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Potential modulated reflectance spectroscopy of anodic oxide films on titanium
Elrcrrcxhv,vca Aern Vol 35, No 6, pp 1073_1@!lO,1990 Pnnted ,¶IGreat Bntmn
00134646,?W E300+0.00 Q 1990 Pcrgamon Press pk.
POTENTIAL MODULATED REFLECTANCE SPECTROSCOPY OF ANODIC OXIDE FILMS ON TITANIUM D J BLACKWOOD and L M PETER Department of Chemistry, Umverslty of Southampton, Southampton SO9 5NH, U K (Recewed 10 May 1989, m rewedfirm
I September 1989)
Ahtract-Potential modulated reflectance (PMR) spectroscopy has been used to mvestlgate thm anodlc oxide films formed on tltamum m sulphunc acid The ongm of the reflectance modulation ISdlscussed and the expenmental results are compared with theoretlcal calculations based on the three layer model The overall shape and the dependence of the PMR spectra on film thickness have been modelled satlsfactonly by assummg that the band gap of the oxide m the presence of an electric field IS Increased due to dlelectnc polarlsatlon The potential dependence of the modulated reflectance response for films of constant thickness was related to the electric field dlstrlbutlon m the oxide and the analysis showed that the modulated reflectance response 1s dominated by electroabsorptlon The results demonstrate that PMR spectroscopy offers a more reliable method than Mott-Schottky plots for determining the flat-band potential of the oxide
INTRODUCTION
mterest m the solid state properties of the anodlc oxide on titanium since It can protect the underlying metal m a variety of corrosive envlronments It 1s generally supposed that the anodlc film behaves as a highly doped n-type semiconductor layer, but the photocurrent and impedance behavlour mdlcate the presence of a non-uniform dlstrlbutlon of defect states which cause slgmficant departures from the simple behavlour associated with bulk semlconductor electrodes[l, 21 Non-linear Mott-Schottky plots of reciprocal square capacitance us potential are commonly observed, so that it 1s not possible to determine reliable values of the donor density N, or of the flat-band potential E,, Smce recombmatlon effects displace the photocurrent onset potential away from flat-band, E,, 1s not readily accessible from photocurrent measurements either In view of these comphcatlons, we chose to use potential modulated reflectance (PMR) spectroscopy to obtain an mdependent estimate of E,, and to characterlse the the potential dlstrlbutlon m the oxide films The technique 1s often referred to as electrolyte electroreflectance (EER), but we use the more general term PMR since effects other than electric field modulation of the optical constants may be mvolved m the case of thm anodlc films The first PMR study of anodlc oxide films on titanium appears to have been carried out by Frova et al [3] as part of a detailed mvestlgatlon of the optical constants of rutde These authors observed very large modulation effects which they attributed to electroabsorption Later, Paatsch[ll] used PMR and photopotential spectroscopy to study the electrochemical propertles of titanium, and more recently Blondeau et al [S] and Froehhcher et al [6] have used PMR to investigate the optical properties of the three layer system formed by anodised titanium m aqueous solution The authors of[S, 61 concluded that “mterference effects” can lead to substantial differences between the modulated spectra of bulk materials and
There ts considerable
of thm films on metallic substrates The importance of “back wall reflectlon” has also been recogmsed by Nonomura et al [7] and Hamakawa[8] m their work on amorphous skcon, where the modulation spectra are dominated by the effects of electroabsorptlon on light reflected at the rear contact The interpretation of the PMR spectra of anodlc films ISa controversial area In the case of anodlc films on tantalum, for example, Holden and Ullman[9] have attnbuted the spectra to modulation of the film thickness by electrostrlctlon However, this mterpretatlon has been disputed by Frova and Mlghorato[lO, 111, who consider that the spectra anse from the second order electrooptlc effect, te from the modulatlon of the refractive mdex of the oxide film by the electnc field In fact, It 1s possible that the two effects are coupled, and indeed Matthews et ~I[121 have interpreted elhpsometrlc measurements of the same system as evidence that the electrostrlctlve effect 1s accompanied by a correspondmg change m refractive mdex These authors concluded that the relative changes of the thickness and refractive mdex are similar in magmtude (about 0 5% for a field of 4 x lo6 V cm-‘) The theoretical background of electroreflectance (EER) spectroscopy has been discussed extensively m the hterature[l3-151, and spectra have been obtamed for a wide range of single crystal semiconductors and msulators Aspnes[lS] has shown that under certain low field condltlons, electroreflectance spectra correspond to the third denvatlve of the optical drelectnc constant The spectral hneshape then becomes mdependent of applied potential bias, and under depletion condltlons the EER signal scales linearly with the amplitude of the potential modulation Frequent and often uncntlcal use has been made of the low field electroreflectance theory derived by Aspnes, but even m the case of single crystal semiconductors, It 1s clear that It only applies under a relatively narrow set of condltlons[16] In the case of a thm oxide film on a reflecting metal substrate, the sltuatlon 1s more complicated smce the PMR signal contams a contnbutlon from light that has been reflected at the oxide-metal
1073
D J BLACKWOODand L M PETER
1074
AR /R
I
I
300
350
100
wavelength/nm
Fig 1 PMR spectra obtamed from an oxide film grown on tltamum at 10 mV s-l to 3 0 V us Hg/Hg,SO, m 3 0 mol drn-j H$O, at room temperature (dc potential 3 0 V, (ICmodulation 270 Hz, 100 mV p-p)
boundary Near the band edge, we may expect electroabsorption to be the dommant modulation mechanism In addition, however, modulation of the optical constants and field induced changes m film thickness (electrostnction) may give nse to interference effects which appear at other photon energes m the PMR spectrum It 1sclear that the mterpretatlon of modulated reflectance spectra requires formulation of the reflectance problem wlthm the framework of the three layer model as well as a physical model for the perturbation mechanism In this paper, we discuss PMR spectra obtained for thin (c 30 nm) oxide films on titanium The dependence of the PMR spectra on film thickness and on electrode potential has been mvestlgated, and the data are related to Impedance measurements made under the same condltlons The PMR results are interpreted within the framework of theoretlcal calculations based on the three layer model EXPERIMENTAL Titanium electrodes were prepared from sections of Johnson Matthey ‘Specpure’ grade tltanmm rod sealed m glass synnge pistons with epoxy resin The exposed surfaces were pohshed to a mirror finish on successively finer grades of alumma slurry, and the electrodes were Inserted through a syringe barrel mounted on a glass cell, allowmg accurate posltlonmg m the incident monochromatic light beam which entered the cell through a quartz window at an angle of incidence of 45” A 150 W xenon lamp and a computer controlled dlffractlon grating monochromator were used to provide mcldent dlummatlon over the spectral range 250-500 nm, and the polansatlon of
the mcldent beam was selected by a Glan-Thompson polarlser Filters were used where necessary to remove stray and harmonic hght The specularly reflected beam was focused onto a photomultlpher tube and the output was fed uzu an autorangmg current amplrfier to a lock-m amplifier mterfaced to a mlcrocomputer Data acqmsltlon, signal averagmg and ratlomg were carried out under software control by the computer The electrode potential was controlled by an operatlonal amplifier potentlostat, and spectra were recorded using square wave modulation, usually at 270 Hz All potentials are referred to the Hg/Hg,SO,/K,SO, (sat) electrode It has been established that the properties of the anodlc oxide on titanium depend on the rate at which the film IS formed[20], films grown potentlodynamltally at low sweep rates appear to be less defective than those formed at higher sweep rates, and there 1s evidence that crystalline areas with preferred onentatlon may be formedC21-J For this reason, we chose to grow all films for the PMR study at a sweep rate of 10 mVs-’ RESULTS AND DISCUSSION Figure 1 shows PMR spectra measured with s-and p-polansed light for an anodlc oxide film which was grown by a linear sweep to a final potential of 3 0 V and then held at the anodlc limit The amplitude and hneshape of the spectra were found to be independent of the modulatton frequency over the range 27 Hz to 2 7 kHz, indicating that the effect 1s not associated with Faradalc processes (by contrast, PMR spectra recorded for anodlc films on iron, for example, show a characterlstlc frequency dlsperslon which 1s related to
Potential modulated reflectance spectroscopy
1075
I>
lo3 ARA n-
mcdulatlon/Vp_p Fig 2 Dependence of AR/R on ac modulation amphtude Measurements made with s-polansed light at 342 nm for a film grown to 3 0 V us Hg/Hg,SO, (frequency 270 Hz, dc potential 3 0 V) changes brought about by charge transfer[ 173) Spectra were recorded for modulation amplitudes between 100 and 500 mV pp and were found to scale hnearly with the amplitude of the ac modulation as shown tn Fig 2 Lmearlty of this kmd 1s predicted by the Aspnes theory of Schottky barrier electroreflectance m the low field hmlt[15], and the results shown m Fig 2 could be taken to indicate that the low field electro-reflectance crlterta are satisfied and that the electric field dlstrrbutlon corresponds to a Schottky barrier configuration However, neither of these conclusions 1s appropriate m the present case Firstly, the electric field Imposed by the dc potential at the anodlc limit 1s high, smce the oxide IS formed by field assisted ion mlgratlon The anodlsmg ratio for titanium m H,SO, 1s 2 5 nm V- ’ at room temperature[18], so that it follows that the average electric field at the anodlc hmlt 1s of the order of 4 x lo6 V cm- ’ Even d the potential 1s reduced subsequently so that the electnc field 1sdetermined by the space charge (see below), the Schottky model may not apply since the donor distribution 1s not uniform and deep donor states may be important The spectra shown m Fig 1 are relatively broad and they appear to correspond to a first derlvatlve lmeshape function In this respect, they are slmdar to the electroreflectance spectra reported for stngle crystal rutlle by Vos and Krusemeyer[19] Vos[20] has dlscussed the band structure of rutlle and has concluded that the broad features m the electro-reflectance spectra are not associated with lifetime broadened transltlons at critical points m the Joint density of states function, but rather from changes m the band energies arising from dlelectrlc polarlsatton of the rutde lattice This conclusion 1s borne out by the observation that the line width changes httle with temperature down to 80 K Vos has shown that the electroreflectance spectra correspond qmte closely to the wavelength or energy denvatlve of the complex dlelectrlc function, with the mam structure m the spectrum centred at about 300 nm, although some additional osallations, particularly at lower photon energies, appear to anse from the Franz-Keldysh effect In view of the uncertamty concermng the mechamsm of the PMR effect, calculations were carned out using two different theoretical models The reflection coefficient of the metal surface covered with a film of
stcnch~ometrlc
thickness d with a complex refractive mdex A, IS given
by
f= f12+f23 ev(-4 1 +P,,D,, exp(-16)’
where 6 = 4lrdA, cos F12 and
6, ,
(14
(1’4
F,, are the Fresnel coefficients of the solution-o_xlde and oxide-metal interfaces respectlvely and & 1s the complex angle of refractlon at the solution oxide mterface In the case of the anodlc oxide film on tltamum, the film thickness, d, IS determmed by the formation voltage, and under the condltlons of the present expenments, the anodlsmg ratlo was 2 5 nmV-‘[20] Gagnalre and Joseph[Zl, 223 have reported data for the optical constants of titanium and of Its anodlc oxide determined by spectroscopic elhpsometry The energy dependence of the real and lmagmary components of the optlcal dielectric constant of the oxlde[22] 1s similar to that derived by Vos and Krusemeyer[19] for smgle crystal rutde by Kramers Kromg analysis of reflectance spectra The data given m[21] were used to compute reflectance spectra (R = )EZI) from equatton (1) for s- and p-polansed hght at 45” Incidence, and Fig 3 compares the reflectlvlty of the bare tltamum surface with the reflectance of an electrode covered by a thm oxide film It can be seen that the presence of the oxide leads to the appearance of a mmlmum m the reflectance signal at around 320 nm, the effect 1s particularly marked m the case of s-polarised light It ISclear from this figure, that small perturbations of the optlcal constants or of the film thickness are likely to have a large effect on the normahsed dlfferentlal reflectance AR/R m this wavelength region We consider next that the reflectance could be perturbed by an applied ac voltage m one of two different ways Firstly, the thickness of the oxide film may change due to the electrostrlctlve effect Secondly, the complex optlcal dlelectrlc constant may be perturbed m the presence of the electric field, this 1s the electrooptlc effect These effects have been discussed widely m the hterature[9-151, but conclusive proof of the apphcablhty of any particular model IS lackmg m the case of thm dlelectrlc films on metal substrates For this reason model calculations were performed for the two hmltmg cases
D J BLACKWOOD and L M PETER
1076
lo
I-
a sp____
a
s-
polarlsec
4 c------I’
p-_-
polartse
--__----________
,I’
/’
I’
Aq/R
o;:J _----------_/-----___
200
_
*I
A’
I
300
400
wavelength/nm
I
500
200
300
I
400
500
wavelength/nm
Fig 3 Reflectance spectra calculated from the data m[21] (a) bare tltamum surface, (b) tltamum covered with a 10 nm oxide film Note m (b) the appearance of a minImum m the reflectance at around 320 nm
Fig 4 PMR spectra calculated from equation (1) by assuming that the oxide film thickness 1sincreased by the electnc field (electrostnctlon effect) Oxide film tluckness (a) 7 5 nm,
The calculation of the perturbation due to the electrostrlctlve effect IS relatively straightforward It 1s assumed that the only term m equation 1 affected by the electric field 1sthe film thickness, d Figure 4 shows examples of theoretlcal spectra derived by assummg that only electrostrlctlon effects are important For the purposes of the calculation, it was assumed that the film thickness was mcreased by the modulating field smce the work of Matthews et al [12] has suggested that this 1s the case for several other oxide films The results of the model calculations presented m Fig 4 show that the A R/R spectra assume a first derivative form only when the film thickness exceeds a cntical value, whereas spectra for thmner films display monopolar bands for both s- and p-polansed hght In this respect, the model fads to predict the experimental behavlour since first derlvatlve spectra were obtamed even for the thmnest oxide films studled In addltlon, the computed A R/R spectra are inverted with respect to those observed expenmentally, so that even If the vahdlty of the model were accepted, it would be necessary to assume that the film thickness decreases rather than increases m the presence of an electnc field On the strength of this comparison, It was concluded that the electrostrictrve effect IS not responsible for the observed PMR spectra The denvatlon of theoretical spectra resulting from perturbation of the optical constants of the oxide 1s less straightforward The low field Aspnes model 1s clearly not apphcable, and the theory developed by Vos[20] for smgle crystal rutde was therefore taken as a startmg point Vos has argued convmcmgly that the broad first derlvatlve features m the electroreflectance spectra of rutlle arlse from perturbation of the energy
bands as the result of dlelectnc polansatlon of the lattice rather than from lifetime broadened Franz-Keldysh oscdlations as proposed by Frova et al [3] The effect proposed by Vos arises from a lowering of crystal symmetry which results m the breaking of optical selectlon rules or, at a more fundamental level, m changes of the optlcal matrix elements for mterband transltlons The polarlsatlon induced blrefrmgence of ferroelectncs with the perovsklte structure 1s well established, and It appears that T10, behaves similarly The theory mdlcates that the lowest energy oscdlator moves towards higher energies by an amount proportional to the square of the macroscopic polarlsatlon P Vos[20] has performed LCAO calculations of the band structure of rutlle and used the results to derive the elements of the polarisatlon potential tensor for optical transltlons The agreement with experlmentally derived shifts m the optical transltlons ISvery satafactory, and It seems reasonable to suppose that the model IS also appropnate for anodlc films, although the oxide 1s polycrystalline m this case so that much of the fine structure may be lost The shift m transitIon energies proposed by Vos leads to modulated spectra which correspond closely to the energy derivative of the optical dtelectnc constant We therefore used the data of Gagnaire and Joseph[21] to derive theoretlcal PMR spectra for the anodlc oxide by numerical dlfferentiatlon The electnc field was taken to be constant throughout the film so that n, 1s not a function of posltlon (but see below for further discussion of this pomt) Figure 5 shows examples of calculated PMR spectra which can be compared with the experlmental spectra m Fig 1 Two
(b) 12 5 nm Angle of mcldence 45”
Potential modulated reflectance spectroscopy
1077
38
p _____
polarlsed
hv/eV
36-
t
3b-
AR/R
32-
I
boo 300 uavelength/nm Rg 5 PMR spectra calculated from eqn 1 by assummg that the band gap energy ISIncreased m the presence of an electric field Oxide film thickness (a) 7 5 nm, (b) 12 5 nm Angie of
3 0. 0
5
10 15 20 film thlckness/nm
I 25
Rg 6 Dependence of the posItIon of the low energy maxlmum m AR/R on oxide ttnckness for s-polansed hght Open cwcles calculated by assummg modulation of band gap energy Closed cncles experlmental pomts
mcldence 45 D
important facts emerge from the calculations Firstly, the computed spectra exhibit a first derlvatlve shape even for the thmnest films Secondly, the amplitude of the AR/R signal passes through a maxlmum as the film thickness 1s mcreased The spectra computed on the basis of the Vos model appear to be more m accord with experlmental results than those derived by consldermg electrostnctlve effects The theoretical spectra predict a marked dependence of the location and amplitude of the peaks on oxide thickness which IS contrasted with experimental results m Figs 6 and 7 The occurrence of a maxlmum m the plot of AR/R us film thickness may appear surpnsmg at first The orlgm of the maxlmum becomes clear from an mspectlon of Fig 2, the reflectlvlty of the oxide covered metal falls to extraordmanly low values m the region where the PMR spectra are observed, and the maximum m AR/R as a function of film thickness corresponds to a mmlmum m the reflectlvlty Figure 6 and 7 show that the calculations based on the Vos model are m semiquantltatlve agreement with the experimental spectra The deviations between theory and experiment probably anse m part from the fact that the optical constants of the oxide depend on the way m which the film is formed In addition, the low reflectlvlty of the three layer system 1slikely to lead to large errors m the amplitude of the normahsed AR/R signal from scattered hght, depressing the maxlmum in AR/R It 1s also posstble that electrostrlctlve effects may make a minor contrlbutlon to AR/R The experimental spectra m Fig 1 were measured under high field condrtlons correspondmg to the
103AR/R
-
6-
fdm thwkness/mn
Fig 7 Dependence of amphtude of the energy maxImum m AR/R on oxide film tlnckness for s-polansed hght Open circles calculated by assummg modulation of the bandgap energy Closed circles expenmental pomts
anodlc hmlt m the growth sweep It 1s reasonable to assume that the electnc field extends throughout the oxide to the metal mterface under these arcumstances, but it 1s probably not constant, however, smce there IS
1078
D J BLACKWOOD and L M PETER
good evidence from capacitance measurements that the oxide behaves as a hrghly doped n-type semlconductor Whereas at the anodlc limit, the space charge repon must extend to the metal m order to facilitate ion migration, it will collapse at lower potentials, leaving a field-free region This will happen when the Schottky length, W, which ts given by W=(2A&c,/qN,)“Z,
(2)
becomes smaller than the film thickness If the oxide 1s homogeneously doped, the donor density and flatband potential can m prmclple be obtained by plotting the inverse capacitance against potential according to the Mott-Schottky equation C-‘=(2/qs&,N,)(A+kT/q)
(3)
In the application of equation (3), it 1s normally assumed that the Helmholtz capacitance, which appears m senes with the space charge capacitance C,,, IS constant, so that a linear dependence of the inverse square of the total measured capacitance is obtamed In the case of anodlc oxide films on titanium, however, Mott-Schottky plots are nonhnear[2], so that the donor density can only be estimated by taking tangent approxlmatlons At the same time, the curvature of the plots makes it difficult to determine the flat-band potential by extrapolation There are several possible reasons for the observed behavlour For example, the curvature could anse from a non uniform donor datnbutlon, with the donor profile falling from a high value at the metal-oxlde interface towards a lower value at the oxide-solution interface Alternatively, the donors may be &stnbuted m energy below the conduction band, so that they become progressively lomsed as the Fermi level moves down through the band gap with increasing potential Finally, the assumption that the Helmholtz capacitance 1s mdependent of potential can be questloned If electromc or lomc charge ts stored at defects at the oxide-solution interface, the Helmholtz capacitance 1s likely to be potential dependent by analogy with metal surfaces It 1s therefore essential to have some independent measure of the potential dlstnbutlon m the system, the PMR response 1s ideal m this respect, since It 1s sensltlve to the electnc field m the oxide phase PMR spectra were recorded as a function of potential for a titanium electrode on which the oxide film was formed initially by sweepmg the potential to 3 0 V The set of spectra obtamed 1s shown m Fig 8 The most obvious feature of the results IS the clearly defined mverslon of the spectra which 1s observed when the electrode potential 1s made progressively more negative The amplitude of the PMR signal passes through zero at about - 0 4 V us Hg/Hg, SO,, and then increases rapidly again at more negative potentials The mverslon of the spectrum 1s clear evidence for a reversal of the electric field m the film If the oxide behaves as a semiconductor, then it follows that the inverted spectrum recorded at -0 6 V corresponds to accumulation condltlons Figure 8 shows that the spectral hneshape 1s mdependent of potential and therefore the ARfR signal at the low energy peak (342 nm) was recorded as the potential was swept at 5 mV s-I from 3 0 to -0 5 V This measurement IS contrasted in Fig 9 with the
I
I
300
I
350
I
kO0
wavelength/m
Fig 8 Set of AR,fR spectra for a film grown to 3 0 V us Hg/Hg,SO, and then measured at successwelvlower ootenhis Moduiatlon 1OOmVp-p s-polansed light Ndte the mverslon of the spectrum as the potential passes through flatband
correspondmg capacitance data m the form of a Mott-Schottky plot The ddl’iculty associated with the determmatlon of the flat band potential from capacltance data 1s evident, the Mott-Schottky plot IS nonlinear and consequently the intercept on the potential axis 1s unreliable In any case, for such a highly doped oxide with a large relative permlttmty, a substantial correction to the intercept 1srequired m order to allow for the Helmholtz capacltance[23] By contrast, the AR/R signal gwes a direct measure of the electnc field m the oxide, and the point of inversion pinpoints the flatband at -0 37 V us Hg/Hg,SO, without the need for a correction term (it is also not necessary to make any assumptions about the potential independence of the Helmholtz capacitance) The potential dependence of AR/R in Fig 9 contrasts sharply with the behavlour expected for lowfield depletion layer electroreflectance m semi-infinite samples, where A R/R 1s independent of bias It can be shown that this difference arises from the contnbutlon to R of light which has been reflected at the oxide-metal boundary It is reasonable to assume that the space charge regon no longer extends to the metal interface when the potential 1s reduced below the ongmal anodlc hmtt of the growth sweep, so that the
Potential modulated reflectance spectroscopy
1079
30 -30
103AR/R 20-20
-1 o-1 0
I
I
I
0
10
20
pohtlalbolts
vs Hg/Hg#O&
30
Fig 9 Recordmg of AR/R durmg a potential scan at 5 mV s- 1 showmg mverslon at -0 37 V The film was grown mltlally to 30V vs see and the potential was swept subsequently m the negative dIrectIon Wavelength 342 nm, s-polansed hght The figure also shows capacitance. data for the same film m the form of a Mot&Schottky plot (circles and broken line)
The change in A12r on the other hand, depends on the surface field, Es, which m the case of a depletion layer
IS gven by Es= -(2A4qN&,)1’2 The change m f,, IS given by
7%
At,,=
E 1x1
AA2 (4
It 1s readily shown from equations (5) and (6) that the modulation of P,, depends only on the amplitude of the modulation, but not on the dc bias The effect of the electric field on exp (-IS) has been derived by Nonomura et al Using the identity
/ d
metal
w oxide
0
solubon
Rg 10 Electric field dlstnbutlon m the oxide film at potentials lower than the anochc growth hnut Under these condotlons, the space charge remon no longer extends to the metal and the reflectance pz23at the metal-o,xlde boundary IS not perturbed by the modulation The hnear field profile shown m the figure corresponds to a homogeneous donor dlstrlbutlon
electric field dlstnbutlon m the system IS as shown m Fig 10 The perturbation of the reflectance can be seen by reference to equation (l), F,, and 6 will both be affected by the field-induced changes m A,, but P,,, on the other hand will remam unchanged smce the perturbation of A2 1s restricted to x < W, the width of the space charge region This situation 1s very similar to the case of back wall electroreflectance m amorphous silicon devices that has been discussed by Nonomura et al [7], except that we are dealing with a depleted ntype semiconductor rather than an msulator The perturbation of A, depends quadratically on the local field, E(x), so that we may write AA,={B(I)+C(1)}AE2
+fi2J2
(4)
y2 =exp (-t6),
(7)
they show that Ay2 o(4n/L)y2jAA2(x)dx (8) In the abrupt depletion approxlmatlon, we can assume that the electric field 1s a linear function of distance as shown m Fig 10, and after some algebraic mampulatlon we obtain Ay2x(4n/l)y2[(2qN&,)1’2A@‘26Aqi] IW)+C(W, (9) where SA4 1s the ac modulation amplitude Equation (9) shows that AR/R should depend on the square root of the band bending A4 as well as linearly on modulatlon amplitude SA4 It follows from the preceding dlscusslon that both contrlbutIons to the modulated reflectance should scale linearly with SA& but that only the term assoclated with light transmitted through the oxide varies with A4 In the present case, the potential dependence of AR/R shows that this second contnbutlon IS doml-
1080
D J
BLACKWOOD and L A4 PETER
dance measurements of passive metal systems Further work 1s needed, however, to clanfy the mechamsms involved m reflectance modulation m mdlvldual cases Acknowledgements-This work was supported by the Snence. and Engmeermg Research Councd under the CASE scheme and by the United Kmgdom Atomic Energy Authonty Hanvell Laboratory as part of the Underlying Science. Programme The authors are grateful to Prof David Wllhams for encouragement and support
REFERENCES
Fig 11 Plot of (AR/R)* us potential (data taken from Ra 9) The nlot shows that the modulation of the reflectance ISzoommat& by electro-absorption and that the contnbutlon from modulation of P,, at the solutlon-oxlde boundary IS small
nant me we are dealing wtth an electroabsorptton effect[3, 7, 83 Figure 11 shows that a plot of (AR/R)* agamst
electrode potential 1s approximately linear as would mdeed be expected if electroabsorptlon predommates, the intercept on the potential axis corresponds to the flat band potential The curvature of the plot 1s comparable to that observed m the Mott-Schottky plot shown m Fig 9 and the ongm of the curvature may well be the same m both cases, namely a nonhomogeneous donor dlstnbutton or contnbutlons from deep levels The observation that the inverted AR/R spectrum m the accumulation regime 1s similar m shape to the spectra dlscussed above suggests that the effects of the non-urnform field[l4, IS] are of secondary Importance, probably because the films studled here are thm
CONCLUSIONS The PMR results presented m this paper illustrate the power of the method for the exammatlon of the potential dlstnbutlon m metal-oxlde-solutlon systems It ISclear that interpretation of the PMR spectra must be made wlthm the framework of the three layer model, and the analysis 1s only possible d reliable values of the optical constants of the system are available PMR spectroscopy therefore forms a useful adjunct to spectroscopic ellipsometry and to UCimpe-
J F McAleer and L M Peter, Faraday Dtsc R Sot Chem 70, 67 (1980) D J Blackwood and L M Peter, Electrocham Actn, m press A Frova,P J BoddyandY S Chen, Phys Rev 157,700 (1967) W Paatsch, Ber Bunsenges phys Chem 79,922 (1975) G Blondeau, M Froehhcher, V Jovanclcevlc and A Hugot-Le Gaff, Su$ SCI 80, 151 (1979) M Fr&hhcher, A Hugot-Le Goff aid V .Jovanacevlc, Z’hmSoled Fzlms 82. 81 (1981) S Nonomura, H (!lkamoto ind Y Hamakawa, Appl Phys A32, 31 (1983) Y Hamakawa, m SemIconductors and Semrmetals, Vol 21, Part B (Edited by J I Parkove), _ p 141, Academic Press, New ‘York (1984) 9 B J Holden and F G Ullman. .I electrochem Sot 116. 280 (1969) 10 A Frova and P Mlghorato, Appl Phys Lett 13, 328 (1968)
11 A Frova and P Mlghorato, Appl Phys L.&t 15, 406 (1969) 12 C G Mathews, J L Ord and W P Wang, J electrothem Sot 130,285 (1983) 13 B 0 Seraphim, m Optical Properties ofSobds (Edited by F Abeles), p 163, North Holland, Amsterdam (1972) 14 D E Aspnes, m Optical Properttes of Sohds New DewE opments (Edited by B 0 Seraphim), p 799, North Holland, Amsterdam (1976) 15 D E Aspnes, m Handbook on Semiconductors, Vol 2 (Edlted by M BalkanskI), p 110, North Holland, Amsterdam (1980) 16 A Hamnett, L M Abrantes, R Peat and L M Peter, Ber Bunsenges phys Chem 91, 369 (1987) 17 S P Brown and L M Peter, m preparation 18 D J Blackwood, R Greef and L M Peter, Electrochzm Acta 34, 875 (1989)
19 K Vos and H J Krusemeyer, J Phys C Soled St Phys lo,3893 (1977) 20 K Vos, J Phys C Sobd St Phys 10, 3917 (1977) 21 A Gagnalre and J Joseph, J Phys 44, ClO, Suppl 12, 195 (1983) 22 J Joseph and A Gagnalre, Zlun Solid F11ms 103, 257 (1983) 23 B Pettmger, H R Schoppel and H Genscher, Ber Bunsenges phys Chem 7&I,450 (1967)
00134646,?W E300+0.00 Q 1990 Pcrgamon Press pk.
POTENTIAL MODULATED REFLECTANCE SPECTROSCOPY OF ANODIC OXIDE FILMS ON TITANIUM D J BLACKWOOD and L M PETER Department of Chemistry, Umverslty of Southampton, Southampton SO9 5NH, U K (Recewed 10 May 1989, m rewedfirm
I September 1989)
Ahtract-Potential modulated reflectance (PMR) spectroscopy has been used to mvestlgate thm anodlc oxide films formed on tltamum m sulphunc acid The ongm of the reflectance modulation ISdlscussed and the expenmental results are compared with theoretlcal calculations based on the three layer model The overall shape and the dependence of the PMR spectra on film thickness have been modelled satlsfactonly by assummg that the band gap of the oxide m the presence of an electric field IS Increased due to dlelectnc polarlsatlon The potential dependence of the modulated reflectance response for films of constant thickness was related to the electric field dlstrlbutlon m the oxide and the analysis showed that the modulated reflectance response 1s dominated by electroabsorptlon The results demonstrate that PMR spectroscopy offers a more reliable method than Mott-Schottky plots for determining the flat-band potential of the oxide
INTRODUCTION
mterest m the solid state properties of the anodlc oxide on titanium since It can protect the underlying metal m a variety of corrosive envlronments It 1s generally supposed that the anodlc film behaves as a highly doped n-type semiconductor layer, but the photocurrent and impedance behavlour mdlcate the presence of a non-uniform dlstrlbutlon of defect states which cause slgmficant departures from the simple behavlour associated with bulk semlconductor electrodes[l, 21 Non-linear Mott-Schottky plots of reciprocal square capacitance us potential are commonly observed, so that it 1s not possible to determine reliable values of the donor density N, or of the flat-band potential E,, Smce recombmatlon effects displace the photocurrent onset potential away from flat-band, E,, 1s not readily accessible from photocurrent measurements either In view of these comphcatlons, we chose to use potential modulated reflectance (PMR) spectroscopy to obtain an mdependent estimate of E,, and to characterlse the the potential dlstrlbutlon m the oxide films The technique 1s often referred to as electrolyte electroreflectance (EER), but we use the more general term PMR since effects other than electric field modulation of the optical constants may be mvolved m the case of thm anodlc films The first PMR study of anodlc oxide films on titanium appears to have been carried out by Frova et al [3] as part of a detailed mvestlgatlon of the optical constants of rutde These authors observed very large modulation effects which they attributed to electroabsorption Later, Paatsch[ll] used PMR and photopotential spectroscopy to study the electrochemical propertles of titanium, and more recently Blondeau et al [S] and Froehhcher et al [6] have used PMR to investigate the optical properties of the three layer system formed by anodised titanium m aqueous solution The authors of[S, 61 concluded that “mterference effects” can lead to substantial differences between the modulated spectra of bulk materials and
There ts considerable
of thm films on metallic substrates The importance of “back wall reflectlon” has also been recogmsed by Nonomura et al [7] and Hamakawa[8] m their work on amorphous skcon, where the modulation spectra are dominated by the effects of electroabsorptlon on light reflected at the rear contact The interpretation of the PMR spectra of anodlc films ISa controversial area In the case of anodlc films on tantalum, for example, Holden and Ullman[9] have attnbuted the spectra to modulation of the film thickness by electrostrlctlon However, this mterpretatlon has been disputed by Frova and Mlghorato[lO, 111, who consider that the spectra anse from the second order electrooptlc effect, te from the modulatlon of the refractive mdex of the oxide film by the electnc field In fact, It 1s possible that the two effects are coupled, and indeed Matthews et ~I[121 have interpreted elhpsometrlc measurements of the same system as evidence that the electrostrlctlve effect 1s accompanied by a correspondmg change m refractive mdex These authors concluded that the relative changes of the thickness and refractive mdex are similar in magmtude (about 0 5% for a field of 4 x lo6 V cm-‘) The theoretical background of electroreflectance (EER) spectroscopy has been discussed extensively m the hterature[l3-151, and spectra have been obtamed for a wide range of single crystal semiconductors and msulators Aspnes[lS] has shown that under certain low field condltlons, electroreflectance spectra correspond to the third denvatlve of the optical drelectnc constant The spectral hneshape then becomes mdependent of applied potential bias, and under depletion condltlons the EER signal scales linearly with the amplitude of the potential modulation Frequent and often uncntlcal use has been made of the low field electroreflectance theory derived by Aspnes, but even m the case of single crystal semiconductors, It 1s clear that It only applies under a relatively narrow set of condltlons[16] In the case of a thm oxide film on a reflecting metal substrate, the sltuatlon 1s more complicated smce the PMR signal contams a contnbutlon from light that has been reflected at the oxide-metal
1073
D J BLACKWOODand L M PETER
1074
AR /R
I
I
300
350
100
wavelength/nm
Fig 1 PMR spectra obtamed from an oxide film grown on tltamum at 10 mV s-l to 3 0 V us Hg/Hg,SO, m 3 0 mol drn-j H$O, at room temperature (dc potential 3 0 V, (ICmodulation 270 Hz, 100 mV p-p)
boundary Near the band edge, we may expect electroabsorption to be the dommant modulation mechanism In addition, however, modulation of the optical constants and field induced changes m film thickness (electrostnction) may give nse to interference effects which appear at other photon energes m the PMR spectrum It 1sclear that the mterpretatlon of modulated reflectance spectra requires formulation of the reflectance problem wlthm the framework of the three layer model as well as a physical model for the perturbation mechanism In this paper, we discuss PMR spectra obtained for thin (c 30 nm) oxide films on titanium The dependence of the PMR spectra on film thickness and on electrode potential has been mvestlgated, and the data are related to Impedance measurements made under the same condltlons The PMR results are interpreted within the framework of theoretlcal calculations based on the three layer model EXPERIMENTAL Titanium electrodes were prepared from sections of Johnson Matthey ‘Specpure’ grade tltanmm rod sealed m glass synnge pistons with epoxy resin The exposed surfaces were pohshed to a mirror finish on successively finer grades of alumma slurry, and the electrodes were Inserted through a syringe barrel mounted on a glass cell, allowmg accurate posltlonmg m the incident monochromatic light beam which entered the cell through a quartz window at an angle of incidence of 45” A 150 W xenon lamp and a computer controlled dlffractlon grating monochromator were used to provide mcldent dlummatlon over the spectral range 250-500 nm, and the polansatlon of
the mcldent beam was selected by a Glan-Thompson polarlser Filters were used where necessary to remove stray and harmonic hght The specularly reflected beam was focused onto a photomultlpher tube and the output was fed uzu an autorangmg current amplrfier to a lock-m amplifier mterfaced to a mlcrocomputer Data acqmsltlon, signal averagmg and ratlomg were carried out under software control by the computer The electrode potential was controlled by an operatlonal amplifier potentlostat, and spectra were recorded using square wave modulation, usually at 270 Hz All potentials are referred to the Hg/Hg,SO,/K,SO, (sat) electrode It has been established that the properties of the anodlc oxide on titanium depend on the rate at which the film IS formed[20], films grown potentlodynamltally at low sweep rates appear to be less defective than those formed at higher sweep rates, and there 1s evidence that crystalline areas with preferred onentatlon may be formedC21-J For this reason, we chose to grow all films for the PMR study at a sweep rate of 10 mVs-’ RESULTS AND DISCUSSION Figure 1 shows PMR spectra measured with s-and p-polansed light for an anodlc oxide film which was grown by a linear sweep to a final potential of 3 0 V and then held at the anodlc limit The amplitude and hneshape of the spectra were found to be independent of the modulatton frequency over the range 27 Hz to 2 7 kHz, indicating that the effect 1s not associated with Faradalc processes (by contrast, PMR spectra recorded for anodlc films on iron, for example, show a characterlstlc frequency dlsperslon which 1s related to
Potential modulated reflectance spectroscopy
1075
I>
lo3 ARA n-
mcdulatlon/Vp_p Fig 2 Dependence of AR/R on ac modulation amphtude Measurements made with s-polansed light at 342 nm for a film grown to 3 0 V us Hg/Hg,SO, (frequency 270 Hz, dc potential 3 0 V) changes brought about by charge transfer[ 173) Spectra were recorded for modulation amplitudes between 100 and 500 mV pp and were found to scale hnearly with the amplitude of the ac modulation as shown tn Fig 2 Lmearlty of this kmd 1s predicted by the Aspnes theory of Schottky barrier electroreflectance m the low field hmlt[15], and the results shown m Fig 2 could be taken to indicate that the low field electro-reflectance crlterta are satisfied and that the electric field dlstrrbutlon corresponds to a Schottky barrier configuration However, neither of these conclusions 1s appropriate m the present case Firstly, the electric field Imposed by the dc potential at the anodlc limit 1s high, smce the oxide IS formed by field assisted ion mlgratlon The anodlsmg ratio for titanium m H,SO, 1s 2 5 nm V- ’ at room temperature[18], so that it follows that the average electric field at the anodlc hmlt 1s of the order of 4 x lo6 V cm- ’ Even d the potential 1s reduced subsequently so that the electnc field 1sdetermined by the space charge (see below), the Schottky model may not apply since the donor distribution 1s not uniform and deep donor states may be important The spectra shown m Fig 1 are relatively broad and they appear to correspond to a first derlvatlve lmeshape function In this respect, they are slmdar to the electroreflectance spectra reported for stngle crystal rutlle by Vos and Krusemeyer[19] Vos[20] has dlscussed the band structure of rutlle and has concluded that the broad features m the electro-reflectance spectra are not associated with lifetime broadened transltlons at critical points m the Joint density of states function, but rather from changes m the band energies arising from dlelectrlc polarlsatton of the rutde lattice This conclusion 1s borne out by the observation that the line width changes httle with temperature down to 80 K Vos has shown that the electroreflectance spectra correspond qmte closely to the wavelength or energy denvatlve of the complex dlelectrlc function, with the mam structure m the spectrum centred at about 300 nm, although some additional osallations, particularly at lower photon energies, appear to anse from the Franz-Keldysh effect In view of the uncertamty concermng the mechamsm of the PMR effect, calculations were carned out using two different theoretical models The reflection coefficient of the metal surface covered with a film of
stcnch~ometrlc
thickness d with a complex refractive mdex A, IS given
by
f= f12+f23 ev(-4 1 +P,,D,, exp(-16)’
where 6 = 4lrdA, cos F12 and
6, ,
(14
(1’4
F,, are the Fresnel coefficients of the solution-o_xlde and oxide-metal interfaces respectlvely and & 1s the complex angle of refractlon at the solution oxide mterface In the case of the anodlc oxide film on tltamum, the film thickness, d, IS determmed by the formation voltage, and under the condltlons of the present expenments, the anodlsmg ratlo was 2 5 nmV-‘[20] Gagnalre and Joseph[Zl, 223 have reported data for the optical constants of titanium and of Its anodlc oxide determined by spectroscopic elhpsometry The energy dependence of the real and lmagmary components of the optlcal dielectric constant of the oxlde[22] 1s similar to that derived by Vos and Krusemeyer[19] for smgle crystal rutde by Kramers Kromg analysis of reflectance spectra The data given m[21] were used to compute reflectance spectra (R = )EZI) from equatton (1) for s- and p-polansed hght at 45” Incidence, and Fig 3 compares the reflectlvlty of the bare tltamum surface with the reflectance of an electrode covered by a thm oxide film It can be seen that the presence of the oxide leads to the appearance of a mmlmum m the reflectance signal at around 320 nm, the effect 1s particularly marked m the case of s-polarised light It ISclear from this figure, that small perturbations of the optlcal constants or of the film thickness are likely to have a large effect on the normahsed dlfferentlal reflectance AR/R m this wavelength region We consider next that the reflectance could be perturbed by an applied ac voltage m one of two different ways Firstly, the thickness of the oxide film may change due to the electrostrlctlve effect Secondly, the complex optlcal dlelectrlc constant may be perturbed m the presence of the electric field, this 1s the electrooptlc effect These effects have been discussed widely m the hterature[9-151, but conclusive proof of the apphcablhty of any particular model IS lackmg m the case of thm dlelectrlc films on metal substrates For this reason model calculations were performed for the two hmltmg cases
D J BLACKWOOD and L M PETER
1076
lo
I-
a sp____
a
s-
polarlsec
4 c------I’
p-_-
polartse
--__----________
,I’
/’
I’
Aq/R
o;:J _----------_/-----___
200
_
*I
A’
I
300
400
wavelength/nm
I
500
200
300
I
400
500
wavelength/nm
Fig 3 Reflectance spectra calculated from the data m[21] (a) bare tltamum surface, (b) tltamum covered with a 10 nm oxide film Note m (b) the appearance of a minImum m the reflectance at around 320 nm
Fig 4 PMR spectra calculated from equation (1) by assuming that the oxide film thickness 1sincreased by the electnc field (electrostnctlon effect) Oxide film tluckness (a) 7 5 nm,
The calculation of the perturbation due to the electrostrlctlve effect IS relatively straightforward It 1s assumed that the only term m equation 1 affected by the electric field 1sthe film thickness, d Figure 4 shows examples of theoretlcal spectra derived by assummg that only electrostrlctlon effects are important For the purposes of the calculation, it was assumed that the film thickness was mcreased by the modulating field smce the work of Matthews et al [12] has suggested that this 1s the case for several other oxide films The results of the model calculations presented m Fig 4 show that the A R/R spectra assume a first derivative form only when the film thickness exceeds a cntical value, whereas spectra for thmner films display monopolar bands for both s- and p-polansed hght In this respect, the model fads to predict the experimental behavlour since first derlvatlve spectra were obtamed even for the thmnest oxide films studled In addltlon, the computed A R/R spectra are inverted with respect to those observed expenmentally, so that even If the vahdlty of the model were accepted, it would be necessary to assume that the film thickness decreases rather than increases m the presence of an electnc field On the strength of this comparison, It was concluded that the electrostrictrve effect IS not responsible for the observed PMR spectra The denvatlon of theoretical spectra resulting from perturbation of the optical constants of the oxide 1s less straightforward The low field Aspnes model 1s clearly not apphcable, and the theory developed by Vos[20] for smgle crystal rutde was therefore taken as a startmg point Vos has argued convmcmgly that the broad first derlvatlve features m the electroreflectance spectra of rutlle arlse from perturbation of the energy
bands as the result of dlelectnc polansatlon of the lattice rather than from lifetime broadened Franz-Keldysh oscdlations as proposed by Frova et al [3] The effect proposed by Vos arises from a lowering of crystal symmetry which results m the breaking of optical selectlon rules or, at a more fundamental level, m changes of the optlcal matrix elements for mterband transltlons The polarlsatlon induced blrefrmgence of ferroelectncs with the perovsklte structure 1s well established, and It appears that T10, behaves similarly The theory mdlcates that the lowest energy oscdlator moves towards higher energies by an amount proportional to the square of the macroscopic polarlsatlon P Vos[20] has performed LCAO calculations of the band structure of rutlle and used the results to derive the elements of the polarisatlon potential tensor for optical transltlons The agreement with experlmentally derived shifts m the optical transltlons ISvery satafactory, and It seems reasonable to suppose that the model IS also appropnate for anodlc films, although the oxide 1s polycrystalline m this case so that much of the fine structure may be lost The shift m transitIon energies proposed by Vos leads to modulated spectra which correspond closely to the energy derivative of the optical dtelectnc constant We therefore used the data of Gagnaire and Joseph[21] to derive theoretlcal PMR spectra for the anodlc oxide by numerical dlfferentiatlon The electnc field was taken to be constant throughout the film so that n, 1s not a function of posltlon (but see below for further discussion of this pomt) Figure 5 shows examples of calculated PMR spectra which can be compared with the experlmental spectra m Fig 1 Two
(b) 12 5 nm Angle of mcldence 45”
Potential modulated reflectance spectroscopy
1077
38
p _____
polarlsed
hv/eV
36-
t
3b-
AR/R
32-
I
boo 300 uavelength/nm Rg 5 PMR spectra calculated from eqn 1 by assummg that the band gap energy ISIncreased m the presence of an electric field Oxide film thickness (a) 7 5 nm, (b) 12 5 nm Angie of
3 0. 0
5
10 15 20 film thlckness/nm
I 25
Rg 6 Dependence of the posItIon of the low energy maxlmum m AR/R on oxide ttnckness for s-polansed hght Open cwcles calculated by assummg modulation of band gap energy Closed cncles experlmental pomts
mcldence 45 D
important facts emerge from the calculations Firstly, the computed spectra exhibit a first derlvatlve shape even for the thmnest films Secondly, the amplitude of the AR/R signal passes through a maxlmum as the film thickness 1s mcreased The spectra computed on the basis of the Vos model appear to be more m accord with experlmental results than those derived by consldermg electrostnctlve effects The theoretical spectra predict a marked dependence of the location and amplitude of the peaks on oxide thickness which IS contrasted with experimental results m Figs 6 and 7 The occurrence of a maxlmum m the plot of AR/R us film thickness may appear surpnsmg at first The orlgm of the maxlmum becomes clear from an mspectlon of Fig 2, the reflectlvlty of the oxide covered metal falls to extraordmanly low values m the region where the PMR spectra are observed, and the maximum m AR/R as a function of film thickness corresponds to a mmlmum m the reflectlvlty Figure 6 and 7 show that the calculations based on the Vos model are m semiquantltatlve agreement with the experimental spectra The deviations between theory and experiment probably anse m part from the fact that the optical constants of the oxide depend on the way m which the film is formed In addition, the low reflectlvlty of the three layer system 1slikely to lead to large errors m the amplitude of the normahsed AR/R signal from scattered hght, depressing the maxlmum in AR/R It 1s also posstble that electrostrlctlve effects may make a minor contrlbutlon to AR/R The experimental spectra m Fig 1 were measured under high field condrtlons correspondmg to the
103AR/R
-
6-
fdm thwkness/mn
Fig 7 Dependence of amphtude of the energy maxImum m AR/R on oxide film tlnckness for s-polansed hght Open circles calculated by assummg modulation of the bandgap energy Closed circles expenmental pomts
anodlc hmlt m the growth sweep It 1s reasonable to assume that the electnc field extends throughout the oxide to the metal mterface under these arcumstances, but it 1s probably not constant, however, smce there IS
1078
D J BLACKWOOD and L M PETER
good evidence from capacitance measurements that the oxide behaves as a hrghly doped n-type semlconductor Whereas at the anodlc limit, the space charge repon must extend to the metal m order to facilitate ion migration, it will collapse at lower potentials, leaving a field-free region This will happen when the Schottky length, W, which ts given by W=(2A&c,/qN,)“Z,
(2)
becomes smaller than the film thickness If the oxide 1s homogeneously doped, the donor density and flatband potential can m prmclple be obtained by plotting the inverse capacitance against potential according to the Mott-Schottky equation C-‘=(2/qs&,N,)(A+kT/q)
(3)
In the application of equation (3), it 1s normally assumed that the Helmholtz capacitance, which appears m senes with the space charge capacitance C,,, IS constant, so that a linear dependence of the inverse square of the total measured capacitance is obtamed In the case of anodlc oxide films on titanium, however, Mott-Schottky plots are nonhnear[2], so that the donor density can only be estimated by taking tangent approxlmatlons At the same time, the curvature of the plots makes it difficult to determine the flat-band potential by extrapolation There are several possible reasons for the observed behavlour For example, the curvature could anse from a non uniform donor datnbutlon, with the donor profile falling from a high value at the metal-oxlde interface towards a lower value at the oxide-solution interface Alternatively, the donors may be &stnbuted m energy below the conduction band, so that they become progressively lomsed as the Fermi level moves down through the band gap with increasing potential Finally, the assumption that the Helmholtz capacitance 1s mdependent of potential can be questloned If electromc or lomc charge ts stored at defects at the oxide-solution interface, the Helmholtz capacitance 1s likely to be potential dependent by analogy with metal surfaces It 1s therefore essential to have some independent measure of the potential dlstnbutlon m the system, the PMR response 1s ideal m this respect, since It 1s sensltlve to the electnc field m the oxide phase PMR spectra were recorded as a function of potential for a titanium electrode on which the oxide film was formed initially by sweepmg the potential to 3 0 V The set of spectra obtamed 1s shown m Fig 8 The most obvious feature of the results IS the clearly defined mverslon of the spectra which 1s observed when the electrode potential 1s made progressively more negative The amplitude of the PMR signal passes through zero at about - 0 4 V us Hg/Hg, SO,, and then increases rapidly again at more negative potentials The mverslon of the spectrum 1s clear evidence for a reversal of the electric field m the film If the oxide behaves as a semiconductor, then it follows that the inverted spectrum recorded at -0 6 V corresponds to accumulation condltlons Figure 8 shows that the spectral hneshape 1s mdependent of potential and therefore the ARfR signal at the low energy peak (342 nm) was recorded as the potential was swept at 5 mV s-I from 3 0 to -0 5 V This measurement IS contrasted in Fig 9 with the
I
I
300
I
350
I
kO0
wavelength/m
Fig 8 Set of AR,fR spectra for a film grown to 3 0 V us Hg/Hg,SO, and then measured at successwelvlower ootenhis Moduiatlon 1OOmVp-p s-polansed light Ndte the mverslon of the spectrum as the potential passes through flatband
correspondmg capacitance data m the form of a Mott-Schottky plot The ddl’iculty associated with the determmatlon of the flat band potential from capacltance data 1s evident, the Mott-Schottky plot IS nonlinear and consequently the intercept on the potential axis 1s unreliable In any case, for such a highly doped oxide with a large relative permlttmty, a substantial correction to the intercept 1srequired m order to allow for the Helmholtz capacltance[23] By contrast, the AR/R signal gwes a direct measure of the electnc field m the oxide, and the point of inversion pinpoints the flatband at -0 37 V us Hg/Hg,SO, without the need for a correction term (it is also not necessary to make any assumptions about the potential independence of the Helmholtz capacitance) The potential dependence of AR/R in Fig 9 contrasts sharply with the behavlour expected for lowfield depletion layer electroreflectance m semi-infinite samples, where A R/R 1s independent of bias It can be shown that this difference arises from the contnbutlon to R of light which has been reflected at the oxide-metal boundary It is reasonable to assume that the space charge regon no longer extends to the metal interface when the potential 1s reduced below the ongmal anodlc hmtt of the growth sweep, so that the
Potential modulated reflectance spectroscopy
1079
30 -30
103AR/R 20-20
-1 o-1 0
I
I
I
0
10
20
pohtlalbolts
vs Hg/Hg#O&
30
Fig 9 Recordmg of AR/R durmg a potential scan at 5 mV s- 1 showmg mverslon at -0 37 V The film was grown mltlally to 30V vs see and the potential was swept subsequently m the negative dIrectIon Wavelength 342 nm, s-polansed hght The figure also shows capacitance. data for the same film m the form of a Mot&Schottky plot (circles and broken line)
The change in A12r on the other hand, depends on the surface field, Es, which m the case of a depletion layer
IS gven by Es= -(2A4qN&,)1’2 The change m f,, IS given by
7%
At,,=
E 1x1
AA2 (4
It 1s readily shown from equations (5) and (6) that the modulation of P,, depends only on the amplitude of the modulation, but not on the dc bias The effect of the electric field on exp (-IS) has been derived by Nonomura et al Using the identity
/ d
metal
w oxide
0
solubon
Rg 10 Electric field dlstnbutlon m the oxide film at potentials lower than the anochc growth hnut Under these condotlons, the space charge remon no longer extends to the metal and the reflectance pz23at the metal-o,xlde boundary IS not perturbed by the modulation The hnear field profile shown m the figure corresponds to a homogeneous donor dlstrlbutlon
electric field dlstnbutlon m the system IS as shown m Fig 10 The perturbation of the reflectance can be seen by reference to equation (l), F,, and 6 will both be affected by the field-induced changes m A,, but P,,, on the other hand will remam unchanged smce the perturbation of A2 1s restricted to x < W, the width of the space charge region This situation 1s very similar to the case of back wall electroreflectance m amorphous silicon devices that has been discussed by Nonomura et al [7], except that we are dealing with a depleted ntype semiconductor rather than an msulator The perturbation of A, depends quadratically on the local field, E(x), so that we may write AA,={B(I)+C(1)}AE2
+fi2J2
(4)
y2 =exp (-t6),
(7)
they show that Ay2 o(4n/L)y2jAA2(x)dx (8) In the abrupt depletion approxlmatlon, we can assume that the electric field 1s a linear function of distance as shown m Fig 10, and after some algebraic mampulatlon we obtain Ay2x(4n/l)y2[(2qN&,)1’2A@‘26Aqi] IW)+C(W, (9) where SA4 1s the ac modulation amplitude Equation (9) shows that AR/R should depend on the square root of the band bending A4 as well as linearly on modulatlon amplitude SA4 It follows from the preceding dlscusslon that both contrlbutIons to the modulated reflectance should scale linearly with SA& but that only the term assoclated with light transmitted through the oxide varies with A4 In the present case, the potential dependence of AR/R shows that this second contnbutlon IS doml-
1080
D J
BLACKWOOD and L A4 PETER
dance measurements of passive metal systems Further work 1s needed, however, to clanfy the mechamsms involved m reflectance modulation m mdlvldual cases Acknowledgements-This work was supported by the Snence. and Engmeermg Research Councd under the CASE scheme and by the United Kmgdom Atomic Energy Authonty Hanvell Laboratory as part of the Underlying Science. Programme The authors are grateful to Prof David Wllhams for encouragement and support
REFERENCES
Fig 11 Plot of (AR/R)* us potential (data taken from Ra 9) The nlot shows that the modulation of the reflectance ISzoommat& by electro-absorption and that the contnbutlon from modulation of P,, at the solutlon-oxlde boundary IS small
nant me we are dealing wtth an electroabsorptton effect[3, 7, 83 Figure 11 shows that a plot of (AR/R)* agamst
electrode potential 1s approximately linear as would mdeed be expected if electroabsorptlon predommates, the intercept on the potential axis corresponds to the flat band potential The curvature of the plot 1s comparable to that observed m the Mott-Schottky plot shown m Fig 9 and the ongm of the curvature may well be the same m both cases, namely a nonhomogeneous donor dlstnbutton or contnbutlons from deep levels The observation that the inverted AR/R spectrum m the accumulation regime 1s similar m shape to the spectra dlscussed above suggests that the effects of the non-urnform field[l4, IS] are of secondary Importance, probably because the films studled here are thm
CONCLUSIONS The PMR results presented m this paper illustrate the power of the method for the exammatlon of the potential dlstnbutlon m metal-oxlde-solutlon systems It ISclear that interpretation of the PMR spectra must be made wlthm the framework of the three layer model, and the analysis 1s only possible d reliable values of the optical constants of the system are available PMR spectroscopy therefore forms a useful adjunct to spectroscopic ellipsometry and to UCimpe-
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