- Email: [email protected]
The electronic properties of disordered passive films
Corrosion Science, Vol. 29, No. 2/3, pp. 199-211, 1989 Printed in Great Britain
0010-938)(/89 $3.00 + 0.00 © 1989Pergamon Press plc
THE ELECTRONIC PROPERTIES OF DISORDERED PASSIVE FILMS* MARY HELEN DEAN a n d ULRICH STIMMING Electrochemistry Laboratory, Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, NY 10027, U.S.A. Abstract--The understanding of passivity and its role in corrosion research is closely connected with the electronic properties of passive films. The approach of describing passive films in terms of their semiconducting properties can be improved by using models developed for amorphous semiconductors where localized electronic states play an important role. It is shown that localized states in passive films are of importance for the photo-electrochemical behavior where it expresses itself in sub-band gap photocurrents and a potential dependence of the photocurrent according to the Poole-Frenkel effect. Non-linear Schottky-Mott plots resulting from capacity data can be attributed to bulk localized states in the band gap and can thus be used to characterize highly disordered and/or non-stoichiometric passive films. The use of a photo-electrochemical laser scanning technique for the in-situ imaging of passivated surfaces and of corroding surfaces is also shown. INTRODUCTION
IN STUDYING the phenomenon of passivity and the properties of passive films, consideration of the electronic properties of the film has become increasingly important. This is largely due to the rapid development of semiconductor electrochemistry during the past two decades which provided the concepts for the description of photo-electrochemical behavior, capacity behavior and electron transfer reactions. These models have been successfully applied to passive films. It has been shown that a semiconductor approach to the description of passive films is a successful one. The large number of photo-electrochemical investigations of passive films demonstrate this. 1It has also been shown that a band structure model of the passive film on iron, based on capacity measurements, was able to describe wide ranges of electrochemical behavior of passive iron including electron transfer reactions and ionic processes. 2'3 Although this description of passive films using the semiconductor picture is qualitatively successful, it is partly in contrast to theoretical expectations as well as in contrast to some experimental results. The concepts that have been borrowed from semiconductor electrochemistry refer to bulk crystalline materials; passive films may be amorphous in structure, and may be non-stoichiometric in composition (which may even vary within the film), and they are often thin, i.e. they may not have a developed band structure normal to the surface. Any of these reasons may result in diffuse band edges and a large number of localized states in the band gap. Consequently, concepts developed for amorphous semiconductors4should represent a more appropriate approach. In the following, some of the electronic properties that are due to the presence of localized states are discussed and their * This paper was given at the German-American Colloquium on Electrochemical Passivation, which was held in Niimbrecht in the Federal Republic of Germany from 8--13 September 1987. Manuscript received 20 June 1988. 199
200
MARYHELENDEANand ULRICHSTIMMING
effect on photo-electrochemistry, capacity and electron transfer reactions on passive films is considered. In addition, some preliminary results will be presented for the use of photo-electrochemistry in obtaining in-situ images of passivated metal surfaces under non-corroding and corroding conditions. PHOTO-ELECTROCHEMISTRY The presence of localized states in the band gap of the passive film which may be due to non-crystallinity and/or non-stoichiometry of the film makes photo-excitation possible at photon energies hv < Eg where Eg is the band gap of the crystalline stoichiometric material forming the passive film. Such additional absorption processes are indicated in Fig. 1. Depending on the concentration and the distribution function of the localized states this can lead to considerable sub-band gap response. In the case of hv < E v excitation is possible from extended states e.g. the valence band, to localized states, from localized to extended states, e.g. the conduction band, and from localized states to localized states. In order to give rise to a photocurrent, iph, the photo-excited carriers on localized states must eventually escape into the underlying metal and into the electrolyte. This can be a field-assisted thermal excitation according to the Poole-Frenkel effect or tunnelling processes into either of the bands, into the metal or the electrolyte. The importance of the Poole-Frenkel effect for photo-electrochemical behavior was pointed out earlier for passive films on tungsten 5 and bulk amorphous non-stoichiometric iron-titanium oxides. 6 Figure 2 illustrates the various escape processes of the photo-excited charge carrier from the trap where it is assumed to be bound by coulombic forces. Process 1 denotes the classical Poole-Frenkel effect describing the effect of the electric field on the barrier. The escape probability PPF from the trap is given by PPF = exp [-- (Ei -
flFl/2)/kT~
(1)
where Ei is the ionization energy from the trap to the band and/5 is a material constant. At high fields, when the barrier becomes thin enough, tunnelling processes are possible and can lead to an additional current. This is shown by processes 2 and 3
E~
~,,
X
Ev
D(E) (0)
(b)
FIG. 1. (a) Absorption processes in an amorphous semiconductor showing excitation from extended to localized, localized to extended, and localized to localized states; (b) schematic representation of a possible density of states distribution in the band gap (taken from ref. 13).
The electronic properties of disordered passive films
201
/ ~,----- AX Possive firm
Etectroly~
FIG. 2. The energetic situation of a photoexcited electron on a localized state experiencing a coulombic force that is modified by a superimposed electric field: (1) classical overbarrier process; (2) phonon-assisted tunnelling; (3) direct tunnelling. (1)-(3) are in the direction of the field as treated in refs 8 and 9. (4) Classical overbarrier process and (5) direct tunnelling process, both against the field. AX denotes the distance of the localized state from the passive film-electrolyte interface (taken from ref. 13).
which describe phonon-assisted tunnelling and tunnelling at the trap level, respectively, which are both based on a charge separation following the direction of the field. In a Poole-Frenkel plot, In iph VS F 1/2, process i would yield a straight line and processes 2 and 3 would result in a field-dependent further increase of the current at very high fields. An indication lor such behavior has been found for passive films on hafnium that were ion-implanted with Pt or Xe after anodic oxide formation. The ion implantation process strongly disorders the oxide film, which is the most pronounced effect of the implantation process as found from the comparison of metal ion implantation with Xe implantation. Figure 3 shows a Poole-Frenkel plot 7 mainly for sub-band gap photon energies (the band gap is approximately 5.5 eV). It has been assumed that the potential drop in the insulating hafnium oxide film is linear and the field is given by F = (U-
Uro)/dox
where U is the electrode potential, Uro is the flatband potential and dox is the film thickness. While straight lines are obtained at intermediate fields, at high fields an increase of the photocurrent is observed which is more pronounced at low photon energies. Such an increase at high fields has also been found in model calculations for the Poole-Frenkel effect applied to photo-excitation when processes 2 and 3 start to contribute to the photocurrent. 8'9 If, on the other hand, the trap is close enough to the passive film--electrolyte interface, the photo-excited carrier can tunnel directly into the electrolyte, provided donor or acceptor states are available at that energy (process 5). Such an escape
202
MARYHELEN DEAN and ULRICH STIMMING HfOz (10% Xe) 0.SM H2SO4 hy / eV
-3
6
-4
5.5 J
I
I
J
2
-
I
3
J'~.~+
I
4
I
5
I
6
F '/2 / I 0 2 V I/2 c m - l / 2
FIG. 3.
Poole-Frenkel plot of the quantum efficiency at several photon energies measured on a hafnium passive film implanted with 10% Xe (taken from refs 7 and 11).
would be against the field and would detract from the overall photocurrent or, if dominant, the photocurrent would show an opposite sign, i.e. the photocurrent is cathodic at U > U~ and anodic at U < U~. The corresponding classical process, process 4, will obviously have only a neglible contribution, since the barrier for process 1 is much smaller. There are several indications that such processes can be observed experimentally. In the first example, thin passive films on zirconium, photocurrent spectra are shown for various potentials in Fig. 4.1° The data are reported in terms of the quantum efficiency, ~/, which is a normalized photocurrent defined as the ratio of the photocurrent to the incident photon flux. The passive film was formed at Uox = 3V (NHE) and the resulting film thickness is approximately 10 nm. Spectra taken at potentials U > - 0 . 4 V show anodic photocurrents with an extensive tailing down to below 3 eV. However, at potentials U < - 0 . 4 V, which are still more positive than the flat-band potential ( U ~ - - - 1 . 5 V), photocurrents change sign at lower photon energies. The photon energy hv(iph = 0), at which the photocurrent changes sign, increases with decreasing potential. A corresponding behavior can be seen in the potential dependence recorded at various photon energies. It is shown in Fig. 5 for 0.1% Xe-implanted passive film on hafnium in a semi-logarithmic representation, In r/vs F. 11It can be seen that the field at which the photocurrent changes sign from anodic to cathodic increases for decreasing photon energy. This behavior clearly indicates that an evaluation of the flat-band potential from the potential U(iph = 0) where the photocurrent changes sign can lead to erroneous results if it has not been established that U(iph = 0) is wavelength independent. 12 The cathodic photocurrents can be explained by process 5 in Fig. 2.13 In simple model calculations the escape probability of the photo-excited charge carrier from a trap located at a distance AX from the passive film-electrolyte interface has been calculated for various ionization energies as a function of the field. The ionization
The electronic properties of disordered passive films
203
O. IC Zr in IM No2S04
Uox-3V
U/V
0.0~.
=(
I
0.0~
[
4
5
h~ / eV
FIG. 4, The quantum efficiency as a function of photon energies measured at various electrode potentials for a film formed on Zr in 1 M Na2SO4 at Uox = 3 V (taken from ref. 10).
energy, Ei, d e n o t e s the distance of the trap f r o m the conduction b a n d and is assumed to be related to the p h o t o n energy by Ei = Eg - hv, i.e. lower p h o t o n energies are c o n n e c t e d to higher Ei and vice versa. T h e probability, Pa, for the escape in direction of the field is given by the P o o l e - F r e n k e l effect and possible tunnelling t h r o u g h the field-dependent barrier. T h e probability, Pc, for the escape directly into the electrolyte, on the o t h e r hand, is a tunnelling process that mainly d e p e n d s on A X and only
-4--
HfO~ (0.1%Xe ) hv / e V ~6 a5 ~4
-I(
I
2
3
4
F / I O 5 (V/era)
Fto. 5. The field dependence of the quantum efficiency at three photon energies for a hafnium passive film implanted with 0.1% Xe (taken from ref. 11).
204
MARYHELENDEAN and ULRICHSTIMMING
o/
E~ • 0.2
0.5
2
3
4
5
6
F/I06 (V/¢m)
FIG. 6. M o d e l calculations for various ionization energies, Ei, f o r a distance ~c = 2 nm;
m* = 0.5me (taken from refs 11 and 13). weakly on the field. While Pa is strongly dependent on E~ and F, Pc is not. This can be seen in Fig. 6 where P = Pa + Pc is plotted versus the field. The process in the direction of the field is given a positive and the process against the field a negative sign. It can be seen from Fig. 6 that processes against the field, i.e. process 5 in Fig. 2, are the dominant contribution to the photocurrent for certain parameters, such as Ei = 0.5 eV and F = 106 V/cm. The general shape of the curves in Fig. 6 is qualitatively very similar to the experimental results shown in Fig. 5. THE CAPACITY OF PASSIVE FILMS In interpreting capacity measurements of passive metal electrodes, semiconductor models have often been invoked. The Schottky-Mott equation has usually been applied to the analyses of such data. Straight lines are expected in 1/C 2 vs U plots, and from the linear portion the density of charge carriers can be estimated, knowing or assuming the dielectric constant of the passive film. The estimates for donor or acceptor concentrations are generally very high, of the order of 1020 - 1021 cm -3. These values are a strong indication of a non-stoichiometric and/or highly disordered character of passive films. In most instances, non-linearities or breaks in the slope of straight lines are observed in Schottky-Mott plots. Interpretations such as multiple donor (or acceptor) levels or varying donor (acceptor) concentrations in the film are often given, for the latter case using a "local" donor (acceptor) density as derived from a potential-dependent slope in a Schottky-Mott plot. Since such interpretations are usually at variance with the limitations and simplifications of the Schottky-Mott equation, efforts have been undertaken to derive a capacity-potential relation that takes into account multiple levels or even a continuous distribution function of localized states in the band gap. ~4.~5 In deriving the Schottky-Mott equation from the Poisson equation one important assumption is that the charge density is not a function of the electrode potential. This assumption is usually valid when all donors or acceptors are ionized under flat-band conditions. However, when multiple levels are present, this condition may not be
The electronic properties of disordered passive films
205
true since low lying traps may become ionized when the Fermi level passes through the energy of these traps. Consequently, the charge density in the film becomes potential dependent. Beginning with the Poisson equation, an expression for the space charge capacity, Csc, can be derived that takes into account a potential-dependent charge density:14 Csc -
--(~.0_1 112
dqsc
d--'~s c
\/.]
~)(A~sc) l- (A~O~c
-]1/2
(2)
where qsc is the space charge, Aq~ is the potential difference between the bulk and a point in the space charge layer, A~sc is the total potential difference across the space charge layer, O(A~) is the charge density at a point where the potential is Aq, e is the relative dielectric constant, and e0 is the permittivity of space. For a crystalline n-type semiconductor with M discrete donor levels the charge density can be expressed by: o(A~)) =
(
e ~ 1 + exp .EF j=l NDj
EDi kr
eA¢~
)]1
- Nc exp
(
Er
)}
Ec - eaq~ k-T
(3) where e is the electronic charge, k is the Boltzmann constant, T is the absolute temperature, Ec is the energy of the lower conduction band edge with Arcthe effective density of states at Ec, and the density of donor states in the jth level is NDj with their energy at EDi. The results of calculations have been reported in terms of a dimensionless capacity defined as: C'sc = Csc/(eeoe2Nc/2kT) 1/2.
(4)
The dimensionless charge density is:
O' = o/eNc.
(5)
Model calculations for the situation of a second donor level, which is not ionized at flat-band conditions for various N62 at a given ED2 and various ED2 at a given N~2 are shown as Schottky-Mott plots in Figs 7 and 8, respectively. {4It is obvious from both figures that the slope at low potentials is determined by N61 while at high potentials it reflects N/~l + N/~2. The extrapolation from the high potential straight line does not yield the flat-band potential and at the potential where the second donor level becomes ionized the capacity increases and 1/C2c decreases. , The capacity-potential behavior for distributions of localized states described by continuous density of states functions has been studied using this model. In this case, the potential-dependent charge density appearing in equation (2) is: 15 ~(A~) = e f ~
D(E)[{I + exp [(E - EF)/kT]}-' - {1 + exp [(E - EF + eacp)/kT]}-l]dE.
(6)
When the concentration of localized states below Ec is described by an expotentially decaying conduction band tail, curved Schottky-Mott plots result as shown in Fig. 9 for three different values of the decay parameter. The slopes of these curves increase with increasing potential and linear behavior is approached at higher potentials. In
206
MARY HELEN DEAN a n d ULRICH STIMMING
200
2
e~ p A
I00
I
I
0.5
I
I
Z~/V
FIG. 7. Schottky-Mott plot of results from model calculations using equation (3) in equation (2) with/ = 2, Eol = -0.05 eV. The dimensionless donor concentration in level 1 was Ni~a = 0.10. The concentration of deep donors, N~2, was varied. N~2: (1) 0.20; (2) 0.10; (3) 0.05; (4) 0.025; (5) 0.01 (taken from ref. 14).
2oo -
I
,oo I
I
0.5
~/V
FIG. 8. Schottky-Mott plot of results from model calculations using equation (3) in equation (2) with/' = 2, N~] = N(92= 0.10 and EDn = --0.05 eV. The energy of the deep donor was varied. Eo2: ( 1 ) - 0 . 0 5 eV; ( 2 ) - 0 . 2 0 eV; ( 3 ) - 0 . 3 5 eV; ( 4 ) - 0 . 5 0 eV; (5) -0.80 eV (taken from ref. 14).
The electronic properties of disordered passive films
f 3/
/
/
?
e"
I00
/
//
/
/
/
/
21-"
I ....
0
I
05
I
A , ~ /v
Fro. 9. Schottky-Mott plot of results from model calculations using equation (4) in equation (2) with varying values of the conduction band tail decay parameter. A,.: (1) 0.001 ;
(2) 0.05;(3) 0.10.
//:~
....
/
/ -~ t~
ioc
]
,.y'"
/
/'
/'"3"'"
//// i!
//
I/ / t/ /
0
.-.-"
./"
-.-4 /
/
/
/
1
O5
A~/V
Flo. 10. Schottky-Mott plot of results from model calculations using equation (4) in equation (2) in which a constant density of states is present below the conduction band tail. The decay parameter of the conduction band tail is varied. A~: (1) 1,0; (2) 0.7; (3) 0,3; (4) 0.1 (taken from ref. 15).
207
208
MARY HELEN DEAN and ULRICH STIMMING
another series of calculations, it was assumed that a band of localized states whose concentration does not depend on energy lies below the the conduction band tail. The results presented in Fig. 10 for a band of localized states extending throughout the gap with varying conduction band tail decay parameters indicate that curved Schottky-Mott plots may be observed. When the conduction band tail decays rapidly with energy below Ec, as in curves 1 and 2, the effect of the constant band of localized states is dominant at higher potentials and the capacity becomes nearly potentialindependent. Qualitively similar Schottky-Mott plots have been observed experimentally for bulk, amorphous Fe-Ti oxides 6 and also for passive films. 2'16 If the density of states in the band gap is reflected in the capacity-potential curve in such an obvious way, an analysis of experimental data should be able to reveal the distribution of localized states. This can be done by differentiating the capacitypotential curve. Using certain assumptions the slope is given by: 14 dC~ _ 2 1 - e eo dA~bs~ e e0Q(A~sc) ~
C~c
(7) "
This equation has been applied to the analysis of capacity data of passive iron electrodes. 17The data show a pronounced potential and thickness dependence of the capacity and are very similar to data obtained earlier. 2 Because of the relatively large experimental capacities, contributions from the Helmholtz layer have to be taken into account. In addition, a roughness factor, r = 2, has been assumed. The results of the procedure are shown in Fig. 11 in a plot representing the distribution function on the abscissa and the energy on the ordinate. Pronounced variations are found within the energy range that is supposedly the band gap with the valley in the distribution function becoming broader for increasing thickness of the passive film. This procedure should demonstrate that, although the Schottky-Mott plot loses its significance if applied in a formal sense, capacity-potential measurements still bear a large amount of information on electronic properties of passive films. This can be
0-
>. -05 I
d
-I
I
I
2.5
5
D ( E ) x 10-2°/ crn -3 e V -I
FI6. 11. Approximate density of states functions f o r iron passive films of varying thickness. Results were obtained using equation (5) after correcting the measured capacity data for Helmholtz layer effects and surface roughness, assuming CH = 20 /~F/cm 2 and r = 2, respectively.
The electronic properties of disordered passivefilms
209
advantageously used, for example, in the interpretation of electrochemical behavior of passive films. PHOTO-ELECTROCHEMICAL LASER SCANNING A further example of the usefulness of the photo-electrochemical effect in studying passive films is shown in this section. As originally demonstrated by Butler, 18when a laser beam is focused on a small spot on the passivated metal electrode and then rastered over the surface, an image of the passive film based on the photoresponse can be obtained.19'z° Property changes of the film are readily reflected in the photo-signal. A few examples will be given to illustrate some of the possibilities. The image of a passivated titanium sample measured under relatively insensitive conditions is shown in Fig. 12.19 The step size and the beam size are approximately 100 ~m and a flat response is obtained. Subjecting passive titanium to H B r solutions results in pitting corrosion and changes in the film can be imaged using the laser scanning technique. A titanium sample passivated at 10 V in 0.5 M H2SO 4 has been corroded at 9 V for a total time of 30 s. After transferring it back to sulphuric acid the image clearly shows the locations of pitting corrosion Fig. 13; 19here the step size was 10/~m and the beam size <20 #m. In an improved procedure, the sample was left in the H B r solution. It was corroded at 9 V and then imaged at 1 V where pitting ceases and the sample is stablefl ~ The laser scanning technique offers the possibility to investigate inhibition and corrosion processes under in-situ conditions without removing the sample from the electrolyte. In addition to systems like titanium which is pure metal and one whose passive film shows a strong photoresponse, alloys can also be successfully imaged using the laser scanning technique. This is demonstrated in Fig. 14. 22The sample was 304 stainless steel on which a passive film was grown for 30 min at 0.88 V (SHE) in 1 M NaESO 4. The image clearly indicates areas of quite different photoresponse which probably reflect a different structure and/or composition of the passive film at these locations. For a more quantitative assessment a comparison of such an image with another technique such as SEM is necessary, but the results obtained to date demonstrate that imaging of such important materials as stainless steel is also possible.
FIG. 12. Image of an uncorroded titanium film in 0.5 M H2SO 4 obtained with a 100/xm step-size and a beam diameter that was approximately100/xm (taken from ref. 19).
210
MARYHELENDEANand ULmc~aS~WMING
I FI6. 13. hnage of a corroded titanium passive film in 0.5 M H:SO4 after undergoing pitting corrosion in an electrolyte containing HBr, Step-size was 10 #m and the beam diameter was <20 p.m (taken from ref. 19).
Fl6. 14.
i
Image of a passive film o n 304 stainless steel in 1 M Na2SO4. Step-size was 10 txm and the beam diameter was <20 ~m (taken from ref. 21).
The electronic properties of disordered passive films
211
CONCLUSIONS I n s t u d y i n g passivity, an i n v e s t i g a t i o n of the e l e c t r o n i c p r o p e r t i e s of the passive film is a v a l u a b l e a p p r o a c h . It has b e e n s h o w n that localized states play an i m p o r t a n t role for the b e h a v i o r of passive films. D e v i a t i o n s from linearity in S c h o t t k y - M o t t plots, s u b - b a n d gap effects in the p h o t o - r e s p o n s e , the i m p o r t a n c e of the P o o l e F r e n k e l effect for the p o t e n t i a l d e p e n d e n c e of the p h o t o c u r r e n t a n d cathodic p h o t o c u r r e n t s at p o t e n t i a l s a b o v e the flat-band p o t e n t i a l are indicators for the p r e s e n c e of localized states. Such b e h a v i o r , which is clearly in c o n t r a s t to crystalline materials, indicates an a m o r p h o u s a n d possibly n o n - s t o i c h i o m e t r i c character of passive films. P h o t o - e l e c t r o c h e m i s t r y in its a p p l i c a t i o n to a laser s c a n n i n g t e c h n i q u e is a v a l u a b l e tool for i n - s i t u i m a g i n g of electrode surfaces u n d e r c o r r o d i n g a n d non-corroding conditions. Acknowledgements--This work has been supported in part by the National Science Foundation and the
National Association of Corrosion Engineers.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21. 22.
REFERENCES U. STIMM1NG,Electrochim. Acta 31,415 (1986). U. STIMMINGand J. W. SCHULTZE,Ber. Bunsenges. Phys. Chem. 80, 1297 (1976). U. STIMMINGand J. W. SCHULTZE,Electrochim. Acta 24,852 (1979). N.F. Mo-rrand E. A. DAVIS,Electronic Processes in Non-crystalline Solids. Clarendon Press, Oxford (1979). F. DtQUARTO,G. Russo, C. SUNSERIand A. DIPAOLA,J. Chem. Soc. Faraday Trans. 1.78, 3433 (1982). B. DANZFUSSand U. STIMMING,J. Electroanal. Chem. 164, 89 (1984), U. ST1MMING,Nucl. Instr. Meth. B23,505 (1987). A. R. NEWMARKand U. STIMMING,J. Electroanal. Chem. 204,197 (1986). A. R. NEWMARKand U. STIMMING,Electrochim. Acta 32, 1217 (1987). A. R. NEWMARKand U. STIMM1NG,Langmuir3, 905 (1987). A. R. NEWMARKand U. STIMMING,Electrochim. Acta 34, 47-55. M. H. DEAN,A. R. NEWMARKand U. STIMM1NG,J. Electroanal. Chem. 244,307 (1988). U. STIMMING,Langmuir 3,423 (1987). M. H. DEANand U. STIMM1NG,J. Electroanal. Chem. 228, 135 (1987). M. H. DEANand U. STIMMING(submitted for publication). J. W. SCHULTZE,U. STIMMINGand J. WEISE,Bet. Bunsenges. Phys. Chem. 86,276 (1982). P. ME1STERJAHN,J. W. SCHULTZE,M. H. DEANand U. STIMMING(to be published). M. A. BUTLER,J. Electrochem. Soc. 130, 2358 (1983); and 131, 2158 (1984). D. SHUKLA,T. WINESand U. STIMMING,J. Electrochem. Soc. 134, 2086 (1987). M. R. KOZLOWSKI,P. TYLER, W. H. SMYRLand R. T. ATANASOSKI,in Electrode Materials and Processes for Energy Conversion and Storage (eds S. SRINIVASAN,S. WAGNERand H. WROBLOWA). Electrochemical Society, Pennington, New Jersey (1987). D. SHUKLAand U. STIMM1NG(submitted for publication). D. SHUKLAand U. STIMMING(submitted for publication).
0010-938)(/89 $3.00 + 0.00 © 1989Pergamon Press plc
THE ELECTRONIC PROPERTIES OF DISORDERED PASSIVE FILMS* MARY HELEN DEAN a n d ULRICH STIMMING Electrochemistry Laboratory, Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, NY 10027, U.S.A. Abstract--The understanding of passivity and its role in corrosion research is closely connected with the electronic properties of passive films. The approach of describing passive films in terms of their semiconducting properties can be improved by using models developed for amorphous semiconductors where localized electronic states play an important role. It is shown that localized states in passive films are of importance for the photo-electrochemical behavior where it expresses itself in sub-band gap photocurrents and a potential dependence of the photocurrent according to the Poole-Frenkel effect. Non-linear Schottky-Mott plots resulting from capacity data can be attributed to bulk localized states in the band gap and can thus be used to characterize highly disordered and/or non-stoichiometric passive films. The use of a photo-electrochemical laser scanning technique for the in-situ imaging of passivated surfaces and of corroding surfaces is also shown. INTRODUCTION
IN STUDYING the phenomenon of passivity and the properties of passive films, consideration of the electronic properties of the film has become increasingly important. This is largely due to the rapid development of semiconductor electrochemistry during the past two decades which provided the concepts for the description of photo-electrochemical behavior, capacity behavior and electron transfer reactions. These models have been successfully applied to passive films. It has been shown that a semiconductor approach to the description of passive films is a successful one. The large number of photo-electrochemical investigations of passive films demonstrate this. 1It has also been shown that a band structure model of the passive film on iron, based on capacity measurements, was able to describe wide ranges of electrochemical behavior of passive iron including electron transfer reactions and ionic processes. 2'3 Although this description of passive films using the semiconductor picture is qualitatively successful, it is partly in contrast to theoretical expectations as well as in contrast to some experimental results. The concepts that have been borrowed from semiconductor electrochemistry refer to bulk crystalline materials; passive films may be amorphous in structure, and may be non-stoichiometric in composition (which may even vary within the film), and they are often thin, i.e. they may not have a developed band structure normal to the surface. Any of these reasons may result in diffuse band edges and a large number of localized states in the band gap. Consequently, concepts developed for amorphous semiconductors4should represent a more appropriate approach. In the following, some of the electronic properties that are due to the presence of localized states are discussed and their * This paper was given at the German-American Colloquium on Electrochemical Passivation, which was held in Niimbrecht in the Federal Republic of Germany from 8--13 September 1987. Manuscript received 20 June 1988. 199
200
MARYHELENDEANand ULRICHSTIMMING
effect on photo-electrochemistry, capacity and electron transfer reactions on passive films is considered. In addition, some preliminary results will be presented for the use of photo-electrochemistry in obtaining in-situ images of passivated metal surfaces under non-corroding and corroding conditions. PHOTO-ELECTROCHEMISTRY The presence of localized states in the band gap of the passive film which may be due to non-crystallinity and/or non-stoichiometry of the film makes photo-excitation possible at photon energies hv < Eg where Eg is the band gap of the crystalline stoichiometric material forming the passive film. Such additional absorption processes are indicated in Fig. 1. Depending on the concentration and the distribution function of the localized states this can lead to considerable sub-band gap response. In the case of hv < E v excitation is possible from extended states e.g. the valence band, to localized states, from localized to extended states, e.g. the conduction band, and from localized states to localized states. In order to give rise to a photocurrent, iph, the photo-excited carriers on localized states must eventually escape into the underlying metal and into the electrolyte. This can be a field-assisted thermal excitation according to the Poole-Frenkel effect or tunnelling processes into either of the bands, into the metal or the electrolyte. The importance of the Poole-Frenkel effect for photo-electrochemical behavior was pointed out earlier for passive films on tungsten 5 and bulk amorphous non-stoichiometric iron-titanium oxides. 6 Figure 2 illustrates the various escape processes of the photo-excited charge carrier from the trap where it is assumed to be bound by coulombic forces. Process 1 denotes the classical Poole-Frenkel effect describing the effect of the electric field on the barrier. The escape probability PPF from the trap is given by PPF = exp [-- (Ei -
flFl/2)/kT~
(1)
where Ei is the ionization energy from the trap to the band and/5 is a material constant. At high fields, when the barrier becomes thin enough, tunnelling processes are possible and can lead to an additional current. This is shown by processes 2 and 3
E~
~,,
X
Ev
D(E) (0)
(b)
FIG. 1. (a) Absorption processes in an amorphous semiconductor showing excitation from extended to localized, localized to extended, and localized to localized states; (b) schematic representation of a possible density of states distribution in the band gap (taken from ref. 13).
The electronic properties of disordered passive films
201
/ ~,----- AX Possive firm
Etectroly~
FIG. 2. The energetic situation of a photoexcited electron on a localized state experiencing a coulombic force that is modified by a superimposed electric field: (1) classical overbarrier process; (2) phonon-assisted tunnelling; (3) direct tunnelling. (1)-(3) are in the direction of the field as treated in refs 8 and 9. (4) Classical overbarrier process and (5) direct tunnelling process, both against the field. AX denotes the distance of the localized state from the passive film-electrolyte interface (taken from ref. 13).
which describe phonon-assisted tunnelling and tunnelling at the trap level, respectively, which are both based on a charge separation following the direction of the field. In a Poole-Frenkel plot, In iph VS F 1/2, process i would yield a straight line and processes 2 and 3 would result in a field-dependent further increase of the current at very high fields. An indication lor such behavior has been found for passive films on hafnium that were ion-implanted with Pt or Xe after anodic oxide formation. The ion implantation process strongly disorders the oxide film, which is the most pronounced effect of the implantation process as found from the comparison of metal ion implantation with Xe implantation. Figure 3 shows a Poole-Frenkel plot 7 mainly for sub-band gap photon energies (the band gap is approximately 5.5 eV). It has been assumed that the potential drop in the insulating hafnium oxide film is linear and the field is given by F = (U-
Uro)/dox
where U is the electrode potential, Uro is the flatband potential and dox is the film thickness. While straight lines are obtained at intermediate fields, at high fields an increase of the photocurrent is observed which is more pronounced at low photon energies. Such an increase at high fields has also been found in model calculations for the Poole-Frenkel effect applied to photo-excitation when processes 2 and 3 start to contribute to the photocurrent. 8'9 If, on the other hand, the trap is close enough to the passive film--electrolyte interface, the photo-excited carrier can tunnel directly into the electrolyte, provided donor or acceptor states are available at that energy (process 5). Such an escape
202
MARYHELEN DEAN and ULRICH STIMMING HfOz (10% Xe) 0.SM H2SO4 hy / eV
-3
6
-4
5.5 J
I
I
J
2
-
I
3
J'~.~+
I
4
I
5
I
6
F '/2 / I 0 2 V I/2 c m - l / 2
FIG. 3.
Poole-Frenkel plot of the quantum efficiency at several photon energies measured on a hafnium passive film implanted with 10% Xe (taken from refs 7 and 11).
would be against the field and would detract from the overall photocurrent or, if dominant, the photocurrent would show an opposite sign, i.e. the photocurrent is cathodic at U > U~ and anodic at U < U~. The corresponding classical process, process 4, will obviously have only a neglible contribution, since the barrier for process 1 is much smaller. There are several indications that such processes can be observed experimentally. In the first example, thin passive films on zirconium, photocurrent spectra are shown for various potentials in Fig. 4.1° The data are reported in terms of the quantum efficiency, ~/, which is a normalized photocurrent defined as the ratio of the photocurrent to the incident photon flux. The passive film was formed at Uox = 3V (NHE) and the resulting film thickness is approximately 10 nm. Spectra taken at potentials U > - 0 . 4 V show anodic photocurrents with an extensive tailing down to below 3 eV. However, at potentials U < - 0 . 4 V, which are still more positive than the flat-band potential ( U ~ - - - 1 . 5 V), photocurrents change sign at lower photon energies. The photon energy hv(iph = 0), at which the photocurrent changes sign, increases with decreasing potential. A corresponding behavior can be seen in the potential dependence recorded at various photon energies. It is shown in Fig. 5 for 0.1% Xe-implanted passive film on hafnium in a semi-logarithmic representation, In r/vs F. 11It can be seen that the field at which the photocurrent changes sign from anodic to cathodic increases for decreasing photon energy. This behavior clearly indicates that an evaluation of the flat-band potential from the potential U(iph = 0) where the photocurrent changes sign can lead to erroneous results if it has not been established that U(iph = 0) is wavelength independent. 12 The cathodic photocurrents can be explained by process 5 in Fig. 2.13 In simple model calculations the escape probability of the photo-excited charge carrier from a trap located at a distance AX from the passive film-electrolyte interface has been calculated for various ionization energies as a function of the field. The ionization
The electronic properties of disordered passive films
203
O. IC Zr in IM No2S04
Uox-3V
U/V
0.0~.
=(
I
0.0~
[
4
5
h~ / eV
FIG. 4, The quantum efficiency as a function of photon energies measured at various electrode potentials for a film formed on Zr in 1 M Na2SO4 at Uox = 3 V (taken from ref. 10).
energy, Ei, d e n o t e s the distance of the trap f r o m the conduction b a n d and is assumed to be related to the p h o t o n energy by Ei = Eg - hv, i.e. lower p h o t o n energies are c o n n e c t e d to higher Ei and vice versa. T h e probability, Pa, for the escape in direction of the field is given by the P o o l e - F r e n k e l effect and possible tunnelling t h r o u g h the field-dependent barrier. T h e probability, Pc, for the escape directly into the electrolyte, on the o t h e r hand, is a tunnelling process that mainly d e p e n d s on A X and only
-4--
HfO~ (0.1%Xe ) hv / e V ~6 a5 ~4
-I(
I
2
3
4
F / I O 5 (V/era)
Fto. 5. The field dependence of the quantum efficiency at three photon energies for a hafnium passive film implanted with 0.1% Xe (taken from ref. 11).
204
MARYHELENDEAN and ULRICHSTIMMING
o/
E~ • 0.2
0.5
2
3
4
5
6
F/I06 (V/¢m)
FIG. 6. M o d e l calculations for various ionization energies, Ei, f o r a distance ~c = 2 nm;
m* = 0.5me (taken from refs 11 and 13). weakly on the field. While Pa is strongly dependent on E~ and F, Pc is not. This can be seen in Fig. 6 where P = Pa + Pc is plotted versus the field. The process in the direction of the field is given a positive and the process against the field a negative sign. It can be seen from Fig. 6 that processes against the field, i.e. process 5 in Fig. 2, are the dominant contribution to the photocurrent for certain parameters, such as Ei = 0.5 eV and F = 106 V/cm. The general shape of the curves in Fig. 6 is qualitatively very similar to the experimental results shown in Fig. 5. THE CAPACITY OF PASSIVE FILMS In interpreting capacity measurements of passive metal electrodes, semiconductor models have often been invoked. The Schottky-Mott equation has usually been applied to the analyses of such data. Straight lines are expected in 1/C 2 vs U plots, and from the linear portion the density of charge carriers can be estimated, knowing or assuming the dielectric constant of the passive film. The estimates for donor or acceptor concentrations are generally very high, of the order of 1020 - 1021 cm -3. These values are a strong indication of a non-stoichiometric and/or highly disordered character of passive films. In most instances, non-linearities or breaks in the slope of straight lines are observed in Schottky-Mott plots. Interpretations such as multiple donor (or acceptor) levels or varying donor (acceptor) concentrations in the film are often given, for the latter case using a "local" donor (acceptor) density as derived from a potential-dependent slope in a Schottky-Mott plot. Since such interpretations are usually at variance with the limitations and simplifications of the Schottky-Mott equation, efforts have been undertaken to derive a capacity-potential relation that takes into account multiple levels or even a continuous distribution function of localized states in the band gap. ~4.~5 In deriving the Schottky-Mott equation from the Poisson equation one important assumption is that the charge density is not a function of the electrode potential. This assumption is usually valid when all donors or acceptors are ionized under flat-band conditions. However, when multiple levels are present, this condition may not be
The electronic properties of disordered passive films
205
true since low lying traps may become ionized when the Fermi level passes through the energy of these traps. Consequently, the charge density in the film becomes potential dependent. Beginning with the Poisson equation, an expression for the space charge capacity, Csc, can be derived that takes into account a potential-dependent charge density:14 Csc -
--(~.0_1 112
dqsc
d--'~s c
\/.]
~)(A~sc) l- (A~O~c
-]1/2
(2)
where qsc is the space charge, Aq~ is the potential difference between the bulk and a point in the space charge layer, A~sc is the total potential difference across the space charge layer, O(A~) is the charge density at a point where the potential is Aq, e is the relative dielectric constant, and e0 is the permittivity of space. For a crystalline n-type semiconductor with M discrete donor levels the charge density can be expressed by: o(A~)) =
(
e ~ 1 + exp .EF j=l NDj
EDi kr
eA¢~
)]1
- Nc exp
(
Er
)}
Ec - eaq~ k-T
(3) where e is the electronic charge, k is the Boltzmann constant, T is the absolute temperature, Ec is the energy of the lower conduction band edge with Arcthe effective density of states at Ec, and the density of donor states in the jth level is NDj with their energy at EDi. The results of calculations have been reported in terms of a dimensionless capacity defined as: C'sc = Csc/(eeoe2Nc/2kT) 1/2.
(4)
The dimensionless charge density is:
O' = o/eNc.
(5)
Model calculations for the situation of a second donor level, which is not ionized at flat-band conditions for various N62 at a given ED2 and various ED2 at a given N~2 are shown as Schottky-Mott plots in Figs 7 and 8, respectively. {4It is obvious from both figures that the slope at low potentials is determined by N61 while at high potentials it reflects N/~l + N/~2. The extrapolation from the high potential straight line does not yield the flat-band potential and at the potential where the second donor level becomes ionized the capacity increases and 1/C2c decreases. , The capacity-potential behavior for distributions of localized states described by continuous density of states functions has been studied using this model. In this case, the potential-dependent charge density appearing in equation (2) is: 15 ~(A~) = e f ~
D(E)[{I + exp [(E - EF)/kT]}-' - {1 + exp [(E - EF + eacp)/kT]}-l]dE.
(6)
When the concentration of localized states below Ec is described by an expotentially decaying conduction band tail, curved Schottky-Mott plots result as shown in Fig. 9 for three different values of the decay parameter. The slopes of these curves increase with increasing potential and linear behavior is approached at higher potentials. In
206
MARY HELEN DEAN a n d ULRICH STIMMING
200
2
e~ p A
I00
I
I
0.5
I
I
Z~/V
FIG. 7. Schottky-Mott plot of results from model calculations using equation (3) in equation (2) with/ = 2, Eol = -0.05 eV. The dimensionless donor concentration in level 1 was Ni~a = 0.10. The concentration of deep donors, N~2, was varied. N~2: (1) 0.20; (2) 0.10; (3) 0.05; (4) 0.025; (5) 0.01 (taken from ref. 14).
2oo -
I
,oo I
I
0.5
~/V
FIG. 8. Schottky-Mott plot of results from model calculations using equation (3) in equation (2) with/' = 2, N~] = N(92= 0.10 and EDn = --0.05 eV. The energy of the deep donor was varied. Eo2: ( 1 ) - 0 . 0 5 eV; ( 2 ) - 0 . 2 0 eV; ( 3 ) - 0 . 3 5 eV; ( 4 ) - 0 . 5 0 eV; (5) -0.80 eV (taken from ref. 14).
The electronic properties of disordered passive films
f 3/
/
/
?
e"
I00
/
//
/
/
/
/
21-"
I ....
0
I
05
I
A , ~ /v
Fro. 9. Schottky-Mott plot of results from model calculations using equation (4) in equation (2) with varying values of the conduction band tail decay parameter. A,.: (1) 0.001 ;
(2) 0.05;(3) 0.10.
//:~
....
/
/ -~ t~
ioc
]
,.y'"
/
/'
/'"3"'"
//// i!
//
I/ / t/ /
0
.-.-"
./"
-.-4 /
/
/
/
1
O5
A~/V
Flo. 10. Schottky-Mott plot of results from model calculations using equation (4) in equation (2) in which a constant density of states is present below the conduction band tail. The decay parameter of the conduction band tail is varied. A~: (1) 1,0; (2) 0.7; (3) 0,3; (4) 0.1 (taken from ref. 15).
207
208
MARY HELEN DEAN and ULRICH STIMMING
another series of calculations, it was assumed that a band of localized states whose concentration does not depend on energy lies below the the conduction band tail. The results presented in Fig. 10 for a band of localized states extending throughout the gap with varying conduction band tail decay parameters indicate that curved Schottky-Mott plots may be observed. When the conduction band tail decays rapidly with energy below Ec, as in curves 1 and 2, the effect of the constant band of localized states is dominant at higher potentials and the capacity becomes nearly potentialindependent. Qualitively similar Schottky-Mott plots have been observed experimentally for bulk, amorphous Fe-Ti oxides 6 and also for passive films. 2'16 If the density of states in the band gap is reflected in the capacity-potential curve in such an obvious way, an analysis of experimental data should be able to reveal the distribution of localized states. This can be done by differentiating the capacitypotential curve. Using certain assumptions the slope is given by: 14 dC~ _ 2 1 - e eo dA~bs~ e e0Q(A~sc) ~
C~c
(7) "
This equation has been applied to the analysis of capacity data of passive iron electrodes. 17The data show a pronounced potential and thickness dependence of the capacity and are very similar to data obtained earlier. 2 Because of the relatively large experimental capacities, contributions from the Helmholtz layer have to be taken into account. In addition, a roughness factor, r = 2, has been assumed. The results of the procedure are shown in Fig. 11 in a plot representing the distribution function on the abscissa and the energy on the ordinate. Pronounced variations are found within the energy range that is supposedly the band gap with the valley in the distribution function becoming broader for increasing thickness of the passive film. This procedure should demonstrate that, although the Schottky-Mott plot loses its significance if applied in a formal sense, capacity-potential measurements still bear a large amount of information on electronic properties of passive films. This can be
0-
>. -05 I
d
-I
I
I
2.5
5
D ( E ) x 10-2°/ crn -3 e V -I
FI6. 11. Approximate density of states functions f o r iron passive films of varying thickness. Results were obtained using equation (5) after correcting the measured capacity data for Helmholtz layer effects and surface roughness, assuming CH = 20 /~F/cm 2 and r = 2, respectively.
The electronic properties of disordered passivefilms
209
advantageously used, for example, in the interpretation of electrochemical behavior of passive films. PHOTO-ELECTROCHEMICAL LASER SCANNING A further example of the usefulness of the photo-electrochemical effect in studying passive films is shown in this section. As originally demonstrated by Butler, 18when a laser beam is focused on a small spot on the passivated metal electrode and then rastered over the surface, an image of the passive film based on the photoresponse can be obtained.19'z° Property changes of the film are readily reflected in the photo-signal. A few examples will be given to illustrate some of the possibilities. The image of a passivated titanium sample measured under relatively insensitive conditions is shown in Fig. 12.19 The step size and the beam size are approximately 100 ~m and a flat response is obtained. Subjecting passive titanium to H B r solutions results in pitting corrosion and changes in the film can be imaged using the laser scanning technique. A titanium sample passivated at 10 V in 0.5 M H2SO 4 has been corroded at 9 V for a total time of 30 s. After transferring it back to sulphuric acid the image clearly shows the locations of pitting corrosion Fig. 13; 19here the step size was 10/~m and the beam size <20 #m. In an improved procedure, the sample was left in the H B r solution. It was corroded at 9 V and then imaged at 1 V where pitting ceases and the sample is stablefl ~ The laser scanning technique offers the possibility to investigate inhibition and corrosion processes under in-situ conditions without removing the sample from the electrolyte. In addition to systems like titanium which is pure metal and one whose passive film shows a strong photoresponse, alloys can also be successfully imaged using the laser scanning technique. This is demonstrated in Fig. 14. 22The sample was 304 stainless steel on which a passive film was grown for 30 min at 0.88 V (SHE) in 1 M NaESO 4. The image clearly indicates areas of quite different photoresponse which probably reflect a different structure and/or composition of the passive film at these locations. For a more quantitative assessment a comparison of such an image with another technique such as SEM is necessary, but the results obtained to date demonstrate that imaging of such important materials as stainless steel is also possible.
FIG. 12. Image of an uncorroded titanium film in 0.5 M H2SO 4 obtained with a 100/xm step-size and a beam diameter that was approximately100/xm (taken from ref. 19).
210
MARYHELENDEANand ULmc~aS~WMING
I FI6. 13. hnage of a corroded titanium passive film in 0.5 M H:SO4 after undergoing pitting corrosion in an electrolyte containing HBr, Step-size was 10 #m and the beam diameter was <20 p.m (taken from ref. 19).
Fl6. 14.
i
Image of a passive film o n 304 stainless steel in 1 M Na2SO4. Step-size was 10 txm and the beam diameter was <20 ~m (taken from ref. 21).
The electronic properties of disordered passive films
211
CONCLUSIONS I n s t u d y i n g passivity, an i n v e s t i g a t i o n of the e l e c t r o n i c p r o p e r t i e s of the passive film is a v a l u a b l e a p p r o a c h . It has b e e n s h o w n that localized states play an i m p o r t a n t role for the b e h a v i o r of passive films. D e v i a t i o n s from linearity in S c h o t t k y - M o t t plots, s u b - b a n d gap effects in the p h o t o - r e s p o n s e , the i m p o r t a n c e of the P o o l e F r e n k e l effect for the p o t e n t i a l d e p e n d e n c e of the p h o t o c u r r e n t a n d cathodic p h o t o c u r r e n t s at p o t e n t i a l s a b o v e the flat-band p o t e n t i a l are indicators for the p r e s e n c e of localized states. Such b e h a v i o r , which is clearly in c o n t r a s t to crystalline materials, indicates an a m o r p h o u s a n d possibly n o n - s t o i c h i o m e t r i c character of passive films. P h o t o - e l e c t r o c h e m i s t r y in its a p p l i c a t i o n to a laser s c a n n i n g t e c h n i q u e is a v a l u a b l e tool for i n - s i t u i m a g i n g of electrode surfaces u n d e r c o r r o d i n g a n d non-corroding conditions. Acknowledgements--This work has been supported in part by the National Science Foundation and the
National Association of Corrosion Engineers.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
21. 22.
REFERENCES U. STIMM1NG,Electrochim. Acta 31,415 (1986). U. STIMMINGand J. W. SCHULTZE,Ber. Bunsenges. Phys. Chem. 80, 1297 (1976). U. STIMMINGand J. W. SCHULTZE,Electrochim. Acta 24,852 (1979). N.F. Mo-rrand E. A. DAVIS,Electronic Processes in Non-crystalline Solids. Clarendon Press, Oxford (1979). F. DtQUARTO,G. Russo, C. SUNSERIand A. DIPAOLA,J. Chem. Soc. Faraday Trans. 1.78, 3433 (1982). B. DANZFUSSand U. STIMMING,J. Electroanal. Chem. 164, 89 (1984), U. ST1MMING,Nucl. Instr. Meth. B23,505 (1987). A. R. NEWMARKand U. STIMMING,J. Electroanal. Chem. 204,197 (1986). A. R. NEWMARKand U. STIMMING,Electrochim. Acta 32, 1217 (1987). A. R. NEWMARKand U. STIMM1NG,Langmuir3, 905 (1987). A. R. NEWMARKand U. STIMMING,Electrochim. Acta 34, 47-55. M. H. DEAN,A. R. NEWMARKand U. STIMM1NG,J. Electroanal. Chem. 244,307 (1988). U. STIMMING,Langmuir 3,423 (1987). M. H. DEANand U. STIMM1NG,J. Electroanal. Chem. 228, 135 (1987). M. H. DEANand U. STIMMING(submitted for publication). J. W. SCHULTZE,U. STIMMINGand J. WEISE,Bet. Bunsenges. Phys. Chem. 86,276 (1982). P. ME1STERJAHN,J. W. SCHULTZE,M. H. DEANand U. STIMMING(to be published). M. A. BUTLER,J. Electrochem. Soc. 130, 2358 (1983); and 131, 2158 (1984). D. SHUKLA,T. WINESand U. STIMMING,J. Electrochem. Soc. 134, 2086 (1987). M. R. KOZLOWSKI,P. TYLER, W. H. SMYRLand R. T. ATANASOSKI,in Electrode Materials and Processes for Energy Conversion and Storage (eds S. SRINIVASAN,S. WAGNERand H. WROBLOWA). Electrochemical Society, Pennington, New Jersey (1987). D. SHUKLAand U. STIMM1NG(submitted for publication). D. SHUKLAand U. STIMMING(submitted for publication).