Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
results in 1.5 to 2.5 microns of movement of the top surface
of the sample. However, our sensitivity analysis
measurements show that the movement of the sample needs
to be limited to within a few tenths of nanometers for the
entire range of ΔT during the overall measurement process.
For the typical ΔT values of between 30 and 50K, this
translates to a movement of a few nanometers per K. The
authors believe that this level of movement control can only
be achieved by an active control system which must contain
nanometer level movement capabilities such as in high-end
piezo stages. The advantage of using an XYZ piezo stage is
that it allows the system to compensate for any movement in
the horizontal plane as well. It turns out that the movement
in the horizontal plane has to be controlled with deep subpixel
resolution (for 100X, the pixel size is 210 nm), which
translates to resolutions less than 100 nm with 10 nm or
better preferred.
In order to achieve the necessary level of thermal and
positioning control, a special module was constructed,
shown as a simplified schematic in Fig. 1. The heating stage
contains a thermoelectric element that heats up and cools
down the DUT; several temperature sensors – thermistors,
for control and overheating protection; a heat sink for
removal of the heat produced by the thermoelectric element;
a highly precise piezoelectric XYZ translation stage with
built-in thermally compensated position measurement;
vacuum lines, etc. Both the cooling and heating cycles were
significantly sped-up by the use of an intelligent PID
(Proportional-Integral-Derivative) control scheme to obtain
the smallest possible heating/cooling cycle times. A
Proportion-Integral scheme was also used to control the 3D
movement of the piezo-stage.
II.
RESULTS
A. Calibration Approaches
As mentioned above, in order to obtain the actual
temperature of the device the change in the reflectivity,
ΔR/R, needs to be divided by the thermoreflectance
coefficient. When only one surface material is involved and
only its temperature map is required this is a trivial algebraic
procedure. However, when investigating complex
microelectronic devices, that is rarely the case and typically
several materials need to be calibrated and factored in for the
final temperature map. To make matters even more
complicated, the thermoreflectance coefficient turns out to
be highly dependent not only on the material type but also on
the wavelength of the probing light (as depicted in Fig. 2)
and event the numerical aperture of the objective lenses,
focus level, light uniformity, and other measurement effects.
The C TR dependence on the wavelength of the light can be
utilized to the users’ advantage by building the system with a
variable wavelength light source and tuning the wavelength
to an optimal wavelength value that will offer the maximum
C TR value for a specific material. To exemplify, the
thermoreflectance coefficient of the polysilicon region of the
device shown in the top part of Fig. 3, which is embedded in
a transparent layer composed of several microns of field
oxide and passivation layers, was measured at various
wavelengths of the illumination light and the obtained data
Fig. 2 Thermoreflectance coefficient of oxide covered polysilicon
and gold versus the wavelength of probing light
are plotted in Fig. 2. The thermoreflectance coefficient of
Au is also plotted in Fig. 2. Since the value of the
thermoreflectance coefficient is close to zero at 500 nm for
both materials, obviously tuning the wavelength to a value in
the vicinity of this value will produce either no results at all
or extremely poor results. However, if one tunes the light
wavelength to a value of 485 nm for gold or either 605 nm or
640 nm for polysilicon, the C TR value becomes optimal and
thus the thermal map would have the highest accuracy.
In obtaining the final temperature map, i.e., while
combining the change in the reflectivity, ΔR/R, with the
thermoreflectance coefficient, C TR , the user has three
calibration approaches:
i) Whole-area calibration: If only one material is
considered, the ΔT map is obtained by dividing the ΔR/R
value of each pixel with the (fixed) C TR value of the
measured material.
ii) Zone-by-zone calibration: When multiple materials
are considered, a 2D map of the zones of different materials
can be built manually with the thermoreflectance coefficient
being determined separately for each zone. The temperature
map is obtained by combining the ΔR/R map with the final
C TR map.
iii) Pixel-by-pixel calibration: In the case of complex
devices using either one of the previous approaches could be
cumbersome and thus the pixel-by-pixel approach might be
more feasible. In this approach the both the calibration and
the change in the reflectivity data is obtained for each pixel
and the temperature map is obtained by combining the CTR
value with the ΔR/R value of the corresponding pixel on the
ΔR/R map.
The pixel-by-pixel calibration method is clearly preferred
to the other mentioned methods due to its automated nature
and being applicable to deal with any level of device
complexity. However there are instances for which there is
no single wavelength that will offer good C TR values for all
the measured materials and thus the zone-by-zone approach
©EDA Publishing/THERMINIC 2009 132
ISBN: 978-2-35500-010-2