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 methacrylate interface. 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
reflectivity or 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
VAIRRS is 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 toluene across the discontinuity.
A representation of the experiment appears in Fig. 1.
The incident medium is an internal reflection element
IRE made 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
IRE at 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 IRE and 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
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