Modeling refraction characteristics of silicon nitride film deposited in a SiH4-NH3-N2 plasma using neural network

Silicon nitride has been deposited using plasma-enhanced chemical deposition (PECVD) equipment. The PECVD process was characterized by conducting a 2^6-1 fractional factorial experiment on six experimental factors, including substrate temperature, pressure, radio frequency (RF) power, ammonia NH₃, silane SiH₄, and nitrogen N₂ flow rates. Refractive characteristics of the deposited film were examined by modeling the refractive index as a function of experimental factors. A helium-neon laser with a wavelength 6328 Å was used to measure the refractive index. To evaluate the appropriateness of the model, the network trained with 32 experiments was then tested with 12 experiments not pertaining to the training data. Several learning factors involved in training neural networks were optimized and an accurate prediction model with the root mean-squared error of 0.018 was achieved. Compared to statistical regression model, the neural network model demonstrated an improvement of more than 65%. Using various three-dimensional plots, underlying deposition mechanisms were qualitatively estimated. For the limited experimental ranges, the index increased with increasing SiH₄ flow rate. With an increase in either NH₃ or N₂, meanwhile, the index decreased consistently. The index also increased with increasing substrate temperature or pressure. The effects of the temperature were very complex as it interacted with other factors.