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Fig. 5 Computed absolute temperature contours, T (°C), at the
surface level of the polysilicon resistor for P = 250 mW
activation power. Maximum computed temperature is 69.8°C
(the reference temperature was 20 °C and the shown area is a
54 by 54 μm square portion of the domain)
C. Validation of temperature results: numerical simulation
results
The experimental results obtained here were validated
using the authors’ ultra-fast self-adaptive numerical
simulation engine [8,9] A model was built based on the
device design data from Austria Microsystems and computed
using our solver with the results presented in Fig. 5, for an
activation power of 250 mW. The power was considered to
be uniform and covers the entire area of the polysilicon
resistor. The temperature presented in Fig. 5 is the absolute
temperature in °C; thus, to obtain the temperature change,
the reference temperature of 20°C should be subtracted from
this value. The computed maximum temperature difference
of 69.8°C agrees well, within 5%, with the experimentally
measured temperature plotted in Fig. 4.
D. Validation of temperature results: built-in diode results
In addition to comparing the experimental results to the
results of the numerical simulation, the results are also
Fig. 6 Temperature measured using the built-in diode versus
applied electrical power to the polysilicon resistor.
7-9 October 2009, Leuven, Belgium
checked against temperature readings obtained from an
embedded temperature sensor. A diode was used to measure
the temperature which is located in the center region of the
C-shaped microresistor.
First, the diode was calibrated using our thermoelectric
element based stage by measuring the change in the voltage
value with the change in the base temperature while the
current was kept constant at 1 μA. It was found that the
voltage decreases linearly with the temperature at a rate of
2.55 mV/°C for the range of temperature considered here.
After calibrating the diode, the polysilicon resistor was
activated at various power levels and the voltage of the diode
was recorded while again keeping the diode current constant
at 1 μA. The obtained data is plotted in Fig. 6 and shows
that the diode voltage is linearly proportional to the applied
microresistor power. For the 250 mW of applied power, the
diode reads a temperature gradient of 23.5°C which grossly
underestimates the computed 69.8°C maximum temperature
obtained for the polysilicon resistor. Nevertheless, by
investigating both the experimental results shown in Fig. 4
and the numerical results presented in Fig. 5 one might find
out that indeed the temperature at the center location of the
poly resistor is expected to be much lower than the
maximum temperature observed on the surface of the
resistor itself. Therefore, we must conclude that the
embedded diode sensor may not be as useful as initially
thought at determining the average temperature of the poly
resistor.
III. CONCLUSIONS
This work presented for the first time a successful method
for calibrating pixel-by-pixel and in-situ a CCD camerabased
thermoreflectance thermography system with
nanometer spatial resolution. This article described the
measurement system and methodology used and presents
relevant results. Using the thermoreflectance method to
determine the temperature map of an activated device
requires two steps: first, the thermal image is acquired using
a CCD camera and, second, the obtained thermal image is
converted to the actual temperature map by multiplying each
pixel of the thermal image with the corresponding
thermoreflectance coefficient. The critical aspect is that even
if the thermoreflectance coefficient is known, or measured
independently for each material present on the surface of the
sample, converting the thermal image to the temperature
map requires building manually the exact corresponding map
of the thermoreflectance coefficient, which in the case of
complex microelectronic devices might be difficult. In
addition, it turns out that the thermoreflectance coefficient is
highly dependent on the wavelength of the probing light,
numerical aperture, focus level, light uniformity, and other
measurement effects. To mitigate these issues, one must
obtain the thermoreflectance coefficient map of the same
measurement area of interest, while ensuring that the same
objective lens is used, the same focus level is maintained,
and the same exact position is kept for frame acquisition at
both the low and high temperature settings. To satisfy all of
these requirements, the position of the sample must be
adjusted in 3D space with nanometer spatial resolution.
©EDA Publishing/THERMINIC 2009 134
ISBN: 978-2-35500-010-2