Optical method for determining the mechanical properties of a material

Disclosed is a method for characterizing a sample, comprising the steps of: (a) acquiring data from the sample using at least one probe beam wavelength to measure, for times less than a few nanoseconds, a change in the reflectivity of the sample induced by a pump beam; (b) analyzing the data to determine at least one material property by comparing a background signal component of the data with data obtained for a similar delay time range from one or more samples prepared under conditions known to give rise to certain physical and chemical material properties; and (c) analyzing a component of the measured time dependent reflectivity caused by ultrasonic waves generated by the pump beam using the at least one determined material property. The first step of analyzing may include a step of interpolating between reference samples to obtain an intermediate set of material properties. The material properties may include sound velocity, density, and optical constants. In one embodiment, only a correlation is made with the background signal, and at least one of the structural phase, grain orientation, and stoichiometry is determined.

This application claims the benefit of U.S. Provisional application(s) Ser. 
No(s). 60/017,481 Apr. 26, 1996, 60/017,391 May 8, 1996. 
CLAIM OF PRIORITY FROM COPENDING PROVISIONAL PATENT APPLICATIONS 
Priority is herewith claimed under 35 U.S.C. .sctn.119 (e) from copending 
Provisional Patent Application 60/017,481, filed Apr. 26, 1996, entitled 
"Optical Method for Determining the Mechanical Properties of a Material", 
by Humphrey J. Maris and Robert J. Stoner. Priority is herewith also 
claimed under 35 U.S.C. .sctn.119 (e) from copending Provisional Patent 
Application 60/017,391, filed May 8, 1996, entitled "Optical Method for 
Determining the Mechanical Properties of a Material", by Humphrey J. Maris 
and Robert J. Stoner. The disclosures of both of these Provisional Patent 
Applications are incorporated by reference herein in their entireties. 
FIELD OF THE INVENTION 
This invention relates generally to a method and apparatus for 
characterizing a sample using electromagnetic radiation. 
BACKGROUND OF THE INVENTION 
Presently, the nondestructive evaluation of thin films and interfaces is of 
interest to manufacturers of electrical, optical and mechanical devices 
which employ thin films. In one nondestructive technique a radio frequency 
pulse is applied to a piezoelectric transducer mounted on a substrate 
between the transducer and the film to be studied. A stress pulse 
propagates through the substrate toward the film. At the boundary between 
the substrate and the film, part of the pulse is reflected back to the 
transducer. The remainder enters the film and is partially reflected at 
the opposite side to return through the substrate to the transducer. The 
pulses are converted into electrical signals, amplified electronically, 
and displayed on an oscilloscope. The time delay between the two pulses 
indicates the film thickness, if the sound velocity in the film is known, 
or indicates the sound velocity, if the film thickness is known. Relative 
amplitudes of the pulses provide information on the attenuation in the 
film or the quality of the bond between the film and the substrate. 
The minimum thickness of films which can be measured and the sensitivity to 
film interface conditions using conventional ultrasonics is limited by the 
pulse length. The duration of the stress pulse is normally at least 0.1 
.mu.sec corresponding to a spatial length of at least 3.times.10.sup.-2 cm 
for an acoustic velocity of 3.times.10.sup.5 cm/sec. Unless the film is 
thicker than the length of the acoustic pulse, the pulses returning to the 
transducer will overlap in time. Even if pulses as short in duration as 
0.001 .mu.sec are used, the film thickness must be at least a few microns. 
Another technique, acoustic microscopy, projects sound through a rod having 
a spherical lens at its tip. The tip is immersed in a liquid covering the 
film. Sound propagates through the liquid, reflects off the surface of the 
sample, and returns through the rod to the transducer. The amplitude of 
the signal returning to the transducer is measured while the sample is 
moved horizontally. The amplitudes are converted to a computer-generated 
photograph of the sample surface. Sample features below the surface are 
observed by raising the sample to bring the focal point beneath the 
surface. The lateral and vertical resolution of the acoustic microscope 
are approximately equal. 
Resolution is greatest for the acoustic microscope when a very short 
wavelength is passed through the coupling liquid. This requires a liquid 
with a low sound velocity, such as liquid helium. An acoustic microscope 
using liquid helium can resolve surface features as small as 500 
Angstroms, but only when the sample is cooled to 0.1 K. 
Several additional techniques, not involving generation and detection of 
stress pulses, are available for measuring film thickness. Ellipsometers 
direct elliptically polarized light at a film sample and analyze the 
polarization state of the reflected light to determine film thickness with 
an accuracy of 3-10 Angstroms. The elliptically polarized light is 
resolved into two components having separate polarization orientations and 
a relative phase shift. Changes in polarization state, beam amplitudes, 
and phase of the two polarization components are observed after 
reflection. 
The ellipsometer technique employs films which are reasonably transparent. 
Typically, at least 10% of the polarized radiation must pass through the 
film. The thickness of metal sample films thus cannot exceed a few hundred 
Angstroms. 
Another technique uses a small stylus to mechanically measure film 
thickness. The stylus is moved across the surface of a substrate and, upon 
reaching the edge of a sample film, measures the difference in height 
between the substrate and the film. Accuracies of 10-100 Angstroms can be 
obtained. This method cannot be used if the film lacks a sharp, distinct 
edge, or is too soft in consistency to accurately support the stylus. 
Another non-destructive method, based on Rutherford Scattering, measures 
the energy of backscattered helium ions. The lateral resolution of this 
method is poor. 
Yet another technique uses resistance measurements to determine film 
thickness. For a material of known resistivity, the film thickness is 
determined by measuring the electrical resistance of the film. For films 
less than 1000 Angstroms, however, this method is of limited accuracy 
because the resistivity may be non-uniformly dependent on the film 
thickness. 
In yet another technique, the change in the direction of a reflected light 
beam off a surface is studied when a stress pulse arrives at the surface. 
In a particular application, stress pulses are generated by a 
piezoelectric transducer on one side of a film to be studied. A laser beam 
focused onto the other side detects the stress pulses after they traverse 
the sample. This method is useful for film thicknesses greater than 10 
microns. 
A film may also be examined by striking a surface of the film with an 
intense optical pump beam to disrupt the film's surface. Rather than 
observe propagation of stress pulses, however, this method observes 
destructive excitation of the surface. The disruption, such as thermal 
melting, is observed by illuminating the site of impingement of the pump 
beam with an optical probe beam and measuring changes in intensity of the 
probe beam. The probe beam's intensity is altered by such destructive, 
disruptive effects as boiling of the film's surface, ejection of molten 
material, and subsequent cooling of the surface. See Downer, M. C.; Fork, 
R. L.; and Shank, C. V., "Imaging with Femtosecond Optical Pulses", 
Ultrafast Phenomena IV, Ed. D. H. Auston and K. B. Eisenthal 
(Spinger-Verlag, N.Y. 1984), pp. 106-110. 
Other systems measure thickness, composition or concentration of material 
by measuring absorption of suitably-chosen wavelengths of radiation. This 
method is generally applicable only if the film is on a transparent 
substrate. 
In a nondestructive ultrasonic technique described in U.S. Pat. No. 
4,710,030 (Tauc et al.), a very high frequency sound pulse is generated 
and detected by means of an ultrafast laser pulse. The sound pulse is used 
to probe an interface. The ultrasonic frequencies used in this technique 
typically are less than 1 THz, and the corresponding sonic wavelengths in 
typical materials are greater than several hundred Angstroms. It is 
equivalent to refer to the high frequency ultrasonic pulses generated in 
this technique as coherent longitudinal acoustic phonons. 
In more detail, Tauc et al. teach the use of pump and probe beams having 
durations of 0.01 to 100 psec. These beams may impinge at the same 
location on a sample's surface, or the point of impingement of the probe 
beam may be shifted relative to the point of impingement of the pump beam. 
In one embodiment the film being measured can be translated in relation to 
the pump and probe beams. The probe beam may be transmitted or reflected 
by the sample. In a method taught by Tauc et al. the pump pulse has at 
least one wavelength for non-destructively generating a stress pulse in 
the sample. The probe pulse is guided to the sample to intercept the 
stress pulse, and the method further detects a change in optical constants 
induced by the stress pulse by measuring an intensity of the probe beam 
after it intercepts the stress pulse. 
In one embodiment a distance between a mirror and a corner cube is varied 
to vary the delay between the impingement of the pump beam and the probe 
beam on the sample. In a further embodiment an opto-acoustically inactive 
film is studied by using an overlying film comprised of an 
opto-acoustically active medium, such as arsenic telluride. In another 
embodiment the quality of the bonding between a film and the substrate can 
be determined from a measurement of the reflection coefficient of the 
stress pulse at the boundary, and comparing the measured value to a 
theoretical value. 
The methods and apparatus of Tauc et al. are not limited to simple films, 
but can be extended to obtaining information about layer thicknesses and 
interfaces in superlattices, multilayer thin-film structures, and other 
inhomogeneous films. Tauc et al. also provide for scanning the pump and 
probe beams over an area of the sample, as small as 1 micron by 1 micron, 
and plotting the change in intensity of the reflected or transmitted probe 
beam. 
While well-suited for use in many measurement applications, it is an object 
of this invention to extend and enhance the teachings of Tauc et al. 
More particularly, for situations in which the material properties (i.e. 
sound velocity, density, optical constants etc.) are known with adequate 
precision (for example, because the deposition source is known to be pure, 
and the deposition process is known to give highly repeatable grain 
structure and structural phase), fitting may be performed using 
predetermined values for many of the material properties (such as density, 
sound velocity, optical constants) in order to determine a sample 
characteristic of interest (such as thickness, or adhesion strength). This 
is often a preferred approach for samples containing pure metal films 
since it is computationally efficient, and therefore allows measurements 
to be made quickly. 
However, this approach can lead to inaccurate results for samples 
containing films whose material properties (for example, sound velocity, 
density and optical constants) may be affected by deposition conditions 
such as temperature, gas mixture, and substrate species. In such cases it 
may not be possible to unambiguously determine the contributions to the 
time dependence of the detected probe signal due to the sample thickness 
and sound velocity. 
OBJECTS OF THE INVENTION 
It is a first object of this invention to provide an improved method for 
the non-destructive evaluation of materials that overcomes the foregoing 
and other problems. 
It is a further object of this invention to provide a two step method to 
analyze data obtained with pump and probe optical beams, wherein a 
background signal is employed to determine mechanical properties of a 
material, and wherein a component of a measured time dependent change in 
an optical property generated by the pump beam, such as the reflectivity 
(.DELTA.R(t)), is analyzed using the determined material properties. 
SUMMARY OF THE INVENTION 
Disclosed herein is a method for characterizing a sample, comprising the 
steps of: (a) acquiring data from the sample using at least one probe beam 
wavelength to measure, for times less than a few nanoseconds, a transient 
change in an optical response, such as the reflectivity, of the sample 
induced by a pump beam; (b) analyzing the data to determine at least one 
material property by comparing a background signal component of the data 
with data obtained for a similar delay time range from one or more samples 
prepared under conditions known to give rise to certain physical and 
chemical material properties; and (c) analyzing a component of the 
transient response of the probe beam that is caused by ultrasonic waves 
generated by the pump beam, using the at least one determined material 
property. The first step of analyzing may include a step of interpolating 
between reference samples to obtain an intermediate set of material 
properties. 
The step of acquiring is accomplished with a non-destructive system and 
method for measuring at least one transient response of the sample to a 
pump pulse of optical radiation, the measured transient response or 
responses can include at least one of a measurement of a modulated change 
.DELTA.R in an intensity of a reflected portion of a probe pulse, a change 
.DELTA.T in an intensity of a transmitted portion of the probe pulse, a 
change .DELTA.P in a polarization of the reflected probe pulse, a change 
.DELTA..phi. in an optical phase of the reflected probe pulse, and a 
change in an angle of reflection .DELTA..beta. of the probe pulse, each of 
which may be considered as a change in a characteristic of a reflected or 
transmitted portion of the probe pulse. The measured transient response or 
responses are then associated with at least one characteristic of interest 
of the sample. 
In one embodiment an association is made with a characteristic such as at 
least one of the structural phase, grain orientation, and stoichiometry. 
This invention also teaches a method for characterizing a sample, 
comprising the steps of: (a) acquiring data from the sample using at least 
one probe beam wavelength to measure, for times less than a few 
nanoseconds, a transient change in the optical response of the sample 
induced by a pump beam; (b) analyzing the data to determine at least a 
sample preparation technique by comparing a background signal component of 
the data with data obtained for a similar delay time range from one or 
more samples prepared by similar sample preparation techniques; and (c) 
analyzing a component of the measured time dependent reflectivity caused 
by ultrasonic waves generated by the pump beam using data corresponding to 
the determined sample preparation technique. 
Further in accordance with this invention a method is taught for 
characterizing a sample, comprising the steps of: (a) acquiring data from 
the sample using at least one probe beam wavelength to measure, for a 
range of delay times, a change in at least one transient optical response 
of the sample induced by a pump beam; (b) assuming a value for a thickness 
of the film; (c) comparing a background signal, resulting from a 
non-acoustical component of the acquired data, to data that corresponds to 
a film of the same general type having the assumed thickness, to determine 
a most probable composition for the film; and (d) associating determined 
physical properties of the film as a result of the execution of step (c) 
with the sample film. The method further comprises the steps of (e) 
deducing an improved value for the thickness from an analysis of the 
acoustical component of the acquired data; and (f) repeating steps c-e 
until convergence between film thickness and material properties is 
achieved. 
This invention also encompasses a method of characterizing a sample that 
includes the steps of: (a) acquiring data from the sample using at least 
one probe beam wavelength to measure, for a range of delay times, a change 
in at least one transient optical response of the sample induced by a pump 
beam; (b) assuming a composition of the film; (c) deducing a value for a 
thickness of the film from an analysis of an acoustical part of the data, 
the step of deducing including a step of considering the film's material 
properties based on a film having the assumed composition; and (d) 
comparing a background signal corresponding to a film of the same general 
type, having the deduced thickness, to determine an improved composition 
for the film. The method further includes the steps of (e) associating 
material properties of the film from step (d) with the sample film; and 
(f) repeating steps c-e until convergence between the sample film's 
composition and thickness is achieved.

DETAILED DESCRIPTION OF THE INVENTION 
The teaching of this invention, as described in detail below, can be used 
in conjunction with the teaching of Tauc et al. to augment the 
characterization of samples, although the use of this or a similar 
non-destructive, optically-based system should not be construed as a 
limitation upon the practice of this invention. 
In accordance with the teaching of this invention, a light pulse is 
directed onto a sample, and is partially absorbed by electronic carriers 
in the sample, which subsequently transfer their energy to the materials 
comprising the sample. This gives rise to a small, localized increase in 
the temperature of the sample. Associated with the increase in the 
temperature of the sample is a small, localized transient change in the 
sample's optical response. That is, there is manifested at least one 
transient and measurable response of the sample to the pump pulse of 
optical radiation. A measured transient response or responses can include 
at least one of a measurement of a modulated change .DELTA.R in an 
intensity of a reflected portion of a probe pulse, a change .DELTA.T in an 
intensity of a transmitted portion of the probe pulse, a change .DELTA.P 
in a polarization of the reflected probe pulse, a change .DELTA..phi. in 
an optical phase of the reflected probe pulse, and a change in an angle of 
reflection .DELTA..beta. of the probe pulse, each of which may be 
considered as a change in a characteristic of a reflected or transmitted 
portion of the probe pulse. The transient response of the sample to the 
pump pulse decays at a rate which depends mainly on the rates at which the 
excited electronic carriers transfer their energy to the remainder of the 
sample, and also on the thermal diffusivities and thicknesses of the 
materials comprising the sample. 
As disclosed previously by Tauc et al., a second effect of the light pulse 
may be to generate ultrasonic waves in the sample. These ultrasonic waves 
also give rise to changes in the optical reflectivity of the sample which 
vary more rapidly in time than the reflectivity changes associated with 
the sample's return to thermal equilibrium. In a typical sample the 
reflectivity changes associated with the ultrasonic waves and with the 
change in temperature occur concomitantly. 
Herein, all transient changes in the optical response of the sample, such 
as the reflectivity, and excluding the ultrasonic contribution, are 
referred to as the "background" signal. Accordingly, the ultrasonic 
component of the net reflectivity change may be said to ride on a thermal 
"background" signal. Typical data are illustrated in FIG. 2. The 
reflectivity changes associated with the propagating ultrasonic waves may 
be analyzed in the manner disclosed by Tauc et al. to determine the 
mechanical properties of a sample. 
The reflectivity change is measured by means of a second light pulse, the 
"probe", which is delayed relative to the heating pulse, the "pump", by a 
time .tau.. The value of .tau. is typically in the range of 0.01 
picosecond to 100 nanoseconds. The sign, magnitude, and rate of decay of 
the "background" reflectivity change depends on the wavelength, angle of 
incidence and polarization of the probe light pulse, and on the electronic 
and thermal properties of the sample material. Thus, the background 
reflectivity change for samples of the same material may differ 
substantially due to different preparation conditions. By example, the 
inventors have observed that different background signals arise for 
samples composed of the same metal, but having a different structural 
phase, and also for alloys having differing compositions. These 
observations are indicative of the differences which exist between the 
thermal and electronic properties of such materials. 
In addition to the intrinsic electronic and thermal properties, the factors 
referred to above (structural phase, alloy content, impurity 
concentration, stoichiometry, phase mixture, grain orientation, etc.) may 
affect the elastic properties of a sample material. For example, the 
elastic constants and densities of two structural phases of a particular 
metal may differ significantly, corresponding to readily observed 
differences in the sound velocity and volume of samples having identical 
stoichiometry. Similar differences may be seen for samples such as thin 
films which have been deposited under conditions leading to different 
grain orientations and shapes. 
Consequently, it is desirable that at least one of these parameters be 
known in advance when making a "best-fit" analysis. This invention 
provides a method for obtaining greater accuracy, than that obtained by 
previous techniques, by removing possible ambiguities. 
In accordance with the teachings of this invention, data are acquired 
according to methods and apparatus described below by using at least one 
probe wavelength to measure, for times generally less than a few 
nanoseconds, a transient change in an optical property, such as the 
reflectivity, of the sample induced by the pump laser. Referring also to 
FIG. 4, the data are then analyzed in two steps as follows. 
In Step 1, the "background" signal is compared with data obtained for a 
similar delay time range from samples prepared under conditions known to 
give rise to certain physical and chemical material properties, such as, 
by example, structural phase. This may involve interpolation between 
reference samples to obtain an intermediate set of material properties. 
Properties including sound velocity, density, optical constants etc. are 
then associated with the sample of interest. 
It should be noted that the background signal can be compared also, or 
instead, with results obtained from a modeled diffusion process and the 
associated physical parameters, such as the thermal reflectance. 
In Step 2, one or more sample characteristics of interest, such as sound 
velocity, film thickness, film adhesion, etc., are determined from the 
measured time dependent change in the optical property, such as 
reflectivity, caused by the ultrasonic waves generated by the pump beam. 
These are analyzed in accordance with the material properties determined 
in Step 1. 
As such, the present invention provides a method for obtaining greater 
accuracy by removing possible ambiguities. 
Furthermore, a correlation can be made with a characteristic of the sample 
preparation technique, rather than a material property per se. For 
example, the sound velocity appropriate to CVD (Chemical Vapor Deposition) 
TiN may be different than the sound velocity appropriate to sputtered TiN. 
EXAMPLE 
Reference can now be had to FIGS. 4-6. A sample series consisted of 10 
samples which had been subjected to a range of RTP (Rapid Thermal 
Processing) annealing temperatures. The annealing cycles differed slightly 
for different annealing temperatures. 
A reaction between Ti and Si during the anneal cycle produces a layer whose 
electronic band structure changes as the reaction proceeds. The 
accompanying change in the transient reflectivity of the samples was 
measured in response to a short laser pulse, as described above. As was 
described above, there are two components of the measured signals. One 
component is a slowly varying "background" signal which is due to a 
combination of relaxation phenomena which take place after the laser pulse 
is absorbed by the film. The second component varies more rapidly, and is 
associated with acoustical vibrations of the layer. In accordance with an 
aspect of this invention, both components may be interpreted and used to 
characterize a given sample. 
FIG. 4 is a graph which shows transient reflectivity signals measured for 
all samples. The temperatures at which the samples were annealed is 
indicated on the graph. The data show acoustical oscillations for times 
less than about 30 picoseconds which are superimposed on the slowly 
varying background signal. To simplify the discussion, the acoustical and 
background signals are separated, and the acoustical signals are plotted 
separately in FIG. 5. The curves in FIG. 5 have been intentionally offset 
from one another for the sake of clarity; and the ordering of the curves 
in FIG. 5 bears no relation to the ordering of the curves in FIG. 4 (to 
which no offsets have been applied). 
Based on FIG. 4, from a qualitative perspective, it is clear that the 
350.degree. C. sample is substantially like the unannealed sample, from 
which it can be concluded that Ti and Si react very little at temperatures 
up to 350.degree. C. There is some evidence in the acoustical signals that 
some change has occurred as a result of the 350.degree. C. treatment, 
however, since the amplitudes of the "echoes" (for example, the "spiky" 
feature in the curve for the unannealed sample around 10 psec) is smaller 
for the 350.degree. C. sample. This may be an indication that the 
interface has become roughened or blurred as a result of the annealing, 
and so makes a poorer acoustical reflector than the as-deposited Ti-Si 
interface. However, a large change can be seen to occur between 
350.degree. C. and 450.degree. C. Based on the change in the background 
signal from negative to positive, and on the further weakening of the 
acoustical vibrations, it is clear that this change has begun to take 
place even at 400.degree. C. By 450.degree. C. the background signal has 
become strongly positive, and the acoustical signals have become quite 
strong. It is believed that this is an indication that a new layer has 
formed which is separated from the underlying Si substrate by a 
well-defined interface. Raman scattering data suggests that this is not a 
(C49) TiSi2 layer; nevertheless, the acoustics data suggests that, 
whatever the molecular structure, this layer is reasonably homogeneous. 
Between 450.degree. C. and 550.degree. C. the properties of the mixed 
layer slowly change. The acoustics signal becomes weaker and less regular 
than those observed at lower annealing temperatures, indicating the 
formation of internal structure within the layer. Between 550.degree. C. 
and 600.degree. C. there is a sudden change in both the background and the 
acoustics data. From the Raman data it was concluded that this change is 
associated with the sudden formation of the C49 phase. A slow increase in 
the thickness of this C49 layer is observed with further annealing up to 
700.degree. C., with a smaller change between 650.degree. C. and 
700.degree. C. than between 600.degree. C. and 650.degree. C., which may 
suggest saturation. The increase in thickness is apparent from the shift 
to longer times of the acoustic peaks (which may be thought of as the 
vibrations of a slab, whose frequency becomes lower as its thickness is 
increased). Also observed was an increase in the amplitude of the acoustic 
signal, indicating that the interface between the TiSi.sub.2 layer and the 
underlying Si becomes more distinct with annealing at higher temperatures. 
There is a final large change in the background signal for the sample 
annealed at 765.degree. C., which the Raman data showed to be due to the 
formation of the C54 phase. The largest acoustical signal of the entire 
series was observed for this sample. It should also be noted that the rate 
of decay of the vibrations of the C54 film is smaller than that observed 
for the C49 samples, indicating that the interface between the C54 layer 
and Si may be smoother. 
From the period of the acoustical oscillations of the as-deposited film and 
the known velocity of sound in titanium; the thickness of the Ti layer was 
determined to be 231 .ANG.. For an ideal C54 TiSi2 layer, the 
corresponding theoretical thickness can be shown to be 580 .ANG.. Assuming 
the 765.degree. C. sample to be C54, a measured thickness of 581.+-.3 
.ANG. was obtained, in very close agreement with the expected result. This 
is important because it shows how the acoustic information itself can be 
used to identify the silicide phase; i.e., the vibrational period of the 
silicide layer can be used as a measure of the completeness of the C54 
formation if the initial Ti thickness is known. In this regard reference 
can be had to the flow chart of FIGS. 7A and 7B. 
Qualitatively, curves similar to those in FIG. 4 are obtained for other 
thicknesses of Ti silicide, however, the details depend on the thickness 
to some degree. 
There are at least two techniques that can be employed to provide an 
effective silicide monitor. A first technique, illustrated in FIGS. 7A and 
7B, uses a family of reference curves corresponding to FIG. 4 for a 
starting target Ti thickness over a wide range of annealing temperatures. 
For a subsequent "unknown" sample having the same starting Ti thickness, 
the phase is determined by comparing its picosecond reflectivity with the 
reference curves. 
A second technique employs a series of curves like those of FIG. 4, but 
corresponding to several thicknesses of Ti, and then determines the 
structural phase via Raman scattering (or any other suitable technique) 
for each curve. From this data the curves are constructed in accordance 
with the underlying physical parameters which govern the sign, amplitude, 
and rate of decay of the picosecond reflectivity for each phase. 
As can be seen in FIGS. 8A and 8B, for a subsequent "unknown" sample having 
any starting Ti thickness, the phase is determined by parametrizing its 
picosecond reflectivity in terms of the same parameters, and these 
parameters are then compared with their known values for each phase. 
The second technique has the advantage of being potentially more 
transportable, although the first technique also provides satisfactory 
results. 
As a simplified illustration of the operation of the first technique for 
the Ti thickness used in the present sample series (231 .ANG.), the 
transient reflectivity change is plotted at an arbitrary point on the FIG. 
4 curves versus the annealing temperature. The result is shown in FIG. 6. 
In constructing this Figure the transient reflectivity change at 45 
picoseconds was used, expressed as a percentage change relative to the 
value obtained for the unannealed sample. The qualitative features of the 
curve correlate well with the graph of resistivity versus annealing 
temperature. As with the reflectivity data, the resistivities have been 
expressed as a percent change relative to the resistivity obtained for the 
unannealed sample. 
The optical measurement system in accordance with this invention can be 
packaged as an in-fab optical metrology tool. It is completely 
nondestructive, and has a small spot size. For silicide monitoring it can 
be used to make measurements on product wafers within device or scribeline 
structures which are at least, by example, 5 microns in diameter. This 
value is a function of the particular focussing optics used. The use of 
fiber optic focussing optics, such as those having a reduced tip diameter, 
are especially attractive. Depending on such factors as pattern complexity 
and film thickness, measurement times range from, by example, 0.1 to 10 
seconds per site. This technique can also be applied to small structures, 
such as regular arrays of lines and dots, using analogous analysis 
techniques. 
An important aspect of the teaching of this invention is that it uses two 
independent components of the measured silicide response (i.e. the 
"background" signal and the "acoustical vibration" signal) to perform a 
self-consistent analysis. This readily distinguishes the technique of this 
invention from other silicide monitoring techniques which rely, for 
example, on resistivity or only reflectivity measurements. Self-consistent 
analysis allows the technique to not just detect a silicide misprocessing 
event, but to identify its cause. Whereas a sheet resistance measurement 
for a silicide can be misleading (for example, an out of control reading 
can arise because of variation of the deposited Ti layer, or because of 
incomplete silicide formation), the technique in accordance with this 
invention provides an unambiguous determination of the phase and thickness 
of an annealed film. It is ideally suited to high-throughput measurements 
on product wafers, and can produce high resolution film maps comparable to 
those obtained via four point probe measurements. 
FIGS. 1A-1E illustrate various embodiments of sample measurement apparatus 
that are suitable for practicing this invention. These various embodiments 
are disclosed in copending U.S. patent application Ser. No. 08/689,287, 
filed Aug. 6, 1996, entitled "Improved Optical Stress Generator and 
Detector", by H. J. Maris and R. J. Stoner. 
Reference is now made to FIG. 1A for illustrating an embodiment of 
apparatus 100 suitable for practicing this invention. The embodiment is 
referred to as a parallel, oblique embodiment. 
This embodiment includes an optical/heat source 120, which functions as a 
variable high density illuminator, and which provides illumination for a 
video camera 124 and a sample heat source for temperature-dependent 
measurements under computer control. An alternative heating method employs 
a resistive heater embedded in a sample stage 122. The advantage of the 
optical heater is that it makes possible rapid sequential measurements at 
different temperatures. The video camera 124 provides a displayed image 
for an operator, and facilitates the set-up of the measurement system. 
Appropriate pattern recognition software can also be used for this 
purpose, thereby minimizing or eliminating operator involvement. 
The sample stage 122 is preferably a multiple-degree of freedom stage that 
is adjustable in height (z-axis), position (x and y-axes), and tilt 
(.theta.), and allows motor controlled positioning of a portion of the 
sample relative to the pump and probe beams. The z-axis is used to 
translate the sample vertically into the focus region of the pump and 
probe, the x and y-axes translate the sample parallel to the focal plane, 
and the tilt axes adjust the orientation of the stage 122 to establish a 
desired angle of incidence for the probe beam. This is achieved via 
detector PSD1 and a local processor, as described below. 
In an alternative embodiment, the optical head may be moved relative to a 
stationary, tiltable stage 122' (not shown). This is particularly 
important for scanning large objects (such as 300 mm diameter wafers, or 
mechanical structures, etc.) In this embodiment the pump beam, probe beam, 
and video signal can be delivered to or from the translatable head via 
optical fibers or fiber bundles. 
BS5 is a broad band beam splitter that directs video and a small amount of 
laser light to the video camera 124. The camera 124 and local processor 
can be used to automatically position the pump and probe beams on a 
measurement site. 
The pump-probe beam splitter 126 splits an incident laser beam pulse 
(preferably of picosecond or shorter duration) into pump and probe beams, 
and includes a rotatable half-wave plate (WP1) that rotates the 
polarization of the unsplit beam. WP1 is used in combination with 
polarizing beam splitter PBS1 to effect a continuously variable split 
between pump and probe power. This split may be controlled by the computer 
by means of a motor to achieve an optimal signal to noise ratio for a 
particular sample. The appropriate split depend on factors such as the 
reflectivity and roughness of the sample. Adjustment is effected by having 
a motorized mount rotate WP1 under computer control. 
A first acousto-optic modulator (AOM1) chops the pump beam at a frequency 
of about 1 MHz. A second acousto-optic modulator (AOM2) chops the probe 
beam at a frequency that differs by a small amount from that of the pump 
modulator AOM1. The use of AOM2 is optional in the system illustrated in 
FIG. 1A. As will be discussed below, the AOMs may be synchronized to a 
common clock source, and may further be synchronized to the pulse 
repetition rate (PRR) of the laser that generates the pump and probe 
beams. 
A spatial filter 128 is used to preserve at its output a substantially 
invariant probe beam profile, diameter, and propagation direction for an 
input probe beam which may vary due to the action of the mechanical delay 
line shown as a retroreflector 129. The spatial filter 128 includes a pair 
of apertures A1 and A2, and a pair of lenses L4 and L5. An alternative 
embodiment of the spatial filter incorporates an optical fiber, as 
described above. 
WP2 is a second adjustable half wave plate which functions in a similar 
manner, with PBS2, to the WP1/PBS1 of the beamsplitter 126. With WP2 the 
intent is to vary the ratio of the part of the probe beam impinging on the 
sample to that of the portion of the beam used as a reference (input to D5 
of the detector 130. WP2 may be motor controlled in order to achieve a 
ratio of approximately unity. The electrical signals produced by the beams 
are subtracted, leaving only the modulated part of the probe to be 
amplified and processed. PSD2 is used in conjunction with WP2 to achieve 
any desired ratio of the intensities of the probe beam and reference beam. 
The processor may adjust this ratio by making a rotation of WP2 prior to a 
measurement in order to achieve a nulling of the unmodulated part of the 
probe and reference beam. This allows the difference signal (the modulated 
part of the probe) alone to be amplified and passed to the electronics. 
The beamsplitter BS2 is used to sample the intensity of the incident probe 
beam in combination with detector D2. The linear polarizer 132 is employed 
to block scattered pump light polarization, and to pass the probe beam. 
Lenses L2 and L3 are pump and probe beam focusing and collimating 
objectives respectively. The beamsplitter BS1 is used to direct a small 
part of pump and probe beams onto a first Position Sensitive Detector 
(PSD1) that is used for autofocusing, in conjunction with the processor 
and movements of the sample stage 122. The PSD1 is employed in combination 
with the processor and the computer-controlled stage 122 (tilt and z-axis) 
to automatically focus the pump and probe beams onto the sample to achieve 
a desired focusing condition. 
The detector D1 may be used in common for transient optical, ellipsometry 
and reflectometry embodiments of this invention. However, the resultant 
signal processing is different for each application. For transient optical 
measurements, the DC component of the signal is suppressed, such as by 
subtracting reference beam input D5, or part of it as needed, to cancel 
the unmodulated part of D1, or by electrically filtering the output of D1 
so as to suppress frequencies other than that of the modulation. The small 
modulated part of the signal is then amplified and stored. For 
ellipsometry, there is no small modulated part, rather the entire signal 
is sampled many times during each rotation of the rotation compensator 
(see FIG. 1B), and the resulting waveform is analyzed to yield the 
ellipsometric parameters. For reflectometry, the change in the intensity 
of the entire unmodulated probe beam due to the sample is determined by 
using the D1 and D2 output signals (D2 measures a signal proportional to 
the intensity of the incident probe). Similarly, additional reflectometry 
data can be obtained from the pump beam using detectors D3 and D4. The 
analysis of the reflectometry data from either or both beams may be used 
to characterize the sample. The use of two beams is useful for improving 
resolution, and for resolving any ambiguities in the solution of the 
relevant equations. 
A third beamsplitter BS3 is used to direct a small fraction of the pump 
beam onto detector D4, which measures a signal proportional to the 
incident pump intensity. A fourth beamsplitter BS4 is positioned so as to 
direct a small fraction of the pump beam onto detector D3, which measures 
a signal proportional to the reflected pump intensity. 
FIG. 1B illustrates a normal pump beam, oblique probe beam embodiment of 
apparatus 102. Components labelled as in FIG. 1A function in a similar 
manner, unless indicated differently below. In FIG. 1B there is provided 
the above-mentioned rotation compensator 132, embodied as a linear quarter 
wave plate on a motorized rotational mount, and which forms a portion of 
an ellipsometer mode of the system. The plate is rotated in the probe beam 
at a rate of, by example, a few tens of Hz to continuously vary the 
optical phase of the probe beam incident on the sample. The reflected 
light passes through an analyzer 134 and the intensity is measured and 
transferred to the processor many times during each rotation. The signals 
are analyzed according to known types of ellipsometry methods to determine 
the characteristics of the sample (transparent or semitransparent films). 
This allows the (pulsed) probe beam to be used to carry out ellipsometry 
measurements. 
The ellipsometry measurements are carried out using a pulsed laser, which 
is disadvantageous under normal conditions, since the bandwidth of the 
pulsed laser is much greater than that of a CW laser of a type normally 
employed for ellipsometry measurements. 
If transient optical measurements are being made, the rotation compensator 
132 is oriented such that the probe beam is linearly polarized orthogonal 
to the pump beam. The analyzer 134 may be embodied as a fixed polarizer, 
and also forms a portion of the ellipsometer mode of the system. When the 
system is used for transient optical measurements the polarizer 134 is 
oriented to block the pump beam. 
The analyzer 134 may be embodied as a fixed polarizer, and also forms a 
portion of the ellipsometer mode of the system. When the system is used 
for acoustics measurements the polarizer 134 is oriented to block the pump 
polarization. When used in the ellipsometer mode, the polarizer 134 is 
oriented so as to block light polarized at 45 degrees relative to the 
plane of the incident and reflected probe beam. 
The embodiment of FIG. 1B further includes a dichroic mirror (DM2), which 
is highly reflective for light in a narrow band near the pump wavelength, 
and is substantially transparent for other wavelengths. 
It should be noted in FIG. 1B that BS4 is moved to sample the pump beam in 
conjunction with BS3, and to reflect a portion of the pump to D3 and to a 
second PSD (PSD2). PSD2 (pump PSD) is employed in combination with the 
processor, computer controlled stage 122 (tilt and z-axis), and PSD1 
(Probe PSD) to automatically focus the pump and probe beams onto the 
sample to achieve a desired focusing condition. Also, a lens L1 is 
employed as a pump, video, and optical heating focussing objective, while 
an optional lens L6 is used to focus the sampled light from BS5 onto the 
video camera 124. 
Reference is now made to FIG. 1C for illustrating an embodiment of 
apparatus 104, specifically a single wavelength, normal pump, oblique 
probe, combined ellipsometer embodiment. As before, only those elements 
not described previously will be described below. 
Shutter 1 and shutter 2 are computer controlled shutters, and allow the 
system to use a He-Ne laser 136 in the ellipsometer mode, instead of the 
pulsed probe beam. For transient optical measurements shutter 1 is open 
and shutter 2 is closed. For ellipsometer measurements shutter 1 is closed 
and shutter 2 is opened. The HeNe laser 136 is a low power CW laser, and 
has been found to yield superior ellipsometer performance for some films. 
FIG. 1D is a dual wavelength embodiment 1D of the system illustrated in 
FIG. 1C. In this embodiment the beamsplitter 126 is replaced by a harmonic 
splitter, an optical harmonic generator that generates one or more optical 
harmonics of the incident unsplit incident laser beam. This is 
accomplished by means of lenses L7, L8 and a nonlinear optical material 
(DX) that is suitable for generating the second harmonic from the incident 
laser beam. The pump beam is shown transmitted by the dichroic mirror (DM 
138a) to the AOM1, while the probe beam is reflected to the 
retroreflector. The reverse situation is also possible. The shorter 
wavelength may be transmitted, and the longer wavelength may be reflected, 
or vice versa. In the simplest case the pump beam is the second harmonic 
of the probe beam (i.e., the pump beam has one half the wavelength of the 
probe beam). 
It should be noted that in this embodiment the AOM2 is eliminated since 
rejection of the pump beam is effected by means of color filter F1, which 
is simpler and more cost effective than heterodyning. F1 is a filter 
having high transmission for the probe beam and the He-Ne wavelengths, but 
very low transmission for the pump wavelength. 
Finally, FIG. 1E illustrates a normal incidence, dual wavelength, combined 
ellipsometer embodiment 108. In FIG. 1E the probe beam impinges on PBS2 
and is polarized along the direction which is passed by the PBS2. After 
the probe beam passes through WP3, a quarter wave plate, and reflects from 
the sample, it returns to PBS2 polarized along the direction which is 
highly reflected, and is then directed to a detector D0 in detector block 
130. D0 measures the reflected probe beam intensity. 
In greater detail, WP3 causes the incoming plane polarized probe beam to 
become circularly polarized. The handedness of the polarization is 
reversed on reflection from the sample, and on emerging from WP3 after 
reflection, the probe beam is linearly polarized orthogonal to its 
original polarization. BS4 reflects a small fraction of the reflected 
probe onto an Autofocus Detector AFD. 
DM3, a dichroic mirror, combines the probe beam onto a common axis with the 
illuminator and the pump beam. DM3 is highly reflective for the probe 
wavelength, and is substantially transparent at most other wavelengths. 
D1, a reflected He-Ne laser 136 detector, is used only for ellipsometric 
measurements. 
It should be noted that, when contrasting FIG. 1E to FIGS. 1C and 1D, that 
the shutter 1 is relocated so as to intercept the incident laser beam 
prior to the harmonic splitter 138. 
Based on the foregoing descriptions, a selected one of these presently 
preferred embodiments of measurement apparatus provide for the 
characterization of samples in which a short optical pulse (the pump beam) 
is directed to an area of the surface of the sample, and then a second 
light pulse (the probe beam) is directed to the same or an adjacent area 
at a later time. The retroreflector 129 shown in all of the illustrated 
embodiments of FIGS. 1A-1E can be employed to provide a desired temporal 
separation of the pump and probe beams. 
The apparatus 100, 102, 104, 106 and 108 is capable of measuring some or 
all of the following quantities: (1) the small modulated change .DELTA.R 
in the intensity of the reflected probe beam, (2) the change .DELTA.T in 
the intensity of the transmitted probe beam, (3) the change .DELTA.P in 
the polarization of the reflected probe beam, (4) the change .DELTA..phi. 
in the optical phase of the reflected probe beam, and/or (5) the change in 
the angle of reflection .DELTA..beta. of the probe beam. These quantities 
(1)-(5) may all be considered as transient responses of the sample which 
are induced by the pump pulse. These measurements can be made together 
with one or several of the following: (a) measurements of any or all of 
the quantities (1)-(5) just listed as a function of the incident angle of 
the pump or probe light, (b) measurements of any of the quantities (1)-(5) 
as a function of more than one wavelength for the pump and/or probe light, 
(c) measurements of the optical reflectivity through measurements of the 
incident and reflected average intensity of the pump and/or probe beams; 
(d) measurements of the average phase change of the pump and/or probe 
beams upon reflection; and/or (e) measurements of the average polarization 
and optical phase of the incident and reflected pump and/or probe beams. 
The quantities (c), (d) and (e) may be considered to be average or static 
responses of the sample to the pump beam. 
It is within the scope of this invention to employ computer simulations to 
calculate the change in the optical reflectivity .DELTA.R.sub.sim (t) of 
the sample when it is illuminated with a pump pulse of unit energy per 
unit area of the sample. The simulation may also give a value for the 
static reflection coefficient of the pump and probe beams. The system 
measures the transient change .DELTA.P.sub.probe-refl in the power of the 
reflected probe pulse as determined, for example, by photodiode D1 in FIG. 
1C. It also measures the static reflection coefficients of the pump and 
probe beams from a ratio of the power in the incident and reflected beams. 
The incident probe power is measured by photodiode D2 in FIG. 1C, the 
reflected probe power is measured by D1, the incident pump power is 
measured by D4, and the reflected pump power is measured by D3. 
To relate such simulation results for the transient change in the optical 
reflectivity to the actual system measurement it is necessary to know: (a) 
the power of the pump and probe beams; (b) the intensity profiles of these 
beams; and (c) their overlap on the sample surface. 
Let us suppose first that the pump beam is incident over an area A.sub.pump 
and that within this area the pump intensity is uniform. Then for each 
applied pump pulse the pump energy absorbed per unit area is: 
##EQU1## 
where f is the repetition rate of the pump pulse train, and R.sub.pump is 
the reflection coefficient for the pump beam. 
Thus, the change in optical reflectivity of the each probe light pulse will 
be: 
##EQU2## 
and the change in power of the reflected probe beam will be 
##EQU3## 
In a practical system the illumination of the sample does not, in fact, 
produce a uniform intensity of the incident pump beam. Moreover, the 
intensity of the probe light will also vary with position on the sample 
surface. To account for these variations the equation for 
.DELTA.P.sub.probe-refl is modified to read: 
##EQU4## 
where the effective area A.sub.effective is defined by the relation 
##EQU5## 
where I.sub.probe-inc (r) and I.sub.pump-inc (r) are respectively the 
intensities of the probe and pump beams on the surface of the sample. One 
amy consider A.sub.effective to be an effective area of overlap of the 
pump and probe beams. 
Analogous expressions can be derived for the change in optical transmission 
.DELTA.T(t), the change in optical phase .DELTA..phi.(t), the change in 
polarization .DELTA.P(t), and the change .DELTA..beta.(t) in the angle of 
reflection of the probe light. 
The following quantities are measured by the system: 
.DELTA.P.sub.probe-refl, P.sub.probe-inc, P.sub.pump-inc, R.sub.pump, 
R.sub.probe. A computer simulation gives predicted values for AR.sub.sim 
(t), R.sub.pump, and R.sub.probe. Thus, the following comparisons can be 
made between the simulation and the system measurements in order to 
determine the characteristics of the sample. 
(1) A comparison of the simulated and measured reflection coefficient 
R.sub.pump. 
(2) A comparison of the simulated and measured reflection coefficient 
R.sub.probe. 
(3) A comparison of the simulated and measured transient change 
.DELTA.P.sub.probe-refl in the power of the reflected probe light. 
To make a comparison of the simulated and measured change, it can be seen 
from the preceding equation (4) that it is necessary to know the value of 
A.sub.effective. This can be accomplished by one or more of the following 
methods. 
(a) A first method directly measures the intensity variations of the pump 
and probe beams over the surface of the sample, i.e, I.sub.probe-inc (r) 
and I.sub.pump (r) as a function of position, and uses the results of 
these measurements to calculate A.sub.effective. This is possible to 
accomplish but requires very careful measurements which may be difficult 
to accomplish in an industrial environment. 
(b) A second method measures the transient response .DELTA.P.sub.probe-refl 
for a sample on a system S for which the area A.sub.effective is known. 
This method then measures the response .DELTA.P.sub.probe-refl of the same 
sample on the system S' for which A.sub.effective is to be determined. The 
ratio of the responses on the two systems gives the inverse of the ratio 
of the effective areas for the two systems. This can be an effective 
method because the system S can be chosen to be a specially constructed 
system in which the areas illuminated by the pump and probe beams are 
larger than would be desirable for an instrument with rapid measurement 
capability. Since the areas are large for this system it is simpler to 
measure the intensity variations of the pump and probe beams over the 
surface of the sample, i.e, I.sub.probe-inc (r) and I.sup.pump-inc (r) as 
a function of position. This method is effective even if the quantities 
which enter into the calculation of the simulated reflectivity change 
.DELTA.R.sub.sim (t) are not known. 
(c) A third method measures the transient response .DELTA.P.sub.probe-refl 
for a sample in which all of the quantities are known which enter into the 
calculation of the simulated reflectivity change .DELTA.R.sub.sim (t) of 
the sample when it is illuminated with a pump pulse of unit energy per 
unit area of the sample. Then by comparison of the measured transient 
response .DELTA.P.sub.probe-refl with the response predicted from the Eq. 
6, the effective area A.sub.effective is determined. 
It is important that the effective area A.sub.effective be stable 
throughout the course of a sequence of measurements. To ensure this, the 
apparatus shown in FIGS. 1A-1E incorporate means for automatically 
focusing the pump and probe beams onto the surface of the sample so as to 
achieve a reproducible intensity variation of the two beams during every 
measurement. The automatic focusing system provides a mechanism for 
maintaining the system in a previously determined state in which the size 
and relative positions of the beams on the sample surface are appropriate 
for effective transient response measurements. 
It should be noted that for any application in which the amplitude of an 
optical transient response is used to draw quantitative conclusions about 
a sample (for example, when the magnitude of the background signal is 
influenced by the phase of a material), a calibration scheme such as 
described above is an important feature of the measurement system, wherein 
calibration includes determining a size and an area of overlap of the pump 
and probe beams on a surface of the sample. 
The preceding description of the method for the comparison of the computer 
simulation results and the system measurements supposes that the several 
detectors in the measurement system are calibrated. It is contemplated 
that such a system will use detectors operating in the linear range so 
that the output voltage V of each detector is proportional to the incident 
optical power P. For each detector there is thus a constant G such that 
V=GP. The preceding description assumes that the constant G is known for 
each and every detector. In the case that this information is not 
available, the individual calibration factors associated with each of the 
individual detectors measuring P.sub.probe-inc, P.sub.pump-inc, and 
.DELTA.P.sub.probe-refl may be combined with A.sub.effective and f into a 
single overall system calibration constant C. Therefore in terms of a 
calibration factor C, Eq. 4 could be expressed as 
EQU .DELTA.V.sub.probe-refl =C V.sub.probe-inc .DELTA.R.sub.sim (t) 
V.sub.pump-inc (1-R.sub.pump) (6), 
where .DELTA.V.sub.probe-refl is the output voltage from the detector used 
to measure the change in the power of the reflected probe light (D1), 
V.sub.pumpinc is the output voltage from the detector used to measure the 
incident pump light (D4), and V.sub.probe-inc is the output voltage of the 
detector used to measure the incident probe light (D2). Thus, it is 
sufficient to determine the constant C. This can be accomplished by either 
of the following two methods. 
(a) A first method measures the transient response .DELTA.V.sub.probe-refl 
for a sample in which all of the quantities are known which enter into the 
calculation of the simulated reflectivity change .DELTA.R.sub.sim (t) of 
the sample, when it is illuminated with a pump pulse of unit energy per 
unit area of the sample. Next, the method measures V.sub.probe-inc and 
V.sub.pump-inc, then determines R.sub.pump either by measurement or from 
the computer simulation. The method then finds the value of the constant C 
such that Eq. 6 is satisfied. 
(b) A second method measures the transient response .DELTA.V.sub.probe-refl 
for a reference sample for which the transient optical response 
.DELTA.R(t), when it is illuminated with a pump pulse of unit energy per 
unit area of the sample, has been measured using a system which has been 
previously calibrated, for example, by one or more of the methods 
described above. The method then measure V.sub.probe-inc and 
V.sub.pump-inc., determines R.sub.pump by measurement, and then finds the 
value of the constant C such that the following equation is satisfied: 
EQU .DELTA.V.sub.probe-refl =C V.sub.probe-inc .DELTA.R(t) V.sub.pump-inc 
(1=R.sub.pump) (7) 
For both of these methods it is important to establish the autofocus 
conditions prior to making measurements of .DELTA.V.sub.probe-refl, since 
C depends on the value of A.sub.effective. 
In view of the foregoing, it can be appreciated that this invention employs 
an analysis of the background and acoustical data from a sample in order 
to get a best result for two sample properties, namely the thickness and 
the composition of the material comprising a thin film, wherein the term 
"composition" is herein intended to include characteristics such as phase, 
morphology, crystalline orientation, grain size, etc. 
The analysis may assume a value for one of the properties, and then 
determine the other by simulation and/or by comparison to data obtained 
from known reference samples. The analysis may also be self-consistent by 
assuming a value for one property, then determining the other by 
simulation and/or by comparison to data obtained from known reference 
samples, then improving the value for the assumed property, and then 
continuing to iterate until to obtain a best result for both properties. 
For example, this iteration can be begun by first assuming a thickness of 
the film, and then determining the film's composition, or by first 
assuming a composition for the film and then determining the thickness. 
Both are equally valid approaches. 
By example, in a first method the following steps are executed. 
(A) Calibrate the measurement system, such as that shown in FIG. 1C, 
autofocus, and measure the sample. 
(B) Assume a value for the thickness (d) of the film. 
(C) Compare the background signal corresponding to a film of the same 
general type (e.g., TiSi.sub.2) having the assumed thickness to determine 
a most probable composition for the film. This implies the use of a 
specific set of material properties, such as sound velocity, density, 
optical constants such as n and .kappa., thermal expansion coefficient, 
specific heat, thermal conductivity, the derivatives of n and .kappa. with 
respect to strain, etc. By example, the material properties for 46-54 TiN 
differ from the material properties for 47-53 TiN. 
(D) Associate the physical properties of the film from step C with the 
sample film. 
(E) Deduce an improved value for d from an analysis of the acoustical part 
of the data. 
(F) Optionally repeat steps B-E until convergence (a correct answer) is 
obtained. 
In a second method the following steps are executed. 
(A) Calibrate the measurement system, autofocus, and measure the sample. 
(B) Assume a composition of the film (e.g., 50--50 TiN). 
(C) Deduce a value for the thickness from an analysis of the acoustical 
part of the data. 
(D) Compare the background signal corresponding to a film of the same 
general type (e.g., TiN) having the assumed thickness to determine an 
improved composition for the film. This again implies the use of a 
specific set of material properties, such as sound velocity, density, 
optical constants and derivatives with respect to strain, etc. 
(E) Associate the physical properties of the film from step C with the 
sample film. 
(F) Optionally repeat steps B-E until convergence is obtained. 
In a third method, a simplified variant of the first, the following steps 
are executed. 
(A) Calibrate the measurement system, such as that shown in FIG. 1C, 
autofocus, and measure the sample. 
(B) Assume a value for the thickness (d) of the film. 
(C) Compare the background signal corresponding to a film of the same 
general type having the assumed thickness to determine a most probable 
composition for the film. 
(D) Associate the physical properties of the film from step C with the 
sample film. 
In a fourth method, a simplified variant of the second, the following steps 
are executed. 
(A) Calibrate the measurement system, autofocus, and measure the sample. 
(B) Assume a composition of the film. 
(C) Deduce a value for the thickness from an analysis of the acoustical 
part of the data. 
(D) Associate the physical properties of the film from step C with the 
sample film. 
Any of the forgoing steps of comparing can optionally interpolate between 
reference data or parameters that are measured or deduced from a plurality 
of reference samples. 
Furthermore, the methods can include a step of modifying an assumed 
composition of the sample or film by one or more of the stoichiometry, 
crystal structure, morphology, structural phase, alloy composition, 
impurity content, doping level, defect density, isotope content, grain 
orientation, etc. 
The teaching of this invention can also be employed with compound 
semiconductors, such as Group III-V and Group II-VI compound 
semiconductors, having an unknown content of one or more constituent 
elements. 
The teaching of this invention is especially beneficial for use with 
samples comprised of a semiconductor material and a metal or silicide. 
Related to the foregoing, the teaching of this invention is also useful 
with samples comprised of an alloy of at least two elements having an 
unknown ratio. Examples include Ti-W, Au-Cr, Al-Cu, Al-Cu-Si, Si-Ge, 
In-Ga-As, Ga-Al-As, and Hg-Cd-Te. 
The methods of this invention are particularly useful with thermally 
annealed samples for determining annealing temperature, the thickness of 
an annealed layer, and the phase of an annealed layer. 
This invention can be employed to advantage with a wide range of materials 
and material systems having a finite (useable) absorption of the pump 
wavelength that is sufficient to excite strain waves in the sample. As was 
described above in reference to the embodiment shown in FIG. 1D, the 
wavelengths of the pump and probe pulses may be different. 
Thus, while the invention has been particularly shown and described with 
respect to preferred embodiments thereof, it will be understood by those 
skilled in the art that changes in form and details may be made therein 
without departing from the scope and spirit of the invention.