This article explains the phenomenon of sintering and the sintering process. Starting from the principle of sintering technology, it proposes methods and relevant principles for formulating sintering standards, providing the best sintering conditions for achieving a high yield of finished products.

I. Preface 
In the manufacturing of thick-film hybrid integrated circuits, sintering is a very important process. The thick-film components that have been dried on the substrate must undergo sintering to acquire certain electrical properties. For instance, thick-film resistors, after being printed and dried, do not have resistive characteristics if they do not undergo sintering; that is, they do not have a definite resistance value. Therefore, the sintering process is a characteristic process that distinguishes thick-film technology from thin-film technology. Although the characteristics of thick-film resistors mainly depend on the properties and composition of the thick-film material, sintering is decisive. The crucial condition is the sintering temperature. Only when sintering is carried out under the most suitable conditions can the best performance of the used material be achieved. Therefore, sintering is the key process that gives life to the thick-film components. Thus, most of the characteristics of thick-film components and their integrated circuits depend on sintering. 
The sintering temperatures of various thick-film components range from 600 to 1000 degrees Celsius. Moreover, the sintering temperature must be reached within a short period of time. In production, in order to achieve the predetermined performance indicators and obtain a good yield rate, it is necessary to explore the sintering laws and accurately control their reproducibility; at the same time, the correct supply of air or other atmospheres and the control of exhaust should be carried out to prevent volatile and combusted organic substances from polluting the thick film and deteriorating its performance. 
II. Sintering and Its Phenomena 
Sintering mainly refers to the sintering of solid substances. During sintering, complex physical and chemical processes occur. When solid particles are placed at an appropriately high temperature, due to the sintering effect, they undergo contraction, the porosity significantly decreases, and the density and mechanical strength are greatly enhanced, as shown in Figure 1. 
During the sintering process, the solid particles are heated, the voids within the structure are eliminated, and the volume shrinks. At the same time, the density and mechanical strength are improved, which reduces crystal defects, promotes grain growth, and decreases the specific surface area and free energy of the grains. Therefore, the contraction rate, porosity, and surface condition are generally used as indicators to measure the sintering quality. 
In summary, the sintering phenomenon can be characterized by the following points: 
(1) Since the sintered body undergoes a series of physical and chemical changes during the sintering process, its appearance, structure and properties will all change. 
(2) During the sintering process, the rates of various changes in the sintered body are different, and the sensitivity of each change to various factors of sintering is also distinct. Therefore, in order to achieve good performance and repeatability, strict control of the sintering conditions is necessary. 
(3) During the sintering process, the changes in the sintered body are very complex. Therefore, the sintering conditions for different materials and components vary. It should be noted that the optimal sintering conditions are not easy to master and control. For specific materials, a detailed analysis of the components is required, and the optimal sintering conditions can only be determined through multiple experiments. 
(4) The requirements for materials in sintering are as follows: ① Select materials that are not sensitive to changes in sintering factors to achieve excellent repeatability and facilitate production. ② Choose an appropriate material composition to obtain good processability and shorten the production cycle. ③ Consider the feasibility of equipment and process conditions. Try to select materials with relatively lower sintering temperatures to save energy and reduce costs. 
(5)  The sintering of thick film components and thick film integrated circuits is not the same as the sintering of ordinary powders. Not only is it required to form a single, dense and highly mechanically strong piece, but it must also be firmly attached to the substrate and possess certain electrical properties. Clearly, the electrical properties of the thick film depend on the structure and composition of the thick film. Therefore, although thick film sintering and general powder sintering have no essential differences, the requirements and manifestations are different, which is the peculiarity of thick film sintering. 
(6) The quality of flat-plate sintering is mainly determined by the characteristics of thick-film components and the requirements for their performance. In production, performance parameters that are decisive are usually measured to determine whether the sintering is successful or whether the expected sintering goal has been achieved. 
(7) For powder sintering, the properties of the powder are of great significance. For materials of the same composition, if the methods of powder preparation and processing techniques are different, the properties of the sintered materials will also vary. In most cases, the sintering performance is not determined by the materials used, but by the properties of the powder. The powder properties include particle size, particle size distribution, particle shape, surface condition, and the internal crystal structure, etc. 
III. Sintering Process 
The sintering process is divided into four stages: such as the resistance paste of RuO2 and Pb2Ru2O6 and the sintering process. 
1. Combustion stage 
During this process, the main adhesive undergoes volatilization, decomposition and combustion. Generally, it is basically completed at a temperature range of 300 to 400 degrees Celsius or even at 350 degrees Celsius. 
During the sintering process, when there is an adequate supply of oxygen, the reaction of organic substances is as follows: 
Organic substances + O2 → CO2↑ + H2O 
When there is insufficient air, the reaction of organic substances proceeds as follows: 
Organic substances + O2 → CO↑ + CH4↑ + H2O = C + CH3OH... 
The above-mentioned products will undergo a chemical reaction with (Ru), and the reaction is as follows: 
RuO2+C→Ru+CO2↑

RuO2+2CH3OH→3Ru+2CO2+4H2O

Therefore, during resistance sintering, in order to meet the reaction requirements under this specific condition, sufficient oxygen must be supplied. To fully burn out the polymer compounds and avoid the formation of bubbles and bulges on the thick film surface, the heating rate should not be too fast. Generally, it is advisable to maintain a rate of 50 to 100℃ per minute. 
2. Glass softening stage 
When the temperature rises above the glass softening point, the glass material begins to soften and gradually melts. The general temperature range is around 480℃ to 550℃. The glass glaze melts and penetrates the conductive phase, allowing it to be evenly distributed throughout the thick film. It also bonds the thick film to the substrate and serves as a covering and sealing function. 
3. Resistance melting stage 
After the glass melts, due to the wetting of the conductive phase particles by the glass and the plastic flow, the particles adhere to each other and "grain bond" together, forming what is called the "chain-like structure". As shown in Figure 2. 
4. Cooling stage 
After being held at the highest sintering temperature for a certain period of time, it can be cooled down at a specified rate to bring it to the ambient temperature. During this process, the glass gradually hardens and basically solidifies completely at around 550℃. The film is then fixed and firmly attached to the substrate. 
IV. Sintering Process 
It is of great importance to determine the sintering specifications for thick film products. The specifications mainly include the rising speed, the maximum sintering temperature, the holding time, the speed and method of cooling, as well as the atmosphere. The determination of these conditions is not only related to the composition of the raw materials, the processing and grinding situation, the film-forming method, and the solid-phase reaction process, but also to the structure of the sintering furnace, the heating method, and the loading situation. 
A reasonable sintering specification should be based on the principles of fast sintering speed, short cycle and good quality. While ensuring the quality of thick film products, efforts should be made to save time and energy. Therefore, whether one can obtain high-quality and low-cost thick film products is the criterion for evaluating whether the sintering specification is reasonable. 
Starting from the process principles, methods and relevant principles for formulating sintering specifications are proposed and established. 
1. Rate of temperature increase 
In thick film sintering, the period from room temperature to the highest sintering temperature is called the heating time. Under the condition of meeting the performance requirements of the thick film, the heating period should be as short as possible. Since the heating speed mainly affects various reactions during sintering, heating too fast causes organic substances to volatilize vigorously, forming bubbles and pinholes. Due to the short heating time, the organic substances cannot be completely burned, which affects the performance and properties of the film. However, the heating speed cannot be too slow either, otherwise it will affect the productivity. 
Generally speaking, for large-scale products, those with complex structures and multi-layer thick films, the heating speed should be slower to avoid excessive local temperature differences, which could cause deformation, delamination, cracking, etc. For small-sized products that are stacked or buried for firing, since the heat transfer is relatively uniform, the heating speed can be faster. 
2. Maximum sintering temperature and holding time 
The maximum sintering temperature and the holding time mutually restrict and compensate each other. By adjusting the values of both, it is possible to achieve a single-stage development and maturity process, with distinct grain boundaries, no excessive secondary crystallization, uniform shrinkage, very few pores, and the highest density. 
1) Determination of the maximum sintering temperature 
In actual production or firing research, the determination of the high sintering temperature of thick film pastes mainly relies on the data from comprehensive thermal analysis experiments. This is because the composition, particle size, ratio, film formation and density, doping phase and dosage of the thick film pastes are all closely related to their maximum sintering temperature. 
The highest sintering temperature should be selected within a certain range. For thick films with strong crystallization ability and a narrow sintering temperature range, the lower limit of the range should be used first, and the holding time should be appropriately increased; for thick films with complex composition, weak crystallization ability, and a wide sintering temperature range, the upper limit of the temperature range can be selected, while the holding time should be appropriately shortened to save energy. 
2) The relationship between the maximum sintering temperature and the holding time 
For most thick-film components, during the recrystallization process in the later stage of sintering, it is mainly restricted by the diffusion-transport mechanism, and the grain boundary movement velocity V is in an exponential relationship with the absolute temperature T: 
V=V0esp(-b /T)

In the formula: V0 - frequency factor, which is closely related to interfacial energy, interfacial curvature, etc., and has little relation to temperature. 
b - Coefficient related to activation energy. If during a single grain growth process, the average distance that the grain boundary moves is X, then: 
X=Vt=V0texp(-b /T)

In the formula: t - diffusion time, which can be regarded as the corresponding sintering time. If we replace T in the above formula with T0, then we can obtain the relationship between the highest sintering temperature T0 and the holding time t: 
t=t0exp(-b /Tf)

In the formula: t0 = X / V0 It can be seen that the holding time is in an exponential relationship with the maximum sintering temperature. When the distance of grain boundary movement is the same, T0 will change, and t will need to be adjusted accordingly. Generally, the holding time directly affects whether the sintering reaction is sufficient, whether the thick film structure is uniform, and the growth of crystals, etc. For conductive materials containing glass, a shorter holding time is preferable. Because if the holding time is too long, the glass in the conductive slurry will float on the surface of the thick film, reducing its weldability and adhesion. 
3. Cooling rate and cooling method 
According to the sintering specifications, after being heated at the maximum sintering temperature for a certain period of time, the temperature should be gradually reduced at a certain rate. The cooling method refers to the cooling speed of thick film products after sintering and related issues. Since the requirements for the performance of thick film products vary, depending on the speed of cooling, the common cooling methods include three types: 
1) Slow cooling: Based on the structure of the sintering furnace and its heat capacity, a small amount of heat supply is provided and the temperature is slowly reduced at a specified rate. 
2) Furnace cooling: After the holding period, cut off the power supply and let the equipment cool naturally in the furnace. 
3) Rapid cooling: This is done to ensure that the crystal phase structure at high temperatures can be retained as much as possible, avoiding the possible decomposition of compounds, the detachment of solid solutions, the reduction of glass phase, excessive movement of grain boundaries, further growth of crystal grains, the transformation to polycrystals, the continuation of oxidation-reduction reactions, and the diffusion of certain substances during slow cooling. 
4. Sintering Curve 
Changing the maximum sintering temperature and holding time has a significant impact on the performance of the thick film. Figure 3 shows the sintering curve of the salt-based thick film. The sintering effect is the best within the range of 800-900℃. The maximum sintering temperature is 850℃, the holding time is 9-10 minutes, and the sintering cycle is 60 minutes. 
(b) For the short-cycle sintering curve, the cycle is 30 minutes, the maximum sintering temperature is 850℃, and the holding temperature rate is between 300 and 500℃, at 100℃/minute. The ISTU sintering furnace introduced by the slurry plant adopts this curve. 
V. Factors Affecting Sintering 
There are numerous factors that affect the sintering process and the sintering outcome, mainly including: the maximum sintering temperature, the holding time, the environmental atmosphere during sintering, and the characteristics of the solid phase particles.