Use of Langmuir probes in strong RF plasmas Francis F. Chen, UCLA KAIST, Daejeon, S. Korea, April 2011.

Use of Langmuir probesin strong RF plasmas

Francis F. Chen, UCLA

KAIST, Daejeon, S. Korea, April 2011

Commercial probe systems

Shown here is the Hiden ESPION probe. I use the older Hiden ESP probe software, but I make my own probes.

I presume you are familiar with the PlasMart probe.

The Chen B probe

To reject RF pickup, resonant chokes (inductors) and a good auxiliary electrode are needed.

The choke must be >200 k

This is a good choke. High Z is good for low density. High frequency can use lower Z. It is sometimes possible

to adjust the RF frequency to match the choke.

0

200

400

600

800

1000

10 15 20 25 30f (MHz)

Z (

k)

Probe 61110

2Rp = .005" = .0127 cm,L = 1.2 cm, R = 12.7

How RF distorts the I-V characteristic

The RF shifts Vp back and forth. Since the I-V curve is nonlinear, the average current does not reproduce the curve.

This shows what the uncompensated I-V curve would look as the RF pickup voltage is varied.

Why the auxiliary electrode is needed

Probe tip

Cs1 causes the choke to lose part of the oscillation of the probe. The large,floating auxiliary electrode (Zx) strongly drives the choke to oscillate with the plasma’s RF fluctuations.

The orbital-motion-limited theory

Large probe, dense plasma, thin sheath

½sat p sI neA c

Small probe, weak plasma, thick sheath

Langmuir’s Orbital-Motion-Limited (OML) theory

Langmuir’s simple OML formula

1/ 22 p

i sat pi

eVI I A ne

M

OML is valid only when the sheath is so thick that there is no “absorption radius”.

However, it works better than other theories even when it should not be applicable.

Both Hiden and PlasmArt use this simple formula.

To use this formula, probe tips should be as thin as possible to minimize Rp/D.

The simple OML formula

1/ 22 p

i sat pi

eVI I A ne

M

The ion saturation current Isat is independent of Te and

can be used easily to measure density n. Isat varies as the square root of Vp. This is a characteristic

of ion orbiting when there is no absorption radius. However, the linear I2 – Vp relation is followed even when

the Rp/D is not so large!

Ap is the probe tip area, Mi the ion mass, and Vp the probe

potential relative to the plasma potential.

A typical I2 – Vp curve for n < 1012 cm-3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-100 -80 -60 -40 -20 0 20Vp (volts)

I2 (

mA

)2

Ii (data)

Ii (OML)

1/2/ 2i p iI A ne KT M F

½ ½1erf ( ) erfc( )F e

/ 0p ieV KT

2 2/ 1, /( 1) , /(1 )pR s .

How did Langmuir get such a simple formula?

This is what he started with for Maxwellian ions:

s is an assumed sheath radius at which ions start with their thermal velocities

½ ½2( ) erfc( )F e

½½ 2

1 3 1erfc( ) 1 ...

2 4( )

e

½ ½ ½ ½½

2 1 1 2( ) 2

( )F e e

1/ 2 1/ 21/ 22 2

2p pi

i p pi i

eV eVKTI A ne A ne

M KT M

Then he made some dubious approximations

The ion temperature cancels out!

Attempt to use the exact OML formula

0

50

100

150

200

250

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

I2 (

mA

)2

Ii squared

Ii(OML)

Exact

At high density, the curve does not fit a straight line. Using the exact OML formula gives too much curvature even if the sheath radius is adjusted to give the best fit.

It is still unknown why the I2-V curve is so close to linear.

The semilog electron curve 1

0

1

2

3

4

5

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

I2 (

mA

)2

Ii squared

Ii(OML)

File 110313_62

27.12 MHz400W

1.2 mTorr

n= 5.8E11

First, we have to fit the ions so that we can subtract them

The semilog electron curve 2

Now we make the semilog electron curve

0.01

0.1

1

10

-5 0 5 10 15 20 25 30 35V

I (m

A)

Ie

Ie(fit)

Ie (0)

File 110313_62

27.12 MHz400W

1.2 mTorr

Te=7.19 eV

Vs=50.3V

Note that the right amount of ion current added back is essential

False indication of electron beams

0

10

20

30

40

50

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

I2 (

mA

)2

Ii squared

Ii(OML)

File 110314_12

27.12 MHz400W

15 mTorr

n= 15.2E11

0.01

0.1

1

10

100

-5 0 5 10 15 20 25V

I (m

A)

Ie

Ie(fit)

Ie (0)

File 110314_12

27.12 MHz400W

15 mTorr

Te=3.29 eV

Vs=28.8 V

0

10

20

30

40

50

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

I2 (m

A)2

Ii squared

Ii(OML)

File 110314_12

27.12 MHz400W

15 mTorr

n= 15.9E11

0.01

0.1

1

10

100

-5 0 5 10 15 20 25V

I (m

A)

Ie

Ie(fit)

Ie (0)

File 110314_12

27.12 MHz400W

15 mTorr

Te=2.75 eV

Vs=26.5 V

Apparatus for helicon thruster

PERMANENT MAGNET

GAS FEED

HEIGHT ADJUSTMENT

LANGMUIR PROBE

PERMANENT MAGNET

GAS FEED

HEIGHT ADJUSTMENT

LANGMUIR PROBE

1 magnet, 65 gauss 2 magnets, 280 gauss max (lower)

Very thin vertical probe

Effect of auxiliary electrode 1: no electrode

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

-100 -80 -6 0 -40 -20 0 20V

I (A

)

0

10

20

30

40

50

60

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

I2 (m

A)2

Ii squared

Ii(OML)

0.01

0.1

1

10

100

-30 -25 -20 -15 -10 -5 0 5 10 15 20

V

I (m

A)

Ie

Ie(fit)

Ie (2)

0.01

0.1

1

10

100

-30 -25 -20 -15 -10 -5 0 5 10 15 20

V

I (m

A)

Ie

Ie(fit)

Ie (2)

The I-V curve looks more rounded. The I2-V curve is linear, but goes down fast.

N = 15.8E11

Te = 3.65 eV

Te = 10.4 eV

Effect of auxiliary electrode 2: with electrode

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

0.120

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

I (A

)

0

10

20

30

40

50

60

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

I2 (m

A)2

Ii squared

Ii(OML)

0.01

0.1

1

10

100

-10 -5 0 5 10 15 20 25 30

V

I (m

A)

Ie

Ie(fit)

Ie (2)

I-V curve more normal.

n = 16.8E11

Te = 3.01 eV

The temperature is more normal, but the high-Te part still exists. Need a larger auxiliary electrode.

1000 W with a 5-mil probe

0

50

100

150

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

I2 (

mA

)2

Ii squared

Ii(OML)

File 110314_39

27.12 MHz1000W

15 mTorr

n= 27.4E11

0.01

0.1

1

10

100

0 5 10 15 20 25V

I (m

A)

Ie

Ie(fit)

Ie (0)

File 110314_39

27.12 MHz1000W

15 mTorr

Te=2.66 eV

Vs=31.1 V

The thinnest probe (125 m diam) gives I2-V curves that bend at high density.

There is no theory that predicts the curve shape.

This probe will glow in the discharge unless the sweep time is minimized.

We can use a thick probe and thin-sheath theory, but the discharge will be disturbed by the probe current.