Pore evolution during high pressure atomic vapor deposition

D. D. HassÆ Y. Y. Yang Æ H. N. G. Wadley

Published online: 31 January 2009

� Springer Science+Business Media, LLC 2009

Abstract The development of physical vapor deposition

systems that employ inert gas jets to entrain and deposit

atomic and molecular fluxes have created an interest in the

atomic assembly of thin films under high pressure (10–

500 Pa) deposition conditions. Thin films grown under

elevated pressure and low surface mobility conditions can

contain a higher volume fraction of porosity and a different

pore morphology to coatings created by conventional, low

pressure (\10-4 Pa) deposition processes. A recent direct

simulation Monte Carlo simulation analysis of binary

vapor–gas jet atom interactions has shown that the incident

angle distribution (IAD) for vapor atom impacts with a

substrate is strongly effected by the background pressure.

Here, these results are combined with a kinetic Monte

Carlo technique to simulate the high pressure growth of

vapor deposited nickel films and identify the mechanisms

of pore formation. We find that when the surface atom

mobility is low, shadowing of oblique angle arrivals by

features on the substrate result in the incorporation of

porosity with a hierarchical size distribution that includes

elongated, inter-columnar pores and finer scale intra-

columnar pores. The nucleation of the inter-columnar pores

is related not only to the IAD, but also to the height and

spacing of the initial asperities on the substrate and to those

that subsequently evolve during deposition. The volume

fraction of the inter-columnar pores is found to increase as

both the fraction of oblique atom arrivals and the height of

the asperities increase. For each prescribed IAD and

asperity height, an asperity spacing is found that maximizes

the inter-columnar pore fraction. By varying the IAD for a

given substrate surface topology, in conjunction with

intermittent observations of the coating structure during the

growth process, the flux shadowing mechanisms that gov-

ern the inter-columnar pore nucleation have been

determined.

Keywords Physical vapor deposition (PVD) �Computer simulation � Coatings

1 Introduction

Physical vapor deposited coatings containing controlled

pore volume fractions and morphologies are utilized for

many applications including thermal barrier coatings [1, 2],

the anodes and cathodes of solid oxide fuels cells [3], in

batteries [4] and numerous other optical, medical, chemical

and biological applications [5–7]. Porosity is incorporated

in these coatings to manipulate their properties. For

instance, the yttria stabilized zirconia (YSZ) coatings used

for the thermal protection of gas turbine engine compo-

nents contain large (micron size) inter-columnar pores

aligned perpendicular to the substrate surface that are uti-

lized to increase the in-plane compliance of the coating.

Smaller, intra-columnar pores are also exploited to reduce

the thermal conductivity of the coating by interrupting the

conductive and radiative mechanisms of thermal transport

[8]. The performance of these porous coatings is governed

by the size, volume fraction and inclination of the pores [9–

11].

Porosity is entrained in vapor deposited coatings when

the surface atoms are unable able to diffuse from their

impact positions on a surface to vacant, low energy lattice

sites, Fig. 1. The adatom surface mobility is effected by

D. D. Hass � Y. Y. Yang � H. N. G. Wadley (&)

Department of Materials Science and Engineering, School of

Engineering and Applied Science, University of Virginia,

Charlottesville, VA 22903, USA

e-mail: haydn@virginia.edu

123

J Porous Mater (2010) 17:27–38

DOI 10.1007/s10934-008-9261-4

several properties of the vapor flux; the vapor atom’s

translation energy [12], its latent heat of condensation [13]

or heat of reaction with the surface [14], and by the flux of

energetic, assisting ions that sometimes accompany the

condensing atoms [15]. It also depends upon properties of

the substrate such as its temperature [16], and surface

topology [17]. The coatings lattice cohesive energy estab-

lishes the magnitude of the energy barriers impeding

surface migration and thus the thermal or ion impact

energy required to overcome them [13].

Pores are entrained when the surface atom jump fre-

quency is too low to allow complete migration to unfilled

lattice sites before jumping atoms are covered by new

atoms. The jump frequency can be approximated by an

Arrhenius equation of the form, t = toexp(-Q/jT), where

t is the jump frequency, to is the jump attempt frequency,

Q is the activation energy, j is Boltzmann’s constant and T

is the absolute temperature of the solid.

Columnar porosity in a vapor deposited coating is cre-

ated when; (a) the adatom surface mobility is low and (b)

incident vapor atoms are shadowed by features on the

growth surface resulting in flux depleted regions on the

substrate. Columnar voids then become entrained between

local high spots on the surface [18]. The local high spots

themselves are often rough and so under some conditions

the process of void entrainment is simultaneously perpet-

uated at many length scales resulting in a hierarchical pore

topology and a coating surface that has fractal-like form

[19]. Pores ranging from elongated, micron-scaled inter-

columnar pores to nanometer-scaled intra-columnar

porosity then result.

Shadowing of the incident atoms is more likely when

atoms arrive at oblique angles to a surface. These oblique

atom arrivals are ‘‘shadowed’’ by surface asperities or

atomistic irregularities on the surface of the growing film.

These can form, even on initially smooth surfaces, by

variations in the growth rate of differently orientated grains

whose growth rate is crystal orientation dependent [20]. If

the reduced local vapor flux in the shadowed region cannot

be fully compensated by surface diffusion, these regions

eventually become pores. The interplay between the dis-

tribution of adatom’s deposited on the growth surface and

the distance of adatom diffusion determines both the vol-

ume fraction and morphology of pores in a coating.

The incident angle distribution (IAD) of an atomic flux

has a significant effect upon both the pore volume fraction

and morphology, and its manipulation has been used to

control pore morphology. Techniques have included the

use of substrate inclination variation such as tilting or

rotating [5, 11, 21, 22] and methods that exploit vapor

atom–background gas atom collisions. Gas jet enhanced

deposition in a high pressure environment is an example of

the latter approach [23]. In all cases, these techniques alter

the IAD at the substrate which in turn modifies flux

shadowing.

Inert gas jet assisted methods of vapor deposition [24]

enable control of the IAD provided the pressure is suffi-

ciently high (typically [ 5 Pa) that the mean free path

between vapor atom–inert gas atom collisions is significantly

less than the evaporation source-to-substrate distance. This

results in many binary collisions between the vapor atoms

and the atoms in the gas jet. Recent results for the deposition

of yttria stabilized zirconia onto nickel substrates using an

EB-DVD process operating at high pressures indicate that

the pore topology can be manipulated over wide ranges by

modifying the gas jet conditions [25]. Figure 2 shows an

Fig. 1 Pores can form because of flux shadowing by local asperities

on the growth surface. Surface diffusion can transport material into

shadowed regions. The diffusion rate on the surface is controlled by

the material type/local atom configuration dependent activation

barriers for hopping and by the substrate temperature

Fig. 2 Shows the effect of increased the deposition chamber pressure

upon the morphology of yttria stabilized zirconia coatings grown

using an inert gas assisted directed vapor deposition process. All the

coatings have columnar morphologies with elongated inter-columnar

pores (see the inset on the right) and nanoscopic intra-columnar

porosity (the micrograph on the left). The volume fraction of both

types of porosity is shown for coatings deposited at 1,000�C. The

variations arise from changes to the angular incidence distribution of

the condensing flux [25]

28 J Porous Mater (2010) 17:27–38

123

example where the total pore fraction and its components all

depend strongly on the background pressure.

The effects of background pressure upon the IAD during

deposition in gas jet assisted deposition processes have

recently been characterized using a Direct Simulation

Monte Carlo (DSMC) approach [25, 26]. It was shown that

high pressures increase the width of the incidence angle

distribution (Pw) while increases in gas jet velocities results

in a shift in the median impact angle (hm) away from the

substrate normal that alters the shadowing mechanisms that

control pore formation. In addition to the IAD changes, it

was also shown that, as the deposition pressure increases,

gas phase collisions multiply leading to the vapor phase

nucleation and growth of clusters of atoms. The ‘‘cluster’’

component of the flux is not as strongly scattered by

background atoms and arrives at near normal incidence

angles. The inter-columnar pore width has been found to

track the increase on IAD as pressure is increased, Fig. 3,

until the transition from an atomic to cluster mode of

deposition occurs [25].

Here, we explore the effects of pressure upon the pore

morphology in the cluster-free limit. The relationships

between changes in the IAD and porosity are studied using

a kinetic Monte Carlo (KMC) simulation technique. Using

2D estimates for the surface diffusion energy barriers of

nickel we use the KMC method to simulate the growth of

coatings for a range of incidence angle distributions. This

then enables a systematic investigation of the role of

process pressure (via the IAD reported in [25]) upon pore

evolution during vapor deposition under diffusion con-

strained conditions.

2 Kinetic Monte Carlo modeling

Simulating atomic assembly during the condensation of a

vapor is extremely complicated, even for the mono-

atomic deposition of a close packing metal species such

as nickel. This complexity arises from the many surface

and bulk diffusion pathways (each with a different energy

barrier) available for atomic reassembly during growth.

Further complexity is introduced by the surface topogra-

phy which dynamically evolves. This causes the

significance of flux shadowing to also evolve during

coating growth. Under high deposition rate conditions,

these changes in local flux also modify the local

‘‘equivalent’’ surface temperature (and hence surface atom

mobility) because of the associated latent heat of con-

densation release.

Many approaches are being explored for the atomic

scale simulation porous film growth [27]. Here, a relatively

simple kinetic Monte Carlo (KMC) simulation approach

has been employed to link the flux incident upon a surface

to the resulting film morphology [28]. In a kinetic Monte

Carlo simulation, particles (atoms) are added to an evolv-

ing topography surface and their subsequent assembly (by

atomic hopping) is simulated by assuming a thermally

activated jumping process. In principle, the approach is

simple; the probability of thermally activated hopping for

every atom in an ensemble is calculated and one is ran-

domly selected. The inverse of its probability yields a time

between two hops which is subtracted from the mean time

between atom arrivals on the surface. Hops are allowed to

continue (and the surface topography to change) until the

time between consecutive atom arrivals is consumed

whereupon the new atom is deposited and the process

repeats.

In practice the multiplicity of hopping paths (each with

its own activation barrier) creates a complex, computa-

tionally significant problem to solve. Great simplification

is achieved by resorting to a 2D approximation and is

used here. The activation barriers in a 2D approximation

lose much of their quantitative significance, but key dif-

ferences are maintained so that the competition between

the various assembly mechanisms remains (see reference

[27] for a detailed discussion). The kinetic Monte Carlo

method used here utilizes this multi-path diffusion anal-

ysis to determine the surface topography and the

evolution of the coatings interior atomic structure. It

effectively captures many of the key phenomena during

Fig. 3 Shows both the measured width of the inter-columnar pores

for YSZ coatings deposited at 1,000�C and the breadth (Pw) of the

simulated IAD distribution as a function of the chamber pressure.

Note that a good correlation exists between these parameters until

very high pressures are reached where cluster deposition then

becomes prevalent

J Porous Mater (2010) 17:27–38 29

123

thin film growth including the role of the Ehrlich-

Schwoebel barrier which is critical for a realistic treat-

ment of the competition between step-flow (terrace) [29]

and island modes of growth [30]. Individual atom jump

rates are taken to depend upon a local, configuration

dependent activation barrier which is pre-computed using

a molecular statics approach [31]. The calculated activa-

tion energies for several different configurational

transitions in nickel are given in Table 1. The approach

includes a treatment of the latent heat of condensation

release and its effect upon local mobility [13].

3 Implementation

The input parameters required for the simulations are

shown in Table 2. The code allowed the IAD to be pre-

scribed by a cosn(h) distribution where h is the angle

between the substrate normal and the incidence direction of

the atom. A typical IAD is shown in Fig. 4. Symmetrical

Table 1 Calculated activation energies for different configurational

transitions in nickel

Table 2 Simulation conditions used for KMC study

Atom type Nickel

Simulated atoms 250,000

T/Tm 0.22

Deposition rate (lm/min) 0.30

Activation barrier [surface jump](eV) 0.472

Activation barrier [Schwoebel jumps] s1 = 1.090, s2 = 0.706 eV

Fig. 4 A schematic illustration showing the simulation setup

employed. A 2.0 lm wide substrate was used. The substrate

temperature, substrate roughness (in the form of asperities described

by a height, h, and a spacing, s), and IAD were all systematically

varied

30 J Porous Mater (2010) 17:27–38

123

distributions defined by the peak width at half maximum,

Pw, and a peak maximum angle, hm, were used in all cases.

The peak width was controlled by the parameter, n, in the

cosine distribution and the position of a peak maximum

angle in the IAD could be altered by tilting the substrate,

Table 3.

In many applications, porous coatings are deposited onto

substrates that are not atomically smooth. Shadowing of the

flux by an initially rough surface was therefore included in

the analysis. This roughness was introduced in the form of

truncated triangular asperities. The effect of varying the

height, h, spacing, s, and degree of truncation of the

asperities was studied using substrates of a fixed width

(1.8 lm) and periodic lateral boundary conditions. The

deposition rate was 3.0 lm/min and the substrate temper-

ature was T/Tm = 0.22 (here T is the absolute substrate

temperature and Tm is the absolute melting point of nickel).

This temperature was chosen for the 2D simulation since it

resulted in a similar level of atomic assembly between

atom arrivals to that observed in the experiments.

4 Results

4.1 Coating morphology

The morphologies of the simulated nickel films using an

IAD described by Pw = 75� and hm = 0� and a substrate

temperature of T/Tm = 0.22 are shown in Fig. 5. When

deposited onto an atomistically smooth substrate a porous

morphology without columnar pores resulted, Fig. 5a.

Columnar pores occurred when surface asperities with

height, h, and spacing, s, equal to 125 nm were present on

the substrate, Fig. 5b. At least two scales of porosity could

be observed in these coatings, the elongated inter-columnar

pores (that nucleated in the trough regions created between

surface asperities) and finer scaled intra-columnar porosity

that was sometimes also elongated. In Fig. 5c, the width of

the IAD, Pw was increased to 150� and the asperities were

removed. This resulted in the formation of a columnar

morphology with distinct inter-columnar pores (similar to

the case shown in Fig. 5b). These simulations indicate that

columnar porosity develops on rough surfaces even for

relatively narrow vapor atom incidence angle distributions

and just above the surfaces of smooth substrates when the

distribution is broad. Surface roughness was also observed

to develop naturally during the growth process. For a fixed

initial surface roughness and incidence angle distribution

the pore fraction increased with the thickness of the coat-

ing. To untangle the interrelationships between the

properties of the surface and those of the incident flux we

conducted a series of simulations where each variable was

varied independently.

4.2 Adatom angle of incidence

4.2.1 Peak distribution width, Pw

KMC simulations were performed using IAD’s with peak

widths from 35� to 150�. For these simulations h and s were

125 nm and hm was 0�. The coating morphologies are

shown in Fig. 6. When Pw was low (35�) no inter-columnar

pores were observed to form, however, at higher Pw values

(75�–150�) distinct inter-columnar pores were seen. These

pores initiated in the troughs between surface asperities.

The pore fraction increased with Pw, Fig. 7. The inclination

angle of these pores remained constant as did the volume

fraction of the intra-columnar porosity.

4.2.2 Distribution angle at peak maximum, hm

Variations in the angle at peak maximum were studied by

altering hm from 0� to 45�, Fig. 8. For these simulations h

and s were 125 nm and Pw was 120o. In all the simulations

inter-columnar pores were initiated in the troughs of the

substrate. As hm increased (i.e. as the flux became less

normal to the substrate) the inclination of the pores

increased, Fig. 9a. The inclination angle of the pores

directly correlates with the peak maximum angle. In this

case, the pore inclination angle was proportional to the

incidence angle maximum and not its tangent. Thus, when

a broad angular flux distribution exists the tangent rule for

pore inclination [32] is not followed. The pore volume also

increased as hm was increased, Fig. 9b. However, this

Table 3 Experimental design (variation in model parameters for KMC simulations)

Parameter

altered

Peak distribution

width, Pw (�)

Peak maximum

angle hm (�)

Asperity height,

h (lm)

Asperity height,

s (lm)

Substrate temperature

(T/Tm)

Pw 35–150 0 0.125 0.125 0.22

hm 75 0–40 0.175 0.125 0.22

h 120 0 0.0–0.21 0.125 0.22

s 80 0 0.066 0.125–0.750 0.22

J Porous Mater (2010) 17:27–38 31

123

Fig. 5 KMC simulations of nickel growth onto a an atomically

smooth substrate and b a substrate having surface asperities. In these

cases the IAD was defined by Pw = 75� and hm = 0�. The substrate

temperature was T/Tm = 0.22. Note the formation of inter-columnar

pores in b that nucleated at the trough formed by two closely spaced

asperities. Also shown is the intra-porosity that exists in these

coatings. In c inter-columnar pores are shown to form on an

atomically smooth substrate as Pw is increased to 150�

Fig. 6 KMC simulations of nickel growth showing the effect of Pw

on the coating morphology. Note that as the Pw was increased from

35� to 150� the inter-columnar porosity became more prevalent

32 J Porous Mater (2010) 17:27–38

123

increase was entirely made up of inter-columnar pore

volume increases. The intra-columnar pore volume was

unaffected by hm.

4.2.3 Substrate geometry

Asperity height: The role of asperity height, h, was sys-

tematically investigated by increasing h from 25 to 150 nm

while holding the spacing, s, (125 nm) and incidence angle

distribution Pw = 120�, hm = 0�) constant, Fig. 10. The

shape of the asperities was maintained so that the width of

the asperities also increased with the height. Note that no

inter-columnar pores are formed for the smallest asperity

height (25 nm). However, as the asperity height was

increased, inter-columnar pores began to form and became

increasingly prevalent, Fig. 11. Since, the modeled sub-

strate had a fixed width, increasing the asperity width (with

a constant asperity spacing) resulted in a change in the

number of ‘‘peaks and valleys’’ in the modeled region.

Since the inter-columnar pores are observed to nucleate in

the valleys, the inter-columnar pore volume is related to the

number of pore nucleation sites on the substrate. To

account for this change, the average volumes of each

individual inter-columnar pore was calculated and this is

plotted against the asperity height in Fig. 11. The pore

volume fraction was found to be a very strong function of

the pre-existing asperity height.

Fig. 7 A plot showing the dependence of the inter-columnar and total

pore volume fractions upon Pw. The shaded area corresponds to a

region where no inter-columnar pores were observed. The intra-

columnar pore volume fraction increased with Pw beyond this region.

The intra-columnar pore volume fraction (which is the difference

between the total and inter-columnar pore volume) remained constant

with increase in Pw

Fig. 8 KMC simulations of nickel growth showing the effect of hm

on the coating morphology. As hm increased from 0� to 40� the inter-

columnar porosity became more prevalent and the inclination angle of

the pores increased away from the substrate normal

J Porous Mater (2010) 17:27–38 33

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Asperity spacing: The effect of the spacing, s, between

surface asperities was systematically investigated by

increasing s from 125 to 750 nm while holding the asperity

height (67 nm) and the IAD distribution (Pw = 75�,

hm = 0�) constant. The simulations are shown in Fig. 12.

These simulations indicate that inter-columnar pore for-

mation was strongly affected by the asperity spacing. Since

the number of pore nucleation sites also varied in this case,

the average volume of each inter-columnar pore was cal-

culated and is plotted against the asperity spacing in

Fig. 9 Plots showing the change in a the inter-columnar pore

inclination angle and b the inter-columnar and total pore volume

fraction as hm was varied. Note the both parameters systematically

increased as hm was increased while the intra-columnar pore volume

fraction remained constant. The solid lines are best fits to the data

Fig. 10 Increasing the asperity height from 0.025 to 0.150 lm

resulted in an increased average pore width

34 J Porous Mater (2010) 17:27–38

123

Fig. 13. The results reveal a systematic increase in inter-

columnar pore volume as the spacing is initially increased.

This trend continues until a critical spacing is reached

whereupon the inter-columnar pore volume then decreased

rapidly. Clearly an optimal spacing for nucleating inter-

columnar porosity exists.

5 Pore evolution

The simulations conducted above have indicated that inter-

columnar pores initiate in the valleys between adjacent

surface asperities provided; (i) the substrate temperature is

sufficiently low to inhibit surface diffusion of the deposited

atoms and (ii) the incidence angle distribution is suffi-

ciently broad that a large fraction of oblique atom arrivals

are shadowed. When these criteria are achieved, inter-

columnar pores are formed and perpetuated through the

coating thickness.

To explore how the porosity evolves during the depo-

sition of a thin film, simulations were interrupted during

the film growth. For these analyses, the incidence angle

distribution was defined by Pw = 120� and hm = 0�. The

substrate had asperities 125 nm in height and 125 nm

apart. The substrate temperature T/Tm = 0.22. A typical

result is shown in Fig. 14. It can be seen that after depo-

sition of all atoms, Fig. 14a, the deposited film directly

over the asperities is significantly higher than that above

the initial valley regions. This occurs because the initial

asperity peaks ‘‘shadow’’ the oblique component of the flux

allowing a larger fraction of the atoms to be deposited on

Fig. 11 Plots showing the increase in the inter-columnar pore

volume fraction with asperity height

Fig. 12 KMC simulations showing the effect of increasing the

asperity spacing from 0.25 to 0.625 lm on the coating morphology.

Inter-columnar pores are not observed for asperity spacing’s greater

than 0.375 lm

J Porous Mater (2010) 17:27–38 35

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hilltops. This is facilitated by a broad angular flux distri-

bution. As growth continues, the peaks of the faster

growing columns, Fig. 14b, further decrease the vapor flux

incident on the columns growing in the troughs. Eventually

a pore is formed above the trough as the vapor flux is

almost completely depleted in this region of the substrate,

Fig. 14c and d.

The ratio of atoms deposited on column peaks to trough

bottoms as a function of the number of atoms deposited for

three incidence angle distribution widths (Pw = 75, 90,

120�) shown in Fig. 15. It can be seen that the flux fraction

in the trough region decreases fastest for the Pw = 120�case where the fraction of oblique adatom arrivals is the

greatest. The pore volume is also the largest when Pw is the

broadest and systematically decreases to zero when the flux

is collimated, Fig. 7.

6 Discussion

The results above show that the morphology of vapor

deposited coatings created under low adatom mobility is

controlled by flux shadowing. This promotes the formation

of columnar morphologies with elongated, inter-columnar

pores. The volume and inclination of these pores are

determined by the angular distribution of the flux and the

surface topology. Valleys between asperities on the growth

surface are the nucleation sites for pores. In these regions

the flux of oblique adatom arrivals is depleted which

Fig. 13 The plot shows the effects of changing the asperity spacing

upon the inter-columnar pore volume fraction. Note that the pore

volume reached a maximum at an intermediate value as the spacing

was increased. Further increases past this intermediate value resulted

in a reduced the pore volume

Fig. 14 KMC simulations of nickel growth onto a substrate having

surface asperities. Results are shown after a 25,000 atoms, b 50,000

atoms, c 75,000 atoms and d 100,000 atoms have been deposited.

Note that the asperities result in variations in the vapor flux

distribution that result in inter-columnar pore formation

36 J Porous Mater (2010) 17:27–38

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locally reduces the film growth rate. A faster than average

growth rate in the non-shadowed regions further enhances

shadowing. This eventually leads to the formation of an

inter-columnar pore. IAD’s that result in a high fraction of

oblique adatom arrivals (large Pw or hm value) promote

pore formation and also increase the volume of the inter-

columnar pores. As growth progresses, the column peaks

become higher and the area that is flux depleted increases

resulting in an increase in porosity with coating thickness.

The pore content of the coating was observed to exhibit

a maximum at a critical inter-asperity spacing, Sc. This can

be understood by considering Fig. 16 where the spacing of

a pair of asperities on a surface is varied as a flux, fo,

impinges at either ±60� to the surface normal. Flux

shadowing of one or the other sources occurs near the

asperities (the lightly shaded regions in Fig. 16a. When the

inter-asperity spacing is small, Fig. 16a, the shadowed

regions can overlap in the trough. In the shadow overlap

region the flux is zero. A pore with a small width will

initiate in this overlap region. As s increases, the overlap

region decreases but the width of the region where flux

depletion occurs increases and so does the width of the

resulting pores, Fig. 16b. The asperity tops continue to

receive the full flux and so the effective height of the

shadow causing asperity grows, perpetuating the nucleated

pore. When the asperity spacing is further increased,

Fig. 16c, no overlap of the shadowed regions occurs. Thin

pores would then be nucleated at the sides of the asperity

and would grow at an angle to the asperity to create a

triangular growth region defined by two intersecting inter-

columnar pores. The angular growth in this case results

because of outward growth from the sides of the asperity

leading to nodular features in the coatings. A smaller pore

width results as the flux depleted area is reduced. This

results in a reduced pore volume even though the number

of pores is increased (doubled). The maximum pore vol-

ume occurs when an intermediate spacing is used that

maximizes the continuous flux depleted area created by the

asperities.

The mechanisms above are consistent with the experi-

mental observations summarized in Figs. 2 and 3. During

high pressure deposition of YSZ [25], the inter-columnar

Fig. 15 Plot showing the change in the relative vapor flux in the

trough region of the substrate as the coating was deposited. Results

are shown for three asperity peak widths. Note that the vapor flux in

the trough region is eventually reduced to zero as the growth of the

coating progresses. The flux incident upon the peak of the surface

asperities is also shown and this does not change as the coating is

grown

Fig. 16 Schematic illustration showing the shadowed substrate area

for the case of a vapor flux, fo, impinging on a rough substrate from

either 60� and -60�. The effect of altering the asperity spacing is

shown in a, b and c

J Porous Mater (2010) 17:27–38 37

123

pore width is observed to be closely related to the flux

incidence angle peak width simulated using direct simu-

lation Monte Carlo (DSMC) methods, Fig. 7. Thus, broad

angular distributions are experimentally observed to

increase the pore volume as shown in this work. Process

conditions resulting in a highly off-normal peak maximum

angle in DSMC simulations also lead to coatings with

highly inclined inter-columnar pores, Fig. 9a [26].

7 Conclusions

The role of the incidence angle distribution and substrate

topology upon the initiation and volume fraction of inter-

columnar porosity in vapor deposited coatings has been

explored using a kinetic Monte Carlo modeling approach.

The results show that:

(1) The incidence angle distribution of an atomistic flux

together with the height and spacing of surface

asperities on a substrate combine to control the

volume and inclination of the inter-columnar pores

under constrained surface mobility conditions.

(2) The nucleation of the inter-columnar pores is deter-

mined by the incidence angle distribution and the

height and spacing of the initial asperities on the

substrate (or those that subsequently evolve during

deposition). An increase in the frequency of oblique

atom arrivals promotes inter-columnar pore

nucleation.

(3) The volume fraction of the inter-columnar pores

increases with the fraction of oblique adatom arrivals

and the height of surface asperities. For each

prescribed incidence angle distribution and asperity

height, an asperity spacing exists that maximizes the

inter-columnar pore fraction.

(4) The volume fraction of intra-columnar porosity

(finest-scale) is not strongly affected by changes in

the incidence angle distribution or changes in the

substrate roughness when constrained surface mobil-

ity conditions are used.

Acknowledgments This research was supported by the Office of

Naval Research (Grant number N00014-00-0147) under the program

direction of Drs. Steve Fishman and David Shifler.

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