Controlling Factor of Self-Ordering of Anodic Porous Alumina
Sachiko Ono,
*
,z
Makiko Saito, Miyuki Ishiguro, and Hidetaka Asoh
Department of Applied Chemistry, Faculty of Engineering, Kogakuin University, 1-24-2 Nishi-shinjuku,
Shinjuku-ku, Tokyo 163-8677, Japan
The controlling factor of self-ordering of anodic porous alumina was investigated by focusing on the current density during film
growth. The homogeneity of cell size was improved with increasing formation voltage accompanied by the exponential increase
in current density. The maximum anodizing voltage for proceeding uniform oxide growth while avoiding extremely high current
accompanied by gas evolution was identical with the previously established self-ordering voltage. With the increase in formation
voltage up to the self-ordering voltage, the ratio of pore diameter to cell diameter d
pore
/d
cell
lowered and converged to ϳ0.3
regardless of the electrolyte type. Moreover, domains of highly self-ordered pore arrays were found in the film formed during
burning, where extremely high current was locally concentrated. This suggests that the condition inducing film growth under high
current density, i.e., high electric field strength is the key controlling factor of self-ordering. Based on the above knowledge, a new
self-ordered porous alumina with a 600 nm pore interval was fabricated in citric acid just under the critical voltage of burning.
© 2004 The Electrochemical Society. ͓DOI: 10.1149/1.1767838͔ All rights reserved.
Manuscript submitted September 9, 2003; revised manuscript received February 9, 2004. Available electronically June 25, 2004.
Anodic porous alumina film, a typical self-ordered nanohole ma-
terial formed by anodizing aluminum in an appropriate acidic solu-
tion, is a promising candidate for starting materials of nanofabrica-
tion of various devices.
1-5
Except for the pretexturing methods for
an aluminum substrate such as an imprinting process,
6,7
highly or-

have a linear relationship with log of current density. According to
the classical theory of ionic conduction at the high field strength for
the anodic barrier film grown on various metals,
17,18
the film thick-
ness of each metal is inversely proportional to the logarithm of ionic
current when the film is formed up to the same voltage. Thus, it is
indicated that the log of current density log i is proportional to the
electric field strength E, i.e., the formation voltage/film thickness
ratio at the barrier layer.
19
The purpose of the present study is the
confirmation of the controlling factor of the self-ordering of porous
alumina and the fabrication of a new self-ordering film by applying
the proposed mechanism.
Experimental
High-purity ͑99.99%͒ aluminum sheets were electropolished in a
4:1 mixture of ethanol and 60% perchloric acid at 10°C. Anodizing
was performed at constant voltages in 0.3 mol dm
Ϫ3
sulfuric acid
solution at 20°C, 0.3 mol dm
Ϫ3
oxalic acid solution at 20°C, and 0.2
mol dm
Ϫ3
phosphoric acid solution at 0°C-5°C. 2 mol dm
Ϫ3
citric
acid solution at 20°C was used to fabricate a new self-ordering film

20,21
␣ ϭ
͑
␤TAl
3ϩ
͒
/
͑
1 Ϫ ␤TO
2Ϫ
͒
͓1͔
where
␤ ϭ m
2
/m
1
͓2͔
m
1
is the slope of the V-t curve during re-anodizing of the aluminum
specimen having porous alumina layer, and m
2
is the slope of the V-t
curve during the growth of barrier film by anodizing of an aluminum
substrate.
This method for porosity measurement is well established
20,21
and called as a ‘‘Pore-filling’’ technique. Under the condition of the
present set of work, m

the most simple and accurate method for the evaluation of the cell
homogeneity. The level of self-ordering can be assessed by the frac-
tion of regular hexagonal cells, which neighboring to six cells indi-
vidually. When self-ordering progresses, the size of the domain con-
sist of only regular hexagonal cells increases.
Results and Discussion
Current-time transients at constant voltage.—Figure 2 shows
current-time ͑I-t͒ transients during constant-voltage anodizing in
sulfuric acid solution as a typical case. This type of stable I-t curve
is usually obtained when the stable porous film growth proceeds.
With increasing formation voltage, current density increased. When
the formation voltage exceeded the value of self-ordering voltage,
i.e., at 27 V, a high current accompanying intense gas evolution at
*
Electrochemical Society Active Member.
z
E-mail: [email protected]
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the entire surface was observed. In these cases, no film growth at the
entire specimen surface proceeded. In the case of oxalic acid solu-
tion, similar phenomenon of a high current was appeared at 45 V. As
revealed by the intense gas evolution, electronic current caused by
the electric breakdown at the barrier layer is preferential than the
ionic current. While, in the case of phosphoric acid solution, local
film thickening was observed at 200 V accompanying high current
concentration.
If local film thickening is observed as a result of such an ex-

high current and prevents uniform film growth.
Change in the porosity of anodic alumina with increasing
formation voltage.—The high field theory suggests that log of cur-
rent density has a linear relationship with electric field strength. We
reported previously
16
that the theory was applicable to the porous
film growth and confirmed the linear relationship between log of
current density and the ratio of pore diameter d
pore
to cell diameter
d
cell
. This suggests that the d
pore
/d
cell
ratio is controlled by the
electric field strength E at the barrier layer and the ratio decreased
Figure 1. Schematic representation of ‘‘Pore filling’’ in a neutral solution.
Dotted area corresponds to the oxide layer formed during re-anodizing show-
ing the slope of m
1
.m
1
: The slope of the V-t curve during re-anodizing of
an anodized aluminum specimen having porous alumina layer, which is de-
pendent on the pore volume, i.e., porosity. m
2
: The slope of the V-t curve

to the self-ordering voltage V
s
. The three lines corresponding to the
three different electrolytes decreased almost in the same manner
regardless of the electrolyte type and the formation voltage. The
minimum porosity of the films obtained just under the critical volt-
age of extremely high current appears to be 0.1. This indicates an
important fact that self-ordering can be attained when the d
pore
/d
cell
ratio approached 0.3 with the increase in electric field strength re-
gardless of the electrolyte type and the formation voltage itself.
Thus, the mechanism of self-ordering is assumed to be closely re-
lated to the high electric field strength at the barrier layer during
anodic film growth, rather than to the individual self-ordering volt-
age itself.
Nielsch et al.
24
suggested recently that three types of self-
ordered porous alumina all gave a porosity value of 0.1. They ex-
plained that the porosity value of ϳ0.1, which was produced as a
balance of formation and dissolution of anodic oxide, was morpho-
logically most stable from the viewpoint of mechanical stress. They
also claimed that 0.1 was a transitional and optimum porosity value
for self-ordering. However, according to the present results, the po-
rosity value of 0.1 for porous alumina was the optimum and also the
minimum value.
FE-SEM observation of self-ordering behavior.—When anodiz-
ing voltage was three-fourths of the established self-ordering volt-

ing the anodic oxide formed for 1 h. Aluminum pillars formed at
irregular cell junctions, namely, junctions of four to six cells, were
clearly observed, while no such pillars were found at triple cell
junctions where self-ordered cell arrays were formed. It is apparent
Figure 4. Porosity plotted as a function of the ratio of formation voltage V
f
to self-ordering voltage V
s
.
Figure 5. SEM images of the metal/oxide interface after removal of porous
alumina formed in 0.3 mol dm
Ϫ3
oxalic acid at 20°C showing the depen-
dence of cell arrangement on formation voltage and anodizing time. ͑a͒ 30 V
for1h,͑b͒ 40 V 2% for 1 h, ͑c͒ 30 V for 1 h and 40 min, and ͑d͒ 40Vfor
6h.
Figure 6. SEM images of the metal/oxide interface after removal of porous
alumina formed in 0.3 mol dm
Ϫ3
sulfuric acid at 20°C. ͑a͒ 20Vfor1h,͑b͒
25 V for 1 h, and ͑c͒ 25 V for 6 h.
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that these pillars are only formed at the boundaries of domains in
which regular hexagonal cells were arranged in the same direction.
In the case of phosphoric acid electrolyte, it was not easy to
continue electrolysis for a long time without burning, namely, local
current concentration. The addition of Al
3ϩ
ions, vigorous agitation

/d
cell
ratio of this part was 0.28, i.e.,
ϳ0.3 as shown in Fig. 10b.
Clearly, film thickness is an important factor because the highly
ordered porous structure is only obtained after prolonged anodizing,
as previous studies have indicated. However, as shown in Fig. 10a,
the self-ordering proceeded instantaneously when current was con-
centrated during the burning. Therefore, it can be said that a high
electric field strength is the more significant factor in self-ordering
than the thickening of the anodic alumina itself.
Figure 10a shows an SEM image of a burnt area indicating the
protrusion of thickened anodic film with a large number of cracks.
The protrusion is divided into three regions: ͑A͒ center, ͑B͒ inter-
mediate, and ͑C͒ outer regions. The substrate surface images of the
corresponding regions after the removal of the anodic films are also
shown in Fig. 10b-d. Apparently, the regularity of the cell arrange-
ment is higher at the center region than that at the outer region.
Because the current density seems to be higher at the center, the
regularity of cell arrangement could be further improved. Thus, it is
suggested again that the condition of high current density, i.e., high
electric field, is the most important factor that determines the self-
ordering of the pore arrangement. In addition, the cell size is smaller
when the regularity of the cell arrangement is higher. Because the
voltage dropped to 160 V instantaneously, followed by a rapid cur-
rent increase with burning, the average cell size ratio is 1.7 nm/V at
the center region, 2.1 nm/V at the intermediate region and 2.36
nm/V at the outer region if the final voltage affects the size of whole
cells. Compared to the ratio of cell size to applied voltage of 2.5
͑nm/V͒ observed for the standard anodic porous films,

V at 0-5°C.
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self-ordering voltage itself. The highly self-ordered cells produced
by burning were also found at the film formed in malonic acid.
25
To confirm the relationship between current density and electric
field strength, cross sections of the barrier layer of the film were
examined. In this experiment, the electric power was switched off
before the voltage drop to maintain the formation voltage of 195 V.
As shown in Fig. 11, the thickness of the barrier layer near the
center of the burned spot was 150 nm giving the smaller anodizing
ratio such as 0.76, while that of outer region was 216 nm giving the
standard anodizing ratio of 1.1. It was clearly observed that the
barrier layer thickness decreased with increasing distance from the
center of burnt spot.
As revealed in the present results, even burning could produce a
highly ordered porous structure. Thus, it is verified that the condi-
tion of high current density, i.e., the high electric field strength E at
the barrier layer is a strong controlling factor of the self-ordering of
cell arrangement.
Newly developed self-ordered porous alumina with 600 nm pore
interval.—Based on the understanding of high electric field as the
self-ordering condition, a new self-ordering porous alumina with a
pore interval of 600 nm formed in 2 mol dm
Ϫ3
citric acid solution at
240 V was developed. When a constant anodizing voltage was ap-
plied in the range from 225 to 245 V, current density increased
gradually with increasing voltage, as shown in Fig. 12. The film

Ϫ3
citric
acid at 20°C in the voltage range from 225 to 245 V.
Journal of The Electrochemical Society, 151 ͑8͒ B473-B478 ͑2004͒ B477
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Concurrently, the ratio of pore diameter to cell diameter con-
verged to 0.3, which corresponded to a porosity value of 0.1 regard-
less of the electrolyte type when the formation voltage approached
the individual self-ordering voltage, independent of the formation
voltage itself.
Self-ordering of the pore arrangement of anodic alumina was
found even during burning indicating also a d
pore
/d
cell
ratio of 0.3.
This self-ordering at burning was considered to occur under the high
local current concentration and the resultant high electric field
strength in the specific area.
Based on the above results, a new self-ordering anodic porous
alumina with 600 nm pore interval was successfully fabricated in
citric acid.
Therefore, it can be concluded that the self-ordering of the arbi-
trary pore interval is achievable by choosing adequate electrolyte
and electrolytic condition at the appropriate formation voltage for
maintaining a high current condition, i.e., high electric field on the
entire specimen area, while avoiding extremely high current leading
to burning or electric breakdown.
Acknowledgments
Parts of this work were financially supported by the Promotion

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Figure 13. SEM images of ͑a͒ substrate surface and ͑b͒ film cross section