A calibration method for accurate prediction of amorphous to nanocrystalline transition from line intensities of optical emission spectrum

To be able to use the simple technique of optical emission spectroscopy (OES) for the prediction of the transition of growth from a-Si to nc-Si via the H_α/Si^? emission ratio, a regime-dependent correction factor is required to relate the measured H_α/Si^? emission ratio to the true flux (to the substrate) ratio of atomic hydrogen to deposited silicon radicals. Through an in-depth study in a very high frequency plasma enhanced chemical vapor deposition process, we obtained that the flux ratio of atomic hydrogen and deposited silicon radicals to the growing surface,Γ^H/Γ^Si, is related to the emission ratio of H_α and Si^?, I_rad^H_α/I_rad^Si*, by the relation, $R_{\text{rad}}\frac{I_{\text{rad}}^{{\text{H}}_{\alpha }}}{I_{\text{rad}}^{{\text{Si}}^{\text{*}}}}/\frac{{\Gamma }^{\text{H}}}{{\Gamma }^{\text{Si}}}=a\left\{{\left(p{d}_{}\right)}^2/k{T}_{\text{gas}}\right\}+b$, where the parameters p (pressure), d (inter-electrode distance) and T_gas (gas temperature) are experimentally obtained quantities and R_rad is the ratio of the rate coefficients for radiation of Si^? and H_α. We obtained the calibration parameters a and b to be 1.9·10^? 21 ± 2·10^? 22 Pa m^? 1 and 5.5 ± 1.9 respectively which is valid in a broad range of power and pressure settings. With these parameters, it is easy to estimate the flux ratio of atomic hydrogen and silicon species at any deposition condition using the OES data and this will allow accurate prediction of the phase transition. According to simulations in the linear low-pressure regime, the amorphous to nanocrystalline phase transformation occurs at the flux ratio Γ^H/Γ^Si = 12, which translates, using the factors a and b, to the required emission ratio.