Reaction Kinetics and Transport Model for Gallium
Nitride MOVPE Reactor Showerhead Design
Rinku P. Parikh, Raymond A. Adomaitis, Brendan D. Hoffman, Michael E. Aumer, Deborah Partlow, Darren Thomson
M
MOTIV
OTIVATION
ATION
CH
CHEM
EMICAL
ICALK
KINETICS
INETICS
The growth of quality GaN thin films is complicated by complex gas phase
reactions between the common precursors: trimethylgallium (TMG) and
ammonia (NH3). Two competing reaction pathways exist which lead to either
adduct formation or pyrolysis of TMG.
Applications of GaN based Materials
R4
1. Model Development
Thermal Model
R5
(CH3)3Ga:NH3
[(CH3)2Ga:NH2]3
R3
R6
S1
1,2,3
2Powerful new radar
technology which will
detect smaller and
faster targets.
3A blue laser that
will increase the
storage capacity of
a compact disc.
6CH4 + GaN-compounds
Deposition
1Aerospace devices that
can function over a wide
temperature range and
remain unaffected by
radiation.
NH3
Ga(CH3)3
Problem: Adduct formation
and deposition within the
showerhead can contribute to
poor growth rate and film
quality.
Plume Spread Model
Gas Flow Field Model
R2
SG_1 = QuadGrid(‘ cyln ', nrFirst, ‘ r ’, [Rft, ringLoc(2)]);
Newton-Raphson
Equation
Solver
Wafer
Goal: Develop a model that captures mass transfer and kinetic effects
(gas phase and surface reaction) inside showerhead
Dr = LinearOperator(SG_1, ‘ d ‘ ,‘ r ');
4. Construct ScalarField object
for variables
X1 = ScalarField(SG_1, Xin(1,1));
X2 = ScalarField(SG_1, Xin(2,1));
Solutions
Velocity
Pressure
Density
Temperature
Mole Fractions
etc.
GaCH3 + CH3
2. Set up Quadrature Grid
3. Create LinearOperator Object
R1
Ga(CH3)2 + CH3
Pictures taken from www.northropgrumman.com
M
MOV
OVPE
PEREACTOR
REACTORSYSTEM
SYSTEM
The simulator was developed using an object-oriented approach.
Modeling equations for the showerhead thermal and gas flow field model,
the plume spread model, and gas phase reaction model were decoupled
from each other and placed in different model classes (modules).
Gas Phase
Reaction Model
(CH3)2Ga:NH2 + CH4
Adducts
Gallium Nitride (GaN) is a compound semiconductor material with tremendous
potential in the electronics industry. Metalorganic vapor phase epitaxy
(MOVPE) is the principal method used to grow thin films of this material.
Therefore, fundamental understanding of complex gas phase and surface
reactions combined with flow, heat transfer, and mass transfer processes is
critical for the production of high quality deposited layers.
M
MODEL
ODELDEV
DEVEL
ELOPM
OPMENT
ENT
1D Simulation Results: Thermal model, Gas Flow Field, Kinetics
1D Modeling Equations:
Consider the gas phase thermal decomposition of TMG
TMG -> DMG -> MMG
Precursors: TMG, NH3, H2
Continuity Equation:
d
(vˆr )
dr
0
Thermal Energy Balance: 1 d (vr )
r dr
Showerhead
h(Ts T)
Velocity Profile
Species Balance Equations:
Susceptor & Wafer
1 d 1
( rvxTMG )
r dr T
1
k1 (T ) xTMG k dep xTMG
T
1 d 1
( rvx DMG )
r dr T
1
1
k 2 (T ) xDMG k1 (T ) xTMG
T
T
1 d 1
( rvxMMG )
r dr T
1
k 2 (T ) xDMG
T
Species Profile for
Gas Phase Reactions
A(g) -> B(g) -> C(g)
Species Profile for Gas Phase
and Deposition Reactions
A(g) -> B(g) -> C(g)
2D Modeling Equations:
Cross-section of showerhead configuration
hole ring radii : R1,…,RM
gas radial velocity inside showerhead : u1,…,u2M-1
reactant gas velocity through holes : v1,…,vM
showerhead gas pressure : P1,…,P2M-1
œCi
(v ½
·Ci )
œt
Di · Ci R
2
i
G
(eq .1)
Ci
œ2C
1 œ œ
Di [
(r
) 2 i ] RGi
r
z
r œ
r
œ
œ
Ci
œ
vr
r
œ
General form of the species
conservation equation for
a pseudobinary mixture
Surface
(eq .2)
Neglecting vz and v‰ and
Assuming Ci(r,z)
Boundary Conditions:
r – direction:
Showerhead internal heat transfer
conduction thru plates : qctp , qcbp
plate/reactant gas : qcgt , qcgb
gas sensible heat : qsin , qsout
Wafer/showerhead heat transfer
radiation : qrrw , qrw
conduction : qcw
Wafer/liner heat transfer
radiation : qrli
conduction : qcli
Ci ( rin , z )
Ci 0
œCi (rout , z )
œr
0
z – direction:
Di
Di
œCi (r ,
'z / 2)
œz
RSi ,bot
œCi (r , 'z / 2)
RSi ,top
œz
Assumptions:
1) Surface reactions are controlled
by arrival rate of gas phase
species to top and bottom
showerhead plates. (Arrival rate
is approximated by kinetic
theory)
SUM
SUMM
MARY
ARY&
&FUTURE
FUTUREW
WORK
ORK
•
2) Diffusional interaction among
Rate of Adsorption (RS)
- Controlled by the rate of arrival of molecules to the surface, F, and the
fraction of incident molecules which are adsorbed, S
RS
S ½F
(eq. 3)
P
1
( 2‡mkT )1/ 2 N A
(eq. 4)
Ultimate Goal: Compute the
amount of deposited material
inside the showerhead. This will
give a better indication of the
intrinsic chemistry responsible
for GaN growth.
Summary
– Object oriented techniques create an efficient approach to
assembling models of this form, and allow the addition of more
model components without much difficulty.
– Developed a model that describes mass transport and kinetic effects
within the showerhead
minor species can be neglected.
F
Temperature Profile
•
Future Work
– Examine kinetic theory of gases: bimolecular collision rate vs.
impingement rate of molecules on a surface.