Starting point langmuir s oml theory
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Starting point: Langmuir’s OML theory. No integration necessary; very simple formula for ion current. This requires very small R p / l D , so that there is no absorption radius. UCLA. Post-Langmuir probe theories - 1. Sheath, but no orbiting. UCLA. Post-Langmuir probe theories - 2. UCLA.

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Starting point langmuir s oml theory

Starting point: Langmuir’s OML theory

No integration necessary; very simple formula for ion current.

This requires very small Rp / lD, so that there is no absorption radius.

UCLA


Starting point langmuir s oml theory

Post-Langmuir probe theories - 1

Sheath, but no orbiting

UCLA







Starting point langmuir s oml theory

Experimental verification in Q-machine - 2

Such nice exponentials were never seen again!

UCLA



Starting point langmuir s oml theory

Problems in partially ionized, RF plasmas

  • Ion currents are not as predicted

  • Electron currents are distorted by RF

  • The dc plasma potential is not fixed

Getting good probe data is much more difficult!

UCLA


Starting point langmuir s oml theory

Ion currents in an ICP discharge

They fit the OML theory, which is not applicable!

UCLA



Starting point langmuir s oml theory

The real density is close to the

geometric mean!

UCLA


Starting point langmuir s oml theory

Reason: collisions destroy orbiting

An orbiting ion loses its angular momentum in a charge-exchange collision and is accelerated directly to probe. Thus, the collected current is larger than predicted, and the apparent density is higher than it actually is.

UCLA


Starting point langmuir s oml theory

This collisional effect has been verified

Sternovsky, Robertson, and Lampe, Phys. Plasmas 10, 300 (2003).

Sternovsky, Robertson, and Lampe, J. Appl. Phys. 94, 1374 (2003).

Rp/lD = 0.05

Rp/lD = 0.49

Rp/lD = 0.26

The extra ion current due to collisions is calculated and added to the OML current. The result agrees with measurements only for very low density (< 108 cm-3).

The theory is incomplete because the loss of orbiting ions is not accounted for. Also, there is no easy computer program.

UCLA


Starting point langmuir s oml theory

Summary: how to measure density with Isat

High density, large probe: use Bohm current as if plane probe. Ii does not really saturate, so must extrapolate to floating potential.

Intermediate Rp / lD: Use BRL and ABR theories and take the geometric mean.

Small probe, low density: Use OML theory and correct for collisions.

Upshot: Design very thin probes so that OML applies. There will still be corrections needed for collisions.

UCLA


Starting point langmuir s oml theory

Problems in partially ionized, RF plasmas

  • Ion currents are not as predicted

  • Electron currents are distorted by RF

  • The dc plasma potential is not fixed

UCLA



Starting point langmuir s oml theory

Solution: RF compensation circuit*

* V.A. Godyak, R.B. Piejak, and B.M. Alexandrovich, Plasma Sources Sci. Technol. 1, 36 (19920.

I.D. Sudit and F.F. Chen, RF compensated probes for high-density discharges, Plasma Sources Sci.

Technol. 3, 162 (1994)

UCLA


Starting point langmuir s oml theory

Self-resonance of choke chains

To get high impedance, self-resonance of chokes must be used. Chokes must be individually chosen because of manufacturing variations.

UCLA



Starting point langmuir s oml theory

Ideal OML curve

What is the sheath capacitance as Vs oscillates?

A small RF oscillation will bring the probe from the Child-Langmuir sheath to the Debye sheath to electron saturation

UCLA


Starting point langmuir s oml theory

Sheath capacitance: exact vs. C-L

This is an extension of the work by Godyak:

V.A. Godyak and N. Sternberg, Phys. Rev. A 42, 2299 (1990)

V.A. Godyak and N. Sternberg, Proc. 20th ICPIG, Barga, Italy, 1991, p. 661

UCLA


Starting point langmuir s oml theory

Variation of Csh during an RF cycle

Large probe, which draws enough current to affect Vs.

These curves will give rise to harmonics!

A normal small probe, which goes into electron saturation.

Cylindrical effects will smooth over the dip.

UCLA


Starting point langmuir s oml theory

Problems in partially ionized, RF plasmas

  • Ion currents are not as predicted

  • Electron currents are distorted by RF

  • The dc plasma potential is not fixed

UCLA


Starting point langmuir s oml theory

Ideal OML curve

Peculiar I-V curves: not caused by RF

UCLA


Starting point langmuir s oml theory

Potential pulling by probe

Curves taken with two probes, slowly, point by point

UCLA


Starting point langmuir s oml theory

1.9 MHz, 60-100W, 3-10 mTorr Ar

Apparatus: anodized walls, floating top plate

Ceramic shaft

UCLA



Starting point langmuir s oml theory

Correcting for Vf shift gives better I-V curve

UCLA


Starting point langmuir s oml theory

Slow drift of probe currents: ions

A scan takes 2-3 sec (200 points), and ~3 sec between scans.

The time constant is very long.

UCLA


Starting point langmuir s oml theory

Slow drift of probe currents: electrons

The drift direction depends on the parking voltage between scans.

The drift can continue for >10 sec.

UCLA


Starting point langmuir s oml theory

Reason: the walls are charged through the probe

  • The only connection to ground is through the probe.

  • The plasma potential has to follow Vp.

  • Hence the capacitance of the insulating layer has to be charged.

CV = Q = I*t, t = CV/ I

C = R0Aw/d, Aw = 0.44 m, R ~ 3, d ~ 1 m

C ~ 10 F, V ~ 100 V, Ie ~ 2 mA

 t ~ 0.5 sec

This is the right order of magnitude.

Slower drifts may be due to small leaks in the insulation.

UCLA



Starting point langmuir s oml theory

Grounding plate reduces change in Vf

High pressure (9.7 mTorr)

Low pressure (2.7 mTorr)

UCLA



Starting point langmuir s oml theory

Compare with ideal OML curve

The ion part fits well.

The electron part, after correcting for the Vf shift, fits the exponential region better, but still fails at saturation.

The remaining discrepancy must be due to inadequate RF compensation.

UCLA


Starting point langmuir s oml theory

Applying +100V to probe suddenly

SOURCE

e

+

+

+

+

+

e

+

WALL

e

+

+

+

e

+

+

e

Vs ~ Vs0

e

e

e

There is an initial transient, but a normal electron sheath at electron saturation should come to equilibrium in several ion plasma periods (<< 1 msec).

UCLA


Starting point langmuir s oml theory

e

i

i

e

e

With a grounding plane, how can a probe affect Vs?

Normally, the probe current Ie is balanced by a slight adjustment of the electron current to the walls, Iew, via a small change in sheath drop. Since Iew = Iiw, Vs should not change detectably if Ie << Iiw.

UCLA


Let s work out the numbers
Let’s work out the numbers

Bohm current density: Ii = 0.5 neAwcs ( n = 2 x 1010 cm3, KTe = 1.6 eV)

Ion current to grounding plate (25 cm2) » 8.5 mA

Electron saturation current at +100V = 25 mA (measured)

(Same order of magnitude, within variations.)

Thus, at high Vp, ion loss is too small to balance electron loss.

BUT: Vs changes well before Ie reaches 25 mA

The ion flux to ground may be less than Bohm.

UCLA


Starting point langmuir s oml theory

If no grounding plate, how long does it take for the ions to redistribute themselves?

If the probe draws excess electrons at the center, an ambipolar field will develop to drive ions faster to the wall. The density profile n(r) will change from essentially uniform to peaked.

The diffusion equation for a nearly spherical chamber is

where D = Da, the ambipolar diffusion coefficient. The solution is

The time constant for the lowest radial mode j = 1 is then

UCLA


Starting point langmuir s oml theory

Time to change from uniform to peaked profile redistribute themselves?

Thus, the time required for the ions to adjust to a new equilibrium is only about 1 msec or less.

UCLA


Starting point langmuir s oml theory

A measured radial density profile redistribute themselves?

UCLA


Starting point langmuir s oml theory

Conclusion: timing is critical redistribute themselves?

  • The dwell time must be long enough for the sheath to come into

  • equilibrium. This is several ion plasma periods (>100 nsec).

  • The total sweep time must be << 1 msec, or the plasma potential

  • will change.

  • With very slow sweeps, Vs will change and must be monitored.

Even a DC, point-by-point measured I-V curve may not be correct.

UCLA


Starting point langmuir s oml theory

Too fast a scan: sheath not in equilibrium redistribute themselves?

UCLA


Starting point langmuir s oml theory

Hence we must use a dc reference electrode. redistribute themselves?

HERE

UCLA