Time dependent analytical modelling of multi-frequency capacityvely coupled collisional sheath

Abstract

Capacitively coupled plasma (CCP) has been widely used in plasma assisted processing such as plasma etching, deposition and other surface treatments in microelectronics industries. High plasma density and ion bombarding energy, which are crucial in these applications, particularly in etching, cannot be controlled independently in traditional single frequency (SF) driven CCP. Dual frequency (DF) CCP is already in use in the fabrication industries for the new generation ultra-large-scale integrated (ULSI) circuits. But it is reported that the quality of separate control of ion energy and flux in DF discharge is limited due to the coupling of two frequencies and effect of secondary electrons. It is not very far that more frequencies will be used simultaneously in the CCP in order to achieve better control etch parameters. An analytical model of sheath parameters for a multi-frequency driven collisional CCP has been developed considering time dependent ion density and electric field within the sheath. Sheath parameters for DF and triple frequency (TF) case have been determined and studied against different operating parameters, e.g., chamber pressure, plasma density, RF frequencies, phase differences etc. The determined values of the sheath parameters are compared with some published DF and TF models. In the analyses for DF and TF case different properties of sheath width and potential have been observed. The oscillating behaviour of the parameters increases as the number of RF source frequencies increases. More oscillation in the sheath parameters increases the ion-neutral collisions within the sheath resulting in a reduced ion bombarding energy at the electrode. The oscillation pattern of the parameters depend on the ratio of RF frequencies. Compared with collisional time independent models this model estimates lower values of the sheath parameters. Lower values of the parameters is another reflection of the lower ion energy. The sheath parameters show inverse relationship with both pressure and plasma density. The parameters also show smaller values at higher pressure ranges when compared with a collisionless time dependent model, as collisionality is not considered in that model. It has been found that proper choice of phase difference may facilitate to have better control over the sheath properties. As this model considers the instantaneous ion motion and the instantaneous electric field, so this model will estimate the sheath parameters of CCP more accurately when multi-frequency source is used. This will facilitate the plasma users to have better control on the etch properties.