Characterizing thetemperature-induced
evolution of the shape andtexture of a silicon wafer
In this case study, Linkam and Sensofar Metrology demonstrate theircollaboration in producing an experimental setup for temperature-controlled
optical profilometry experiments. This has historically been a difficult procedure
due to imaging issues caused by spherical aberrations. Using Linkam’s precision
temperature control chamber with Sensofar’s Linnik objective lens eliminates
these problems and allows accurate measurement of 3D topographic profilesof nanoscale materials. Here, we observe the changes in topography of siliconwafers as they evolve with temperature from 20°C up to 380°C.
Rapid Thermal Processing (RTP) is an important step in the manufacturing
process of silicon wafers, in which the wafer is rapidly heated to high temperatures
for a short period of time, then slowly cooled in a controlled manner, in orderto impart the desired semiconducting properties to the wafer. However, RTP,
causes thermal stress which leads to other problems in photolithography thatmay affect the performance of the device, such as breakage due to thermalshock or dislocation of the molecular lattice. Understanding the behavior ofa wafer under these conditions can help optimize the process, improving
semiconductor properties and wafer durability.
CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

This work was carried out by Robert
Gurney from Linkam Scientific
Instruments Ltd. and David
Páez from Sensofar Metrology.
Linkam makes temperatureand environmental control
instruments to help youto characterize materials
from polymers to biologicaltissue, and from metals tonanocomposites.

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A key method of evaluating the effects of temperature change duringwafer manufacturing is to measure the surface roughness of the wafer asa function of temperature. To do this, the surface roughness is observed byan interferometry technique in conjunction with use a thermal chamber,allowing temperature to be raised precisely to values similar to those during
the manufacturing process while observing the sample through microscopy.

Figure 1. Patterned silicon wafer

There are several factors which introduce some complexity in obtaining theseinterferometric measurements. Firstly, in order to visualize the sample andobtain the data while accurately controlling the temperature in the chamber,
it is necessary to make observations through the chamber’s optical window.
This window is 0.5mm in thickness, but in some cases it can be as much as
1mm, depending on the degree of thermal insulation required. This window,
being of a different refractive index to air, would introduce optical aberrations
and misalignments that, when analysing silicon wafers, should be corrected
in order to obtain reliable data. Furthermore, when the temperature insidechamber is increased, heat is emitted to the exterior through the observation
window, and this is not ideal for optical microscopy. In the air close to thatwindow, temperature can reach 60 degrees Celsius, which can lead to
deformation of the objective lens, introducing aberrations.
In order to address the experimental issues of interferometry at varying
temperatures, a Linnik interferometer can be used. The Linnik interferometer
introduces the use of measurement optics within the reference arm of a classic
interferometer. This allows for compensation and correction of the effect ofthe optical window such as chromatic dispersion and optical aberrations,enabling work with brightfield objectives that have a greater working distancethan traditional interferometric objectives.

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CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

■ Experimental details
In this work, we study the effect of the RTP process on the silicon wafers whileaccounting for optical aberrations brought about by temperature changes.
Two different samples were used, corresponding to different chip designs
from silicon wafers. Sample A was 2.8mm x 1mm in size, whereas Sample B
was 3.0mm by 2.35mm. Silicon wafers have typical surface roughness values
on the sub-micron scale , so the ideal optical technology for this application isCoherence Scanning Interferometry (CSI, ISO 25178, part 604). CSI offers only
1 nm of system noise, regardless of the magnification of the lens being used.
For the design and construction of the Linnik objective, two Nikon 10x EPIobjectives (Nikon, MUE12100) with 17.5 mm working distance were used. Thesame configuration is available with 10xSLWD objectives (Nikon, MUE31100),providing a 37 mm working distance. This makes the thermal emissions fromthe camera almost imperceptible to the lens and will not affect or damage themeasurement quality. The Linnik objective was mounted on the 3D opticalprofilometer (Sensofar, S neox) , which combines 4 optical technologies in thesame sensor head: Confocal, CSI, PSI and focus variation. These techniques arecovered in ISO25178.
The temperature is controlled using a Linkam LTS420 chamber and the T96
temperature controller, which allows the temperature to be ramped andcontrolled between -195° and 420°C to a precision of 0.01°C, while the sample
roughness is observed through the chamber window. The chamber also allows
control of the pressure and humidity, but it this has not been investigated inthis study.

Ability tocompensate opticalaberrations

Beam
splitter

Objective#1

Objective#2

OpticalWindow

ReferencemirrorLarge working
distance

SampleFigure 2. Experimental setup of Linkam LTS420 and Sensofar Linnik configuration).

Linkam Temperature
Control Stage

Schematic of the Linnik Optical Configuration

The wafer sample was placed in the Linkam chamber under the S neox
optical profiler with the Linnik configuration. The acquisition routine consistedof ramping the temperature from 30°C to 380°C in 50°C steps, taking 8
topographic measurements of the sample at each step. This procedure wasrepeated for three samples.
CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

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Figure 3. Time-temperature graph showing the temperature steps at which opticalmeasurements were taken.

Using SensoMAP software, the results were visualized an analyzed by creatinga template and applying it to all samples. The template allows the extractionof 3 profiles in each topography (horizontal, diagonal and vertical) andrepresentation in the same plot, and furthermore builds a sequence of thetopographies to export it as a video and represent it in a 4D plot.

■ Results
Two topographic images of the same sample were imaged using the above
methodology and are shown in Figure 5 as two-dimensional height maps.
The three solid lines represent the three different profiles (horizontal, verticaland diagonal) extracted for each topography. The profiles in each direction
are shown in Figure 6, where we can see the evolution for the different
temperatures at which the sample was taken. The images show that when
heating the sample, its topography changes.

Figure 4. Two-dimensional height maps showing the topography of sample A at (a)30ºC and (b) 80ºC. The black lines indicate the three directions at which profiles weretaken for further studies.

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CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

Figure 5. (a) Horizontal, (b) diagonal, and (c) vertical profiles extracted from themeasurements of the sample A at eight different temperatures.

The data can be plotted in 3D topographic image as shown in Figure 7. Bystacking the 3D images as a function of temperature, creating a “4D plot”,
showing the topographical changes at different temperatures using the sameheight color scale, showing how the samples bend as temperature changes. It
is clear that the higher the temperature, the greater the bending experienced
by the samples.

CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

5

Figure 6. Stacked 4D view of the topographies extracted from (a) sample A and (b)sample B for visual comparison of the experimented bow change when samples gofrom 30 ºC to 380ºC.

To quantify the bow of the samples, two different parameters were used. The
first is Sz, which is the surface roughness parameter for the maximum heightof a surface according to ISO 25178. The second is Wz, corresponding to thecounterpart of Sz in profile analysis (ISO 4287). Both Sz and Wz were obtainedafter applying a S-filter to the surface (or profile) with a 0.8mm cut-off. In thisway, only the longer spatial wavelengths remain in the surface, getting rid ofroughness and only leaving waviness for bow analysis.
The resulting parameters for samples A and B are depicted in Figure 9. For
sample A, an almost-linear relationship is observed between bow andtemperature up to 180ºC, that stabilizes from 180ºC to 380ºC. On the other
hand, sample B didn’t show any remarkable bow change until it surpassed
230ºC.

Figure 7. Bow evolution in (a) sample A and (b) sample B as a function of temperature.

Waviness parameters Wz were extracted from the horizontal, diagonal and verticalprofiles in Figure 5. Roughness parameter Sz was computed from the surface after
applying an S-filter of 0.8 mm.

6CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER

Figure 8. (a),(b) Filtered roughness topographies of Sample A (above) and Sample B(below) at 30 ºC and 380ºC respectively. S-filter 2.5 μm, L-filter 0.8 mm. (c),(d) Heightand hybrid roughness parameters of topographies (a) and (b) respectively.

■ Conclusion
The feasibility of the proposed configuration has been proven to carry out
successful roughness and waviness measurements at different temperatures.
Two different behaviours of the surface topography were observed dependingon the chip design. Sample A showed an early bending behaviour when
heating up the sample, whereas sample B showed the bending in a later stage.
S neox 3D optical profiler with a Linnik objective has been shown to be theperfect complement for Linkam’s LTS420 chamber to perform such experimental
measurements. Moreover, different brightfield objectives are compatible
with the Linnik configuration, offering working distances up to 37mm andmagnifications up to 100x for applications that require high lateral resolution.

Figure 9. (left) The Linkam LTS420 – Sensofar Linnik system in use in the lab, and (right) and aclose-up of the sample placed in Linkam’s LTS420 chamber before starting the measurements
CASE STUDY CHARACTERIZING THE TEMPERATURE-INDUCED EVOLUTION OF THE SHAPE ANDTEXTURE OF A SILICON WAFER7SENSOFAR is a leading-edge technology
company that has the highest quality standards
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