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Mathematical modeling for chemical vapor deposition in a single-wafer reactor: Application to low-pressure deposition of Tungsten

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Abstract

A mathematical model for low pressure chemical vapor deposition in a single-wafer reactor in stagnation point flow has been developed to investigate the reactor performance. The transient transport equations for a simulated reactor include continuity, momentum, energy, and gaseous species balances. The model equations are simultaneously solved by using a numerical technique of orthogonal collocation on finite element method. Simulation studies have been performed to gain an understanding of tungsten low pressure chemical vapor deposition process. The model is then used to optimize the deposition rate and uniformity on a wafer, and the effects of operating conditions on deposition rate are studied to examine how system responses are affected by changes in process parameters. Deposition rate and uniformity calculated at the steady state are observed to be very sensitive to both temperature and total pressure. In addition, the model predictions for tungsten deposition from hydrogen reduction of tungsten hexafluoride have been compared with available experimental data in order to demonstrate the validity of the model.

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Abbreviations

cp :

molar heat capacity [cal/mole K or cal/g K]

D:

diffusion coefficient [cm2/sec]

DT :

thermal diffusion coefficient [g cm/sec]

G:

deposition rate [å/min]

g:

gravitational acceleration [cm/sec2]

m:

molecular weight [g/mol]

n:

number of gaseous species

p:

pressure [torr or atm]

r:

radial coordinate [cm]

Rg :

universal gas constant [atm cm3/mol K, or cal/mol K]

ℜ:

surface reaction rate [mol/cm2 sec]

t:

time [sec]

T:

temperature [K]

T*:

reduced temperature [κT/ε]

v:

gas velocity [cm/sec]

x:

mole fraction

z:

axial coordinate [cm]

ε:

Lennard-Jones potential energy between two molecules [gcm2/sec2]

κ:

Boltzmann’s constant [=3.30×10-24 cal/K]

λ:

thermal conductivity [cal/cm sec K]

Μ:

viscosity [g/cm sec]

Ν:

stoichiometric coefficient of the surface reaction

ρ:

fluid density [g/cm3]

Σ:

collision diameter for the Lennard-Jones parameter [å]

Ω:

mass fraction

o:

reactor inlet

i:

index or species

j:

index

m:

mixture

r:

radial direction

s:

susceptor

T:

thermal diffusion

w:

wall

z:

axial direction

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  1. Dept. of Chemical and Environmental Technology, Inha Technical College, 402-752, Incheon, Korea

    Jung-Hwan Park

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Park, JH. Mathematical modeling for chemical vapor deposition in a single-wafer reactor: Application to low-pressure deposition of Tungsten. Korean J. Chem. Eng. 19, 391–399 (2002). https://doi.org/10.1007/BF02697145

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