Comprehensive Guide: How to Determine Energy in a Plasma Window

Summary

Determining the energy in a plasma window involves the use of various measurable and quantifiable techniques, including Quadrupole Mass Spectrometers (QMS), radio-frequency current and voltage measurements, and the calculation of ion energy distribution functions (IEDs) and the energy stored in the electric field. These methods provide insights into ion fluxes, sheath voltages, plasma potential, and the overall energy characteristics of the plasma, enabling a comprehensive understanding of the energy stored within the plasma window.

Quadrupole Mass Spectrometry (QMS) for Ion Energy Measurement

Quadrupole Mass Spectrometers (QMS) are a powerful tool for measuring ion energies in a plasma window. A QMS setup typically comprises an energy analyzer, a quadrupole mass filter, and an ion detector, allowing for the measurement of ion fluxes with specific energies that can pass through the energy analyzer.

Principle of QMS Ion Energy Measurement

The energy analyzer in a QMS setup selects ions with a specific energy range, which are then filtered by the quadrupole mass filter and detected by the ion detector. By sweeping the energy of the analyzer, the ion energy distribution function (IEDF) can be obtained, providing insights into the energy distribution of ions in the plasma.

Advantages of QMS for Ion Energy Measurement

1. Noninvasive Monitoring: QMS measurements are noninvasive, allowing for the determination of ion energies and ion currents at the wafer surface during plasma etching without disturbing the plasma.
2. Ion Energy Drift Monitoring: QMS can be used to monitor the ion energy drift in an inductively coupled plasma reactor, enabling the tracking of changes in the ion energy distribution over time.
3. Quantitative Data: QMS provides quantitative data on ion fluxes and energies, which can be used to calculate the total energy stored in the plasma.

Practical Considerations for QMS Measurements

1. Energy Analyzer Settings: The energy analyzer settings, such as the applied voltage and the energy resolution, need to be carefully optimized to obtain accurate ion energy measurements.
2. Plasma Conditions: The plasma conditions, such as pressure, power, and gas composition, can affect the ion energy distribution and should be taken into account when interpreting the QMS data.
3. Calibration and Validation: Proper calibration and validation of the QMS system are essential to ensure the reliability of the ion energy measurements.

Radio-Frequency Current and Voltage Measurements

Radio-frequency (RF) current and voltage measurements can be used to monitor sheath voltages and ion energies in high-density plasmas, providing real-time data on ion energy and ion current at the wafer surface during plasma etching.

Principle of RF Current and Voltage Measurements

By measuring the RF current and voltage at the wafer surface or the electrode, the sheath voltage and ion energy can be calculated. The sheath voltage is directly related to the ion energy, as the ions are accelerated through the sheath region before reaching the wafer surface.

Advantages of RF Current and Voltage Measurements

1. Noninvasive Monitoring: RF current and voltage measurements are noninvasive, allowing for the real-time monitoring of ion energy and ion current without disturbing the plasma.
2. Plasma Parameter Calculation: The measured RF current and voltage can be used to calculate various plasma parameters, such as the sheath voltage, plasma potential, and ion energy, which are essential for determining the energy stored in the plasma.
3. Temporal Resolution: RF current and voltage measurements provide high temporal resolution, enabling the tracking of changes in ion energy and ion current during the plasma etching process.

Practical Considerations for RF Current and Voltage Measurements

1. Probe Placement: The placement of the RF current and voltage probes is crucial, as they need to be positioned to accurately measure the relevant parameters at the wafer surface or the electrode.
2. Calibration and Validation: Proper calibration and validation of the RF measurement system are necessary to ensure the accuracy of the sheath voltage and ion energy calculations.
3. Plasma Conditions: The plasma conditions, such as pressure, power, and gas composition, can affect the sheath voltage and ion energy, and should be taken into account when interpreting the RF measurement data.

Ion Energy Distribution Function (IEDF) Calculation

The calculation of the ion energy distribution function (IEDF) provides insights into the energy distribution of ions in the plasma, which can be used to determine the total energy stored in the plasma.

Methods for IEDF Calculation

1. Number of Ions Method: The IEDF can be calculated by considering the number of ions with a specific energy, as shown in Figure 5(a) in the reference.
2. Cross-Section Method: The IEDF can also be calculated by considering the cross-section of the ions, as depicted in Figure 5(c) in the reference.

Advantages of IEDF Calculation

1. Energy Distribution Insights: The IEDF calculation provides detailed information about the energy distribution of ions in the plasma, which is essential for understanding the overall energy characteristics of the plasma.
2. Total Energy Determination: The IEDF can be used to calculate the total energy stored in the plasma by integrating the energy distribution over the entire energy range.
3. Plasma Optimization: The IEDF calculation can be used to optimize the plasma conditions, such as pressure, power, and gas composition, to achieve the desired ion energy distribution and energy storage in the plasma.

Practical Considerations for IEDF Calculation

1. Measurement Techniques: The accuracy of the IEDF calculation depends on the reliability of the ion energy measurement techniques, such as QMS or RF current and voltage measurements.
2. Plasma Conditions: The IEDF can be affected by the plasma conditions, such as pressure, power, and gas composition, and these factors should be taken into account when interpreting the IEDF data.
3. Numerical Modeling: In some cases, numerical modeling may be required to accurately calculate the IEDF, especially in complex plasma environments.

Energy Stored in the Electric Field

The energy stored in the electric field of a plasma can be calculated using the formula $U = \frac{1}{2} \epsilon E^{2}$, where $U$ is the energy, $\epsilon$ is the permittivity of the medium, and $E$ is the electric field.

Advantages of Electric Field Energy Calculation

1. Comprehensive Energy Determination: The energy stored in the electric field is an important component of the total energy stored in the plasma, and its calculation provides a more complete understanding of the energy characteristics of the plasma.
2. Plasma Diagnostics: The calculation of the electric field energy can be used as a diagnostic tool to monitor changes in the plasma’s electric field and its impact on the overall energy storage.
3. Plasma Optimization: The electric field energy calculation can be used to optimize the plasma conditions, such as power and gas composition, to achieve the desired energy storage in the electric field.

Practical Considerations for Electric Field Energy Calculation

1. Electric Field Measurement: Accurate measurement of the electric field in the plasma is essential for the energy calculation, and this may require the use of specialized diagnostic techniques, such as Langmuir probes or optical methods.
2. Permittivity Determination: The permittivity of the medium in the plasma window needs to be accurately determined, as it can vary depending on the plasma conditions and the gas composition.
3. Spatial Variations: The electric field and the permittivity in the plasma can have spatial variations, and these variations should be taken into account when calculating the energy stored in the electric field.

Conclusion

Determining the energy in a plasma window is a crucial aspect of understanding and optimizing the performance of plasma-based processes. By employing a combination of Quadrupole Mass Spectrometry (QMS), radio-frequency current and voltage measurements, ion energy distribution function (IEDF) calculations, and electric field energy calculations, researchers and engineers can obtain a comprehensive understanding of the energy characteristics of the plasma, enabling the optimization of plasma-based applications.

Reference:

1. Xu, Z., Ding, Z., Jiang, W., Jiang, Y., & Ding, H. (2022). Noninvasive Monitoring of Ion Energy Drift in an Inductively Coupled Plasma Reactor Using Quadrupole Mass Spectrometry. Sensors, 22(16), 6254. https://www.mdpi.com/1424-8220/22/16/6254
2. Xu, Z., Ding, Z., Jiang, W., Jiang, Y., & Ding, H. (2022). Noninvasive Monitoring of Ion Energy Drift in an Inductively Coupled Plasma Reactor Using Quadrupole Mass Spectrometry. Sensors, 22(16), 6254. https://www.mdpi.com/1424-8220/22/16/6254
3. Physics Stack Exchange. (n.d.). Quantifying electrical energy stored in a plasma. https://physics.stackexchange.com/questions/429780/quantifying-electrical-energy-stored-in-a-plasma