1203
Anal, Chem. 1985, 57, 1203-1208
Theory of Spectroscopic Sampling in Thin Amorphous Films Paul W.Bohn Department of Chemistry and Materials Research Laboratory, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
Expressions for the electric field intensity spatial distribution in an optical waveguide are given and used to calculate spatial intensity profiles normal to the film plane for the TE, TE4 modes of a (PS) poiy(styrene)-poly(vinyi alcohol) (PVA) structure on silica. Using guided waves to detect the presence of a surface adiayer of known optical properties in the absence of interfering adsorbents by measuring the mode perturbation it causes is explored. The inherent sensitivity of this perturbation technique is calculated for different modes and used to predict detection limits of ca. 2.0 nm of a material with an index difference An = 0.02 from the main guiding layer. The experimental approach to attain these detection limits is also discussed. Expressions are derived for the power In each region of an arbitrary complex waveguide structure. These are then used to show how quantitative preferential sampling can be accomplished in three- and four-layer thin film structures.
-
errors in the computational inputs and experimental reproducibility, how perturbations to the waveguide structure, such as those presented by the growth of a small surface adlayer, affect the waveguiding behavior, and how the field distributions are translated into spectroscopic intensities outside the guide medium. Each of these points is considered in detail in the present work. Development of the theory of waveguiding in both threeand four-layer all-dielectric structures has been discussed in detail (23,29-31). With reference to Figure 1, the conditions for waveguiding are that the internal angle of incidence, e2 or 03, be above the critical angle for total internal reflection and that the total phase shift upon traveling one complete cycle in the film be an integral muliple of 2a. Equations 1-6 express the latter conditions mathematically.
l/zK2t2- tan-l(K\/Kz) - tan-l ( K 1 / K 2 )= m a
(1)
Ki= V i= 27rJneff2- ni211/2/X TE modes
(2)
Ki= Ui/n: Traditionally problems with existing analytical techniques have made nondestructive condensed-phase interface and matrix studies especially difficult experimentally. The most significant problem lies in the relevance of existing techniques to real systems. The need for a high-vacuum environment and the relatively primitive nature of model systems make the various electron and X-ray spectroscopies less than ideal candidates for investigating condensed-condensed interfaces. Micrometer-sized systems are also difficult to study optically because position-specific probes require a localized signal which is at or below the optical diffraction limit. In addition typical monolayer and doped thin film systems may contain picomoles or less of sample, requiring an extraordinarily sensitive and specific analytical probe. Clearly novel experimental tools are needed to make significant progress in studying the analytical chemistry of these systems at small dimensions. The various optical spectroscopies offer many attractive features for the problems of speciation and quantitation in thin film systems; however, the sensitivity problem has been a long-standing barrier to the implementation of these techniques at small dimensions. Recently several laboratories have made significant progress in overcoming the sensitivity problem by utilizing a variety of specialized optical phenomena including spectroscopy with the evanescent wave from internal reflection (1-5), use of p-polarized light at glancing incidence in reflection-absorption spectroscopy (6-1 01, enhanced sensitivity spectroscopy at metal-liquid interfaces (11-13), and excitation of molecular scattering and fluorescence with surface plasmons (14-22) and integrated optical techniques (23-28). Among these techniques the use of integrated optical assemblies alone is potentially capable of yielding spatially resolved molecular profiles. Obtaining this information, however, implies a thorough understanding of the coupling mechanism and the spatial electric field distributions upon excitation of resonant modes in asymmetric slab dielectric waveguides. Specifically, this means understanding how the precision and accuracy of the measurements are affected by
K\ = K3
TM modes three layers
(3)
(4)
where
neff= n2 sin d2 (=n3sin 0,)
(6)
In eq 1, the fist term on the left-hand side is the phase shift due to propagation in the film, while the second and third terms are due to reflection at the film-superstrate (layers 2 and 3) and film-substrate (layers 2 and 1) interfaces, respectively. When a four-layer structure is considered instead of the simple three-layer waveguide, propagation can take place in one or both layers as shown in Figure 1, and the eigenvalue equation (eq 1) is altered to include a correction term at the film-superstrate interface (eq 5 ) (31). Equation 5 is appropriate for the situation in which propagation takes place in both media. If one layer was cut off, then the tangents in eq 5 would be replaced by hyperbolic tangents (32). These equations form a set of nonlinear transcendental equations describing characteristic eigenmodes of the thin film structure. Different modes are specified by varying values of the parameter m in eq l. Solutions may be obtained by a variety of numerical techniques. In our laboratory a Newton-Raphson algorithm is used to solve the equation for three-layer structures, while an iterative linear interpolation is used for four-layer structures, due to the complexity of the derivative of the left-hand side of eq 1 in the four-layer case. Both algorithms are very efficient, finding solutions (i.e., values of 82 satisfying eq 1) accurate to 1.6 X mrad in less than five iterations typically. Equations 1-6 imply that a knowledge of the optical properties (ni,ti)of the thin film system infer the ability to predict the waveguiding behavior. The converse is also true. Measurement of the set of angles between the laser propagation axis and film surface permits the set of coupling angles (Le., 4 and in Figure 1) to be calculated from simple Snell’s
0003-2700/85/0357-1203$01.50/00 1985 American Chemical Society
1204
ANALYTICAL CHEMISTRY, VOL. 57, NO. 7, JUNE 1985 ," 0,9-
-
-
0.8
5
a6-
0.7 -
3
0.5
-
VI
5
0.4-
z
a3-
-
0.2 0.1
-
0POSITION (MICRONS)
Plot of the guided mode electric field intensity as a function of position perpendicular to the film plane for the five allowed modes of a four-layer structure consistlng of fused silica, PVA, PS, and air. Both films are 1.25 pm thick. Intensities in the left half of the figure have been multiplied by 1.4, and all intensities have been normalized to yield constant total power among modes. Figure 2.
Figure 1. Schematic of a four-layer thin film structure in which the thicknesses of layers 2 and 3 have been exaggerated. Wavegulding can occur when n2,n 3 > n,, n4. The expressions for three-layer structure are obtained by deleting n4 and t , and letting n4 = n3. The angles e2 and 8, are related through Snell's law.
~~
law considerations. These coupling angles then serve as the input data from which the unknown optical properties of an experimental thin film structure can be determined. In the present work an algorithm adapted from that of Ulrich and Torge (33) is used. In this paper, extensive use is made of eq 1-6 to calculate the optical properties (ni,ti) from the coupling angles, Oi, in order to gain an understanding of how changes in the materials and the excitation process can affect spectroscopic data. Being able to interconvert optical property data and waveguide coupling angles becomes important in spatially selective spectroscopic sampling, because knowledge of these parameters for a particular thin film system permits calculation of the spatial distribution of the electric field amplitude, E, and ita square, the electric field intensity. Rabolt and co-workers (34) have derived explicit expressions for the magnitide of the electric field amplitude in each of the four regions of a four-layer waveguide starting from the general expressions for an n-layer structure given by Polky and Mitchell (35).When those expressions are translated for the coordinate system of Figure 1, the following relations are obtained.
E4 = A1C2C3exp(-U4(z - ( t 2 + tJ)) E3 = A,C2[cos (U& - t z ) )+ ( K t z / K 3sin ) (U&
(7) -
tJ)l (8)
E 2 = Al[cos (U2z)+ ( K , / K 2 )sin (U2z)]
(9)
El = A, exp(U,z)
(10)
C3 = cos U3t3+ (Kt2/K3)sin U3t3
(11)
C2 = cos U2tz+ (K,/K2)sin U2t2
(12)
where
K', = K 2 [ ( K 1 / K 2- )t a n Uzt21/[l + (K1/K2) t a n U2t2l (13) where, in each expression, Al is a constant of proportionality. The expressions for the three-layer problem are given in eq 14-16. These expressions then allow calculation of the electric E3 = Al[cos U2tz+ (Kl/Kz) sin U2t2]exp(-U3(z - t 2 ) ) (14)
E 2 = Al[cos U2z + (Kl/Kz) sin Uzz]
(15)
El = Al expUlz
(16)
field amplitudes of intensities as a function of position perpendicular to the plane of the thin film(s) for systems which do not exhibit appreciable absorption. An example of such a calculation is shown in Figure 2 for a sample of nearly equal
Table I. Waveguiding Angles for the Structure of Figure 2 mode 02, deg 03, deg
neff mode 02, deg 03, deg
n,ff
83.616 1.5848 TEo CO" 83.842 1.5855 TMo co 77.381 1.5562 77.777 1.5585 TM, co TE1 co TE2 84.845 72.913 1.5243 TM2 84.431 72.787 1.5233 TE3 81.147 71.497 1.5123 TM3 80.509 71.192 1.5095 TE, 76.423 68.895 1.4877 TMI 76.044 68.656 1.4853 " The designation co signifies that the mode is formally cut off in that layer and that energy propogates principally in the other layer.
thicknesses of poly(viny1 alcohol) (PVA) and poly(styrene) (PS) on fused silica. Figure 2 shows a total of five transverse electric modes, the first two of which (i.e., TEo and TE,) are formally confined to the poly(styrene) layer. Modes TE2-TE4 propagate in both layers, though not with equal intensities. A geometric optics model of radiation propagation may be used to understand the above observations (36). At the eigenvalues shown in Table I for the TEoand TE1 modes, the refractive index of the PVA gives a Snell's law angle of reflection a t the PSIPVA interface which is above the critical angle for reflection at that interface. Also, as indicated in Table I, a cutoff mode is characterized by an effective index which is higher than the real index of that layer. This is the case for the two lowest order TE and T M modes in the PVA layer. The full intensity distribution for all modes contains information which is important to both bulk and surface sampling applications for two reasons. Bulk information is obtained, because spatially asymmetric electric field intensity distributions are in general obtained from asymmetric optical structures (i.e., those in which nl # n3 or nl # n4in four-layer systems). As pointed out by Swalen et al. (37), distributions may be adjusted to exhibit intensity maxima (and minima) in different portions of the multilayer structure by exciting different resonant modes of the structure (Le., different m values in eq 1). Surface sampling is affected, because the intensity a t an interface and the characteristic decay length of the intensity moving away from an interface into a cutoff region (e.g., the SiOz substrate for modes TE2-TE4, the underlying PVA layer for modes TEo-TEl, and the air superstrate for all modes) are obtained from these plots.
SURFACE SAMPLING With the theory outlined above, the question of the effect of a relatively thin surface overlayer can be addressed from an empirical point of view. The question may be stated as follows. If the known properties of a thin film waveguide are perturbed by the addition of a surface adlayer, what is the magnitude of the perturbation as measured by its effect on
ANALYTICAL CHEMISTRY, VOL. 57, NO. 7, JUNE 1985 td:
1205
imdeghm)
!-
156
76 0
16 4
816
820
824
808
eez
880
8,
(doe1
Figure 3. Plot of the calculated wavegulding angle vs. overlayer thickness for the modes TE,-TE, in a structure consisting of the following: fused silica substrate, n , = 1.4614; main layer, n 2 = 1.5100, t , = 2.00 pm; overlayer, n 3 = 1.4900; air, n 3 = 1.0003. I n each case, the slope of the curve at small overlayer thicknesses is the quantity of interest. The TM modes give similar results.
the waveguiding angles, 0,, in the main layer? Another way of stating this problem asks if a waveguide perturbation measurement can be used as the basis for chemical sensing by relating the change in waveguiding angle to the total amount of an adsorbed molecular layei. The model used to address this question is the four-layer model discussed in the previous section, However, in the cases under consideration here, the overlayer thickness is sufficiently small that propagation always occurs in the main guiding layer (Le., layer 2) only. In this configuration, incoupling must occur through the low-index overlayer as well as the prism-surface air gap. Generally the imposition of a low-index layer between the prism surface and the waveguiding medium would be expected to diminish the coupling efficiency (38). However satisfactory coupling with PVA overlayers up to 0.5 pm thick on PS waveguides has been observed in our laboratory. Thus, for the very thin overlayers to be discussed below, satisfactory incoupling can be expected even in the presence of a low-index medium. To investigate the sensitivity of the waveguide perturbation measurement, the magnitude of the change in the coupling angle for a given change in overlayer thickness must be known. This desired quantity is but since eq 1 cannot be solved analytically, the required partial derivative must be evaluated numerically. This was done by solving eq 1for a series of samples of varying overlayer thickness and evaluating the derivative in the low overlayer thickness regime. The results of one such series of calculations are shown in Figure 3. The derivative is evaluated a t low overlayer thickness which corresponds to the case most likely to be of analytical interest. However, Figure 4 shows that the sensitivity of the measurement is not constant but actually improves with decreasing overlayer thickness until a limiting value is reached near t3 = 10 nm. As is evident from Figure 4, although the sensitivity is roughly constant over wide ranges of thickness, sensitivity increased monotonically with mode number. This can be interpreted in light of the data plotted in Figure 2. Here higher order modes are characterized by having higher electric field intensities in the surrounding media than low order modes. It is not surprising that the modes carrying the largest relative fraction of their intensity outside the guiding filmshould experience the largest perturbation upon changing the properties of the external ambient. In fact the amount of power flow in the guide or substrate as a fraction of the total power flow can be calculated by using results derived in the next section. Anticipating those results for an asymmetric guide with nl = 1.4614, n2 = 1.51, tz = 2.0 pm, and n3 = 1.0003 yields values of 0.86% for the amount of total TEo power carried in the substrate, 3.93% for TE,, and 13.15% for the TE, mode.
t inm) 5
0 '
2
'
8
2
10'
'
5
2
IO
'
1
2
+
I
d O,l& 3, of waveguide perturbation measurements for the TE0-TE2 modes of the thin film structure described in Figure 3. The TM modes give similar results. Figure 4. Plot of the sensitivity,
I t is instructive to compare the predictions inherent in Figures 3 and 4 to experimental data. Swalen et al. have examined the mode perturbations of poly(methy1 methacrylate) and glass waveguides obtained by fabricating controlled thickness cadmium arachidate overlayers to determine the dispersion of the optical anisotropy in these films (39). Overlayer thicknesses ranging from 2.7 to 110 nm were employed, and experimental coupling angle determinations were published for the cases t3= 2.7 nm and t3 = 94.4 nm. Coupling angle shifts from Figure 2 of ref 39 are 0.071 f 0.059', 0.329 f 0.059', and 0.471 f 0.059' for the TEo-TE2 modes, respectively. The present calculational method, assuming the published data were obtained with the same coupling geometry and materials as used in that group's other publications and using their optical constants, yield shifts of 0.079', 0.299', and 0.587' for the TEo-TE2 modes. Thus, the agreement is very good for the two lower order modes and somewhat worse for the TE, mode. Part of the discrepancy can be attributed to the fact that the optical properties of arachidate films were obtained by a nonlinear least-sqaures fit to the same experimental data. The specific case of Figures 3 and 4 involves a relatively small (An = 0.02) difference in the optical properties of layers 2 and 3 in Figure 1. In general larger differences will be encountered in practice. The quantitative effect of changes in the difference An between film and overlayer refractive index of the waveguide perturbations is shown in Figure 5. As expected, larger An values lead to smaller perturbations. Again this can be understood in terms of the amount of power carried out in the substrate. More power is carried in the substrate for relatively small values of An, meaning that changes in the thickness of the overlayer would have a larger absolute effect than would be the case for interfaces with larger An values. The predictions inherent in Figures 4 and 5 beg the question, what is the likely detection limit for a thin molecular overlayer in these systems. Monolayer detection has been reported in the literature by using a grating coupler to observe changes in the eigenvalues upon adsorption of water vapor directly on the grating (40). These authors calculate that a change in the effective index neffof 1 X lo4, corresponding roughly to one monolayer of HzO, would be required for switching applications, whereas sensing could be accomplished with much smaller amounts. In a prism-coupled waveguide, such as the ones used in our laboratory, the molecular adsorption would occur on the surface of the guide itself and not necessarily in the coupling region. The sensitivity would then translate into detection
-
1206
ANALYTICAL CHEMISTRY, VOL. 57, NO. 7, JUNE 1985
A0
(deglnm)
,070 ,060
,050
.040 ,030 ,020 ,010
t L
\
.20
,IO
.30
An
Figure 5. Plot of the changes in waveguiding angle, 02,vs. the refractive index differences, An, between layers 2 and 3 of Figure 1 for a structure in which n , = 1.46, n P = 1.56, t P = 2.0 bm, f3 =10 nm, and n 4 = 1.00. The curves from top to bottom are for the TE,-TE, modes, respectively.
limit by considering how small a change in the position of an outcoupled beam could be detected reliably. Using a 100% efficient outcoupling prism to illuminate the active area of a micrometer driven photodiode would mean that the detected power is determined by the cross-correlation of the area of the photodiode and the beam intensity profile. Photodiode active area is fixed in a particular experiment, while beam size at the detector depends on beam divergence and the distance of the photodiode away from the waveguide. In a well-designed optical train, the beam waist occurs at the air gap at the corner of the incoupling prism. Then the size of the beam in a Gaussian system is given by eq 17 and 18, where wi = r
4f wo = TWi
(18)
initial beam radius (at the laser output mirror), f = focal length of a focusing optic, w o = miniumum beam radius at the focal spot, z = distance traveled along the direction of propagation, and w ( z ) = beam radius as a function of distance (41). In typical prism-coupled systems, the input light is only mildly convergent, so employing an f = 500-mm lens, Ar+ laser light at 514.5 nm has a diameter of 825 pm at a distance of 500 mm from the incoupling prism, in the absence of scattering. Two specific limiting causes can be distinguished. In each case, the detected intensity function is just the cross-correlation of the Gaussian beam profile, I(%),with the detector sensitivity profile, S(x),as given by eq 19 (42). If the detector
is much larger than the beam waist, and if S ( x ) is constant across the active area, then the detected intensity will rise, become constant, and then fall. That is, the cross-correlation will resemble the detector sensitivity function, S(x). As the size of the beam waist becomes smaller with respect to the detector, the slope of the rising portion of the detected in-
tensity curve becomes larger, giving rise to sharper profile edges. In the case in which the detector area is much smaller than the beam profile, the detected intensity profile follows approximately the beam intensity profile I(%). In the former case, the position of the beam is taken as the center of the intensity plateau, whereas for the latter case the position is taken from the peak in intensity as a function of position. This latter technique is expected to be more accurate. Thus, maximum accuracy in measuring the position of a shifted beam may be obtained by expanding the outcoupled beam before detection. When these arguments and measurements of the reproducibility of the determination of the coupling angles in 1.0-pm poly(styrene) waveguides (43) are used, it should be possible to reliably measure changes of AOi 1 0.02O. Coupling this with the sensitivity calculations shown in Figure 4 implies detection limits for adsorbed Iayers of 5.2,2.6, and 2.1 nm for the TE+2 modes, respectively. This compares well with the data of ref 39. Here a change of ca. 0.07' was easily measured for the TEo mode for an arachidate overlayer thickness change of 93.7 nm. If the same difference was measured at the TE, mode in this system, the corresponding thickness change would be 10.0 nm.
BULK SAMPLING Another area of current analytical interest lies in developing techniques to selectively probe the concentration profile of an atomic or molecular dopant in a solid matrix. With atomic dopants in crystalline solids, this can be done by various depth-profiling techniques based on the vacuum spectroscopies (44-46). However, it is far more difficult to profile molecular dopants in amorphous matrices due to problems with sample charging, bulk rearrangement, and dopant decomposition when applying Auger or secondary ion mass spectrometry. Here again use of optical guided waves in thin film structures can be of use. Whereas the vacuum spectroscopies probe the depth dimension by measuring the surface concentration of the analyte as the sample is sputtered, guided waves have the capability to sample different portions of the solid simultaneously. In addition, each mode spectroscopically samples the thin film structure differently. In three-layer structures, the electric field amplitude profiles are given by eq 14-16. Plots of the intensity as a function of position in these structures show that there is a sinusoidally varying intensity in the guide itself and an exponentially decaying field outside the guide. The number of nodes in the intensity profile is just equal to the node number, and the characteristic decay length of the field outside the guide depends on the optical properties of the guide-ambient interface, with smaller differences in refractive index, An, corresponding to longer decay lengths. In threelayer systems, for example, the ability to measure whether a molecular component is nearer the substrate or superstrate depends on the fact that Anlz # Anz3,where Anif = In, - n,l. As can be seen from Figure 2, the situation is far different in a four-layer structure. Here the nature of the field intensity profiles depends on the refractive indexes and thicknesses of both layers as well as the properties of the ambient media. In the PVA/PS thin film sandwich structure for which the calculations shown in Figure 2 were done, preferential sampling of the PS film can be achieved by excitation of the TEo mode, while excitation in the PVA film can be obtained by exciting the TE3 mode. The PS excitation for TEWlmodes is another consequence of the fact that these modes are cut off in the PVA film. Mode TE3,however, exhibits intensity in the PS layer in addition to the bulk of the intensity which is carried in the PVA layer. In order to have a better idea of how the total power being carried in each layer changes as a function of the optical
ANALYTICAL CHEMISTRY, VOL. 57, NO. 7, JUNE 1985
properties of the media involved, it is necessary to calculate the total power in each region explicitly. The power is just the irradiance, Z, integrated over the cross-sectional area of the beam. However, in waveguides, the electric field amplitude does not vary in the transverse direction which is parallel to the film plane, so the integration need only be performed over the transverse direction perpendicular to the film plane, i.e., the z direction in Figure 1. That is
Pij = const
X
lCiJ(y,z) dy dz
= const X L I i j dz =
const X I E Z , ( z ) dz (20) where the constant in each equation is different and the subscripts, j and i, run over the set of allowed modes of the waveguide and the various regions respectively. Thus, considering the three-layer structure
P2j = const
U2jz+ Lt2 U2jz+ (K1j/K2j)2 X
(2Klj/K2j)cos U2jz sin
[cos2
sin2 UZiz]dz =
where C, is given by eq 11 and B is a constant required to convert to units of power. For a four-layer structure, PI, and PZi are given by eq 21 and 22 and
r
+
cos2 U3j(z- t2)
2Kkj K'zj2 -cos U3j (z - t z ) sin U3j( z - t z )+ -sin2 U3j(z
K,? -,
K3j
-
t 2 ) ] dz = BCzr[
( l
P4/= const
X
X
--)+.Kj2 K3?
]
K2j' sin2 U3jt3 u3j
(24)
dz = BC212C3J2/2 U4]
C3J2e-2U4J(z-t2-t3)
(25) where C,, is given by eq 12 and K ; by eq 13. Thus, knowledge of the waveguiding angles obtained from a solution of eq 1-6 for a hypothetical structure or by direct measurement of an experimental structure is necessary and sufficient information for the calculation of the amount of incoupled power carried in each section of the thin film composite. The elements PIJmay be collected in the form of a p matrix whose rows give the power distribution among the various layers for a given mode and whose columns show how the power in a particular layer varies with the mode excited. Normalization of the individual elements is accomplished by dividing each element PcJby the sum of elements in that row, ~ , P I JIn. this way the power in each layer of the four-layer
1207
Table 11. Modified Transverse Electric p Matrix for the Structure of Figure 2 mode TEOn TE,' TE2
TE3 TE4
IPVA/XZ
IPS/
CI
0.9801 0.8978 0.2648 0.4440 0.2592
0.0191 0.0990 0.7268 0.5300 0.6500
(Isio2 + I d / X I 0.0008 0.0032 0.0084 0.0260 0.0908
OThese modes are formally cut off in the PVA layer, so the last column contains only a contribution from the air region. structure, for which the mode profiles are shown in Figure 2, can be calculated. The results, which agree closely with results of numerical integrations on the same structure, are shown in Table 11. These data confirm the visual interpretation of Figure 2. Very little power is present in the PVA layers for the TEhl modes because the PVA layer is cut off, above TE1 the PVA layer is dominant, and the substrate plus superstrate power increases monotonically for modes TE3+ As can be seen from Figure 2 and Table 11,the amount of power in the PVA layer is maximixed in the TE2 mode but is still quite large for the TE3 and TE, modes. The first conclusion to be drawn for bulk sampling concerns spatially homogeneous distributions of dopant molecules. In any experiment in which the signal intensity is proportional to excitation intensity (e.g., fluorescence or Raman scattering at low incident powers), a homogeneous distribution of analyte molecules will yield a signal which is proportional to the product of the normalized p-matrix element for the doped layer for the particular mode excited, the mode-dependent coupling efficiency parameter, and the concentration of the analyte. Appropriate p-matrix elements can now be calculated from eq 21-25, and efforts are currently under way to characterize the coupling efficiency parameters. These two pieces of information then are necessary and sufficient for the quantitative determination of analytes homogeneously distributed in a thin film. For analyte distributions which are not spatially homogeneous, the situation is more complex. A dopant molecule number density distribution, N ( z ) ,and a mode-dependent coupling efficiency, y I ,would yield a signal intensity in a Raman or fluorescence experiment given by t
Ij =
T R , F y i S , E j 2 ( z ) N ( z )dz
(26)
where TR,F represents an experiment-dependent efficiency factor. In the general case, N ( z )is not known, so the integral in eq 26 cannot be evaluated directly. However, the set of signal intensities, Zj, for a large number of modes will necessarily contain information about the dopant molecule distribution, and, under certain sets of circumstances, can be used to reconstruct the molecular concentration profile of the dopant. In addition for relatively thick films (> 2 pm) spatially asymmetric sampling is possible as pointed out by Swalen and co-workers (37). This is accomplished by adjusting the individual layer thicknesses and refractive indexes to bring the intensity maxima to the desired position, such as a material interface.
CONCLUSIONS It has been shown that exploiting different aspects of the guided wave electric field intensity distribution can address different portions of a thin film structure. Examining the evanescent portions of the distribution can lead to information on the optical properties of the surrounding media and ultimately to adlayer concentration measurements with detection limits in the picomole regime. Conversely turning attention to the bulk intensity profiles can allow spatially selective fluorescence and scattering measurements to be made.
1208
Anal. Chem. 1985, 57, 1208-1210
In four-layer structures, this technique can be utilized to excite dopants in one layer perferentially, while in three-layer structures molecular concentration profiles are amenable to measurement. Registry No. SOz,7631-86-9 PVA (homopolymer),9002-89-5; polystyrene, 9003-53-6. LITERATURE CITED (1) Hatta, A.; ashima, T.; Suetaka, W. Appl. Phys. A 1982, A29, 71. (2) Tompklns, H. G. Appl. Spectrosc. 1974, 28, 335. (3) Blackwell, C. S.;Degen, P. J.; Osterholtz, F. D. Appl. Spectrosc. 1978, 3 2 , 480. (4) Palik, E. D.; Gllson, J. W.; Holm, R. T.; Hass, M.; Braunsteln, M.; Garcia, 13.Appl. Opt. 1978, 77, 1776. (5) Iwamoto, R.; Miya, M.; Ohta, K.; Mima, S.J . Chem. Phys. 1981, 74, 4780. (6) Tompkins, H. G.; Allara, D. L. Rev. Scl. Instrum. 1974, 4 5 , 1221. (7) Boerlo, F. J.; Chen, S. L. Appl. Spectrosc. 1979, 33, 121. (8) Aliara, D. L.; Baca, A,; Pryde, C. A. Macromolecules 1978, 7 1 , 1215. (9) Ishitanl, A.; Ishlda, H.; Soieda, F.; Nagasawa, Y. Anal. Chem. 1982, 5 4 , 682. (IO) Golden, W. 0.; Saperstein, D. D. J . Nectron Spectrosc. Relat. Phenom, 1983, 3 0 , 43. (11) Zhizhin, G. N.; Moskalova, M. A.; Sigarev, A. A.; Yakovlev, V. Opt. Commun. 1982, 4 3 , 31. (12) Aravind, P. K.; Rendell, R. W.; Metiu, H. Chem. Phys. Lett. 1982, 85,
396. (13) Yamada, H. Appl. Spectrosc. Rev. 1981, 77, 227. (14) Bhasln, K.; Bryan, D.; Alexander, R. W.; Bell. R. J. J . Chem. Phys. 1978, 6 4 , 5019. (15) Pockrand, I.;Swalen, J. D.; Gordon, J. G., 11; Phllpott, M. R. Surf. Sei. 1977, 7 4 , 237. (16) Gordon, J. G., 11; Swalen, J. D. Opt. Commun. 1977, 2 2 , 374. (17) Weber, W. H.; Eagen, C. F. Opt. Lett. 1979, 4 , 236. (18) Chabal, Y. J.; Severs, A. J. J . Vac. Scl. Techno/. 1978, 15, 638. (19) Benner, R. E.; Dornhaus, R.; Chang, R. K. Opt. Commun. 1979, 3 0 , 145
(20) Girlando, A.; Phllpott, M. R.; Heitmann, D.; Swalen, J. D.; Santo, R. J . Chem. Phys. 1980, 72, 5187. (21) Weltz, D. A.; Garoff, S.; Hanson, C. D.; Gramila, T. J.; Gersten, J. I. ODt. Left. 1982. 7.89. (22) Kholl, W.; Phllpott, M. R.; Swalen, J. D.; Glrlando, A. J. Chem. Phys. 1982, 77, 2254.
(23) Swalen, J. D.; Tacke, M.; Santo, R.; Rleckhoff, K. E.; Fischer, J. Helv. Chim. Acta 1978, 67, 960. (24) Rabolt, J. F.; Santo, R.; Swalen, J. D. Appl. Spectrosc. 1979, 33, 549. (25) Rabolt, J. F.; Santo, R.; Swalen, J. D. Appl. Spectrosc. 1980, 3 4 , 517. (26) Stegeman, G. I.; Fortenberry, R.; Karaguleff, C.; Moshrefzadeh, R.; Hetherington, W. M., 111; VanWyck, N. E.; Slpe, J. E. Opt. Lett. 1984, 8 , 295. (27) Hetherington, W. M., 111; Van Wyck, N. E.; Koenlg, E. W.; Stegemann, G. I.; Fortenberry, R. M. Opf.Lett. 1984, 9,88. (28) Schlotter, N. E.; Rabolt, J. F. Appl. Spectrosc. 1984, 38, 208. (29) Tlen, P. K. Appl. Opt. 1971, 70, 2395. (30) Kogelnlk, H.;Weber, H. P. J . Opt. SOC.Am. 1974, 6 4 , 174. (31) Swalen, J. D.; Santo, R.; Tacke, M.; Fischer, J. IBM J . Res. Dev. 1977, 2 7 , 168. (32) Reisinger, A. Appl. Opt. 1973, 12, 1015. (33) Ulrlch, R.; Torge, R. Appl. Opt. 1973, 72, 2901. (34) Rabolt, J. F.; Santo, R.; Schlotter, N. E.; Swalen, J. D. IBM J . Res. Dev. 1982, 2 6 , 209. (35) Polky, J. N.; Mitchell, G. L. J . Opt. SOC.Am. 1974, 6 4 , 274. (36) Tlen, P. K. Rev. M o d . Phys. 1977, 4 9 , 381. (37) Rabolt, J. F.; Schlotter, N. E.; Swalen, J. D. J . Phys. Chem. 1981, 85, 4141. (38) Ulrich, R. Appl. Opt. 1970, 6 0 , 1337. (39) Swalen, J. D.; Rleckhoff, K. E.; Tacke, M. Opt. Commun. 1978, 2 4 , 146. (40) Tiefenthaler, K.; Lukosz, W. Opt. Lett. 1984, 10, 137. (41) Marcuse, D. "Light Transmlsslon Optics"; Van Nostrand Relnhold: New York, 1972;Chapter 8. (42) Bracewell, R. N. "The Fourier Transform and Its Applications"; McGraw Hill: New York, 1978;p 46. (43) Han, 0.H.; Bohn, P. W., unpublished results. (44) Winograd, N. Prog . Solid State Chem. 1982, 13, 285. (45) Swingle, R. S.,11; Riggs, W. M. CRC Crit. Rev. Anal. Chem. 7975, 5,267. (46) Holm, R Scannlng Nectron Mlcrosc. 1982, 7, 1043
RECEIVED for review November 1,1984. Accepted February 4,1985. Support of this work by the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the National Science Foundation Grant DMR83-16981 is gratefully acknowledged.
Tandem Mass Spectrometry with Fast Atom Bombardment Ionization of Cobalamins I. Jonathan Amster and Fred W. McLafferty* Department of Chemistry, Cornel1 University, Ithaca, New York 14850
Artifact peaks in mass spectra from fast atom bombardment (FAB) lonlzatlon can be characterized by tandem mass spectrometry. FAB of vitamin B,, (molecular weight 1354) produces a m / z 1388 peak whose abundance grows at the H)' with continuing bombardment. The expense of (M secondary mass spectrum of m / z 1388 produced by colllsionally actlvated dissociation (CAD) indicates that It Is formed by Intermolecular transfer of a cobalt atom from one molecule to the phosphate group of another. The CAD mass spectra of m / z 1329 formed by loss of the axlal substituent on Co from four different cobalamins are virtually identical, evidence that matching CAD reference spectra to characterize ion structures is also applicable to much larger fragment ions.
+
Fast atom bombardment (FAB) has shown itself to be a powerful ionization method for the mass spectral analysis of high molecular weight compounds ( I , 2). Labile organic molecules as large as human proinsulin, molecular weight 9390,
have been found to produce detectable molecular ion species (3). For many compounds, FAB produces both molecular and fragment ion species that give important molecular weight and substructural information. When FAB ionization does not form appreciable fragment ions, as in the case of the heptadecapeptide gastrin (4),tandem mass spectrometry (5) can supply substructural information; the molecular ion species separated by the first mass analyzer (MS-I) is made to undergo collisionally activated dissociation (CAD) producing fragment ions which are mass analyzed in MS-I1 (6-10). Another application of tandem mass spectrometry to an important problem of FAB, spurious peaks, is described here (9). In FAB, the sample is desorbed from a solution, usually glycerol, by irradiation with an intense atom beam for several minutes, so that sample degradation or chemical reactions between sample and solute can occur (11,12). Solvent-molecular ion complexes have been observed in the FAB mass spectrum of folic acid (13),(M 12n)+ions in the FAB spectra of amines (14),amine replacement o f a halogen atom by a solvent proton in the FAB spectra of halogen substituted nucleotides (151, and hydrogenation by glycerol in the FAB
0003-2700/85/0357-1208$01.50/00 1985 American Chemical Society
+
