Using modeling to determine wafer bias associated with a plasma system

Patent metadata

Field	Value
Publication number	US-9502216-B2
Application number	US-201313756390-A
Country	US
Kind code	B2
Filing date	Jan 31, 2013
Priority date	Jan 31, 2013
Publication date	Nov 22, 2016
Grant date	Nov 22, 2016

Abstract

Systems and methods for determining wafer bias are described. One of the methods includes detecting output of a generator to identify a generator output complex voltage and current (V&I). The generator is coupled to an impedance matching circuit and the impedance matching circuit is coupled to an electrostatic chuck (ESC). The method further includes determining from the generator output complex V&I a projected complex V&I at a point along a path between an output of a model of the impedance matching circuit and a model of the ESC. The operation of determining of the projected complex V&I is performed using a model for at least part of the path. The method includes applying the projected complex V&I as an input to a function to map the projected complex V&I to a wafer bias value at the ESC model.

First claim

The invention claimed is:

1. A method for determining wafer bias, the method comprising:
receiving, by a processor from an output of a generator, a generator output complex voltage and current, the generator coupled to an impedance matching circuit, the impedance matching circuit coupled via a radio frequency (RF) transmission line to an electrostatic chuck (ESC) of a plasma chamber;
determining, by the processor, from the generator output complex voltage and current a projected complex voltage and current at a point along a path between an output of a model of the impedance matching circuit and a model of the ESC, the determining of the projected complex voltage and current performed using a model for at least part of the path, the model for at least part of the path characterizing physical components along the path, the model for at least part of the path including an RF transmission model of the RF transmission line, wherein the RF transmission model includes a model of an RF tunnel and a model of an RF strap, the RF tunnel model coupled with the RF strap model; and
applying, by the processor, the projected complex voltage and current as an input to a function to map the projected complex voltage and current to a wafer bias value at the ESC model.

2. The method of claim 1 , wherein the function is characterized by a summation of values that represent physical attributes of the path, wherein the projected complex voltage and current is used in the summation of the values.

3. The method of claim 2 , wherein the physical attributes of the path are derived values from test data.

4. The method of claim 1 , wherein the function is a sum of characterized values and a constant, the characterized values including magnitudes and coefficients, the magnitudes derived from the projected complex voltage and current, the coefficients and the constant incorporating empirical modeling data.

5. The method of claim 4 , wherein the coefficients are coefficients of the magnitudes.

6. The method of claim 4 , wherein the empirical modeling data includes data obtained based on measurements of wafer bias at the ESC, based on determinations of magnitudes of complex voltages and currents, and based on an application of estimation statistical method to the measurements of the wafer bias at the ESC and the magnitudes of complex voltages and currents, the determination of the magnitudes of complex voltages and currents made based on the model of the impedance matching circuit and the model for at least part of the path.

7. The method of claim 1 , wherein the function includes a sum of a first product, a second product, a third product, and a constant, wherein the first product is a product of a coefficient and a voltage magnitude, the second product is a product of a coefficient and a current magnitude, the third product is a product of a coefficient and a square root of power magnitude, the voltage magnitude extracted from the projected complex voltage and current, the current magnitude extracted from the projected complex voltage and current, the power magnitude calculated from the current magnitude and the voltage magnitude.

8. A method for determining wafer bias, the method comprising:
receiving, by a processor, one or more generator output complex voltages and currents measured at one or more outputs of one or more generators, the one or more generators coupled to an impedance matching circuit, the impedance matching circuit coupled via a radio frequency (RF) transmission line to an electrostatic chuck (ESC) of a plasma chamber;
determining, by the processor, from the one or more generator output complex voltages and currents a projected complex voltage and current at a point along a path between a model of the impedance matching circuit and a model of the ESC, the model of the impedance matching circuit characterizing the impedance matching circuit and the model of the ESC characterizing the ESC, wherein the path includes an RF transmission model of the RF transmission line, wherein the RF transmission model includes a model of an RF tunnel and a model of an RF strap, the RF tunnel model coupled with the RF strap model; and
calculating, by the processor, a wafer bias at the point by using the projected complex voltage and current as an input to a function.

9. The method of claim 8 , wherein the function is characterized by a summation of values that represent physical attributes of the path, wherein the projected complex voltage and current is used in the summation of the values.

10. The method of claim 9 , wherein the physical attributes of the path are derived values from test data.

11. The method of claim 8 , wherein the function is a sum of characterized values and a constant, the characterized values including magnitudes and coefficients, the magnitudes derived from the projected complex voltage and current, the coefficients and the constant incorporating empirical modeling data.

12. The method of claim 11 , wherein the coefficients are coefficients of the magnitudes.

13. The method of claim 11 , wherein the empirical modeling data includes data obtained based on measurements of wafer bias at the ESC, based on determinations of magnitudes of complex voltages and currents, and based on an application of estimation statistical method to the measurements of the wafer bias at the ESC and the magnitudes of complex voltages and currents, the determination of the magnitudes of complex voltages and currents made based on the model of the impedance matching circuit and a model for at least part of the path.

14. The method of claim 8 , wherein the function includes a sum of a first product, a second product, a third product, and a constant, wherein the first product is a product of a coefficient and a voltage magnitude, the second product is a product of a coefficient and a current magnitude, the third product is a product of a coefficient and a square root of power magnitude, the voltage magnitude identified from the projected complex voltage and current, the current magnitude identified from the projected complex voltage and current, the power magnitude determined from the current magnitude and the voltage magnitude.

15. A method for determining wafer bias, the method comprising:
identifying, by a processor, a first complex voltage and current measured at an output of a radio frequency (RF) generator when the RF generator is coupled to a plasma chamber via an impedance matching circuit, the impedance matching circuit having an input coupled to the output of the RF generator and an output coupled to an RF transmission line;
generating, by the processor, an impedance matching model based on electrical components defined in the impedance matching circuit, the impedance matching model having an input and an output, the input of the impedance matching model receiving the first complex voltage and current, the impedance matching model having one or more elements;
generating, by the processor, an RF transmission model based on circuit components defined in the RF transmission line, wherein the RF transmission model includes a model of an RF tunnel and a model of an RF strap, the RF tunnel model coupled with the RF strap model;
propagating, by the processor, the first complex voltage and current through the one or more elements from the input of the impedance matching model to the output of the impedance matching model to determine a second complex voltage and current, wherein the second complex voltage and current is at the output of the impedance matching model; and
determining, by the processor, a wafer bias based on a voltage magnitude of the second com

Assignees

• Valcore Jr John C
• Lyndaker Bradford J
• Lam Res Corp

Inventors

• Valcore Jr John C
• Lyndaker Bradford J

Classifications

• H01J37/32926 Primary

  Software, data control or modelling · CPC title

• H01J37/32174 Primary

  Circuits specially adapted for controlling the RF discharge · CPC title

• H01J37/32183 Primary

  Matching circuits · CPC title

• H01J37/32697

  Electrostatic control · CPC title

• H01J37/32706

  Polarising the substrate · CPC title