The Ellipsometry of Anisotropic Manganese Dioxide Films
Electrodeposited at Anodic Potentials
*J.0. Zerbinoa,#B. A. López de Mishimab, **M. López Teijeloc,##A. Maltzd, and #M. Hernández Úbedab
aInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Suc.4 C.C.16, 1900
La Plata, Ar gen tina
bInstituto de Ciencias Químicas, Fac. de Agronomía y Agroindustrias, Univ. Nac. de
San ti ago del Estero, Avda. Belgrano(s) 1912, 4200 San ti ago del Estero, Ar gen tina
cDepartamento de Fisicoquímica, INFIQC, Facultad de Ciencias Químicas, Univ. Nac.
de Córdoba, Ag. Postal 4, C.C. 61, 5000 Córdoba, Ar gen tina
dDepartamento de Matemática, Facultad de Ciencias Exactas, Univ. Nac. de La Plata,
Calle 50 y 115, 1900 La Plata, Ar gen tina
Re ceived: June 30, 1996; No vem ber 28, 1996
A eletrodepositação galvanostática de filmes de dióxido de manganês com espessuras en tre 0 e 1000 nm foi investigada por elipsometriain situ. Os resultados obtidos podem ser ajustados em termos de uma anisotropia uni ax ial do filme para o intervalo completo de espessuras. Os índices ópticos e as espessuras foram calculados. As propriedades anisotrópicas podem ser relacionadas a uma orientação preferencial do depósito.
The galvanostatic electrodeposition of man ga nese di ox ide films in the thick ness range from 0 to 1000 nm was in ves ti gated byin situ ellipsometry. The re sults ob tained can be fit into the whole thick ness range in terms of the uni ax ial ani so tropy of the film. The op ti cal in di ces and thick nesses were cal cu lated. The anisotropic prop er ties may be re lated to a pref er en tial ori-en ta tion of the de pos its.
Key words:ellipsometry, man ga nese ox ide, ani so tropy
In tro duc tion
The man ga nese ox ides are nu mer ous and many of their struc tures are poorly known1. Mn02 has been widely
stud-ied and many phys i cal and chem i cal prop er ties such as elec tri cal con duc tiv ity, po ros ity, man ga nese con tent, sur-face area, elec trode po ten tial, pore size, and par ti cle shape and size, have been mea sured and dis cussed in terms of the dry cell per for mance2. The ac tiv ity of the man ga nese ox ide lay ers de pends strongly on the de po si tion con di tions3,4. The op ti cal char ac ter iza tion of Mn02 is very valu able for
the cor re la tion ofin situ charge stor age ca pac ity and struc-tural changes as a func tion of the ap plied po ten tial.
How-ever, ellipsometric stud ies are lim ited to a few ar ti cles5,6. Re cently, an od i cally de pos ited Mn02 films were in ves ti
-gated by ellipsometry7. Op ti cal re sults could not be
ex-plained as the growth of iso tro pic or anisotropic lay ers in the case of thick films and the re ported data were in ter -preted as sum ing a de pend ence of the ex tinc tion co ef fi cient on the thick ness6,7.
In the pres ent pa per, we re port anin situ ellipsometric in ves ti ga tion of an odic man ga nese ox ide films grown galvanostatically. The re sults ob tained give ev i dence of the uni ax ial ani so tropy of the films, which may be re lated to a pref er en tial ori en ta tion of the de pos its.
Ar ti cle
Ex per i men tal
Man ga nese ox ide films were de pos ited onto a plat i num elec trode at a con trolled cur rent den sity from 0.1 M MnS04
and 0.17 M H2S04 so lu tions. The work ing plat i num
elec-trode (0.95 cm2 area) was mir ror pol ished with 0.3 and 0.05µm alu mina, rinsed with MilliQ* wa ter and fi nally im-mersed in a con ven tional op ti cal cell8. The wave length em-ployed wasλ = 546.1 nm, with the in ci dent light beam at 70°. Ex per i ments were per formed at room tem per a ture un-der ni tro gen bub bling.
The ex per i men tal pro ce dures were as fol lows: the re-frac tive in di ces of the sub strate (n - i k) were ob tained at the open cir cuit po ten tial Eoc = 0.90 V vs. RHE from the
ellipsometric pa ram e ters of the re cently pol ished elec trode. The re sult ing val ues are in good agree ment with pre vi ously re ported data7,8. The op ti cal ef fect of the plat i num ox ide monolayer can be dis re garded7.
The∆ andΨ val ues dur ing the an odic film growth were mea sured as fol lows:
i) ev ery 1 s in a Rudolph Re search (ver ti cal type, 2000 FT model) ro tat ing an a lyzer au to matic ellipsometer7; ii) ev ery 2 min in a Rudolph Re search man ual type 437002/200E ellipsometer used in the null mode with the com pen sa tor set at 135°8.
Cal cu la tion Method
When the op tic axis of the uni ax ial crys tal lies in the plane of in ci dence, the ex pres sions ob tained for ellipsometry are rel a tively sim ple. We re stricted our selves to uni ax ial films with the op tic axis in the di rec tion of strat i -fi ca tion, that is, par al lel to the z axis9. The com plete so lu -tions to this par tic u lar prob lem have been pre vi ously re ported9-11.
The ex per i men tal data were fit with the o ret i cal mod els us ing the gra di ent tech niques12-14. The functíon to be min i
-mized was G =Σ (∆ex -∆th)2 + (Ψex -Ψth)2 + (d - a tb)2, where
d is the thick ness, t is the time, and a and b are the pa ram e -ters to be ad justed. The last term was added to fit the closed packed loops cor re spond ing to the high thick nesses. The val ues of the op ti cal pa ram e ters used for cal cu lat ing these lines were es ti mated by mak ing ini tial guesses, then the value of each pa ram e ter was var ied un til a cal cu lated curve was found that better ap prox i mated the ex per i men tal data in the sense that the root-mean-square de vi a tion of the dis-tance be tween the point and the curve was re duced. This pro ce dure was re peated us ing re duced vari a tion of the param e ters un til the RMS de vi a tion failed to change sig nif i -cantly. If G(x1,...,xm) is the dif fer en tial func tion to be
min i mized and a = (a1,...,am) is a point in the m di men sional
space, the di rec tion of max i mal de crease of G in the po si -tion a is given by v = -∇G(a) = (-∂G(a)/∂x1,..., -∂G(a)/ ∂xm). Dif fer ent it er a tive meth ods are em ployed to find the
min i mum of G12-14 which con sist of a suc ces sion of ap prox i ma tions a(o), a(1), a(2), in the m di men sional space
con verg ing on the so lu tion b = (b1,... ,bm) which is at tained
within the de gree of ac cu racy re quired.
When the con ver gence of the ap prox i ma tions is ful-filled, then: a) G(a(o)) > G(a(1)) > G(a(2))...; b)∂G(a(n))/∂xi will
tend to 0 as n in creases; and c) the dis tances //a(n)- a(n+1)//
will tend to 0 for in creas ing n.
The Anisotropic Model
The ef fect of uni ax ial ani so tropy is to dis place the suc-ces sive loops par al lel to the axis by an amount that de pends on the mag ni tude of the ani so tropy and in a di rec tion that de pends on whether the film is uni ax ial pos i tive or uni ax ial neg a tive15. For an ex per i men tal con fig u ra tion in which the quar ter-wave plate is placed at 45 de grees be tween the po-lar izer and the sam ple, a uni ax ial pos i tive film (nz > nx = ny)
will cause suc ces sive loops to be dis placed to wards lower val ues, whereas a uni ax ial neg a tive film ((nz < nx = ny) will
cause a dis place ment to wards higher val ues.
For nonabsorbing ma te ri als, and as sum ing an as sem -bly of par al lel cy lin dri cal rods of in dex n1, im mersed in a
me dium of in dex n2, the struc ture will be uni ax i ally pos i
-tive15-16:
n n f f n n
f n f n
z x
2 2 1 2 1 2 2 2 2 1 2 2 2 1 2 1 − = − + + ( )
[( ) ] (1)
where f1 and f2 are the frac tions of the to tal vol ume oc cu
-pied by the rods and the me dium and f1 << 1. nz2 - nx2 will
al ways be pos i tive for n12 > n22 or n12 < n22.
Anal o gously, for an as sem bly of par ti cles that have the form of thin par al lel plates, Eq. 1 may be writ ten as:
n n f f n n
f n f n
z x
2 2 1 2 1 2 2 2 2 1 2 2 2 1 2 − = − + ( ) (2)
This im plies that the as sem bly al ways be haves like a neg a tive uni ax ial crys tal.
Re sults and Dis cus sion
The the o ret i cal curve (as sum ing op ti cal in di ces in de -pend ent of the thick ness) fits the ex per i men tal data in the whole range of thick nesses re pro duc ing the var i ous loops. As suming a uni ax ial anisotropic film with the op ti cal axis co in cid ing with the axis nor mal to the sur face re sults in the op ti cal in di ces np = 1.788, ns = 1.756, kp = 0.0187,
ks = 0.2260. The cor re spond ing time vs. thick ness plot
shows a lin ear de pend ence (Fig. 2).
A sim i lar galvanostatic ex per i ment for i = 44µA cm-2
for a to tal time of 110 min, ob tained with the man ual ellipsometer, is shown in Fig. 3. The fit ting was per formed tak ing dif fer ent sets of data cor re spond ing to in creas ing ranges of thick ness. Fig. 3a shows the fit ted curve ob tained for 10 < d < 130 nm, whereas in Fig. 3b the curve for
200 < d < 730 nm range is in cluded. The val ues of op ti cal in di ces cor re spond ing to the dif fer ent ranges show a slight de pend ence on d (Fig. 4). Nev er the less, the cal cu lated thick nesses are al most in de pend ent of the cho sen range of thick ness (up per part of Fig. 4), in di cat ing that the cal cu lated thick nesses are not strongly de pend ent on the vari a -tion in the op ti cal in di ces ob tained.
For iso tro pic ma te ri als, the de pend ence of n and k on the vol ume frac tion of the com pos ite, fi can be tested with
ef fec tive me dium the o ries8. In the case of birefringent layers, the num ber of fit ted pa ram e ters in creases and the re la -tion ship be tween com po si -tion or den sity of the film and op ti cal in di ces is un cer tain. There fore, only the av er age op-ti cal in di ces, in de pend ent of thick ness, were con sid ered sig nif i cant.
The re frac tive in di ces and ab sorp tion co ef fi cients cal-cu lated, as sum ing op ti cal prop er ties in de pend ent of
thick-Fig ure 1. The evo lu tion of the ellipsometric pa ram e ters ∆ andΨ us-ing the au to matic ellipsometer. i = 100µA cm-2. The fig ures in di cate the thick nesses d in nm.
(•) The o ret i cal curve for thick ness in cre ments of 10 nm. (o) Ex per i -men tal points.
Fig ure 2. The time vs. thick ness plot cor re spond ing to the ex per i ment of Fig. 1.
Fig ure 3. The∆ andΨ plot ob tained us ing the man ual ellipsometer. i = 44 µA cm-2.
(•) The o ret i cal curve. (o) Ex per i men tal mea sure ments.
A) The o ret i cal fit ting in the 10 < d < 130 nm range; B) in the 200 < d < 730 nm range.
ness, or ad sorp tion of ori ented mol e cules8,21-33. Pores or
nee dles could also cause a struc tural di rec tional ani so tropy.
The op ti cal ani so tropy shown by Mn02 films may be
re-lated to the de posit mor phol ogy. Elec tro lytic man ga nese di ox ide is usu ally de scribed as aγ orε-Mn02 struc ture34.
Theγ ma te rial was re ported as microporous or con sist ing of nee dle-shaped par ti cles35. Theγ-Mn02 made up of flat
nee-dles of 40,000 x 2,000 x 500 Ao have been ob tained by treat ing Mn304 with di luted ni tric acid36. The mor phol ogy
of Mn02 ob tained by an odic ox i da tion of Mn2+ de pends on
both com po si tion and cur rent den sity37-38. Polycrystalline
Mn02 with a ran dom dis tri bu tion of the lat tice ori en ta tions
is ob tained in hot sul fu ric acid con tain ing MnS04, whereas
acidic so lu tions of chlo ride, ni trate, or per chlor ate, ex hibit a fi brous struc ture, the fi bers be ing par al lel to the di rec tion of growth. How ever, it has been dem on strated by X-ray dif frac tion that it is pos si ble to pro duce a fi brous man ga -nese di ox ide from an acid i fied sul fate bath39,40.
The op ti cal in di ces ob tained for the anisotropic Mn02
(Fig. 4) in di cate that the np and ns val ues are com pa ra ble,
while ks is cer tainly higher than kp. This be hav ior may be
re lated to a pref er en tial ori en ta tion of mi cro fi bers in the de posit. The fit ting pro ce dure as sum ing con stant in di ces in de pend ent of thick ness, in di cates that the struc ture of the de pos its re mains rel a tively con stant dur ing growth.
Fur ther work on the de pend ence of the anisotropic op ti -cal in di ces for dif fer ent de po si tion con di tions will pro vide more use ful in for ma tion to elu ci date this com plex de po si -tion mech a nism41.
Ac knowl edg ments
This re search was sup ported by the Consejo Nacional de Investigaciones Científicas (CONlCET), the Comisión de Investigaciones Científicas de la Provincia de Bue nos Ai res (ClC), and the Fundación Antorchas. B.A. López de Mishima and M. López Teijelo are re search mem bers of CONICET and J.0. Zerbino is a re searcher with CIC.
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