JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

An Efficient Surface Smoothing Method for Microstructures
Based on Vibration-assisted Digital Grayscale Lithography
Shengzhou Huang1,2,3, Bowen Ren2, Chengwei Jiang2, Fanglin Xie*2, Yuanzhuo Tang2, Zhaowei Tian2, Jinjin
Huang4, and Zhi Li5
1

2

School of Artificial Intelligence, Anhui Polytechnic University, Wuhu 241000, China
School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, China
3
Anhui East China Photoelectric Technology Research Institute, Wuhu 241002, China
4
Wuhu Changpeng Parts Co., LTD, Wuhu 241002, China
5
Hefei core Acer Microelectronics Equipment Co., LTD, Hefei 230000, China*Corresponding author’s e-mail: 019172@ahpu.edu.cn

In this paper, an efficient surface smoothing method for improving the microstructure quality was proposed. A
mechanical vibration-assisted smoothing microstructures surface strategy based on maskless grayscale lithography of
digital micromirror device (DMD) was developed, which can effectively improve the microstructures surface quality andalleviate the effects of DMD pixel quantization errors. The experimental results showed that the micro-lens arraymicrostructure surface roughness was reduced from 1.657 μm to 0.207 μm by the above strategy. The proposed method
will have great potential for application in the field of micro-optical components high efficiency and high precision
manufacturing.
DOI: 10.2961/jlmn.2024.02.2004
Keywords: digital micromirror device (DMD), vibration-assisted, digital grayscale lithography, microstructures, surface
smoothing
1.Introduction
With the escalating demand for the miniaturization of
optoelectronic devices, the micro-lens array microstructure has
become a crucial miniature optical device, characterized by a highsurface finish and superior optical performance [1]. This device iswidely utilized in compact imaging [2,3], sensing [4,5], biomedical[6-8], 3D display [9-12], photovoltaic [13, 14], and other fields.
Currently, methods for fabricating micro-lens structures, such as
photoresist thermal reflow [15], micro-drop injection [11,16], andlaser direct writing [17,18], are challenging to balance efficiency andcost, and are plagued by lengthy processing times, high processcomplexity, and difficulty in maintaining consistency. Digital
lithography, based on a digital micromirror device (DMD), offers
benefits such as high processing efficiency, low-cost, and excellent
flexibility [19-21]. This technology has garnered significant attention
from scholars in recent years, and is considered a new digital
lithography technology, following the single dot laser direct writing
technology.
However, due to the structural characteristics of DMD, there is a 1
μm gap between each micromirror. When the digital mask isdisplayed on the DMD, the device will sample and quantize the digitalmask based on the pixel size. The pixels of the mask graphics are not
all integer multiples, leading to non-integer pixel quantization errors
in the lithography process. This results in discrete pixels, which cangenerate dark grids, leading to rough micro-lens surfaces. To address
this issue, scholars at home and abroad have employed various
methods. These include using high magnification objectives [22, 23],
graphic staggered overlay exposures, DMD oblique scanning
lithography [24-26], or designing DMD pixel integer masks and linear
staggered imaging of micromirror arrays [27-29]. These methods havebeen employed to improve lithography resolution and consequently
reduce pixel quantization errors. While these methods have improved
the resolution of DMD digital lithography to varying degrees, they
have not eliminated the quantization error of DMD pixels. Instead,they have reduced the size of the gap between DMD discrete pixels tovarying degrees, making it challenging to achieve a smooth surface
microstructure.
In this paper, we propose a mechanical vibration-assisted method,
based on the mechanism of DMD pixel quantization errors. The
impact of pixel quantization errors is mitigated by applying periodic
vibrations to the projection objective and smearing the DMD discrete
pixels. To determine the optimal vibration parameters, a theoreticalsimulation was initially conducted. Based on the simulation data, theoptimal vibration parameters were analyzed and determined.
Subsequently, a vibration-assisted digital lithography system wasdesigned and constructed, which was subsequently experimentally
verified. The results demonstrated that this method effectively
enhances the surface quality of micro-lens array structures.
2. Design of vibration-assisted digital lithography system
2.1. Lithography system design
Fig.1 shows the basic components of the vibration-assisted digitalgrayscale lithography system schematically. Fig.1(a) shows theschematic diagram of the grayscale lithography system, which
consists of five components: illumination system, DMD graphics
control system, projection imaging system, precise stage motion
control system and mechanical vibration assistance system. In theillumination s ystem, the control s trategy of l i ght source
synchronization is adopted. It is composed of UV-LED chip, LED
constant current driver, pulse width modulation (PWM) generator,
DMD chip and DMD control board. The working frequency of PWM
generator is above 10KHZ, and the exposure brightness of lightsource can be adjusted by adjusting the duty cycle. As a spatial light
modulator, DMD can realize the dynamic update of the exposure
graph data, and control the on-off of the exposure light source throughthe real-time update data, that is, only when the graph is displayed, thesignal switch of PWM generator will be opened. In the DMD graphics
control system, the model of DLP 6500 (Texas Instruments, Texas,
USA) was utilized with a resolution of 1920×1080, a single
micromirror size of 7.56 μm and a micromirror gap of 1 μm. In the

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Fig. 2 The diagram of DMD pixel quantization error.

Tx≥ Wx ,
2

Ty
2

≥ Wy

(1)

can be represented as follows.
Since there is a certain deviation between the DMD pixel size andthe mask size, the DMD pixel error should be considered when
designing the mask size, and the error can be expressed by thefollowing formula.
Fig. 1 Schematic diagram of the basic components of a vibrationassisted digital grayscale lithography system. (a) Schematic diagramof the system. (b) Physical diagram of the system.
projection imaging system, a flat-field achromatic objective lens(Olympus, PLN4X) was utilized to project on the photoresist substrate,
which can effectively reduce the image aberration. In the precise stage
motion control system, a precise piezoelectric stage (Coremorrow,
XYZ100, E70.D3S closed loop piezoelectric controller) was adopted,
which can effectively ensure the accuracy of exposure. In themechanical vibration assistance system, it is consisting of vibration
generator (Mode U56001, 3B Scientific, Germany), function
generator (Mode FG100-1009956, 3B Scientific, Germany).
The mechanical vibration-assisted digital grayscale lithographysystems work on the following principles. Initially, a 405 nm UVLED light source emits an ultraviolet beam, which is thenhomogenized by a homogenizing collimating element. This beam issubsequently irradiated onto the DMD surface. Simultaneously, thetarget graphic information, which has been designed in advance, isuploaded to the DMD controller by the computer. The light beam isthen reflected by the DMD to form a real-time dynamic virtual mask
graphic. This graphic is scaled through the projection objective andsubsequently arrives at the 3D precise motion stage. The
photosensitive resin (Water Washable Resin, eSUN, Shen Zhen,
China) used in the experiment is cured by the polymerization reaction
under the influence of UV light [30, 31]. In the process of water
washing, the unexposed photosensitive resin will be dissolved in thewater, and the final cured photosensitive resin is retained to complete
the engraving of the graphics. Fig.1(b) shows the physical diagram ofthe built vibration-assisted digital lithography system. According to
the Rayleigh criterion, the system imaging resolution of 2.03 μm, andthe actual minimum resolution of the system measured experimentallyis 4.56 μm measured by optical microscope (DC3000, Jiangnan
Yongxin Optical Co., LTD). In the process of measurement, themeasurement accuracy is improved by averaging multiple samples.
2.2. DMD pixel quantization error
The occurrence of pixel quantization errors is shown in Fig. 2. Tx
and Ty are the width and length of the watch mask, respectively. And
Wx and Wy represent the width and length of DMD pixels,
respectively. According to the principle of DMD pixel sampling, it


Ty

 
T
∆d = 2∆d x × 2∆d y =  mod( x ) / B  ×  mod( ) / B 
W
W
x
y

 


(2)

where B represents the zoom ratio of the projection objective.
2.3. Simulation of the influence of mechanical vibration onlithography system
The technical route of the specific method of applying vibration to
the projection objective is as follows. Firstly, Abaqus finite element
analysis (FEA) software was used for theoretical simulation to study
the effect of periodic sinusoidal mechanical vibration on DMD
lithography quality, so as to determine the optimal vibration
frequency-amplitude parameters as the initial experimental parameters.
Next, the experimental verification is carried out by digital gray-scale
lithography system. The specific experimental process is as follows: A
micro-lens digital mask consisting of 256 rings of grayscale from 0255 is produced; After inputting the digital mask version information
into the DMD, the DMD is switched on via the DMD graphics control
software. Since the DMD maskless lithography system is designedwith the light source pre-linked to the DMD switch, the UV-LED
light source is switched on at the same time as the DMD is switchedon; Finally, the vibration generator is switched on to cause theprojection objective to move periodically to coat the discrete pixels
according to a set function; After exposure, the substrate is washedand dried and the surface quality of the micro-lens is measured. If theresults are not very good, further vibration parameter adjustment andoptimization can be carried out to obtain the best combination ofvibration parameters.
The influence of the vibration direction of different projection
objectives on the image quality is studied by finite element simulation,that is, the unidirectional vibration direction and the diagonal
vibration direction relative to the projection region, as shown in Fig. 3.
From Fig.3(a) and 3(c), it is evident that the unidirectional vibration
has an uneven impact on the X and Y directional displacements.
Furthermore, the diagonal vibration can simultaneously affect discrete
pixels in the X and Y directions. Fig.3(b) and 3(d) were the effects ofdifferent frequencies and amplitudes on the displacements,
respectively. The results showed that the frequency has a great
influence on the displacement. When the frequency is close to 160 Hz,
the X and Y displacement are 0.23 μm, and the displacement size justcovers the DMD micromirror gap, which provides a reference for the
next experimental parameter setting. Here, it should be noted that inJLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024

Fig. 3 Simulation of mechanical vibration acting on projection
objective. (a) Unidirectional vibration, effect of frequency on
displacement. (b) Diagonal vibration, effect of frequency on
displacement. (c) Unidirectional vibration, effect of amplitude on
displacement. (d) Diagonal vibration, effect of amplitude on
displacement.
Fig.3(a) and 3(b), the ordinate X/Y displacement unit is micron.
Although there are fluctuations, the difference is very small, and the
maximum fluctuation is not more than 100 nm. This irregularfluctuation may be caused by the interaction of many factors in thesystem, such as the resonance effect of the system vibration frequency
and the nonlinear response of the system. The main purpose of thissimulation study is to show that diagonal vibration is significantly
better than unidirectional vibration. The simulation results illustrate
the effect of mechanical vibration on the exposure pattern, serving asa guide for uncovering the mechanism of vibration-assisted digital
lithography-based DMD pixel quantization error elimination.
The change of surface quality of micro-lens before and after
vibration was further quantitatively characterized by experimental
verification. During the lithography process, the unidirectional linear
motion of the vibration generator driving rod is firmly connected tothe projection objective. The projection objective is controlled by thefunction generator, and the sinusoidal function mode is selected todrive the projection objective to control the projection UV pattern.
The vibration is carried out in a diagonal direction along the
projection area. According to the simulation results, it is obvious thatthe amplitude parameter of the vibration generator has a minimal
impact on the results. The experimental verification has also been
conducted, which demonstrates that the influence of amplitude on theroughness and shape of the micro-lens is negligible. Therefore, theamplitude was set at 1V.
3. Experimental verification
To verify the influence of the vibration direction mentioned in thesimulation on the experimental results, the lithography experiments ofunidirectional vibration and diagonal vibration were carried out, asshown in Fig.4. It’s obviously from the Fig.4(a) and 4(b), thedistortion of unidirectional (X/Y) vibration is the largest, while
thedistortion of diagonal vibration is the smallest shown in Fig.4(d),which is closest to the original no vibration experimental data in
Fig.4(c). Moreover, the experimental results are also consistent withthe previous simulation results. The distortion mentioned in this paper
refers to the distortion of the exposure pattern under the action ofFig. 4 The experimental results of both unidirectional vibration anddiagonal vibration. (a) X direction; (b) Y direction; (c) No vibration;(d) Diagonal vibration.
unreasonable vibration parameters. Although the roughness can besignificantly reduced at this time, this result is not what we expected.
Therefore, through detailed experimental and simulation research, thepurpose of this paper is to find the best and reasonable vibration
parameters (frequency and amplitude) to ensure that the roughness iseffectively reduced and the graphics are not distorted. The coretechnology is to apply the DMD discrete pixel gap through theauxiliary effect of mechanical vibration. For unreasonable vibration, it
will cause serious deformation of the exposed MLA, which will affectits imaging quality, optical efficiency, and other problems.
To determine the optimal vibration parameters, an array of nine
micro-lens (3×3, each lens diameter: 380 μm) was made, withfrequencies gradually increasing from 0-400. The corresponding
displacement was characterized by measuring the central offset of the
micro-lens and the corresponding roughness was measured, as shownin Fig. 5. It is evident that when the frequency is 50 Hz, the center
shift of the micro-lens is the largest, which is due to the low frequency
and high amplitude currently, leading to graphics distortion. At thefrequency of 150 Hz, the roughness is the smallest, which is close to
the simulation result of 160 Hz. As the frequency continues toincrease, the roughness and lens central offset increase, this is becausethat higher frequencies result in smaller amplitudes and the resulting
vibrations are insufficient to smear the discrete pixels and smooth themicro-lens surfaces. Therefore, the optimal vibration frequency wasset as 150 Hz.

Fig. 5 Effect of vibration frequency on the central offset androughness of micro-lens arrays by experiments.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024
the micro-lens. Compared with the existing DMD pixel error
optimization methods, the mechanical vibration-assisted method
ensures high fidelity and high surface quality of the micro-lensstructure, which has significant industrial applications.
Acknowledgments
This work was supported by funding from the National Natural
Science Foundation of China (62305001), Key Study anddevelopment program of Anhui Province (2022a05020008), Natural
Science Foundation of Anhui Province (2308085MF210,
2008085QE258), Major Project of Natural Science Study in
Universities of Anhui Province (2022AH040138), China Postdoctoral
Science Foundation (2022M710175), Open Project of Special Display
and Imaging Technology Innovation Center of Anhui Province(2022AJ05002), Research activities of postdoctoral researchers in
Anhui Province (2023B707), the Anhui Province college young andmiddle-aged teachers training action project (JNFX2023015), theAnhui Polytechnic University Graduate Education Innovation Fundand the New Era Education Quality Project (Postgraduate Education).

Fig. 6 Morphology and roughness of the micro-lens array before andafter vibration. (a) The optical microscope morphology image before
vibration. (b) The optical microscope morphology image after
vibration. (c) A local magnification of any region of the micro-lens of(a). (d) A local magnification of any region of the micro-lens of (b).
(e) A 3D view of the micro-lens roughness before vibration. (f) A 3Dview of the micro-lens roughness after vibration.
Fig.6 showed the measured morphology and roughness of the
micro-lens array. Fig.6(a) and 6(b) showed the optical microscope
image of the measured micro-lens array before and after vibration,
respectively. It can be obviously seen that the surface quality of the
micro-lens after vibration is better than that before vibration. Fig. 6(c)and 6(d) are the local magnifications of Fig.6(a) and 6(b), respectively,
which can be clearly seen that the surface of the micro-lens after
vibration is smoother than that before vibration. To further
characterize the surface quality of micro-lens quantitatively, 3D
optical profilometer (PS50, Nanovea company) was used to measure
the surface roughness, as depicted in Fig.6(e) and 6(f). The roughness
measured represents the average roughness value of the measured
middle region. Here, the selected middle region is an optional region
on the MLA after processing, and there is no specificity. And because
the middle region of the microlens is an important region that affects
the quality of optical imaging, it is also an important reason to choose
the middle region. In the actual experiment, several regions were also
selected for measurement. Because the 3D optical profilometer used
could not measure the roughness in a large range, the roughness
measurement effect in the paper was finally presented in a small range(50 μm x 50 μm). The roughness values of each region are also very
close. The experimental results showed that the surface roughness canbe obviously reduced from 1.657 μm to 0.207 μm after applying
vibration, a reduction of about 88%. Consequently, the surface qualityof the micro-lens array can be significantly enhanced after theapplication of mechanical vibration, thereby validating theeffectiveness of the proposed method.
4. Conclusions
In summary, we propose an efficient and cost-effective method toeliminate the effects of pixel quantization errors and to improve thesurface quality of microstructure. By applying mechanical vibration to
the projection objective, the DMD discrete pixel gap can be coatedand the roughness is reduced by 88% while ensuring no distortion ofReferences[1] A. Camposeo A, L. Persano, M. Farsari, and D. Pisignano: Adv.
Opt. Mater., 7, (2019) 1800419.
[2]

M. Sieler, P. Schreiber, and A. Bräuer: Proc. SPIE, Vol. 8643,(2013) 86430B.

[3]

S.H. Hong, J.S. Jang, and B. Javidi: Opt. Express, 12, (2004)
483.

[4]

S. Kim, H. Kim, and S. Kang: Opt. Express, 12, (2004) 483.

[5]

F. Zhang, Q. Yang, H. Bian, F. Liu, M. Li, X. Hou, and F. Chen:
IEEE Photonic. Tech. L., 32, (2020) 1327.

[6]

L. J. Wang, R. Sun, T. Vasile, Y. C. Chang, and L. Li: Anal.
Chem., 88, (2016) 8302.

[7]

L.J. Wang, Y.C. Chang, R. Sun, and L. Li: Biosens. Bioelectron.,87, (2017) 686.

[8]

A. Hassanfiroozi, Y.P. Huang, B. Javidi, and H.P.D. Shieh: Opt.
Express, 24, (2016) 8527.

[9]

X.Q. Liu, L. Yu, S.N. Yang, Q.D. Chen, L. Wang, S. Juodkazis,and H.B. Sun: Laser & Photonics Reviews, 13, (2019) 1800272.

[10] S.I. Bae, K. Kin, S. Yang, K.W. Jang, and K.H. Jeong: Opt.
Express, 28, (2020) 9082.
[11] X. Zhou, Y. Peng, R. Peng, X. Zeng, Y.A. Zhang, and T. Guo:ACS Appl. Mater. Interfaces, 8, (2016) 24248.
[12] L. Meng, Y. Zhang, X. Wan, C. Li, X. Zhang, Y. Wang, X. Ke,
Z. Xiao, L. Ding, R. Xia, H.L. Yip, Y. Cao, and Y. Chen:
Science, 361, (2018) 1094.
[13] Y. Xing, X.Y. Lin, L.B. Zhang, Y.P. Xia, H.L. Zhang, H.Y. Cui,
S. Li, T.Y. Wang, H. Ren, D. Wang, H. Deng, and Q.H. Wang:
Opto-Electron. Adv., 6, (2023) 220178.
[14] R.E. Alsaigh, R. Bauer, and M.P.J. Lavery: Opt. Express, 28,(2020) 31714.
[15] V. Grigaliūnas, A. Lazauskas, D. Jucius, D. Viržonis, B.
Abakevičienė, S. Smetona, and S. Tamulevičius: Microelectron.
Eng., 164, (2016) 23.
[16] J. Li, W. Wang, X. Mei, D. Hou, A. Pan, B. Liu, and J. Cui:ACS Appl. Mater. Interfaces, 12, (2020) 8870.

JLMN-Journal of Laser Micro/Nanoengineering Vol. 19, No. 2, 2024
[17] T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen: Nat.
Photonics, 10, (2016) 554.
[18] H. Zhang, F. Yang, J. Dong, L. Du, C. Wang, J. Zhang, C.F.
Guo, and Q. Liu: Nat. Commun., 7, (2016) 13743.
[19] Z. Xiong, H. Li, P. Kunwar, Y. Zhu, R. Ramos, S. Mcloughlin,
T. Winston, Z. Ma, and P. Soman: Biofabrication, 11, (2019)035005.
[20] P. Kunwar, Z. Xiong, Y. Zhu, H. Li, A. Filip, and P. Soman:
Adv. Opt. Mater., 7, (2019) 900656.
[21] M. Kang, C. Han, and H. Jeon: Optica, 7, (2020) 1788.
[22] Y.M. Ha, I.B. Park, H.C. Kim, and S.H. Lee: Int. J. Precis. Eng.
Man, 11, (2010) 335.
[23] J. Choi, G. Kim, W.S. Lee, W.S. Chang, and H. Yoo: Opt.
Express, 30, (2022) 22487.
[24] J. Lee, H. Lee, and J. Yang: J. Mech. Sci. Tech, 32, (2018) 2209.
[25] R. Chen, H. Liu, H. Zhang, W. Zhang, J. Xu, W. Xu, and J. Li:
Opt. Express, 25, (2017) 21958.
[26] S. Huang, L. Wang, Y. Zheng, F. Wang, and Y. Su, Appl. Phys.
Express, 13, (2020) 116501.
[27] Y. Sun, H. Liu, J. Li, Z. Lu, Y. Zhang, and Y. Luo: Acta
Photonica Sinic., 48, (2019) 0411002.
[28] S. Guo, Z. Lu, Z. Xiong, L. Huang, H. Liu, and J. Li: Opt. Lett,
46, (2021) 1377.
[29] Y. Zhang, J. Luo, Z. Xiong, H. Liu, L. Wang, Y. Gu, Z. Lu, J.
Li, and J. Huang: Opt. Express, 27, (2019) 31956.
[30] Z. Huang, G. Shao, and L. Li: Prog. Mater. Sci., 131, (2023)
101020.
[31] L. Huang, C. Liu, H. Zhang, S. Zhao, M. Tan, M. Liu, Z. Jia, R.
Zhai, and H. Liu: Opt. Laser Technol., 157, (2023) 108666.

(Received: October 22, 2023, Accepted May 15, 2024)