1. Analyze the mechanism of “bulb blackening” in a tungsten filament lamp from a
PVD/ CVD viewpoint. What was the design innovation that virtually eliminated
this problem? Derive the condition of “zero element flux” in terms of relevant
partial pressures of species.
2. Analyze, from a CVD viewpoint, the mechanism of “hot corrosion” of protective
oxide-coated gas turbine blades due to molten alkali salt deposition. What are
the different mass fluxes involved, and how do they determine local thickness of
the molten layer on a rotor blade? Derive expressions for the deposition flux,
including correction factors for thermophoresis, homogeneous kinetics and
heterogeneous kinetics.
3. Illustrate the application of multi-scale modeling in CVD reactors using the
example of carbon nano-tube synthesis. Identify the four length and time scales
involved, and the two approaches used for integrated modeling.
4. CVD systems are characterized by non-uniqueness (“hysteresis”) of dewpoints.
Explain this concept via a graph relating deposition rate to surface temperature.
Identify the various regimes in this graph, and outline their implications for
reactor design.
5. State the Mass Transfer Analogy Condition (MTAC), and the conditions under
which it applies. Does Stefan flow break the MTAC, and if so, how? What are the
conditions for neglecting convective mass transfer in the presence of natural
convection and Stefan flow?
6. Mullite (3Al 2 O 3 .2SiO 2 ) coatings are typically deposited in an atmosphericpressure cold-wall horizontal-flow CVD reactor from a gas mixture containing
AlCl 3 , SiCl 4 , CO 2 and H 2 . You are asked to develop a model to predict the rate of
growth of the CVD film.
a. State 5 key assumptions you would make to begin your analysis, and
identify the relevant dimensionless parameter associated with each.
b. Identify an appropriate control volume to enable the prediction of
temperature, velocity and mass fraction distributions in the CVD reactor.
c. Write the conservations laws for species mass, element mass,
momentum and energy for the control volume selected.
d. Write the constitutive relationship for species and element mass fluxes,
including at least one phoretic mechanism.
e. What are the conditions for a stoichiometric mullite coating to be feasible
at the substrate? Consider both thermodynamic and transport
constraints.
f. How is the Nusselt number for mass-transfer, Nu m,0 , calculated under
baseline conditions? How would you quantify the effect of the phoretic
field on that parameter?
g. How are the Damkohler numbers for homogeneous & heterogeneous
reactions defined? What effect do they have on the mass-heat transfer
analogy?
7. In a hot-wall, cross-flow LPCVD reactor used for silicon deposition, SiCl 4 and H 2
are the reactants. Possible species in the product are: Si, Si(s), SiCl 4 , SiH 2 Cl 2 , HCl,
Cl 2 , H 2 , H, and SiHCl 3 . You are asked to develop a predictive model for film
growth as a function of time and position along the substrate.
a. State five key assumptions in your model. Discuss their validity in the CVD
system being analyzed.
b. Construct an appropriate control volume for your transport model, and
state the corresponding conservation equations for total mass, Sicontaining species mass, and elemental silicon mass.
c. Write the total depositional flux term for (Si) element, including all major
contributors. In order for CVD of silicon to be feasible from
thermodynamic & transport considerations, what would be the necessary
constraints to be satisfied?
d. Assuming that mass transport in this reactor is diffusion-dominated,
define an appropriate dimensionless number for the diffusive flux of
silicon, assuming MTAC (mass-transfer analogy conditions).
e. Assuming that mass transport in this reactor is convection-dominated,
define an appropriate dimensionless number for the diffusive flux of
silicon, assuming MTAC (mass-transfer analogy conditions). How is this
related to capture efficiency? Provide some suggestions for enhancing
both parameters.
8. You are asked to make a stoichiometric film of Si 3 N 4 over GaAs using a roomtemperature CVD process. How would you design a reactor and a process to
achieve this? Consider all relevant kinetic, thermodynamic and transport
parameters.
9. In an epitaxial silicon CVD reactor, SiCl 4 and H 2 are used as reactants. Possible
species in the product are: Si, Si(s), SiCl 4 , SiH 2 Cl 2 , HCl, Cl 2 , H 2 , H, and SiHCl 3 .
Outline a procedure to obtain the chemical equilibrium composition of the
product stream.
10. Sketch the temperature dependence of the deposition rate in a typical CVD
reactor. Identify the two distinct regimes of deposition. What are the ratecontrolling mechanisms in each regime? What are the corresponding
implications for single-wafer vs batch processing? Show how the curve shifts
when:
a. Pressure is reduced in half
b. Flow-rate is doubled
c. Parasite reactions take place at higher temperatures.
11. In a horizontal-flow CVD reactor, reactant stream (with hydrogen as carrier gas)
enters in plug flow, and exits in parabolic flow. A wafer is mounted on its holder
such that its leading edge is 2.5 m from the inlet. The prevailing Reynolds
number is 100, and the tube radius of the reactor is 10 cm. Is this an optimum
design for uniform deposition? What would be the relative advantage of a
stagnation-point flow configuration?
12. Identify five critical parameters used to characterize a CVD film, along with
appropriate measurement techniques. Outline the operating principle of each of
the measuring instruments.
13. Sketch a typical deposition rate versus substrate temperature curve for a CVD
reactor, and identify the rate-controlling mechanisms as a function of
temperature. In which regime would you operate a single-wafer CVD system?
Show how this curve would be shifted if: (other conditions being the same)
a. The operating pressure is reduced by half,
b. The flowrate is doubled,
c. The mean molecular weight of the precursor species is reduced by half,
d. The carrier gas is replaced by a more reactive gas.
14. How would you grow an epitaxial silicon film on a silicon wafer? How would you
change process conditions if a polycrystalline or amorphous Si film was desired?
15. In a thermal CVD reactor to form Si(s) from silane (SiH 4 ) gas, the following gasphase species are thermodynamically feasible: SiH 4 , SiH 3 , SiH 2 , SiH, Si, H 2 , H.
Define a procedure to estimate the equilibrium composition of the product
stream. Formulate the appropriate equations and constraints.
16. In a CVD reactor where the reactants and carrier gas enter in plug flow parallel
to the wafer substrate, the entry velocity is 1 m/sec. The density of the gas
mixture is 4 X 10-4 g/cm3, and dynamic viscosity is 0.04 g/cm-sec. The diameter of
the inlet pipe is 25 cm. The length of the wafer is 40 cm, and its leading edge is
located 50 cm from the inlet.
a. Will the flow become and remain laminar until it reaches the wafer? The
transition Reynolds number is 500.
b. Estimate the thickness of the boundary layer (BL) at the midpoint of the
wafer and at its trailing edge.
c. What would be a viable strategy to keep the BL thickness nearly constant
over the wafer surface? Why is that important?
17. In a tungsten-filament incandescent lamp, explain how CVD helps to delay the
onset of “bulb blackening”.
18. In a hot-wall, cross-flow LPCVD reactor used for silicon deposition, SiCl 4 and H 2
are the reactants. Possible species in the product are: Si, Si(s), SiCl 4 , SiH 2 Cl 2 , HCl,
Cl 2 , H 2 , H, and SiHCl 3 . You are asked to develop a predictive model for film
growth as a function of time and position along the substrate.
a. State five key assumptions in your model. Discuss their validity in the CVD
system being analyzed.
b. Construct an appropriate control volume for your transport model, and
state the corresponding conservation equations for total mass, Sicontaining species mass, and elemental silicon mass.
c. Write the total depositional flux term for (Si) element, including all major
contributors. In order for CVD of silicon to be feasible from
thermodynamic & transport considerations, what would be the necessary
constraints to be satisfied?
d. Assuming that mass transport in this reactor is diffusion-dominated,
define an appropriate dimensionless number for the diffusive flux of
silicon, assuming MTAC (mass-transfer analogy conditions). How would
this be augmented in the case of thermophoresis?
e. Establish the “jump condition” at the substrate/ gas interface in the case
of
non-equilibrium
heterogeneous
reactions,
and
derive
the
corresponding surface Damkohler number.
19.
You are asked to make a stoichiometric film of Si 3 N 4 over GaAs using a roomtemperature CVD process. How would you design a reactor and a process to
achieve this? Consider all relevant kinetic, thermodynamic and transport
parameters.
20.
In an epitaxial silicon CVD reactor, SiCl 4 and H 2 are used as reactants. Possible
species in the product are: Si, Si(s), SiCl 4 , SiH 2 Cl 2 , HCl, Cl 2 , H 2 , H, and SiHCl 3 . How
would you obtain the chemical equilibrium composition of the product stream?
For this deposition system, how would the three dew-points be defined?
21.
Compare the following with respect to the likely rate-controlling mechanism
(reaction versus transport):
a. Hot-wall, low-pressure CVD reactor
b. Cold-wall, low-pressure CVD reactor
c. Hot-wall, atmospheric-pressure CVD reactor
d. Cold-wall, atmospheric-pressure CVD reactor
Of these, which configuration is most appropriate for the high-volume
production of low-cost dielectric films?
22. Analyze the vapor deposition mechanism(s) involved in “bulb blackening” in a tungsten
filament lamp in the following cases:
i. Vacuum lamp
ii. Inert-gas filled lamp
iii. Halogen-cycle lamp
In which of these cases is the theoretical limit of “no bulb blackening” achievable?
Formulate the corresponding “zero element flux” expression.
23. How is the quasi-steady thickness of the protective oxide coating on marine gas turbine
rotor blades related to the prevailing molten salt deposition rate? How would you use this
relationship to define an optimum strategy for protection from “hot corrosion” of gasturbine blade alloy materials?
24. Develop a multi-scale model of the CVD process associated with the formation of an
SiO 2 film in a CW/AP/CVD reactor. Of the time-scales involved, which are likely to be
the shortest and longest?
25. How would you model the transport processes in a horizontal-flow LP/CVD reactor for
growth of epitaxial silicon? State your assumptions. How does a hot-wire CVD reactor
work, and what additional benefits does it provide?
26. Mullite (3Al 2 O 3 .2SiO 2 ) coatings are typically deposited from a gas mixture containing
AlCl 3 , SiCl 4 , CO 2 and H 2 . How would you construct the thermodynamic phase diagram,
indicating onset of mullite formation as a function of temperature, and ratio of Al-to-Si
elemental concentration in the reactant mixture? How would this phase diagram be
“shifted” when transport constraints are taken into account?
27. Define the “local flux ratio constraint” (LFRC) for the formation of Na 2 SO 4 (l) deposit
on turbine blades exposed to product gases from combustion of marine air, and fuel
containing sulfur impurity. How is the LFRC condition altered in the presence of a
mobile condensate, such as on a rotor blade? What implication does this have for “hot
corrosion” induced by dissolution of the protective oxide coating?
28. A customer is very demanding with respect to the thickness (in 50-80 Ao range), purity,
uniformity, resistance, critical dimensions and grain size of a film that is being deposited
via a CVD process. As the responsible Process Engineer, how would you design the
reactor to optimize control over these parameters? What measurements would you
perform to ensure conformance to customer specifications for these parameters?
29. How would you model the transport processes in a horizontal-flow LPCVD reactor for
growth of epitaxial silicon? State your assumptions. What additional benefits does a Hot
Wire CVD reactor provide?
30. TiB 2 is a CVD coating obtained using TiCl 4 , BCl 3 and H 2 as reactant gases. How would
you construct the thermodynamic phase diagram, indicating onset of TiB 2 (S) as a
function of temperature, and ratio of Ti-to-B elemental concentration in the reactant
mixture? How would this phase diagram be “shifted” when transport constraints are taken
into account?
31. In a Nitridation CVD reactor, SiH 2 Cl 2 and NH 3 are used as reactants; possible
product species are: Si 3 N 4 , H 2 , HCl, SiH 2 Cl 2 (un-reacted), NH 3 (un-reacted), Si 3 N 4
(S) and Si (S).
a. How would you write the general species mass balance equation for Si?
How would you write the mass conservation equation for elemental Si?
b. Given that Si 3 N 4 (S) is the desired CVD film, how would you write the
diffusive mass transport constraint equation for this deposit?
c. Given that Si 3 N 4 (S) is more viable at higher temperatures, define and
graphically illustrate the three dew-points: T dp (0), T dp (-), and T dp (+).
d. In a hot-wall APCVD reactor, what is likely to be the dominant “phoretic”
force? How would you incorporate that mechanism into your overall
mass transport flux?
e. What effect would an increase in substrate temperature have on the
uniformity of the CVD film, and why?
32. You are asked to deposit an 80 A0 film of SiO 2 on a silicon substrate at a
temperature of 900 C.
a. Design an optimum CVD process for this purpose (including reactant
species, operating pressure, reactor design, etc.)
b. What would be the structure of this film? Describe two methods by
which its mechanical properties may be enhanced to match a thermallygrown oxide.
c. Describe a method to obtain chemical equilibrium compositions for this
system.
d. How would you model gas dynamics inside the reactor? State your
assumptions.
e. How would you analyze the thickness and grain size of the film? State the
operating principle of the instrumentation you would select.
33. Describe how the dewpoint T dp (0) can be calculated for a CVD system containing
SiH 4 , SiH 2 , H 2 and Si 2 H 6 as reactants, and Si (S) as the CVD film.
34. Explain the difference between the following flow regimes, using dimensionless
numbers where appropriate:
a. Continuum vs Free-Molecular
b. Viscid vs Inviscid
c. Laminar vs Turbulent
d. Steady vs Unsteady
e. Multi-dimensional vs One-dimensional
35. How is effective diffusivity of a dilute species in a mixture of low-density gases
estimated?
36. Define the following dimensionless numbers:
a. Nusselt # for mass transfer
b. Stanton # for mass transfer
c. Captured Fraction
How are the last two related for a typical CVD target?
37. What are the two phenomena that can break the heat/ mass transfer analogy in
CVD reactors? Name the dimensionless numbers used to characterize these. How
are the corresponding mass-flux correction factors estimated?
38. What are the four major types of CVD reactions? Give an example for each.
39. Sketch a typical CVD apparatus, and name the components.
40. Name the critical transport processes involved in delivery of reactants to the
deposition surface. Identify them as convective or diffusive.
41. List and describe five key techniques to characterize particle contaminants and
chemical species in CVD films.
42. Name the critical steps in CVD film growth on a substrate. Of these, which is
most dependent on substrate quality, and why?
43. List five critical properties of CVD deposits and the instruments used to measure
these.
44. Sketch the temperature dependence of the deposition rate in a typical CVD
reactor. Identify the two distinct regimes of deposition. What are the ratecontrolling mechanisms in each regime? What are the corresponding
implications for single-wafer vs batch processing?
45. Gas AB is introduced into a CVD reactor, and reacts as follows:
AB

A+B

If this is an APCVD process at a temperature of 1000K and it reaches chemical
equilibrium, calculate the partial pressure of each species. The equilibrium
constant at 1000K is 2.0E-04 atmospheres. State any necessary assumptions.
46. You are asked to develop CVD processes to deposit SiO 2 over silicon at three
different substrate temperatures: (i) > 900 C, (ii) 400 – 900 C, and (iii) < 400 C. In
each case, state what would be the most appropriate type of CVD process to use,
and what the corresponding reactant species would be.
47. Develop a simple model for gas dynamics inside a tubular CVD reactor. In a
horizontal CVD reactor, what causes the deposition rate on a flat wafer to
decrease from the front of the tube to the back, and from the edge of each
wafer to the center? How can deposit uniformity be improved?
48.
49.