A Numerical Study on Tuned Substrate Self-Bias in a Radio-Frequency Inductively Coupled Plasma

The tuned substrate self-bias in a radio-frequency inductively coupled plasma is controlled by varying the impedance of an external tuning LCR (inductor, capacitor and resistor) network inserted between the substrate and the ground. In experiments, it was found that the variation of the tuned substrate self-bias with the tuning capacitance demonstrated three features, namely, continuity, instability and bistability. In this paper, a numerical study is focused on the elucidation of the physical mechanisms underlying continuity and bistability. For the sake of simplicity and feasibility to include the key factors influencing the tuned substrate bias, the tedious calculation of inductive-coupling to obtain the plasma density and electron temperature is omitted, and discussion of the tuned substrate self-bias is made under the prescribed plasma density and electron temperature. On the other hand, the parameters influencing capacitive- coupling are retained in modeling the system with an equivalent circuit. It is found that multi-stable state appears when one of the parameters, such as the resistance in LCR, substrate area and plasma density, decreased to its critical value, or the rf voltage or electron temperature increased to the critical value individually. In the reverse cases, the tuned substrate self-bias varies continuously with the tuning capacitance