1. XIII International Conference on Gas Discharges and their Applications (GD2000) in Glasgow
Strathclyde University, 3-8 September 2000
Spatiotemporal Analysis of Plasma Kinetics of Radio Frequency Glow Discharge in Nitrogen
K Satoh, H Itoh and H Tagashira
Department of Electrical & Electronic Engineering,
Muroran Institute of Technology, Muroran , JAPAN
Agenda 1. Motivation & Objective
2. Experimental results
3. Simulation model & conditions
4. Simulation results
5. Conclusions

2. Introduction Motivation Objective
Radio frequency glow discharge in nitrogen and its mixtures are used for
- plasma nitriding, thin film deposition, removal of pollutant gases
to control discharge plasmas
to improve efficiency of the processes
quality of devices
Spatiotemporal variation of excited molecule (C3Pu) density has been measured.
Objective
To clarify the plasma kinetics of capacitively coupled rf discharge at MHz in nitrogen by spatiotemporally resolved optical emission spectroscopy and by the self-consistent Propagator method.
Particularly, mechanism of the double layer formation in nitrogen rf discharge is interpreted with the modelling.
understanding the kinetics of the discharge plasmas is essential

3. EXCITED MOLECULE DENSITY(N2) & EXCITATION RATE(H2)
nitrogen
hydrogen
Olivier Leroy et al, J.Phys.D: Appl. Phys. 28, pp.500-7, (1995) K K
Time (ns) A A
V0cosq
double
layer A
wave-ride
electron K G G P
Distance (mm) P
Powered electrode 0.0(cm)
Grounded electrode 3.0(cm)
C3Pu density profile
p=1.5Torr, f=13.56MHz
Excitation rate H(n=3)
p=1Torr, f=13.56MHz
Two relative maxima of the excitation rate are observed near the both electrodes.
Similar profile is observed in hydrogen rf discharge.
Relative maxima are due to the double layer formation (Leroy et al.)
The double layer formation has been reported for the discharges in electro-negative gases, but only in hydrogen rf discharge in electropositive gases.

4. SIMULATION MODEL One dimensional model in the field direction
Discharge space is divided into 40 thick slabs and
the velocity distributions of electrons and ions f(e,q)
are defined in the slabs.
The behaviour of the charged particles is calculated
using Propagator method.
Each of the thick slabs is divided into 20 thin slabs
in order to calculate the diffusion of the particles
accurately.
External circuit
Space charge field (1D Poisson’s eq.)
where e : the electronic charge
ne, n+ : densities of electrons & positive ion at x and at t
we, w+ : velocities of electrons & positive ion at x and at t
S : area of electrodes
e0 : the permittivity in vacuum
Vg(t) : gap voltage
r(x, t) : net charge density

5. PROPAGATOR METHOD (one dimensional)
Velocity distribution f(e, q, x) is stored in the memory of computer using multi-dimension array. The balance of a volume cell in the distribution f(e, q, x) in unit time t is calculated using Newton’s law and expectation values.
The Balance in unit time t
Acceleration vx=vx0 + (eE/2m)t
Drift x=x0 + vx0t + (eE/2m)t2
The expectation values of
momentum collision f(i,j, xk)・ PT・qm/qT
excitation collision f(i,j, xk)・ PT・qex/qT
ionisation collision f(i,j, xk)・ PT・qion/qT
free flight (no collision) f(i,j, xk) ・(1- PT )
the probability of collision PT=exp(-NqTvt)
Velocity distribution f(e, q, x)

6. Simulation conditions
gas length ： d=3.0cm
gas pressure & temp. ： p=0.5, T=20.0 ℃
applied voltage & freq. ： Vs sin wt, f=13.56MHz
electrodes ： fully absorbing walls
for charged particles
second coefficient ： i=0.05
cross sections ： Ohmori et al.
collision frequency ： nT_ion=69.306×v×p (s-1)
(positive ion) v - ion speed (cm/s)
p - gas pressure (Torr)
time step ： t　=7.37x10-12 (s)
mesh number of f (, , x )
energy  0 ～ 40eV 40 meshes  = 1.0eV (electron)
0 ～ 10eV 40 meshes  = 0.2eV (positive ion)
angle  0 ～  rad 20 meshes  = /20 (0.157) rad
position x 0 ～ 3 cm 40 meshes  x = cm(thick), x’= 3.75×10-3 cm(thin)
initial density distribution of electrons & ions
： 1.0x107 (cm-3) uniformly distributed in a gap
electron collision cross section
Y Ohmori,et al, J. Phys. D: Appl. Phys., vol.21, pp (1988)

7. Spatiotemporal profile of C3Pu density ―experiment―
p=0.5 Torr
p=1.5 Torr K K A A A A K K G G P P
The large (first) maxima in front of the instantaneous cathode and the small (second) relative maxima in front of the instantaneous anode are observed.
These profiles are qualitatively good agreement with that of the excitation rate observed in hydrogen rf discharge by Leroy et al, and this suggests that the double layer is formed in nitrogen rf discharge

8. optical emission spectroscopy
Excitation rate of C3Pu
Simulation result
optical emission spectroscopy K K A A A A K G K G P P
The excitation profile obtained by this simulation qualitatively agrees well with that obtained by the emission spectroscopy.
Remarkable point is
simplified model used here gives the spatiotemporally correct position of the excitation maxima.

9. Electron, Ion & net charge densities and electric field
net charge density
Electric field ne A K K G P A K np A A
(T/8) K G P G P G P
The net charge density immediately in front of the both electrodes is always positive during one rf cycle, however, that two maxima of negative space charge appear near the instantaneous anodes.
The maxima of the negative space charge and the relative maxima of the electric field are seen at the spatiotemporally same position.
Spatiotemporal position of the second maxima of the excitation rate agrees well with those of maxima of net charge density.

10. Spatial variations of ne, ni, vx, e & electric field at T/8
Electric field in the plasma is slightly positive. A K
This field accelerates electrons towards the powered electrode (x=0cm) . (velocity is negative)
Net charge density in left hall of the plasma is negative, so that electric field increases towards the powered electrode. P G
These electrons
contribute to the double layer formation
have excitation collision with nitrogen molecules.
Small peaks of C3Pu
Electrons are accelerated further by this field.

11. Fourier expansion of the electric field
Spatial variations of the amplitude of the first three terms of Fourier expansion of the electric field written as below
where an and bn are coefficients.
Plasma : cosine component is dominant
p/2(rad) leads against the phase of applied voltage
Sheath : sine component is dominant
The electrons in the plasma are accelerated by the weak electric field.
The phase of the field leads p/2 (rad) against that of the applied voltage.
The electrons accelerated by this field contributes to the double layer formation.

12. Conclusions
Spatiotemporally resolved optical emission spectroscopy in nitrogen rf glow discharge is performed and the spatiotemporal profile of the excitation rate of C3Pu state is obtained.
Self-consistent simulation of rf glow discharge in nitrogen using the Propagator method has been carried out, and the spatiotemporal profile of the excitation rate of C3Pu is obtained. This profile qualitatively agrees well with that obtained by the emission spectroscopy.
From the simulation, the double layer is formed in nitrogen rf discharge.
The electrons accelerated by the weak electric field in the plasma, the phase of which leads p/2 (rad) against that of the applied voltage, make a contribution to the double layer formation.