Graph theory applied to microelectronics intergranular relations

Abstract

The focus of this study is on the control of layers between grains by applying graph theory. We performed modification of BaTiO₃ nanoparticles with Y₂O₃. The results of capacitance change on submicron level are the part of the measured values on the bulk samples. The original idea is to develop the new approach to use graph theory for networking of electronic parameters between the neighboring grains in order to compare the values measured on the sample, and to present them through the edges in graph between corresponding vertices. Capacitance change with DC bias was measured on bulk samples, and the modified nanoparticles showed stability up to 90 V. After using graph theory with the different number of neighboring grains and on different voltages, it has been shown that capacitance change can be successfully calculated on the layers between grains. Original calculations presented as 1D cases were performed, confirming graph application as a tool with which measured bulk results can be downsized to an appropriate intergranular level, opening the new perspectives in the area of miniaturization and micropackaging.

Keywords:

• intergranular capacitance change
• graph theory
• electronic signal
• computing technology