J. Phys. Chem. C 2008, 112, 6027-6032
6027
Surface Plasmon Polaritons and Screened Plasma Absorption in Indium Tin Oxide Compared to Silver and Gold Stefan Franzen Department of Chemistry, North Carolina State UniVersity, Raleigh, North Carolina 27695 ReceiVed: October 6, 2007; In Final Form: January 18, 2008
This study addresses the ability of a conducting metal oxide to act as a material capable of supporting surface plasmon polaritons (SPPs). By use of a two-phase Fresnel model that provides insight into the difference between polariton-induced and absorptive decreases in reflectivity, indium tin oxide (ITO) is compared to the noble metals gold and silver, which are widely used as materials for surface plasmon resonance (SPR) detection of analytes. The study builds on application of the Drude free electron model that provides an explanation for the observed optical extinctions as a function of ITO film thickness, including the dependence of wavenumber on angle, by use of only two adjustable parameters, the plasma frequency ωp and the damping Γ. Herein, models of the dispersion and absorption include both the real and imaginary parts of the dielectric function to obtain the plasma absorption spectra and dispersion curves for ITO, Ag, and Au. ITO is found to have surface plasmon dispersion curves and plasma absorption free from interband transitions as observed in Ag but not Au. Au has significant contribution from bound electrons that damps the plasma absorption and broadens the dispersion curve of the SPP. Ag is more like a free-electron conductor than Au but still has some absorption in the frequency range above the observed surface plasmon. ITO is a nearly ideal freeelectron conductor.
Introduction Surface plasmon resonance (SPR) spectroscopy has emerged as a powerful method for the detection of analytes. The technology is based on the coupling of electromagnetic radiation into a conducting thin film, usually gold or silver, in a totally internally reflecting (TIR) mode.1-2 The most widely used geometry, known as the Kretschmann configuration (Figure 1), permits wave vector matching on both sides of a conducting layer. In order for coupling to occur, the frequency of the light must be at or lower than the screened plasma absorption frequency for the conductor, ωps ) ωp/x(c + s). For most analytes in aqueous solution the index of refraction of the solution is nearly equal to that of water, nH2O ) 1.33, so that s ) nH2O2 ) 1.77. Yet, this minute change in index of refraction when an analyte binds near the surface of the conductor provides the signal in SPR sensing. In order to provide wave vector matching across a boundary that consists of a conductor (c) and a sample (s), the light must be p-polarized and incident at an angle greater than the critical angle. For example, a prism made of BK-7 glass (nBK-7 ) 1.52) can used as the internal reflecting element (IRE) shown in Figure 1A to achieve the condition for light at incident angle θ. The indices of refraction will be approximately matched, satisfying the condition nBK-7 sin θ ) nH2O when θ ) 61°. When this condition is met, light will drive a plasmon resonance and the reflectance drops significantly.3-4 The decrease in reflectance is sensitive to changes in the index of refraction in the water layer when analytes bind. SPR sensors have been designed to detect analyte binding to or near a conducting surface.1,5,6 The binding results in a change in the index of refraction in the aqueous layer near the conducting surface. The change can be measured by use of the Kretschmann geometry shown in Figure 1 by modulating the angle of incidence of the radiation to detect the change in the
Figure 1. Geometries of incident radiation on three- and two-layer models for the interface responsible for SPR. (A) Kretschmann geometry for TIR with an internal reflecting element (IRE). The dielectric functions of the IRE, conductor (c), and sample (s) are indicated. The evanescent waves that extend into both the conductor and the sample are shown. (B) Features shown in this panel refer to the delocalized plasmon along the interface and the exponential damping due to the TIR condition.
angle of maximum extinction. Although the change in the index of refraction is relatively small, SPR sensors are sufficiently
10.1021/jp7097813 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/27/2008
6028 J. Phys. Chem. C, Vol. 112, No. 15, 2008 sensitive that the method has led to numerous applications.5-16 In the most common implementation, measurement of analyte binding does not occur on a monolayer surface but rather in a swellable polymer that is in contact with the surface.17,18 More recently, signal enhancement has been achieved by colloidal capture13 or based on amplification by secondary polymerization processes.16 Although most sensors are constructed with gold and silver, these are not the only conductors that can provide SPR sensing.19-21 Most other metals are not appropriate for SPR applications since their bulk plasma frequencies are significantly higher than silver and gold.14,15,22-25 The noble metals are, in fact, a special case among the transition metals. The d-electron energy levels tend to lower across the transition series due to the contraction of the d-orbitals with increasing atomic number and concomitant nuclear charge.26 Consequently, plasmons can derive oscillator strength from intense d-sp interband transitions of the noble metals. The bulk plasma frequencies of gold and silver are in the range of 6.5 and 9.2 eV, respectively, as a consequence. The lower values of bulk plasma frequencies lead to observation of screened plasma frequency in visible and nearUV for gold and silver, respectively. The remaining transition metals have significantly higher plasma frequencies (ωp > 12 eV). As a practical matter, these high frequencies are not accessible for sensor applications since they require excitation in the hard UV. On the other hand, the class of conducting metal oxides has plasma frequencies ωp < 3 eV. Conducting indium tin oxide thin films provide an attractive proving ground for testing novel sensor technologies27 and optical technologies28 as well as fundamental studies of plasmon polariton physics. In the following, the term polariton is reserved for in-phase coupling of the incident light to drive plasmon oscillations. This is distinct from plasma absorption, which is a response that arises from the out-of-phase dielectric response that gives rise to plasma absorption. Despite 50 years of study, there are many issues that remain in the study of the physics of plasmons. The first observation of plasmons was based on the energy loss of high-energy electrons as they traverse a thin film.29 The material response to fast electrons is a longitudinal excitation that is typically observed between 16 and 28 eV. The longitudinal response can be distinguished from the transverse response of a material in response to electromagnetic radiation.30 The optical response to p-polarized electromagnetic radiation under TIR conditions leads to both x-polarized absorption and to a surface plasmon polariton (SPP) with a z-polarized evanescent wave (Figure 1B). If absorption occurs at the wavelength of the radiation, the reflected intensity is attenuated. This phenomenon leads to attenuated total reflection (ATR) spectroscopy. Under most conditions SPR is a TIR phenomenon, but it is not an ATR spectroscopy. The change in reflectance at the surface is due to the condition for wave vector matching, and hence the index of refraction, rather than the absorption of specific wavelengths across the dielectric boundary. It is the x-polarized in-phase wave along the interface, the SPP, that has become the object of a great deal of interest for sensor development.5-7 Unlike TIR in insulators, the x-polarized SPP is sensitive to the dielectric environment and can potentially give rise to local field enhancement effects. In the most common mode of detection, the index of refraction change is sensed with exponentially decreasing sensitivity as a function of the distance as analyte binds to molecules in the active volume. The theory of SPR using Fresnel equations has led to the application of dispersion relations that predict the frequency and angle dependence of the absorption due to the SPP.30,31 The
Franzen origin of optical resonance due to surface plasmon resonance has been observed in reflectance spectroscopy.19,20,32,33 Unlike the noble metals, conducting metal oxides such as indium tin oxide (ITO) have contributions only from free carriers, and no transitions among bound states, in the spectral region of interest.34 When only free carriers are present, one can express the dielectric function by use of the Drude model for conduction:
c(ω) ) ∞ -
ωp2 ω2 + iωΓ
(1)
where ∞ is the static dielectric constant, which has a value of 3.8 for ITO. The plasma frequency is
ωp )
x
ne2 µ0
(2)
where n is the charge carrier density, e is the electronic charge, µ is the effective mass, and 0 is the permittivity of vacuum. Recently, we have observed that the character of the angledependent SPP in ITO is a function of the film thickness.34 The SPR effect on ITO exhibits novel features that have not yet been observed in gold or silver.21 Although these features have been completely explained by a free electron model using the three-layer Fresnel equations, physical insight can be obtained from the two-layer Fresnel model used here. The observation of SPP on a new substrate, that is not a noble metal, can be instructive for comparison with data obtained on noble metal thin films and nanoparticle suspensions that can be treated by the inhomogeneous medium theory of Maxwell-Garnett.35 The conducting metal oxide SPP is phenomenologically the same as that observed in the noble metals despite the fact that ITO has a lower charge carrier density (n ∼ 1021 electrons/cm3) relative to typical metals (n ∼ 1023 electrons/cm3). For this reason, the surface plasmon polaritons in ITO are observed in the near-infrared spectral region. One of the important attributes of conducting metal oxides is that n can be controlled by the thin film preparative conditions. Thus the plasma frequency, ωp, can be tuned in ITO and other conducting metal oxides.20 For the present comparison we have used a value for ωp here that is observed for an optimal film thickness of 160 nm, standard annealing conditions with low oxygen partial pressure, and argon sputter gas pressure of 9 mTorr for optimal mobility. Such conditions lead to an excellent SPP determined by optimization of preparative conditions described elsewhere.34 The 50-fold lower charge carrier density and 3-fold smaller effective mass36.37 of ITO lowers ωp by roughly a factor of 4 compared to silver (eq 2). In the free electron model, the damping Γ ) µσ/ne,2 where σ is the conductivity. The smaller charge carrier density of ITO nearly compensates for the lower conductivity and smaller effective mass. Thus, according to the classical free-electron model, Γ for ITO is roughly in the same range as that for the noble metals gold and silver. Given the smaller value of ωp, the ratio ωp/Γ is larger for ITO than for gold or silver. While it is desirable to maximize the ratio ωp/Γ in order to increase the sharpness of dispersion curves for SPPs, it is of interest to understand whether the smaller value ωp/Γ is compensated to some extent by the fact that ITO has less interference from transitions that involve d or sp bands. The transparency of ITO in the near-IR and visible regions is a consequence of the lack of interband transitions. In order to evaluate the role of damping in ITO, the dispersion relation was calculated for SPR on ITO, Au, and Ag by use of the complex dielectric response. The real and imaginary parts
Surface Plasmon Polaritons in Indium Tin Oxide
J. Phys. Chem. C, Vol. 112, No. 15, 2008 6029 has the appearance given in Figure 2. The dispersion curves for gold and silver are qualitatively similar at this level of approximation. Such curves have been widely used to represent optical coupling to drive SPPs.5 Coupling of electromagnetic radiation is represented by the inclusion of light lines as shown in Figure 2. SPPs can be driven at the intersection of a light line, calculated from the equation ω ) kIREc/nIRE sin θ, and the dispersion curve. Figure 2 shows the dispersion curves with a light line at an angle of 70°, assuming that the light was coupled in from a medium with an index of refraction nIRE ) 1.5. This treatment does not account for absorption due to out-of-phase plasma oscillations or interband transitions. In order to include plasma absorption in the optical model, I calculate the dielectric response using the complex dielectric response. The interfacial index of refraction is
Figure 2. Dispersion curve of x-polarized electronic oscillations in a free electron conductor, using only the real part of the dielectric response obtained from a two-layer model. The parameters used are ωp ) 17 700 cm-1 and Γ ) 900 cm-1, obtained from a fit of data for ITO to a free electron model.
of the complex dielectric response correspond to the in-phase and out-of-phase contributions of incident radiation, respectively. Although any conducting material inherently has contributions from both the real and imaginary parts of the dielectric function, the analysis of SPR has always focused on the real part,5,6,30,31 because the SPP is an in-phase contribution. A recent study includes corrections to the standard treatment that include the imaginary part of the dielectric response in the treatment of waveguides of silver metal.38 In that work they used the experimental dielectric function rather than the free dielectric function used in most studies. The first report of an absorptionbased SPR dates from 2002.39 These authors state that analysis of “conventional” SPR uses the real part of the dielectric response. Their observation is an application of SPR to detect molecular absorptions detected in an ATR mode. The comparison of ITO and the noble metals requires a more complete development of the complex treatment of the dispersion relation, which is the motivation for the present study. Theory The most common treatment of surface plasmon resonance (SPR) uses only the real part of the dielectric response. When the Drude model (eq 1) is used for a free electron conductor, the complex dielectric response is 1(ω) + i2(ω), where the terms are
1(ω) ) ∞ -
ωp2
2(ω) )
ω2 + Γ2
Γωp2 ω(ω2 + Γ2)
(3)
Calculated dielectric functions can be obtained from the indices of refraction (optical constants) for conductors.40 The experimental dielectric functions are given in Figure 3 for gold and silver. The x and z components for the optical responses shown in Figure 1 are
nx )
x
cs s + c
(4)
where c is the conducting layer and s is the substrate.5,6 These terms predict a response along the interface nx ) kxc/ω, which has both in-phase and out-of-phase contributions. If only the real part of the response is used, the dispersion curve for ITO
nx ) )
x
s(1 + i2)
(s + 1 + i2)
x
s(1s + 12 + 22 + i2s) (s2 + 12 + 21s + 22)
(5)
which can be written in the form
nx ) xa + ib
(6)
where
a)
b)
s(1s + 12 + 22) (s2 + 12 + 21s + 22) 2s2 (s2 + 12 + 21s + 22)
(7)
The analysis of these terms is carried out by use of the following relations for the square root of a complex number. By use of the identity
xa + ib )
xx(a
1 ( x2
2
+ b2) + a + i sgn(b)xxa2 + b2 - a) (8)
one can calculate the complex wave vector that includes the dispersion term k1(ω) and the absorption coefficient k2(ω). Both real and imaginary parts of the wave vector k1(ω) + ik2(ω) are plotted on the same plot in Figure 4 for ITO, Au, and Ag. The out-of-phase (imaginary) component represents the plasma absorption and the in-phase (real) part represents the SPP. However, as was considered for the conventional treatment using only the real part, the wave vector of the incident light must be matched with the wave vector of the SPP in order for coupling to occur that permits the polariton to be driven. The dispersion curves in the complex response that lie above and below the plasmon band gap are nearly identical to the curves obtained when only the real part of the dielectric response is used. These are known as the radiative plasmon polariton (RPP) and the SPP, respectively. There is an additional contribution to the real part of the dispersion curve within the plasmon band gap known as the quasi-bound mode (QBM).38 Thus far, there
6030 J. Phys. Chem. C, Vol. 112, No. 15, 2008
Franzen
Figure 3. Dielectric function, plotted by use of free electron optical constants (ITO) and experimental optical constants (gold and silver). The values are obtained from 1(ω) ) n(ω)2 - κ(ω)2 and 2(ω) ) 2n(ω)κ(ω). (A) ITO; (B) Au; (C) Ag.
Figure 4. Optical response of each material, given as the wave vector versus the incident frequency. The real and imaginary parts corresponding to absorption and dispersion, respectively, were calculated by use of eqs 5-8. (A) ITO; (B) Au; (C) Ag.
is evidence for coupling of light into thin films to drive the SPP, but no direct evidence for coupling into the RPP or QBM. Discussion The nature of surface plasmon polaritons (SPP) has continued to interest researchers interested in optics and optical applications such as sensors9-15 and waveguides. The SPP is a delocalized in-phase x-polarized response to electromagnetic radiation. Therefore, it can act to enhance the incident field at the interface5 and it also has the potential to permit transmission of signals or information in a conducting waveguide.38 The local field effect is responsible for surface enhancement in infrared and Raman spectroscopies.41 Although these effects are significantly larger on nonplanar surfaces,41 there is a theoretical enhancement of the absorption and Raman scattering of molecules with transition moments aligned along to the x-direction (parallel to the interface and in the plane of incidence of p-polarized radiation) as shown in Figure 1. Despite the fact that the SPP is an in-phase response, it is also associated with a large decrease in reflectance. Normally, in a conductor one would associate an in-phase response (real part of k) with dispersion, which could be transmission, reflection, or scattering, and an out-of-phase response (imaginary part of k) with absorption. The origin of absorption in noble metals is obscured by the fact that the strong absorbance in gold and silver could be attributed to the contribution of interband transitions, that is, transitions that do not involve conduction electrons. The d-sp transition in gold and silver is an intense absorptive transition that is manifest in the relatively large values of 2 shown in Figure 3.28 In order to understand the role of interband transitions, it is instructive to compare ITO with gold and silver. The use of a Drude model to represent the dielectric function of ITO has
been justified by the excellent agreement of calculated threelayer models with experimental reflectance of ITO thin films.21,34,42 Specifically, the plasma frequency ωp (∼1 eV) is significantly below the band gap (∼3.2 eV) for ITO. ITO is completely transparent throughout the near-infrared and visible regions, which means that there are no interband transitions at or above ωp. Moreover, the experimental dielectric function of ITO shows no structure in contrast to Au and Ag, which have significant absorption in the region of their plasma frequency.28 The properties of ITO are consistent with a free-electron model. Given that ωp and Γ in ITO films can vary significantly depending on their fabrication conditions, the Drude model is an ideal means to account for their properties in a general way. Figure 4A shows that the Drude model predicts both plasma absorption and dispersive SPP responses in ITO due to the oscillations of the free charge carriers. Figure 4 panels B and C show similar features in Au and Ag, based on the experimentally determined optical constants. The dispersive component of Au in Figure 4B has a large offset and was multiplied by a factor of 1/2 for clarity of presentation. This background is largest for visible excitation of gold films, which may account for the excellent SPR effects in Au thin films observed in the nearinfrared region where there is less broadening due to the imaginary part of the dielectric function.43 One significant difference between the noble metals and ITO is that both the noble metals have additional absorption at or above the plasma frequency. This arises from the interband transitions, which are absent in ITO. The imaginary part of the dielectric response can be identified with the absorption bands in Au and Ag. Although these absorption bands exist in thin films, they are observed experimentally in nanoparticle suspensions. Figure 4B also shows that the interband transitions give rise to significant absorption in Au that is not observed in either
Surface Plasmon Polaritons in Indium Tin Oxide
J. Phys. Chem. C, Vol. 112, No. 15, 2008 6031
Figure 5. Dispersion curves of the real part of the x-polarized electronic oscillations in a free electron conductor using the complex dielectric function (red), compared to a calculation that does not include the imaginary part (blue dashed lines). (A) ITO; (B) Au; (C) Ag.
ITO or Ag. While the calculation is performed here for thin films, the dielectric function for a composite of Au or Ag nanoparticles in a medium is similar, as has been determined by use of Maxwell-Garnett theory for dilute suspensions.35 The x-polarized plasma absorption shown in Figure 4 accounts for the absorption observed in thin films and is not a contribution to the SPP. The two-phase model used here cannot be applied to threelayer systems used to experimentally observe the SPP of ITO.21,34 However, the insight gained by separation of the complex dielectric function into real and imaginary components can be used as an aid to understand the data obtained with the three-layer Kretschmann configuration. Very thin films cannot support SPP and only the z-polarized screened bulk plasmon polariton (SBPP) is observed.34 As the film thickness surpasses the skin depth, the x-polarized SPP is observed in ITO, Ag, and Au.20 Clearly ITO, Ag, and Au each have different skin depths and different optimum thicknesses. For example, Au thin films are observed to give optimal SPP response for 40-50 nm films, while ITO is optimal at 160-170 nm.34 Both the x-polarized SPP and z-polarized SBPP can lead to absorption, which is due to the absorption coefficient, k2. The x-polarized component for ITO absorption is shown in Figure 4A. The z-polarized response can also be shown to have a similar absorption maximum (not shown). The imaginary component is essential to understanding absorption, as opposed to dispersion in thin films. Absorption by thin films is observed in thin ITO films. It is difficult to observe the x-polarized absorption and essentially impossible to observe the z-polarized SBPP in Au. These absorptions are contributions to localized surface plasmon resonance (LSPR) in nanoparticles or colloids.44,45 The absorption process gives rise to electronic relaxation on the time scale of at most a few picoseconds,46 which leads to quenching of both the SBPP and any molecular luminescence that occurs due to molecules near the surface.47 On the other hand, the nature of the SPP may lead to a local field that can enhance the electric field near the surface and therefore does not necessarily quench luminscence.5 The dispersion curves used in analysis of SPR substrates such as gold5,6 are identical to those shown in Figure 4 but are presented with rotated axes as shown in Figure 5. In Figure 5 these curves are plotted with the wave vector k on the abcissa and the driven frequency response ω/c on the ordinate, as shown in Figure 2. The curve with only the real part of the dielectric function, 1(ω), is compared to the complex dielectric response, 1(ω) + i2(ω). The nature of the RPP differs in these calculations since 1(ω) < 0 for gold and silver in regions of the visible and near-IR. In an ideal conductor 1(ω) > 0 once
the curves 1(ω) and 2(ω) cross, which occurs at the screened plasma frequency ωps ∼ ωp/x(c + c). Aside from this difference, all of the curves show the same qualitative behavior. They all show a quasi-bound mode (QBM) in the plasmon band gap. Figure 5 shows that the SPP observed in ITO is similar to that observed in Au and Ag3-6 but at lower energy. Compared to ITO, the energy of both plasma absorption and the screened plasmon is approximately a factor of 2 and 3 larger for Au and Ag, respectively. The similarity of the dispersion curve for ITO thin films with Au and Ag has relevance for SPR in conductors generally and not just the noble metals. ITO is a material with a tunable plasma frequency that is free from interference of interband transitions.19,32,34 The comparison presented here reveals that ITO and Ag resemble a pure plasmonic material much more so than Au. Conclusion The SPR optical properties of the transparent conducting oxide ITO compare favorably with those of the noble metals Ag and Au. The Drude free electron model has been applied to a treatment of the absorption spectrum and dispersion relationship for ITO to obtain both the SPP dispersion curve and the plasma absorption frequency. The use of a free electron model is justified by the fact that ITO thin films have almost no absorption below their band gap and therefore all of the optical properties arise solely from the conduction electrons. Although ITO films vary a great deal depending on their preparation conditions, they have in common that the imaginary part of the dielectric function is small, 2(ω) ∼ 0, everywhere above the screened bulk plasma frequency. The optical properties of ITO thin films can be modeled with only two adjustable parameters, the plasma frequency ωp and the damping Γ of the Drude model. While Ag is closer to a Drude metal due to the small contribution of 2(ω), Au shows a large deviation due to interband transitions. These transitions in Au lead to a significant contribution to the imaginary dielectric function, 2(ω), in the near-IR and visible regions. This contribution leads to a significant broadening of the features in the dispersion curve. Ag has less of a contribution from interband transitions and these are essentially all higher in energy than the screened plasma absorption band. ITO has no interfering transitions and represents a free-electron conductor that can be used to systematically study the origin of optical effects that derive from the SPP of conduction electrons. The conclusion of this study is that ITO is an excellent model system for the study of surface plasmons and has advantages over both Au and Ag because the materials properties can be tuned systematically by alteration of preparation conditions.
6032 J. Phys. Chem. C, Vol. 112, No. 15, 2008 Acknowledgment. I thank Professor David Aspnes for insightful comments. References and Notes (1) Kretschmann, E. Z. Phys. 1971, 241, 313-324. (2) Haes, A. J.; Duyne, R. P. V. Anal. Bioanal. Chem. 2004, 379, 920. (3) Kretschmann, E. Jpn. J. Appl. Phys. 1974, A862. (4) Kretschmann, E.; Raether, H. Z. Naturforsch. 1968, A 23, 2135. (5) Knoll, W. Annu. ReV. Phys. Chem. 1998, 49, 569-638. (6) Brockman, J. M.; Nelson, B. P.; Corn, R. M. Annu. ReV. Phys. Chem. 2000, 51, 41-63. (7) Hillebrandt, H.; Tanaka, M.; Sackmann, E. J. Phys. Chem. B 2002, 106, 477. (8) Guo, J.; Koch, N.; Schwartz, J.; Bernasek, S. L. J. Phys. Chem. B 2005, 109, 3966. (9) Campbell, C. T.; Kim, G. Biomaterials 2007, 28, 2380. (10) Haseley, S. R.; Kamerling, J. P.; Vliegenthart, J. F. G. In Topics in Current Chemistry; Springer Verlag: Berlin, 2002; Vol. 218, pp 93114. (11) Mullett, W. M.; Lai, E. P. C.; Yeung, J. M. Methods 2000, 22, 77-91. (12) Lee, H. J.; Yan, Y. L.; Marriott, G.; Corn, R. M. J. Physiol. (London) 2005, 563, 61-71. (13) He, L.; Smith, E. A.; Natan, M. J.; Keating, C. D. J. Phys. Chem. B 2004, 108, 10973-10980. (14) Elwing, H. Biomaterials 1998, 19, 397-406. (15) Andersson, K.; Areskoug, D.; Hardenborg, E. J. Mol. Recognit. 1999, 12, 310-315. (16) Fang, S. P.; Lee, H. J.; Wark, A. W.; Corn, R. M. J. Am. Chem. Soc. 2006, 128, 14044-14046. (17) Malmqvist, M. Biochem. Soc. Trans. 1999, 27, 335-340. (18) Karlsson, R.; Kullman-Magnusson, M.; Hamalainen, M. D.; Remaeus, A.; Andersson, K.; Borg, P.; Gyzander, E.; Deinum, J. Anal. Biochem. 2000, 278, 1-13. (19) Brewer, S. H.; Franzen, S. J. Phys. Chem. B 2002, 106, 1298612992. (20) Brewer, S. H.; Franzen, S. J. Alloys Compd. 2002, 338, 73-79. (21) Rhodes, C.; Franzen, S.; Maria, J.-P.; Losego, M.; Leonard, D. N.; Laughlin, B.; Duscher, G.; Weibel, S. J. Appl. Phys. 2006, 100, 054905.
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