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3D Magnetic Field Imaging for Non-destructive Fault Isolation
A. Orozco*, J. Gaudestad, N. E. Gagliolo, C. Rowlett, E. Wong
Neocera, LLC, 10000 Virginia Manor Road, Beltsville, MD, 20705, USA
A. Jeffers, B. Cheng, F. C. Wellstood
Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park MD, 20742
A. B. Cawthorne
Department of Science and Mathematics, Trevecca Nazarene University, Nashville, TN 37210
F. Infante
Intraspec Technologies, 3 avenue Didier Daurat, 31400 Toulouse, France
Abstract
While transistor gate lengths may continue to shrink for some time, the semiconductor industry faces increasing
difficulties to satisfy Moore’s Law. One solution to satisfying Moore’s Law in the future is to stack transistors in
a 3-dimensional (3D) formation. In addition, the need for expanding functionality, real-estate management and
faster connections has pushed the industry to develop complex 3D package technology which includes System-
in-Package (SiP), wafer-level packaging, through-silicon-vias (TSV), stacked-die and flex packages. These
stacks of microchips, metal layers and transistors have caused major challenges for existing Fault Isolation (FI)
techniques. We describe in this paper innovations in Magnetic Field Imaging for FI which have the potential to
allow 3D characterization of currents for non-destructive fault isolation at every chip level in a 3D stack.
1. Introduction
In 1965 Gordon Moore predicted that the
number of transistors on an integrated circuit would
double approximately every two years [1]. The
International Technology Roadmap for
Semiconductors (ITRS) has been setting the CMOS
technology nodes according to Moore’s Law. In
addition to traditional scaling per Moore's Law, the
Semiconductor industry is also focused on increasing
transistor density by stacking transistors in 3D, also
called “More than Moore” (MtM) [2]. In addition, the
need to expand functionality, real-estate management
and faster connections has pushed the industry to
develop complex 3D package technology, which
includes System-in-Package (SiP), wafer-level
packaging, through-silicon-vias (TSV), stacked-die
and flex packages among others. As microelectronics
has moved further in the MtM direction, more
electronic components are being designed with a 3D
geometry, making fault isolation (FI) and failure
analysis (FA) more complex due to the difficulties of
imaging through metal layers and semiconductor
materials [3].
The challenges that 3D integration present to FA
require the development of new FI techniques that
allow for non-destructive, true 3D failure localization.
1.1. 3D Magnetic Field Imaging (MFI)
Magnetic Field Imaging (MFI), using a
Superconducting Quantum Interference Device
(SQUID) as the sensing element, was introduced in
1998 as a way to detect short circuit failures in ICs
[4]. The principle is very simple: the circuit of interest
in the device under test (DUT) is powered up. The
current generates a magnetic field around the path it
takes and this magnetic field is detected by a sensor
positioned above the device. The sample is raster
scanned and its magnetic field is acquired at multiple
predetermined steps providing an image of the
magnetic field distribution. This magnetic field data is
typically processed using a standard inversion
technique [5,6] to obtain a current density map of the
device. The resulting current map can then be
compared to a circuit diagram, an optical or infrared
image, or a non-failing part to determine the fault
location. Today, giant-magnetoresistive sensors have
been added to the imaging system to allow higher
resolution and FI at die level where the sensor can be
brought close to the circuit. A description of the
technique and the applications to FA can be found in
the literature [7-14].
Magnetic field imaging is a natural candidate for
3D FI of complex 3D interconnected devices. This is
because the low-frequency magnetic field generated
by the currents in the DUT is unaffected through the
vast majority of materials used in device fabrication
as they are non-ferrous; the presence of multiple
metal layers, dies or other opaque layers do not have
ISTFA 2013: Conference Proceedings from the
39th International Symposium for Testing and Failure Analysis
November 3–7, 2013, San Jose, California, USA
Copyright © 2013 ASM International®
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189
any impact on the magnetic field signal. The
technique is not affected by the number of layers.
The capabilities and limitations of this technique have
been extensively discussed and tested in the literature
[12-14].
A serious limitation with the standard inversion
technique is that, in order to compute the current
based on the acquired magnetic data, it is assumed
that all currents are confined to a single plane.
Although this is a good assumption in many
situations, this is a 2D technique and the vertical
information is lost. Nonetheless, it has been
successfully applied to 3D devices in some situations
[3,15-17].
Unfortunately, there is no way to generalize the
standard inverse solution to the 3D case, as it can be
easily demonstrated that there are an infinite number
of possible solutions to the generic 3D inverse
problem.
Here we demonstrate that by imposing
reasonable constraints on the current paths
compatible with typical device fabrication, it is
possible to extract the 3D current path in a DUT using
a new solver rather than the standard inverse method.
In this paper, we first apply the solver to simulated
data to evaluate the accuracy of the results, then
experimentally validate the results using control
samples with well-known geometries.
1.2. The Magnetic Field 3D Solver
Through investigation and analysis of the
magnetic field signal, we have developed an
algorithm capable of successfully reconstructing a 3D
current path based on an acquired magnetic field
image. The generally intractable problem has been
reduced to a manageable problem by carefully
constraining the search.
One key to success is the selection of adequate
constraints. For example, current is mainly contained
in layers and each of them is connected vertically.
Similarly we impose Manhattan geometry restrictions
on the current paths. A second key ingredient is a
starting current path that is not far from the correct
solution. This is not trivial but we have found that the
magnetic field image itself can be sometimes used to
determine a good-enough starting path that allows
for convergence.
The ultimate limits of the resolution capability
depend in a complex manner on different system and
scan parameters. Scanning distance (distance from the
magnetic sensor to the current) and noise in the image
are the most important factors affecting lateral and
vertical resolution.
1.3. Examples
1.3.1. Simulations
Simulated 3D current paths were used to
generate the expected magnetic field image
corresponding to typical real scanning conditions,
sensor noise level and device geometries (vertical
current separation, number of layers, lateral
resolution, etc.). This allowed us to determine if the
3D solver was capable of finding a 3D current path
solution and how good this solution was compared
with the true path.
Figure 1 shows 3D solver results for a GMR
image simulated 4-layer linear via chain. The
separation between current layers is approximately 10
mm and the current meanders vertically among the 4
different layers. The path is formed by segments of 4
mm length each. This path can be seen as the red line
in the 3D axonometric projection in Figure 1 (b).
Figure 1 (a) shows a top view of the 3D solver
computed current path overlaid on the magnetic field
data used. Figure 1 (b) shows a comparison of the 3D
true path (red) and the path computed by the 3D
solver (blue). As can be seen, the computed path
matches almost identically with the true path. There
are only 3 areas in which we can see discrepancies
(blue segments in Figure 1 (a)).
The solver also allows us to determine critical
geometrical parameters, like the distance from the
sensor to the top current layer (z-distance), as well as
the relative vertical separation of layers (h12 denoting
separation between layer 1 and 2, h23 between layer
2 and 3 and h34 for layers 3 and 4). The computed
values from the 3D solver and the true values are
shown in Table 1.
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It should be noted that the error for all
parameters is less than 1 mm.
The importance of accurately determining these
parameters is evident if we understand their meaning.
The sensor distance allows the FA engineer to
determine how deep inside the device is the closest
current layer being detected. This allows identifying,
for example, the specific problem die in a stacked die
device. Accurately being able to position each current
segment in a layer allows the FA engineer to follow
the current as it vertically moves from one die (or
layer) to another.
A more complex current pattern is shown in
Figure 2. In this case, a 4-layer meander pattern is
used to generate the magnetic field shown in Figure
2(a). Again, the path is formed by segments of length
4 mm and the layer separation is about 10 mm for all
layers.
Figure 2 (a) shows the path from the 3D solver
overlaid on the magnetic field data while from t a top-
view perspective. Figure 2 (b) shows a comparison of
the true path (red) and the 3D solver computed path
(blue) in a 3D axonometric view. Again, the overall
good match between the computed and true paths is
remarkable considering the complexity and
dimensions of the meandering pattern. Most of the
errors occur in assigning the correct vertical layer
between layers 3 and 4. A few lateral errors are also
visible but we can say that the majority of the
segments have been correctly assigned laterally
within a lateral resolution of 4 mm.
1.3.2. Test Samples
To test the 3D solver on real samples we built
control samples with well know geometries. We used
an SU8/metallization layer technique to build 3 layer
structures with each metal layer simulating die
stacking. The layer separation was 10 mm, while the
metal width was about 4 mm and the via xy
dimensions were about 8 mm x 8 mm. Figure 3 (i)
shows an optical image of a 3-layer linear via chain
from the top. The vertical vias connecting the
Figure 1: Simulated 4-layer linear via chain 3D solver
results. (a) Top view of the 3D solver computed current
path overlaid on the magnetic field data. (b) 3D
axonometric view compariing true path (red) and
computed 3D solver path (blue).
Figure 2: 3D solver applied to a more complex situation:
4-layer XY-meandering pattern. (a) 3D solver computed
3D path overlaid on the magnetic data. (b) Comparison of
true path (red) and 3D solver computed path (blue).
Table 1: Comparison of true parameters (scanning
distance, layer separations) with those obtained from the
3D solver.
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different metallization layers are visible as the big
squares. The focal plane was changed to focus on the
top layer (top image), middle layer (middle image)
and bottom layer (bottom image). The apparent
optical thickness, after refraction index correction,
showed layer separation h12 = 9 mm and h23 = 9.3
mm. The intended layer separation was 10 mm.
Figure 3 (ii) shows a sketch of the cross-section
of the structure shown in figure 3 (i), roughly aligned
with the correcpondiing sections in Figure 3 (i).
Figure 3 (iii) shows the CAD design of the 3-layer
linear via chain pictured in Figure 3 (i).
Different structures were powered up and
scanned under a magnetic microscope using a SQUID
sensor. The resulting magnetic field images were then
analyzed using the 3D solver. As an example, Figure
4 shows the results of the 3D solver applied to a 3-
layer linear via chain structure on the
SU8/metallization sample.
The top image of Figure 4 shows the acquired
magnetic field image using a SQUID sensor and it
looks at the device from the top. The middle image
shows the path computed by the 3D solver overlaid
on the optical scan image (top view as well). Note
that different colors denote different layers. The
bottom image of Figure 4 shows a zoomed-in image
of the area marked with a yellow rectangle. Further
comparison with the CAD shows that the layer
assignment for the different segments is correct. Also,
there is no lateral error as all segments are correctly
aligned and they are positioned within 1 mm of the
physical center of the metal trace on the optical
image.
In addition, the 3D solver estimates the layer
separations to be h12 = 8.7 mm and h23 = 13.3 mm, to
be compared with the measured h12 = 9 mm and h23
= 9.3 mm. This results in errors of 0.3 mm and 4 mm
respectively.
1.4. Conclusions
Innovations in magnetic field imaging suggests
we can extend a widely used 2D fault isolation
technique into a true, non-invasive 3D fault isolation
technique. The development of a novel 3D solver
algorithm allows us to extract 3D current paths along
with critical 3D information like the current to sensor
separation, which can be used to identify the layer
where the failure occurs, as well as the separation
between layers of current. Vertical resolution better
than 10 mm, lateral resolution of 4 mm and capability
to differentiate dies in a stacked configuration are
possible and being currently improved.
Figure 3: (i) Top view, high resolution optical image of the
SU8/metallization device focusing on the top layer (top),
middle layer (middle) and bottom layer (bottom). (ii)
Cross-section sketch. (ii) Three different types of
patterned structures. Squares denote vertical vias: black
denoting top-middle layer connection; green denotes
middle-bottom layer connection. Turquoise (bottom layer),
light green (middle layer) and purple (top layer) denote
the different metallization layers
Figure 4: SU8/metallization sample 3D solver results on 3-
layer linear via chain structure. (Top) SQUID acquired
magnetic image. (middle) 3D solver somputed current path
overlaid on optical image of the sample. (bottom) Zoom-in
image on the yellow rectangle area.
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The authors would like to acknowledge many
useful conversations with L. Knauss, H. Kwon, W.
Vanderbild and P. Perdue.
Supported by the Intelligence Advanced
Research Projects Activity (IARPA) via Air Force
Research Laboratory (AFRL) contract number
FA8650-11-C-7101. The U.S. Government is
authorized to reproduce and distribute reprints for
Governmental purposes notwithstanding any
copyright annotation thereon. Disclaimer: The views
and conclusions contained herein are those of the
authors and should not be interpreted as necessarily
representing the official policies or endorsements,
either expressed or implied, of IARPA, AFRL, or the
U.S. Government.
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