Porous Al2O3 nanogeometry sensor films: Growth and analysis

Article abstract of DOI:10.1149/1.1421608

Material studies of thin films of porous anodized Al₂O₃ have been undertaken to determine their applicability as sensing films for application on surface acoustic wave sensors. We describe the production of these films including their growth parameters and provide an analysis of their crystal morphology. These films were then exposed to various concentrations of analyte and their surface areas determined using Brunauer-Emmett-Teller-type analysis. Finally, the surface area as a function of anodization potential is provided for the films.

Full text of DOI:10.1149/1.1421608

Journal of The Electrochemical Society, 149 ͑1͒ H1-H5 ͑2002͒
H1
0013-4651/2001/149͑1͒/H1/5/$7.00 © The Electrochemical Society, Inc.
Porous Al2O3 Nanogeometry Sensor Films
Growth and Analysis
,z
*
*
W. G. Yelton, K. B. Pfeifer, and A. W. Staton
Sandia National Laboratories, Albuquerque, New Mexico 87185-1425, USA
Material studies of thin films of porous anodized Al2O3 have been undertaken to determine their applicability as sensing films for
application on surface acoustic wave sensors. We describe the production of these films including their growth parameters and
provide an analysis of their crystal morphology. These films were then exposed to various concentrations of analyte and their
surface areas determined using Brunauer-Emmett-Teller-type analysis. Finally, the surface area as a function of anodization
potential is provided for the films.
© 2001 The Electrochemical Society. ͓DOI: 10.1149/1.1421608͔ All rights reserved.
Manuscript submitted April 16, 2001; revised manuscript received September 6, 2001. Available electronically November 27,
2001.
Recent efforts have focused on the chemical and physical diver-
sity of interface materials for surface acoustic wave ͑SAW͒
technology.1 These materials provide SAW sensors with their ana-
lyte selectivity. Issues of wide dynamic range and high sensitivity
must also be addressed for sensor arrays to compete in applications
requiring low detection limits such as the development of sensor
systems useful in the detection of chemical plumes for security ap-
plications. Each chemical sensor consists of interdigital transducers
patterned on the surface of an ST-cut quartz substrate with a thin-
film coating placed in the SAW propagation path to perturb the
acoustic wave velocity during analyte sorption. Since no single coat-
ing provides absolute analyte specificity, an array of sensors pro-
vides a high degree of discrimination ability. By providing a diverse
set of material coatings, the sensor array offers a degree of chemical
sensitivity and selectivity. Because SAW devices respond in propor-
tion to change in mass per nominal unit area of the device surface,
sensitivity is enhanced by surface modification with high area, thin-
film coating materials to allow a greater mass of analyte adsorption
at a given ambient concentration. A number of anodization studies in
the literature have dealt primarily with bulk materials and their re-
sultant properties, which are significantly different from evaporative
deposited thin-film systems.2,3 Other studies have dealt with the
growth of porous alumina films formed on foil templates.4 This
study deals with porous films grown in situ on a sensor substrate
where the pore morphology and pore size is controlled by the sub-
strate temperature and the anodization conditions.
Material studies of thin ͑Ͻ1 ␮m͒, high surface area, metal/oxide
films developed to improve SAW sensitivity, reveal common factors
that, in fact, diminish sensor sensitivity. These factors include non-
uniformity in the density of the material, the rigidity of the micro-
structure, and nonuniformity in the thickness of the coating. For
example, films developed from high density materials such as Pt,
Pd, or Au, have yielded higher dendritic nanogeometries but suffer
greater insertion losses for a given thickness. In contrast, because of
its low density, microstructure rigidity, ordered porosity, and con-
trollable pore volume, anodized aluminum (Al2O3) formed from
evaporated deposition of metallic Al suggests promising films for
enhanced sensor sensitivity. In the context of this paper, anodized
aluminum and alumina refer to two different coatings. Anodized
aluminum is a coating where only part of the evaporated aluminum
has been converted to alumina. Under this oxidized layer remains
metallic aluminum. For alumina, on the other hand, the evaporative
aluminum film has been completely converted to an oxide, no addi-
tional aluminum is available for anodizing.
Experimental
Growth and deposition.—During physical evaporative deposi-
tions, the dominant influence on the final microstructure of an Al2O3
coating is strongly linked to the surface mobility of the adatoms,
which is affected by the substrate temperature and deposition rate.
The microstructure of evaporative films can be viewed in terms of
the Movchan-Demchishin model also known as the zone structure
model ͑ZSM͒.5 In this model, coatings are deposited under three
distinct conditions or ‘‘zones.’’ At a constant evaporation rate, the
material morphology in each zone can be manipulated by the tem-
perature of the substrate (Ts) onto which the Al is deposited. Zones
Ͻ
Ͻ
are classified as zone I (Ts
0.3Tm), zone II (0.3Tm
Ts
Ͼ
Ͻ 0.45Tm), and zone III (Ts
0.45Tm) where Tm refers to the
melting point of bulk Al.
In zone I, film growth is more agglomerated with ‘‘islands’’ of
crystalline structures separated by small columnar voids. Because of
low thermal energy, due in part to the relatively low substrate tem-
perature as compared to the melting point of the material, the sur-
face mobility of adatoms is limited. The image in Fig. 1 is a cross-
sectional view of an agglomerated structure of alumina formed by
the anodizing process of evaporated aluminum on a quartz substrate
deposited under zone I conditions. After sulfuric acid ͑0.5 M͒ anod-
ization under fixed ͑16 V͒ anodic potential, the crystal morphology
of the Al2O3 in Fig. 1 is characterized by disordered alumina micro-
structures with low effective surface areas. From tunneling electron
microscopy ͑TEM͒ analysis, these agglomerated oxides reveal tor-
tuous pore openings with diameters on the same order as films de-
veloped under zone II conditions, but with limited pore length and
corresponding limited pore volume. These features are not visible
with high resolution scanning electron microscopy ͑SEM͒
examination.
Anodization.—Figure 2 is the cross section of an alumina film
formed by the anodizing process of evaporated aluminum grown
under zone II conditions. The initial film was vapor deposited under
the same conditions as the film in Fig. 1, except that the substrate
temperature was held at 0.4 Tm . Under zone II conditions, film
growth occurs with greater adatom mobility, and favors columnar
grain structures with dense intercrystalline boundaries that extend
through the coating thickness. The anodization conditions were
identical for both films and consist of mounting an Al coated SAW
device to a rigid Teflon fixture that was centered in a 250 mL beaker
1 cm from a Pt counter electrode. Electrical contact to the Al film
was made through a 1 mm Ti wire mounted on the Teflon fixture.
DC resistance was observed at the Ti wire tip ͑opposite the Ti/Al
contact͒ and a point on the Al surface. If the resistance was 3 ⍀/cm2
or higher, the contact points were filed and cleaned and then the
resistance was rechecked.
Prior to entering the solution, power was activated to the elec-
trochemical cell. Before and during the anodizing process, N2 gas
was bubbled through the anodizing solution in front of the SAW
* Electrochemical Society Active Member.
z E-mail: kbpfeif@sandia.gov
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Journal of The Electrochemical Society, 149 ͑1͒ H1-H5 ͑2002͒
Figure 1. SEM cross section of an alumina film formed by anodizing ͑16 V
applied͒ evaporated aluminum that was thermally evaporated on quartz at
low temperature of 53°C substrate temperature (0.08 Tm). Because of low
adatom mobility, the microstructure of the deposit is more agglomerated with
voids.
Figure 3. The current decay of 500 nm aluminum evaporated film during
constant potential anodization. Solid line is a spline fit of the data as guide to
the eye. Note that the current asymptotically approaches a constant value at
the end of the stage 3 growth.
tance of the film increases dramatically. The solid line in Fig. 3 is a
guide for the eye. The film undergoes three stages of change under
potentiostatic mode. During the first ͑growth͒ stage ͑the first 60 s in
this example͒, the current drops at a rapid rate, indicating that the
nucleation of oxides and crystal structure ordering of the Al2O3 is
occurring. During the second stage ͑see Fig. 4͒, SEM micrographs at
1, 3.5, and 10 min reveal the formation of the oxide with increasing
depths as a function of time. From zone II deposition, the unanod-
ized aluminum film evaporated on quartz appears quite rough with a
number of large voids. After 60 s of anodization with an applied
potential of 10 V, a uniform oxide of 100-150 nm consumes and
covers the surface. At 3.5 min, more that 25% of the aluminum is
consumed. When 10 min have passed, most of the available alumi-
num is gone.
device. The N2 helped to agitate the solution, and for small surface
areas, was sufficient for maintaining the temperature of the cell. The
samples in Fig. 1 and 2 were anodized at a constant potential of 16
V. For all samples anodized at potentials from 2-25 V, we used 0.5
M H2SO4 as the electrolyte. Samples used for the adsorption study
were prepared under zone II conditions and anodized for 40 min.
These 500 nm films were completely converted to alumina. At these
exposures, the finished film thickness ranged from 550-620 nm de-
pending on the driving potential, with higher potentials yielding
thicker films and larger pore diameters. Films anodized much longer
͑stage III͒ were thinner than the initial 500 nm seed layer with larger
pore diameters for a given fixed potential, as compared to alumina
films formed under identical conditions but for shorter anodizing
times.
As anodization time increases, the thickness of the oxide film
grows, consuming and converting the aluminum underlying to an
oxide. During stage II ͑see Fig. 3͒, the current is fairly stable and the
general morphology of the crystal structure in now ordered and the
remaining aluminum is converted to oxides by the slow diffusion of
oxygen through the thicker oxide film above. During this second
stage, the porous film reaches its highest level of impedance for a
given overall thickness.
Figure 2 reveals straight ordered columns extending from the
surface to the substrate. This scanning electron micrograph ͑SEM͒ is
viewed using a 300 nm scale to clearly reveal the ordered columnar
structure in contrast to Fig. 1, which is viewed from a slightly
macroview ͑600 nm scale͒ to reveal the disorder surface as well as
the cross-sectional structure.
The graph in Fig. 3 reflects the current decay over time as an
aluminum film, formed under zone II evaporation, is anodized under
constant potential. As the aluminum oxide forms, the surface resis-
Figure 4. SEM cross sections of films that have been anodized for various
times. The four images are viewed from samples that were fractured to reveal
cross sections of aluminum oxide, aluminum, and the quartz substrate. The
unanodized film is in the upper left-hand corner and proceeding clockwise
the photographs are 1, 10, and 3.5 min. All films were deposited under zone
II conditions and were anodized at a 10 V potential.
Figure 2. Fractured SEM cross section of an alumina film formed by anod-
izing ͑16 V applied͒ evaporated aluminum. The aluminum was thermally
evaporated on quartz at 250°C substrate temperature (0.4 Tm). Due to in-
creased adatom mobility, the microstructure of the deposit is more columnar
with distinct intercrystalline boundaries.
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Journal of The Electrochemical Society, 149 ͑1͒ H1-H5 ͑2002͒
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Table I. Table of pore diameter compared to applied potential
and anodization time. Data was obtained from SEM micrographs
that were near the resolution limit for the smaller pores. How-
ever, the general trend toward larger pores with larger applied
potential is illustrated.
Applied potential ͑V͒
Time ͑min͒
Pore diameter ͑nm͒
3
10
10
10
12
16
125
1
60
200
120
120
12 Ϯ 2
7 Ϯ 2
10 Ϯ 2
17 Ϯ 3
20 Ϯ 5
30 Ϯ 10
For a film of 500 nm thickness, when anodized at a potential of
10 V, the evaporated bulk aluminum was completely consumed after
approximately 40 min corresponding to the observed drop in current
illustrated in Fig. 3. During stage III ͑see Fig. 3͒, the elemental
aluminum has been consumed and converted to oxides. SEM micro-
graphs at 60 and 105 min ͑not shown͒ reveal discreet columnar
ordering of the oxide down to the supporting quartz substrate.
Table I is a summary of the pore size data obtained from the
experiment compared to the applied potential and anodization time.
This data was obtained by measuring the pore sizes from SEM pho-
tos of the anodized films. Each measurement was obtained by mak-
ing six to seven measurements from a level section of the coating
while avoiding the grain boundaries. An attempt was made to pick
points in clusters that represented the bulk surface finish. Since each
surface has mountain and valley-like features, the measurements
were made on flat mountain-like mesas. At these points, the low
voltage ͑Ͻ10 V͒ formed oxides had similar pore sizes and very little
variance. The limited variance in pore size measurements is the
result of the SEM resolution. However, at larger voltages, larger
pores were very clear and easily measurable. Table I illustrates the
trend for larger pore size resulting from higher applied anodization
potentials.
Figure 6. Plot of frequency change vs. concentration (P/Psat) for EtOH on
SAW devices with Al2O3 films produced by the described process. Each
curve represents a different anodization voltage and the lines are modified
BET fits to the data.
are uniformly spaced with uniform pore openings ͑ca. 10 nm͒. At
105 min ͑not shown͒, the pores remain fairly uniformly spaced but
the pore openings at the surface begin to show signs of widening.
From a cross-sectional view of this film, the columnar structures are
showing signs of separation at the surface. In this final stage of the
process, the current in Fig. 3 drops off at an accelerated rate. During
this stage, the film is no longer highly conductive as when there was
a source of electroactive aluminum available, and the acid electro-
lyte surrounding the film in the anodizing solution now acts as an
etchant. As the film is continuously exposed to the acid electrolyte,
the pores are widened and the film becomes thinner. Even though
the supporting electrolyte is able to maintain a small flow of current
between electrodes, the current is converging asymptotically to a
constant value. In Fig. 5, the SEM micrograph of a film processed at
200 min reveals wider pore openings ͑ca. 20 nm͒, and a breakdown
in structure uniformity, along with a thinner overall film thickness.
Figure 5 illustrates the surface of four aluminum films. The unan-
odized film, scaled at 600 nm, reveals large grain structures with two
voids centered among the cluster of grain structures. Viewed at 200
nm, the surface is covered with pores within 60 s of the beginning of
the anodization process. From the plane view after 60 min, the pores
Analysis
A series of metallic Al films were vapor deposited ͑500 nm͒ on
SAW devices and anodized at various applied potentials ͑2-12 V͒ for
40 to 60 min. The pore diameters measured from SEM micrographs
for samples prepared at 2 V are ca. 7 nm, and for samples anodized
at 12 V are ca. 20 nm. A fractured cross section of a film is shown
in Fig. 4.
The functionality of these films as sensors was tested. Each SAW
device was used as the feedback element of an oscillator circuit
operating at approximately 97 MHz. The frequency outputs from the
oscillators were then measured using a frequency counter. Figure 6
is the frequency shift of four SAW devices during the adsorption of
ethanol at increasing normalized vapor pressures. Insertion losses
for these coated devices were less than 1 dB greater than for a bare
device, but film sensitivity increases were of an order of magnitude
over a bare device. A decrease in pore size yielded an increase in
sensitivity.
The modified adsorption model of Brunauer, Emmett, and Teller
͑BET͒6,7 has been applied to the problem of measurement of heat of
adsorption and surface area for the sensitive films of Al2O3 created
using processes described above. The films were formed on ST-cut
quartza SAW devices and the adsorption of ethanol ͑EtOH͒ was
Figure 5. SEM photograph of Al2O3 surface as a function of anodization
potential. Clockwise from the upper left-hand corner the films are unanod-
ized, anodized for 1 min at 10 V, anodized for 200 min at 10 V, and anodized
for 60 min at 10 V. These photos illustrate that after 60 min of anodization,
the films are etched by the process and begin to open the pores.
a ST-cut quartz is a singly rotated cut having Euler angles ␭ ϭ 0°, ␪ ϭ 90°, and
␮ ϭ 132.75°.
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Journal of The Electrochemical Society, 149 ͑1͒ H1-H5 ͑2002͒
measured. The adsorption isotherms were then fit using the
Marquardt-Levenberg algorithm to extract the values of the heat of
adsorption of the first monolayer onto the surface and the limiting
number of surface layers adsorbed.8 This information was then com-
pared to published values for the heat of adsorption and the surface
areas of the films was estimated and compared to the preparation
conditions.
The BET adsorption model is a widely accepted technique for
experimentally determining the surface area and heat of adsorption
of the first monolayer of adsorbate onto a surface.7 BET measure-
ments are routinely made with N2 as the adsorbate on a surface
cooled to 77 K and are used to study the properties of materials
ranging from soils to sol-gels.9-11 N2 is the adsorbate of choice due
to its well known adsorption cross section ͑16.2 Å2͒; however, typi-
cal instrumentation designed to make BET measurements is limited
to bulk materials and does not allow for measurements of thin-film
adsorption. The adsorption characteristics of a bulk material may or
may not be representative of the adsorption characteristics of thin
films made from that material. Previously, SAW technology has
been used to make BET measurements of thin silicate-based sol-gel
films by adsorbing N2 in a He matrix onto a test film cooled to 77 K
that was deposited on a SAW device.12 We have used this technique
at room temperature to measure the heat of adsorption and surface
area of the Al2O3 films described in this paper.
The surface acoustic wave sensor system used to make the mea-
surements was similar to the system reported previously.13 The sys-
tem used six SAW devices, each with a different film; all were
exposed to the same atmosphere of interest at the same time. Each
SAW device was used as the feedback element of an oscillator cir-
cuit operating at approximately 97 MHz. The frequency outputs
from the oscillators were then measured to 1 Hz resolution using a
frequency counter ͑HP5385A͒. All SAW devices were mounted in a
single brass test fixture whose temperature was actively controlled
using a liquid flow from a temperature controlled bath ͑Haake model
K͒. The brass fixture was designed to provide excellent radio fre-
quency ͑rf͒ shielding for the test SAW devices and to provide suf-
ficient thermal mass to moderate the frequency changes due to en-
vironmental temperature fluctuations.
Various concentrations of EtOH in N2 were passed over the sen-
sors and the frequencies were measured at a single temperature
͑20°C͒. These isothermal data are illustrated in Fig. 6 as a plot
showing the change in the frequency between the initial frequency
and the current frequency at a given concentration. The concentra-
tion is represented as the ratio between the partial pressure of the
alcohol and that alcohol’s saturation vapor pressure at the test tem-
perature ͑20°C͒. The data points on the plot are the measured data
and the solid line is a fit of the data to the modified BET experi-
mental isotherm model. The modified BET model of chemical ad-
sorption postulates that there are two heats of adsorption of the
adsorbate onto the film: the larger heat of adsorption is that of the
first monolayer binding to the film surface and the smaller heat of
adsorption is that of the adsorbate binding to itself ͑i.e., the heat of
vaporization of the adsorbate͒. The modification of the BET from its
initial form is the addition of the parameter n, which is the limiting
number of monolayers that will adsorb onto the surface. The pore
size or other physical limitations usually determine this limit. The
standard BET model is limited in applicability to a concentration
range of 0-30% P/Psat where P is the partial pressure of the absor-
bate and Psat is the saturation vapor pressure of the absorbate; how-
ever, the modified form has been shown to have a much greater
range of applicability.8
It is apparent from Eq. 2 that the change in the number of mol-
ecules (⌬N) binding to a surface is proportional to the change in
frequency of the SAW oscillator. Therefore, we may write the modi-
fied BET equation in terms of frequency changes rather than
changes in the number of molecules as is commonly seen
n
nϩ1
⌬␯
⌬␯
⌬N
c␰
1 Ϫ n ϩ 1͒␰ ϩ n␰
͑
ϭ
ϭ
͓3͔
nϩ1
⌬Nm
1 Ϫ ␰͒ 1 ϩ c Ϫ 1͒␰ Ϫ c␰
͑
͑
m
where ␰ is the ratio between the partial pressure of the adsorbate and
its saturation vapor pressure (P/Psat); ⌬␯ is the frequency change
due to the adsorbate at the current partial pressure; ⌬␯ is the fre-
m
quency change due to one monolayer coverage on the surface; c is a
constant that depends on the difference in the heat of adsorption
between the adsorbate and the surface (Q1), the heat of vaporization
The SAW device-based oscillators respond to the adsorption of a
chemical species by changes in the wave propagation velocity of the
film and this is observed as a change in the frequency of the oscil-
lator. The mechanical influences that effect the frequency of a SAW
sensor in an oscillating loop can be written as14
of the adsorbate (Q ), the temperature of the surface (T), and the
␯
universal gas constant ͑R͒
͑Q ϪQ ͒/RT
1
␯
c ϭ e
͓4͔
The data were fit to Eq. 3 using a nonlinear Marquardt-
Levenberg regression algorithm with three adjustable parameters:
the monolayer coverage frequency change (⌬␯m), the heat of ad-
sorption constant (c), and the limiting number of monolayers ad-
sorbed ͑n͒. The heat of adsorption of the first monolayer of EtOH
onto Al2O3 was estimated from Eq. 4 to be 9.78 kcal/mol ͑the heat
of vaporization for EtOH is approximately 9.67 kcal/mol16͒. The
value for the heat of adsorption of EtOH compares favorably to the
values found in the literature of 10.1 kcal/mol.17
From the single monolayer frequency change (⌬␯m), it is pos-
sible to estimate the surface area of the film given convenient as-
sumptions. We assume that EtOH is a spherical molecule with a
standard area (AEtOH) of 32.5 Å2. This value was found by using the
van der Waals constant for the volume occupied by 1 L of molecules
and calculating the area. A similar calculation was performed on
H2O as a check of the validity of the method and the area was found
to be consistent with the literature value for the standard area of
H2O. The area of the film can then be calculated from the following
formula
⌬␯
⌬␳
⌬S
⌬␴
␴
⌬␥
⌬T
q
ϭ Ϫkm
ϩ ks
ϩ k
ϩ k␥
Ϫ kT
␴
␯
␳
S0
␥
T0
0
0
q0
0
͓1͔
where ␯ is the frequency of oscillation, ␳ is the surface mass density
of material on the surface of the SAW device, S is the modulus of
elasticity of the ST-cut quartz, ␴ is the conductivity of the film, ␥ is
the stress parameter in the sensing film, and T is the temperature of
the SAW surface. The values of k are constants for each parameter
of the equation, and the subscript 0 refers to the initial conditions of
the unloaded sensor. For our films constructed from Al2O3 in a tem-
perature controlled environment, the change in all terms except the
surface mass density is approximately zero. Therefore, to first order,
the wave velocity is reduced as material is adsorbed onto the surface
of the device; the frequency change can be written as a function of
surface mass change according to the following relationship12
⌬␯ ϭ Ϫ␩ ␯2⌬␳
͓2͔
m
0
Ϫ ⌬␯m A
␯
where ⌬␳ is the change in surface mass density due to the adsorption
of the adsorbate onto the film, ⌬␯ is the change in frequency due
Afilm
ϭ
AEtOH
͓5͔
2
0
␯ ␩ MW
͒
͑
EtOH
to the adsorbate,
␩
is the mass sensitivity factor (1.3
m
ϫ 10Ϫ6 cm2/g) of the ST-cut quartz substrate,15 and ␯ is the base-
where A is Avogadro’s number and MWEtOH is the molecular
weight of ethanol ͑46 g/mol͒.
0
␯
line frequency of the SAW oscillator ͑ϳ97 MHz͒.
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Journal of The Electrochemical Society, 149 ͑1͒ H1-H5 ͑2002͒
H5
Figure 8. Plot of average number of monolayers that form on the surface of
the films as determined from a fit of the data to the BET model. While the
average value (n ϭ 19) is inconsistent with the number that is calculated to
fit in a pore ͑assuming a diam of 0.6 nm͒ as found from the spherical model,
the results found for the surface area are calculated from the single mono-
layer response and are therefore, consistent.
Figure 7. Plot of single layer frequency shift as a function of anodization
voltage. The right-hand axis is scaled to provide the ratio of film surface area
as a function of anodization voltage. ͑᭹͒ Indicates the SAW data. ͑᭿͒ Are
data obtained from SEM bi-imaging measurements of similarly grown films.
͑᭡͒ Are measurements made by visually examining SEM photographs of the
films and calculating the surface area from the pore density, pore diameter,
and known film thickness.
electrolyte during the third stage only deteriorates the columnar
morphology. In addition, we have measured the surface area of the
films by measuring the adsorption isotherms of the films and extract-
ing the surface area and heat of adsorption using the modified BET
model of adsorption. The results indicate that the heat of adsorption
of the first monolayer is 9.78 kcal/mol and the surface areas de-
crease over the values of potential tested at a rate of Ϫ1.9
͑cm2/cm2͒/V. This allows the film surface area to be engineered to a
precise surface area as desired. These types of studies will allow
further development of chemically sensitive films for application in
detection, quantification, and speciation of unknown chemical
plumes found in the environment.
We have plotted the single monolayer frequency change as a func-
tion of anodization potential in Fig. 7. From these data, we can
estimate the change in surface area as a function of anodization
voltage. In addition, we have estimated that the film formed at 2 V
anodization potential has a surface area of about 40 ͑cm2/cm2͒ and
the surface area decreases at a rate of 1.9 ͑cm2/cm2͒ for each 1 V
increase in potential. The nomenclature A ͑cm2/cm2͒ implies that
for every 1 cm2 of planar coverage, the film has A cm2 of actual
surface area. The surface areas of several similar films were mea-
sured using other techniques, including SEM bi-imaging and manu-
ally computing the surface area by measuring the pore diameter
from an SEM image and assuming a cylindrical pore of known
depth. Both of these techniques compare favorably with the BET
technique as is clear from Fig. 7.
The parameter n has an average value of 19 layers for all of the
films tested ͑Fig. 8͒. Our SEM measurements of pore size indicate
that the pores of the samples tested are between 7 nm and 20 nm in
diam for films in the 2 and 12 V range; the diameter of the spherical
EtOH model is on the order of 0.64 nm. Thus, 19 monolayers of
rigid spherical molecules will not fit in the pores. Thus, we might
conclude that the packing density of the molecules is higher when
packed into the pores increasing the average number of monolayers
on the surface. However, the value of n is not critical to the calcu-
lation of the surface area since surface area is derived from the
single monolayer coverage value. Thus, the surface area value re-
ported is unaffected by this inconsistency in the modeled results.
Acknowledgment
Sandia is a multiprogram laboratory operated by Sandia Corpo-
ration, a Lockheed Martin Company, for the United States Depart-
ment of Energy under contract DE-AC04-94AL85000.
Sandia National Laboratories assisted in meeting the publication costs of
this article.
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Conclusion
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Thus, we have illustrated the utility of a surface acoustic wave
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tallic Al films that were deposited under greater surface mobility
͑zone II conditions͒. We have calculated the surface area and found
that for every 1 V decrease in anodization potential the surface area
of the film increased by 1.9 ͑cm2/cm2͒ over the range tested. This
rate will not continue at either the lower or upper limits of potential;
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