**2. Photon sieve array X-ray maskless nanolithography**

Lithography has been the key technology in the semiconductor industry. Beyond the semiconductor industry, lithography has also been widely employed in such technological fields as microoptics, nanophotonics, MOEMS, nanotechnology, etc. In order to achieve the minimum feature size, the development of lithography has resulted in setups with high throughput and reliability regardless of cost and flexibility.

For nanoscale science and engineering, however, the lower cost and higher flexibility of lithography must be considered. Fortunately, maskless lithography can meet the requirements of nanotechnology. There are various forms of maskless lithography that include scanning electron-beam lithography, focused ion-beam lithography, multiaxis electron-beam lithography, interference lithography, maskless optical-projection lithography, scanning probe lithography, zone plate array lithography (ZPAL) (Menon et al., 2005), etc. It is a very complex process of selecting an optimum lithography tool that requires knowledge and experience in several disciplines including physics, chemistry, electronics, device design, manufacturing, processing, cost and marketing. Although the selection strategy consists of many aspects, the technical aspect is the dominant item because the tool has to be technically performable. Menon et al. showed the feasibility of ZPAL operating at a wavelength of 400nm and its potential for the fabrication of novel devices.

Photon sieve is a novel diffractive optical element which consists of a great number of pinholes distributed appropriately over the Fresnel zones for the focusing and imaging of soft X-rays (Kipp et al., 2001). Photon sieve has advantages of the diameter of pinholes beyond the limitation of the corresponding Fresnel zone width and the minimum background in the focal

Emerging Maskless Nanolithography Based on Novel Diffraction Gratings 339

PSAL utilizes very short wavelength synchrotron radiation source emitted. Synchrotron radiation arises from the changing direction of a high energy relativistic beam of electrons caused to run a circular modified elliptical path. The key characteristics of synchrotron radiation light are high brightness, very small divergence, extremely narrow bandwidth, and so on. In the case of synchrotron radiation, the operating wavelength ranged from

Resolution limits are caused by the diffraction effects and photoelectron spreading. On one hand, the minimum diffraction-limited resolution of a PSAL system is determined by

> *R k NA* min 1

On the other hand, the incident x-ray photon usually transforms all its energy into a single high energy photoelectron in the incident solid. Both a secondary electron shower and the chemical alterations in photoresist necessary for exposure are caused by this primary photoelectron. Therefore, resolution limits arise also from the range of this photoelectron.

> <sup>2</sup> *DOF k NA* <sup>2</sup>

where *k2* is determined by the lithography process in use, ranging from 0.5 to 1. DOF defines the maximum tolerable displacement of the image plane from its ideal position. The approach to optically polishing imaging surfaces tends to make lithography easier by eliminating depth-of-focus problems. For example, a photon sieve of *NA* = 0.8 and *k2* = 0.6,

If tiny variations in exposure and development conditions cause large varieties in the exposed pattern, the process is worthless. Process latitude is defined that the variety of some critical process parameters (such as line width, edge acuity, etc.) concerning the processing conditions (such as exposure time, development time, etc.). Ideally, a process whose critical parameters change as little as possible for a given change in process condition is desired.

Photon sieve can produce effects on their own depending on what the optical engineer is trying to achieve for a particular design goal. In situations where size or weight are critical, photon sieves bring substantial advantages. The flexibility in constructing wavefronts gives an optical designer the ability to use photon sieves fabricated microscopic structures on flat surfaces as converging lenses all by themselves. Acted as a diffractive optical element,

 is the exposure wavelength of the incident light, *k1* is a factor between 0.5 and 1. The shortest exposure wavelength contemplated is 0.5nm. *NA* of approximately 0.8 is expected. As a result, the minimum feature size Rmin for such a system may approach 0.3nm.

/ (1)

/ (2)

0.5nm to 2nm is very suitable for nanolithographic research.

Therefore, PSAL is very promising for the fabrication of nanodevices.

The depth of focus (DOF) of a PSAL system is given by

operating at 2 nm, the DOF is 1.9 *nm* .

**2.2 Source of X-ray** 

**2.3 Resolution** 

**2.4 Depth of focus** 

**2.5 Process latitude** 

**2.6 Design of photon sieve** 

where 

plane, which is shown in figure 3. The focal spot produced by a Fresnel zone plate is surrounded by rings of intensity (secondary maxima) that blur the images. For a zone plate, each ring contributes equally to the amplitude at the focus. This contribution drops abruptly to zero beyond the outermost ring which leads to strong intensity oscillations in the diffraction pattern (top row). With a photon sieve, the number of pinholes per ring can be readily adjusted to yield a smooth transition which minimizes the secondary maxima (bottom row). This provides sharper images. Note that diffraction intensities are plotted on a log scale (right column). Furthermore, photon sieve can be fabricated on a single surface without any supporting struts required unlike the Fresnel zone plate.

Fig. 3. Schematic of photon sieve suppressing side lobes.

In this section, we present the scheme of maskless nanolithography using a large array of photon sieves, each of which focuses incident X-ray into a diffraction-limited on-axis spot on the surface of a photoresist-coated substrate (PSAL). The X-ray intensity of each spot is modulated by means of a spatial light modulator. Patterns of arbitrary geometry are written in a dot matrix fashion while the photoresist-coated substrate on a precision stepping stage is exposed to the properly modulated X-ray. In combination with the synchrotron light sources, PSAL can offer a new tool for high-resolution X-ray nanolithography in physical and nano sciences. Lastly, the design and fabrication of photon sieve are illustrated with a low-*NA* amplitude-photon sieve fabricated on a chrome-coated quartz plate using laserbeam lithographic process.

#### **2.1 Scheme of photon sieve array X-ray maskless nanolithography**

In PSAL system operating at wavelength of 0.5~2nm synchrotron light sources radiated, each of a large array of photon sieves focuses incident X-ray into a diffraction-limited onaxis nanoscale spot on the substrate coated photoresist. Patterns of arbitrary geometry are exposed in a dot matrix fashion while the substrate on a stepping stage is precisely driven in two dimensions according to the computer program. A Schematic of PSAL is shown in Figure 1. PSAL provides a promising approach for the fabrication of nanometric device and integrated circuit (IC). There are emphases on light source, resolution, depth of focus and process latitude in both nanodevice and the IC areas. In the section, we will go into detail the four characteristics.

#### **2.2 Source of X-ray**

338 Recent Advances in Nanofabrication Techniques and Applications

plane, which is shown in figure 3. The focal spot produced by a Fresnel zone plate is surrounded by rings of intensity (secondary maxima) that blur the images. For a zone plate, each ring contributes equally to the amplitude at the focus. This contribution drops abruptly to zero beyond the outermost ring which leads to strong intensity oscillations in the diffraction pattern (top row). With a photon sieve, the number of pinholes per ring can be readily adjusted to yield a smooth transition which minimizes the secondary maxima (bottom row). This provides sharper images. Note that diffraction intensities are plotted on a log scale (right column). Furthermore, photon sieve can be fabricated on a single surface without any

In this section, we present the scheme of maskless nanolithography using a large array of photon sieves, each of which focuses incident X-ray into a diffraction-limited on-axis spot on the surface of a photoresist-coated substrate (PSAL). The X-ray intensity of each spot is modulated by means of a spatial light modulator. Patterns of arbitrary geometry are written in a dot matrix fashion while the photoresist-coated substrate on a precision stepping stage is exposed to the properly modulated X-ray. In combination with the synchrotron light sources, PSAL can offer a new tool for high-resolution X-ray nanolithography in physical and nano sciences. Lastly, the design and fabrication of photon sieve are illustrated with a low-*NA* amplitude-photon sieve fabricated on a chrome-coated quartz plate using laser-

In PSAL system operating at wavelength of 0.5~2nm synchrotron light sources radiated, each of a large array of photon sieves focuses incident X-ray into a diffraction-limited onaxis nanoscale spot on the substrate coated photoresist. Patterns of arbitrary geometry are exposed in a dot matrix fashion while the substrate on a stepping stage is precisely driven in two dimensions according to the computer program. A Schematic of PSAL is shown in Figure 1. PSAL provides a promising approach for the fabrication of nanometric device and integrated circuit (IC). There are emphases on light source, resolution, depth of focus and process latitude in both nanodevice and the IC areas. In the section, we will go into detail

supporting struts required unlike the Fresnel zone plate.

Fig. 3. Schematic of photon sieve suppressing side lobes.

**2.1 Scheme of photon sieve array X-ray maskless nanolithography** 

beam lithographic process.

the four characteristics.

PSAL utilizes very short wavelength synchrotron radiation source emitted. Synchrotron radiation arises from the changing direction of a high energy relativistic beam of electrons caused to run a circular modified elliptical path. The key characteristics of synchrotron radiation light are high brightness, very small divergence, extremely narrow bandwidth, and so on. In the case of synchrotron radiation, the operating wavelength ranged from 0.5nm to 2nm is very suitable for nanolithographic research.

#### **2.3 Resolution**

Resolution limits are caused by the diffraction effects and photoelectron spreading. On one hand, the minimum diffraction-limited resolution of a PSAL system is determined by

$$R\_{\rm min} = k\_1 \mathcal{X} / \text{NA} \tag{1}$$

where is the exposure wavelength of the incident light, *k1* is a factor between 0.5 and 1. The shortest exposure wavelength contemplated is 0.5nm. *NA* of approximately 0.8 is expected. As a result, the minimum feature size Rmin for such a system may approach 0.3nm. Therefore, PSAL is very promising for the fabrication of nanodevices.

On the other hand, the incident x-ray photon usually transforms all its energy into a single high energy photoelectron in the incident solid. Both a secondary electron shower and the chemical alterations in photoresist necessary for exposure are caused by this primary photoelectron. Therefore, resolution limits arise also from the range of this photoelectron.

#### **2.4 Depth of focus**

The depth of focus (DOF) of a PSAL system is given by

$$\text{DOF} = \pm k\_2 \mathcal{k} / \text{NA}^2 \tag{2}$$

where *k2* is determined by the lithography process in use, ranging from 0.5 to 1. DOF defines the maximum tolerable displacement of the image plane from its ideal position. The approach to optically polishing imaging surfaces tends to make lithography easier by eliminating depth-of-focus problems. For example, a photon sieve of *NA* = 0.8 and *k2* = 0.6, operating at 2 nm, the DOF is 1.9 *nm* .

#### **2.5 Process latitude**

If tiny variations in exposure and development conditions cause large varieties in the exposed pattern, the process is worthless. Process latitude is defined that the variety of some critical process parameters (such as line width, edge acuity, etc.) concerning the processing conditions (such as exposure time, development time, etc.). Ideally, a process whose critical parameters change as little as possible for a given change in process condition is desired.

#### **2.6 Design of photon sieve**

Photon sieve can produce effects on their own depending on what the optical engineer is trying to achieve for a particular design goal. In situations where size or weight are critical, photon sieves bring substantial advantages. The flexibility in constructing wavefronts gives an optical designer the ability to use photon sieves fabricated microscopic structures on flat surfaces as converging lenses all by themselves. Acted as a diffractive optical element,

Emerging Maskless Nanolithography Based on Novel Diffraction Gratings 341

where r is the radius at the center of the underlying zone pattern and is the parameter that controls the strength of apodization. The apodization parameter may be adjusted to achieve the optimum desired intensity distribution at the focal plane (Cheng et al., 2010, 2011). We calculated the PSF intensity distribution of photon sieves with different apodization parameters at focal plane compared with a zone plates. Figure 5(a) shows a plot of the pupil intensity transmission of a zone plate with rectangular transmission window and two

rectangular transmission pupil can also be derived from the Gaussian transmission pupil

Fig. 5. Comparison of calculated intensity distributions of photon sieves and zone plate with different apodization windows. (a) Transmission windows in pupil plane for a zone plate (solid line) with a rectangular apodization window and two different photon sieves with Gaussian apodization window: σ=1 (dotted line), σ=0.5 (solid-dot line), respectively. (b) Transverse intensity point-spread function distribution in focal plane for the corresponding

We designed an amplitude-photon sieve. The diffraction element had a diameter of 30mm and a focus length of 175 mm for an operating wavelength 632.8 nm. The pinholes were distributed over zones of order ranged from 2 to 1000. The minimum diameter of pinhole

of order from 2 to 100 and the point spread function of the former 10 zones, which are

A Gaussian apodized X-rays amplitude-photon sieve at a wavelength of 0.5nm (20mm focal length, 2mm pupil diameter, 0.05 *NA*) is simulated based on the scalar diffraction theory. The minimum feature size and total number of pinholes is 7.5nm, 14215227, respectively. The spatial resolution of 6.1nm can be obtained. Figure 7 shows the distribution of central

*m* . We give the simulation results of pinhole positions distributed over the zones

 . Figure 5(b) shows cross sections of the intensity PSF for the three cases. The logarithm of intensity is plotted vertically in order to emphasize the side-lobes, and the intensity normalization is proportional to the total integrated intensity passed by the pupil in each case. It may be seen that the Gaussian apodization significantly suppresses the sidelobes at the expense of slightly broadening the main lobe. The relative attenuation of sidelobes of the zone plate and photon sieves is -13.2dB, -16.7dB, -32.8dB, respectively. The full width at half maximum (FWHM) of these main lobes is 0.05, 0.05, 0.07, respectively.

produces a narrower window and a less strength of side-lobes at

1,0.5 , respectively. In fact, the

photon sieves with Gaussian transmission windows

the expense of a somewhat wider main lobe.

when

Therefore, a less value of

zone plate and photon sieves.

was 5.6

shown in Figure 6.

photon sieves can also be used to correct image aberrations and color aberrations in a lens in a manner similar to the use of aspheric surfaces and additional refractive components. For example, the hybrid lens, consisting of a photon sieves with a conventional refractive lens, can provide the required color correction.

One useful method of the approaches to designing photon sieve is the paraxially individual far-field model and the nonparaxial model (Cao & Jahns, 2002, 2003). The former derived from the paraxial Fresnel diffraction is valid for the low-NA photon sieve. The latter based on the nonparaxial expression for the far field of individual pinholes and the linear superposition principle is valid for high-*NA* photon sieve, such as the photon sieves operating in X-ray region.

The key methods designing photon sieve are to optimize positions and radii of pinholes. Kipp et al. pointed out that photon sieve consists of a large number of pinholes distributed appropriately over the zones of a Fresnel zone plate pattern. The size of the focused spot is approximately equal to the width of the smallest zone in the underlying zone plate pattern. The diffracted field of a single pinhole can be expressed as

$$\mathbf{U} \ll \mathbf{K} \mathbf{J}\_1 \mathbf{(0.5\pi K)}\tag{3}$$

where *K* is the ratio of pinhole diameter to the corresponding zone width and *J1* is the first order Bessel function of the first kind. The maximum modulus of U appears when *K* is approximately equal to 1.5, 3.5, 5.5, etc, as shown in figure 4. The parameter *K* may be utilized to relax the fabrication requirements for the photon sieve considerably as compared with a zone plate of the same *NA.*

Fig. 4. The diffracted field of a single pinhole.

The point-spread function (PSF) of a traditional Fresnel zone plates generally has side-lobes of noticeable strength. The side-lobes blur the image obtained by the zone plates. The photon sieve may create a PSF that has lower side-lobes at the expense of a slightly wider main lobe than the zone plates. Moreover, an additional benefit of the photon sieve is that it breaks the periodicity that is inherent in the zone plates, thus strongly attenuating the higher diffracted orders. For an amplitude-photon sieve, apodization may be achieved by varying the transmissivity of its pupil gradually, i.e., the number of its pinholes, as a function of radial distance so as to follow approximately the function form of a Gaussian distribution

$$G(r) = \exp(-0.5r^2/\sigma^2) \tag{4}$$

photon sieves can also be used to correct image aberrations and color aberrations in a lens in a manner similar to the use of aspheric surfaces and additional refractive components. For example, the hybrid lens, consisting of a photon sieves with a conventional refractive lens,

One useful method of the approaches to designing photon sieve is the paraxially individual far-field model and the nonparaxial model (Cao & Jahns, 2002, 2003). The former derived from the paraxial Fresnel diffraction is valid for the low-NA photon sieve. The latter based on the nonparaxial expression for the far field of individual pinholes and the linear superposition principle is valid for high-*NA* photon sieve, such as the photon sieves

The key methods designing photon sieve are to optimize positions and radii of pinholes. Kipp et al. pointed out that photon sieve consists of a large number of pinholes distributed appropriately over the zones of a Fresnel zone plate pattern. The size of the focused spot is approximately equal to the width of the smallest zone in the underlying zone plate pattern.

*U KJ K* <sup>1</sup> 0.5

where *K* is the ratio of pinhole diameter to the corresponding zone width and *J1* is the first order Bessel function of the first kind. The maximum modulus of U appears when *K* is approximately equal to 1.5, 3.5, 5.5, etc, as shown in figure 4. The parameter *K* may be utilized to relax the fabrication requirements for the photon sieve considerably as compared

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> <sup>9</sup> <sup>10</sup> -2

The point-spread function (PSF) of a traditional Fresnel zone plates generally has side-lobes of noticeable strength. The side-lobes blur the image obtained by the zone plates. The photon sieve may create a PSF that has lower side-lobes at the expense of a slightly wider main lobe than the zone plates. Moreover, an additional benefit of the photon sieve is that it breaks the periodicity that is inherent in the zone plates, thus strongly attenuating the higher diffracted orders. For an amplitude-photon sieve, apodization may be achieved by varying the transmissivity of its pupil gradually, i.e., the number of its pinholes, as a function of radial distance so as to follow approximately the function form of a Gaussian

2 2 *Gr r* ( ) exp( 0.5 )

d/w

(3)

(4)

can provide the required color correction.

The diffracted field of a single pinhole can be expressed as

operating in X-ray region.

with a zone plate of the same *NA.*


Fig. 4. The diffracted field of a single pinhole.

Amplitude

distribution

where r is the radius at the center of the underlying zone pattern and is the parameter that controls the strength of apodization. The apodization parameter may be adjusted to achieve the optimum desired intensity distribution at the focal plane (Cheng et al., 2010, 2011).

We calculated the PSF intensity distribution of photon sieves with different apodization parameters at focal plane compared with a zone plates. Figure 5(a) shows a plot of the pupil intensity transmission of a zone plate with rectangular transmission window and two photon sieves with Gaussian transmission windows 1,0.5 , respectively. In fact, the rectangular transmission pupil can also be derived from the Gaussian transmission pupil when . Figure 5(b) shows cross sections of the intensity PSF for the three cases. The logarithm of intensity is plotted vertically in order to emphasize the side-lobes, and the intensity normalization is proportional to the total integrated intensity passed by the pupil in each case. It may be seen that the Gaussian apodization significantly suppresses the sidelobes at the expense of slightly broadening the main lobe. The relative attenuation of sidelobes of the zone plate and photon sieves is -13.2dB, -16.7dB, -32.8dB, respectively. The full width at half maximum (FWHM) of these main lobes is 0.05, 0.05, 0.07, respectively. Therefore, a less value of produces a narrower window and a less strength of side-lobes at the expense of a somewhat wider main lobe.

Fig. 5. Comparison of calculated intensity distributions of photon sieves and zone plate with different apodization windows. (a) Transmission windows in pupil plane for a zone plate (solid line) with a rectangular apodization window and two different photon sieves with Gaussian apodization window: σ=1 (dotted line), σ=0.5 (solid-dot line), respectively. (b) Transverse intensity point-spread function distribution in focal plane for the corresponding zone plate and photon sieves.

We designed an amplitude-photon sieve. The diffraction element had a diameter of 30mm and a focus length of 175 mm for an operating wavelength 632.8 nm. The pinholes were distributed over zones of order ranged from 2 to 1000. The minimum diameter of pinhole was 5.6 *m* . We give the simulation results of pinhole positions distributed over the zones of order from 2 to 100 and the point spread function of the former 10 zones, which are shown in Figure 6.

A Gaussian apodized X-rays amplitude-photon sieve at a wavelength of 0.5nm (20mm focal length, 2mm pupil diameter, 0.05 *NA*) is simulated based on the scalar diffraction theory. The minimum feature size and total number of pinholes is 7.5nm, 14215227, respectively. The spatial resolution of 6.1nm can be obtained. Figure 7 shows the distribution of central

Emerging Maskless Nanolithography Based on Novel Diffraction Gratings 343

In order to verify the feasibility of the above methods, we fabricated a Gaussian apodized amplitude-photon sieve (633nm design wavelength, 175mm focal length, 30mm pupil diameter, 0.08 *NA*) on chrome-coated quartz plate using laser-beam lithographic techniques. The resolution image was recorded at 627nm peak-wavelength and 20nm spectral halfwidth produced by a light-emitting diode. Figure 8 demonstrates the pinholes distribution of the central part of the Gaussian apodized amplitude-photon sieve and the ratio of pinhole

**2.7 Fabrication and experiment** 

portion, (b)the outermost portion.

diameter to underlying zone width is chosen as 1.5.

(a) (b)

the wavelength difference and chromatic aberration.

Fig. 8. Scanning electron microscope images of an amplitude-photon sieve. (a)Central

Fig. 9. Resolution test target imaged with an apodized photon sieve at 627 nm.

For the purpose of testing the imaging property, a beam of even illumination was produced by a light-emitting diode (LED, with peak-wavelength 627nm and spectral half-width 20nm) and a ground-glass diffuser. The beam transmitted through a WT1005-62 resolution test target was then incident upon the photon sieve. The resolution images were recorded by an intensified charge coupled device (ICCD). Figure 9 shows that good agreement between experimental and theoretical results concerning reduction of side-lobes but the resolution of 5.9um obtained is somewhat lower than the expected resolution limit of 4.8um because of

part of the photon sieve, which the ratio of pinhole diameter to underlying zone width is chosen as 1.5.

Fig. 6. Simulated pinholes distribution and PSF of a photon sieve.

Fig. 7. Pinholes distribution of an apodized X-rays photon sieve.

The diffraction efficiency scales as the square of the transmission area. A photon sieve transmits only 15~30% of the incident light because of the Gaussian apodization whereas an amplitude-zone plate has a transmission of 50%. Therefore, the first-order diffraction efficiency of a photon sieve is lower than that of a zone plate of equal *NA* by a factor of 10. However, the photon sieve is an attractive alternative to conventional zone plates for the Xrays focusing and imaging elements in the situation using the brilliant X-rays from synchrotron light sources as illumination, the diffraction efficiency is not a very important consideration but the side-lobes suppression and the fabrication ease are relatively more important.

The process of designing an amplitude-photon sieve is shown as follows. Firstly, the operating wavelength, diameter and focal length of photon sieve are given according to the purpose of imaging or focusing. Secondly, the number of corresponding Fresnel zones is calculated. Lastly, the optimum radius and coordinate of each pinhole in each corresponding zone are determined, and then the data of all pinholes are stored in the same file in order to create the photon sieve.
