The ellipsometry of anisotropic manganese dioxide films electrodeposited at anodic potentials

The galvanostatic electrodeposition of manganese dioxide films in the thickness range from 0 to 1000 nm was investigated by in situ ellipsometry. The results obtained can be fit into the whole thickness range in terms of the uniaxial anisotropy of the film. The optical indices and thicknesses were calculated. The anisotropic properties may be related to a preferential orientation of the deposits.

The man ga nese ox ides are nu mer ous and many of their struc tures are poorly known 1 .Mn0 2 has been widely studied 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, surface 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 mance 2 .The ac tiv ity of the man ga nese ox ide lay ers de pends strongly on the de po si tion con di tions 3,4 .The op ti cal char ac ter iza tion of Mn0 2 is very valu able for the cor re la tion of in situ charge stor age ca pac ity and structural 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 cles 5,6 .Re cently, an od i cally de pos ited Mn0 2 films were in ves tigated by ellipsometry 7 .Op ti cal re sults could not be explained as the growth of iso tro pic or anisotropic lay ers in the case of thick films and the re ported data were in terpreted as sum ing a de pend ence of the ex tinc tion co ef fi cient on the thick ness 6,7 .
In the pres ent pa per, we re port an in 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.

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 MnS0 4 and 0.17 M H 2 S0 4 so lu tions.The work ing plat i num electrode (0.95 cm 2 area) was mir ror pol ished with 0.3 and 0.05 µm alu mina, rinsed with MilliQ* wa ter and fi nally immersed in a con ven tional op ti cal cell 8 .The wave length employed was λ = 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 under ni tro gen bub bling.
The ex per i men tal pro ce dures were as fol lows: the refrac 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 data 7,8 .The op ti cal ef fect of the plat i num ox ide monolayer can be dis re garded 7 .
The ∆ and Ψ 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 ellipsometer 7 ; 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 ifi ca tion, that is, par al lel to the z axis 9 .The com plete so lutions to this par tic u lar prob lem have been pre vi ously re ported [9][10][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 niques [12][13][14] .The functíon to be min i - 2 , where d is the thick ness, t is the time, and a and b are the pa ram eters 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 distance 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 icantly.If G(x 1 ,...,x m ) is the dif fer en tial func tion to be min i mized and a = (a 1 ,...,a m ) 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 sition a is given by v = -∇G(a) = (-∂G(a)/ ∂x 1 ,..., -∂G(a)/ ∂xm).Dif fer ent it er a tive meth ods are em ployed to find the min i mum of G [12][13][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 = (b 1 ,... ,b m ) 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 fulfilled, then: a) G (a(o)) > G (a(1)) > G (a(2)) ...; b) ∂G (a(n)) / ∂x i 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 succes 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 tive 15 .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 polar izer and the sam ple, a uni ax ial pos i tive film (n z > n x = n y ) will cause suc ces sive loops to be dis placed to wards lower val ues, whereas a uni ax ial neg a tive film ((n z < n x = n y ) will cause a dis place ment to wards higher val ues.
For non-absorbing ma te ri als, and as sum ing an as sembly of par al lel cy lin dri cal rods of in dex n 1 , im mersed in a me dium of in dex n 2 , the struc ture will be uni ax i ally pos itive [15][16] : where f 1 and f 2 are the frac tions of the to tal vol ume oc cupied by the rods and the me dium and f 1 << 1. n z 2 -n x 2 will al ways be pos i tive for n 1 2 > n 2 2 or n 1 2 < n 2 2 .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: 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 ∆ vs. Ψ plot ob tained by ap ply ing an an odic cur rent den sity i =100 µA cm -2 for a to tal time of 45 min is shown in Fig. 1.Ex per i men tal mea sure ments were ob tained with the au to matic ellipsometer for neg a tive val ues of el lip tici ty.In this case, the er rors in the az i muth were larger when the ellip tici ty ap proached 45 de grees; there fore the indetermination in the ∆ and Ψ val ues also in creases un der these con di tions 17 .In the same fig ure the the o ret i cal fit ted curve is plot ted, ob tained ac cord ing to the cal cu la tion method de scribed above.
The the o ret i cal curve (as sum ing op ti cal in di ces in depend 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 n p = 1.788, n s = 1.756, k p = 0.0187, k s = 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 = 44 µA 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 culated thick nesses are not strongly de pend ent on the vari ation 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, f i can be tested with ef fec tive me dium the o ries 8 .In the case of birefringent layers, the num ber of fit ted pa ram e ters in creases and the re lation 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 opti cal in di ces, in de pend ent of thick ness, were con sid ered sig nif i cant.
The op ti cal ani so tropy shown by Mn0 2 films may be related to the de posit mor phol ogy.Elec tro lytic man ga nese di ox ide is usu ally de scribed as a γ or ε-Mn0 2 struc ture 34 .The γ ma te rial was re ported as microporous or con sist ing of nee dle-shaped par ti cles 35 .The γ-Mn02 made up of flat needles of 40,000 x 2,000 x 500 A o have been ob tained by treat ing Mn 3 0 4 with di luted ni tric acid 36 .The mor phol ogy of Mn02 ob tained by an odic ox i da tion of Mn 2+ de pends on both com po si tion and cur rent den sity [37][38] .Polycrystalline Mn0 2 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 ganese di ox ide from an acid i fied sul fate bath 39,40 .
The op ti cal in di ces ob tained for the anisotropic Mn0 2 (Fig. 4) in di cate that the n p and n s val ues are com pa ra ble, while k s is cer tainly higher than k p .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 tical 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 sition mech a nism 41 .
Fig ure 4. Re frac tive in di ces ns, and np, and the ab sorp tion co ef ficients ks and kp, and the de po si tion time as a func tion of thick ness for the ex per i ment of Fig. 3.

Fig ure 1 .Fig ure 2 .
Fig ure 1.The evo lu tion of the ellipsometric pa ram e ters ∆ and Ψ using the au to matic ellipsometer.i = 100 µA 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 imen tal points.

Fig ure 3 .
Fig ure 3. The ∆ and Ψ 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.The fig ures in di cate the thick ness d in nm.