2064
J. Phys. Chem. B 2006, 110, 2064-2073
Optical Analysis of the Light Emission from Porous Silicon: A Hybrid Polyatom Surface-Coupled Fluorophor James L. Gole* and Erling Veje School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
R. G. Egeberg Oersted Laboratory, Niels Bohr Institute, UniVersitetsparken 5, DK-2100 Copenhagan, Denmark
A. Ferreira da Silva and I. Pepe Instituto de Fisica, UniVersidade Federal da Bahia, 40210-340 SalVador, Bahia, Brazil
David A. Dixon*,§ Department of Chemistry, UniVersity of Alabama, Tuscaloosa, Alabama 35487-0336 ReceiVed: September 28, 2005; In Final Form: NoVember 30, 2005
The most extensive data set yet generated correlating photoluminescence excitation (PLE) and photoluminescence (PL) spectra is presented for aged (equilibrated) porous silicon (PS) samples. The observed features, which are temperature independent over the range 10-300 K, show a detailed correlation with the results of photoacoustic spectroscopy (PAS) and with molecular electronic structure calculations. The observed energy level patterns are reproduced in the photoabsorption (PA) of PS films released after the etching of a silicon wafer. It is concluded that the energy level pattern found for the photoluminescing surface of PS results from a structure which is neither uniquely molecule- or bulk-like but represents a hybrid form for which the density of states associated with a polyatomic vibrationally excited surface-bound fluorophor dominates the nature of the observed features which are not those of a semiconductor. These fluorophor features are broadened and shifted to lower excitation energy as a result of the intimate presence of the silicon surface to which the fluorophor is bound. The dominance of the surface-bound fluorophor accounts for the temperature-independent PLE and PL features. The observed spectral features are thus suggested to be the result of a strong synergistic interaction in which the silicon surface influences the location of surface-bound fluorophor excited states whereas the nature of the vibrationally excited surface-bound fluorophor coupling to the silicon surface provides the mechanism for an enhanced vibronic structure dominated interaction and energy transfer. The observed PLE, PL, PAS, and PA measurements are found to be consistent with previous photovoltaic and photoconductivity measurements, correlating well with a surface-bound oxyhydride-like emitter. This study suggests the important role that the overtone structure of a molecule bound to a surface can play as one forms a hybrid system.
Introduction High surface area, luminescent porous silicon (PS) has attracted considerable attention for its potential use in siliconbased optoelectronics and, to a lesser extent, sensors and displays.1 Here we combine the most extensive data generated to date, correlating photoluminescence excitation (PLE) and photoluminescence (PL) spectroscopy with the unique photoacoustic spectroscopy (PAS) and photoabsorption (PA) of PS, and with molecular electronic structure calculations, to focus on the nature of the PL from PS and suggest its origins. We have performed these experiments on equilibrated PS samples, all of which are formed in an aqueous etch process producing a nanoporous arrayed structure. * To whom correspondence should be addressed. E-mails: jim.gole@ physics.gatech.edu;
[email protected]. § Current address: Haldor Topsoe A/S, Nymollevej 55, DK-2800 Kgs Lyngby, Denmark.
The light-induced PL from PS has been associated with a variety of mechanisms, including emission from quantum confined silicon crystallites,2-6 surface localized states,7 surface confined defects,8,9 or surface confined molecular emitters.10-13 Stutzmann and co-workers have used the optical detection of magnetic resonance (ODMR) to establish that the PS “orangered” emission results from the excitation of a triplet exciton. Prokes14 et al. have suggested a source based on defect site localized oxyhydrides, having an Si-O core, as the origin of the red PL, following their high temperature heating and electron spin resonance studies. More recently, we have suggested a correlation with the manifold of electronic states associated with the silanone-based silicon oxyhydrides of the form OdSi(OH)-15,16 or OdSi(-OSiH3)- bound at the surface of the PS skeleton. We have suggested that changes in bonding associated with electronic transitions involving the silanonebased oxyhydride ground electronic and low-lying triplet states, especially in the SiO-related bonds, and the substantial shift to
10.1021/jp0555302 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/19/2006
Optical Analysis of the Light Emission from PS larger SiO internuclear distance of these excited electronic states relative to their ground states can be used to explain the observed character of the PL spectra. The excitation to a low-lying triplet state fluorophor, strongly bound to the surface of the PS substrate and whose effective potential is greatly shifted from the ground electronic state, does much to explain the significant red shift of the PL spectrum (550-900 nm, 2.25-1.38 eV) from the known absorption peak wavelength of the (PLE) excitation spectrum (∼350 nm, 3.54 eV).17 Furthermore, calculated IR spectra are in excellent agreement with experimental FTIR data.18 This brief introduction implies that controversy exists concerning the origin of the ubiquitous emission associated with PS. On one hand there is significant support for a model that indicates that the emission is associated with an inhomogeneous distribution of quantum confined crystallites (intrinsic) with which should be associated with a band gap and phonon-like structure. On the other hand equally convincing evidence has been obtained to indicate that the emission should be associated with surface-bound emitters or fluorophors. As the assignment of the PL rests with the ability to fit one or the other of these limiting models, the nature of the PL must be both correlated and contrasted with the variety of pore structures associated with PS.19-21 The electrochemical etching of silicon in a variety of electrolytes produces an intriguing multitude of sizes and shapes.19-21 Pore sizes can be made to vary21-29 from the 1-10 nm range to sizes of the order of 3 µm, and mixtures of two pore types are possible.30 Porous silicon formed from the HFbased etch of a silicon wafer is characterized by an extensive visible PL which, when excited by UV radiation, initially displays a time-dependent behavior resulting primarily from surface-based oxidation processes. However, within a time frame characteristic of the effective radiative lifetime of the emitter,31 the PL begins to equilibrate to a virtually constant emission localized largely to the orange-red spectral region. The development, enhancement, and evolution of this PL can be significantly influenced through the introduction of a variety of surface treatments with, for example, HCl31 or select dyes.32 For bulk crystalline semiconductors, the existence of a welldefined band gap is closely related to the long-range periodicity of atom ordering in a crystal, as the number of atoms experiencing the presence of a surface must be small in comparison to the number of atoms in the bulk. For such semiconductor materials, there is no distinction between the electrical band gap and the optical band gap. In contrast to this, PS is a highly disordered and inhomogeneous material where the ratio of surface to bulk atoms is quite large. Assigning a single value to a “band gap” energy is not a simple matter. In fact, Andersen and Veje33 have reported an average threshold of 1.59 eV for the PLE spectrum of aqueous etched silicon whereas the onset of photoexcitation across the electrical band gap has been found to be 1.80 eV for a similarly formed sample.34,35 Furthermore, the clear distinction between the optical and electrical band gaps of PS is also evidenced with a variable surface morphology. Whereas PS fabricated from aqueous electrolytes consists of highly nanoporous branched structures, PS fabricated from nonaqueous electrolytes is comprised of open and accessible microporous structures (p-micropores19) with deep, wide, wellordered channels.36 Taking advantage of this distinction, Gole et al.37 developed a procedure to form microporous structures with nanoporous sidewalls. These hybrid microporous/nanoporous structures display a dramatically different photovoltaic (PV)
J. Phys. Chem. B, Vol. 110, No. 5, 2006 2065 response versus either crystalline silicon or nanoporous PS generated using an aqueous etch procedure. Yet, the relative responses of the corresponding time-dependent photoluminescence from the aqueous and hybrid etched samples are found to be virtually identical. This suggests that the effective band gap for the distinctly different morphologies associated with the aqueous etched and hybrid etched samples, as manifest in the PV responsesa bulk characteristic, is not reflected in the observed photoluminescence from the aqueous or hybrid etched porous silicon samples. Whereas the results obtained in the PV study suggest a band gap of order 1.25 eV for the hybrid PS sample, what is most relevant is not whether the peak in the photovoltaic response is at 1.25 eV but that this response is (1) distinct from that of aqueous etched PS and (2) intermediate to that of aqueous etched PS and that of crystalline silicon. The fact that the PL response for both the aqueous and hybrid etched samples is virtually identical suggests that the photoluminescence, in contrast to the PV response, emanates from a surface localized source, virtually identical for both samples. It has been reported that the PL spectral distributions associated with various etch parameters can be tuned through a significant wavelength interval.1,38 However, it can be demonstrated that while samples may show somewhat different PL spectral distributions shortly after they have been produced,39,40 when stored in air at room temperature, they slowly change to a steady state or equilibrated distribution after aging for periods of a few months. The data we report thus result from the study of several samples which all have reached the same final PL spectral distribution with no sample-to-sample variations. All samples display a PL spectral distribution that extends from approximately 550 to 940 nm (2.25-1.32 eV) with a broad maximum near 700 nm (1.77 eV) (with correction for detector response).40 Realizing the need to equilibrate the PS, we have studied the optical emission and absorption properties of aqueous etched aged PS samples using an extensive correlation of photoluminescence excitation, photoluminescence, photoabsorption, and photoacoustic spectroscopies, and compared these results with those obtained from photovoltaic studies.33-35 The established energy level schemes can be correlated with the results of high level molecular electronic structure calculations in order to assign the observed energy level pattern with a hybrid emitter whose character is that of a bulk silicon perturbed surface-bound fluorophor. Experimental Section The samples used in this study were produced by etching boron-doped, (100) p-type, c-Si wafers electrochemically in aqueous hydrofluoric acid. Wafers with a wide range of resistivities from 0.02 to 30 Ω cm were studied. Over this range, the rate at which samples are etched decreases with increasing resistivity, and the morphologies of the PS surface are expected to differ. However, for the aqueous etch procedure used in these studies, the surface is dominated by random nanopores.1-10,19-21 The etching cell used in this study and the etch procedure are described in detail elsewhere.33-35 In addition to samples produced under different etching conditions, and for which the PS layer remained on the c-Si backing on which it had been grown, a number of PS films were released from their c-Si backings using established techniques41,42 and studied using PA spectroscopy. These films were grown under etching conditions similar to those for the ordinary samples. However, after the etching had been carried out, the current density through the electrolytic cell was increased to 600 mA/cm2 for 20-30 s and then turned down slowly and switched off. Using this approach,
2066 J. Phys. Chem. B, Vol. 110, No. 5, 2006 films with surface areas up to several mm2 were obtained. Samples, once formed, were stored and characterized at room temperature. All of these samples, despite the range of resistivities yielded a virtually identical equilibrated PL (quite distinct from that of SiO2). PLE, PL, and PA measurements were carried out at several sample temperatures between 10 and 300 K. Briefly, the detecting device consisted of a 1 m scanning monochromator (McPherson model 2051), with a ruled grating blazed at 1000 nm, and a photomultiplier (Hamamatsu model R943-02) used with a personal-computer-based single-photon counting technique or a germanium diode detector (North Coast model EO817L) used with lock-in detection. The overall quantum efficiency was determined as described elsewhere43 using a coiled-coil filament lamp standard of spectral irradiance (Optronic Laboratories model L-97). All spectrograms have been corrected for variation in quantum efficiency as a function of detection wavelength. The light source used for the PLE measurements was a stabilized 250 W filament lamp coupled to a 0.67 m scanning monochromator (McPherson model 207) with a grating blazed at 1000 nm. The resulting output photon fluence was measured versus wavelength with the quantum efficiency calibrated 1 m spectrometer. For all of the PLE spectra, data points were normalized to the same number of exciting photons. The experimental configuration for the PAS measurements44 consists of a periodically exciting light source, a photoacoustic cell containing the sample, and a microphone. An Osram 100 W halogen lamp was used as the light source as the output light was applied to a Jarrel Ash monochromator. The monochromatic light is modulated by an HMS 220 mechanical chopper, whose modulation frequency can be varied from 20 to 150 Hz. No glass optical elements, except for a thin window, are used between the light source and the sample, in order to minimize aberrations. The acoustic signal produced in the cell cavity by the sample is detected by a Sennheiser condenser microphone (model KE 4-211.2), preamplified by a homemade low-noise preamplifier and analyzed with respect to the modulator reference by a lock-in amplifier (ITHACO model 3961 B). The amplitude and the phase angle of the acoustic signal are recorded as the data acquisition system is connected to a personal computer. Results A. Approach to Data Analysis. The major results of this work are derived from the thresholds for photoabsorption-based processes. Therefore, we must use an appropriate approach to extract threshold energy level locations from experimental data sets. In all those measurements in which a signal was recorded versus the wavelength or photon energy of the illuminating light, a well-defined threshold was observed. Additional structures could be seen at higher illumination energies, indicating the opening of further excitation channels above the fundamental onset (i.e. where the signal rose above the background level). To determine the threshold excitation energy, the signal, corrected for background level, was simply extrapolated to its zero level, yielding the fundamental threshold energy. In almost all cases this could be done with small uncertainty (of the order of 10-20 meV); however, the extraction of the threshold energy positions of the illuminating light for higher-lying structures was more problematic. The additional signal, caused by the opening of a new channel, was superimposed on an underlying, smoothly varying signal. At such a threshold, the additional signal related to the opening of the new channel will be zero
Gole et al. for illumination energies below its onset and will, in a limited region above the onset, increase linearly with increasing photon energy. This will be manifest as an increase in the slope of the intensity curve, producing a kink at the onset in the curve. The threshold energy has been correlated with the position of the kink associated with this illuminating energy. This procedure has been applied, where the underlying smoothly varying signal has an unknown curve shape and also, in many cases, is large compared to the new, additional signal. This prohibits a safe subtraction of a smoothly varying underlying signal with the subsequent extrapolation to zero level of the new, additional signal. For the PAS data, this procedure was mandatory because the PAS spectrograms were unusually rich in structure which, on one hand, yielded significant supportive information and, on the other hand, complicated the extraction of information. This richness in structure results in slightly larger uncertainties for the PAS data than for PLE measurements. It is also necessary to consider possible corrections for phonon-assisted processes. For an ideal semiconductor with a direct band gap, a plot of the square root of the absorption coefficient is proportional to the difference between the photon energy and the band gap energy.45 For an ideal semiconductor with an indirect band gap, a plot of the square root of the absorption coefficient consists of two straight lines, one corresponding to absorption of a phonon and the other to emission of a phonon. In the present work, neither of these two behaviors was observed.46 Consequently, in our data treatment, no correction related to phonon assistance has been applied. B. Results from Correlated PLE, PL, and PA Measurements. The photoluminescence from an equilibrated sample has been shown to display a broad spectral distribution spanning the wavelength interval 550 (2.25 eV) to 940 nm (1.32 eV) and peaking (broad maximum) near 700 nm (1.77 eV). These broad spectral features do not extend to higher emission energies (shorter PL wavelengths) when the exciting light source is at 3.4 (nitrogen laser) or 5.0 eV (KrF laser) as the lower (1.32 eV) and upper (2.25 eV) PL emission energies manifest themselves repeatedly.1,15,33 This indicates a virtually invariant PL spectral distribution for energies above approximately 2.4 eV in agreement with a previous study15 of photoluminescence excitation (PLE) from 3.4 to 6.4 eV (ArF laser). Studies at several sample temperatures from 10 to 300 K yielded identical PL distributions, indicating that the PL spectra are temperature independent. In the present study, we have not observed either the previously reported infrared bands or spectral features at higher energies than 2.25 eV.47 Figure 1 maps the results from a number of characteristic PLE spectra in the vicinities of their respective fundamental thresholds. For excitation energies (PLE) below 1.59 eV (780 nm), no indication of PL is observed. However, excitation with a photon energy of 1.59 eV leads to PL emission energies extending across the interval 1.32-1.47 eV. From this, and the fact that the PLE process is dictated by the absorption from the lowest levels of the ground electronic state, it is deduced that the lowest-lying upper accessible PL-related level is 1.59 eV above the highest-occupied molecular orbital (HOMO) for the “ground state” of porous silicon. The minimum energy separation of 1.32 eV between the upper and lower PL-related levels suggests that the upper-most region of the terminal state to which emission occurs may be as much as 0.27 eV above the HOMO whereas the maximum emission energy of 1.47 eV suggests a change in ground or excited state energy such that the terminal lower state level could be as much as 0.12 eV above the HOMO
Optical Analysis of the Light Emission from PS
J. Phys. Chem. B, Vol. 110, No. 5, 2006 2067 TABLE 1: Photoabsorption Thresholds Predicted from the Energy Level Plots Shown in Figure 2, Which Are Based on the Correlation of PL and PLE Dataa
Figure 1. Characteristic PLE spectra of equilibrated PS plotted versus the illuminating light wavelength. To the right are listed detection wavelengths (nm) with the corresponding photon energies of the detected light (eV) given in parentheses. Different data sets are on different relative scales chosen for clarification of individual data points. The range of energy is from 2.25 eV (550 nm) to 1.46 eV (850 nm).
Figure 2. Threshold energy versus detection energy, as observed in PLE.
or the energy increment could reflect excited state structure. We suggest that the latter possibility is more likely. Figure 2 corresponds to a plot of threshold energy versus detection energy as observed in PLE for PS remaining on the c-Si backing from which it was produced. Besides the plateau at 1.59 eV as introduced and discussed above, two more plateaus are observed in Figure 2 at 1.72 eV and at 1.80 eV. For each of the three plateaus in threshold energy, the difference between the photon energy of the illuminating light (identical to the position of the plateau) and the highest observable detection energy is 0.12 eV. Thus, the highest detection energy attainable at each of the three plateaus in Figure 2, combined with the photon energy of the illuminating light in question, results consistently in an energy separation of 0.12 eV. For photon detection energies above 1.68 eV, no further plateaus have been found. Instead, as can be seen from Figure 2, the threshold energy increases monotonically for increasing detection energy. We interpret this result to indicate that, for excitation energies above 1.80 eV, the excitation takes place to a virtually continuous set of energy levels (density of states), the lower edge of which is situated 1.80 eV above the HOMO. It is worth noting that, in previous studies34,35 based on
predicted from PL and PLE data (Figure 2) (eV)
observed in PAS (eV)
1.32 ( 0.02 1.40 ( 0.02 1.47 ( 0.02 1.53 ( 0.02 1.59 ( 0.01 1.67 ( 0.01 1.72 ( 0.01 1.80 ( 0.01 1.96 ( 0.01 2.20 ( 0.01
1.32 ( 0.02 1.39 ( 0.02 1.44 ( 0.03 1.51 ( 0.02 1.60 ( 0.03 1.65 ( 0.03 1.73 ( 0.02 1.84 ( 0.03 2.00 ( 0.03 2.17 ( 0.03
a The second column presents corresponding data obtained with PAS. The lowest two rows yield absorption thresholds, first observed in PAS and confirmed using PLE. See text for discussion.
photoconductivity measurements, the “electrical band gap” energy of aqueous etched PS has been determined to be 1.80 eV, which is identical to the value given above, deduced from the PLE measurements. Thus, these previous studies34,35 and the present study agree on locating a conduction band edge at 1.80 eV above the HOMO, and, from the photoconductivity measurements, this band edge may well be identified as the lower edge of a conduction band-like structure. As noted above, the maximum photon energy detected in PL is 2.25 eV, independent of excitation energy. Thus, in Figure 2, the parameter plotted along the horizontal axis, the detection energy, is defined only for values below 2.25 eV, independent of the excitation energy (see also Figure 2 of reference 15). PLE measurements on transparent PS films were found to be in good agreement with those carried out on the PS remaining on the c-Si wafer. However, for the PS films, an additional plateau was seen at 1.67 eV. In Figure 2, for detection energies close to 1.7 eV, the difference between the threshold energy and the detection energy is 0.12 eV. However, for detection energies in the interval 1.72-1.82 eV, the difference between the threshold energy and detection energy increases slowly and steadily from 0.12 to 0.16 eV in this complex region, whereupon it remains 0.16 eV for detection energies above 1.82 eV. This is represented in Figure 2 as a straight line of slope unity, fit to the high-energy range of the data. It is apparent that the nature of the decay possibilities from the upper PL-related band changes gradually in the excitation energy region 1.82-1.98 eV. For energy sites above 1.98 eV, it is also clear that no emission to the lowest level of the lower PL-related band occurs as only those transitions can take place which access regions in the lower PL-related band situated more than 0.16 eV above the HOMO. As seen from Figure 2, this bottleneck manifests itself in a smooth and gradual shift rather than a sudden step. The PLE/PL measurements suggest that there are three levels above the HOMO which are directly accessed by electric dipole allowed photoabsorption from the HOMO. They are, respectively, 1.59, 1.67, and 1.72 eV above the HOMO. In addition, the conduction band edge is 1.80 eV above the HOMO. Not only does the excitation at 1.59 eV result in a PL emission red shifted by as much as 0.27 eV, but also this same overall relaxation with respect to the 1.67, 1.72, and 1.80 eV features results in three additional energy levels indicated in the first column of Table 1. These data are in reasonably good agreement with the initial results presented by Andersen and Veje,33 but the two data sets are not identical. The most likely reason for the difference is that, here, we study samples which have aged
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Figure 3. Relative absorption coefficient obtained (versus the wavelength of illuminating light) for a thin PS film. Arrows show onsets at 1.59 eV (779 nm) and 1.80 eV (688 nm). See text for discussion. The range of energy is from 2.07 eV (600 nm) to 1.38 eV (900 nm).
and equilibrated, whereas in the previous work,33 the samples were studied shortly after they were produced. The PLE data sets presented in Figure 2 and Table 1 considerably exceed the information obtained previously with PLE for a few detection energies.48-50 Especially, it is worth noting that the threshold for PLE is always found to be above the detection energy, and never very close to it, corresponding, in the plateau region, to a value of 0.12 eV. A further internal check of the data presented in Figure 2 was carried out using a He-Ne laser as a light source (1.96 eV). In this way, one single data point in Figure 2 could be checked. The agreement was within the overall uncertainty limits of 0.01 eV. We also carried out PA measurements on the PS films removed from the crystalline silicon surface. Since the thickness of the film was unknown, only the product of the film thickness and the absorption coefficient could be measured. This product is the relative absorption coefficient, and in Figure 3 it is plotted versus the wavelength of the incident light. Clearly, an onset for absorption is observed at 780 nm, corresponding to a photon energy of 1.59 eV, and this is identical to the value obtained for the sharp onset of PLE which correlates with excitation from the lowest “zero-point” level in the ground electronic state. Also, a kink is seen in the relative absorption at 690 nm, and the corresponding photon energy, 1.80 eV, equals the electrical band gap energy previously reported for aqueous etched PS.34,35 However, no additional structures could be observed using the PA measurements. Further PLE measurements were carried out, not only close to threshold but also at higher photon energies in a search for structure which might indicate the opening of some additional absorption channels. An example of such a PLE spectrum is shown in Figure 4, the data of which were recorded at a detection energy of 1.46 eV (850 nm). Besides the threshold located at 780 nm (1.59 eV), three discontinuities in slope can be seen, at excitation wavelengths of 742, 720, and 690 nm, corresponding to excitation photon energies of 1.67, 1.72, and 1.80 eV, respectively. These energies agree very well with those for transparent PS films and supported PS shown in Figure 2 and listed in Table 1, confirming the data in this figure. C. Results Obtained with PAS Measurements. Like PLEPL and PA, the PAS technique is based on photoabsorption, but the spectra result from the heat generated in the sample due to nonradiative photoabsorption processes. Thus, information concerning all possible absorption processes may be obtained, regardless of whether the absorption takes place to discrete shallow levels, surface bands with localized levels, or a
Figure 4. PLE signal obtained at a detection photon energy of 1.46 eV (850 nm) plotted versus the wavelength of the illuminating light. The data have been normalized to the photon fluence of the illuminating light. The arrows, extending to shorter wavelength, indicate inflections corresponding to energies of 1.59 eV (779 nm), 1.68 eV (738 nm), 1.72 eV (720 nm), and 1.80 eV (688 nm), respectively. See Table 1. The range of energy is from 2.07 eV (600 nm) to 1.55 eV (800 nm).
Figure 5. Typical PAS spectrum for a PS sample. The PAS signal is plotted versus the photon energy of the illuminating light.
conduction band of bulk nature with delocalized states. A signal will be generated as long as the level to which photoexcitation takes place has a radiationless deexcitation channel, which can generate sufficient heat to produce a measurable PAS signal. Figures 5 and 6 present two typical PAS spectrograms in which several spectral features can be seen. The data in Figure 6 differs in some respects from that presented by Silva et al.;51 however, the energy level structure is quite similar. It is important to note that these PAS spectra differ markedly in structure from similar spectra obtained for semiconductors of bulk type with their attendant band structure.44 For such materials, one sharp absorption onset is seen in the PAS spectra, the position of which corresponds to the band gap energy. Here, however, several absorption onsets are seen. This, in itself, demonstrates that PS possesses a more complicated multilevel
Optical Analysis of the Light Emission from PS
Figure 6. Extension of the PAS spectrum of Figure 5 for the same PS sample. The PAS signal is plotted versus the photon energy of the illuminating light.
energy structure indicative of a hybrid surface structure. The richness in structure of the PAS spectra can offer important information, but the extraction of this information can be hampered as the spectral structure is only partially resolved. From our PL- and PLE-based energy level data as summarized in Table 1, a total of eight absorption features are predicted for the PAS spectrum. The energy positions of these, as derived from the PLE results, are given in the first 8 rows of the first column in Table 1. From inspection of the PAS spectra, and by applying the data treatment procedure previously outlined, a total of eight corresponding features could be identified. They are given in the second column in Table 1. Note that the onset of the PAS spectrum, given in Figure 5, is at 1.32 eV (vs the 1.59 eV onset for PLE). There is very good agreement between the two data sets presented in Table 1. In addition, we emphasize that, in the energy region of interest, no features appear in the PAS spectra which cannot be correlated with the PLE-PL results. Thus, we believe that the PAS measurements have, in detail, confirmed the energy structure for PS deduced from the PL-correlated PLE study. Using PAS, some additional features were observed at (2.00 ( 0.03) eV and at (2.17 ( 0.03) eV. With this information, some of the PLE spectra were revisited and extended to higher excitation energies. An example is presented in Figure 7, where discontinuities in the slope of the curve are perceptible at (1.97 ( 0.01) eV and (2.19 ( 0.01) eV, in good agreement with the PAS data. Thus, both measurement techniques indicate some additional structure in the band systems of PS. In section B we showed that, for excitation energies between 1.82 and 1.98 eV, the difference between the detection energy and the corresponding excitation energy in PLE, as shown in Figure 2, increases steadily from 0.12 to 0.16 eV, indicating some modification of the upper PL-related band at 1.98 eV. This conforms well with the spectral structures seen in PAS at (2.00 ( 0.03) eV and in PLE at (1.97 ( 0.01) eV. D. Correlation with Molecular Electronic Structure Calculations. The extensive experimental data that we have obtained in this study and its correlation with previous studies suggests that the room temperature PL from porous silicon is not well represented by models that associate the PLE-PL correlations outlined in Figure 2 and Table 1 with an ideal semiconductor. To this end, we will suggest an alternate model, consistent with the temperature-independent nature of the PL and based, in part, on the density of states associated with a polyatomic surface-bound fluorophor as it interacts with the PS
J. Phys. Chem. B, Vol. 110, No. 5, 2006 2069
Figure 7. High-energy part of the PLE signal obtained at a detection photon energy of 1.49 eV (830 nm) is plotted versus the wavelength of the illuminating light. The data have been normalized to the photon fluence of the illuminating light. The arrows, extending to shorter wavelength, indicate inflections corresponding to 1.59 eV (779 nm), 1.80 eV (688 nm), 1.97 eV (629 nm), and 2.20 eV (563 nm), respectively. The range of energy is from 2.48 eV (500 nm) to 1.55 eV (800 nm).
surface. Here, we suggest that the source of the observed PL is a surface-bound fluorophor that, as it represents a surface-bound entity, is strongly coupled to the bulk silicon surface. The energy levels of this surface-bound fluorophor are temperature independent. The effect of the surface (as has long been known for diatomic molecules52) is not only to (1) broaden the infrared and electronic emission features but also (2) to induce a significant red shift of the strongly surface-bound polyatomic fluorophor’s electronic emission spectrum. We have carried out electronic structure calculations on several silicon (silanone)-based fluorophors at the molecular orbital theory and density functional theory levels. Our initial calculations focused on the structures of the ground state singlet and the lowest energy triplet as well as the adiabatic energy difference between the ground and excited state. The species RR′Si(dO) was used to represent a model for the binding of an -Si(dO)R chromophore to a PS surface. Subsequently, timedependent density-functional theory (TD-DFT)53 with a proper treatment of the asymptotic form of the B3LYP exchangecorrelation potential54 was used to predict vertical excitation energies for species of the form RR′Si(dO).55 Our most recent calculations55 provide the best available calculated values for the vertical excitation energies of the model chromophore in contrast to less accurate predictions of these energies.56 In our previous work,57 we optimized the geometries, calculated the vibrational frequencies (to guarantee that the geometries were indeed minima) at the MP2 level with a polarized double-ζ basis set58 for the lowest energy singlet and triplet species, and predicted adiabatic energy differences.56 However, most of the frequencies were not reported in the literature. In Table 2, we summarize the vibrational frequencies associated with SidO bond vibrations in the ground singlet and lowest-lying triplet states, obtained at the MP2 level with a polarized double-ζ basis set. Those vibrations associated with the SidO bond and their changes with excitation will dominate the observed infrared and electronic spectra of aged and equilibrated PS. The results of these calculations are significant, for they indicate the possibility that a 0.15-0.16 eV (1200-1250 cm-1) energy increment can readily be associated with a ground state silanone-based SidO stretch frequency. In addition they show that the corresponding vibrational frequency associated with the low-lying excited PS triplet state (as observed and analyzed by Stutzmann et al.11,12 in ODMR) can be of the order 0.10-0.11 eV (800-850 cm-1), close to the energy increment correspond-
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TABLE 2: MP2 Calculated Vibrational Frequencies in cm-1 for the SidO Bond in the Ground and First Excited Triplet State of the Silanonesa molecule SidO(H)2 SidO(H)(OH) SidO(OH)2 SidO(OH)(SiH3) SidO(H)(SiH3) SidO(OH)(OCH3) SidO(H)(NH2) SidO(H)(SiH3) SidO(SiH3)2 SidO(OSiH3)2 SidO(SiH3)(OSiH3) SidO(OCH3)2 SidO(CH3)2 SidO(CH3)(OCH3) SidO(CH3)(OSiH3) SidO(OCH3)(OSiH3) SidO(C1)(OH) SidO(C1)(CH3)
singlet ground state
triplet excited state
1182/1065 1244 1276 1222 1247 1281 1240 1150 1125 1277 1225 1284/1213 1205 1256/1215 1244 1281 1261 1195
860/745 913/812 876/844/760 778 850 856/806/734 822/742/889 818 796 827 805 842/807/717 753/876 865/739 861/745 831 847 813
a Many of the modes are not purely SidO stretches. Modes to which the SiO stretch contributes substantially based on visual analysis of the modes are given. This is more prevalent in the triplet than in the ground state singlet.
ing to the maximum energy differential associated with the pump (PLE)-probe (PL) process outlined for the plateau structure depicted in Figure 2. With this correlation considered and associating the observed energy increments primarily with Sid O-based silanone-like modes,15,16,18 we construct the energy level diagram depicted in Figure 8. Here, we focus primarily on the excited state structure, indicating only the zero-point (HOMO) and lowest vibrationally excited SiO-related mode in the ground electronic state which should dominate the absorption process. We note, however, that several additional higher lying discrete vibrational states exist for the fluorophor.55 In Figure 8, the 1.59 ( 0.01, 1.72 ( 0.01, and 1.80 ( 0.01 eV absorptions corresponding to the plateau excitation energies in Figure 2 and the 1.67 ( 0.01 eV energy observed for transparent PS films are indicated, as we recall that these plateau regions display a 0.12 eV shift to the maximum PL detection energies of 1.47 ( 0.02, 1.59 ( 0.02, and 1.68 ( 0.02 eV. The 0.56 eV valence band offset relative to the fluorophor zeropoint energy34 is also indicated in the figure. These energy levels will be the subject of further discussion. The lack of a temperature dependence for the 1.80 eV onset of the measured photocurrent associated with PS, coupled with the calculated vibrational frequencies associated with the Sid O bond, provide an explanation for the observed character of the PLE-PL correlations. The density of states of a polyatomic molecule increases rapidly with vibrational excitation such that one observes a virtually continuous energy level structure when only a few vibrational quanta are excited. Whereas the plateaulike structure which transforms to a conduction band-like character at 1.80 eV might reflect an inherent level structure below a conduction band and a correlated lower state energy increment of 0.12 eV, we suggest that this plateau structure is, in large part, indicative of a discrete excited state level structure where the density of surface perturbed rovibronic levels of the fluorophor soon merges into a near continuum of excited state levels (Figure 8). As the density of states increases and a nearcontinuous level structure is established, the effective coupling to the surface onto which a polyatomic fluorophor is bound will certainly be enhanced due to the larger availability of states with which to interact. Furthermore, any PLE-PL correlations
which demonstrate an observable energy increment within this virtually continuous region will manifest only a discrete structure for the lower state, (∼0.15-0.16 eV increments in the SiO stretch) mapped through the complement of reflectance spectroscopy. Thus, our suggested model is that of a discrete excited state structure, associated with the PLE-PL plateaus and the observed PAS absorptions, which merges rapidly to an effective continuum of levels. This behavior is not only consistent with the level structure outlined in Figure 2, but this density of states based model also allows for rapid excited state relaxation that reflects itself in the PLE-PL correlations at energies in excess of 1.80 eV where the level structure displays the character of a virtual continuum, much like that of a conduction band. The cutoff in the PL energy at 2.25 eV, with increasing excitation energy, not only reflects the continuum structure but also is consistent with unfavorable “Franck-Condon” factors for emission from higher-lying excited levels (pumped in PLE) to the ground electronic state. This situation favors rapid nonradiative relaxation down the excited state manifold to those levels in the near continuum of levels which have sufficiently large Franck-Condon factors so that they can readily access the ground state of the system through PL. Discussion The origin of the PL from PS has been discussed at length, and a number of different mechanisms have been proposed.1-6 Of all the models considered, we assess two, one of which is based on quantum confinement and the presence of crystallites of c-Si of nm size and the other which relates the PL to radiative centers associated with molecule-like species bound to the PS surface. In model 1, quantum confined energy levels for crystalline silicon are superimposed on the fundamental band gap energy of c-Si. Consequently the energy separations between levels for electrons and for holes should follow the temperature variation of the fundamental band gap energy for c-Si. The PL spectral distributions of PS and also the electrical band gap energy of PS should shift to lower energies with increasing temperature in analogy with the band gap shift for c-Si, the temperature variation of which is well established.59 In contrast, the PL spectral distributions from PS are remarkably independent of temperature.1(b),33 In addition, photocurrent spectroscopy, for a large number of samples, has demonstrated that the electrical “band gap” energy of an aqueous etched porous silicon surface is independent of the sample temperature from 10 to 300 K (within an uncertainty of 0.01 eV).34,35 For aqueous etched PS, photocurrent and photovoltaic measurements on aged samples repeatedly indicate a sharp threshold of 1.80 eV,34-36 independent of the choice of sample preparation parameters. Such a sharp, sample-independent threshold is difficult to relate to an ensemble of crystallites possessing a fairly broad distribution in particle geometry. Of fundamental importance are the PAS spectra whose first absorption threshold is sharp and located at 1.32 eV (Figure 5), whereas this onset is followed by compound, complicated, absorption features (Figures 5 and 6). These observations are incompatible with the quantum confinement model, for which one would expect a smoothly increasing absorption with increasing photon energy, no sharp threshold, and some dependence on sample preparation parameters even for aged and equilibrated samples. The smaller the size of a nanocrystallite, the more its absorption should be blue shifted. Further, additional studies have established difficulties with the quantum confinement model,15 noting the observation of visible PL from
Optical Analysis of the Light Emission from PS
J. Phys. Chem. B, Vol. 110, No. 5, 2006 2071
Figure 8. Energy level diagram developed from PL, PLE, and PAS measurements and molecular electronic structure calculations as described in detail in the text. The highest-occupied fluorophor molecular orbital is called the HOMO, and the energy levels of the fluorophor from experiment are compared to the energetics for the silicon surface to which the fluorophor is bound. Only the zero-point energy level and first SiO dominated vibrational mode are indicated, although several higher-lying discrete vibrational quanta exist in the fluorophor ground electronic state.55 The 0.56 eV valence band offset from the fluorophor zero-point energy is also indicated in the figure.34,35
samples etched so slightly that pores were not formed, thus excluding these pores from being a necessary ingredient for PL emission. A discussion of the energetics associated with Figures 2, 5, and 6, and Table 1 in terms of the properties of radiative centers correlating with molecule-like species is more feasible. First, a model (Figure 8) based on molecule-like hybrid surface-bound fluorophors can account for the temperature invariance observed for the electrical band gap energy of aqueous etched PS35 and also for the PL spectral distributions. Furthermore, the complicated features in Figures 2, 5, and 6 are compatible with an interpretation in terms of molecule-like properties and not those of a semiconductor. Several studies have reported correlations between the PL and oxygen-related sites15,60-64 on the PS surface. Prokes and Carlos64 have observed a direct correlation between the presence of nonbridging oxygen-hole centers (NBOHC) and the PL from PS. The NBOHC may form clusters which can act as shallow traps. For amorphous silicon oxide and silica glass, it is well established,65-68 that NBOHC clusters form luminescence centers with peak intensities at photon energies in the range of 1.9-2 eV. The overall similarities between the luminescent properties of such centers65-68 and those active in PS are striking. Such centers show broad band gap energy distributions at the Si/SiO2 interface,69 and the many optically active centers observed makes unambiguous characterization considerably more difficult than in elemental materials.70
Besides the role of the NBOHC, an interpretation of the Fourier transform infrared spectrum71 of PS and the luminescent properties of PS has previously demonstrated a potential correlation with a surface-bound silanone-based SidO-related bond of the form -Si(dO)(OR) where R can be hydrogen, but
is most likely a silyl or hydrocarbon group. At a specific site, the actual choice of R will influence the electronic energy manifold. Many experiments show that the luminescent centers of PS contain oxygen. Further, several theoretical studies focused on the structural preferences of (SiO2)n clusters have been reported during the past decade. It is now well established that linear D2h- and D2d-symmetric chains composed of Si2O2 rings with doubly bridging oxygens contain SidO terminal groups, which are favored when n < 7.72 This is apparently due to the large number of coordinatively saturated silicon and oxygen atoms in short isomer chains. To this framework we introduce the detailed molecular electronic structure calculations15,16,18,31,55,56 that we have outlined. When correlated with the PLE, PL, and PAS data from experiment, these results suggest that the surface of PS is a hybrid that is neither completely molecular nor completely bulk-like. Within this interpretation, we suggest that the observed features result from the perturbation of a poly-
2072 J. Phys. Chem. B, Vol. 110, No. 5, 2006 atomic surface-bound fluorophor, whose signature as shown in the energy level structure of Figure 2 and Table 1, at least in part, results from a coupling involving ground and excited state SiO vibrational frequency increments. Our proposed model (Figure 8) reflects in part a discrete excited state level structure that merges to a virtual continuum of levels, looking much like a conduction band. As a consequence, once we encounter a density of states that approaches a continuum of levels similar to a conduction band, the PLEPL correlation diagram, as outlined in Figure 2, will map the ground state SiO stretch. This expected behavior, which is indicated in Figure 8, occurs at energies in excess of 1.80 eV in Figure 2. However, the density of states at energies below 1.80 eV is still significant, and these levels are broadened through interaction with the PS surface. As the density of states increases, the potential for coupling to the bulk silicon surface increases. Such a coupling may control the onset of the observed photocurrent at 1.80 eV. This onset, if it is controlled by the density of states of a surface-bound fluorophor, should not be temperature dependent. Even with a 0.56 eV valence band offset, the 1.80 eV pump energy exceeds the minimum energy corresponding to the onset of the bulk silicon conduction band. If we adopt a molecular fluorophor model whose temperature independence is consistent with the PLE-PL correlations and the PAS data, a red shift of the PL vs the PLE is expected especially in view of the time-dependent density functional theory results55 for the independent silanone-based fluorophors. While the potential curves for the ground and excited states of these fluorophors are complex, we can say that the SiO bond lengthens in the upper triplet state versus the ground electronic singlet state. In a molecule, this will result in a fluorescence spectrum that is red shifted from the absorption spectrum. Pumping (PLE, PA, absorption) to an excited state vibrational level from the lowest ground state level will produce a spectrum determined by the best vibrational overlaps of the ground and excited state, dictated by the ground state and its population distribution at the temperature of the experiment. In emission (PL) the spectrum is determined again by vibrational overlaps, but now the intensity distribution is dictated by the excited state levels. We suggest that the onset of PL emission for PLE energies in excess of 1.59 eV and the subsequent range of emission from 1.32 to 1.47 eV for a 1.59 eV excitation are directly related to the Franck-Condon factors between the ground and triplet excited state. We suggest that the level structure of the excited state changes relative to the ground state (SidO bond lengthens). As a result, the “Franck-Condon factors” for pumping from the ground state to the excited state potential differ from those in PL so that the lowest excited state levels may not be accessed in optical pumping. However, the emission from these levels can produce lower energy PL limits which result from a small amount of excited state vibrational deexcitation and possible subsequent emission, and the emission is further limited by excited state-ground state overlaps with the vibrationally excited ground state level (or levels) indicated in Figure 8. The onset of the PAS spectrum in Figure 5 is consistent with the range of PL associated with the 1.59 eV PLE pump and a shift of the excited state potential due to a weakening of the SidO bond. We can extend this logic to the higher energy plateau structure observed in Figure 2. The 1.72 eV PLE plateau region indicates relaxation to a level close to 1.60 eV virtually isoergic with the 1.59 eV level observed in excitation. The 1.80 eV PLE plateau region indicates relaxation to a level near 1.68 eV which is
Gole et al. virtually isoergic with the 1.67 ( 0.01 eV level in Table 1 that lies 0.15-0.16 eV above a level at 1.52 eV. This level at 1.52 eV can be assigned to the termination of a transition from the 1.68 eV level to the vibrationally excited ground state at 0.150.16 eV. Similar correlations involve the level observed at 1.67 eV that might relax to an energy in the range 1.55 eV and subsequently emits to the vibrationally excited SiO level of the ground state at an emission energy of 1.39-1.40 eV. Although other correlations are possible, we limit our discussion to potential SiO level structure. Finally, the termination of the increase in detection energy (PL) at excitation energies (PLE) of 2.25 eV also is consistent with the suggested model as it implies regions in the excited state “potential” above 2.25 eV which are less efficiently accessed from ground electronic state levels and which, in emission, do not readily access the ground state. Furthermore, nonradiative processes (relaxation) can compete with and dominate radiative processes above a given energy in the continuum region and are especially relevant to the long radiative lifetime (∼10-4 seconds) established for the PS excited state emission.5-7 This, in concert with a significant density of states, can promote rapid nonradiative relaxation to those levels which readily access the ground state of the system. In some cases, at low temperatures, spectral features have been observed in the resonantly excited PL from PS and interpreted in terms of phonon replicas.1(a) The clear distinction between these replicas, which are observed at 4 Κ, and the PL spectrum obtained at room temperature has been discussed previously.69 By using resonant excitation to study a number of aged samples at the slightly higher temperature of 10 K, we have repeatedly failed to observe the phonon replica features. These facts suggest that the features observed at low temperature bear little correlation with those observed at room temperature.73 Further, the stepwise clustering of threshold energies seen in Figure 2 and the data given in Figure 1 are incompatible with an interpretation involving phonon replicas, which should yield a constant difference between threshold energy and detection energy, in contrast to the stepwise relation seen in Figure 2. Summary The PL from equilibrated porous silicon (PS) exhibits the properties of a polyatomic molecule (fluorophor) whose level structure controls the details of the observed luminescence. The locations of the electronic states associated with this polyatomic emitter are strongly influenced by the silicon surface which lowers the energy of these excited states, from their locations in the gas phase, relative to the ground electronic state. There is a strong synergism between the surface-bound fluorophor and the surface, forming a hybrid structure. However, consistent with the temperature-independent nature of the observed PL spectra from 10 to 300 K and observed PAS spectra, the PL from porous silicon does not result from what would be called an ideal semiconductor. The rovibronic density of states of a polyatomic molecule, especially the electronically excited states of the molecule, increases to a very high level for reasonably low vibrational quanta. This process can be accelerated when a polyatomic molecule is bound to a surface, as the density of states increases to a level which facilitates coupling and efficient energy transfer to the silicon surface at an energy near 1.80 eV. This energy is still above the conduction band minimum in silicon, taking into account the 0.56 eV offset from the fluorophor zero-point energy, and the onset of photoconduction should be sharp and temperature independent. The levels below 1.80 eV in Figure 8 are not a continuum but indicate that the
Optical Analysis of the Light Emission from PS PL emission from these levels is quite dense, especially with the broadening induced by surface interaction, so that the spectra appear to be continuous. Yet the interaction of these levels with the silicon surface would not produce a photocurrent due to the lack of sufficient energy to excite the silicon surface conduction band and/or an effective transfer of the requisite energy to the silicon surface to which the fluorophor is bound. Acknowledgment. The work was financially supported in part by the Brazilian National Research Council (CNPq) and REMAN/CNPq. References and Notes (1) (a) Cullis, A. G.; Canham, L. T.; Calcott, P. D. J. J. Appl. Phys. 1997, 82, 909. Properties of Porous Silicon; Canham, L. T., Ed.; EMIS Data review Series No. 18, INSPEC: London, 1997. (2) See, for example: Calcott, P. D. J.; Nash, K. J.; Canham, L. T.; Kane, M. J.; Brumhead, D. J. Phys Conds. Matter. 1993, 5, L91. (3) Calcott, P. D. J.; Nash, K. J.; Canham, L. T.; Kane, N. J.; Brumhead, D. J. Lumin. 1993, 57, 257. (4) Nash, K. J.; Calcott, P. D. J.; Canham, L. T.; Needs, R. J. Phys. ReV. B, 1995, 51, 17698. (5) Cullis, A. G.; Canham, L. T.; Calcott, P. D. J. Appl. Phys. 1997, 82, 909. (6) (a) Schuppler, S.; Friedman, S. L.; Marcus, M. A.; Adler, D. L.; Xie, Y. H.; Ross, F. M.; Chabal, Y. J.; Harris, T. D.; Brus, L. E.; Brown, W. L.; Chaban, E. E.; Szajowski, P. J.; Christman, S. B.; Citrin, P. H. Phys. ReV. B. 1995, 52, 4910. (b) Schuppler, S.; Friedman, S. L.; Marcus, M. A.; Adler, D. L.; Xie, Y. H.; Ross, E. M.; Harris, T. D.; Brown, W. L.; Brus, L. E.; Citrin, P. H. Phys. ReV. Lett. 1994, 72, 2648. (7) Xie, Y. H.; Wilson, W. L.; Ross, F. M.; Mucha, J. A.; Fitzgerald, E. A.; Macauley, J. M.; Harris, T. D. J. Appl. Phys. 1992, 71, 2403. (8) Prokes, S. M.; Glembocki, O. J.; Bermudez, V. M.; Kaplan, R.; Friedersdorf, L. E.; Jearson, P. C. Phys. ReV. B 1992, 45, 13788. (9) Prokes, S. M. J. Appl. Phys. 1993, 73, 407. (10) Fuchs, H. D.; Rosenbauer, M.; Brandt, M. S.; Ernst, S.; Finkbeiner, S.; Stutzmann, M.; Syassen, K.; Weber, J.; Queisser, H. J.; Cardona, M. Mater. Res. Soc. Proc. 1993, 283, 203. (11) Stutzmann, M.; Brandt, M. S.; Rosenbauer, M.; Fuchs, H. D.; Finkbeiner, S.; Weber, J.; Deak, P. J. Lumin. 1993, 57, 321. (12) Brandt, M. S.; Stutzmann, M. S. Solid State Commun. 1995, 93, 473. (13) Steckl, A. J.; Xu, J.; Mogul, H. C.; Prokes, S. M. J. Electrochem. Soc. 1995, 142, L69-71. (14) Prokes, S. M.; Glembocki, O. J. Phys. ReV. B 1994, 2238. (15) Gole, J. L.; Dudel, F. P.; Grantier, D. R.; Dixon, D. A. Phys. ReV. B 1997, 56, 2137. (16) Gole, J. L.; Dixon, D. A. Phys. ReV. B 1998, 57, 12002. (17) Brus, L. E.; Szajowski, P. F.; Wilson, W. L.; Harris, T. D.; Schuppler, S.; Citrin, P. H. J. Am. Chem. Soc. 1995, 117, 2915. (18) Gole, J. L.; Dixon, D. A. J. Phys. Chem. 1997, 82, 3125. (19) H-A Rifai, M.; Christopher, M.; Ottow, S.; Carstensen, J.; Fo¨ll, H. J. Electrochem. Soc. 2000, 147, 627-635. (20) Fo¨ll, H. Appl. Phys. A 1991, 53, 8. (21) Cullis, A. G.; Canham, L. T.; Calcott, P. D. J. J. Appl. Phys. 1997, 82, 909 and references therein. (22) Theanissen, M. J. J. J. Electrochem. Soc. 1972, 119, 351. (23) Lehmann, V.; Fo¨ll, H. J. Electrochem. Soc. 1990, 137, 653. (24) Searson, P. C., Macaulay, J. M.; Ross, F. M. J. Appl. Phys. 1992, 72, 253. (25) Berbezier, I.; Halimasui, A. J. Appl. Phys. 1993, 74, 5421. (26) Lehmann, V. J. Electrochem. Soc. 1993, 140, 2836. (27) Levy-Clement, C.; Lagoubi, A.; Tomkiewicz, M. J. Electrochem. Soc. 1994, 141, 958. (28) Probst, E. K.; Kohl, P. A. J. Electrochem. Soc. 1994, 141, 1006. (29) Lehmann, V.; Go¨sele, U. AdV. Mater. 1992, 4, 114. (30) Gole, J. L.; Dudel, F. P. J. Appl. Phys. 1997, 82, 402. (31) Gole, J. L.; Seals, L.; DeVincentis, J. A.; Lillehei, P.; Prokes, S. M.; Dixon, D. A. Phys. ReV. B 2000, 61, 5625. (32) Gole, J. L.; DeVincentis, J. A.; Seals, L. J. Phys. Chem. B 1999, 103, 979. (33) Andersen, O. K.; Veje, E. Phys. ReV. B 1996, 53, 15643. (34) Romstad, F. P.; Veje, E. Phys. ReV. B 1997, 55, 5220. (35) Frederiksen, J. T.; Melcher, P. G.; Veje, E. Phys ReV. B, 1998, 58, 802. (36) Propst, E. K.; Kohl, P. A. J. Electrochem. Soc. 1994, 141, 1006. (37) Gole, J. L.; Lillehei, P.; Seals, L.; DeVincentis, J. A.; Narasimha, S. Phys. ReV. B 2000, 61, 7589.
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