Variable-angle internal-reflection Raman spectroscopy for depth-resolved vibrational characterization of polymer thin films N. H. Fontaine and T. E. Furtak Department of Physics, Colorado School of Mines, Golden, Colorado, 80401 Received 26 September 1997 We have developed a general technique that is capable of providing molecular signatures as a function of depth in a multilayer thin film. Variable-angle internal-reflection Raman spectroscopy has been used to locate buried interfaces with nanometer-scale precision and to determine refractive indices to within 0.0001. We have demonstrated this method in several applications, including the detection of toluene diffusion across a polystyrene/polymethyl methacrylateinterface. S0163-18299806307-3 Depth-resolved measurement of the molecular structure of thin polymer films can provide insight about diffusion and interface formation. Although techniques with this capability are available, they either require special facilities neutron reflectivityor are inherently destructive secondary-ion mass spectrometry and other ion milling methods. By con- trast, optical radiation has the potential to provide depth- dependent information without disturbing the sensitive con- ditions that frequently exist in these systems. In particular, variable-angle internal-reflection Raman spectroscopy VAIRRSis well suited to the task of measuring the distri- bution of molecular concentrations and orientations. How- ever, until now, quantitative depth profiling using an internal reflection approach has not advanced beyond the demonstra- tion phase. 1,2 We report here the completion of several essential steps toward developing VAIRRS into a reliable depth-profiling technique. We have identified and quantified precision and accuracy limits as well as common systematic errors. The details of our methodology are presented elsewhere. 3 In this paper, we outline the essentials of our approach, and present a summary of demonstration experiments that show how to extract the depth dependence of a Raman signature. Our ob- jective has been to study a sample containing a fabricated discontinuity. We sought to show that VAIRRS was capable of locating the discontinuity and therefore of yielding a crude depth profile under those conditions. Beyond that, however, our method has also identified the migration of a small mol- ecule tolueneacross the discontinuity. A representation of the experiment appears in Fig. 1. The incident medium is an internal reflection element IREmade of sapphire. Its refractive index is larger than that of the sample, which extends from z =0 to z =d . The scattered light is collected from the air side of the sample with an optical fiber, as shown. Raman scattering that origi- nates at a particular depth, z , within a differential thickness z contributes to a differential detected intensity I ( , z | ¯ ), which is proportional to the local Raman source function C ( z | ¯ ), and the local optical energy density | E ( , z ) | 2 , ac- cording to I , z | ¯ C z | ¯ | E , z | 2 z . 1 We note that is the angle of incidence defined within the IREat the IRE/polymer interface, and that ¯ is the Stokes wave number of the center of a particular feature in the Ra- man spectrum whose integral magnitude is I . By concen- trating on a restricted region of the Raman spectrum, within a range around ¯ , one can tailor a VAIRRS experiment to provide information about specific molecular identities, ori- entations, and other characteristics of the sample to which the Raman effect is sensitive. The measured signal includes contributions from the en- tire sample, at all values of z . I | ¯ = I , z | ¯ . 2 The goal of the VAIRRS experiment is to extract C ( z | ¯ ) from high precision measurement of the dependence of I ( | ¯ ). This is accomplished by modeling I ( | ¯ ) using C ( z | ¯ ) as an adjustable function. The optical field E ( , z ) can, in principle, be calculated. 4 However, this depends on the refractive index n ( z ' ) throughout the sample, not just at z . In general, n ( z ' ) and C ( z ' | ¯ ) are coupled, since both are derived from the local molecular structure. 5 To make the modeling tractable it is practical to divide the film into a small number of layers. This is illustrated in Fig. 1, where layer i , with thickness h ( i ), is one of N -2 layers, and part of the overall system of N media. In this simplifi- cation, each layer is assumed to be homogeneous, with re- FIG. 1. Schematic arrangement for the VAIRRS experiment. The sample extends from z =0 to z =d , and is bounded by the internal reflection element IREand air. The angle of incidence is reported within the IRE. A fiber optic bundle was used to collect the Raman scattered light. PHYSICAL REVIEW B 15 FEBRUARY 1998-I VOLUME 57, NUMBER 7 57 0163-1829/98/577/38074/$15.00 3807 © 1998 The American Physical Society