Anal. Chem. 1888, 60, 407-411
407
Depth Profiling with Standing Waves. Recovery of Thin-Film Functional Group Distributions D. R. Miller and P. W. Bohn* Department of Chemistry and Materials Research Laboratory, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
Spatial concentration distributions of target functional groups in thin organic films were profiled by combining optical waveguide exdtatkm with vibrational spectroscopy. Step function distributions of pyridyi moieties were obtained by fabricating optically homogeneous but chemically inhomogeneous polymer laminate structures. Polystyrene and polystyrene-d, were index matched to poly(4-vkrylpyrk#ne) (An I0.003) by careful control of processing parameters to form both single and double interface structures. The spatially asymmetric electric field distributions of thin-film optical guided eigenmodes were then used to sample the laminate structwes, and the concentration distributions were obtained by fitting trial distributions to the observed Raman signal ratios. Strong secondary minima were distinguished from global minima in the calculated error function by comparhg the calculated and observed Raman cross section ratios. Average absolute uncertainties of 2.2 % and 3.5 % were obtained for interface position determinations in single and double interface structures, respectlveiy.
Thin organic films (t < 5 pm) are ubiquitous in chemical technology, being employed for a range of applications spanning integrated optics (1-3), support matrices for electrocatalysis (4,5), energy conversion (6, 7),membranes with selective permeability (8-12), and more. In each of these the ability to characterize active site distributions perpendicular to the film plane is essential to a fundamental understanding of thin-film structure-function relationships. Consider for example the problem of interfacial mixing at a solid interface between two different polymers. Although different approaches have been tried, e.g. Rutherford backscattering from interfacial microparticulates (13), electron microprobe analysis of heavy elements (14), infrared microdensitometry (15,16), and 3Hlabeling (17),none has been completely satisfactory. One would like to map the concentration distribution of each component as a function of time after the commencement of mixing in order to understand the interdiffusion process. This requires the ability to depth profile one sample sequentially in real time with resolution in the sub-100-nm regime. Unfortunately molecular spatial distributons are extremely difficult to obtain in organic systems. With very limited exceptions, traditional depth profiling experiments have not been feasible in organic films due to extensive beam damage, charging, momentum transfer, other effects of ion beam irradiation (18-21), and the fact that atomic, rather than molecular, information is obtained. The general lack of pertinent characterization techniques is a reflection of the difficulty of depth profiling in organic films. One would like a probe that combines the molecular specificity of the various optical spectroscopies with the extreme sensitivity of the vacuum spectroscopies to overcome the problems inherent to organic thin films. Here we report an optical spectroscopic technique for depth profiling in thin-filmsystems, which can be fabricated as asymmetric slab dielectric optical waveguides. Molecular specificity is con0003-2700/88/0360-0407$01.50/0
ferred via the nature of the vibrational Raman scattering and molecular fluorescence probes, and enhanced sensitivity is afforded by the efficient spectroscopicexcitation in waveguides (22-29). Such a photon-based technique allows both nondestructive sampling and use under realistic environmental conditions, including immersion in solution. In this work the optical depth profiling technique was developed, and functional group distributions were measured in samples with one and two interface step function distributions by using the quantitative sampling capabilities developed earlier (30,31). Frequently new analytical techniques can rely upon established methods to support the validity and test the accuracy of the new method. Unfortunately other methods are not amenable to molecular spatial distribution measurements in organic thin films. Therefore, in order to test the accuracy and validity of this novel optical depth profiling approach, it was imperative to fabricate a concentration distribution that was known, either from fiit principles or via a direct measurement of a physical nature. The simplest distribution that satisfied these criteria was a step function. Thus the structures employed in these experiments consisted of polymer thin film laminates that were optically homogeneous (i.e. same refractive index among layer components) but chemically inhomogeneous (different functional groups). In order to avoid interfacial mixing during fabrication a polymer system involving incompatible solvents was chosen, polystyrene (PS)and poly(4-vinylpyridine) (P4VP). Substitution of nitrogen for carbon in the 4 position of the pendant aromatic group affects the refractive index of the polymer film negligibly, but the vibrational dynamics of the ring are changed sufficiently that the two can easily be distinguished by Raman scattering. The structures thus fabricated can be characterized by a pyridyl (or equivalently phenyl) group concentration which is finite and constant in some regions of the thin film but zero in others.
EXPERIMENTAL SECTION One-interface systems were fabricated by using polystyrene (Aldrich secondary standard, M , = 321000) or deuterated polystyrene (DPS) (99% isotropic purity) in chlorobenzene (4-7% (w/v)), and poly(4-vinylpyridine) (Polysciences,M , = 50 000) in 1-butanol( 4 4 % (w/v)) solutions. These solutions were filtered with 0.45-pm filters and deposited on fused-quartz substrates by a horizontal flow procedure. Samples were then heated at 120 "C under vacuum for 3 h. Tweinterface systems were more difficult to fabricate,because regardless of the order or care of deposition, the top layer solvent penetrated to the bottom layer causing mixing and damage to the composite system. This was avoided by fiit depositing P4VP (Reilly Tar & Chemical, Indianapolis,IN, M , = 200000)with 0.5 mol % 1,5-dibromopentane(Aldrich, 97%) in 1-butanol. The polymer was croas-linked (X-P4VP)in the solid phase by heating at 100 "C for 1h The resulting film was not soluble in the origind solvent. PS followed by P4VP could then be deposited without mixing with the lower layer. After spectroscopic examination of the composite structures the top layers were removed sequentially by rinsing with the appropriatesolvent. The interface positions were then determined both by interferometryand by measuring the resonant coupling angles (32-38). Radiation from an Ar+ laser was coupled into the 0 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 5, MARCH 1, 1968
composite structures with an LaSF-9 prism (n = 1.8624 at 514.5 nm). Spontaneous Raman scattering was collected from the waveguide and coupled to an f/S double monochromator with a fiber optic as described previously (30).
THEORY It is a well-known property of optical waveguides that different eigenmodes are characterized by different spatial distributions of the electric field amplitude in a direction perpendicular to the thin-fii plane (39,401. If electric dipole transitions of the molecules making up the waveguide structure are excited, then the signal from each eigenmode will be composed of contributions from different regions of the thin film. Thus if m modes are observed, a set of m equations is obtained, each one of which relates an observed spectroscopic signal intensity to a convolution of the electric field distribution for that eigenmode and the molecular number density distribution. We wish to recover the number density distribution by an appropriate inversion of the m signal equations. Optical depth profiling in thin-film waveguides then demands quantitative measurement of the molecular spectroscopic intensities as a function of waveguide eigenmode. First the optical properties (filmthickness and refractive indexes) are determined by measuring the resonant angles of the waveguide (30-38). From these properties the electric field intensity distribution perpendicular to the f i b plane for each mode is then calculated (23, 26-28, 31, 39-41). The relationship between the dopant distribution and the spectroscopic intensity for molecule of interest, a, in the presence of a homogeneously distributed internal standards, s, is (29)
where I,j and 1 8 j are spectroscopicintensities from the moiety of interest and the internal standard respectively, z is the distance from the substrate-film interface, Ej(z)is the electric field amplitude distribution, N,(z) and N, are the number density distributions for the molecule of interest and internal standard, respectively, D is a constant indicating the relative detectivities of the two species, and subscript j refers to the jth mode. In this equation, the internal standard is assumed to have a homogeneous distribution in at least one region of the waveguide structure. Ratioing the two spectroscopic signals eliminates all of the mode-dependent quantities from the signal equation as described previously (30,31). An important requirement for the validity of eq 1is that the dopant distribution, Na(z),must not affect the refractive index of the waveguide. Otherwise the electric field intensities would be perturbed, because they are a function of the refractive index (42). In principle the measured spectroscopic intensities contain information on the molecular distribution, Na(z),since all other parameters in eq 1 can be calculated or measured. Unfortunately eq 1is a Fredholm integral equation of the first kind. These equations are ill-posed, so small errors in the measured intensities (left hand side of eq 1)lead to large errors in the N J z ) function recovered by standard integral equation solution methods (43-46). If the functional form of the dopant distribution is known however, the parameters characterizing the distribution may be determined in a straightforward manner. For example in the present work we examined one(eq 2a) and two- (eq 2b) interface step function profiles N ( z ) = 0; 0 Iz Iz1 = No; z 1 < 2 5 t (24 N ( z ) = 0; 0 Iz < z1and z2 Iz It = No; z1 Iz < z2 (2b)
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INTERFRCE POSITION,
,
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1.2 1.4 2 1 IMlCRONSI
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Figure 1. Plot of the slngle Interface error sum for four different structures all of 2.0-pm total thlckness but wlth varylng Interface positlons. The tendency to obtaln secondary mlnlma Increases as the Interface approaches the substrate-fllm boundary.
where zi = position of the ith interface, and t = film thickness. In the single interface case, determination of z1 and No completely describes the spatial distribution. Thus solution of the integral eq 1 is reduced to finding the distribution parameters (zi in this example) which most closely reproduce the observed intensity ratios. Determination of the absolute number density, No,must be treated in combination with other methods (35))so only the parameters determining the spatial form of the distribution are considered here. For an optically homogeneous composite structure consisting of two polymer layers, eq 1 can be rewritten in the following form
where I , and Ib are spectroscopic intensities from the top and bottom layers, respectively, and z1 is the interface position. The effect of changing modes, i.e. changing the ratio of integrals in eq 3, on spectra from multilayer structures can be seen for example in Figure 3 of ref 31. Because the system of equations is ill-conditioned and only one parameter need be fitted, it is practical to allow z1to vary over all possible values and compute the error, G(zl), as
where j is the mode excited, m is the highest order mode, wj is a pseudovariate weight factor, and S = DN,/Nb is the preintegral factor from eq 3. The use of weighted least squares permits optimum use of information from weaker modes, which are frequently characterized by larger uncertainties in the spectroscopic intensity ratio. Figure 1 illustrates the behavior of G(zl). Although the correct interface position is given by the minimum in the error surface for all four cases, note the existence of weaker minima (called secondary minima henceforth) for some of the values of zl. Fortunately, these local minima can easily be distinguished from the correct minimum, if a priori information about S is available. In the case of simple step profiles S is
ANALYTICAL CHEMISTRY, VOL. 60, NO. 5, MARCH 1, 1988 409
Table I. Results of Step Function Interface Determinations Single-Interface Samples sample
zAphys),0nm
z,(spec),*nm
P4VPIPSIBK-7d P4W/DPS/Si02 PSJP4VPJSiOz
501 709 1696
448
t:
error, %
n(composite)/n(lower)c
2.7 3.7 -25
1.597911.5944 1.596511.5966 1.597511.5972
2.03 2.43 2.38
618 1702
Double-Interface Samples sample
zl(phys),Onm
z2(phys),"nm
z,(spec),b nm
z2(apec),bnm
av error, %
P4VPJDPSIX-PQVPISi02 P4vP JPS/X-P4vP/Si02
660 550
1661 1722
640 622
1530 1702
3.2 1.9
I, Interface position determined from resonant coupling angles and/or interferometry after stripping off the top layer. Interface position determined spectroscopically. Comparison of refractive indexes determined by assuming a homogeneous structure (composite) and after stripping off the top layer (lower). dP4vP = poly(4-vinylpyridine),PS = polystyrene, DPS = polystyrene-& e t = total film thickness. 1.0
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Figure 3. plot of the error function vs. position for three different cases an experimental data set in which of a SI02/PS/P4VPstructure: (-) the j = 0 mode was too weak to measure Raman signals, (---) a simulation for an identical structure with simulated data for the j = 0 mode, and (- -) simulated data without the j = 0 mode.
-
600
640
600
;(cm-')
Figure 2. Determination of the interface position in a SI02/PS/P4VP structure. The portion of the Raman spectrum containing the in-plane ring bending vibration of PS and the outof-plane rlng bending from P4VP Is shown at the bottom. The position of the interface determined from physlcai measurements (top)Is labeled rdphys), while the posltlon determlned from wavegulde spectroscopic measurements is labeled 2 o(swc).
simply related to the ratio of sensitivities of the spectroscopic signals from the two layers and can readily be measured. For each position z1a weighted least-squares value of S is calculated, so each local minimum has a characteristic calculated S value. Since the real S value is readily available from experimental intensity ratios, it can be used to distinguish global and local minima in cases where the error sum alone does not permit a statistically valid choice to be made.
RESULTS AND DISCUSSION Single-Interface Structures. Three different thin-film composite structures were examined. Raman scattering from the inplane ring bending deformation of PS (625 cm-') and the out-of-plane P4VP ring bending deformation (675cm-') were used as internal standard and analyte, respectively (Figure 2). For samples containing DPS the C-D, C-H
stretching region was used to spectrally resolve the two polymers. First the intensity ratios of these peaks as a function of mode were used to determine the interface position z1from eq 3 and 4. A physical measurement of the interface position was then performed by first removing the top polymer film with an appropriate solvent and then determining the thickness of the lower film from the resonant coupling angles and interferometry. Results are tabulated in Table I. First note the similarity between the refractive index of the composite structure and the refractive index of the lower film for the single interface structures. This refractive index homogeneity was important, because it allowed the structure to be treated as an optically homogeneous structure in which the concentration of pyridyl moieties is distributed as a step function. In addition this permitted the structure to be treated as a three-layer (single-thin-fii) waveguide structure to which eq 1 is applicable. Interestingly, while the PS/P4VP/Si02 sample gave the most accurate result, it was by far the worst case studied with respect to secondary minima. Figure 3 illustrates both the severity of the problem and the method for identifying the correct minimum. Previous experiments yielded a value of the S parameter from eq 3. Because an S value could be associated with each point on the error curve, the true minimum was identified by its agreement with the experimentally determined S value. This example also illustrates the im-
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ANALYTICAL CHEMISTRY, VOL. 60. NO. 5. MARCH 1, 1988
portance of using the lowest order mode V = 0) for discrimination against secondary minima. For this particular sample the j = 0 mode was not used due to weak in-coupling efficiency. Simulations illustrate the importance of the j = 0 mode (Figure 3). Secondary minima are not present when the j = 0 mode is used but appear if information from this mode is left out. There is no reason to exclude data from weak modes, because pseudovariate weighting techniques largely compensate for the poorer precision in the spectroscopic signals from weak modes, thus enhancing the ability to identify local minima. The relatively small discrepancies in the determination of the interface position can be attibuted to several factors. Significant sources of error include the electric field intensie coupled into nonresonant modes of the waveguide, inaccuracies in the measured Raman intensities (due to a sloping background), and errors in measuring the structure thickness a t the same physical location as the optical depth profiling experiment. Excitation of nonresonant modes in the waveguide structure is caused by in-coupled scattered light a t the base of the prism. In sample 2 (Table I) the nonresonant background constituted as much &s 5% of the weakest mode intensity and perturbed the electric field amplitude distribution, E(z),in an unknown manner. The nonresonant angular background does not appear to vary substantially over small angular regions, so summing the resonant and nonresonant fields gives
1, = ~ ( E J %+)%??,(Z)Eb(Z)
+ Eb2(Z))h%)
dZ ( 5 )
where I, is the measured spectroscopic intensity, and E,(z) and E&) are the resonant and nonresonant electric field amplitude distributions, respectively. Therefore, while it is possible to partially compensate for the nonresonant background hy subtracting the spectrhscopic intensities on either side of the resonance, due to the Eb2(z)term, the cross term, (E,Eb),cannot in general be eliminated. Hence, the nonresonant background must be minimized hy paying careful attention to placement of the coupling prism. The error mused by the second factor, spectral background variation, is unavoidable and represents the ultimate limit in this measurement. The spectral background is, unfortunately, mode dependent and therefore not easily compensated. Finally, the precision in the physical determination of the interface position is limited due to inexact repositioning (fl mm) on a nonuniform film thickness sample. This introduces an uncertainty
