Study on the Wetting Mechanism between Hot-Melt Nano Glass Powder and Different Substrates

The wettability of molten glass powder plays an essential role in the encapsulation of microelectromechanical system (MEMS) devices with glass paste as an intermediate layer. In this study, we first investigated the flow process of nano glass powder melted at a high temperature by simulation in COMSOL. Both the influence of the different viscosity of hot-melt glass on its wettability on SiO2 and the comparison of the wettability of hot-melt glass on Au metal lead and SiO2 were investigated by simulation. Then, in the experiment, the hot-melt glass flew and spread along the length of the Au electrode because of a good wettability, resulting in little coverage of the hot-melt glass on the Au electrode, with a height of only 500 nm. In order to reduce the wettability of the glass paste on the Au electrode, a SiO2 isolation layer was grown on the surface of golden lead by chemical vapor deposition. It successfully reduced the wettability, so the thickness of the hot-melt glass was increased to 1.95 μm. This proved once again that the wettability of hot-melt glass on Au was better.


Introduction
Good vacuum packaging [1], even special packaging in a bad environment [2], is an important means to ensure the reliability of MEMS devices. In the middle layer packaging process with nano glass powder, the MEMS sensor can be electrically interconnected with the outside world through the external lead wire of the metal electrode, and the cap, substrate and lead wire can be tightly sealed together by using nano glass powder through hot press bonding. Nano glass powder or the glass frit inter-layer packaging has the advantages of a high tolerance to the surface roughness of the bonding interface, suitable for various materials in the MEMS, electrical insulation characteristics to simplify the electrode lead extraction process and patterning without an additional lithography process by using screen printing [3][4][5]. It has been widely used in the packaging of the MEMS pressure switch [6,7], MEMS gyroscope [8] and accelerometer [9]. Many scholars only describe the packaging principle, packaging process and packaging results of nano glass powder, but there is no report on both the mechanism of infiltration and flow process of hot-melt glass on the substrate.
After nano glass powder is made on the glass substrate with metal lead through screen printing, during the process of high temperature melting, the wettability of molten nano glass powder on metal lead and the SiO 2 substrate are different due to a different contact angle, surface tension and adhesion work. After cooling and solidification, the adhesion thickness of the glass powder on the metal lead is different from that on the SiO 2 substrate. If the height of the glass powder inter-layer on the Au metal lead is less than 10 µm [10], the package will fail.
In order to improve the results of the direct packaging of nano glass powder in the MEMS structure with metal leads, the wettability of nano glass powder in a hot-melt state was investigated. Firstly, the whole flow process of hot-melt nano glass liquid on silver substrate from the starting point to the material interface wall was simulated by COMSOL. 2 of 9 Then, the wettability of the hot-melt nano glass powder with a different viscosity on the SiO 2 substrate was analyzed and compared by simulation. The wetting effect of hot-melt glass with the same viscosity on SiO 2 and Au substrates were also investigated. Finally, it was verified by experiments that the wettability of hot-melt nano glass on Au metal leads was better than that on SiO 2 , which leads to a too small adhesion thickness. By depositing a SiO 2 isolation layer on the metal leads, the wettability of hot-melt nano glass on a Au metal lead was successfully reduced, so as to improve its adhesion thickness on the Au.

Simulation Analysis of Wettability
Wettability is the degree of difficulty for a liquid to adhere to a solid when it contacts with a solid. It is usually determined by the contact angle between the solid-liquid interface and the liquid-gas interface θ. When the contact angle is less than 90 • , the liquid can wet the solid. When the contact angle is greater than 90 • , the liquid is difficult to wet the solid. Zhu Dingyi et al. [11,12] studied the corresponding relationship between liquid surface tension, solid surface tension and the contact angle. Guan C.H. [13] researched the impact of surface roughness on solid-liquid wettability. Li Wei [14] obtained the contact angle between the hot-melt glass and different substrates through experiments, and the better wettability was attained by polishing the surface of the material. In reference [15], the adhesion work was calculated by measuring the contact angle. The viscosity µ of liquid affected the velocity difference of each layer in the flow, which was one of the key factors affecting the fluidity of the liquid. Reference [16] verified that viscosity µ directly affected the fluidity of the hot-melt alloy liquid, and 1/µ was used to characterize the relationship between the wettability and the temperature of the hot-melt alloy. However, the simulations of the wettability of liquids with a different viscosity on the same substrate and liquids with the same viscosity on different substrates have not been reported.

Simulation Model
The hot-melt glass powder was filled into a silicon pit sputtered with a layer of different substrate materials and heated to reflow to fill the whole pit. Assuming that the bottom radius of the hot-melt glass column was 2 mm and the height was 5 mm, the radius of the sphere equal to its volume was 2.47 mm. Taking the bottom radius of the cylindrical container made of the base material as 3 mm, we got the simulation model as shown in Figure 1. The material properties of nano glass powder at room temperature were indicated in  The material properties of nano glass powder at room temperature were indicated in Table 1: density, 2.221g/cm 3 ; viscosity, 1000 Pa·s; and surface tension, 2003.4 mN/m. According to the relationship between the surface tension and the temperature in Reference [17], the data in Table 2 were preliminarily sorted out and calculated. As shown in Figure 2, the relationship between the contact angle θ and the interfacial tension between solid, liquid and gas can be expressed by "Young's formula".
γ sg , γ sl and γ lg represent solid-gas interfacial tension, solid-liquid interfacial tension and liquid-gas interfacial tension, respectively. The corresponding relationship between the liquid surface tension, solid surface tension and contact angle [18,19] was expressed by Equation (2): According to the data of hot-melted glass in Table 1 and the surface tension data of the substrate material in Table 2, the contact angle formed when the substrate material and the hot-melted glass were infiltrated and could be calculated by Formula (2).
The liquid-gas surface tension γ lg = 2003.4 mN/m. At the same time, Equation (2) was transformed as follows: (√1 + sin 2 θ + cos θ) 2 According to Equation (2), when the contact angle is 90°, the solid surface tension is 1416.6 mN/m. Thus, to consider the positive and negative values of cos θ and convert further: The corresponding relationship between the liquid surface tension, solid surface tension and contact angle [18,19] was expressed by Equation (2): According to the data of hot-melted glass in Table 1 and the surface tension data of the substrate material in Table 2, the contact angle formed when the substrate material and the hot-melted glass were infiltrated and could be calculated by Formula (2).
The liquid-gas surface tension γ lg = 2003.4 mN/m. At the same time, Equation (2) was transformed as follows: Micromachines 2022, 13, 1683 According to Equation (2), when the contact angle is 90 • , the solid surface tension is 1416.6 mN/m. Thus, to consider the positive and negative values of cos θ and convert further: According to Equations (4) and (5), the contact angles between each substrate and hot-melted glass could be obtained from the data in Tables 1 and 2.
Adhesion work is the energy released in the process of adhesion. In the process of adhesion, the surface energy of the solid and liquid is lost, and the surface energy of the solid-liquid interface is generated. The calculation formula of the adhesion work was as follows: Combined with "Young's formula" (1), we could obtain: According to Formula (8), the adhesion work between hot-melted glass and different substrates could be obtained. The contact angle and the adhesion work which were calculated are shown in Table 3. Table 3. Contact angle and adhesion work between hot-melt glass and each substrate [14].

Simulation of Wettability of Hot-Melt Glass with Different Viscosity on SiO 2 Substrate
By changing the viscosity of hot-melt glass from 500 Pa·s to 1000 Pa·s, the influence of the viscosity of the hot-melt glass on the flow velocity and wettability of the hot-melt glass was studied with the SiO 2 as a substrate. Taking the yellow light band as the reference point, the relationship between the viscosity of hot-melt glass and the time needed to flow to the junction of the material bottom and the material wall was explored in this paper. On the SiO 2 substrate, the steady state of hot-melt glass with a different viscosity flowing to the junction is shown in Figure 3, which corresponds to a different flow time.
Therefore, when the viscosity of the hot-melt glass was 1000, 900, 800, 700, 600 and 500 Pa·s, respectively, the time of the hot-melt glass flowing to the specified distance on the SiO 2 substrate could also be obtained, as shown in Figure 4. It could be seen that the lower the viscosity of the hot-melt glass, the shorter the flow time to the specified distance, the higher the flow speed and the better the wettability. For the same SiO 2 substrate, the solid surface energy of hot-melt glass with a different viscosity was the same, but the lower the viscosity was, the higher the wettability was.
By changing the viscosity of hot-melt glass from 500 Pa·s to 1000 Pa·s, the influence of the viscosity of the hot-melt glass on the flow velocity and wettability of the hot-melt glass was studied with the SiO2 as a substrate. Taking the yellow light band as the reference point, the relationship between the viscosity of hot-melt glass and the time needed to flow to the junction of the material bottom and the material wall was explored in this paper. On the SiO2 substrate, the steady state of hot-melt glass with a different viscosity flowing to the junction is shown in Figure 3, which corresponds to a different flow time. Therefore, when the viscosity of the hot-melt glass was 1000, 900, 800, 700, 600 and 500 Pa·s, respectively, the time of the hot-melt glass flowing to the specified distance on the SiO2 substrate could also be obtained, as shown in Figure 4. It could be seen that the lower the viscosity of the hot-melt glass, the shorter the flow time to the specified distance, the higher the flow speed and the better the wettability. For the same SiO2 substrate, the solid surface energy of hot-melt glass with a different viscosity was the same, but the lower the viscosity was, the higher the wettability was.

Comparison of Wettability of Hot-Melt Glass Solution between SiO2 and Au Substrates
Then, the viscosity of the hot-melt glass was kept at 1000 Pa·s, the simulation was carried out on the SiO2 and Au substrates and the simulation results, as shown in Figure  5, were obtained. It could be clearly seen from Figure 5 that it took 22 s for the hot-melt glass to flow to the junction on the SiO2 substrate and 16.5 s on the Au substrate. With the same viscosity, the surface free energy of the liquid was the same. Yet, combined with the

Comparison of Wettability of Hot-Melt Glass Solution between SiO 2 and Au Substrates
Then, the viscosity of the hot-melt glass was kept at 1000 Pa·s, the simulation was carried out on the SiO 2 and Au substrates and the simulation results, as shown in Figure 5, were obtained. It could be clearly seen from Figure 5 that it took 22 s for the hot-melt glass to flow to the junction on the SiO 2 substrate and 16.5 s on the Au substrate. With the same viscosity, the surface free energy of the liquid was the same. Yet, combined with the parameters in Table 2, the contact angle between the hot-melt glass and the Au substrate was smaller than that of SiO 2 , and the adhesion work and surface tension on the Au substrate were larger, so the wettability was higher and the flow velocity was higher.

Comparison of Wettability of Hot-Melt Glass Solution between SiO2 and Au Substrates
Then, the viscosity of the hot-melt glass was kept at 1000 Pa·s, the simulation was carried out on the SiO2 and Au substrates and the simulation results, as shown in Figure  5, were obtained. It could be clearly seen from Figure 5 that it took 22 s for the hot-melt glass to flow to the junction on the SiO2 substrate and 16.5 s on the Au substrate. With the same viscosity, the surface free energy of the liquid was the same. Yet, combined with the parameters in Table 2, the contact angle between the hot-melt glass and the Au substrate was smaller than that of SiO2, and the adhesion work and surface tension on the Au substrate were larger, so the wettability was higher and the flow velocity was higher.

Experimental
The micro pressure switch was packaged with nano glass powder. The hot-melt glass was transparent and the surface morphology was compact and smooth, as shown in Figure 6. However, because the wettability between the hot-melt glass and the Au electrode

Experimental
The micro pressure switch was packaged with nano glass powder. The hot-melt glass was transparent and the surface morphology was compact and smooth, as shown in Figure 6. However, because the wettability between the hot-melt glass and the Au electrode were stronger than that between the hot-melt glass and the SiO 2 substrate, the hot-melt glass flowed rapidly along the length direction of the Au electrode lead and spread out rapidly, resulting in little coverage of this part of the hot-melt glass. After measurement, the thickness of the hot-melt glass on the Au electrode lead was only 500 nm, as shown in Figure 6b. This thickness was not enough to form a sealed package during bonding. were stronger than that between the hot-melt glass and the SiO2 substrate, the hot-melt glass flowed rapidly along the length direction of the Au electrode lead and spread out rapidly, resulting in little coverage of this part of the hot-melt glass. After measurement, the thickness of the hot-melt glass on the Au electrode lead was only 500 nm, as shown in Figure 6b. This thickness was not enough to form a sealed package during bonding. The wettability of hot-melt glass to different materials varies greatly [20,21]. From the above simulation and experimental results, it could be seen that the wettability of hotmelt glass on the Au metal lead was good, so the volume of hot-melt glass passing through the Au metal lead decreased sharply. A silicon wafer sputtered when a large area of Au lines was selected and a thin layer of nano glass powder was manually coated on the whole surface and melted at a high temperature. Figure 7b showed that the amount of hot-melt glass on the Au metal leads was very small, and a small part shrank to the metal free area on the silicon wafer. It was proved that the wettability of glass paste on the Au wire was very strong and the adhesion thickness of the glass paste was not as good as that The wettability of hot-melt glass to different materials varies greatly [20,21]. From the above simulation and experimental results, it could be seen that the wettability of hot-melt glass on the Au metal lead was good, so the volume of hot-melt glass passing through the Au metal lead decreased sharply. A silicon wafer sputtered when a large area of Au lines was selected and a thin layer of nano glass powder was manually coated on the whole surface and melted at a high temperature. Figure 7b showed that the amount of hot-melt glass on the Au metal leads was very small, and a small part shrank to the metal free area on the silicon wafer. It was proved that the wettability of glass paste on the Au wire was very strong and the adhesion thickness of the glass paste was not as good as that of the silicon or glass. Based on the verification results, it was proposed that a SiO 2 isolation layer should be formed on the surface of the metal lead by chemical vapor deposition to reduce the wettability of the glass slurry in this area. The wettability of hot-melt glass to different materials varies greatly [20,21]. From the above simulation and experimental results, it could be seen that the wettability of hotmelt glass on the Au metal lead was good, so the volume of hot-melt glass passing through the Au metal lead decreased sharply. A silicon wafer sputtered when a large area of Au lines was selected and a thin layer of nano glass powder was manually coated on the whole surface and melted at a high temperature. Figure 7b showed that the amount of hot-melt glass on the Au metal leads was very small, and a small part shrank to the metal free area on the silicon wafer. It was proved that the wettability of glass paste on the Au wire was very strong and the adhesion thickness of the glass paste was not as good as that of the silicon or glass. Based on the verification results, it was proposed that a SiO2 isolation layer should be formed on the surface of the metal lead by chemical vapor deposition to reduce the wettability of the glass slurry in this area. The experimental process and results are shown in Figure 8. The SiO2 isolation layer successfully reduced the wettability of the hot-melt glass on the Au metal lead, and this part of the hot-melt glass was consistent with that on the glass sheet. The thickness of the hot-melt glass increased from 500 nm to 1.95 µ m. It could be seen that there was a significant difference between the thickness of the glass powder on the metal lead covered with The experimental process and results are shown in Figure 8. The SiO 2 isolation layer successfully reduced the wettability of the hot-melt glass on the Au metal lead, and this part of the hot-melt glass was consistent with that on the glass sheet. The thickness of the hot-melt glass increased from 500 nm to 1.95 µm. It could be seen that there was a significant difference between the thickness of the glass powder on the metal lead covered with a thin layer of SiO 2 and that on the metal lead not covered with SiO 2 . This proved once again that the wettability of hot-melt glass on a Au substrate was better. a thin layer of SiO2 and that on the metal lead not covered with SiO2. This proved once again that the wettability of hot-melt glass on a Au substrate was better.

Conclusions
The wettability of the molten glass powder was studied by simulation and experimentally. The conclusions obtained in this research are summarized as follows: 1. The smaller the viscosity of the hot-melt glass, the smaller the surface energy of the liquid, the greater the wettability and the higher the flow velocity on SiO2. When the