A helicon source requires a DC magnetic field..

U. Wisconsin

...and is based on launching a circularly polarized wave in the plasma

UCLA

+

_+

_ _

+

+ +

_ _

_

B

k

(a)

(b)

(c)

+

The antenna can be twisted to match the helicon's helical waveform

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B, k

Right Helical Antenna

B

Nagoya III Antenna

(a) (b)

The R-wave propagates to the right, andthe L-wave to the left (for this antenna helicity)

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--

+ --

+

--

+ --

+

(a)

(b)

(c)

B

But the L-wave is very weak, and this antenna is unidirectional

Why do helicons ionize so well?

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Trivelpiece-Gould mode

Helicon mode

Landau damping (1985)F.F. Chen, Plasma Phys. Control. Fusion 33, 339 (1991).

This was disproved (1999)F.F. Chen and D.D. Blackwell, Phys. Rev. Lett. 82, 2677 (1999).

Mode-coupling to TG modes(1996)K.P. Shamrai and V.B. Taranov, Plasma Sources Sci. Technol. 5, 474 (1996).

Parametric excitation of ion acoustic waves (2005).B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci.Technol. 14, 623 (2005).

Two commercial helicon reactors

UCLAThe Boswell source

The PMT (Trikon) MØRI source

Distributed source: first attempt

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QUARTZ TUBE

PVC PIPE

ANTENNA

MAGNET WINDING

7 cm

5 cm

13 cm

BNC connector

5 mm

17 mm

1 cm

1 cm

10 cm

ELECTROSTATIC CHUCK

WAFER

MULTI-TUBE HELICON PLASMA SOURCE

PE

RM

AN

EN

T M

AG

NE

T A

RR

AY

Conceptual RF plasma source for etching and depostion of semiconductor wafers and flat-panel display substrates.

Each tube with a solenoidal coil and helical m = +1 antenna

A 7-tube circular array.This failed to produce high density.

Reason: Diverging field lines

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-10

0

10

20

30

z (cm)

Distributed source: Second attempt

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ELECTROSTATIC CHUCK

WAFER

PE

RM

AN

EN

T M

AG

NE

T A

RR

AY

SOURCE WITH LARGE MAGNETS

This was better

Distributed source: Third attempt

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ROTATING PROBE ARRAY

PERMANENT MAGNETS

3"

DC MAGNET COIL

18"

54 mm2.4 mm

6.4 mm10 cm

2.5

cm

The “stubby” tube

This worked beautifully! But…

Plasmas merged; density is uniform

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Power scan at z = 7 cm, 5 mT A, 20 G, 13.56 MHz,

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20 25 30R (cm)

N (

1012

cm

-3) 3.0

2.52.01.51.0

P(kW)

7-tube m=0 array

ARGON

…but the size is limited by the single large electromagnet.

Characteristics of permanent magnet rings

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Internal field

External field

Experiments with 7-cm diam tube

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Gate Valve

To Turbo Pump

34 cm

36 cm

D

Z1

Z2

0

20

40

60

80

100

120

5 10 15 20 25 30 35 40z (cm)

Bz

(G)

B (0)2319283338

D (cm)

-300

-250

-200

-150

-100

-50

0

50

100

150

0 5 10 15 20 25 30z (cm)

Bz

(G)

CalculatedMeasured

External field

Internal field

Radial density profiles at Z1 and Z2

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0

2

4

6

8

10

-5 0 5 10 15 20r (cm)

n (1

010cm

-3)

Z1, 40Z1, 35Z1, 30Z1, 21Z1, 1

D (cm)500W, 1mTorr

0

1

2

3

4

5

6

7

-5 0 5 10 15 20r (cm)

n (1

010cm

-3)

Z2, 40Z2, 35Z2, 30Z2, 21Z2, 1

D (cm)

500W, 1 mTorr

Upper probe Lower probex 1010 cm-3

Proof of principle: discharge in the external field gives much more plasma downstream.

Optimization of magnet geometry

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Result: Field strength magnet volumeSpacing improves uniformity slightly

actual

actual

Optimization of discharge tube: HELIC code

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a

b

c

Distant conducting shell

antenna

plasma

LLc

dEndplates have arbitrary reflectivity

D. Arnush, Phys. Plasmas 7, 3042 (2000).

Radial profiles are arbitrary, but B and n must be uniform axially.

HELIC gives not only the wave fields but also R, the loading resistance.

The low-field peak

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

100 G

63 G

40 G

25 G

16 G10 G Typical HELIC result

Relation of R to plasma density

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pin rf

p c

RP P

R R

7 1/ ½ 1.0 10 secsdN dt Snc n

c i eW E W W 101.1 10 WattsoutP n

Rp << Rc

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

100 G

63 G

40 G

25 G

16 G10 G

Relation of R to plasma density

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pin rf

p c

RP P

R R

7 1/ ½ 1.0 10 secsdN dt Snc n

c i eW E W W 101.1 10 WattsoutP n

10

100

1000

1E+11 1E+12 1E+13n (cm-3)

Pin (

W)

1000500200100Loss

P rf (W)

Rp > Rc

HELIC and expt. matrices varied a, L, f, p, endplate

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Matrix A: tube dimensions Matrix B: frequency-diameter

2" long 2.0 MHz

4" long 13.56 MHz

6" long 27.12 MHz

Matrix C: pressure-frequency Matrix D: Boundary condition

2.0 MHz ei = -1

13.56 MHz ei = +1

Use MatrixD.csv input file Goes to higher density.27.12 MHz Diam = 4", freq. = 27.12

DL2ins DL4ins DL6ins

ZA = 0.975 ZA = 0.949 ZA = 0.924

ZA = 0.975 ZA = 0.949 ZA = 0.924

DL2cond DL4cond DL6cond

2" long 4" long 6" long

ZA = 0.949

Cp1f27_

ZA = 0.949

Cp3f27_

Cp1f13_

a = .038

Cp3f13_

a = .038

ZA = 0.949

ZA = 0.949 ZA = 0.949Standard

ZA = 0.949

a = .038ZA = 0.949

AD2L6_ AD3L6_ AD4L6_ BD3f27_ BD4f27_

2" diam 3" diam 4" diam

ZA = 0.949 ZA = 0.949 ZA = 0.949a = .025 a = .038 a = .051

ZA = 0.949 ZA = 0.949

ZA = 0.949 ZA = 0.949Standard

a = .038 a = .051

BD2f13_ BD3f13_ BD4f13_

BD3f2_ BD4f2_

a = .025 a = .038 a = .051

BD2f2_

ZA = 0.949

a = .025

BD2f27_

ZA = 0.924

ZA = 0.949 ZA = 0.949

ZA = 0.924 ZA = 0.924

StandardAD2L4_ AD3L4_ AD4L4_

a = .051

a = .051

AD3L2_ AD4L2_

4" diam

ZA = 0.975

a = .025

a = .025

ZA = 0.975

AD2L2_

ZA = 0.975

ZA = 0.949a = .038

a = .038

1 mTorr 3 mTorr 10 mTorr

a = .038a = .025 a = .0512" diam 3" diam

a = .038ZA = 0.949

Cp10f2_

a = .038 a = .038 a = .038

Cp1f2_ Cp3f2_

a = .038ZA = 0.949

Cp10f13_

a = .038ZA = 0.949

Cp10f27_

Examples: Tube diameter, frequency

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1E+11 1E+12 1E+13n (cm-3)

R (

ohm

s)

d = 10.2 cmd = 7.6 cmd = 5.1 cm

Tube diameter

0.0

0.5

1.0

1.5

2.0

1E+11 1E+12 1E+13n (cm-3)

R (o

hms)

100795020805020

13 MHz: solid points2 MHz: open points

B(G)

Larger diameter gives higher plasma resistance, but this is

not practical.

13.56 MHz is much better than 2 MHz.

Final design

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5.1 cm

10 cm

5 cmANTENNA

GAS INLET

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

-10 -8 -6 -4 -2 0 2 4 6 8 10Very similar to “stubby” tube, designed by intuition! Only improvement is the metal top. A single NdFeB magnet

The magnets are dangerous!

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12.7 cm

7.6 cm

PLASMA

Material: NdFeB

Bmax = 12 kG

Attractive force between two magnets 2 cm apart:

516 Newtons = 53 kG

Wooden frame for safe storage

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Single tube, final configuration

UCLA0

50

100

150

200

250

300

350

-4 -2 0 2 4r (cm)

Bz

(G)

56789101214

z (cm from midplane of magnet)

0

2

4

6

8

10

-5 0 5 10 15 20r (cm)

n (1

011

cm-3

)

Z1, single magnetZ1, with neighborsZ2, single magnetZ2, with neighbors

Radial density profilesat Z1 = 7.4 cm and Z2 = 17.6 cm below discharge.

Radial Bz profiles at various distances below the magnet.

Discharge tube

Design of array

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0

2

4

6

8

10

12

15 20 25 30L (cm)

Rip

ple

(+/-

%)

L = 17.5 cm gives < 2% ripple at 17 cm below source

The density at Z2 is summed over nearest tubes.

For a single row, a distance L = 17.5 cm between two tubes gives less than 2% ripple in density.

Computed uniformity n(x) for various y

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (1

011

cm

-3)

SumRow1Row2Avg: all y

y = 0

(a)

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (1

011

cm

-3)

SumRow1Row2Avg: all y

y = 7.5

(b)

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30x (cm)

n (1

011

cm

-3)

SumRow1Row2Avg: all y

y = 15

(c)

0

1

2

3

4

5

6

-30 -20 -10 0 10 20 30x (cm)

n (1

011

cm

-3)

SumRow1Row2Avg: all y

y = 22.5

(d)

Half-way between rows 1/4-way between rows

Directly under a row Beyond both rows

An 8-tube linear test array

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165 cm

53.3 cm

17.8

17.8

17.8

17.8 cm73.7 cm

8.9 cm

x

y

The array source is vertically compact

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165 cm

30.5

17.8 cm

The magnets are to be stuck onto an iron plate, which holds them and also concentrates the flux.

Once placed, the magnets cannot easily be moved, so for testing we use a wooden support.

The wooden magnet frame is used in testing

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64"

21"

3.5"

12"

Wooden magnet support

2.00

5.00

3.75

2.5

24 ea. 2.5 x 5.5 x 1/2"4 ea. 2.5 x 64 x ¾”

1 ea. 21 x 64 x 1/2”16 ea. 1/4” diam dowels

An 8-tube staggered array in operation

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Possible applications

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• Web coaters• Flat panel displays• Solar cells• Optical coatings

A web coater