an experimental and analytical study of an asymmetric … · 2018. 11. 8. · global model...

A. Michelmore, J.D. Whittle, R.D. Short, R.W. Boswell and

C. Charles

Plasma Processes Polym., 2014, DOI:10.1002/ppap.201400026

An Experimental and Analytical Study of an Asymmetric Capacitively

Coupled Plasma Used for Plasma Polymerization

Mawson Institute

Project Aims • To develop a simple model of a capacitively coupled

plasma

• To verify the model experimentally using a simple, commercially available device (OctIV probe)

• Parameters of interest – Ion flux

– Bias voltages

– Electrode separation

Experimental setup and model

Reactor check (OctIV pre-match)

Load impedance and Q factor relatively constant with applied RF power

Model development (symmetric)

• For all plasma discharges: – mi = nsheaths uB (Bohm flux)

– Pi = e nsheaths uB DV (Ion Energy Flux) • Where nsheaths is the plasma density at the sheath edge

for a symmetrical discharge

• Power balance gives:

– 𝑛sheath𝑠=

𝑃𝑟𝑚𝑠

𝑒𝑢𝐵 𝐴𝑙𝑖𝑣𝑒 𝐸𝑐+𝐸𝑒+𝑉𝑝𝑠 +𝐴𝑒𝑎𝑟𝑡ℎ 𝐸𝑐+𝐸𝑒+𝑉𝑝𝑠

– =𝑃𝑟𝑚𝑠

2𝑒𝑢𝐵𝐴𝑙𝑖𝑣𝑒 𝐸𝑐+𝐸𝑒+𝑉𝑝𝑠 for Alive = Aearth (symmetric)

Global model (Asymmetric)

• Assume Zplasma ~ 0 and discharge is two capacitors in series

• Plasma potential is affected by asymmetry

• 𝑉𝑝 𝑡 = 𝑉𝑝𝑑𝑐+ 𝑉𝑝𝑟𝑓

sin 𝜔𝑡 and 𝑉𝑝𝑟𝑓=

𝐶live𝐶live+𝐶earth

𝑉𝑟𝑓 ~ 𝐴live

𝐴earth𝑉𝑟𝑓

• 𝑉𝑙𝑖𝑣𝑒 𝑡 = 𝑉𝑑𝑐 + 𝑉𝑟𝑓 sin 𝜔𝑡 and 𝑉𝑑𝑐 = 𝑉self−bias

• Vself-bias can be measured using OctIV probe, or estimated by:

• Vself-bias = -[0.83x1.4xQ(ZPrms)1/2 + 5 kTe] (assume Te = 3eV)

Power Balance

• For asymmetric discharge, ion flux and sheath edge equations must be modified

• 𝑛sheath𝐴=

𝑃𝑟𝑚𝑠

𝑒𝑢𝐵 𝐴live 𝐸𝑐+𝐸𝑒+ 𝑉𝑝𝑑𝑐−𝑉self−bias +𝐴earth

′ 𝐸𝑐+𝐸𝑒+𝑉𝑝𝑑𝑐

• And mi = nsheathA uB

• Ion Energy Flux equations must also be modified for live and earthed electrodes

• 𝑃𝐴live= 𝑒𝑛sheath𝐴

𝑢𝐵(𝑉𝑝𝑑𝑐− 𝑉self−bias)

• 𝑃𝐴earth= 𝑒𝑛sheath𝐴

𝑢𝐵𝑉𝑝𝑑𝑐

Comparison with Ar data (electrode separation 4cm)

Solid lines are model predictions Good agreement observed

Comparison with Ar data (electrode separation 22cm)

Measured self bias voltage (red squares) Solid line is model prediction Measured ion energy (blue diamonds) Dashed line assumes Vp = 5kTe

Dotted line assumes Vp = 8kTe

Measured ion flux Solid line is model prediction

Comparison with a range of depositing monomers (amines, acids, HMDSO etc)

Measured self bias voltage

Measured ion flux (note RF Power = power deposited into plasma)

Power transfer efficiency

Oxygen

Argon

Allylamine

Power transfer efficiency is affected by gas chemistry

Conclusions

• Simple model developed for plasma systems

• Comparison with experimental data shows good agreement

• Modelling with Argon can be used to predict plasma parameters for other gases if power transfer efficiency is taken into account.