Etch Rate Modeling and Use Thereof for In-Chamber and Chamber-to-Chamber Matching

A method comprising:

• receiving a voltage and a current measured at a first time at an output of a radio frequency (RF) generator of a plasma system;
• calculating a sum of a first term, a second term, and a third term, wherein the first term is a first product of a coefficient and a function of the voltage, the second term is a second product of a coefficient and a function of the current, and the third term is a third product of a coefficient, a function of the voltage, and a function of the current;
• determining the sum to be the etch rate associated with the plasma system;
• and
• adjusting power output at a second time from the RF generator of the plasma system to achieve the etch rate,
• wherein the method is executed by a processor.

A plasma system for modeling an etch rate, the plasma system comprising:

• a radio frequency (RF) generator for generating an RF signal, the RF generator including an output for facilitating transfer of the RF signal;
• a complex impedance sensor coupled to the output of the RF generator for measuring a complex voltage and current of the RF signal;
• a plasma chamber for generating plasma when the RF signal is received;
• an impedance matching circuit coupled to the RF generator via a cable and coupled to the plasma chamber via an RF transmission line;
• a processor coupled to the complex impedance sensor for receiving the measurement of the complex voltage and current from the complex impedance sensor, the processor for:
• receiving a voltage and a current measured at an output of an RF generator of a second plasma system;
• calculating a sum of a first term, a second term, and a third term, wherein the first term is a first product of a coefficient and a function of the voltage measured at the output of the second plasma system, and the second term is a second product of a coefficient and a function of the current measured at the output of the RF generator of the second plasma system, and the third term is a third product of a coefficient, a function of the voltage measured at the output of the RF generator of the second plasma system, and a function of the current measured at the output of the RF generator of the second plasma system;
• determining the sum to be the etch rate associated with the second plasma system;
• and
• adjusting power at the output of the RF generator of the first plasma system to achieve the etch rate associated with the second plasma system, wherein adjusting the power is based on the complex voltage and current.