Starting point: Langmuir’s OML theory

Starting point: Langmuir’s OML theoryp

a

Vo

Rp

1/ 2

0

| |2i

ppT

eVI A ne

M

No integration necessary; very simple formula for ion current.

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

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Post-Langmuir probe theories - 1

Sheath, but no orbiting

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Probes in fully ionized plasmas

Experimental verification in Q-machine - 1

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Such nice exponentials were never seen again!

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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!

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Ion currents in an ICP discharge

0

1

2

3

4

-100 -80 -60 -40 -20 0 20V

I2 (

mA

)2

Data

OML, n = 3.45E11

ABR, n = 1.76E11

BRL, n = 5.15E11

They fit the OML theory, which is not applicable!

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Each theory yields a different density

Here

Rp / D

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The real density is close to thegeometric mean!

0

1

2

3

4

5

6

200 400 600 800 1000Prf (W)

De

nsity

(1

01

1 c

m-3

)

BRL

mWave

BRL*ABR

ABR

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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.

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This collisional effect has been verifiedSternovsky, Robertson, and Lampe, Phys. Plasmas 10, 300 (2003).Sternovsky, Robertson, and Lampe, J. Appl. Phys. 94, 1374 (2003).

Rp/D = 0.05 Rp/D = 0.26 Rp/D = 0.49

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.

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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 / D: 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.

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-20 -10 0 10 20 30Vp - Vs

Ele

ctro

n cu

rre

nt

Introduction: RF distortion of I-V trace - 1

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* 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)

Solution: RF compensation circuit*

0.239"0.094"Epoxy seal

10 pF capacitor

compensation electrode

coax

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Self-resonance of choke chains

0

50

100

150

200

250

300

350

400

1.0 1.5 2.0 2.5 3.0 3.5 4.0MHz

k

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

manufacturing variations.

0

50

100

150

200

250

1.0 1.5 2.0 2.5 3.0MHz

k

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A large compensation electrode helps

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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

0.00

0.02

0.04

0.06

-20 -15 -10 -5 0 5 10 15 20Vp

I e (

A)

Vs

Vp

h > 0 h < 0

Ideal OML curve

s p

Debye sheath

V0 V C-L

sheath

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Sheath capacitance: exact vs. C-L

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8h

Csh

(pF

/cm

2)Exact

Approx.

C-L

Floating potential

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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

Variation of Csh during an RF cycle

0

5

10

15

20

25

30

35

40

0 90 180 270 360 450 540 630 720wt (degrees)

Csh

(pF

/cm

2)

Exact

w. cutoff

No RF

Vrf = 10 V

0

5

10

15

20

25

30

35

40

0 90 180 270 360 450 540 630 720wt (degrees)

Csh

(pF

/cm

2)

Exact

w. cutoff

No RF

Vrf = 10 V

Large probe, which draws enough current to affect Vs.

A normal small probe, which goes into electron saturation.

Cylindrical effects will smooth over the dip.

These curves will give rise to harmonics!

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-5.0E-05

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

-20 0 20 40 60 80 100Volts

Am

ps

15 mTorr

3 mTorr

Mk2, short tube, 100W

-0.0001

0.0004

0.0009

0.0014

-100 -80 -60 -40 -20 0 20 40 60 80 100Vp

-I (

A)

Ideal OML curve

Peculiar I-V curves: not caused by RF

Potential pulling by probe

-0.0004

0.0000

0.0004

0.0008

0.0012

0.0016

0.0020

0.0024

0.0028

0.0032

-50 -40 -30 -20 -10 0 10 20 30 40 50Vp (V)

Ie (

A)

1

3

5

7

9

11

13

15

17

19

Vf (V

)

Ie(A)

Vf

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Curves taken with two probes, slowly, point by point

Apparatus: anodized walls, floating top plate

PUMP

antenna

probe21

35.5

10.5

5.4

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

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Ceramic shaft

Direct verification of potential pulling

-0.0003

-0.0002

-0.0001

0.0001

0.0002

0.0003

-100 -75 -50 -25 0 25Volts

Am

ps

-50V

0V

10V

20V

30V

40V

50V

Vp EPN I-V curves as Vp on ChenA is varied

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Correcting for Vf shift gives better I-V curve

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-5.0E-04

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

-50 -40 -30 -20 -10 0 10 20 30 40 50Volts

Am

ps

Manual, Vf corrected

Manual, uncorrected

Hiden MKIU

Slow drift of probe currents: ions

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-0.0005

-0.0003

-0.0001

0.0001

0.0003

0.0005

0.0007

0.0009

0.0011

0.0013

0.0015

-100 -50 0 50Volts

Am

ps

10 mA scale

1 mA, scan 1

1 mA, scan 2

1 mA, scans 3&41mA curves drift, then settle to agree with 10mA curve

A scan takes 2-3 sec (200 points), and ~3 sec between scans.The time constant is very long.

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-5.0E-05

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

3.5E-04

4.0E-04

4.5E-04

-100 -80 -60 -40 -20 0 20 40 60 80 100Volts

Am

ps

0129_02a

0129_02b

0129_02c

0129_02d

0129_02e

100W, 15mTorr

Slow drift of probe currents: electrons

The drift direction depends on the parking voltage between scans.The drift can continue for >10 sec.

Reason: the walls are charged through the probe

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• 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 = R0Aw/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.

Insertion of grounding plate close to probe

`

36.00

21.00

10.50

Port 2Port 1

Pump

Grounding plate

Antenna Not used

Permanentmagnets on

surface

Grounding plate

Port 2EPN in Z-drive

Port 11/4" probe in Wilson seal

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Grounding plate reduces change in Vf

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0

4

8

12

16

-50 -30 -10 10 30 50Vp (V)

Vf

(V)

100/9.7/IN

100/9.7/OUT

Watts/mTorr/Ground plate

0

2

4

6

8

10

12

-50 -40 -30 -20 -10 0 10 20 30 40 50Vp (V)

Vf

(V)

160/2.7/OUT

160/2.7/IN


High pressure (9.7 mTorr)

Low pressure (2.7 mTorr)

But the I-V curves are about the same

-0.0005

0.0045

0.0095

0.0145

0.0195

0.0245

0.0295

0.0345

-50 -30 -10 10 30 50Volts

Am

ps

160/2.7/IN

160/2.7/OUT

100/9.7/IN

100/9.7/OUT


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Compare with ideal OML curve

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-0.0005

0.0045

0.0095

0.0145

0.0195

0.0245

0.0295

0.0345

0.0395

0.0445

-30 -20 -10 0 10 20 30 40 50Volts

Am

ps

Ideal OML

Corrected data

Raw data

-0.0003

-0.0002

-0.0001

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

-50 -40 -30 -20 -10 0 10Volts

Am

ps

Ideal OML

Corrected data

Raw data

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.

Applying +100V to probe suddenly

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e+

+e

ee

+

+

+ ++

+++

+

WA

LL

SOURCE

ee

ee Vs ~ Vs0

There is an initial transient, but a normal electron sheath at electron saturation should come to equilibrium in

several ion plasma periods (<< 1 msec).

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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.

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

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.

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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

2 22

2'' '

n D nD n r D n n

t r r rr

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

2 2

0 21

2 ( 1)( , ) sin exp

j

j

a j r jn r t n Dt

r j a a

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

2 2/ 0.17 msecaa D

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

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Time to change from uniform to peaked profile

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 3 6 9 12 15 18r (cm)

n/n 0

0.01

0.05

0.10

0.15

0.20

0.30

0.40

0.50

t (msec)

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

A measured radial density profile

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0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15r (cm)

n / n

o

Length of probe tip

• 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.

Conclusion: timing is critical

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

Too fast a scan: sheath not in equilibrium

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-1E-04

0E+00

1E-04

2E-04

3E-04

4E-04

5E-04

-100 -80 -60 -40 -20 0 20 40 60 80 100

Volts

Am

ps

Reverse scan

Forward scan

100W, 15mTorrDwell 10/10

Mk2-MKIU Test of effect of dwell

.998 Alumina

Alumina or pyrex

Copper

Tungsten

Epoxy

.005 Tungsten rod

.094 x .063 x 1 1/81

.050 x .020 x 3/82

.001 Nickel.030 Tungsten

.250 x .188 x 5/83

.060 OD vacuum slip joints4

Spot weld

Soft solder Vacuum epoxy6 .125 x .040 x 1/4 double hole5

(1) Coors #65682(2) Coors #65650(3) Coors #65658(4) Ceramaseal #11288-02-X(5) Coors #65673(6) K.J. Lesker #KL-320K(7) Coors #65660(8) Coors 65657 or pyrex tube For large chokes, must use #65658, specially ordered to fit into #65660

ChenB probe with reference electrode

Nickel

Auxiliary electrode: Nickel foil is wrapped around ceramic tube and spotwelded along length. Tabs are then cut, and the rest wrapped tightly to cylinder. A small tab is left for spotwelding to .030 tungsten rod.

Compensation electrode

Reference electrode

.375 x .250 x 187

.219 x .156 x 228

.250 x .188 x 1/43

New, as of 1/1/2005

.998 Alumina

Alumina or pyrex

Copper

Tungsten

Epoxy

.005 Tungsten rod

.094 x .063 x 1 1/81

.050 x .020 x 3/82

.001 Nickel.030 Tungsten

.250 x .188 x 5/83

.060 OD vacuum slip joints4

Spot weld

Soft solder Vacuum epoxy6 .125 x .040 x 1/4 double hole5

(1) Coors #65682(2) Coors #65650(3) Coors #65658(4) Ceramaseal #11288-02-X(5) Coors #65673(6) K.J. Lesker #KL-320K(7) Coors #65660(8) Coors 65657 or pyrex tube For large chokes, must use #65658, specially ordered to fit into #65660

ChenB probe with reference electrode

Nickel

Auxiliary electrode: Nickel foil is wrapped around ceramic tube and spotwelded along length. Tabs are then cut, and the rest wrapped tightly to cylinder. A small tab is left for spotwelding to .030 tungsten rod.

Compensation electrode

Reference electrode

.375 x .250 x 187

.219 x .156 x 228

.250 x .188 x 1/43

New, as of 1/1/2005

Hence we must use a dc reference electrode.

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Starting point: Langmuir’s OML theory

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Starting point: Langmuir’s OML theory