J. Plasma Fusion Res. SERIES, Vol' 2 (1999) 307-309

Role of Secondary Electrons in the a to T Transitionof RF Gapacitive Discharges
TERADA Tadashi, YAMAGUCHI Makoto, MAEDA Joji and KOGOSHI Sumio
Department of Electrical Engineering, Faculty of Science and Technology,
Science IJniversity of Tolqo, Noda 278-8510, Japan(Received: 8 December 1998 / Accepted: 28 June 1999)

Abstract
The role of secondary electrons in the a-y transition of RF capacitive discharges are studied
numerically by means of Particle-in-Cell Monte Carlo Collision (PIC-MCC) simulations with andwithout ion-induced secondary electron emission. As a result, the simulations only with a secondary
electron emission show clearly the a-Ttransition. It suggests that secondary electrons would induce thetransition. Furthermore, the phenomena which occur in the sheath regions are discussed in detail based on
the simulation results.

Keywords:

d-I transition, Particle-in-Cell Monte Carlo Collision (PIC-MCC) simulation, secondary electronemission

control the emission rate of secondary electrons isdifficult. On the other hand, to control the emission ratein numerical simulations, especially in Particle-in-Cell

1. Introduction
In RF capacitive discharges at a medium pressure
range, a transition is found, which accompanies not onlyMonte Carlo Collision (PIC-MCC) simulations, is easy.
So we tried to clarify the mechanism of the phenomena
by means of PIC-MCC simulations with and without

the nonlinear increase in an RF current and a plasma
density but also the drop in an electron temperature withan RF voltage [1,21. It is difficult to explain thephenomena by the fundamental principles of plasmas,

secondary electron em ission.

such as the particle and energy balance. For instance, it

2. Simulation Modelis predicted by the particle balance that an electron

In this study, we used the simulation code which

temperature is kept constant with an RF [3]. Therefore,
it has been considered that the two distinct discharge

has been developed by the Plasma Theory andSimulation Group, the University of California -regimes (a, y regime) differed in their governing

Berkeley t4l. This code is a lD electrostatic simulation
code. And the collision processes, such as electronneutral collision (elasticity, excitation and ionization)discharge mechanisms exist. And the transition between
these discharge regimes has been named as the a to T(a-7) transition.
According to Levitskii, bulk plasma ionization andthe avalanche ionization due to secondary electron("secondary breakdown") are given as their governingdischarge mechanisms respectively [1]. But to confirm
experimentally his hypothesis is difficult, because to

and ion-neutral collision (charge exchange), areconsidered in the code.

The simulation model used in this study is asfollows. The electrode separation is 0.05m, the crossC o rre sp ondin g author' s e -mail : te rada@ ko go s hiO. e e -no da. s ut. ac'i p

307@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Terada T. et al.' Role of Secondary Electrons in the a to0.8[x101610.6?

r secondaries

54o no secondaries{:;tr2a,0.4
dTTransition of RF Capacitive Discharges. secondaries
o no secondaries
oJF

0.2

i---o -o--o2M

100

100

200

200

1.00

Vr.n [v]vnr [v]Vnr [v]

(a)

(b)

(c)

Fig. l DependenceoftheRFcurrent(a),plasmadensity(b)andelectrontemperature(c)section of electrode is 0.001m2, the RF voltage (/ =13.56MH2) is changed from 50 to 225V, gas species isAr, gas pressure is 0.5Torr. The secondary electron
emission coefficient is fixed at 0.2 or 0.0, for ion whichcollides with electrodes.

ontheRFvottage.

6Ix10211-J<'oaE4a(oa3. Results and Discussion=i:J

The dependence of the RF current, plasma densityand electron temperature on the RF voltage is shown in€2. secondaries:Ottraao no secondaries

I.1.l

aaaoN'E1Iao.,,II

Figs. l(a-c), respectively. The RF current and plasma
density with secondary electron emission show
nonlinear increase, while those without the secondary
electron emission show nearly linear increase. The
electron temperatures with and without the secondary

a'00 0.01 0.02 0.03 0.04 0.05
L [m]electron emission suddenly start to drop around the RF

voltage 120V, although the former drops more
drastically. Thus, the experimentally observed
phenomena which accompany the a-7 transition is
confirmed also in the PIC-MCC simulations with thesecondary electron emission. Without secondary

Fig. 2 Profile of the ionization rate on the RF voltage
200v.

Ixto-3;

electron emission, the clear phenomena are not observed

except for the weak drop in the dependence of theelectron temperature on the RF voltage (Fig. l(c)).

5a4E;

These simulation results indicate that secondary
electrons emitted from electrodes would induce ther;Jtransition.

To investigate in detail the contribution ofC).q)

secondary electrons emitted from RF electrodes, wefocused our attention on the sheath region. As a result,the appearance of peaks in the profile of the ionization
rate near the electrodes (Fig. 2) and the contraction of(t. secondaries
o no secondaries

100

sheath width defined as the distance between an

200

Vnr [V]

electrode and a point that time-averaged E-field is zeroas the RF voltage increases (Fig. 3 ) are found. Fig. 2
also shows that the ionization in a bulk plasma is not theFig.3 Dependence of the sheath width on the RFvoltage.
308

Terada T. et al., Role of Secondary Electrons in the a to TTransition of RF Capacitive

Discharges

In consequence of this, our hypothesis can explain

governing mechanisms in the 7 regime. These results
lead us a hypothesis for a role of secondary electrons in

the experiments and simulations for the a-Ttransition'

the a-Ttransition.
When an RF voltage is low, secondary electrons do
not play the dominant role in maintenance of a plasma(a regime). As an RF voltage increases, secondary
electrons emitted from electrodes gain enough energy to4. Gonclusions
The a-Ttransition of RF capacitive discharges isreproduced numerically by the PIC-MCC simulations
for the first time. The simulations show the clear a-ytransition only with a secondary electron emission'
However, the weak drop in the electron temperature isionize neutral particles from electric field in sheathregions. Then, in sheath regions' such ionization isrepeated and results in an avalanche ionization (7predicted in the simulations without secondary electronemission. It would be caused from other electrons in thesheath. The mechanism of the d-l transition is alsoregime). But if an RF voltage increase further, a plasma
density increased by an avalanche ionization wouldinduce the contraction of a sheath width, and thediscussed, which explains that the occurrence of the a'ytransition is restricted in more than medium pressure (pavalanche ionization would be suppressed because thenumber of an ionization by a secondary electron in a> 0.1Torr).

sheath would be reduced.

Acknowledgement
We appreciate the kind policy of the Plasma
Theory and Simulation Group, the University of

The additional condition for the occurrence of theo-Itransition on the hypothesis is that a mean free pathshould be shorter enough than the sheath width, which isCalifornia - Berkeley to open the Particle-in-Cell Monte
Carlo Collision (PIC-MCC) simulation code (xpdpl) toa necessruy condition for an avalanche ionization. The
additional condition explains that the occurrence of thed-ltransition is restricted in more than medium pressure

the public.

(p > 0.lTon).

References

The difference between with and without asecondary electron emission can be understood by thefollowing way. The electric field in a sheath region has
the strongest intensity on the electrode. And it istll S.M. Levitskii, Sov. Phys. Tech. Phys. 2, 887

shielded gradually to zero at a bulk plasma edge.
Secondary electrons gain energy from intense electricAlexandrovich, Phys. Rev. Lett. 68,40 (1992).
t3l M.A. Lieberman and A.J. Lichtenberg, Principles

field, while other electrons in a sheath region gain fromshielded electric field. For this reason, secondary
electrons can induce an avalanche ionization, and otherof Plasma Physics and Materials Processing.

( 1958).

t2l V.A. Godyak, R.B. Piejak and B.M.

(Wiley, New York, 1994).

t4l V. Vahedi, G. DiPeso, C.K. Birdsall, M'A.
Lieberman and T.D. Rognlien, Plasma Sources Sci.
Technol. 2,261 (1993).

electrons can not induce it so strongly.

309