Research Article  Open Access
Simulation and Experimental Study on Properties of Ag/SnO_{2} Contact Materials Doped with Different Ratios of Ce
Abstract
SnO_{2} in the Ag/SnO_{2} contact material is a kind of high hardness and almost insulated wide bandgap semiconductor material. In the process of use, the contact resistance is larger and the temperature rise is higher, which reduces the reliability of contacts and shortens the electrical life. In order to improve the properties of Ag/SnO_{2} contact materials, based on the first principle of density functional theory, this paper presents a method of doping SnO_{2} with the calculation of different proportions of rare earth Ce electrical and mechanical properties. The results of energy band, density of state, and elastic constant show that when the doping ratio of Ce is 0.125, the electron mobility is the highest, the conductivity is the best; the hardness decreases, and the universal elastic anisotropy index is the smallest. Finally, in the experiment, SnO_{2} powders with different doping ratios are prepared by the solgel method, and Ag/SnO_{2} contacts with different doping proportions are prepared by powder metallurgy. Arc energy, contact resistance, and hardness are measured; scanning electron microscopy was used to observe and analyze the surface morphology. The final simulation and experimental results are well matched.
1. Introduction
The contact resistance and the temperature rise in the process of using automotive relay contacts are increased, making life expectancy to decrease [1–3]. This is because SnO_{2} in Ag/SnO_{2} contact material is a kind of wide bandgap semiconductor material, which is almost insulator [4]. At the same time, SnO_{2} is a high hardness brittle reinforcing phase, making contact material processing and composite molding extremely difficult. The study shows that the doping modification of Ag/SnO_{2} with rare earth materials is a good method to solve the above problems [5].
For now, improving the performance of Ag/SnO_{2} contact materials by doping is still in the experimental stage. How to get the best performance by doping with the proper amount of rare earth elements depends on the original experiments and experience, and there are some difficulties in the preparation of samples and the accuracy of experimental equipment, which restrict the development of Ag/SnO_{2} materials.
Zhu Yancai and others in the study on new type of Ag/SnO_{2}/CeO_{2} electrical contact material preparation and electrical properties found that CeO_{2}doped Ag/SnO_{2} improved electrical performance [6]. From the experimental point of view, they had only selected a single ratio of doping, not knowing the best proportion of doping to get better performance. In the study of the structure and optical properties of Cedoped SnO_{2}, Shan Linting et al found that the Cedoped SnO_{2} makes conduction band bottom to move toward the lowenergy side, the bandgap becomes smaller, and the conductivity increases [7]. The conductivity was only studied by simulation calculations.
Wang Qingwei et al found that CeO_{2}doped SnO_{2} when doping too little is not conducive to the sintering and growth of tin oxide crystals, while excessive doping will prevent the lattice growth and affects the stability of the lattice, easily leading to serious cracking of the product [8, 9]. So, the doping amount of CeO_{2} should be controlled.
It is of great significance to understand the basic properties of Ag/SnO_{2} contact material. In this paper, based on the firstprinciples calculation of density functional theory [10], different proportions of rare earth Ce are doped into the contact material of SnO_{2}, conducting geometric optimization, energy band, density of states and elastic constant, and then analyzing the conductivity and hardness to theoretical study the electronic structure and mechanical properties.
2. Cell Model and Calculation Method
2.1. Cell Model
In this paper, we had constructed a SnO_{2} primary cell model, as shown in Figure 1(a). SnO_{2} (cassiterite) has the rutile structure space group P42/mnm [11]. Each SnO_{2} contains 2 Sn atoms and 4 O atoms. The atomic substitution method was used to construct the supercell model Sn_{1−x}Ce_{x}O_{2} (x = 0, 0.083, 0.125, and 0.167). Table 1 shows the relationship between the doping ratio and the supercell. Taking the doping ratio of 0.125 as an example, the supercell model of SnO_{2} is established and one of the Sn atoms is replaced by a rare earth atom Ce, as shown in Figure 1(b).
(a)
(b)

2.2. Calculation Method
In this article, we used Materials Studio software and completed the calculation by using the CASTEP module. The calculation process uses periodic boundary conditions based on DFT [12]. Since generalized gradient approximation (GGA) considers the effect of charge density near a certain location on the exchangecorrelation energy, for example, taking into account the effect of the firstorder gradient of density to correct local variations, it is possible to properly correct the effects of charge density regions exponential form; in the geometric optimization, energy band and density of state calculations have achieved good results [13].
The local density approximation (LDA) assumes that the nucleus spacing in the system is far apart, and the motion of electrons in its lattice background can be approximated as a behavior in a uniform field. It is suitable for the calculation of the ground state properties of various systems, and very good results are achieved when calculating the elastic properties of the system [14]. Therefore, the geometric optimization process uses the PBE method under GGA; the CAPZ method under LDA is used to calculate the elastic constants in the mechanical properties on the basis of optimization. For geometric optimization, energy band, density of states, and elastic constants are calculated adopting the plane wave ultrasoft pseudopotential (Ultrasoft) method.
In order to compare the calculated results of SnO_{2} doped with different proportions of Ce, the parameters of software simulation are set to be consistent. The calculated parameters are as follows: the cutoff energy of the plane wave is 370 eV, the SCF tolerance is 1.0 × 10^{−6} eV/atom, and the K point in the Brillouin region is . The calculation process is carried out in the reciprocal space.
3. Results and Discussion
3.1. Crystal Structure
The crystal parameters of geometry optimization and experimentation of SnO_{2} doped with different proportions of Ce are optimized, and the parameters after optimization are shown in Table 2.

According to the optimization results, the experimental values and calculated values of the lattice parameters of Cedoped SnO_{2} with different proportions are not much different. The lattice constant and volume of SnO_{2} after doping have different growth degrees compared with SnO_{2}, which is consistent with Vegard’s law [15], indicating that the calculation results are reliable. This shows that doping Ce can cause slight distortion of the crystal structure and thus can adjust the structural parameters of SnO_{2}, thereby improving the performance of SnO_{2}.
3.2. Conductivity
3.2.1. Density of States and Electron Concentration
The density of states of SnO_{2} and SnO_{2} doped with different proportions of rare earth Ce is shown in Figure 2. Figure 2(a) shows the density of states of SnO_{2}, and Figures 2(b)–2(d) show the density of states of SnO_{2} with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively. The Fermi level is chosen to be zero of the energy scale. The energy level above the Fermi surface (0 eV) is the conduction band, and the energy level below the Fermi surface is the valence band.
(a)
(b)
(c)
(d)
It can be seen from Figure 2 that the density of states undoped and doped with different ratios of Ce shows that the Fermi surface of the SnO_{2} supercell after doping moves to the valence band in different degrees, while the conduction band of undoped SnO_{2} is about 0 eV–20 eV, and the conduction band of SnO_{2} is about 0 eV–7 eV after doping. The conduction band is narrowed, which indicates that the SnO_{2} model after different ratios of doping enhances the electronic state near the Fermi level, and more partial waves cross the Fermi level, the interaction between electrons is enhanced, and the conductivity is enhanced.
The Fermi surface of the Cedoped SnO2 supercell with different ratios of rare earth elements enters the conduction band to a different extent, which indicates that the relative electron concentration entering the conduction band of SnO2 supercell is different. The relative number of electrons entering the conduction band can be obtained by integrating the density of states of Figures 2(a)–2(d) by Origin software. The obtained Sn_{1−x}Ce_{x}O_{2} (x = 0.083, 0.125, 0.167) is shown in Table 3.

As can be seen from Table 3, the higher the doping concentration, the higher the relative electron number into the conduction band and the higher the concentration of relative electron.
The conductive performance of the material can be expressed by the conductivity . The conductivity of the material by semiconductor physics theory is [16]where is the electron charge constant, and the conductivity is proportional to the electron concentration and the electron mobility , which can be obtained from the above formula.
In addition to being affected by the relative number of electrons, the conductivity is also affected by the electron mobility. According to the characteristics of the CASTEP software. When applying the firstprinciples study, the software sets the temperature to a low temperature of 0 K. According to semiconductor theory, the crystal scattering is dominated by ionized impurities. Therefore, it is necessary to fully consider the influence of the relative electron number and electron mobility into the conduction band on the conductivity of SnO_{2} to obtain a correct conclusion.
3.2.2. Band and Electronic Effective Mass
The band structure of SnO_{2} and different ratios of Cedoped SnO_{2} shown in Figure 3(a) is the band of SnO_{2}, and Figures 3(b)–3(d) are the band of SnO_{2} with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively.
(a)
(b)
(c)
(d)
From Figure 3, the bandgap decreases after doping. The band of SnO_{2} after doping is introduced in the region of −35 eV∼−30 eV new energy level, but this energy level is in the deeprail region and has little effect on the conductivity. Therefore, we do not consider it. At the same time, new energy levels appear in the doping system near −15 eV and the distribution of electrons increases, providing more electronic states, and the valence band to the conduction band energy level jump probability is greatly increased. Band fluctuations become gentle, indicating that the doping of the electronic locality enhancement. Hence, when SnO_{2} is doped with Ce, it makes metal properties to enhance to increase the conductivity of the material.
The electron mobility is inversely proportional to the effective electron mass, and the data derived from two derivation of the band by software are shown in Table 4.

The formula for the effective electron mass is as follows:where is the Planck constant, is the wave vector, and is the electron energy at the wave vector.
3.2.3. Conductivity Analysis
The following equation is the relationship between the electron mobility , the doping concentration , and the electron effective mass :
The following equation is derived from the formulas (1)–(3), and the conductivity is proportional to the relative electron concentration and inversely proportional to the doping concentration and the electron effective mass [17]:
The doping ratio of 12.5% is used as a reference to get the relative conductivity, as shown in Table 5.

It can be seen from Table 5 that the conductivity of SnO_{2} with the Ce doping ratio of 12.5% is the highest.
3.3. Elastic Constant
3.3.1. The Formula for the Elastic Constant
For polycrystalline systems, Hill proved that VRH (Voigt–Reuss–Hill) is closer to the experimental results [18]. The formula for bulk modulus () and shear modulus () is as follows:where and are the elastic modulus and shear modulus of the Voigt model, respectively, and and are the elastic modulus and shear modulus of the Reuss model, respectively. The formula between bulk modulus, shear modulus, and elastic constant C_{ij} (i, j = 1∼6) under the Voigt and Reuss model is as follows [19, 20]:
Poisson’s ratio () is related to the bulk modulus and the shear modulus as calculated by Hill as follows:
When studying the mechanical properties of materials, we usually consider the effects of microcracks and lattice distortion on the mechanical properties of materials, and the universal elastic anisotropy index is usually the determinant of microcracks and lattice distortion [21]:
The Vickers hardness in GPa is evaluated based on the empirical formula of Tian (2012). When the hardness is greater than 5 GPa, the correlation between the empirical formula and the experimentally measured hardness value is quite good. The formula is as follows [22]:where .
3.3.2. Calculation and Analysis of Elastic Constants
In order to study the dynamic stability of the doped system, the corresponding relationship between the elastic constants (C_{ij} (GPa)) of SnO_{2} and different ratios of Cedoped SnO_{2} is given in Table 6.

For tetragonal systems, if the dynamics are stable, the elastic constants satisfy the following requirements [23]: , .
The elastic constants of SnO_{2} and different ratios of Cedoped SnO_{2} in Table 6 are calculated, and all satisfy the stability criterion. Therefore, SnO_{2} and different ratios of Cedoped SnO_{2} are stable in dynamics.
In order to further predict theoretically the mechanical properties such as hardness () and crack, the bulk modulus (), shear modulus (), hardness (), and universal elastic anisotropy index () values are shown in Table 7.

According to the Pugh criterion, it is generally considered that solid materials with are brittle; if they are less than 0.57, it exhibits toughness [24]. From Table 7, the order of G/B values is SnO_{2} > Sn_{0.9166}Ce_{0.0834}O_{2} > Sn_{0.875}Ce_{0.125}O_{2} > Sn_{0.833}Ce_{0.167}O_{2}, which indicates that doping can change the brittleness of the material, and the more the rare earth element Ce, the more obvious the improvement.
Covalent bond orientation directly affects the ability of the material to resist shear strain. Poisson’s ratio can reflect the covalent bond orientation problem of internal structure of the material, the lower the value of the former, the stronger the ability of material to resist shear strain. Table 7 shows that Poisson’s ratio becomes smaller after doping, indicating that their ability to resist shear strain is enhanced. SnO_{2} with the Ce doping ratio of 12.5% has the smaller Poisson’s ratio and the best ability to resist shear strain.
The index of pervasive elastic anisotropy, , is often the decisive factor in the production of cracks. As can be seen from Table 7, the values of SnO_{2} after doping are smaller and closer than those of SnO_{2}, indicating that doping has an important effect on improving microcracks.
4. Experimental Preparation of Ag/SnO_{2} and CeDoped Ag/SnO_{2} Contact Materials
4.1. Preparation of Doped SnO_{2} Powder by SolGel Method and Ag/SnO_{2}Ce Contact Material by Powder Metallurgy
The traditional powder metallurgy method only mixes the doping element powder, SnO_{2} powder, and silver powder, which makes it difficult for the doping element to enter the SnO_{2} crystal. In order to be consistent with the theoretical calculation model of this paper, the solgelation method was used to first prepare different proportions of Cedoped SnO_{2} powder. Then, Ag/SnO_{2} and Cedoped Ag/SnO_{2} contact materials were prepared by the powder metallurgy method. The proportion of silver base in each sample was 88%.
4.2. Test of Contact Resistance and Arcing Energy
The electrical contact properties of test materials were tested by using the JF04C electrical contact material tester. 25000 onoff tests were conducted using each pair of contacts. The contact resistance and arcing energy measurement were done every 100 cycles under load 24 V, 13 A, and contact pressure was 86 cN for the onoff period of 0.4 seconds. Finally, the conductivity of the test material is evaluated by the contact resistance and the arcing energy. The arc energy and contact resistance of Ag/SnO_{2} doped with different proportions of rare earth elements Ce are shown in Table 8.

Because the rare earth elements easily lose the outermost electrons to form a stable structure with a high melting point, they are not easily decomposed under the action of the arc but accumulate on the surface of the contact, thereby reducing the ablation of the contacts by the arc and reducing the arcing energy.
From Table 8, when the doping ratio is 12.5%, the arcing energy has the smallest variation range, average arcing energy, and the actual measured conductivity are also the smallest, indicating that Cedoped SnO_{2} has the smallest fluctuation and the most stable.
It is proved that when the rare earth element Ce doping ratio is 12.5%, the electrical properties of the Ag/SnO_{2} contact material are the best under the applied test conditions here.
4.3. Microstructure Analysis of Contact Material Surface
Scanning electron microscopy (SEM) was used to observe the arc ablation morphology of the four types of Ag/SnO_{2} contact materials, and the arc erosion resistance of the four types of contact materials was analyzed.
After 25,000 electrical contact performance tests of the contact material, the photomicrographs of the contact surface magnified 1000 times are shown in Figure 4, among them Figure 4(a) shows Ag/SnO_{2} and Figures 4(b)–4(d) show the Ag/SnO_{2} with the Ce doping ratios of 16.7%, 12.5%, and 8.34%, respectively.
(a)
(b)
(c)
(d)
The wettability between Ag and SnO_{2} particles is poor, which causes the SnO_{2} particles to be suspended in the liquid Ag molten pool when the Ag/SnO_{2} contact material is in the arc. The surface is easy to form Agrich region and SnO_{2}rich region. The formation of the Agrich region is likely to exacerbate the splash erosion of the contact Ag droplets, and the SnO_{2}rich region tends to increase the contact resistance of the contacts. Doping can effectively improve the wettability between Ag liquid and SnO_{2} particles so that SnO_{2} particles are suspended in the molten system of silver, increasing the viscosity of Ag molten pool, reducing the probability of formation of the SnO_{2} polymerization zone, and thus improving the resistance to arc erosion of the Ag/SnO_{2} contact material.
Comparing the surface topography of the ablation edge regions of three different proportions of doping, when the doping is 12.5%, the contact surface is flat and without pits, which was because the contact surface shows signs of fluid metal activity after slight melting, and the gap and other phenomena were improved because of the movement of the flow metal. At this time, the surface is relatively flat and smooth, and the electrical properties are the best. The other two ratios are doped, the surface of the contact has holes, the surface of the molten layer exhibits a flowing state of liquid metal and a mountain pack forms after solidification, and some of the black nonconductive oxides are precipitated.
4.4. Hardness Measurement
The hardness of the sample was measured using the HXD1000TM digital microhardness tester [17]. The test strength was selected, and the diamond was pressed into the test sample for 5 s. The two diagonal lengths of the diamond indentation on the surface of the sample were observed by a microscope. The hardness value was read, the sample position was changed, and the above process was repeated. Three measurements were made for each sample, and the average value of the hardness was calculated. The hardness values of Ag/SnO_{2} and Ag/SnO_{2} doped with different proportions of Ce are given in Table 9.

It can be seen from the above table that the more the doping, the lower the hardness. By comparing the theoretical and actual hardness values in Tables 7 and 9, it is found that the simulations and experiments are well matched. From the perspective of the application environment of the contact, high hardness plays an important role in improving the service life of the contact; from the perspective of the forming of the contact, high hardness affects the plasticity and reduces the yield. Therefore, the hardness value must be considered comprehensively.
5. Conclusions
Based on the first principle of density functional theory, the calculated and analyzed results of Sn_{1−x}Ce_{x}O_{2} (x = 0, 0.083, 0.125, 0.167) show the following:(1)When the doping proportion of Ce is 0.125, the electron mobility is the highest, and the conductivity and the ability to resist shear strain are the best(2)When the doping is 0.834, the universal elastic anisotropy index is the smallest
Compared with all performances, 0.125 is the best doping ratio.
Finally, Ag/SnO_{2} contacts with different doping ratios were prepared, and arcing energy, contact resistance, and hardness were measured. The final simulation and experimental results can be well matched.
Some people study on Cedoped Ag/SnO_{2} contact material to improve the performance is still in the experimental stage, and the control of the doping amount is also based on the original experience. The innovation of this paper is to obtain the most comprehensive performance by simulating different proportions of Ce doping. A good doping ratio is then verified by experimentation. In the experiment, we not only tested the contact resistance and arc energy but also performed a scanning electron microscope experiment to observe the arc ablation morphology of the contact material. The final theoretical model is well matched to the experiment, providing a method of saving manpower, material resources, and financial resources to improve the electrical properties of Ag/SnO_{2} contact materials.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors have no conflicts of interest.
Acknowledgments
This study was funded by the National Natural Science Foundation (51777057).
References
 H. Li and Y. Hou, “Electroerosion characteristics of Ag/SnO_{2} contact material under DC lamp load,” Electrical Engineering Materials, vol. 2, pp. 12–15, 2005. View at: Google Scholar
 M. Zhang, “Development status of Ag/SnO_{2} contact material and its application in relays,” Electrical Engineering Materials, vol. 4, pp. 20–26, 2004. View at: Google Scholar
 Z. Liu, The Study on NanoDoped Ag/SnO2 Contact material, Tianjin University, Tianjin, China, 2007.
 S. Tingting, Z. Fuchun, and Z. Weihu, “Density functional theory study on the electronic structure and optical properties of SnO_{2},” Rare Metal Materials and Engineering, vol. 44, no. 10, pp. 2409–2414, 2015. View at: Publisher Site  Google Scholar
 Y. Zhu, Study on the Ag/SnO_{2} Contact Materials with the Addition of Rare Earth Oxides, Hebei University of Technology, Tianjin, China, 2007.
 Y. Zhu, J. Wang, and L. An, “Preparation and electrical properties of new Ag/SnO_{2}/CeO_{2} electrical contact materials,” Rare Metal Materials and Engineering, vol. 34908, pp. 2011–2014, 2015. View at: Google Scholar
 L. Shan, B. Dechun, Y. Lin et al., “The structure and optical properties of Cedoped SnO_{2} materials,” Vacuum, vol. 1, pp. 25–28, 2014. View at: Google Scholar
 Q. Wang, Research on Tin Dioxide Electrode and its Strengthening and Toughening, Donghua University, Shanghai, China, 2005.
 Q. Wang, Preparation and Properties of Rare Earth Doped Tin Dioxide Ceramic Electrodes, Donghua University, Shanghai, China, 2012.
 D. Guo and C. Hu, “Firstprinciples study on the electronic structure and optical properties for SnO_{2} with oxygen vacancy,” Applied Surface Science, vol. 258, no. 18, pp. 6987–6992, 2012. View at: Publisher Site  Google Scholar
 S. F. Matar, D. Jung, and M. A. Subramanian, “The predominance of the rutile phase of SnO_{2}: first principles study,” Solid State Communications, vol. 152, no. 5, pp. 349–353, 2012. View at: Publisher Site  Google Scholar
 M. D. Segall, P. J. D. Lindan, M. J. Probert et al., “Firstprinciples simulation: ideas, illustrations and the CASTEP code,” Journal of Physics: Condensed Matter, vol. 14, no. 11, pp. 2717–2744, 2002. View at: Publisher Site  Google Scholar
 K. G. Godinho, A. Walsh, and G. W. Watson, “Energetic and electronic structure analysis of intrinsic defects in SnO_{2},” Journal of Physical Chemistry C, vol. 113, no. 1, pp. 439–448, 2008. View at: Publisher Site  Google Scholar
 D. M. Ceperley and B. J. Alder, “Ground state of the electron gas by a stochastic method,” Physical Review Letters, vol. 45, no. 7, pp. 566–569, 1980. View at: Publisher Site  Google Scholar
 J. A. Berger, L. Reining, and F. Sottile, “Efficient GW calculations for SnO_{2}, ZnO and rubrene: the effectiveenergy technique,” Physical Review B Condensed Matter, vol. 85, no. 8, Article ID 085126, 2012. View at: Publisher Site  Google Scholar
 E. Liu, B. Zhu, and J. Luo, Semiconductor Physics, Electronic Industry Press, Beijing, China, 6th edition, 2003.
 W. Jingqin, Z. Ying, and K. Huiling, “Study on properties of AgSnO_{2} contact materials doped with rare earth Y,” Materials Research Express, vol. 5, no. 8, Article ID 085902, 2018. View at: Publisher Site  Google Scholar
 R. Hill, “The elastic behaviour of a crystalline aggregate,” Proceedings of the Physical Society, vol. 65, no. 5, pp. 349–354, 2002. View at: Publisher Site  Google Scholar
 W. Voigt, Lehrbuch Der Kristallphysik: Teubner, Macmillan, Leipzig, Germany, 1928.
 A. Reuss, “Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals,” ZAMM—Zeitschrift für Angewandte Mathematik und Mechanik, vol. 9, pp. 49–58, 1929. View at: Google Scholar
 S. I. Ranganathan and M. OstojaStarzewski, “Universal elastic anisotropy index,” Physical Review Letters, vol. 101, Article ID 055504, 2008. View at: Publisher Site  Google Scholar
 Y. Tian, B. Xu, and Z. Zhao, “Microscopic theory of hardness and design of novel superhard crystals,” International Journal of Refractory Metals and Hard Materials, vol. 33, pp. 93–106, 2012. View at: Publisher Site  Google Scholar
 F. Zhang, Z. Zhang, W. Zhang et al., “Firstprinciples calculation of the electronic structure and optical properties of In_{2}O_{3},” Journal of Chemistry, vol. 66, no. 16, pp. 1863–1868, 2008. View at: Google Scholar
 Z. Wu, E. Zhao, H. Xiang et al., “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles,” Physical Review B, vol. 76, no. 5, Article ID 054115, 2007. View at: Publisher Site  Google Scholar
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Copyright © 2018 Jingqin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.