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BACKGROUND OF INVENTION
It is well known from photoacoustic theory (A. Rosencwaig and A. Gersho, J.
Appl. Phys. 47, 64 (1976) and A. Rosencwaig, Photoacoustics and
Photoacoustic Spectroscopy, Wiley, Interscience, New York, 1980) that one
can, with thermal waves, obtain information about the thermal
characteristics of a sample as a function of depth beneath its surface.
Thermal characteristics or features are those regions of an otherwise
homogeneous material that exhibit variations relative to their
surroundings in thermal conductivity, thermal expansion coefficient or
volume specific heat. Variations in these thermal parameters can arise
from changes in basic material composition or from the presence of
mechanical defects such cracks, voids and delaminations. Variations in
thermal parameters can also arise from changes in the crystalline order or
structure or due to the presence of small concentrations of foreign ions
or lattice defects in an otherwise perfect crystal. Although there has
been some experimentation in thermal-wave depth-profiling, (M. J. Adams
and G. F. Kirkbright, Analyst 102, 678 (1977)) and A. Rosencwaig, J. Appl.
Phys. 49, 2905 (1978) this capability has not been extensively exploited,
primarily because of the lack of adequate theoretical models. A recent
model of Opsal and Rosencwaig, (J. Opsal and A. Rosencwaig, J. Appl. Phys.
53,4240 (1982)) (O-R model) shows how depth-profiling and multi-layer
thickness analysis can be performed from thermal-wave measurements using
either surface temperature or thermoacoustic probes, and allows for a
fuller exploitation of this depth-profiling capability. There have also
been several experimental impediments to thermal-wave profiling. For
example, one would like, in many cases to operate outside of a
photoacoustic cell, to employ a completely contactless method for
thermal-wave generation and detection, and to couple thickness
measurements with high spatial resolution, this last requirement
necessitating the use of high-frequency (>100kHz) thermal waves.
SUMMARY OF INVENTION
Recently we have been able to satisfy all three requirements by employing a
laser deflection technique whereby one laser is used for generating and
another for detecting the thermal waves. In our method the heating and
probe laser beams are focused and directed normal to the sample surface
where they are slightly spaced apart. This is quite different than the
conventional optical beam deflection technique where the probe beam skims
over the surface of the sample as in (W. B. Jackson, N. M. Amer, A. C.
Boccara and D. Fournier, Appl. Opt. 20 1333 (1981) and J. C. Murphy and L.
C. Aamodt, Appl. Phys. Lett. 38, 196 (1981)).
Other features and advantages of the invention will become apparent from
the following description read in conjunction with the attached drawings
in which:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram of a preferred form of apparatus of this invention for
practice of the method of this invention;
FIG. 2 is a frequency/response curve indicating the performance of the
invention under operational conditions;
FIG. 3 is a diagram on a enlarged scale of the conditions at the inspection
station of the apparatus of FIG. 1;
FIG. 4 is a thickness/amplitude plot showing performance results which the
invention measuring aluminum films on silicon; and
FIG. 5 is a similar thickness amplitude plot for a series of silicon
dioxide on silicon films.
Referring now in detail to the drawings, the heating apparatus illustrated
therein includes a heating laser 10 which may be any convenient laser,
such as Argon or carbon dioxide lasers and in actual experimental work a
Lexel Model 75 Argon laser was used. The output of the laser 10 passes
through a modulator 12 which may take any suitable form but in
experimental work a modulator of Intra Action, Inc. was employed. The
modulator should be operated at a frequency exceeding 10,000 cycles per
second, and in the experimental work, modulation frequencies were used
between 10,000 cycles per second and 10,000,000 cycles per second. The
modulated laser beam passes through a beam expander 14 formed of a
suitable lens system, and then a microscope objective lens 16 to be
focused on a spot in an inspection area 18 when the film under inspection
is positioned.
The detection apparatus in FIG. 1 includes a detection laser 20 which may
take any suitable form, and in the work described herein, the detection
laser was a Spectra Physics Model 120S helium/neon laser. The output beam
of the detection laser 20 passes through a beam expander 22 and a
polarizing splitter 24, quarter wave waveplate 26 to be reflected off a
dichroic mirror 28 into the objective lens 16 and onto the inspection area
18. The optical elements are arranged so that the two focused laser beams
are parallel but non-coaxial. In the work described herein the two beams
were focused to spot sizes of between two and four microns with their
center axes separated by approximately two microns. As explained
hereinafter, the detection laser beam is reflected from the film being
measured. The reflected beam is reflected from the dichroic mirror 28 and
from the polarizing splitter 24 to a helium/neon filter 30 and a bicell
detector 32.
The apparatus of FIG. 1 was operated for measurement of thin films of
aluminum and silicon dioxide in the following way. The heating was
provided from an Ar.sup.+ ion laser whose beam was acousto-optically
modulated at frequencies as high as 10MHz and with an incident peak power
of approximately 30mW at the sample surface. The probe was an unmodulated
5mW He-Ne laser beam (2mW was incident on the sample surface) which was
reflected off the sample surface and diverted by a polarizing beam
splitter, in combination with a quarter-wave plate, onto a knife-edge (eg.
bicell photodiode) detector. The probe beam undergoes periodic deflection
of the order of 10.sup.-5 -10.sup.-4 radian by the thermal-wave induced
changes in the local slope of the sample surface. This is analogous to the
use of a laser probe for the detection of the surface acoustic waves, (R.
L. Whitman and A. Korpel, Appl. Optics 8, 1567 (1969)) although here the
surface deformation are due to the thermal waves. We were able to detect,
at a 1MHz modulation frequency, changes in the local surface slope that
resulted from local surface displacements of approximately 10.sup.-4
.ANG./.sqroot.Hz, a sensitivity that is considerably greater than that
reported in recent experiments done at much lower modulation frequencies
with laser interferometry, (S. Ameri, E. A. Ash, V. Nueman and C. R.
Petts, Electron. Lett. 17, 337 (1981)).
However, before we could combine the O-R model with our laser probe
technique to perform quantitative thin-film thickness measurements, we had
to extend it to three dimensions and to include thermoelastic surface
deformations. In addition to three dimensional effects, and thermoelastic
deflections, we found that in our experiments we also have to include
thermal lens, optical effects, and nonlinear effects arising from the
temperature dependence of the various material parameters.
The thermal lens effects (W. B. Jackson, N. M. Amer, A. C. Bocarra and D.
Fournier, Appl. Opt. 20, 1333 (1981); J. C. Murphy and L. C. Aamodt,
Apply. Phys. Lett. 38, 196 (1981) and R. L. Swofford, M. E. Long and A. C.
Albrecht, J. Chem. Phys. 65, 179 (1979)) occur in the air above the sample
surface and within any layer of the sample that is not optically opaque.
Even though these thermal lenses have only micron-sized dimensions at the
high modulation frequencies employed, their refractive power is still
considerable since the normalized refractive index gradient, n-.sup.1
(dn/dx)=n-.sup.1 (dn/dT) (dT/dx) across the lens is now quite high and of
the same order as the thermal expansion coefficient of a solid. Also, even
though the probe laser beam is incident normal to the sample surface, it
strikes the thermal lens off-axis and thus undergoes refraction in both
incident and reflected directions. Consequently, the theory predicts, and
we find experimentally, that the thermal lens effect is appreciable for
some materials such as Si.
FIG. 2 presents comparisons with experiments for a complete calculation
which includes optical reflectivities, finite absorption depths and finite
probe beam diameters, under vacuum, where there is no thermal lens effect
(dashed curves), and in air (solid curves). The agreement between theory
and experiment is excellent.
In these thermal-wave experiments DC and AC temperature excursions can
range from 30.degree. C. to several hundred degrees depending on the
sample's thermal characteristics. With such temperature excursions, the
dependence on temperature of the various thermal, optical and elastic
parameters has to be considered as well. In general, the most critical
parameters appear to be the refractive index and the thermal conductivity.
These temperature effects introduce appreciable nonlinearities in the
model that cannot be neglected.
Optical effects will, of course, play an important role in these
experiments as well. For example, in Si we have to take into account the
optical absorption length (.perspectiveto.1 .mu.m) for the 488nm Ar.sup.+
ion laser light. Absorption and reflectivities must also be included. In
addition, when dealing with optically transparent films such as SiO.sub.2,
optical interference effects within the film have to be included as well.
FIG. 3 schematically depicts the situation encountered for an SiO.sub.2
film on Si. Here we see the thermoelastic deformations of both the
Si-SiO.sub.2 and the SiO.sub.2 -air surfaces, the thermal lenses in both
the SiO.sub.2 and the air, and the optical interference effects on the
probe beam in the SiO.sub.2 film. Note that the thermal lenses have
opposite signs in air and SiO.sub.2 because of the opposite signs of their
respective dn/dT's.
When all of the thermal lens, optical and nonlinear effects are properly
included into the O-R model, we have a quantitative tool for measuring the
thickness of thin films. This is illustrated in FIG. 4 where we show
theoretical curves and data obtained for single films of Al on Si and for
double films of Al and SiO.sub.2 on Si. We have used the magnitude of the
thermal-wave signal rather than the phase in these measurements, since the
magnitude has a greater dynamic range and can be measured more precisely.
The data in FIG. 4 are in excellent agreement with the theory both for the
single and the double films. The precision of the reading obtained with a
1-sec averaging time translates to a thickness sensitivity of .+-.2% over
the thickness range of 500 .ANG.-25,000 .ANG. for these films.
In FIG. 5 we show the theoretical curves and the data for a series of
transparent SiO.sub.2 films on Si. Although SiO.sub.2 on Si is only a
single film problem, the theory in this case must include thermoelastic
deformations at both the Si-SiO.sub.2 and SiO.sub.2 -air interfaces,
thermal lens effects in both the SiO.sub.2 and the air, and optical
interference effects in the SiO.sub.2 (see FIG. 3). The bit between theory
and experiment is, with all this complexity, quite good, indicating that
transparent as well as opaque films can be measured with this thermal-wave
technique. The thickness sensitivity for SiO.sub.2 films on Si appears to
be .+-.2% over the range 500 .ANG.-15,000 .ANG..
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