Supporting Information
Undulating Topography of HfO2 Thin Films Deposited in a Meso-Scale
Reactor using Hafnium (IV) tert butoxide
Kejing Li
Box 870203, Chemical and Biological Engineering Department, The University of
Alabama, Tuscaloosa, AL 35487, USA
Lin Zhang
Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin
150001, PR China
David A. Dixon
Box 870336, Chemistry Department, The University of Alabama, Tuscaloosa, AL 35487,
USA
Tonya M. Klein*
Box 870203, Chemical and Biological Engineering Department, The University of
Alabama, Tuscaloosa, AL 35487, USA
*
E-mail: tklein@eng.ua.edu
Two MKS Pirani gauges were equipped before (P1) and after (P2) the flow cell
to measure the pressure difference.
Temperature Profile of the Meso-Reactor
In the flow through cell, there are several components. The tubing wall
thickness is 0.889 mm, 0.2 mm for the stainless steel (ss) sheet, 1.5 mm for the Al sheet,
and 1.2 mm for the Kalrez® gasket. The main rectangular body is made of ss, with a top
section and a bottom section. The two sections are sealed together by a Kalrez® O-ring.
The thermal profile is an important issue in the deposition process. A
minimization of the temperature gradient would help the uniformity of film deposited as
the diffusion and reaction rate are exponentially dependent on the substrate
temperature. In normal operating conditions, it is usually difficult to get a complete
profile of the substrate temperature for two reasons: (1) the substrate is usually in a
closed vessel which makes it difficult to attach a thermocouple inside; and (2) the
thermocouple only measures one spot at a time on the surface. With the aid of high
performance computers, finite element analysis (FEA) enables a prediction of the
temperature distribution on the substrate surface without having to disassemble the
compartment during the experiment.
Finite element analysis (FEA) simulation using the ANSYS multiphysics 11.0
was performed to investigate the thermal heat flow loss due to heat convection in air
and the temperature distribution on the surface of Si substrate. The geometry was
generated using the actual dimensions and all of the components were modeled
according to the real system, since simplification of the structure can cause a significant
accuracy drift. The model was generated by 3-D thermal elements and nodes, meshed
with Solid87 elements and a total number of 314851 nodes. The following assumptions
are made in order to simplify the model:
1)The temperature distribution is calculated during steady state;
2) Radiation is negligible at temperatures below 250ºC and not considered.
3) Thermal coefficients of each component at 1 atm are taken from the CRC Handbook
of Thermal Engineering (Kreith F. The CRC Handbook of Thermal Engineering (1st
edition), Boca Raton, FL: CRC Press, 1999.) and the manufacturer’s website
(http://www.harricksci.com).
4) The thermal contact resistance is negligible between the top plate and bottom plate
as these plates are polished flat fastened with good contact by two screws.
Compared to the volume of the substrate together with the heating or
supporting coils, the thin films deposited at thermal CVD conditions are normally less
than 100 nm and the heat released from the reactions has a negligible influence on the
substrate temperature which has a much bigger volume compared to the thin film. We
assume that the reaction heat (either exothermic or endothermic) has a fast transfer
speed through the thin film. The substrate temperature can be controlled the same as
the one with no thin film deposition and the substrate temperature profile can be
assumed to be the adsorption/reaction temperature profile of the substrate.
The heat transport equations for the flow-through cell without gas flow can be
described as three sections: (1) the faces open to air, (2) copper heat generation rods,
and (3) the main section. On the faces open to air, the general heat transport equation
can be described by Fourier’s Law and Newton’s Law of Cooling, where the convection
equals the conduction at steady state:
 k  A  T  h(T  Tsur )  0
(S-1)
B.C.: T  25C ,  2T  0
(S-2)
Where k is the thermal conductivity, A is the cross area, h is the convection coefficient,
and T∞ and Tsurf is the room temperature and wall surface temperature, respectively.
The copper heater has a power range from 0 to 100 W, depending on the
desired temperature for the Si substrate, which determines the final component


temperature profile.  k   2T  q  0 , where q is the rate of heat generation per unit
copper volume. Within other components without heat generation, the heat flux is simply
based on the heat diffusion equation:  k   2T  0 where a corresponding k is applied
with respect to different materials and temperatures.
Figure S2 shows the temperature distribution predicted on the reactor.
Supporting Information Figure S2 (a) is an overview of the temperature at the reactor
cross section. With a heat power 80W, the top heating plate is about 100 degrees
higher than the bottom plate. Figure S2 (b) is the temperature distribution on the Si
substrate surface. It shows that there is a difference of about 10 °Cdifference along the
transverse direction, and the middle area has the highest temperature.
With an Omicron Thermo temperature controller, the temperature profile on the
substrate was measured to test the above FEA model by taking the reactor apart and
measuring five spots on the substrate back (ss sheet). By changing the two heating
rods’ temperature from 60 ºC to 250 ºC, it usually took 10 to 15 min. for the bottom
substrate to reach thermal equilibrium. As shown in Figure S3, the temperature
distribution along the ss plate is wider with a higher heating rod set point. At a set point
of 225 ºC, the ss plate is about 100 ºC lower. Compared to the calculated substrate
temperature distribution, there are only a few degrees deviation from the experimental
values. This indicates that the calculation is accurate enough to determine the Si
surface temperature which is difficult to measure in the closed system.
Annealing Effect
Figure S4 shows a big difference of thickness with annealing effect. There was
a large decrease in thickness when with the sample was taken out after 5.5 hours
annealing. Desorption occurred during the period. During pumping down, the trapped
molecules are also possible to diffuse to downstream on the surface during substrate
cooling down before taken out.
Pressure difference
The pressure difference was measured by two Pirani gauges P1 and P2. The
background pressure drop was about 10.7 Pa. The pressure drop between P1 and P2
was measured as a function of time after opening the bubbler valve. As shown in
Supporting Information Figure S6, the pressure difference went smaller and reached a
steady state after about 3 min. Based on the Clapeyron-Clausius equation, the vapor
pressure should increase exponentially with bubbler temperature. However, in flow
mode, the evaporation coefficient is usually smaller than 1 due to slower evaporation
rate than pumping speed. The vapor pressure as a function of bubbler temperature was
measured by two gauges: P1 at upstream and P2 at downstream.
The pressure drop ΔP between P1 and P2 as a function of different bubbler
temperatures with a crystal ST at 250 ºC can be read from Figure S7. Pressure
differences at different crystal ST with bubbler temperature at 50 ºC is shown in Figure
S8. ΔP decreases with increasing bubbler temperatures or flow rates, and increases
with crystal temperature. The reaction rate can be inferred by the pressure drop. As the
reaction rate is proportional to the concentration of reactants and the reaction coefficient,
with the same crystal temperature (same reaction coefficient), the concentration should
be proportional to the flux. However, decomposition by-products such as tert-butanol
from a hydroxylation reaction and tert-butene from β-hydride elimination can lead to
different pressure effects. As a result, below 65 ºC higher bubbler temperatures have
higher adsorption or reaction rates and a smaller pressure decrease. At 75 ºC, however,
there is a return of the pressure drop, which indicates that the reaction becomes more
mass transfer limited due to a lower diffusion coefficient at higher pressure.
Supporting Information Figure S8 shows the pressure readings at different
crystal setting temperatures. The crystal temperatures were all above the decomposition
temperature of 185 ºC. The pressure difference is larger with higher crystal
temperatures, indicating a faster reaction rate. It can also be deduced that more
adsorption occurred than decomposition reactions by the fact that pressure decreased
after the cell instead of increased.
Heating Cords
Inlet
φ=8.4
Outlet
φ=3.6
50.0
29.0
7.5
16.0
Figure S1. Schematic drawing of ATR flow through cell. Unit in mm.
(a)
(b)
Figure S2. (a) Temperature profile on the flow through cell cross section with a power of
80W; (b) temperature distribution on the Si surface with a power of 80W.
Set T ( C):
120
250
225
200
175
150
120
100
80
60
o
o
Bottom plate temperatures ( C)
140
100
80
60
40
-25
0
Axial distance (mm)
25
Figure S3. Measured temperatures on ss sheet at the back of Si substrate.
100
Thickness (nm)
90
80
1 hr precursor at 250 ºC
70
19 hrs annealing after 1 hr in air
60
1hr precursor + 5 hrs annealing
50
40
0.0
1.0
2.0
3.0
Y (cm)
4.0
5.0
Figure S4. Thickness along the axis for HTB deposited on H-Si(100) crystal with
bubbler at 65 ºC and crystal setting temperature at 250 ºC.
10 sccm
1 sccm
0.15 sccm
Velocity (m/s)
15.0
10.0
5.0
0.0
0.0
0.1
0.2
z (cm)
Figure S5. Velocity profile of the flow at 1.7 Pa-L/s.
0.3
0.4
80.0
P1
P2
Pressure (Torr)
70.0
60.0
50.0
40.0
30.0
20.0
10.0
0.0
0
100
200
300
Time (s)
400
Figure S6. P1 and P2 pressures as a function of time. The substrate is native oxide
with a bubbler temperature at 50 °C.
50.0
P1
Pressure (Pa)
40.0
P2
30.0
20.0
10.0
0.0
20
40
60
Bubbler Temperature (o C)
80
Figure S7. P1 and P2 pressures as a function of different bubbler temperatures. The
substrate ST is 250 °C.
50.0
P1
P2
Pressure (Pa)
40.0
30.0
20.0
10.0
0.0
150
200
250
300
350
o
Reactor Set Temperature ( C)
Figure S8. Pressures upstream P1 and downstream P2 as a function of different
reactor or substrate setting temperatures. The bubbler temperate is 50 °C.