Optimal reduction of a monitoring grid for SiO2 deposition surface over a wafer for semiconductor devices

Normal 0 14 false false false IT X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabella normale"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Semiconductor devices are used in all electronic equipment. These devices, commonly known as integrated circuit (IC) chips, are developed over the surface of a disk, called wafer, after deposition of a thin silicon substrate. The deposition of a SiO 2 film on the top of the wafer is used as interconnection and isolation of different layers. Film deposition is critical to further steps of IC manufacturing. For this reason thickness is monitored during the manufacturing process in correspondence of a grid of points defined on the wafer surface. Considering that collecting thickness measures is quite expensive, this paper addresses the problem of determining whether, given previous measures of the SiO 2 film on the available map, a new sub map of the initial one may be adopted minimizing a suitable loss functions of prediction. This paper presents a general strategy to reduce the monitoring grid based on a spatial prediction algorithm.