Effect of supra thermal electrons on particle charge in RF sheath

A.A.Samarian and S.V. VladimirovSchool of Physics, University of Sydney, NSW 2006, Australia

OutlinesCharge vs Size dependence

The experimental dependence of the dust charge as a function of its size

Modeling of the charge behavior of a dust particle in

the sheath region.

Non-linear dependence

Effect of suprathermal electrons (STE)

Introduction

Dependence of dust particle charge vs. dust size was studied experimentally in an rf discharge plasma.

Particle charge was estimated from vertical equilibrium technique (VET) as well as from vertical resonance technique (VRT).

Experimental results are complimented with results of particle-in-cell (PIC) simulation along with levitation model involving the OLM charging approximation

Experimental Apparatus

Charge measurement techniques

Measurement of Dust Chargefrom Vertical Equilibrium

Measurement of Dust Chargefrom Vertical Resonance

Charge measurements

The comparison between data obtained from VET and VRT techniques shows quite good agreement (VRT data shifted in the x-direction for enhanced viewing).

VET

VRT

120mTorr

80mTorr

VET

VRT

120mTorr

80mTorr

For particles of different density, charge vs. size shows that charge increases for heavier particles of same size. i.e. surface potential of particle increases deeper into sheath

Melamine formaldehyde = 1.5 gcm-3

Carbon = 2.1 gcm-3

Corundum = 4.05 gcm-3

Glass Balloon* = 0.8 gcm-3

Fine Grain Density Calibrator

Charge vs. Dust Radius

5.8Pa, 13W [data from C. Zafiu, A. Meltzer and A. Piel, Phys. Rev. E, 63, 066403 (2001)]

6.67Pa, 13W [data from E. Tomme, B. Annaratone, and J. Allen, Plasma Source Sci. Technol., 9, 87 (2000)]

12.1Pa, 60W [data from A. Samarian et al., (to be published)]

18.3Pa, 60W [data from A. Samarian et al., (to be published)]

13.33Pa, 96.4V [data from E. Tomme, B. Annaratone, and J. Allen, Plasma Source Sci. Technol., 9, 87 (2000)]

~rd2.29

~rd1.61

~rd2.52

~rd1.83 ~rd

1.73

rd

Q

~rd2.29

~rd1.61

~rd2.52

~rd1.83 ~rd

1.73

rd

Q

Charge vs Size Dependence

In frame of OML theory

Sheath position vs Size

(z)(z)E(z)E(z)

zezb

ElectrodeElectrodePlasmaPlasma SheathSheath

(z)(z)E(z)E(z)

zezb

ElectrodeElectrodePlasmaPlasma SheathSheath

Charge vs Size dependence

Charge versus Particle Size

Different dependencies of particle charge on its size can be obtained for variation of effective Te. Linear dependence can only be expected for uniform plasma.

5~ dd RRQ 2.44.1~ dd RRQ 67.367.1~ dd RRQ

dRQ ~

PIC simulation

Size dependence was fitted by power function, which gives characteristic index of 1.38. For bigger grains, grain charge is directly proportional to grain size with good accuracy.

Charging Dynamics Charge Dependence on Particle Size

ModelingResults of a self-consistent hydrodynamic model of the dust levitation and charging in a collisional plasma sheath taking into account plasma ionization. We treat the sheath problem self-consistently and investigate dust charging at various positions corresponding to different particle sizes. In the sheath region, where the speed of the ion flow is expected to exceed the ion sound velocity, a simple approximation describing ion-neutral collisions can be used. In the total pre-sheath/sheath we use a model of momentum transfer between the ion and neutral species, which describes ion-neutral collisions on the basis of kinetic theory, without semi-empirical approximations.The sheath potential is determined by Poisson's equation (We neglect the total charge contributed by the dust grains):

The continuity equation for the ions takes into account plasma production; the main mechanism of ionization is assumed to be electron impact ionization, so that the continuity equation is

Here ion is the plasma ionization frequency, which for argon gas has the form:

)()()( znzvzndz

deionii

002

2 )()(exp4

)(

n

zn

T

zeen

dz

zd i

e

)/8.15exp(105 8e

nion Tn

ModelingThe momentum equation for the plasma ions is written as:

where is the momentum transfer rate between ions and neutrals, and the main mechanism for the ion-neutral collisions is charge exchange.Calculations on the basis of plasma kinetic theory, which allow for ion speeds comparable to the ion thermal speed, give the following expression for Fcoll:

Here

and qE is the characteristic charge exchange momentum transfer cross section.The charge of the dust particles is found from the standard condition of zero total plasma current onto the grain surface in the OLM approximation.

)()()(

)( zFdz

zde

dz

zdvzvm coll

iii

iEcoll vfF )(

)(zFcoll

Modeling

the shift of the step is zo~zsh , where zsh is the sheath and presheath width,

and the width of the step z1~ LDe , LDe is the electron Debye length.

Charge vs. Particle Size

Hydrodynamic model + OLMBy fitting this data, actual power index (0.96) is less than 1 (although very close to unity).This demonstrates the nonlinear dependence of the levitating particles on the grain size where bigger and therefore heavier particles levitate deeper into the sheath (and closer to the electrode).On the other hand, the deviation from the linear dependence is very small.

Charge vs Size

Surface potential

Surface potential

Conclusion

The dependence of the dust particle charge on its size was studied. It was experimentally established that for particles levitated in the sheath, this dependence is nonlinear.The dependence of the dust particle on its size was also studied by PIC simulation along with the levitation model involving the OLM charging approximation, which give us close-to-linear dependencies.Theoretical analysis tells us that the experimentally observed dependence can be explained in the limit of the OLM theory if we take into account the STE.