Probe Measurements of Electron Energy Distributions in Gas Discharge Plasmas V. A. Godyak 1 and V. I. Demidov 2 1 RF Plasma Consulting, Brookline, MA 02446, USA 2 West Virginia University, Morgantown, WV 26506, USA . Electron Distribution Function f. , .
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Probe Measurements of Electron Energy Distributions in Gas Discharge Plasmas
V. A. Godyak1 and V. I. Demidov2
1 RF Plasma Consulting, Brookline, MA 02446, USA
2West Virginia University, Morgantown, WV 26506, USA
Electron Distribution Function Discharge Plasmas
Two-term approximation (small anisotropy, f1 << f0)
Electron Energy Distribution (EEDF) and Discharge PlasmasElectron Energy Probability (EEPF) Functions
F(t,r ε) =
Langmuir formula and Druyvesteyn method Discharge Plasmas
Similarly, all plasma parameters (Tesk, λD, JB) and rates of plasma-chemical processes (νea, νee, ν*, νi, ….) can be found as appropriate integrals of the measured EEPF.
a = 38 μm
b = 175 μm
Probe constructions Discharge Plasmas
a = 0.05 mm, b = 1 mm, c = 2-3 mm
Probe circuit resistance Discharge Plasmas(the most frequent problem)
EEPF Druyvesteynization due to R Discharge Plasmasc
δ = Rc/Rpmin Rpmin= Te/eIesat
Error in EEPF less than 3% requires Rc/Rpmin < 0.01 !
Example of EEPF measurement in argon ICP with a low disturbance probe having Rc and noise compensation
Maximal argon pressure, where measurement was possible, was limited by the chamber surface
Argon, 20 mTorr disturbance probe having R
VGPS: emax = 15-22 eV
νee ∞ NTe-3/2
Argon, 20 mTorr
Espion: emax = 7-11eV
Distorted @ low energy and lost information @ high energy
Comparison of EEPF measured with different commercial probe stations
At maximal discharge power of 2 kW, N ≈ 1·1012 cm-3,thus EEPF has to be Maxwellian
RF plasma potential Maxwellian
Criterion for undistorted by rf sheath voltage EEPF measurement is known for over 30 years (1979)
Zpr/Zf ≤ (0.3-0.5)Te/eVplrf
A presence of a filter in the probe circuit does not guarantee undistorted EEPF measurement. To do the job, the filter has to satisfy the following condition for all relevant harmonics:
Zf ≥ (2-3)ZpreVplrf /Te
For filter design we need to know (measure!)Vplrf and minimize Zpr
Filter design procedure Maxwellian
Zpr is defined by its sheath capacitance at floating potential
Probe measurement circuit incorporating, dc voltage and low frequency noise suppression, rf compensation and rf filter dc resistance compensation with I/V converter having a negative input resistance
Example of EEPF measurement demonstrating a paradoxical Te distribution in argon 13.56 MHz CCP
30 mTorr, Teo < Tes 300 mTorr, Teo > Tes
EEPF and plasma parameters evolution during CCP transition to the γ- mode
EEPF measured in afterglow stage of ICP with internal ferrite core inductor
EEPF and T to the e measured along rf period in an induction lamp operated at 300 mTorr Ar and 7 mTorr Hg
Time resolution δt = 0.5 μS. Note asymmetry in Te(ωt)
Probe sheath capacitance to plasma is the main limiting factor in EEPF measurement speed. The minimal time resolution, δt > (10-30)ωpi
Ion current effect to the
Ip = Ie + Ii and I”p = Ie”+ Ii”
Ion current effect occurs in light gases, low density plasmas and small probes, and is maximal at orbital ion motion (a/λD < 1), according to:
Ie”/Ii” = (4πM/m)1/2η3/2exp(-η)η = eV/Te
In practice, Ii” effect is essentially smaller and can be neglected
Ratio Ie”/Ii” depends on EEPF and a/λD
Relative I to the i” effect for orbital and radial ion motion for Maxwellian and Druyvesteyn distributions
Ie”, Ii”, Ip”
Accounting for I to the i” contribution
In many works and commercial probe instruments, the extrapolated from large negative probe potential Ii(V) is subtracted from Ip(V) with following differentiation. Due to uncertainty of the extrapolation and error augmentation caused by differentiation this way of accounting for Ii” brings more error than correction.
Probe surface effects to the
Ne + 5% benzyl
Mo Ta W
(Wide specter and large amplitude of rf plasma potential and
high rate of probe contamination are the major problems)
Microcrystalline silicon deposition H2/CF4 30 mTorr ICP with Ar/SiF4 10 mTorr ECR. polymer deposition. Ecole Polytechnique University of Maryland
A remark to the
Today, plasma simulation codes are practically main tool for study plasma electrodynamics, plasma transport and plasma kinetics in commercial plasma reactors. These codes applied to complicated processing gas mixture are missing many cross sections for variety of (accounted and not) plasma-chemical reactions.
They also are missing effects of nonlocal and nonlinear plasma electrodynamics that has been proved can be important and even dominant in rf plasmas at low gas pressure.
In such situation, a feasibility of EEDF measurement in plasma chemical reactors would give a valuable experimental data for understanding variety of kinetic process in such plasmas and validation of existing numerical codes.