J. Plasma Fusion Res. SERIES, Vol.4 (2001) 305-308

Effect of Magnetic-Mirror confinement on Electron
Temperature Gontrol in ECR Plasma
ITAGAKI Nahox, UEDA Yoko, ISHII Nobuor and KAWAI yoshinobu
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University,Kasuga, Fukuoka 816-8580, Japan
Ltd., yodogawa, Osaka 532-0003, Japan

lTolcyo Electron Co.

(Received: 5 December 2000 / Accepted: 3 October 2001)

Abstract
The effect of magnetic-mirror confinement on the decrease in the electron temperature wasconfirmed by both of the calculation of particle and power balance and the electron temperature
measurements. It was found from the calculated results that this effect strongly depends on the collisionalcross section between electrons and neutral particles. Furthermore, we succeeded in producing an ECR
plasma with very low electron temperature (<2 eY) and high electron density (- l0t, cm-3; by applying
the mirror magnetic field for Ar gas diluted with N2.

Keywords:
ECR plasma, magnetic mirror, low electron temperature plasma, electron impact cross section

1. Introductionenergy balance including the magnetic mirror
confinement of electrons for Ar, N2 or H2 plasma.

In semiconductor processing, high-density and lowelectron-temperature plasma sources are required for a
progress of microelectronic devices and a minimizationof substrate damage. An electron cyclotron resonance(ECR) plasma source has attracted much attention for its
high electron density that can be achieved at low gaspressure, however, its electron temperature is relatively

Furthermore, we measured the electron temperature anddensity under various experimental conditions incomparison with the calculated results.

2. Experimental
The details of the experimental setup and an ECRhigh and need to be controlled. Recently, we haveplasma source were described in reference [1]. The

succeeded in reduction of the electron temperature in Ar

microwave was introduced through a quartz window anda substrate holder was set around 550 mm from thediluted with N, plasma and H2 plasma by applying themirror magnetic field. Since the electron density wasobserved to increase at the same time, the decrease in
the electron temperature is considered to be due to thereason that the loss of plasma was controlled by thewindow. Ar, N2 and H2 gasses were introduced into thechamber at a total flow rate of 50-70 sccm, and thepressure was kept at2x l0-3,5 x 10-3 or 8 x 10-3 Torr.
Six magnetic coils with a width of 100 mm and an innerdiameter of 32O mm were placed adjacent to thechamber to control the magnetic field distribution. The

magnetic-mirror confinement. However, the mirror
magnetic field had no effect on Ar plasma, and theproduction mechanism of low-electron-temperatureplasma is not still clear. Ir.r this study, we investigatedfrequency and power of microwaves were 2.45 GHz and

0.7-2.5 kW, respectively. The plasma parameters were

this effect in detail by calculating the particle and*Corresponding@2001 by The Japan Society of Plasma

author's e-mail: itagaki@ aees.lcyushu-u.ac.jp
305

Science and Nuclear Fusion Research

Itagaki N. et al., Effect of Magnetic-Mirror Confinement on Electron Temperature Control in ECR Plasma

4. Results and Discussion

measured with a l-mm-diameter Langumuir probe at
520 mm from the window.

The equilibrium relationship between T" and ns
obtained from Eqs. (l)-(4) for different magnetic field
configurations is illustrated in Fig. 1. The value ofn" isalso plotted against the electron temperature in Fig. 2.
Both of T. and n" change little in the Ar plasma, on the

3. Basic Equations
The particle balance equation for electrons is given
approximately by [2]dn^/\n.
--:=n.n"\ov").',-t, T.'or '-\

other hand, Z" decreases and n" increases for fixed valueof the gas density in the N2 plasma when the magnetic-(l)where n" and ns are the local values of electron andneutral gas densities, (ou"), is the ionization rate
coefficient averaged over the electron distribution,(dwhich is assumed to be Maxwellian in our calculation,and f" is the electron confinement time. On the other
hand, the power balance for electrons is given

1015

EJl tOl3
toZ&,

1012&E(2)10ll

Here Z" is the electron temperature, Pr, F,, Fi, Fl and P"
are power densities associated with the absorption of
microwave power, which is roughly estimated to be theincident power density, and the excitation, ionization,dissociation and electron attachment of gas atoms, andzs is the energy confinement time, E,,;,7,, is theexcitation, ionization, dissociation (for molecules) andelectron attachment energies, respectively. Assuming

I otolF^,id.a=n"no\O v " ) r,i,4,o-----B-A;1014

approximately byd(l.ln"z.) p,, p_- p,- p, p- |=- -otlot6

L x.i.d.a'(b)

I 016

1d5o

1 014

U1d3

E()
oc

that the electron loss is caused by the ambipolar
diffusion and the recombination at the chamber wall, r"
and rs are given approximately by

1d2

ldr
1x.=2x"= L/c", c"= r[?Jf JM,(3)otol(c) I

where L is the plasma characteristic length, c, is the ion
1

acoustic speed, and M; is the ion mass. In steady state,
the left-hand side of eqs. (1) and (2) is equal to zero,;lE
Jland the relationship among 7., ns and n" can beobtained. On the other hand, the magnetic-mirror

1-roconfinement of electrons is assumed to be governed by
Coulomb scattering into a loss cone.

1x. =3.5 xl}t Tj/2.n;t. (lnA)-t.(l -20r"ln)2,(4)tang," = (R - 1)-t"I

where Q" is the loss-cone angle. Particle and power
balance in the mirror magnetic field is expressed byadding the term of ?"., which is equal to zero at R = I(the magnetic configuration is flat type), to the electron

Fig. 1 The equilibrium relationship between the electron

temperature and the gas density at the microwave power of 1 kW. Curve A: without magneticmirror confinement of electrons. Curve B: withmagnetic-mirror confinement of electrons at themirror ratio of 2.

and energy confinement times given by Eqs. (3).

306

Itagaki N. et al., Effect of Magnetic-Mirror Confinement on Electron Temperature Control in ECR Plasma(a)__A-B?E lott
Uo6c1q)Uq,

F

Aroa-\- e_ __ o

3.5l0ll .-33t ono'

2.5t5

Te [eV]102(b)/' ---.-toc1

45ol0ll"EUo

4.5

Ar/Nz---.-A-_ --\_..-a.,-\\l0l2
B- -- €I_---- -^o5.5u.-/xi-- A1234
flat mi rror flat divergence(680c)(360c)-B

Iagnetio field configuration typel0l0

Fig. 3 The dependence of electron temperature and(5 mTorr)density on the magnetic field configuration fordifferent microwave powers in Ar plasma diluted
with Nr.
Nzt ono'

5 T, [ev]10

confinement of electrons is governed by Coulomb
scattering into a loss cone. In weekly-ionized plasma

15(c)

__A0r

such as ECR plasma, the Coulomb collision is generally
considered to be negligible, however, the collision
frequency is in inverse proportion to 7"3t2, so that thefrequency becomes higher as I" decrease. ln our-BE"1ou

experimental conditions, the Coulomb collision
frequency is comparable to the collision frequency

oc 10ebetween electrons and neutral particles at 7" of several
eV. This is why the magnetic-mirror confinement has aneffect on the N2 gas whose cross section peaks strongly
where the Coulomb collision frequency is high and littleHzr0t6Te

leVleffect on the Ar gas. A reasonably good agreement
between these calculated results and the results ofexperiment on plasma parameter measurement wasFig. 2 The equilibrium relationship between the electron

temperature and the electron density at themicrowave power of 1 kW. Curve A: withoutobtained. Furthermore, it was also found that Z" in Ar
plasma could be reduced by diluting N2 gas. Figure 3

magnetic-mirror confinement of electrons. Curve
B: with magnetic-mirror confinement of electrons
at the mirror ratio of 2.

shows the dependence of Z" and n" on the magnetic field
configuration in the Ar (91 Vo) diluted with N2 (9 7o)plasma, where the gas pressure was 5 mTorr. It wasobserved that Ze decreases and n" increases when themirror magnetic field is applied, especially, Z" wasobserved to be less than 2 eV at the microwave powerof 1 kW. On the other hand, the relationship between Z"and ns or n"for H2 gas varies little in the case where themagnetic-mirror confinement of electrons in particle andpower balance are included, as shown in Figs I (c) and2 (c). This is understood from that the cross sections inthe H2 gas that peaks at low electron energy is verysmall (-7 x l0-r7 cm2) in comparison with that in the N2

mirror confinement of electrons is taken intoconsideration. This difference of the magnetic-miror
effect between the Ar gas and the N2 gas is considered
to come from the difference in their electron impact
cross section. The various excitation cross sections forN2 peak at low electron energy of several eV, especially,
the vibrational excitation cross section peaks strongly at
2 eV, whose maximum is about 7 x 10-16 cm2. On theother hand, all the collisional cross sections for Ar peaks
at high electron energy of 10r-2 eV. As mentioned

above, we assumed that the magnetic-mirror
307

Itagaki N. et al., Effect of Magnetic-Mirror Confinement on Electron Temperature Control in ECR Plasmathat the magnetic-mirror confinement has an effect on
the N2 gas and little effect on the Ar gas. From thecalculated results, this difference of the magnetic-mirror
effect between the Ar gas and the N2 gas is considered
to come from the difference in their electron impact

gas, however, this numerical results is different from theexperimental results. In the experiment on plasma
parameter measurement, it was observed that Z"
decreases and r" increases when the mirror magnetic
field is applied in the H2 plasma as well as in the N2plasma. It is necessary to clarify the mechanism of lowelectron-temperature plasma production in the H2cross section. Furthermore, it was found from theexperimental results that the electron temperature in Ar
plasma could be also reduced by diluting N2 gas in theplasma, which is under investigation.

mirror magnetic field.

5. Conclusion
ReferencesThe effect of magnetic-mirror confinement on thedecrease in the electron temperature was investigated indetail by calculating the particle and energy balance

tll Y. Ueda and Y. Kawai, Appl. Phys. L74, 14

including the magnetic mirror confinement of electrons

t2l R.A. Dandl and G.E. Guest, J. Vac. Sci. Technol.
A9,3119 (1991).

(1999).

and plasma parameter measurement. It was confirmed

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