Abstract
The electron energy distribution function (EEDF) in low pressure plasmas is typically evaluated by using the second derivative d2I/dV2 of a Langmuir probe I–V characteristic (Druyvesteyn formula). Since measured probe characteristics are inherently noisy, two-time numerical differentiation requires data smoothing techniques. This leads to a dependence on the employed filtering technique, and information particularly in the region near the plasma potential can easily get lost. As an alternative to numerical differentiation of noisy probe data, a well-known AC probe technique is adopted to measure d2I/dV2 directly. This is done by superimposing a sinusoidal AC voltage of 13 kHz on the probe DC bias and performing a Fourier analysis of the current response. Parameters such as the modulation amplitude (up to 1.5 V) and the number of applied sine oscillations per voltage step of the DC ramp are carefully chosen by systematic parameter variations. The AC system is successfully benchmarked in argon and applied to hydrogen plasmas at a laboratory inductively coupled plasma experiment (4–10 Pa gas pressure, 300–1000 W RF power). It is shown that the EEDF is reliably accessible with high accuracy and stability in the low energy range. Hence, a trustworthy determination of basic plasma parameters by integration of the EEDF can be provided.
Highlights
The kinetic energy distribution of electrons in low pressure plasmas is a crucial parameter because it is the main determinant for the rate of occurring reactions such as ionization, dissociation, or excitation processes
The electron energy distribution function (EEDF) in low pressure plasmas is typically evaluated by using the second derivative d2I=dV2 of a Langmuir probe I–V characteristic (Druyvesteyn formula)
Fourier transformation (FFT) processing gain increases with increasing number of samples, the signal-to-noise ratio (SNR) for determining the current amplitude Ip26 kHz at twice the modulation frequency can be improved by a higher number of applied sine oscillations
Summary
The kinetic energy distribution of electrons in low pressure plasmas is a crucial parameter because it is the main determinant for the rate of occurring reactions such as ionization, dissociation, or excitation processes. The most straightforward and commonly used technique to determine the second derivative is two-time numerical differentiation of the I–V characteristic Using this approach, special attention must be paid to the accuracy of the measured probe curve since even small perturbations or fluctuations can lead to enormous distortions in the second derivative due to error magnification.[6,7] As described in detail by Godyak and Demidov,[5] the low energy range of the EEDF is highly sensitive to the differentiation procedure because the second derivative falls from its maximum to zero when reaching the plasma potential. By comparison to a conventional DC probe system using numerical differentiation with Savitzky– Golay (SG) smoothing,[29] it is shown that the AC result is more robust against small fluctuations and errors in the probe current especially near zero energy
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