LASER ULTRASONIC CHARACTERIZATION OF RESIDUAL
STRESSES IN THIN FILMS
Carmen M. Hernandez, Sridhar Krishnaswamy
Center of Quality Engineering and Failure Prevention, Robert R. McCormick School of
Engineering and Applied Science, Northwestern University, Evanston, IL, 60208
ABSTRACT. In previous work, we showed that laser ultrasonics (photo-acoustics) is a promising
tool for the nondestructive and non-contact characterization of thin film structures. In particular it
was shown that the modulus and residual stresses in two-layer freestanding Al/Silicon Nitride films
could be measured using a narrow-band laser ultrasonic technique. In this technique, a microchip
laser deposits pulsed laser energy as a spatially periodic source on the structure. The resulting
narrowband ultrasonic modes are monitored using a broadband Michelson interferometer. By varying
the geometry of the spatially periodic source, a wide range of wavenumbers can be probed. For the
thin films investigated, which were less than a micron in thickness (300-900 nm), only the two lowest
order modes were generated and these in turn can be related to sheet and flexural modes in plates. In
this paper we present an extension of this approach. The sensitivity of the photo-acoustic system is
examined by measuring variable residual stresses. Variable residual stresses are obtained in the thin
films by two methods: by varying the growth rates for silicon nitride and by varying the membrane
INTRODUCTION
A photoacoustic microscope was used to generate and detect narrowband guided
waves in freestanding thin films. The films consist of two layers, one of aluminum and
another of silicon nitride. By crossing two pulsed laser beams on the surface of a film, a
spatially periodic source is created. The result is the generation of narrowband guided
waves with a fixed wavenumber [1-2]. A wide region of wavenumbers can be probed by
varying the geometry of the periodic source. The two lowest order Lamb waves, the
symmetric, S0, and the antisymmetric, A0, modes, are generated in these films. Dispersion
curves for these two modes can be obtained by testing over a wide range of wavenumbers.
Using plate theory, velocity equations can be derived for the two lowest order Lamb
waves [3-4]. The material properties can then be calculated using the velocity equations
and dispersion curves.
Photoacoustic Microscope
A schematic of the photoacoustic microscope is shown in Figure 1. A microchip
laser with a pulse length of 800 ps and pulse energy of 3.9 jiJ was used as the generation
laser. The beam was separated into two parallel beams with a beam spacing of d. The two
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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beams were then focused onto the surface of the film. The beams overlap and the result is
an interference pattern in the form of a spatially periodic grating [1-2]. This spatially
periodic source generates guided waves in the films with a fixed wave number. The
wavenumber generated is a function of the angle, 6, the angle at which the two beams are
crossed and the wavelength of the generation laser, Xe, see Equation 1.
* = ^sin(f|
2
(1)
\ v y
The generated guided waves are detected using a balanced Michelson interferometer. The
detection laser is a CW Nd:YAG laser with a wavelength of 532 nm. The peak frequency
is taken from the spectrum of the time trace and is used to calculate the phase velocity as
shown in Equation 3. The phase velocity for a given wave mode is found using the
wavenumber, k, from the source and the peak circular frequency, GO, of the detected wave
mode.
V=
(2)
I
By varying the beam spacing, d, between the two generation beams, a wide range of
wavenumbers can be probed. Thus, dispersion curves for the two wave modes can be
obtained.
In general, either broadband or narrowband generation can be used to obtain
dispersion measurements [5-6]. The damage threshold of the sample limits the generation
power. Using a point source or line source for broadband generation limits the power for
generation due to ablation of the sample. However, by using narrowband generation,
higher total laser power can be used to generate guided waves on the samples. The result
is a higher signal to noise ratio, because the signal to noise ratio is directly proportional to
the intensity of the generation laser. Also, for broadband detection it is necessary to make
measurements at a number of source to receiver distances to obtain the dispersion of the
velocities [6]. With narrowband generation, measuring the velocity dispersion on small
structures is possible because the source to receiver distance can be placed at essentially a
zero distance.
Beam
Narrowband
Generation system
(source)
S
Plitter
Lens
Q-switched microchip
laser:
800 ps, 3.9 |iJ
Stabilization
electronics
Balanced Michelson
Interferometer
(receiver)
PZT
^
BS
PBS
A/2
Specimen
^1 A/4
v
T
T Photodetectors
Lens
iplifier
Oscilloscope
FIGURE 1. Schematic of the photoacoustic microscope.
1505
Dispersion Curve Measurements
The photoacoustic microscope was used to obtain dispersion curve measurements
of free standing thin films. Only the two lowest order Lamb waves will propagate for
small values of the product of the wavenumber, k, and thickness, h. For the thin films
tested, in the order of hundreds of nanometers in thickness, even at high frequencies, the
k*h values are small enough that only the A0 and S0 modes propagate. Using plate theory,
exact solutions for the velocity equations of the A0 and S0 modes can be found. The S0
phase velocity is given by Equation 3, where the composite stiffness and density are given
by Equations 4 and 5. The volume fraction, Vk, where h is the total thickness of the plate
and hk are the layer thicknesses for the aluminum and silicon nitride films tested, is shown
in Equation 6. The S0 mode is nondispersive and the velocity is dependent on the
composite modulus and composite density.
Vk=hklh
(6)
The velocity equation for the A0 mode depends on the composite flexural rigidity,
composite density and also average residual stress. For the Ao mode, the phase velocity is
given by Equation 7 where ax is the composite (thickness-averaged) residual stress, and D*
is the
_a_ \Ef_
±
(7)
, — , —i/ *
* \P
P
normalized composite flexural rigidity that is dependent on the material properties and
thickness of the layers. The A0 mode is dispersive and the velocity is affected by the
average residual stress in the film.
EXPERIMENTAL RESULTS AND DISCUSSION
Films With Varying Residual Stress
In previous work, it was shown that the modulus values obtained for the silicon
nitride and aluminum were in the range of published values for these two materials [5].
The next step was to evaluate the ability of the photoacoustic system to measure varying
residual stresses. Since only the effects of residual stress affect the Ao mode, only the Ao
mode was used in these experiments. Varying residual stresses in the film were introduced
by modifying the gas flow rates when depositing the silicon nitride films. In this case two
flow rates were chosen. The low gas flow rate film was grown using 6 seem for NH3 and
25 seem for SiffeCk and the thickness of the nitride was 430 nm. The high gas flow rate
film was grown using 12 seem for NH3 and 50 seem for SiH2Cl2 and the thickness of the
nitride was 395 nm. For both cases, the aluminum layer had a thickness of 349 nm. Square
membranes of various sizes were created on one wafer so that size effects on the
measurements could be investigated. Three sizes were chosen, where the lengths of one
side of the square were 0.75 mm, 1 mm and 1.8 mm.
1506
2
2
2
2
Velocity
Velocity (m/s)
(m/s)
300000
300000
250000
250000
300000
200000
250000
200000
(0
150000
200000
1150000
«»"*
M
100000
150000
if 100000
8 100000
50000
50000
1.8 mm
1.8 mm
1.8 mm
1.8 mm
+ 1.81mm
mm
1 mm
*1.80.75
mmmm
0.75 mm
i 1 mm
0
500000
0
0
0.005
0.01
0.015
0.02
0.025
0.005
0.01
0.015
0.02
0.025
o 0—————————————————————
*0.75 mm
0
0.005
0.01
2
0.015
2
(k*h)
(k*h)
0.02
0.025
2
/lr*h\
FIGURE 2. Dispersion curve for the low gas flow rate
silicon
nitride and aluminum film of three square sizes.
FIGURE 2. Dispersion curve for the low gas flow rate silicon nitride and aluminum film of three square sizes.
FIGURE 2. Dispersion curve for the low gas flow rate silicon nitride and aluminum film of three square sizes.
Results
Results
Results
Figures 2 and 3 show the dispersion curves for the low and high gas flow rate
Figures 2 and 3 show the dispersion curves for the low and high gas flow rate
films and Figures
the three and
square
sizes.
As can be
seen,forthe
are gas
dispersive
3 show
the dispersion
curves
the velocities
low and high
flow rateand
films and the three2 square
sizes.
As
2 can be seen, the velocities are dispersive and
essentially
linearly
varying
with
(k*h)
.
The
velocity
equation
for
the
Ao
mode
and a least
2
films andlinearly
the three
squarewith
sizes.
can velocity
be seen, equation
the velocities
essentially
varying
(k*h)As
. The
for theare
Ao dispersive
mode and and
a least
2
squares
fit
was
used
to
calculate
the
flexural
rigidity
and
residual
stress
in
the
films.
These
essentially
linearly
with (k*h)
. The velocity
equation
for the
Ao in
mode
a least
squares
fit was
usedvarying
to calculate
the flexural
rigidity and
residual
stress
the and
films.
These
results
are
shown
in to
Table
1. the flexural rigidity and residual stress in the films. These
squares
fit
was
used
calculate
results are shown in Table 1.
results are shown in Table 1.
Discussion
Discussion
Discussion
Using a range of values published for aluminum and silicon nitride the flexural
of
published
foraluminum
aluminum
andsilicon
nitride
flexural
Usingaarange
range
of values
values
published
for
thethe
flexural
rigidity is Using
expected
to range
between
8.9 to 14.1
GPa.
As and
can
besilicon
seen,nitride
the
flexural
rigidity
rigidity
is
expected
to
range
between
8.9
to
14.1
GPa.
As
can
be
seen,
the
flexural
rigidity
rigidity measured
is expectedexperimentally
to range betweenare
8.9 in
to 14.1
can be
the flexural
rigidity
values
this GPa.
rangeAswith
theseen,
exception
of the
square
values
areand
in athis
this
range
with
exception
square
values measured
measured
experimentally
are
in
with
thethe
exception
of of
thethe
square
membrane
with aexperimentally
side of 0.75 mm
lowrange
gas flow
rate
silicon
nitride
layer.
In this
membrane
with
0.75
and detection
low gas
gaswere
flownear
ratean
silicon
nitride
layer.
In this
membrane
withaa side
side
ofgeneration
0.75 mm
mm and
and
aa low
flow
rate
silicon
In this
case,
it is suspected
thatof
edgenitride
and
solayer.
edge
effects
case,
it
is
suspected
that
generation
and
detection
were
near
an
edge
and
so
edge
effects
case, it is suspected that generation and detection were near an edge and so edge effects
2
2
Velocity
Velocity(m/s)
(m/s)
250000
250000
250000
200000
2
<M 200000
200000
-
II *
^ 150000
150000
150000
M,
JflV"
2
CM
1.8 mm
+ 1.8
1.8mm
mm
1 mm
,11, 1 mm
1 mm
0.75
mm
*0.75
mm
0.75 mm
'o 100000
100000
_0 100000
50000
50000
50000
r\0
0
00
0
0.005
0.005
0.01
0.01
A
(k*h)^2
2
0.005 (k*h)
0.01
(k*h)^2
0.015
0.015
0.015
FIGURE
3. Dispersion
Dispersioncurve
curvefor
forthe
thehigh
high
flow
silicon
nitride
aluminum
of three
FIGURE 3.
gasgas
flow
raterate
silicon
nitride
and and
aluminum
film film
of three
squaresquare
sizes. 3. Dispersion curve for the high gas flow rate silicon nitride and aluminum film of three square
FIGURE
sizes.
1507
TABLE 1. Experimental results for flexural rigidity and residual stress.
Wafer with
Low Gas Size (mm)
Flow Rate
1.8
Nitride
1.8
1
0.75
D*
GPa
15.0
13.1
11.4
25.1
Residual Stress
MPa
483
509
519
364
Wafer with
High Gas Size (mm)
Flow Rate
1.8
Nitride
1
0.75
D*
GPa
12.4
14.4
14.4
Residual Stress
MPa
363
352
352
could have influenced the experimental results. There is a clear variation in residual stress
between the film with a low gas flow rate silicon nitride layer, with stress between 480520 MPa, and a high gas flow rate silicon nitride layer, with a residual stress measurement
between 352-363 MPa. The results for the wafer with a high gas flow rate silicon nitride
layer shows very consistent measurements for the flexural rigidity for the three square
membrane sizes.
CONCLUSION
The photoacoustic microscope was used to measure variation in residual stress
for a two layer free standing thin film. The dispersion curve for the lowest order
antisymmetric Lamb wave was obtained since only this mode is affected by the average
residual stress in the film. A clear difference can be seen in residual stress by varying the
gas flow rates during fabrication of the films and this variation can be measured using laser
ultrasonics. Finally, the values obtained for the flexural rigidity are within the range of
values obtained using a range of published values for the aluminum and silicon nitride.
ACKNOWLEDGEMENTS
This work is supported by the National Science Foundation through grant No.
CMS-0070005.
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2.
3.
4.
5.
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Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, New Jersey, 1965, p.462.
S. Timoshenko, Theory of Plates and Shells, McGraw-Hill, New York, 1940, p. 87.
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