An analytical model of computing ion energy distributions for multiple frequencies capacitive discharges

We have developed an analytical multi-frequency model, which results in accurate multi-peaks of the ion energy distributions (IEDs) for the given control parameters. The model can analytically calculate and predict the IEDs multiple peaks and energy width with necessary plasma parameters. This model can also predict the IEDs from multiple frequencies' drives at any voltage, the associated results are compared with particle-in-cell (PIC) simulations. The IED at a surface is an important parameter for processing in multiple radio frequencies driven capacitive discharges. The analytical model is developed for the IED in a low pressure discharge based on a linear transfer function that relates the time-varying sheath voltage to the time-varying ion energy response at the surface. This model is in good agreement with PIC simulations over a wide range of multiple frequencies driven capacitive discharge excitations.