Acta Polytechnica https://doi.org/10.14311/AP.2025.65.0406 Acta Polytechnica 65(4):406–419, 2025 © 2025 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague IMPROVING THE PRODUCTION PROCESS OF SILICON NANOPARTICLE AND QUARTZ MICROLENS Muaath J. Mahmouda,∗, Bassam G. Rasheedb, Muammel M. Hanonc,† a Scientific Research Commission, Jadriyah, 10070 Baghdad, Iraq b Al-Nahrain University, College of Engineering, Laser & Optoelectronics Engineering Department, Jadriyah, 10072 Baghdad, Iraq c Middle Technical University, Baquba Technical Institute, Muasker Al Rashid Street, 10074 Baghdad, Iraq ∗ corresponding author: muaathjamal@yahoo.com † corresponding author: muammel.m.hanon@mtu.edu.iq Abstract. This study presents a comprehensive investigation into advanced laser micro/nano machining techniques, utilising three distinct laser sources: a Q-switched Nd:YAG laser, a fibre laser, and a CO2 laser. Notably, the creation of remarkably stable silicon nanoparticles was achieved, opening up promising avenues for new applications. The potential of quartz sheets was exploited to produce spherical microlens arrays, thereby demonstrating the precision of optical element engineering. The distribution of surface and subsurface temperatures for both silicon and quartz materials during laser processing was determined through an in-depth thermal analysis facilitated by COMSOL software. Notably, peak temperatures of 5 700 K and 2 630 K were achieved for silicon and quartz, respectively, highlighting the effectiveness of the laser methodologies employed. Numerical optimisations were conducted using Design of Experiments (DOE) software to enhance silicon nanoparticle production, yielding nanoparticles with a remarkable stability parameter of 33.5 mV. Furthermore, notable outcomes were achieved in the production of quartz microlenses with a numerical aperture of 0.494 and a surface roughness of 4.5 nm. The controllable and precise nature of the laser micro/nano machining techniques enables applications in optoelectronics and advanced biological imaging. The exceptional properties of the engineered silicon nanoparticles and microlens arrays demonstrate their potential across various scientific and technological domains. Keywords: Quartz microlens, silicon nanoparticles, laser microprocessing, box Behnken design, ANOVA analysis. 1. Introduction Over the past decade, there has been significant atten- tion and research efforts surrounding the laser micro- processing of brittle materials, including glass, ceram- ics, and semiconductors [1]. This pivotal technology is crucial in producing precise parts and components used across various industries, such as electronics, op- toelectronics, and aerospace engineering [2]. One of the challenges in laser microprocessing of brittle ma- terials is the tendency of these materials to crack and fracture under stress [3]. This can occur due to ther- mal stress generated by heat from laser absorption, as well as mechanical stress. To minimise the risk of cracking and other forms of damage, laser parame- ters, such as pulse duration, intensity, and wavelength, must be carefully chosen [4]. Silicon has been extensively studied due to its crit- ical role in modern electronics and semiconductor applications [5]. It serves as a fundamental substrate material for various electronic devices. In both solar cells and other semiconductor components, crystalline and amorphous silicon are widely used [6]. Silicon nanoparticles (NPs) are also widely used in photo- voltaics, optoelectronics, biomedical applications, and energy storage due to their environmentally friendly nature, high surface-area-to-volume ratio, tunable op- tical properties, and biocompatibility [7]. However, they are susceptible to oxidation, present synthesis challenges, and exhibit low electrical conductivity. On the other hand, glass microstructures are used in many fields, such as biomedicine, biochemistry, lab-on-a-chip devices, sensors, and hydrophobic ap- plications, glass machining, therefore, attracts much attention [8]. There is a significant demand for high- tech macro products for applications in biotechnol- ogy, microelectronics, telecommunications, microelec- tromechanical systems (MEMS), and medical sector. Quartz microlenses, in particular, play a vital role in fibre optic communications, imaging and sensing, laser processing, and lithography due to their broad optical transmission (UV to IR), high thermal stabil- ity, and low optical loss. Despite these advantages, their widespread adoption is sometimes hindered by the complexity of production, high production costs, and the material brittleness [9]. Response surface methodology (RSM) is also known as the Box-Wilson Methodology. Surface methodology responses are a set of statistical and mathematical 406 https://doi.org/10.14311/AP.2025.65.0406 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . Name Symbol Range UnitNd:YAG laser Fiber laser CO2 laser Wavelength λ 1 064 nm 1 064 nm 10.6 µm nm Energy E 0.1–2 - - J Beam diameter D 1 0.1 2 mm Pulse duration τ 10 130 - ns Repetition rate R 6 30 000 - Hz Power P - 0.1–30 0.1–100 W Laser speed s - 10–1 000 1–6 mm s−1 Operation mode O pulse pulse CW - Table 1. Laser parameters. techniques used to model and analyse problems for which the answer is influenced by a variety of variables. The RSM ties a response or result variable (output) to the data (input) that influences it. If an area with an ideal response is discovered, the model is modified to connect to that area so that the analysis can be performed to determine the optimal area. The RSM must be used in the correct sequence according to the method used [10]. Tewari et al. [11] investigated the quality of holes in laser-drilled kenaf/high-density polyethylene com- posites by measuring the kerf taper angle, the size of the heat-affected zone, and the surface roughness. They used microwave-assisted compression moulding to create composites with 20 wt. % kenaf fibre and investigated the effects of laser power and cutting speed. A central composite design produced a mini- mum kerf taper of 0.056° and a surface roughness of 3.83 ± 0.19 µm at 120 W and 2 mm s−1. A regression model demonstrated a high level of agreement with the experimental data, with errors of less than 5.35 %, validating the method’s suitability for precision ma- chining. Theeda et al. [12] studied industrial ultrafast lasers with pulse durations ranging from 300 fs to 10 Ps, powers of up to 150 W, and pulse energy of 10–250 µJ for precision micro-machining. Their research exam- ines the influence of major laser settings on machining speed and quality. It provides recommendations for optimisation based on experimental data for 25 mate- rials. Furthermore, they examine the ultrafast laser business and its industrial uses. Zheng et al. [13] investigated the use of picosecond laser for drilling carbon-fibre reinforced polymer machining and found that it outperformed existing approaches in terms of reducing heat-affected zones and improving the hole quality. Using the RSM, they optimised laser parame- ters, attaining a hole wall taper of 4.160° and a HAZ of 18.577 µm. Experimental validation showed negligible variance, proving the technique’s industrial viability for high-tech applications. In this paper, the experimental and theoretical in- vestigations were carried out to optimise the laser micro/nano processing of brittle materials by apply- ing three lasers to silicon and quartz substrates to synthesise silicon nanoparticles and produce quartz microlens. Additionally, incorporating Box Behnken design and ANOVA analysis together with Design of Experiments (DOE) software offers a unique and systematic approach to optimising the production of silicon nanoparticles and quartz microlenses [14]. This comprehensive methodology not only expands the understanding of the underlying processes but also enables precise control over the final properties of the synthesised nanoparticles and microlens arrays, thus paving the way for more efficient and tailored applications in optoelectronics and biological imaging. 2. Experimental methodology A Q-switched Nd:YAG laser (1 J pulse laser, China) was used on a pure p-type <100> silicon wafer with dimensions of 20 mm × 20 mm × 500 µm. The fibre (SM-30W, China) and CO2 lasers (CO2 laser work station, PI MICOS, Germany) were used on a quartz sheet with dimensions of 10 mm × 10 mm × 1.1 mm in the first and second stages, respectively. All laser parameters are given in Table 1. Before commenc- ing any processing procedures, the silicon wafer and quartz sheets were cleaned in an ultrasonic bath us- ing an ultrasonic device, using ethanol and distilled water as cleaning agents. Ethanol was selected for cleaning the silicon wafer due to its effectiveness in ensuring the required surface cleanliness while provid- ing a milder cleaning method. Its rapid evaporation helps minimising water-related contamination and de- fects, making it a suitable choice for precision cleaning. Although Radio Corporation of America (RCA) clean- ing is commonly used to remove both organic and inorganic contaminants, ethanol was preferred for its efficiency in eliminating organic residues and its ease of handling. Laser ablation is a process involving the expulsion of material as a result of the generation of a signif- icantly elevated vapour pressure [7]. Laser ablation of solid targets in liquids (LAL) is a very effective way to make nanoparticles because it is easy to con- trol and does not harm the environment. It pro- vides significant protection against potential contam- ination during the production of nanoparticles [15]. The pulse laser ablation in liquid (PLAL) process successfully synthesised silicon nanoparticles in an 407 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica Figure 1. Optimisation procedure for silicon nanoparticles and quartz microlens. Nd:YAG laser Fiber laser CO2 laser Energy [J] Silicon Surface Power [W] Quartz Surface Power [W] Quartz Surface Temp. [K] Temp. [K] Temp. [K] 0.1 569 1 190 1 415 0.2 1 137 4 760 2 825 0.4 2 275 7 1 320 4 1 650 0.6 3 411 13 2 480 6 2 480 0.8 4 548 19 3 590 8 3 300 1 5 685 22 4 150 10 4 130 Table 2. The surface temperature of silicon wafers and quartz sheets depending on the applied laser. aqueous medium through a two-step procedure. Ini- tially, the silicon wafer was carefully positioned within a plastic container, which was subsequently filled with a precise volume of 2.5 millilitres of deionised wa- ter (DW). Next, the wafer was subjected to a con- trolled exposure of 300 laser pulses. In the subsequent stage, the suspension underwent exposure to a fibre laser for 10 minutes, producing reduced-size silicon nanoparticles. The production of quartz microlenses involved a two-step procedure. Firstly, a fibre laser with a galvanometer system was used to selectively eliminate material from the sheet’s surface with pre- determined laser parameters. The subsequent stage involves using a CO2 laser beam to modify the sur- face of the quartz sheet, resulting in the formation of polished, spherical microlenses. The high-resolution optical microscope (OLYMPUS BX60M) was used to analyse the interaction between the silicon wafer and the quartz sheet. The acquired optical microscope images were then stored, and the dimensions of the produced microlenses were measured using the ImageJ software. The absorption spectrum in the 300–700 nm wavelength range was conducted using an optical ab- sorption spectrometer (Metrech SP8001). Finally, the residual colloidal solution was transferred to a quartz tube for zeta potential analysis silicon NP stability using (Brookhaven-USA). 3. Results and discussion A comprehensive examination of the fabricated silicon nanoparticles and microlenses involved both empirical investigation and mathematical models. The procedures of all steps are shown in Figure 1. The first one is related to the material (silicon and quartz) properties, and calculating the temperature generated at the surface and beneath the surface of each material when a laser is applied. After setting the laser range and other parameters in the DOE software, the experimental began, during which the optimisa- tion process in the software took place. In the final step, the optimisation parameters were determined for future processing. 3.1. Theoretical calculations The material is heated, melted, and evaporated when the laser beam is applied because the target’s surface absorbs the energy of the laser [16]. The melting point of silicon is 1 687 K, while its vaporisation point is 3 538 K [17]. According to measurements, the melting and vaporisation points of quartz are 1 923 K and 2 503 K, respectively [18]. The high energy density of the laser causes the surface temperatures of silicon and quartz to rapidly raise after just a brief moment of exposure to the laser beam. The surface temperature for each material can be calculated theoretically using the relationship [19]: T = α × F × A p × cp , (1) where α is the absorption coefficient [cm−1], F is the energy density [W A−1], A is the absorptivity [ litres mole cm ], p is the density, and cp is the specific heat [J kg−1 °C−1]. Table 2 presents the relationship be- tween the laser energy/power and surface temperature 408 vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . for silicon and quartz, derived from theoretical cal- culations using Equation (1), where the laser energy varies in order to determine the corresponding surface temperature. In order to theoretically model the laser’s interac- tion with the silicon and quartz, the COMSOL 6.1 program was used [20]. Figure 2 displays the geom- etry and mesh for each model. Figure 2a shows the silicon wafer geometry with a point heat source in the centre (Nd:YAG laser source) with mesh parameters: maximum element size, minimum element size, maxi- mum element growth rate, curvature factor, and the resolution of the narrow region: 7.0 × 10−5, 3 × 10−6, 1.35, 0.3, and 0.85, respectively. Moreover, Figure 2b depicts the quartz wafer geometry with a point heat source in the centre (fibre laser source) with mesh pa- rameters: maximum element size, minimum element size, maximum element growth rate, curvature factor, and the resolution of the narrow region: 5 × 10−5, 5 × 10−6, 1.3, 0.2, and 1, respectively. Figure 2c dis- plays the quartz wafer geometry with a point heat source in the centre (CO2 laser source) with mesh pa- rameters: maximum element size, minimum element size, maximum element growth rate, curvature factor, and the resolution of the narrow region: 4 × 10−5, 4 × 10−6, 1.3, 0.2, and 1, respectively. Surface and sub-surface temperatures are simulated in the model for silicon and quartz, as shown in Fig- ure 3. Figures 3a, 3c and 3e show the temperature of silicon and quartz at different time intervals (1 ns, 0.1 s, and 0.1 s) for Nd:YAG, fibre, and CO2 lasers, respectively. As illustrated in Figure 3, the temper- ature of the silicon surface is approximately 5 700 K. In contrast, the temperature of the quartz surface is approximately 2 630 K for the fibre laser and 2 140 K for the CO2 laser, as shown in Figures 3a, 3c and 3e. Due to silicon’s strong absorption rates of 1 064 nm, it requires low energy with a short time to achieve the ablation process. This occurs because the laser energy used in the experiment is comparable to the bandgap energy of silicon (1.12 eV), which enables the excitation of electrons from the valence band to the conduction band. As a result, increased absorption, photocarrier generation, and material modifications take place, facilitating the ablation process. In con- trast, quartz has a low absorption rate of 1 064 nm, requiring higher power and a longer duration for abla- tion. Unlike the CO2 laser/quartz interaction, where the laser power is sufficient to heat the quartz due to its strong absorption of 10.6 µm [21]. Figures 3b, 3d and 3f show that the Nd:YAG and fi- bre lasers immediately heated the surface and the area beneath it immediately, whereas the CO2 laser oper- ating continuously heated the entire quartz surface and the area beneath it over a longer period. In addition, as illustrated in Table 3, the surface temperature of each material at various time points was determined by executing the model in the COM- (a). Silicon irradiated by Nd:YAG laser. (b). Quartz irradiated by fibre laser at first stage. (c). Quartz irradiated by CO2 laser at final stage. Figure 2. The model geometry, mesh, and heat source for materials irradiated by lasers. SOL software. The results indicate that laser micro- processing begins instantly when lasers are applied to silicon and quartz surface areas. 3.2. The irradiation area Figure 4 shows the irradiation areas of a silicon wafer that were irradiated using an Nd:YAG laser and a quartz sheet that was first irradiated using a fi- bre laser and then using a CO2 laser. The observation has revealed that the shape of the interaction region on the silicon surface exhibits a remarkable resem- blance to a sphere. As depicted in Figure 4a, the diameter of the interaction area is 800 µm. The in- teraction area for quartz, as depicted in Figure 4b, exhibits spherical morphologies with a diameter of 200 µm. The variation in diameter among the shapes can be attributed to the disparity in the spot size for each laser type. The Nd:YAG laser has a spot size of 2 mm, while the fibre laser has a spot size of 0.1 mm. 409 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica (a). Thermal distribution at the surface of Si. (b). Sub-surface temperature of Si. (c). Thermal distribution at the surface of quartz. (d). Sub-surface temperature of quartz at first stage. (e). Thermal distribution at the surface. (f). Sub-surface temperature of quartz at second stage. Figure 3. The theoretical model of silicon and quartz irradiated by Nd:YAG laser and fibre laser, followed by CO2 laser, respectively. Silicon Nd:YAG laser Time [ns] Tmax [K] 1 835 2 1 377 3 1 919 4 2 460 5 3 002 6 3 544 7 4 049 8 4 626 9 5 166 10 5 700 Quartz Time [s] Fiber laser CO2 laser Tmax [K] Tmax [K] 0.1 2 200 1 345 0.2 2 250 1 600 0.3 2 300 1 725 0.4 2 350 1 825 0.5 2 400 1 900 0.6 2 450 1 960 0.7 2 500 2 015 0.8 2 545 2 060 0.9 2 590 2 100 1 2 630 2 140 Table 3. Silicon and quartz maximum surface temperature as a function of time. 410 vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . (a). Silicon. (b). Quartz. Figure 4. The optical microscope image of the interaction area of: silicon and quartz. 3.3. Statistical analysis and numerical optimization The box Behnken design (BBD) was used to inves- tigate the effects of three independent input vari- ables [22], energy, pulse rate, and pulse width of an Nd:YAG laser on a silicon wafer. Additionally, a quartz sheet was used to determine the impact of laser intensity, exposure time, and speed, which are input parameters of a fibre laser, followed by a CO2 laser for the first and second stages. The effect of various input parameters on the output parameters was analysed using an ANOVA. Different input parameters were used to measure various results in each experiment to make an error-free mathemati- cal model that connects input variables to outcome responses. The response was predicted using a gen- eral quadratic equation for varying amounts of each constituent, as shown by [23]: y = γo + n∑ i=1 γixi + n∑ i=1 γiix 2 i + ∑ i ∑ j γijxixj + E, (2) where γo is a constant number, n is the parameter number, γi is a linear coefficient, γii is a quadratic coefficient, γij is a coefficient of laser-material inter- action, and E is the parameter error. The optimisation process includes the combination of various components that were used in combina- tion [24]. The utilisation of numerical optimisation holds significant importance within the Design of Ex- periments (DOE) software domain [25, 26]. 3.4. Silicon nanoparticles According to the experimental plan in Tables 4 and 5, silicon nanoparticles were subjected to many tests using the Design Expert 12 software. The Design of Experiments (DOE) approach is a valuable tool in engineering research, as it systematically determines optimal values by analysing the relationship between the input and output parameters. The first step in- volves selecting the input parameters and defining their respective ranges. The software then arranges these parameters using a specific algorithm, allowing for a structured experimental design. In the experi- mental step, the corresponding output parameters are obtained and recorded based on the arranged input values. Table 4 presents the experimental results for silicon nanoparticles, where the input parameters include the laser energy, the number of pulses, and the pulse repetition rate (PRR). The lower and upper values for laser energy are 100 and 500 mJ, respectively, while the number of laser pulses ranges from 10 to 90. Sim- ilarly, the PRR values range from 1 to 5 Hz. The output parameters measured are the peak wavelength and the absorption peak. This structured experimen- tal design ensures a comprehensive analysis of the relationship between the laser parameters and the silicon nanoparticles. The graphical representation of Table 4 is shown in Figure 5 and Figure 6. Figure 5 shows a three-dimensional graph of the peak wavelength at 1–5 PRR. The max. and min. peaks were 396 and 327 nm, respectively. Increased laser energy resulted in the creation of smaller sili- con nanoparticles, most likely due to more intense ablation dynamics and greater energy densities that promote finer fragmentation of the material. Addi- tionally, a blue shift was observed. Figure 6 shows a three-dimensional graph of the absorption peak at 1–5 PRR. The max. and min. ab- sorption peaks were 0.389 and 0.038, respectively. An increase in the number of laser pulses leads to a higher concentration of silicon nanoparticles in the suspen- sion, as repeated irradiation enhances the ablation rate and cumulative material removal. This elevated nanoparticle concentration contributes to stronger op- 411 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica Run Input parameters Output parameters A: Energy [mJ] B: No. of Pulses C: PRR [Hz] Wavelength [nm] Absorbance 1 500 50 5 332 0.237 2 300 50 3 364 0.151 3 100 50 5 381 0.091 4 500 90 3 331 0.389 5 300 50 3 365 0.156 6 100 50 1 396 0.089 7 300 10 5 388 0.164 8 300 50 3 365 0.156 9 300 10 1 376 0.038 10 300 50 3 367 0.160 11 300 90 5 342 0.312 12 100 90 3 356 0.221 13 500 10 3 327 0.056 14 500 50 1 346 0.226 15 100 10 3 376 0.039 16 300 50 3 367 0.152 17 300 90 1 362 0.291 Table 4. Effects of laser energy, the number of pulses, and (PPR) on the peak wavelength and absorption as determined by the DOE software. Run Input parameters Output parameter A: Time [month] B: Energy [mJ] C: No. of Pulses Zeta Potential [mV] 1 2 300 500 19.08 2 2 100 100 31.43 3 1 200 500 27.21 4 2 200 300 25.65 5 1 200 100 32.72 6 3 300 300 20.45 7 1 300 300 27.76 8 2 300 100 24.29 9 3 100 300 22.6 10 2 200 300 25.61 11 2 200 300 25.68 12 3 200 500 20.09 13 2 200 300 25.64 14 1 100 300 32.51 15 3 200 100 24.03 16 2 200 300 25.62 17 2 100 500 25.6 Table 5. Effects of aging time, laser energy, and the number of pulses on the stability as determined by the DOE software. tical absorption within the medium, due to increased scattering and interaction of the laser beam with the suspended particles. The quadric equation that should be used to eval- uate the peak wavelength (λ) and absorption (A) of silicon nanoparticles, as shown below: λ = 399.117 + 0.0081E + 0.2828N + (−11.1875)R + 0.0008E × N + 0.0006E × R + (−0.1)N × R + (−0.0003)E2 + (−0.0045)N2 + 2.2813R2, (3) A = − 0.0201 + 0.0002E + 0.0005N + 0.0024R + 4.7187 × 10−6 × E × N + 5.625 × 10−6 × E × R + (−0.0003)N × R + (−2.5312) × 10−7 × E2 + 1.898 × 10−5 × N2 + 0.0037R2, (4) where E is the laser energy [J], N is the No. of laser pulses, and R is PRR [Hz]. The final regression equations were also an excellent way to predict and study how the parameters affect each other. 412 vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . (a). PRR: 1. (b). PRR: 3. (c). PRR: 5. Figure 5. The wavelength peak curve for No. of pulses and energy at PRR: 1, 3, and 5. (a). PRR: 1. (b). PRR: 3. (c). PRR: 5. Figure 6. The absorption peak curve for energy and No. of pulses at PRR: 1, 3, and 5. 413 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica The optimum values of the output parameters for Table 4 are shown in Figure 7. Figure 7 illustrates the optimal values of the out- put response for Si NPs. When using the Nd:YAG laser, it was observed that the optimal wavelength for peak absorption was 318.5 nm, with a corresponding absorption value of 0.389. The stability of silicon nanoparticles was examined using a separate software package, as stability analysis requires different computational methods compared to wavelength and absorption measurements. Table 5 presents the stability analysis of silicon nanoparticles, where the input parameters include aging time, laser energy, and the number of pulses. Each output pa- rameter is influenced by different input parameters, ensuring a comprehensive evaluation of stability un- der varying conditions. The lower and upper aging time values are 1 and 3 months, respectively. The lower and upper values of the laser energy are 100 and 300 mJ, respectively. The lower and upper number of laser pulse values are 100 and 500 pulses, respectively. Moreover, the output parameter is the stability of Si NPs. A graphical representation of Table 4 is shown in Figure 8. Figure 8 shows a three-dimensional graph of the high stability at 100–300 pulses. The max. and min. stability values were 31.43 and 19.08 mV, respectively. Large silicon nanoparticles were formed due to the aggregation effect when the laser energy was high with a low laser pulse number. The stability value decreased when the laser energy increased. Equa- tion (5) is the quadratic equation that should be used to evaluate stability: Z = 47.5541 + (−8.2525)T + (−0.02702)E + (−0.01572)N + 0.0065T × E + 0.0019625T × N + 7.5 × 10−6 × E × N + 0.5588T 2 + (−3.4875) × 10−5 × E2 + (−4.15625) × 10−6 × N2, (5) where Z is the Zeta Potential [mv], T is the aging time [months], E is the laser energy [J], and N is the number of laser pulses. The final regression equation was also an excellent way to predict and study how the parameters affect each other. The optimum values of the output param- eters for Table 4 are shown in Figure 9. Figure 9 shows the optimum value of the output response (stability) for silicon nanoparticles. When Nd:YAG laser was used, the optimum stability value was 33.5 mV. 3.5. Quartz microprocessing 3.5.1. Microlens fabrication The fabrication of quartz microlens can be accom- plished by two subsequent stages: material removal by fibre laser and the reshaping process by CO2 laser. The parameters used in the Design Expert software (a). Wavelength peak. (b). Absorption peak. Figure 7. The contour graph of optimum value for silicon NPs. for the experimental stage are presented in Table 6. In this study, all input parameters, including power, speed, and count, were experimentally determined to analyse their influence on the output parameters, such as lens diameter, depth, focal point, F #, and NA. The software organises the experimental data, generates equations that establish relationships between the in- put and output parameters, and then performs an optimisation process to determine the most effective conditions. Table 6 shows the experimental results of the quartz microlens fabrication. The input parameters were laser power, laser speed, and the number of repeated processes. The laser power lower and upper values are 10 and 20 W, respectively. The lower and upper values of the laser speed are 50 and 150 mm s−1, respectively, 414 vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . (a). No. of pulses: 100. (b). No. of pulses: 300. (c). No. of pulses: 500. Figure 8. The stability curve for aging time and energy at No. of pulses: 100, 300, and 500. Figure 9. The contour graph of optimum value for stability. while the number of repeated processes ranges from 1 to 9. the output parameters were the lens diameter, depth, focal length, F #, and numerical aperture. The f-number of a lens (F #) is a dimensionless number that expresses the ratio of the focal length (f) to the diameter of the entrance pupil. It controls the amount of light that enters the lens and affects the depth of field in imaging devices. The numerical aperture (NA) of a lens is a dimensionless metric that indicates its ability to collect light and resolve fine detail. A graph- ical representation of the numerical aperture, which is given in Table 6, is shown in Figure 10. Figure 10 shows the three-dimensional graph of the microlens NA for one to nine times repeated pro- cesses. The max. and min. NA values were 0.108 and 0.543 mV, respectively. A deeper dip is produced when the laser power is increased and the laser speed is decreased, along with a higher number of repeated processes. This is due to an increase in ablated mate- rial and a greater numerical aperture (NA). The quadric equation that should be used to eval- uate the numerical aperture of quartz microlens is shown below: NA = 0.5495 + 0.00054P + 0.0149S + 0.0073C + 0.0017P × S + (−0.0002)P × C + (−0.0145)S × C + 0.0050P 2 + (−0.0125401)S2 + (−0.0054)C2 + (−0.0133)P 2 × S, (6) where P is the fibre laser power [P], S is the laser speed [mm s−1], and C is the number of repeated processes. The final regression equation was also an excellent way to predict and study how parameters affect each other. 415 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica Run Input parameters Output parameters A: Power B: Speed C: Count Lens diameter Depth Focal point F# NA[W] [mm s−1] [µm] [µm] [µm] 1 15 100 5 446 154 433.560 0.972 0.514 2 15 100 5 445 155 431.268 0.969 0.516 3 15 50 9 190 590 550.27 2.897 0.173 4 10 100 1 720 70 1 746.75 2.426 0.206 5 15 50 1 320 420 437.229 1.366 0.366 6 20 150 5 350 205 322.173 0.92 0.543 7 20 50 5 130 657 603.119 4.639 0.108 8 10 150 5 775 91 1 582.79 2.042 0.245 9 20 100 9 150 297 287.218 1.915 0.261 10 15 150 9 595 175 618.864 1.04 0.48 11 15 100 5 446 154 433.560 0.972 0.514 12 15 100 5 445 155 431.268 0.969 0.516 13 10 50 5 382 470 497.836 1.303 0.384 14 10 100 9 470 145 478.056 1.017 0.492 15 20 100 1 210 240 259.943 1.238 0.404 16 15 100 5 444 156 429.021 0.966 0.517 17 15 150 1 705 91 1 324.05 1.878 0.266 Table 6. Effects of laser power, laser speed, and No. of repeated processes on the lens diameter, lens depth, focal point, F #, and NA as determined by the DOE software. (a). No. of repeated processes: 1. (b). No. of repeated processes: 5. (c). No. of repeated processes: 9. Figure 10. The NA 3D curve for laser power and laser speed at No. of repeated processes: 1, 5, and 9 times. 416 vol. 65 no. 4/2025 Improving the production process of silicon nanoparticle . . . Run Input parameters Output parameter A: Power [W] B: Speed [mm s−1] C: Count Roughness [nm] 1 4 3 3 12.3 2 4 3 3 12.2 3 4 1 5 6.7 4 3 3 1 85.1 5 4 1 1 13.4 6 5 5 3 11.9 7 5 1 3 5.2 8 3 5 3 70.5 9 5 3 5 6.7 10 4 5 5 12.1 11 4 3 3 12.4 12 4 3 3 12.2 13 3 1 3 57.1 14 3 3 5 47 15 5 3 1 13.2 16 4 3 3 12.1 17 4 5 1 22.8 Table 7. Effects of laser power, laser speed, and No. of repeated processes on the lens diameter, lens depth, focal point, F #, and NA as measured by the DOE software. 3.5.2. Microlens enhancement Using the CO2 laser during the reshaping stage is of considerable importance for enhancing the quality of microlenses. Table 7 presents the parameters of this stage, which were determined using the Design of Expert software for the experimental strategy. All input parameters, including laser power, laser speed, and the number of repeated processes, were experi- mentally determined to analyse their influence on the output parameter, which is lens roughness. The laser power has lower and upper values of 3 and 5 W, respectively. The lower and upper values of the laser speed are 1 and 5 mm s−1, respectively, while the number of repeated processes ranges from 1 to 5. The software organises the experimental data, gener- ates equations that establish the relationship between the input parameters and lens roughness, and then performs the optimisation process to determine the most effective conditions. A graphical representation of the results in Table 7 is shown in Figure 11. Figure 11 shows a three-dimensional graph of the lens height at one-fifth of the process. The max. and min. roughness values were 5 and 85 nm, respectively. When the laser power reached a high level, the laser speed decreased, and the number of repeated processes increased, resulting in the complete melting of the sur- face. This occurred because the laser power exceeded the melting point of the quartz material. Further- more, it was observed that there was an increase in the roughness value as the laser speed increased. The quadric equation that should be used to evalu- ate the roughness of quartz microlens is shown below: R = 12 + (−28)P + 4.25S + (−7.75)C + (−1.75)P × S + 7.75P × C + (−0.75) × S × C + 24.125P 2 + (−0.375)S2 + 1.625C2, (7) where R is the roughness [nm], P is the CO2 laser power [W], S is the laser speed [mm s−1], and C is the repeated processes. The final regression equation was also an excellent way to predict and study how the parameters affect each other. The optimum values of the output parameters for Tables 5 and 6 are shown in Figure 12. Figure 12 shows the optimum values of the output response for the quartz microlens. The optimum NA and roughness values were 0.494 and 4.5 nm, respec- tively. 4. Conclusion This study used expert analysis software to optimise the parameters of laser micro/nano processing. The COMSOL software simulation was used to analyse the thermal distribution on the surface and in the area beneath the surface of silicon wafers and quartz sheets under laser irradiation. Using the Nd:YAG laser, fi- bre laser, and CO2 laser in micro/nano machining of silicon and quartz resulted in the formation of sta- ble silicon nanoparticles and the creation of a quartz microlens array. Furthermore, the numerical optimisa- tion using the DOE software yielded silicon nanopar- ticles with desired properties and quartz microlenses with specific dimensions and characteristics. The op- timal parameter for silicon NPs (stability) was 33 mV, while for quartz microlenses (NA and roughness), it was 0.494 and 4.5 nm, respectively. Finally, the con- trollable laser micro/nano machining process demon- strated the potential applications of silicon nanopar- ticles and quartz microlenses in optoelectronics and biological imaging, which can benefit from the unique features offered by these lenses. Future endeavours 417 M. J. Mahmoud, B. G. Rasheed, M. M. Hanon Acta Polytechnica (a). No. of repeated processes: 1. (b). No. of repeated processes: 3. (c). No. of repeated processes: 5. Figure 11. The roughness 3D curve for laser power and laser speed at No. of repeated processes: 1, 3, and 5 times. should focus on further parameter optimisation for laser microprocessing, investigating alternative mate- rials and scalable production methods. The aim is to improve precision engineering, increase the versatility of materials, and enable the real-world application of silicon nanoparticles and quartz microlenses for various purposes. (a). NA. (b). Roughness. Figure 12. The contour graph of optimum value for: NA and roughness. References [1] L. Rihakova, H. Chmelickova. Laser micromachining of glass, silicon, and ceramics. A review. European International Journal of Science and Technology 4(7):41–49, 2015. [2] J. Wang, F. Fang, H. An, et al. Laser machining fundamentals: micro, nano, atomic and close-to-atomic scales. International Journal of Extreme Manufacturing 5(1):012005, 2023. https://doi.org/10.1088/2631-7990/acb134 [3] S. N. Grigoriev, M. A. Volosova, A. A. Okunkova. 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