# Kernel-Density-Based Particle Defect Management
## 1 Introduction  
The worldwide semiconductor market is valued at 333 billion dollars [1]. As the semiconductor industry accounts for 10-15% of the total exports of the Republic of Korea, it has a significant influence on the market economy. Owing to the recent proliferation of electronic devices such as mobile phones and tablet PCs (Personal Computers), market competition is becoming increasingly fierce [2]. In the future, as the demand for the internet of things (IoT) products is expected to increase, most manufacturers endeavor to increase the production through maintenance of facilities [3]. The semiconductor manufacturing process consists of numerous steps. As shown in Figure 1, in the front-end process, the ingot is cut to produce wafers and the circuit is designed. The wafers are subsequently undergone fabrication (FAB), which consists of the following eight processes: oxidation, lithography, etching, strip & clean, ion-implantation, chemical vapor deposition, metal deposition, and chemical mechanical planarization. Oxidation refers to a process whereby a thin and uniform silicon oxide film is formed by the chemical reaction of oxygen or water vapor and the surface of the wafer at a high temperature. Lithography is a process whereby patterns on the wafer is formed by photoresist coating, exposure, and development processes. Etching refers to the process whereby unnecessary portions are selectively removed by using the reactive gas to form a circuit pattern. Strip & clean refers to the process of removing particle contamination generated on the wafer amid other ongoing processes. Ion-implantation is the process whereby characteristics of the electronic device aregenerated by the implantation of impurities converted to a gas form in the circuit pattern. Chemical vapor deposition is the process whereby the water vapor formed in the particles are formed by the chemical reaction of gases to form an insulating film. Metal deposition interconnects each circuit formed on the surface of a wafer with aluminum and copper wire. Chemical mechanical planarization is a process whereby the oxide film and the metal thin film coated on the wafer are ground and flattened using chemical and physical processes. The subsequent step is the back-end process, in which the probe test, the assembly, and the package tests are conducted sequentially. Thereby, the final product is manufactured. These processes each have their own facilities, and each facility includes several chambers where a wafer must be placed for fabricating. The above-mentioned processes occur within those chambers. Wafer fabrication for semiconductor devices such as microprocessors, memories, digital signal processors, and consumer electronics applications involves a complex and lengthy process with 30-40 reentrant loops, and the above-mentioned processes (1)-(8), as shown in Figure 1[4]. This study focuses on these eight processes and the inter-process metrology. Semiconductor FAB includes various physical and chemical treatments and takes six to eight weeks. Therefore, there is a considerable difficulty in identifying causes of failure in the fabrication process, which involves numerous facilities. Figure 2 chronologically shows a pitch change in the lithography process used for fabricating DRAM (Dynamic Random-Access Memory), NAND (Negative-AND gate flash memory), and logic products that have been actively manufactured in recent years. The pitch on the \(Y\)-axis illustrates the integration capacity of the semiconductor products and significantly affects product yield, hence the increasing significance of defect management as current FAB processes design and fabricate sophisticated patterns [5]. Figure 1: The semiconductor manufacturing process. IC, Integrated Circuit. The defects in a semiconductor manufacturing process are generally distributed as shown in Figure 3. The pie chart on the left shows that the particle defects account for 75% of the total defects. As shown in the pie chart on the right, 75% of the particle defects are caused by process equipment [6].