⇦Chinese Physics Letters, 2018, Vol. 35, No. 5, Article code 054207⇨ Fabrication of 4-Inch Nano Patterned Wafer with High Uniformity by Laser Interference Lithography * Gen Yue(乐艮)1,2, Yu Lei(雷宇)1,2, Jun-Hui Die(迭俊珲)1,2, Hai-Qiang Jia(贾海强)1,2, Hong Chen(陈弘)1,2** Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2School of Physics, University of Chinese Academy of Sciences, Beijing 100049 Received 19 March 2018, online 30 April 2018 ^*Supported by the Scientific Equipment Research Program of Chinese Academy of Sciences under Grant No 2014Y4201449.
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^**Corresponding author. Email: hchen@iphy.ac.cn Citation Text: Yue G, Lei Y, Die J H, Jia H Q and Chen H 2018 Chin. Phys. Lett. 35 054207 Abstract We report the fabrication of 4-inch nano patterned wafer by two-beam laser interference lithography and analyze the uniformity in detail. The profile of the dots array with a period of 800 nm divided into five regions is characterized by a scanning electron microscope. The average size in each region ranges from 270 nm to 320 nm, and the deviation is almost 4%, which is approaching the applicable value of 3% in the industrial process. We simulate the two-beam laser interference lithography system with MATLAB software and then calculate the distribution of light intensity around the 4 inch area. The experimental data fit very well with the calculated results. Analysis of the experimental data and calculated data indicates that laser beam quality and space filter play important roles in achieving a periodical nanoscale pattern with high uniformity and large area. There is the potential to obtain more practical applications. DOI:10.1088/0256-307X/35/5/054207 PACS:42.25.Hz, 42.50.St, 42.60.By, 78.40.Fy © 2018 Chinese Physics Society Article Text Over the past few decades, micron, submicron and nanoscale structures have developed greatly in various fields including resonant waveguides,[1,2] nano-imprint lithography,[3-5] laser fabrication,[6] thin films,[7,8] self-organization,[9-11] and optical engineering.[12] Patterned substrate technology was introduced in gallium nitride (GaN) light emitting diode fabrication to optimize the performance via the improvement of crystalline quality and light extraction efficiency.[13-16] It was reported that the quality of GeSi alloy on the patterned wafer would be improved greatly.[17,18] Various methods are developing rapidly for fabricating these structures including traditional ultraviolet lithography (TUL),[19] direct laser writing,[20] nano-imprint lithography (NL),[21] electron beam lithography (EBL),[22] laser interference lithography (LIL),[23,24] ion beam lithography (IBL),[25] self-organization, and immersion laser lithography.[26] TUL fabricates a micron scale pattern easily, while it cannot cover the nanoscale range. Although NL, EBL and IBL are suitable for fine nanoscale engineering, they are always expensive to obtain a large area pattern for their poor efficiency. In comparison with those tools, LIL is one of the powerful methods for periodic nanostructures. On the one hand, the structure of the apparatus is very simple without masks and does not require expensive components such as the vacuum system and electronic lens. On the other hand, it is flexible to change the period and size of pattern by changing the lens and developing time. It is very suitable to fabricate high order arrays with a large scale. LIL is an effective micro-nano processing method, which has developed very quickly over the years. Many kinds of LIL have emerged sequentially, such as Lloyd's mirror LIL system,[27] two-beam LIL system,[28,29] multi-beam LIL system,[30] and immersion interference lithography system.[31] Two-dimensional (2D) pattern can be obtained by one or two exposures in these ways. Lloyd's single beam LIL system is most convenient and widely used for its simplest configuration and highest stability, while it brings inevitable distortion for inherent uneven distribution of laser on the specimen holder. The 2D pattern will be obtained by a 3- or more-beam LIL system with only one exposure, but these systems are always very complex and susceptible. A small movement caused by thermal instability, configuration vibration, even air vibration in the paths of beams will bring vital damages. It is always difficult to obtain a repeatable and large area pattern. Two-beam LIL is an ideal candidate for its simple configuration. The distribution of light is almost uniform in the center of the specimen stage. The 2D pattern forms through the two exposures. In this work, we fabricate 4-inch nano patterned dots by laser interference lithography and simulate the distribution of light intensity. By comparing them we realize that there are three important aspects to affect obtaining high uniformity patterns. It is a positive step towards bringing this technology from the lab to industry. This work is based on the two-beam LIL device shown in Fig. 1. A single longitudinal mode (SLM) laser of 355 nm emitted from a cx 355-100 high-power optically pumped semiconductor laser (Coherent) passes through a timing shutter and reflects from a UV mirror, then the laser is divided into two beams with the same intensity by a UV splitter. Two beams go through two sets of space filters. As a result, the laser is purified and enlarged. They reflect from mirrors on the opposite sides of the splitter, and converge on the surface of the sample table. The light distribution with special period emerges.

Fig. 1. (a) The sketch of the two-beam LIL apparatus, (b) the distribution of light intensity after the first exposure, and (c) the distribution of light distribution after a second exposure by rotating the sample.

For the first exposure, a pattern with one-dimensional period depicted in Fig. 1(b) appears. After the second exposure, a 2D arrangement is achieved. The distribution of the light intensity is depicted in Fig. 1(c). The period ${\it \Lambda}$ of interference pattern in the LIL can express as $$\begin{align} {\it \Lambda} =\frac{\lambda}{2\sin \theta},~~ \tag {1} \end{align} $$ where $\lambda$ is the wavelength of the laser, and $\theta$ is the incident angle.

Fig. 2. Schemes of the experimental process.

The experimental process for 2D arrays is depicted in Fig. 2. Firstly, 4 inch silicon was cleaned by sequent acetone, alcohol and deionized water for 5 min, respectively. Then, it was baked at 150$^{\circ}\!$C for 3–5 min to form a dry surface to enhance the adsorption. A 10 nm addictive was spinning coated and baked at 180$^{\circ}\!$C for 2 min. Consequently, the diluted AllResist 3840(1:4) was spin-coated at 4000 rpm for 40 s. After that, the sample was kept at 90$^{\circ}\!$C for 2 min to gain a stable 100-nm-thick photoresist (PR) film. The optical set is depicted in Fig. 1(a) with the incident angle of 12.8$^{\circ}$ shown in Fig. 3(a). The specimen was exposed for the first time. Rotating 90$^{\circ}$, it was exposed another time. Two exposures were in the same dose of 6 mJ/cm$^2$ respectively. After being developed in 60% developer (diluted by deionized water), two-dimensional dots of 800 nm spatial periodicity in Fig. 2(d) are realized on the surface of 4 inch wafer. The profile of the pattern wafer is shown in Fig. 3(b). An XL30S-FEG scanning electron microscope (SEM) was used to reveal the profile of the periodical dots.

Fig. 3. (a) Schematic illustration showing the geometric configuration of the two-beam LIL system, and (b) the 4 inch picture.

Fig. 4. SEM images of the PR arrays. (a) Five areas on the 4 inch wafer, (b) the center area, (c) the right area, (d) the upper area, (e) the left area and (f) the down area.

The profile of the periodical arrays given by the SEM is shown in Fig. 4. To reveal the uniformity of dots in the large area, five areas were chosen in the 4 inch wafer as shown in Figs. 4(a)–4(f). Figures 4(b)–4(f) correspond to the center, right, upper, left and down areas, respectively. Obviously, there is no distortion.

Fig. 5. The 4$\times$4 dots circled by the yellow square was chosen. Here $R_{x}$ and $R_{y}$ are the diameters along the $X$ and $Y$ axes, respectively.

Parameters $R_{x}$, $R_{y}$, $R_{x}^{\ast}$ and $R_{y}^{\ast}$ meant diameters and normalized diameters in the $X$ and $Y$ directions, respectively, are introduced. To confirm the statistical accuracy, we took 16 dots circled by the yellow square in Fig. 5 into consideration. The diameter ranges from 269 nm to 330 nm explicitly shown in Fig. 6(a). Values of $R_{x}^{\ast}$ and $R_{y}^{\ast}$ are from 0.92 to 1.08. To explain the uniformity depicted in Fig. 6, we simulate the light distribution of the two-beam LIL devices. Laser beam modified by the spacing filter is assumed to be a quasi-plane wave. Its electrical vector is $$\begin{alignat}{1} {\boldsymbol E}_{i} ({\boldsymbol r},t)={\boldsymbol E}_{i} ({\boldsymbol r})\exp({\boldsymbol k}\cdot {\boldsymbol r}-wt+\varphi_{i} ),~~i=1,2,~~ \tag {2} \end{alignat} $$ where ${\boldsymbol E}_{1} ({\boldsymbol r},t)$ and ${\boldsymbol E}_{2} ({\boldsymbol r},t)$ come from the left and the right, respectively, $k=2\pi /\lambda$ is the wave vector where $\lambda$ is the wavelength of the 355 nm laser, $w$ is the frequency of the wave, and $\varphi$ is the phase settled by the system. The intensity part of ${\boldsymbol E}_{i} ({\boldsymbol r})$ is given by $$\begin{align} {\boldsymbol E}_{i} ({\boldsymbol r})=\,&I_{0} \exp(-A_{0} \cdot r^{2}/r_{0}^{2} )[({\boldsymbol r}+{\boldsymbol r}_{i} )\\ &\cdot ({\boldsymbol r}+{\boldsymbol r}_{i})^{\ast}]^{-0.5}\cdot {\boldsymbol e}_{i},~~i=1,2,~~ \tag {3} \end{align} $$ where $I_{0}$ and $A_{0}$ are systematical constant values decided by the laser and spacing filter, respectively. As the principle of superposition, the final vector on the wafer can be expressed as $$\begin{align} {\boldsymbol E}({\boldsymbol r})={\boldsymbol E}_{1} ({\boldsymbol r})+{\boldsymbol E}_{2} ({\boldsymbol r}),~~ \tag {4} \end{align} $$ where the final magnitude of the electrical field is $$\begin{align} I({\boldsymbol r})={\boldsymbol E}({\boldsymbol r})\cdot {\boldsymbol E}({\boldsymbol r})^{\ast}.~~ \tag {5} \end{align} $$

Fig. 6. (a) Raw data from SEM images in five regions, and (b) the normalized data of (a). Here $\overline {R_{x}}$ is the mean value of $R_{x}$, $\overline {R_{y}}$ is the mean value of $R_{y}$, $R_{x}^{\ast}=\frac{R_{x}}{\overline {R_{x}}}$, and $R_{y}^{\ast} =\frac{R_{y}}{\overline {R_{y}}}$.

By combining the above theoretical optical field analysis with our experimental setup, we simulated the distribution of the laser beam intensity. Here c, u, d, r and l in the figure represent the center, upper, down, right and left areas, respectively. Figure 8(a) shows the density distribution of each region along the $x$ direction. The patterned dots are well waved with the period of 820 nm in each region. The experimental and simulated data are clearly shown in Fig. 8(b). The dots in the center are smaller than those at the edge of 4 inch wafer, which result from the difference in large area.

Fig. 7. Simulated data by MATLAB program. Here C, U, D, R and l are corresponding to the center, upper, down, right and left areas, respectively.

Fig. 8. (a) The density distribution of each region along the $X$ direction, and (b) the comparison of experimental and simulated data.

**Table 1.** The measured parameters about the uniformity and simulated results in each area.
	Experimental data						Simulated results
Region	$\overline {R_{x}}$	rms $R_{x}$ ($\overline {R_{x}}$)	Deviation	$\overline {R_{y}}$	rms $R_{y}$ ($\overline {R_{y}}$)	Deviation	Dot sizes
C	269.8	11.26	0.041	268.5	7.78	0.029	265
D	302	12.27	0.040	306.43	9.46	0.031	303
L	321.5	12.72	0.039	321.31	14.08	0.043	298
R	296.5	13.37	0.045	301.62	13.09	0.043	298
U	286.5	10.81	0.037	286.68	12.13	0.042	296.7

Finally, we calculate industrial standard parameters to reveal the shape uniformity and the overall uniformity as listed in Table 1. The average size of patterned dots in five regions ranges from 270 nm to 320 nm, and the deviation is almost 4% which is approaching the applicable value of 3% in the industrial process. These result from three main reasons. The diluted PR may be unstable in the total experimental process, which can be reduced by adjusting the PR process. Another major reason is the uneven distribution of the laser came from the spatial filter. Changing the magnitude of the convergence mirror and the size of the pin hole may be a good choice. Furthermore, there is inevitable fringe vibration from the whole set. The dot size varies to a certain extent in the five regions. It results from the quality of the laser including the power and the spatial shape and the uneven light distribution from the spatial filter. With the improvement of higher quality laser and more suitable spatial filter, arrays of more uniform and larger size will be fabricated in the future. In summary, we have reported the fabrication of 2D dots in the period of 800 nm using a two-beam LIL setup in our lab. Patterns on a 4 inch substrate divided into 5 regions are investigated by SEM. Parameters $R_{x}$, $R_{y}$, $R_{x}^{\ast}$ and $R_{y}^{\ast}$ are introduced to reveal the uniformity. To better illustrate our data we simulate the laser distribution of our apparatus. They fit very well. Comparing the experimental data with the simulation, we propose the key points to gain higher uniformity. As the improvement of high quality laser and suitable spatial filter, we are capable of fabricating a more uniform and larger size periodical pattern. Two-beam LIL will make great progress in applications of device making and electronic and optical field. References Towards ultranarrow bandwidth polymer-based resonant grating waveguide structuresResonant grating waveguide structuresFabrication of 100nm metal lines on flexible plastic substrate using ultraviolet curing nanoimprint lithographyFabrication of superconducting NbN meander nanowires by nano-imprint lithographyFabricating omnidirectional low-reflection films by nano-imprinting method for boosting solar power generation of silicon-based solar cellsDirect laser writing of three-dimensional photonic-crystal templates for telecommunicationsFerroelectric thin films for micro-sensors and actuators: a reviewOrganic Thin Film Transistors for Large Area ElectronicsHexagonal pore arrays with a 50–420 nm interpore distance formed by self-organization in anodic aluminaSynthesis and characterization of Co/ZnO nanocomposites: towards new perspectives offered by metal/piezoelectric composite materialsSynthesis and self-organization of γ-Fe2O3 nanoparticles by hydrothermal chemical vapor depositionEngineering the optical response of plasmonic nanoantennasEnhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro- and nanoscale282-nm AlGaN-based deep ultraviolet light-emitting diodes with improved performance on nano-patterned sapphire substratesGaN-Based Light Emitting Diodes with Hybrid Micro-Nano Patterned Sapphire SubstrateTemperature dependence of ordered GeSi island growth on patterned Si (001) substratesHighly Ordered GeSi Quantum Dots Fabrication on Patterned Si Substrates with Gas Source Molecular Beam EpitaxyCrosstalk analysis of silicon-on-insulator nanowire-arrayed waveguide gratingA cheap and abundant alternative to Pt in fuel cells?Step and Flash Nano Imprint Lithography of 80 nm Dense Line Pattern Using Trehalose Derivative Resist MaterialHigh resolution HSQ nanopillar arrays with low energy electron beam lithographyPrefaceOptical Interference Lithography Using Azobenzene-Functionalized Polymers for Micro- and Nanopatterning of SiliconAnalysis of nano-grating-assisted light absorption enhancement in metal–semiconductor–metal photodetectors patterned using focused ion-beam lithographyPeriodic feature patterning by lens based solid immersion multiple beam laser interference lithographyInvestigation on Fabrication of Nanoscale Patterns Using Laser Interference LithographyTunable two-mirror interference lithography system for wafer-scale nanopatterningSPIE ProceedingsMicro and nano dual-scale structures fabricated by amplitude modulation in multi-beam laser interference lithographyFabrication of subwavelength periodic nanostructures using liquid immersion Lloyd’s mirror interference lithography

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