Self-bias calculation on a substrate in a process chamber with bias power for single or multiple frequencies

1. A method for calculating a self-bias on a substrate in a process chamber, comprising:

measuring a DC potential of a substrate disposed on a substrate support of a process chamber while providing a bias power from a power source to a cathode at a first frequency, wherein the DC potential is measured by a probe that contacts the substrate within the process chamber;

measuring a voltage, a current and a phase shift while providing the bias power at the first frequency;

calculating, by a central processing unit of a controller, an effective impedance of the cathode by determining a linear relationship between a calculated voltage and the measured DC potential of the substrate, wherein the calculated voltage is a function of the effective impedance, measured voltage, current and phase shift;

calculating, by the central processing unit, a first linear coefficient and a second linear coefficient of the linear relationship between the calculated voltage and the measured DC potential of the substrate; and

calculating, by the central processing unit, a self bias on the substrate by utilizing the first linear coefficient, second linear coefficient, measured DC potential of the substrate, effective impedance, and measured phase shift.

2. The method of claim 1 , wherein the voltage, current and phase shift is measured at an output of a matching network coupled to the power source or an input of the cathode while providing the bias power at the first frequency.

3. The method of claim 1 , wherein the first linear coefficient is a slope and the second linear coefficient is the shift of the linear relationship between the calculated voltage and the measured DC potential of the substrate.

4. The method of claim 1 , wherein the self bias is defined by:

the first linear coefficient * |V_meas +Zeff*I_meas*e^(j*Phase_meas)|+the second linear coefficient,

wherein V_meas is the measured DC potential of the substrate, Zeff is the effective impedance, I_meas is the measured current, Phase_meas is the measured phase shift, and j is a complex number.

5. The method of claim 1 , wherein the calculated voltage is defined by:

| V _meas+ Z eff* I _meas* e ^( j *Phase_meas)|

wherein V_meas is the measured DC potential of the substrate, Zeff is the effective impedance, I_meas is the measured current, and Phase_meas is the measured phase shift, and j is a complex number.

6. The method of claim 1 , wherein determining the linear relationship between the calculated voltage and the measured DC potential of the substrate comprises:

calculating a Pearson product-moment correlation coefficient (r) between the calculated voltage and the measured DC potential, wherein the linear relationship is determined when the Pearson product-moment correlation coefficient (r) is about −1.

7. The method of claim 1 , further comprising:

repeating the method by measuring the DC potential of the substrate at a second frequency, and measuring the voltage, the current and the phase shift at the matching network at a second frequency;

calculating the effective impedance, first linear coefficient, second linear coefficient and self bias utilizing the DC potential, voltage, current and phase shift measured at the second frequency; and

adding the self-bias calculated at the first frequency to the self-bias calculated at the second frequency to get a total self-bias.

8. The method of claim 1 , wherein measuring the first DC voltage of the substrate comprises:

touching a probe to the substrate; and

obtaining the DC potential of a substrate measurement from the probe.

9. The method of claim 8 , further comprising:

measuring the voltage, the current, and the phase shift while touching the probe to the substrate.

10. The method of claim 1 , further comprising:

forming a plasma in the process chamber; and

measuring the DC potential of the substrate at a second frequency, and measuring the voltage, the current, and the phase shift at the matching network while a plasma is present in the process chamber.

11. A non-transitory computer readable medium, having instructions stored thereon that, when executed, cause a method for calculating a self-bias on a substrate in a process chamber to be performed, the method comprising:

measuring a DC potential of a substrate disposed on a substrate support of a process chamber while providing a bias power from a power source to a cathode at a first frequency, wherein the DC potential is measured by a probe that contacts the substrate;

measuring a voltage, a current and a phase shift while providing the bias power at the first frequency;

calculating, by a central processing unit of a controller, an effective impedance of the cathode by determining a linear relationship between a calculated voltage and the measured DC potential of the substrate, wherein the calculated voltage is a function of the effective impedance, measured voltage, current and phase shift;

calculating, by the central processing unit, a first linear coefficient and a second linear coefficient of the linear relationship between the calculated voltage and the measured DC potential of the substrate; and

calculating, by the central processing unit, a self bias on the substrate by utilizing the first linear coefficient, second linear coefficient, measured DC potential of the substrate, effective impedance, and measured phase shift.

12. The non-transitory computer readable medium of claim 11 , wherein the voltage, current and phase shift is measured at an output of a matching network coupled to the power source or an input of the cathode while providing the bias power at the first frequency.

13. The non-transitory computer readable medium of claim 11 , wherein the first linear coefficient is a slope and the second linear coefficient is the shift of the linear relationship between the calculated voltage and the measured DC potential of the substrate.

14. The non-transitory computer readable medium of claim 11 , wherein the self bias is defined by:

the first linear coefficient * |V_meas +Zeff*I_meas*e^(j*Phase_meas)|+the second linear coefficient,

wherein V_meas is the measured DC potential of the substrate, Zeff is the effective impedance, I_meas is the measured current, Phase_meas is the measured phase shift, and j is a complex number.

15. The non-transitory computer readable medium of claim 11 , wherein the calculated voltage is defined by:

| V _meas+ Z eff* I _meas* e ^( j *P hase_meas)|

wherein V_meas is the measured DC potential of the substrate, Zeff is the effective impedance, I_meas is the measured current, Phase_meas is the measured phase shift, and j is a complex number.

16. The non-transitory computer readable medium of claim 11 , wherein determining the linear relationship between the calculated voltage and the measured DC potential of the substrate comprises:

calculating a Pearson product-moment correlation coefficient (r) between the calculated voltage and the measured DC potential, wherein the linear relationship is determined when the Pearson product-moment correlation coefficient (r) is about −1.

17. The non-transitory computer readable medium of claim 11 , wherein the method further comprises:

repeating the method by measuring the DC potential of the substrate at a second frequency, and measuring the voltage, the current and the phase shift at the matching network at a second frequency;

calculating the effective impedance, first linear coefficient, second linear coefficient and self bias utilizing the DC potential, voltage, current and phase shift measured at the second frequency; and

adding the self-bias calculated at the first frequency to the self-bias calculated at the second frequency to get a total self-bias.

18. The non-transitory computer readable medium of claim 11 , wherein measuring the first DC voltage of the substrate comprises:

touching a probe to the substrate; and

obtaining the DC potential of a substrate measurement from the probe.

19. The non-transitory computer readable medium of claim 18 , further comprising:

measuring the voltage, the current and the phase shift while touching the probe to the substrate.

20. The non-transitory The computer readable medium of claim 11 , further comprising:

forming a plasma in the process chamber; and

measuring the DC potential of the substrate at a second frequency, and measuring the voltage, the current and the phase shift at the matching network while a plasma is present in the process chamber.