System, method and apparatus for refining radio frequency transmission system models
First Claim
1. A method of defining a chuck model for a radio frequency (RF) transmission path to calculate a wafer direct current (DC) bias at a chuck of a plasma chamber, comprising:
- generating, by a computer, a cable model of an RF cable, a match model of an impedance matching circuit, a transmission model of an RF transmission line, and the chuck model, wherein the chuck model includes a series circuit model and a shunt circuit model, wherein the RF cable couples an RF generator to the impedance matching circuit and the RF transmission line couples the impedance matching circuit to the chuck;
identifying an initial term in the chuck model having a first level of impact on a goodness of fit of the chuck model, wherein the initial term is identified from a plurality of initial terms;
removing the initial term having the first level of impact on the goodness of fit from the chuck model, wherein the chuck model has a plurality of remaining ones of the plurality of initial terms after said removing of the initial term;
identifying a non-initial term having a second level of impact on the goodness of fit of the chuck model with the non-initial term added to the chuck model, wherein the non-initial term is not one of the plurality of initial terms and is identified from a plurality of non-initial terms, wherein the second level of impact is greater than the first level of impact;
selecting the remaining ones of the plurality of initial terms and the non-initial term having the second level of impact on the goodness of fit to update the chuck model;
measuring a voltage and current to generate a measured voltage and current, wherein said measuring is performed by a voltage and current probe within the RF generator, wherein the voltage and current probe is coupled to an output of the RF generator;
propagating the measured voltage and current via the cable model, the match model, and the transmission model to generate modeled voltage and current;
calculating the wafer DC bias at a top surface of the chuck of the plasma chamber by propagating the modeled voltage and current via the remaining ones of the plurality of initial terms and the non-initial term in the chuck model; and
controlling the plasma chamber based on the wafer DC bias to process a substrate placed within the plasma chamber.
1 Assignment
0 Petitions
Accused Products
Abstract
Systems and methods for defining a refined RF model of an RF transmission path includes identifying a selected initial term in the RF model having a least significant impact on a goodness of fit of the RF model with the selected initial term removed from the RF model. The initial term having the least significant impact on the goodness of fit is removed from the RF model. A selected non-initial term having a most significant impact on the goodness of fit of the RF model is identified and added to the RF model. The non-initial term being selected from a set of terms describing corresponding elements of the RF transmission path. The initial terms and non-initial terms having the most significant impact of goodness of fit are selected for a refined RF model.
48 Citations
20 Claims
-
1. A method of defining a chuck model for a radio frequency (RF) transmission path to calculate a wafer direct current (DC) bias at a chuck of a plasma chamber, comprising:
-
generating, by a computer, a cable model of an RF cable, a match model of an impedance matching circuit, a transmission model of an RF transmission line, and the chuck model, wherein the chuck model includes a series circuit model and a shunt circuit model, wherein the RF cable couples an RF generator to the impedance matching circuit and the RF transmission line couples the impedance matching circuit to the chuck; identifying an initial term in the chuck model having a first level of impact on a goodness of fit of the chuck model, wherein the initial term is identified from a plurality of initial terms; removing the initial term having the first level of impact on the goodness of fit from the chuck model, wherein the chuck model has a plurality of remaining ones of the plurality of initial terms after said removing of the initial term; identifying a non-initial term having a second level of impact on the goodness of fit of the chuck model with the non-initial term added to the chuck model, wherein the non-initial term is not one of the plurality of initial terms and is identified from a plurality of non-initial terms, wherein the second level of impact is greater than the first level of impact; selecting the remaining ones of the plurality of initial terms and the non-initial term having the second level of impact on the goodness of fit to update the chuck model; measuring a voltage and current to generate a measured voltage and current, wherein said measuring is performed by a voltage and current probe within the RF generator, wherein the voltage and current probe is coupled to an output of the RF generator; propagating the measured voltage and current via the cable model, the match model, and the transmission model to generate modeled voltage and current; calculating the wafer DC bias at a top surface of the chuck of the plasma chamber by propagating the modeled voltage and current via the remaining ones of the plurality of initial terms and the non-initial term in the chuck model; and controlling the plasma chamber based on the wafer DC bias to process a substrate placed within the plasma chamber. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
-
-
10. A method of defining a chuck model for a radio frequency (RF) transmission path to calculate a wafer direct current (DC) bias at a chuck of a plasma chamber, comprising:
-
generating, by a computer, a cable model of an RF cable, a match model of an impedance matching circuit, a transmission model of an RF transmission line, and the chuck model, wherein the chuck model includes a series circuit model and a shunt circuit model, wherein the RF cable couples an RF generator to the impedance matching circuit and the RF transmission line couples the impedance matching circuit to the chuck; selecting a first of a plurality of initial terms of the chuck model and a second of the plurality of initial terms in the chuck model; removing the first and second initial terms from the chuck model; determining a goodness of fit of the chuck model including remaining ones of the plurality of initial terms after said removing the first and second initial terms; recording the goodness of fit of the chuck model including the remaining ones of the plurality of initial terms; selecting a first additional term from a plurality of non-initial terms; adding the first additional term to the chuck model; determining a goodness of fit of the chuck model including the first additional term and the remaining ones of the plurality of initial terms; recording the goodness of fit of the chuck model including the additional term and the remaining ones of the plurality of initial terms to update the chuck model; measuring a voltage and current to generate a measured voltage and current, wherein said measuring is performed by a voltage and current probe within the RF generator, wherein the voltage and current probe is coupled to an output of the RF generator; propagating the measured voltage and current via the cable model, the match model, and the transmission model to generate modeled voltage and current; calculating the wafer DC bias at a top surface of the chuck of the plasma chamber by propagating the modeled voltage and current via the additional term and the remaining ones of the plurality of initial terms in the chuck model; and controlling the plasma chamber based on the wafer DC bias to process a substrate placed within the plasma chamber. - View Dependent Claims (11, 12, 13)
-
-
14. A method of defining a chuck model for a radio frequency (RF) transmission path to calculate a wafer direct current (DC) bias at a chuck of a plasma chamber, comprising:
-
generating, by a computer, a cable model of an RF cable, a match model of an impedance matching circuit, a transmission model of an RF transmission line, and the chuck model, wherein the chuck model includes a series circuit model and a shunt circuit model, wherein the RF cable couples an RF generator to the impedance matching circuit and the RF transmission line couples the impedance matching circuit to the chuck; designating a number of permanent terms and designating a number of random terms in the chuck model; determining a goodness of fit of the chuck model with one of the permanent terms removed from the chuck model; determining a goodness of fit of the chuck model with the one of the permanent terms of the chuck model removed from the chuck model and replaced with an additional term selected from a plurality of terms to update the chuck model; measuring a voltage and current to generate a measured voltage and current, wherein said measuring is performed by a voltage and current probe within the RF generator, wherein the voltage and current probe is coupled to an output of the RF generator; propagating the measured voltage and current via the cable model, the match model, and the transmission model to generate modeled voltage and current; calculating the wafer DC bias at the chuck of the plasma chamber by propagating the modeled voltage and current via remaining ones of the permanent terms, the additional term, and the random terms in the chuck model; and controlling the plasma chamber based on the wafer DC bias to process a substrate placed within the plasma chamber. - View Dependent Claims (15, 16, 17, 18)
-
-
19. A method for defining and optimizing a chuck model for a radio frequency (RF) path to calculate a wafer direct current (DC) bias at a chuck of a plasma chamber, comprising:
-
generating, by a computer, a cable model of an RF cable, a match model of an impedance matching circuit, a transmission model of an RF transmission line, and the chuck model, wherein the RF cable couples an RF generator to the impedance matching circuit and the RF transmission line couples the impedance matching circuit to the chuck; changing a number of terms in the chuck model until a parameter level is achieved to optimize the chuck model to generate an optimized chuck model; measuring a voltage and current to generate a measured voltage and current, wherein said measuring is performed by a voltage and current probe within the RF generator, wherein the voltage and current probe is coupled to an output of the RF generator; propagating the measured voltage and current via the cable model, the match model, and the transmission model to generate model data at an output of the transmission model; applying the model data to the optimized chuck model to calculate the wafer DC bias at the chuck; and controlling the plasma chamber based on the wafer DC bias to process a substrate placed within the plasma chamber. - View Dependent Claims (20)
-
Specification