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Rapid growth of particles by coagulation between particles in silane plasma reactor

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Abstract

The changes of particle size distribution were investigated during the rapid growth of particles in the silane plasma reactor by the discrete-sectional model. The particle size distribution becomes bimodal in the plasma reactor and most of the large sized particles are charged negatively, but some fractions of small sized particles are in a neutral state or even charged positively. As the mass generation rate of monomers increases or as the monomer diameter decreases, the large sized particles grow more quickly and the particle size distribution becomes bimodal earlier. As the mass generation rate of monomers decreases, the electron concentration in the plasmas increases and the fraction of particles charged negatively increases. With the decrease in monomer diameter, the electron concentration decreases in the beginning of plasma discharge but later increases.

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Abbreviations

C:

constant, 0.73

dl :

particle diameter in the lth size regime (DSR+SSR) [cm]

d1 :

monomer diameter [cm]

e:

elementary charge of electron [C]

E(v, v):

enhancement factor of collision frequency function taking into account the particle charge distribution of colliding particles

f(q):

particle charge distribution function

Fl,neg, Fl,neu, Fl,pos :

fractions of particles which are charged negatively, neutral, or charged positively in the lth size regime (DSR+SSR)

I(q):

flux of species which pass through the q particle charges

kB :

Boltzmann constant, 1.38×10-16 [gcm2/sec2K]

mR :

reduced mass between the moving particles

M:

mass of species [g]

n(v, t):

size distribution function [cm-6]

N:

number concentrations of species [cm-3]

Nl :

number concentrations of particles in the lth size regime (DSR+SSR) [cm-3]

q:

particle charges [e]

ql :

average charges of particle in the lth size regime (DSR+SSR) [e/particle]

qi :

volume concentration variable for i-mers in the discrete size regime

Qk :

volume concentration variable for section k particles

S1 :

mass generation rate of monomers [g/cm3s]

t:

time [s]

T:

temperature of species [K]

Tg :

gas temperature, 300 K

v:

particle volume variable [cm3]

V1 :

monomer volume [cm3]

v k :

particle volume upper boundary of sectional k [cm3]

v k-1 :

particle volume lower boundary of sectional k [cm3]

vR :

relative velocity between the moving particles

Β*i,j :

general property coagulation coefficient (Βi, j/(jv1))

Β(u, v):

collision frequency function between particles [Friedlander, 1977]

Β:

collision integral for coagulations of two sectional size regime particles

Βki,k/D:

collision integral for coagulations of sectionk particles and i-mers in discrete size regime

Β DDi,j,k :

collision integral for coagulations of two discrete size regime particles

ε0 :

permittivity of free space, 8.854× 10-21 [C2/dyncm2]

ρd :

particle density [g/cm3]

Σ 2l :

variance in lth discrete size regime or sectional size regime

Τres :

residence time [s]

0:

initial

e:

electron

l :

lth size regime (DSR+SSR)

+:

positive ion

-:

negative ion

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  1. Department of Chemical Engineering, Kangwon National University, Chuncheon, 200-701, Kangwon-Do, Korea

    Dong-Joo Kim & Kyo-Seon Kim

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  1. Dong-Joo Kim
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  2. Kyo-Seon Kim
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Correspondence to Kyo-Seon Kim.

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Kim, DJ., Kim, KS. Rapid growth of particles by coagulation between particles in silane plasma reactor. Korean J. Chem. Eng. 19, 495–504 (2002). https://doi.org/10.1007/BF02697163

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