Quantification of Local Elastic Properties Using Ultrasonic
Force Microscopy
Matthias Kraatz \ Holm Geisler2, Ehrenfried Zschech 2
1
Brandenburgische Technische Universita't Cot thus, Institute of Physics and Chemistry,
P. O. Box 10 13 44, D- 03013 Cottbus, Germany,
2
AMD Saxony LLC & Co. KG, Materials Analysis Department, P. O. Box 11 01 10, D-01330 Dresden, Germany
Abstract A modified Ultrasonic Force Microscopy (UFM) technique is presented that determines the elasticity
(Young's modulus) of a material quantitatively based on the Johnson-Kendall-Roberts model. The periodic oscillation of
the sample with MHz frequencies causes a high dynamical stiffness of the cantilever of a scanning probe microscope
(SPM). The information about the elasticity of a sample can be extracted from the cantilever response to the amplitude
variation. The procedure for the quantitative determination of the reduced Young's modulus is demonstrated for a
partially delaminated thin film. For such a sample, no material inhomogeneities exist for the top layer, i. e., surface
roughness and sample-tip adhesion are assumed to be constant. Consequently, the UFM signal is not influenced by
locally fluctuating material properties and topography. The systematic study shows that film delamination causes a
continuous gradient of film stiffness along the delaminated part of the film. The application of this modified UFM
technique in physical failure analysis is demonstrated for the nondestructive characterization of buried defects.
resolution using a modified, commercially available
scanning probe microscope (SPM) [2,3]. Since the
measured UFM signal is influenced by many
parameters such as surface topography, tip radius and
tip-sample adhesion, this 2D imaging technique has
been applied only qualitatively so far.
INTRODUCTION
With the ongoing seal ing-down of device features
and of interconnect dimensions for high-performance
logic and memory ICs and with the introduction of
new processes and materials, the determination of
properties of the constitutive film materials and the
localization of buried defects become more and more
important for both high manufacturing yield and the
required product reliability. Particularly, the precise
measurement of the Young's modulus of on-chip
inlaid copper interconnect structures and of lowdielectric constant isolating materials is essential for
both process development and process control. The
nondestructive localization of delaminations and of
buried defects like voids and residuals in these
structures is a challenge for physical failure analysis to
exclude both yield-limiting process excursions and
reliability-related failures in ICs [1].
The focus of this paper is primarily on physical
failure analysis using the UFM imaging technique in
the static mode. For a systematic study of stiffness
variation on the UFM signal, a partially delaminated
thin film was chosen as a test sample. In contrast to the
UFM studies published so far, the measured signal is
not influenced by locally fluctuating material
properties (and sample-tip adhesion) and topography.
It will be shown for a particular example in physical
failure analysis that the methodical results can be
applied to a nondestructive characterization of buried
defects, e.g. bubbles at the wafer edge exclusion.
In this paper, an approach of quantification of the
UFM technique is presented that determines the
elasticity of a sample quantitatively. The Young's
modulus is calculated from the measured load-
Ultrasonic force microscopy (UFM) is a
nondestructive, nanomechanical imaging technique
that allows imaging of the elastic (static) and
viscoelastic (dynamic) response of a large variety of
materials and structures with nanometer-scale spatial
CP683, Characterization and Metrology for VLSI Technology: 2003 International Conference,
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343
selected points of the sample for a more precise
quantitative analysis.
dependent indentation depth of the tip into the sample
using the Johnson-Kendall-Roberts (JKR) model [4].
The indentation depth of the SPM tip into the
sample depends on the load applied onto the
cantilever, on the Young's moduli of tip and sample
and on the curvature radius of the tip. Since the
adhesion between tip and sample acts as an additional
load, the indentation depends on the adhesion, too. For
a specific set of material and geometry parameters, the
load-indentation dependence (Fig. 1) can be calculated
using the JKR model [4].
The UFM Principle
The UFM combines the high spatial resolution of
conventional SPMs with the elastic imaging capability
of acoustic or ultrasonic microscopes. The static
nanomechanical imaging mode, also called
waveguide-ultrasonic force microscopy (W-UFM)
mode, is a contact mode that exploits the nonlinear
force-displacement response between an ultrasonically
vibrating nanoprobe tip and a sample surface to record
a scanned image map that visualizes the elasticity in a
wide dynamic range.
1_
Additional components are needed to modify a
SPM in such a way that it can be used for UFM: an
ultrasound transducer, waveform generators and a
lock-in amplifier for analysis of the UFM signal. The
transducer is operated at a constant frequency,
typically about 2 MHz, but the amplitude is modulated
in such a way that it rises from zero to a preset
maximum value, and then it drops to zero again. There
is a pause between the triangular ultrasound pulses
with a pulse frequency in the kHz range.
Setpoint <
2
h/h(0)
F
*/Fo
R = SPM tip radius
Ay = adhesion energy
ajo= jump-off amplitude
In the contact mode, the deflection of the cantilever
is kept constant by monitoring the deflection signal.
As a consequence, the SPM tip at the end of the
cantilever is pressed upon the sample surface with a
constant load. During one ultrasound pulse on tip or
sample, the vibration amplitude eventually reaches a
certain value at which the SPM tip detaches from the
sample surface. The cantilever responds with a sudden
deflection, which is referred to as the force jump. The
deflection signal including the ultrasound response is
called the UFM signal.
FIGURE 1. Normalized force-indentation curve from the
JKR model.
The SPM setpoint, which controls the load onto the
cantilever and the tip, corresponds to one point along
the force-indentation curve. A raised setpoint value
leads to an increased indentation. The UFM jump-off
amplitude is directly related to the indentation. The
ultrasonic amplitude simply has to override the
distance of indentation and adhesion hysteresis for the
AFM tip to detach from the surface. Therefore,
measuring a shift of the jump-off amplitude is
equivalent to measuring a variation of indentation
depth. For a small variation of the cantilever load F,
which can be achieved by adjusting the AFM setpoint,
the corresponding change in indentation depth h can be
measured. As a result, the local stiffness of the sample
can be calculated as AF/Ah. Simultaneously, the
derivative <3F/dh of the force-indentation curve F(h)
provides the stiffness for a chosen load. As a linear
approximation, the derivative can be set equal to the
measured stiffness to solve the equation for the
Young's modulus.
The vibration amplitude at which the cantilever
detaches from the sample depends upon the elastic
properties of the sample. For samples with a high
Young's modulus, the force-jump occurs at small
amplitudes, smaller Young's moduli lead to higher
amplitudes. A lock-in amplifier can extract a measure
from the UFM signal in real time that is inversely
proportional to the jump-off amplitude and correlates
to the surface elasticity of the sample. The lock-in
output can be mapped simultaneously with the SPM
topography, and a qualitative 2D image of the surface
elasticity can be obtained.
In this study, the UFM has not been operated in a
scanning or imaging mode. Instead, the UFM signal
has been recorded with a digital oscilloscope at
344
Experimental
Setpoint:
The test sample was a partially delaminated Ta/Cu
layer on an epoxy/Si substrate. The thicknesses of the
Ta and Cu layers are 30 and 100 nm, respectively. On
one side, the layer stack is intact and on the other side
the Ta/Cu double layer is delaminated between the Cu
and epoxy layer. The distance between the
delamination threshold and the edge of the ascending
ramp is approximately Ijum. The edge reaches a height
of 500 nm above the epoxy substrate (Fig. 2). The
feature was generated by an adhesion test and detected
by AFM measurements. The extend of the feature is 50
jitm.
0,1
0,2
Time in ms
(a)
0,1
x,
Stack
X2
Threshold
0,3
0,2
0,3
Time in ms
X3
X4
Middle Edge
(b)
FIGURE 2. Sample geometry showing a delamination of the
Ta/Cu layer. X } through X4 designate the points of the local
measurements.
Compared to patterned films that have been
investigated so far, this sample has the essential
advantage that its surface is homogeneous. That
means, surface roughness and tip-sample adhesion do
not change along the ascending ramp. Consequently,
the measured stiffness will not be influenced by
topography and adhesion.
0,1
0,2
0,3
Time in ms
(C)
The measurements were performed at four points —
the first at the intact stack, the second at the threshold,
the third at the middle of the ascending ramp and the
forth close to the edge.
In this experiment, the ultrasonic vibrations were
introduced to the sample. The triangular pulses for the
transducer had a length of 0.2 ms and maximum peakto-peak amplitude of 10 V. The enclosed modulated
ultrasonic frequency was set to 1.9 MHz. At the four
points of the sample, the UFM response curves were
recorded with a digital oscilloscope for the duration of
the triangular ultrasound pulse. The measurement was
repeated for 9 different AFM setpoint values, starting
from 0.1 V through 0.9 V. The vertical deflection of
the cantilever prior to AFM engage was set to 0 V, i.e.,
a setpoint of 0 V means no load onto the cantilever.
The setpoint values were transformed into forces after
calibration of the cantilever sensitivity.
0,1
0,2
0,3
Time in ms
(d)
FIGURE 3. UFM curves with shitted force jumps due to
increased setpoints. (a) stack., (b) threshold, (c) middle of
ramp, (d) edge.
345
For each of the four points along the ascending
ramp, the indentation depths were plotted against the
loads (Fig. 4). For all points, a linear relation between
load and indentation could be observed. The closer the
points are to the edge, the higher the slopes of the
linear regression. In the h-F plot, the slope is defined
as Ah/AF, which is the inverse fraction of the stiffness,
also called compliance. The calculated stiffness values
for the intact layer stack, the threshold, the middle of
the ramp and the edge are 4000, 2300, 1000 and 500
N/m, respectively. There is no high frequency
response of the sample structure and therefore the
stiffness refers entirely to material indentation and not
layer deflection.
Results
The plots of the UFM curves show two important
effects (Fig. 3). First, the jump-off generally shifts to
higher amplitudes along the ascending ramp from the
intact layer stack to the edge. This shift points to a
decrease of Young's modulus. Second, the spread of
the jump-off amplitudes for all setpoint values widens
when moving towards the edge. Since a change of the
jump-off amplitude is equivalent to a change of the
indentation depth, larger changes in jump-off
amplitudes for constant setpoint steps mean decreasing
stiffness.
The jump-off amplitude is defined by the time at
which the UFM signal exceeds the mean value. For a
uniform detection of the jump-off amplitudes for the
UFM curves, the mean value of each curve was
calculated. The mean value threshold is a good
approximation for the force-jump.
Load F in nN
100
200
0
0,16-
Edge
"''
-1,6
« 0,14E
So far, the jump-off amplitudes or indentation
depths are only referred to as relative times
corresponding to the beginning of the triangular
ultrasonic pulse. The amplitude of the transducer has
to be measured in order to transform jump-off times
into jump-off amplitudes. Assuming that the
elongation amplitude rises linearly with the drive
amplitude, it is sufficient to measure the maximum
amplitude of the transducer. The amplitude was
measured with prolonged UFM pulses. The duration of
the triangular pulse was set to 1/300 s, which is long
enough for the AFM control units to compensate the
cantilever deflection after the force jump.
Simultaneously, the AFM height channel delivers a
nm-calibrated measure for the compensation distance,
which can be interpreted as the approximate transducer
amplitude. A maximum amplitude of 2.1 nm was
measured. For the regular UFM pulse with a duration
of 0.2 ms, the amplitude rise rate is 10.5 nm/ms. When
multiplying the jump-off time with the rate, the actual
jump-off amplitude (equivalent to indentation depth)
can be calculated.
1.4 |
~ 0,12-
-1,2!
o
1
'
*g 0,10-
-1,0 S
E
* 0,08-
-0,8
0,06-
-0,6
0,0 0,2 0,4 0,6 0,8 1,0
Setpoint in V
FIGURE 4. Load-indentation
compliance values
plot
with
calculated
The curvature of the AFM tip was quantified based
on images of a test sample that contained an array of
very sharp tips pointing upwards. The radius of the test
array tips was 10 nm. When scanning the test sample,
the SPM tip actually images itself due to the smaller
size of the test tips. In the cross-section of the image, a
circle can be fitted into the tip curve to measure the
radius. Subtracting the radius of the test tips (10 nm)
yields a good approximation for the AFM tip radius.
The setpoint can be calibrated by measuring the
cantilever sensitivity based on an AFM force-distance
plot. The unit, at which the cantilever is mounted,
moves towards the sample for a defined distance Az
while monitoring the cantilever deflection signal U.
The value Az/AU provides the cantilever sensitivity.
For this experiment, the measured value was 102
nm/V. Multiplying the sensitivity with the cantilever
spring constant (k=2.5 N/m) yields the actual load per
voltage (255 nN/V), which allows transformation of
the setpoint values into loads.
The last measure to quantify is the adhesion
between the AFM tip and the sample. It can be
determined from the AFM force-distance plot, too.
This time, the unit will be moved away from the
sample until the cantilever detaches. The distance z
between no deflection and detachment of the
cantilever was 55 nm. Considering a spring constant of
2.5 N/m, the pull-off force is 137.5 N. The JKR model
provides a relation between pull-off force F and
adhesion energy Ay, which is F=3/2*R7iAy. R is the
radius of the AFM tip. Using these data, the adhesion
346
energy Ay can be calculated (0.63 J/m2). Due to
ambient conditions, the adhesion energy is rather
dominated by moisture than material properties.
As shown above, a delamination causes a decrease
of the film stiffness. Using UFM, the blisters were
identified as cavities underneath the Ta layer, which
were caused by film delamination.
TABLE 1. Reduced Young's moduli for the
partially delamiriated film._______________
Position
Red. Young's
Modulus in GPa
Stack
150
Threshold
60
Middle of ramp
20
Edge______
10
The utilization of the UFM in a scanning mode
requires the automation of the measuring procedure.
This further development would make 2D images
possible, with increased information about the local
stiffness of a sample with the nanometer-scale spatial
resolution of aSPM.
The dynamic nanomechanical imaging mode
images the nanoscale viscoelastic surface and
subsurface properties using a two-frequency or
heterodyne UFM (HFM). In this mode, ultrasonic
vibrations are introduced to the sample and to the tip.
The nonlinear tip-sample interaction enables the
extraction of the heterodyne interference signal
between the two ultrasonic vibrations so that the
spatial variation of the surface/subsurface viscoelastic
phase (relative to the carrier wave) can be imaged [5].
It is expected that subsurface mechanical data can be
extracted, even for deeper regions (not only in the
near-surface range). That means this technique could
be a potential technique for nondestructive localization
of defects in inlaid copper vias.
All parameters that are needed for the calculation
of the Young's modulus were quantified, including
stiffness, tip radius and adhesion energy. For the intact
layer stack, the delamination threshold, middle of the
ramp and edge the calculation yields 150, 60, 20 and
10 GPa, respectively (Tab. 1). The numbers are
reduced Young's moduli, which combine the elasticity
of the sample material and the AFM tip. The decrease
of the Young's modulus is due to the diminished
contribution of surrounding material.
Conclusion and Outlook
It has been shown that UFM is a potential
nondestructive technique for physical failure analysis
in semiconductor industry. It allows detection of
subsurface defects like film delaminations or voids
with high spatial resolution. For a particular sample, a
partially delaminated thin film, the reduced Young's
moduli were calculated for several points,
independently of surface roughness and tip-sample
adhesion. Parameters like stiffness, tip radius and
adhesion energy were quantified for the system under
investigation.
REFERENCES
1. E. Zschech, E. Langer, II. J. Engelmann, K. Dittmar:
Physical Failure Analysis in Semiconductor Industry —
Challenges of the Copper Interconnect Process.
Materials Science and Semiconductor Processing 5, 457
(2003)
2. O. V. Kolosov, H. Ogiso, H. Tokumoto, K. Yamanaka.
Elastic Imaging with Nanoscale and Atomic Resolution
by Ultrasonic Force Microscopy (UFM). Springer Series
in Material Science, Vol. 31, Springer-Verlag, Berlin
(1994)
The methodical knowledge about the UFM
technique was applied to characterize blister defects
beneath a Ta layer close to the wafer edge. Based on
AFM images of the blisters which represent the
topography only, it could not be decided whether the
defects are solid droplets or delaminations of the Ta
layer. The UFM image reveals clearly a distinct loss of
stiffness (Fig. 5).
3. R.E. Geer, O.V. Kolosov, G.A.D. Briggs, G.S.
Shekhawat.. Nanometer-scale mechanical imaging of
aluminum damascene interconnect structures in a lowdielectric-constant polymer. J. Appl. Phys. 91, 4549
(2002)
4. K. L. Johnson, K. Kendall, A. D. Roberts. Surface Energy
and the Contact of Elastic Solids. Proc. R. Soc. Lond.
A324, 301 (1971)
5. M. T. Cuberes, G. A. D. Briggs, O. V. Kolosov,
Nanotechnology 12, 53 (2001)
FIGURE 5. SPM study of a Ta layer with defects: AFM
(left) and UFM (right) images, 2 \im x 2 (urn scan size.
347