A computational model for plasma chemical reactions has been developed. An ab initio molecular orbital method was used to determine dissociation paths and their threshold energies. Plasma characteristics were calculated by a plasma kinetic method. The radical compositions in C 4 F 8 , with additional gases such as Ar, He and CH 2 F 2 , were calculated. Radicals influencing the selective etching of SiO 2 over Si 3 N 4 were analysed. With increased microwave power or decreased flow rate, CF 2 density decreased and CF, C and F densities increased. The increase of radicals with abundant carbon relative to fluorine would result in high etch selectivity of SiO 2 over Si 3 N 4 and a low etch rate. Increases in the concentration of F radicals are correlated with increases in SiO 2 etch rates. Electron temperature was high with He addition, and dropped with C 4 F 8 alone and Ar addition discharges. On the contrary, the electron density was high in the reverse order. The highest etch selectivity was obtained with He addition. A high electron temperature discharge would be one solution to obtain high etch selectivity of SiO 2 over Si 3 N 4 .
We have developed a direct self-consistent-field ͑SCF͒ molecular-orbital ͑MO͒ method based on the densityfunctional linear combinations of atomic-orbital methods, which is efficient for obtaining total energies of large molecules. In this method, we introduce the Schwartz inequality and efficiently reduce the number of atomicorbital pairs, which must be considered for calculating the matrix elements and electron density. The MO calculations for C 60 confirm that the total number of calculation steps for obtaining the matrix elements and electron density becomes 1 6 of that for an ordinary SCF-MO method, keeping an eight-digit accuracy in total energy.
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