Control of etch rate using modeling, feedback and impedance match

A host controller comprising:

• a memory device for storing a measured complex variable;
• and
• a host processor coupled to the memory device, the host processor configured to:
• receive the measured complex variable, wherein the measured complex variable is measured at an output of a radio frequency (RF) generator, wherein the RF generator is coupled to an impedance matching circuit via an RF cable, wherein the RF cable is coupled between the output of the RF generator and the impedance matching circuit, wherein the impedance matching circuit is coupled to a plasma chamber via an RF transmission line;
• propagate the measured complex variable through a computer-generated model to generate a calculated complex variable at an output of the computer-generated model, wherein to propagate the measured complex variable through the computer-generated model, the host processor is configured to calculate a directional sum of the measured complex variable and a plurality of values of a plurality of electrical circuit elements of the computer-generated model;
• determine whether the calculated complex variable matches a desirable complex variable;
• control a variable circuit component of the impedance matching circuit until the calculated complex variable matches the desirable complex variable, wherein to control the variable circuit component, the host processor is configured to control a shunt capacitor of the impedance matching circuit until a match between a real portion of the calculated complex variable and a real portion of the desirable complex variable is achieved;
• and
• control a series component of the impedance matching circuit until a match between an imaginary portion of the calculated complex variable and an imaginary portion of the desirable complex variable is achieved.

A plasma system comprising:

• a radio frequency (RF) generator configured to generate an RF signal;
• an impedance matching circuit coupled to the RF generator via an RF cable to receive the RF signal via the RF cable, wherein the RF cable is coupled between an output of the RF generator and the impedance matching circuit, wherein the impedance matching circuit is configured to modify the RF signal to generate a modified RF signal;
• a plasma chamber coupled to the impedance matching circuit via an RF transmission line, wherein the RF transmission line is configured to transfer the modified RF signal to the plasma chamber;
• and
• a host controller coupled to the RF generator, wherein the host controller includes:
• a memory device for storing a measured complex variable;
• a host processor coupled to the memory device, the host processor configured to:
• receive the measured complex variable, wherein the measured complex variable is measured at the output of the RF generator;
• propagate the measured complex variable through a computer-generated model to generate a calculated complex variable at an output of the computer-generated model, wherein to propagate the measured complex variable through the computer-generated model, the host processor is configured to calculate a directional sum of the measured complex variable and a plurality of values of a plurality of electrical circuit elements of the computer-generated model;
• determine whether the calculated complex variable matches a desirable complex variable;
• control a variable circuit component of the impedance matching circuit until the calculated complex variable matches the desirable complex variable, wherein to control the variable circuit component, the host processor is configured to control a shunt capacitor of the impedance matching circuit until a match between a real portion of the calculated complex variable and a real portion of the desirable complex variable is achieved;
• and
• control a series component of the impedance matching circuit until a match between an imaginary portion of the calculated complex impedance and an imaginary portion of the desirable complex impedance is achieved.