Nice, Côte d’Azur, France, 27-29 September 2006
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
A COUPLED THERMOREFLECTANCE THERMOGRAPHY EXPERIMENTAL SYSTEM
AND ULTRA-FAST ADAPTIVE COMPUTATIONAL ENGINE
FOR THE COMPLETE THERMAL CHARACTERIZATION
OF THREE-DIMENSIONAL ELECTRONIC DEVICES: VALIDATION
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
Nanoscale Electro-Thermal Sciences Laboratory
Department of Mechanical Engineering
Southern Methodist University
Dallas, TX 75275-0337, U.S.A
ABSTRACT
This work builds on the previous introduction [1] of a
coupled experimental-computational system devised to
fully characterize the thermal behavior of complex 3D
submicron electronic devices. The new system replaces
the laser-based surface temperature scanning approach
with a CCD camera-based approach. As before, the
thermo-reflectance thermography system is used to non-
invasively measure with submicron resolution the 2D
surface temperature field of an activated device. The
measured temperature field is then used as input for an
ultra-fast inverse computational solution to fully
characterize the thermal behavior of the complex three-
dimensional device. For the purposes of this
investigation, basic micro-heater devices were built,
activated, and measured. In order to quantitatively
validate the coupled experimental-computational system,
the system was used to extract geometric features of a
known device, thus assessing the system’s ability to
combine measured experimental results and computations
to fully characterize complex 3D electronic devices.
1. INTRODUCTION
Faster and more powerful devices mean hotter devices,
which can lead to a decrease in performance and
reliability. Thus, understanding and determining the
thermal behavior of modern electronics has become a key
issue in their design. As a result, there is a critical demand
for methods that can be used to determine the temperature
of features at the submicron level, particularly when most
important features are physically inaccessible [2-5].
Computational approaches can provide insight into the
internal thermal behavior of such complex devices, but
can be limited by the inherent necessity of modeling the
heat sources, which in the case of self-heating
microelectronic devices, are the result of electrical fields
whose exact shapes and locations are difficult to specify
with reasonable certainty. Moreover, such devices can
actually experience irreversible changes in thermo-
physical properties and/or geometries that cannot be
otherwise predicted from theory or monitored.
Experimental approaches can also be helpful in
determining thermal behavior, but require either physical
access or a visual path to the region of interest. Contact
methods, for example, present the difficulties of having to
access features of interest with an external probe, or in
the case of embedded features, fabricate a measuring
probe into the device, and then having to isolate and
exclude the influence of the probe itself. Non-contact
methods, on the other hand, can provide surface
temperature profiles, but in and of themselves cannot
impart information on internal behavior. In other words,
these methods provide a two-dimensional perspective on
what otherwise is, in the case of stacked complex devices,
an intricate three-dimensional thermal behavior.
We show herein that by combining an experimental
method capable of mapping the surface temperature of a
complex device with high spatial and temporal accuracy
together with a computational engine capable of rapidly
and accurately resolving the geometric and material
complexities of a full three-dimensional microelectronic
device, it becomes possible to use the independent
information from the experimental measurements to
mitigate the lack of knowledge in the source model
parameters, which directly affect the usefulness of the
computational results. This article builds on the previous
introduction by the authors of a proof of concept of a
coupled computational-experimental approach that uses a
measured two-dimensional surface temperature mapping
to help obtain a fully three-dimensional thermal
characterization of an active micro-device [1].
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
A Coupled Thermoreflectance Thermography System and Ultra-Fast Computational Engine...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
2. METHODOLOGY
The overall approach combines computational and
experimental methods previously developed by the
authors. The transient two-dimensional surface
temperature is measured by the use of the
thermoreflectance thermography system [6], while the
three-dimensional thermal behavior of multi-layered
integrated circuits (with embedded features) is inferred by
solving the inverse heat transfer problem with the self-
adaptive ultra-fast numerical technique [7, 8]. To
minimize the number of uncertainty sources that the
inverse method must deal with, the thermo-physical
properties of the various thin layers can be measured
independently with the Transient Thermo-Reflectance
technique [9, 10].
2.1. Thermo-Reflectance Thermography System
The experimental temperature mapping system is
based on the thermoreflectance (TR) method, where the
change in the surface temperature is measured by
detecting the change in the reflectivity of the sample. The
measurement methodology requires two steps. First, the
thermoreflectance coefficient must be determined for
each of the surface materials in the measurement area.
Second, the changes in the surface reflectivity as a
function of changes in temperature are measured over the
area of interest, with submicron spatial resolution. The
resulting reflectivity data is combined to obtain a
temperature field over that area of interest. The
thermoreflectance coefficient, CTR, varies as a function of
the material under test, material layering, and the
wavelength of the probing light [11]. Thus, in order to
maximize the signal to noise ratio, it is important to use a
light source whose wavelength produces the maximum
value of CTR for the exposed material layer.
A schematic of the TR thermography (TRTG) system
is shown in Fig. 1. The probing light reflects from the
heated surface back along the optical path to the sensitive
element of a CCD camera (512×512 pixels). The intensity
of the reflected light depends on the reflectivity
(temperature) of the sample’s surface. The frames
containing the change in surface reflectivity induced by
the temperature variations of the DUT are acquired and
scaled according to the calibrated data. The details of the
TRTG method are presented in a companion article.
The calibration approach consists of determining the
relationship between the changes in reflectance and
surface temperature. The change in reflectance is
measured by a differential scheme involving two identical
PDs in order to minimize the influence of fluctuations in
the energy output of the probing laser. The sample
temperature is controlled by a thermoelectric (TE)
element and measured with a thermocouple. The
calibration must be performed for each of the materials on
the surface of each device where a temperature mapping
is carried out.
2.2. Computational Engine
The numerical engine is capable of simulating the
transient thermal behavior of active multi-layered devices
whose dimensions vary over several orders of magnitude
and where the thermophysical properties of the materials
used may not be isotropic. The thermal modeling engine
is used for solving the required heat transfer problem of
the corresponding physical device. The measured surface
temperature field (outlined white square in Fig. 2) is then
used as input signature for an optimization scheme that
varies control parameters (e.g., source power, length)
until the RMS error between the computed solution and
the input signature is minimized.
The novel approach begins by solving the
corresponding steady-state problem by the use of a grid
nesting technique. Since the physical dimensions of the
various materials used in modeling high performance
electronic devices vary greatly, a uniform mesh that
resolves all of the details in three dimensions results in a
prohibitively large computational grid. A common
method for dealing with dimensional variation is to skew
the mesh and concentrate more grid points in areas where
higher resolutions are needed. The shortcoming of using a
biased-mesh approach to resolve the geometry is that the
problem geometry, and not the temperature gradients, will
end up dictating the meshing. The meshing strategy used
in the development of the numerical engine [7] was set on
ensuring that it is (i) automatic and adaptive, (ii)
independent of user expertise, and (iii) independent of
materials (including air), geometry features, embedded
Fig. 1 CCD-based TRTG scanning system
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
A Coupled Thermoreflectance Thermography System and Ultra-Fast Computational Engine...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
vias, and heat source locations. The approach makes it
possible to start with the full 3D geometry of a real device
in all of its complexity, and then uses a physics-based
automatic error predictor to focus the entire available
computational power on only those regions that require
further refinement in order to achieve the level of
acceptable error prescribed by the analyst [8]. The power
of the method is that it uses effective thermal properties
that are consistent with the local grid spacing at the
particular grid level in use. As a result, dealing with air,
embedded vias, and ultra-thin multi-layered structures
requires no special treatment.
2.3. Sample Characterization: Geometry and Thermal
Properties
The fidelity of a computational solution depends
directly on the accuracy of the material properties and
geometric characteristics of the features making up the
device of interest. Since it has been shown [12] that the
thermal properties of thin-films vary from those of bulk
materials, it is necessary for the numerical simulation to
use the real values of the thermal conductivity for all of
the materials making up the system under study. The
previously described TTR measurement system [9] can be
used to determine any unknown properties of thin-film
materials and their interface resistances.
In order to carefully characterize the geometry of a
device of interest, an ellipsometer was used to measure
the thicknesses of transparent layers as well as to confirm
the optical properties of surface metals. In addition, a
profiler was used to measure the thicknesses of various
opaque and transparent layers making up the device.
To prove the concept and validate the described
method, we constructed basic reference aluminum micro-
resistor devices buried in a layer of silicon dioxide, and
investigated the accuracy with which the coupled
experimental-computational approach is capable of
determining key geometric features of a known device. In
the micro-resistor device, shown schematically in Fig. 2,
an aluminum (Al) strip heater is sandwiched between top
and bottom oxide layers in the vertical direction, and
between two Al activation pads in the horizontal
direction. When activated at known electrical power
levels, the known heat source will generate a three-
dimensional temperature field throughout the device.
Since the approach calls for measuring the temperature
signature on the surface of the device, a gold (Au) layer
was deposited over the anticipated area of interest, which
includes the heat source and large surrounding regions.
Gold was chosen since when used in conjunction with an
LED light source at 485 nm, it will maximize the CTR
value in the TRTG technique.
The simple construction of this micro-resistor device
makes it possible to specify and measure all essential heat
transfer problem parameters. Specifically, (i) the
geometry of the different layers can be controlled in the
fabrication process and later measured for confirmation;
(ii) the oxide layers and Al strip provide a Joule heat
source with known uniform power distribution; and (iii)
the large pads make it possible to use a four-wire scheme
to simultaneously activate the strip heater and measure its
electrical power. For the purposes of this article, only a
single device is reported on, which has a width of 14 µm
and a length of 200 µm. All other pertinent geometric
parameters are provided in Fig. 2.
3. RESULTS AND DISCUSSION
By using the experimental system and combining it with
the numerical approach presented above it becomes
possible to solve the inverse conduction problem
associated with a complex, multi-layered, deep submicron
electronic device in order to infer the thermal behavior of
the embedded features that cannot be otherwise accessed.
The inverse solution is obtained by varying key
parameters that define the heat transfer problem under
consideration. For the test micro-resistor in this work,
these parameters include the size and location of the
heater strip, its power and distribution, the thicknesses of
the top and bottom layers, and their thermal properties.
Obviously, a solution that comprehends all of these
variables would be impractical. Furthermore, many of
these parameters can be either directly measured (e.g.,
thermal properties, applied power, thicknesses of layers)
and/or have smaller influences on the final temperature
Au Test Pad, 2000Ĺ
Al Heater and Pads
1000 Ĺ
Top SiO2 Layer, 3200 Ĺ
Bottom SiO2 Layer
1360 Ĺ
Si Substrate
Au Test Pad
0.8x0.8 mm
Al Heater, 14x200 µ m
Al Heater Pad
500 µ m wide
Probing Hole
400x300 µ m
600 µ m
Fig. 2 Geometry of test micro-resistor
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
A Coupled Thermoreflectance Thermography System and Ultra-Fast Computational Engine...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
distribution in the device (e.g., layers of SiO2 and Au
above the heater).
Since heat flows primarily toward the substrate, the
thickness of the bottom oxide layer is expected to
strongly affect the temperature distribution because of the
resistance that this layer presents. Therefore this
parameter was chosen for its sensitivity on the final
result. A second parameter was chosen to be the length of
the heat source because (i) it cannot be directly measured
and (ii) it is expected to be longer than the length of the
heater strip itself because of the end effects at the junction
between the aluminum heater strip and its activation pads.
In fact, one would expect that the end effects would
extend beyond the strip by a distance that scales with the
heater’s width.
Figure 3 compares the experimental data along the
mid-plane of the heater strip to the corresponding
numerically computed temperature distributions for
different values of the bottom oxide thickness and for a
fixed heat source length of 200µm. As expected, thicker
layers of bottom oxide result in higher strip temperatures.
It appears that the numerical temperature distribution for
the thickness of 1,500Ĺ fits nicely the measured data in
the center of the heater, X? [400,600], but misses inside
the pad areas. The discrepancy is due to the end effect
previously mentioned.
To examine the end effects, the bottom oxide
thickness was held fixed at 2000Ĺ, and the heat source
length was varied as depicted by the results in Fig. 4.
Indeed, extending the heat source length beyond the ends
of the strip heater pulls the temperature curves outwardly
toward the experimental data at the lower temperatures.
However, the agreement between the numerical and
experimental distributions becomes worse toward the
center of the domain. It should be pointed out that simply
extending the rectangular heat source, as done here, only
captures the spherical nature of the heat distribution at the
pad-heater junction to a first order approximation. In
order to more precisely simulate the end effects, one
would have to introduce a more sophisticated heat power
distribution model in this region.
Nevertheless, taken together, the results of Figs. 3
and 4 point clearly to the importance of both physical
parameters and hence the need to optimize over both of
them simultaneously. The optimization method used in
this work is a variant of the “steepest descent” method
[13]. The search begins with a numerical solution of the
heat transfer problem at nominal values of the two
parameters being considered, i.e., bottom oxide thickness
(h) and heat source length (L). This numerical solution is
compared with the measured signature field (outlined
white square in Fig. 2) on the gold pad at every common
location to compute an RMS error. Then, additional trial
solutions and associated errors are obtained at
neighboring pair values of h and L in the two-
dimensional parameter space. Evaluation of the errors at
the nominal and eight neighboring pairs provides the
direction for modifying h and L in order to decrease the
error. This process continues until the changes in both h
and L are acceptably small.
For the specific device under consideration, Fig. 5
shows the path taken in the (h, L) parameter space to
converge onto the final values of h and L which yield a
numerical solution that matches the measured surface
signature to within the minimum RMS error. Of particular
interest here is that the process of reaching the final result
required 57 solutions of the full three-dimensional heat
transfer problem, each of which was converged to less
than 1% numerical error at the specified h and L values. It
is obvious that such an approach would be impractical
X(µm)
?T(°C)
400 450 500 550 600
2
4
6
8
10
12
14
Measured Data
h=1,000Ĺ
h=1,500Ĺ
h=2,000Ĺ
Fig. 3 Influence of the bottom oxide thickness
X(µm)
?T(°C)
400 450 500 550 600
2
4
6
8
10
12
14
Measured Data
L = 200 µm
L = 220 µm
L = 240 µm
Fig. 4 Influence of the heat source length
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
A Coupled Thermoreflectance Thermography System and Ultra-Fast Computational Engine...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
with traditional numerical solvers. The self-adaptive,
ultra-fast computational engine used here required
approximately 20 minutes to solve this particular problem
on a 3.4 GHz Pentium(R) 4 desktop PC.
To compare the experimental and numerical surface
temperature fields, a surface slice is extracted from the
full 3D solution that corresponds to the size, location, and
resolution of the experimental area. Figure 6(a) shows the
surface temperature slice at stage 9, which represents the
“optimal” solution that is closest to the experimental
signature shown in Fig. 6(b). While the agreement is very
favorable, it is clear that the end effects give the
experimental contours a more “rectangular” shape on the
heater edges. As discussed above, a more sophisticated
model of the power distribution at the pad-heater junction
would be required to further improve the agreement,
which is beyond the scope of this validation article.
The ultimate benefit of the coupled experimental-
numerical system is that it takes an inherently 2D
experimental approach and provides a full 3D thermal
characterization of the complete device. The
optimization-based coupling ensures that the 3D solution
is consistent with the 2D experimental signature within
the chosen heat transfer model as defined by the
combination of known and unknown (i.e., optimizable)
parameters. Figure 7 provides an example of the optimal
3D numerical solution. For clarity, only two slices are
shown and the spatial domain is restricted to the region
surrounding the heater, even though the computational
domain is 1000×500×1000 µm. The horizontal slice is on
the surface of the device and the vertical slice cuts across
the mid-plane of the heater.
1
9
3
2
4 5
6 7
8
Bottom Oxide Thickness (Ĺ)
HeaterLength(µm)
1400
200
205
210
215
220
Fig. 5 Convergence of optimization path toward
final solution at h = 1,413 Ĺ and L = 212.5 µm
Fig. 6 Contours of surface temperature: (a) optimal
numerical solution and (b) experimental signature
Fig. 7 Contours of 3D temperature field from optimal numerical solution (stage 9 in Fig. 5).
The solid white square delineates the 272 µm square measurement surface area, also shown on Fig. 1.
(a)
(b)
Peter E. Raad, Pavel L. Komarov, and Mihai G. Burzo
A Coupled Thermoreflectance Thermography System and Ultra-Fast Computational Engine...
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
4. CONCLUSIONS
This work builds on the previous introduction [1] of
a coupled experimental-computational system that makes
it possible to extend an experimentally-obtained 2D
surface field to a full 3D characterization of the thermal
behavior of complex submicron electronic devices. The
new system improves on the previous one by replacing
the laser-based, point-by-point, surface temperature
scanning approach with a CCD camera-based approach.
The aim of this work was to validate the coupled system
by applying it to a simple test micro-resistor device with
known geometric, material, and thermal characteristics.
The investigation focused on the two parameters that
most influence the heat transfer solution within the
device, which are the thickness of the bottom oxide (h)
and the length of the heat source (L). The obtained
optimal value of h was found to be within 4% of the
physical thickness as measured with an ellipsometer
during the fabrication process. The optimal heat source
length was found to extend into the side pads by a
distance that is approximately equal to half the heater’s
width, which is qualitatively consistent with the physics
of Joule heating in the sudden expansion areas connecting
the strip and the pads. The results herein have provided
the desired validation for the coupled experimental-
computational system as well as demonstrating the power
of the method in providing full 3D temperature field that
agrees very well with the measured 2D surface
temperature signature.
For existing devices, the highly resolved and accurate
3D temperature field would provide the ability to detect
hot spots, diagnose performance, and assess reliability. In
the design and manufacturing of new devices, this new
tool has the potential to provide a rapid approach for
analyzing the thermal behavior of complex stacked
structures, to identify regions of excessive heat densities,
and ultimately to contribute to improved thermal designs,
better device reliability, and shorter design cycle time.
5. ACKNOWLEDGEMENTS
We wish to thank Mr. Jay Kirk of the EE Department at
SMU for his help in fabricating the devices for this work.
6. REFERENCES
[1] P.E. Raad, P.L. Komarov, and M.G. Burzo, “Coupling
Surface Temperature Scanning and Ultra-Fast Adaptive
Computing to Thermally Fully Characterize Complex Three-
Dimensional Electronic Devices,” 22nd SEMITHERM, Dallas,
TX, March 2006.
[2] K.E. Goodson and Y.S. Ju, “Short-time-scale Thermal
Mapping of Microdevices using a Scanning Thermoreflectance
Technique,” ASME J. Heat Transfer, Vol. 120, pp. 306-313,
1998.
[3] S. Grauby, S. Hole, and D. Fournier, “High Resolution
Photothermal Imaging of High Frequency Using Visible Charge
Couple Device Camera Associated with Multichannel Lock-in
Scheme,” Review of Scientific Instruments, pp. 3603-3608,
1999.
[4] G. Tessier, S. Pavageau, B. Charlot, C. Filloy, D. Fournier,
B. Cretin, S. Dilhaire, S. Gomez, N. Trannoy, P. Vairac, and S.
Volz, “Quantitative Thermoreflectance Imaging: Calibration
Method and Validation on a Dedicated Integrated Circuit,” 11th
THERMINIC, Belgirate, Italy, Sep. 2005.
[5] S. Grauby, A. Salhi, L.-D. Patino Lopez, S. Dilhaire, B.
Charlot, W. Claeys, B. Cretin, S. Gomčs, G. Tessier, N.
Trannoy, P. Vairac, and S. Volz, “Qualitative Temperature
Variation Imaging by Thermoreflectance and SThM
Techniques,” 11th THERMINIC, Belgirate, Italy, Sep. 2005.
[6] P.L. Komarov, M.G. Burzo, G. Kaytaz, and P.E. Raad,
“Thermal Characterization of Pulse-Activated Microelectronic
Devices by Thermoreflectance-Based Surface Temperature
Scanning,” InterPACK, San Francisco, CA, July 2005.
[7] P.E. Raad, J.S. Wilson and D.C. Price, “System and Method
for Predicting the Behavior of a Component,” US Patent No.
6,064,810, issued May 16, 2000.
[8] J.S. Wilson and P.E. Raad, “A Transient Self-Adaptive
Technique for Modeling Thermal Problems with Large
Variations in Physical Scales,” International J. of Heat and
Mass Transfer, Vol. 47, pp. 3707-3720, 2004.
[9] M.G. Burzo, P.L. Komarov, and P.E. Raad, “A Study of the
Effect of Surface Metallization on Thermal Conductivity
Measurements by the Transient Thermo-Reflectance Method,”
ASME J. of Heat Transfer, Vol. 124, pp. 1009-1018, 2002.
[10] P.L. Komarov and P.E. Raad, “Performance Analysis of the
Transient Thermo-Reflectance Method for Measuring the
Thermal Conductivity of Single Layer Materials,” International
J. of Heat and Mass Transfer, Vol. 47, pp. 3233-3244, 2004.
[11] K. Ujihara, “Reflectivity of Metals at high Temperatures,”
J. of Applied Physics, Vol. 43, No. 5, pp. 2376-2383, 1972.
[12] M.G. Burzo, P.L. Komarov, and P.E. Raad, “Thermal
Transport Properties of Gold-Covered Thin-Film Silicon
Dioxide”, IEEE Transactions on Components and Packaging
Technologies, Vol. 26(1), pp. 80-88, 2003.
[13] Snyman, J.A., Practical Mathematical Optimization,
Springer, NY, 2005.