AURORA penetrates two 200-m Be windows and, within the exposure chamber, uses light with a 0.15- to 0.95-nm wavelength domain

Fig. 4. Relationship between wavelength and photon density after penetration of the two 200-m Be windows

#### **2.2.2 X-ray mask**

Masks used in SR lithography consist of an X-ray absorber, a high-permeability membrane that supports it, and a frame that forms the entire mask. Figure 5A shows the typical structure of an X-ray mask. It is necessary for an X-ray mask to have high contrast to fabricate structures with the required thickness (Singleton & Detemple, 2003; Suzuki & Sugiyama, 1997). As shown in Figure 5B, the mask contrast indicates the ratio of energy through the "membrane only" to energy through the "membrane and absorber."

The primary requirements of X-ray mask membranes include (1) high X-ray transmission, (2) moderate tensile stress, high Young's modulus and high mechanical strength, (3) strong X-ray exposure resistance, and (4) a low rate of thermal expansion. To meet these requirements, Ti, Be, Si3N4, SiC, and polyimide are typically used as membrane materials. Although Si3N4 and SiC are becoming mainstream, the production cost of X-ray masks based on these materials is high. Thus, polymer materials with low production costs, such as polyimide, are often used as membranes.

The primary requirements for X-ray absorbers of X-ray masks include (1) high X-ray absorptance, (2) a low rate of thermal expansion and no membrane strain, (3) high processing accuracy, and (4) the ability to fabricate high-aspect-ratio structures. To meet these requirements, heavy metals such as Au, Cu, W, and Ta are typically used as X-ray absorber materials. In general, X-ray absorptance increases with increasing atomic number. Additionally, it is possible to fabricate Au or Cu using electroforming. Because the absorptance of Cu in the X-ray region is lower than that of Au, a Cu absorber must be thicker and have a higher aspect ratio to achieve the same contrast. Therefore, fabrication of Cu is difficult. On the other hand, it is possible to pattern W or Ta using RIE.

Experiments described in this article utilized an X-ray mask consisting of a polyimide membrane with a thickness of 50 m and an Au absorber with a thickness of 3 m. The Xray mask was from Optnics Precision Co., Ltd. The linear expansion coefficient of polyimide is very low compared with other organic compounds and is close to that of metals; therefore, thermal expansion produces low strain when polyimide combines with a metal absorber.

Fig. 5. X-ray mask; (A) typical structure of an X-ray mask; and (B) the mask contrast indicates the ratio of energy through the "membrane only" to energy through the "membrane and absorber"

#### **2.2.3 Resist**

318 Recent Advances in Nanofabrication Techniques and Applications

Fig. 3. The outline of the beam line; since wavelengths of 0.2 to 0.5 nm are most suitable for SR lithography, the light from AURORA penetrates two 200-m Be windows and, within

Fig. 4. Relationship between wavelength and photon density after penetration of the two

Masks used in SR lithography consist of an X-ray absorber, a high-permeability membrane that supports it, and a frame that forms the entire mask. Figure 5A shows the typical structure of an X-ray mask. It is necessary for an X-ray mask to have high contrast to fabricate structures with the required thickness (Singleton & Detemple, 2003; Suzuki & Sugiyama, 1997). As shown in Figure 5B, the mask contrast indicates the ratio of energy

The primary requirements of X-ray mask membranes include (1) high X-ray transmission, (2) moderate tensile stress, high Young's modulus and high mechanical strength, (3) strong X-ray exposure resistance, and (4) a low rate of thermal expansion. To meet these requirements, Ti, Be, Si3N4, SiC, and polyimide are typically used as membrane materials. Although Si3N4 and SiC are becoming mainstream, the production cost of X-ray masks based on these materials is high. Thus, polymer materials with low production costs, such as

The primary requirements for X-ray absorbers of X-ray masks include (1) high X-ray absorptance, (2) a low rate of thermal expansion and no membrane strain, (3) high

through the "membrane only" to energy through the "membrane and absorber."

200-m Be windows

**2.2.2 X-ray mask** 

polyimide, are often used as membranes.

the exposure chamber, uses light with a 0.15- to 0.95-nm wavelength domain

When some types of polymer materials are exposed to light, the exposed areas undergo a photochemical reaction, and molecular structures are changed. There are three primary types of photochemical reactions: cross-linking, polarity change, and main-chain breaking. It is possible to design a wide variety of resist materials using these various reaction mechanisms. Additionally, there are two major classes of resist materials: positive resists, in which non-exposed areas are not dissolved after development, and negative resists, in which exposed areas are not dissolved after development.

In general, polymer materials that have high sensitivity and X-ray resolution are suitable as X-ray resists. Most polymer materials used as electron beam resists are not exposed to visible or ultraviolet (UV) light. Therefore, X-ray resists are often used as electron beam resists. Further requirements of X-ray resists include a lack of exposure to small amounts of X-rays through the absorber for fabricating high-aspect-ratio structures and high mechanical strength to endure prolonged exposure and electroforming. To meet these requirements, polymethylmethacrylate (PMMA) is typically used as the X-ray resist.

Fabrication of 3-D Structures Utilizing Synchrotron Radiation Lithography 321

Although the sensitivity of PMMA is low, its resolution is very high (50 Å), and reproducibility of fine structures for moulding can be enhanced by further processing. PMMA is a material in the acrylic plastic group that has a broad range of applications, including lenses, instrument windows, signboards, displays, etc. Among the aforementioned photochemical reactions, PMMA preferentially causes main-chain breaking. If main-chain breaking occurs, molecular mass decreases, and solubility in the developer increases. PMMA has a distinguished transparency and weatherability in many polymer materials. Additionally, because PMMA also has good formability, its mechanical properties are also good. Because PMMA is a malleable optical material, it is possible to use fabricated microstructures directly as optical devices. Experiments described in this article utilized PMMA sheets provided by Nitto Jushi Kogyo Co., Ltd. Figure 6 shows photodegradation reaction mechanisms (Schmal et al., 1996). Figure 6A shows main-chain breaking without side-chain cleavage, and Figure 6B shows main-chain breaking via side-chain cleavage.

This section describes absorbed energy in the PMMA resist after exposure. To achieve highly accurate microfabrication or 3-D fabrication, it is necessary to calculate the absorbed energy distribution in the resist. To calculate the absorbed energy in the vertical direction, the following factors must be considered: the photon density spectrum of SR light, attenuation by distance from the light source to the resist, divergence of light, and attenuation when light is transmitted through Be windows. If the spectrum of synchrotron

*<sup>R</sup> w M <sup>S</sup> P d dz P T T*

energy *I* integrates with the synchrotron orbital radiation spectrum in the wavelength range

*<sup>S</sup> I Pd* 

 0.95 0.15

The exposure energy after polyimide membrane (50 m) penetration, *IPoly*, computed using

The exposure energy density is given per second and milliamp; thus, if the dosage is applied under the experimental conditions, the arbitrary exposure energy per unit area [mJ/mm2] can be calculated. The penetration energy spectrum *SPMMA(x)* in arbitrary depth *x* inside PMMA is given by Formula 4. Additionally, the exposure energy at an arbitrary depth *x* in

> *S xS PMMA Poly* ( ) exp ( )

 

 

*)* is the transmissivity in the constituent factor of a beam line until it reaches the front

*(*  

of a mask, such as the Be window and exposure to atmospheric gas, *TM (*

the conditions described in Section 2.2.2, is given by the following formula.

 

 0.95 0.15

*Poly poly I Sd*

*)*, the absorption of the resist is given by the following formula.

*)* is an absorbing coefficient of the resist. Moreover, the exposure

 

( ) 1.587×102 [mJ/sec mA mm2] (3)

exp *z* (1)

*)x)* is the attenuation in depth *x* to the

( ) (2)

*PMMA PMMA x* (4)

*)* is the

**2.2.4 X-ray absorbed energy** 

orbital radiation is set to *Ps (*

inside of the resist, and

(0.15–0.95 nm).

*TW (* /

transmissivity of the membrane of a mask, *exp(-*

 *(*

PMMA *EPMMA(x)* is given by Formula 5.

Fig. 6. Photodegradation reaction mechanisms; (A) main-chain breaking without side-chain cleavage; and (B) main-chain breaking via side-chain cleavage

Although the sensitivity of PMMA is low, its resolution is very high (50 Å), and reproducibility of fine structures for moulding can be enhanced by further processing. PMMA is a material in the acrylic plastic group that has a broad range of applications, including lenses, instrument windows, signboards, displays, etc. Among the aforementioned photochemical reactions, PMMA preferentially causes main-chain breaking. If main-chain breaking occurs, molecular mass decreases, and solubility in the developer increases. PMMA has a distinguished transparency and weatherability in many polymer materials. Additionally, because PMMA also has good formability, its mechanical properties are also good. Because PMMA is a malleable optical material, it is possible to use fabricated microstructures directly as optical devices. Experiments described in this article utilized PMMA sheets provided by Nitto Jushi Kogyo Co., Ltd. Figure 6 shows photodegradation reaction mechanisms (Schmal et al., 1996). Figure 6A shows main-chain breaking without side-chain cleavage, and Figure 6B shows main-chain breaking via side-chain cleavage.

#### **2.2.4 X-ray absorbed energy**

320 Recent Advances in Nanofabrication Techniques and Applications

Fig. 6. Photodegradation reaction mechanisms; (A) main-chain breaking without side-chain

cleavage; and (B) main-chain breaking via side-chain cleavage

This section describes absorbed energy in the PMMA resist after exposure. To achieve highly accurate microfabrication or 3-D fabrication, it is necessary to calculate the absorbed energy distribution in the resist. To calculate the absorbed energy in the vertical direction, the following factors must be considered: the photon density spectrum of SR light, attenuation by distance from the light source to the resist, divergence of light, and attenuation when light is transmitted through Be windows. If the spectrum of synchrotron orbital radiation is set to *Ps ()*, the absorption of the resist is given by the following formula.

$$d\Delta P\_{\kappa}(\mathcal{A}) = -d \,/\, d\boldsymbol{z} \left\{ P\_{\boldsymbol{s}}\left(\boldsymbol{\lambda}\right) \cdot T\_{\boldsymbol{w}}\left(\boldsymbol{\lambda}\right) \cdot T\_{\boldsymbol{M}}\left(\boldsymbol{\lambda}\right) \cdot \exp\left(-\mu\left(\boldsymbol{\lambda}\right)\boldsymbol{z}\right) \;/\; \right\} \tag{1}$$

*TW ()* is the transmissivity in the constituent factor of a beam line until it reaches the front of a mask, such as the Be window and exposure to atmospheric gas, *TM ()* is the transmissivity of the membrane of a mask, *exp(-()x)* is the attenuation in depth *x* to the inside of the resist, and  *()* is an absorbing coefficient of the resist. Moreover, the exposure energy *I* integrates with the synchrotron orbital radiation spectrum in the wavelength range (0.15–0.95 nm).

$$I = \int\_{0.15}^{0.95} P\_s(\mathcal{X}) \cdot d\mathcal{X} \tag{2}$$

The exposure energy after polyimide membrane (50 m) penetration, *IPoly*, computed using the conditions described in Section 2.2.2, is given by the following formula.

$$I\_{p\_{dy}} = \int\_{0.15}^{0.95} S\_{pay}(\lambda) \cdot d\lambda = 1.587 \times 10^2 \text{ [mJ/sec mA mm2]} \tag{3}$$

The exposure energy density is given per second and milliamp; thus, if the dosage is applied under the experimental conditions, the arbitrary exposure energy per unit area [mJ/mm2] can be calculated. The penetration energy spectrum *SPMMA(x)* in arbitrary depth *x* inside PMMA is given by Formula 4. Additionally, the exposure energy at an arbitrary depth *x* in PMMA *EPMMA(x)* is given by Formula 5.

$$S\_{\text{PAM}}\left(\mathbf{x}\right) = S\_{\text{poly}}\left(\mathcal{Z}\right) \times \exp\left(-\mu\_{\text{PAM}}\left(\mathcal{Z}\right)\mathbf{x}\_{\text{PAM}\Lambda}\right) \tag{4}$$

Fabrication of 3-D Structures Utilizing Synchrotron Radiation Lithography 323

We multiplied *Fpoly(x*) and *Fpoly+Au(x)* by the dosage, an exposure condition, and the amount of absorbed energy that was actually exposed was calculated. Because the dose was 1 Ah = 3,600,000 mAs, multiplication of *Fpoly(x*) and *Fpoly+Au(x)* by the dosage (converted to mAs) results in a unit of [kJ/cm3]. The relationship between depth and absorbed energy can be

An important consideration of resist development is the etching rate ratio of the exposed area to the non-exposed area. The developer must select a ratio that decreases the etching rate of the non-exposed area and increases the etching rate of the exposed area. Experiments described in this article utilized GG developer (60 vol% 2-(2-butoxy-ethoxy) ethanol; 20 vol% tetra-hydro-1, 4-oxazine; 5 vol% 2-amino-ethanol-1; and 15 vol% water). Next, stopper liquid (80 vol% 2-(2-butoxy-ethoxy) ethanol and 20 vol% water) was used for 10 min, followed by rinsing with water for another 10 min. All processes were performed at exactly 37°C. PMMA was exposed, and its molecular mass decreased due to a photochemical reaction. Although the molecular mass of PMMA is usually between 105 and 106 g/mol, it

began to dissolve in GG developer when its molecular mass reached 104 g/mol.

Fig. 9. Relationship between development time and processed depth

Fig. 10. Relationship between the absorbed energy and the etching rate

The relationship between development time and processed depth was investigated experimentally (Figure 9). The relationship between the absorbed energy and the etching rate is shown Figure 10. Etching rate is proportional to the amount of absorbed energy. In general, when the development temperature was high, the etching rate, and thus the processing depth, increased. Figure 11 shows the relationship between dosage and

calculated from *Fpoly(x)* – *Fpoly+Au(x)* (Figure 8).

**2.3 Development** 

$$E\_{\text{PAM}}\left(\mathbf{x}\right) = \int\_{0.15}^{0.95} S\_{\text{PAM}}\left(\mathbf{x}\right) \cdot d\mathcal{X} \tag{5}$$

The penetration energy spectrum *SPMMA(x)* was differentiated by the depth direction, and the absorbed energy spectrum *SABS(x)* of PMMA was calculated.

$$S\_{\rm AdS} \left( \mathbf{x} \right) = d \;/\, d\mathbf{x} \; S\_{\rm quantum} \left( \mathbf{x} \right) = S\_{\rm poly} \left\{ \exp \left[ -\mu\_{\rm muon} (\lambda) \left( \mathbf{x}\_{\rm muon} + \Delta \mathbf{x} \right) \right] - \exp \left( -\mu\_{\rm muon} (\lambda) \mathbf{x}\_{\rm muon} \right) \right\} \tag{6}$$

Therefore, the absorbed energy *EABS(x)* at the arbitrary depth *x* is given by the following formula.

$$E\_{\rm AIS} \left(\mathbf{x}\right) = \int\_{\rm 0.5}^{\rm 0.95} S\_{\rm AIS} \left(\mathbf{x}\right) \cdot d\mathcal{X} = \int\_{\rm 0.5}^{\rm 0.6} d\left(\mathbf{x}\right) \cdot \mathbf{E} \cdot \mathbf{S}\_{\rm pmax} \left(\mathbf{x}\right) \cdot d\mathcal{X} = E\_{\rm pmax} \left(\mathbf{x} + \Delta \mathbf{x}\right) d\mathcal{X} - E\_{\rm pmax} \left(\mathbf{x}\right) \cdot d\mathcal{X} \tag{7}$$

The amount of absorbed energy in PMMA after SR was transmitted through the mask was calculated (Figure 7). The amount of absorbed energy [J/smAmm3] to a depth *x* [m] when SR penetrated the membrane (50-m-thick polyimide) was approximated as *Fpoly(x)*, and the amount of absorbed energy after SR penetrated the membrane (polyimide) and the absorber (3-m-thick Au) was approximated as *Fpoly+Au(x)*.

Fig. 7. Amount of absorbed energy in PMMA after SR was transmitted through the mask was calculated

Fig. 8. Relationship between depth and absorbed energy

We multiplied *Fpoly(x*) and *Fpoly+Au(x)* by the dosage, an exposure condition, and the amount of absorbed energy that was actually exposed was calculated. Because the dose was 1 Ah = 3,600,000 mAs, multiplication of *Fpoly(x*) and *Fpoly+Au(x)* by the dosage (converted to mAs) results in a unit of [kJ/cm3]. The relationship between depth and absorbed energy can be calculated from *Fpoly(x)* – *Fpoly+Au(x)* (Figure 8).

#### **2.3 Development**

322 Recent Advances in Nanofabrication Techniques and Applications

*PMMA PMMA xx x* exp ( )

/ *E x xd E x d PMMA*

 *PMMA PMMA* (6)

*PMMA*

(7)

(5)

*E x S xd PMMA PMMA*

*d dxS x d PMMA*

the absorbed energy spectrum *SABS(x)* of PMMA was calculated.

formula.

was calculated

*E x S xd ABS ABS*

 0.95 0.15

(3-m-thick Au) was approximated as *Fpoly+Au(x)*.

Fig. 8. Relationship between depth and absorbed energy

*S x d dx S x ABS* / *PMMA Spoly* exp ( )

0.95 0.15

0.95 0.15

The penetration energy spectrum *SPMMA(x)* was differentiated by the depth direction, and

Therefore, the absorbed energy *EABS(x)* at the arbitrary depth *x* is given by the following

The amount of absorbed energy in PMMA after SR was transmitted through the mask was calculated (Figure 7). The amount of absorbed energy [J/smAmm3] to a depth *x* [m] when SR penetrated the membrane (50-m-thick polyimide) was approximated as *Fpoly(x)*, and the amount of absorbed energy after SR penetrated the membrane (polyimide) and the absorber

Fig. 7. Amount of absorbed energy in PMMA after SR was transmitted through the mask

 

An important consideration of resist development is the etching rate ratio of the exposed area to the non-exposed area. The developer must select a ratio that decreases the etching rate of the non-exposed area and increases the etching rate of the exposed area. Experiments described in this article utilized GG developer (60 vol% 2-(2-butoxy-ethoxy) ethanol; 20 vol% tetra-hydro-1, 4-oxazine; 5 vol% 2-amino-ethanol-1; and 15 vol% water). Next, stopper liquid (80 vol% 2-(2-butoxy-ethoxy) ethanol and 20 vol% water) was used for 10 min, followed by rinsing with water for another 10 min. All processes were performed at exactly 37°C. PMMA was exposed, and its molecular mass decreased due to a photochemical reaction. Although the molecular mass of PMMA is usually between 105 and 106 g/mol, it began to dissolve in GG developer when its molecular mass reached 104 g/mol.

Fig. 9. Relationship between development time and processed depth

Fig. 10. Relationship between the absorbed energy and the etching rate

The relationship between development time and processed depth was investigated experimentally (Figure 9). The relationship between the absorbed energy and the etching rate is shown Figure 10. Etching rate is proportional to the amount of absorbed energy. In general, when the development temperature was high, the etching rate, and thus the processing depth, increased. Figure 11 shows the relationship between dosage and

Fabrication of 3-D Structures Utilizing Synchrotron Radiation Lithography 325

increase processing depth, even when the dosage is small, the development time or temperature must increase. On the other hand, when the dosage is high, the development time can be short. However, to achieve high-accuracy microfabrication, it is necessary to

When the dosage is too high, bubbles often form inside the resist, especially near the surface. Figure 13 shows a microscopic photograph of damage to the PMMA sheet after exposure. Figure 13B shows exposed microchannel patterns. As seen in the figure, bubbles spread not only to the exposed area but also to the non-exposed area. We confirmed that bubbles influenced the structure after development. Because bubbles often form when the amount of absorbed energy exceeds 80 kJ/cm3, it is necessary to select a dosage that does

As mentioned in Section 2.3, the molecular mass of PMMA must be below a certain value in order for PMMA to dissolve in developer. The minimum energy required for dissolution is called the "development-limit energy amount." Although the development limit energy amount varies in the literature, it is approximately 1 kJ/cm3 based on previous experiments. Variation in the literature values is due to differences in the molecular mass of the PMMA. As the depth from the surface increases, the absorbed energy decreases exponentially; thus, it is necessary to consider not only the surface-damage energy amount but also the

Next, we discuss the development temperature. As mentioned in Section 2.3, the etching rate increases with increasing development temperature. Because of the higher development temperature and faster etching rate, the processing depth may become large in a short amount of time. However, when the development temperature is too high, the etching rate increases, but the development-limit energy amount decreases. Thus, it is necessary to select the optimum development temperature (Fujinawa et al., 2006). If the development-limit energy amount is too low, PMMA resist develops not only in the exposed area, but also in the non-exposed areas (through the absorber). Therefore, sloped-sidewall structures are fabricated. On the other hand, when the development temperature is low, the processing depth is low, and a long development time is required. Because PMMA swells in water, a long development time is a disadvantage. For these reasons, the development process was

determine optimum experimental conditions.

not exceed this "surface-damage energy amount."

performed at 37°C.

**2.4.3 Micro-loading effect** 

development-limit energy amount to determine the optimum dosage.

(A) (B)

Fig. 13. Microscope photographs of damaged to the PMMA sheet after exposure

In this section, the influence of the micro-loading effect is described. The micro-loading effect is a phenomenon that leads to different processing depths depending on the line width. If the line width is narrow, circulation of the developer worsens, it is difficult to

processed depth at a development time of 180 min. Figures 9 and 11 show the experimental values and formula approximations. The processing depth is determined by the dosage and development time, as shown in Figures 9 and 11. Thus, it is possible to determine the processing depth using these approximation formulas.

Fig. 11. Relationship between dosage and processed depth at a development time of 180 min
