Model for Bias Frequency Effects on Plasma-Damaged Layer Formation in Si Substrates

Bias frequency effects on damaged-layer formation during plasma processing were investigated. High-energy ion bombardment on Si substrates and subsequent damaged-layer formation are modeled on the basis of range theory. We propose a simplified model introducing a stopping power Sd(Eion) with a power-law dependence on the energy of incident ions (Eion). We applied this model to damaged-layer formation in plasma with an rf bias, where various energies of incident ions are expected. The ion energy distribution function (IEDF) was considered, and the distribution profile of defect sites was estimated. We found that, owing to the characteristic ion-energy-dependent stopping power Sd(Eion) and the straggling, the bias frequency effect was subject to suppression, i.e., the thickness of the damaged layer is a weak function of bias frequency. These predicted features were compared with experimental data on the damage created using an inductively coupled plasma reactor with two different bias frequencies; 13.56 MHz and 400 kHz. The model prediction showed good agreement with experimental observations of the samples exposed to plasmas with various bias configurations.