1.1 Temperature Measurements in Microelectronics Industry
Rapid thermal processing has become a widely used technique in silicon processing when
short processing times and very high temperatures are a necessity . Rapid thermal
oxidation and annealing are some of the most common applications of RTP. RTP is a
single wafer process, where wafers are processed individually under radiant heating by a
bank of tungsten halogen lamps. They may undergo heating rates of up to 100 ºC/sec,
and reach a temperature of more than 1000 ºC for very short processing times (~seconds).
The short processing time prevents unwanted diffusion within the silicon wafer, while the
high temperature allows thermally activated process to proceed. During these processes,
temperature uniformity and accuracy on the wafer is a key to ensure a successful process.
It is expected that by the year 2000, temperature uniformity across a wafer must be less
than ? 2 ºC over a 30 mm wafer. Furthermore, the accuracy of temperature must be
better than ? 3 ºC within the target temperature . While uniformity over the wafer is
affected by design factors such as wafer patterning, non-uniform irradiation, and edge
cooling, achieving temperature accuracy depends largely on temperature measurement techniques available.
Currently, temperature measurements in RTP is most commonly done by thermocouples or pyrometers. Thermocouples are highly intrusive; they require good physical contact with the wafer which involves cementing the thermocouple onto the wafer. Even with good contact, however, temperature readings indicated by the wafer may differ by as much as 25 ºC for a wafer at ~1000 ?C due to the contact resistance through the cement . Thermocouple wires often need to be individually cemented onto the wafer, which is a time-intensive procedure, not practical in the industry. Furthermore, delicate wires make handling of wafers especially difficult, and pose a problem in sealing vacuum chambers which are often used during RTP.
A non-intrusive alternative to thermocouples are pyrometers, which use radiation emitted by the hot substrate surface to optically measure temperature. However, since they rely on the emission from a surface, the emissivity of the substrate is an important consideration in temperature determination. For surfaces having thin films and/or patterns, the emissivity is often unknown and results in a large uncertainty in pyrometer readings. Furthermore, emission from heating lamps often leak into the pyrometer either by passing through the wafer at low temperatures where the wafer is transparent or by scattering around the wafer, leading to erroneous measurements .
Currently, alternative methods of temperature measurements are being developed. One area of active research is the thin-film thermocouples , which uses thin film layers, deposited on the wafer, as thermocouple wires. This eliminates the contact issue encountered in traditional thermocouple use; however, the handling of the wafers is still an issue. Temperature sensors based on microelectromechanical systems (MEMS) are under development as well. In one example, bilayered beams, which curve at high temperatures, are monitored optically by a laser and position-sensitive photodetector to yield temperature readings .
MEMS-based devices were designed to address the needs for accurate temperature measurement during RTP [7,8]. The designs, called “T-MEMS,” are thin-film devices
which undergo permanent mechanical change at high temperatures, which can then be correlated to physical models to determine the temperature at which the deformation took place. Two designs are under consideration: the “breaking” structures and “bending” structures. The breaking structures consist of an array of silicon nitride (SiN) x
membranes, suspended over Si substrate. The membranes are designed with a dog-bone shape with a neck in the center. At high temperatures, SiN film is put under x
tension due to the small thermal expansion coefficient of the material with respect to that of silicon. When the stress at the neck exceeds the fracture strength of the film, the membrane breaks. Inspection of the membranes after cool-down to room temperature will reveal the maximum temperature reached during the thermal process. These structures are currently under study at Northeastern University, and will not be discussed further here.
The study presented in the following chapters involve the second design, the “bending T-
and MEMS”. The device consists of an array of bilayered cantilever beams of SiO2
polycrystalline silicon layers, each measuring ~10 ?m in width and between 50 and 100 ?m in length. The beams are designed to be suspended 6 ?m over the Si wafer substrate. The beams, with the SiO layer on bottom, bend down at high temperature due to the 2
smaller thermal expansion coefficient of SiO relative to poly-Si. At some temperature, 2
the beams will come in contact with and will adhere to the substrate. Due to the
geometrical relation between curvature and deflection, longer beams reach this state at a
lower temperature. By observing the beams under an optical microscope after cooling,
the beams become an ex situ temperature sensor that indicates the maximum temperature
reached during processing.
Both T-MEMS designs do not offer the in situ monitoring of temperature. However, they are an inexpensive and non-intrusive alternative to above mentioned temperature
measurement methods more commonly used, with only an optical microscope necessary
to collect information.
1.2 Thermophysical Properties of Thin Films
In order for the T-MEMS to be modeled and calibrated as temperature sensors,
thermophysical properties of film materials must be found. Properties of interest are the
Young’s modulus (E) and thermal expansion coefficient (?) of the layers. The need for material property determination is a result of lack of published data on thin film
properties at high temperatures, and this need is shared by much of the growing MEMS community.
MEMS refer to any small (sub-micron to mm scale) devices fabricated using thin film technology. They typically operate on combination of mechanical, electrical, and/or optical effects. The sizes of the devices range from sub-micron to ~mm, and their applications are numerous, from micro-sensors, chemical analyzers, switches, and miniaturized mechanical components. It has been forecasted that by the year 2000, MEMS-based systems sales will reach 100 billion dollars . Despite this growing interest in MEMS, little is known about the properties of the materials involved, and design and modeling of MEMS often depends on trial-and-error. As device sizes decrease and applications extend do more demanding mechanical operations, there is a need for the determination of properties such as Young’s modulus, Poisson’s ratio, and
the fracture strength of the materials used. MEMS are based on thin films, which often have properties that are dramatically different from those of corresponding bulk material. Much research has gone into the measurement of these properties; however, a “standard”
technique is yet to be established and there is a large scatter in data [10,11]. The scatter is largely due to the difference in the films used in each test; the film property can change as a function of deposition conditions which created the film. However, measured properties vary even for films deposited under same conditions, and testing conditions are believed to be the cause of this disparity .
Young’s modulus of polycrystalline silicon films have been widely studied using various methods, and the values obtained by different researchers are summarized in Table 1.1.
One method is the direct tensile testing of dog-bone type specimen [13-15]. The
specimen are fabricated by microfabrication techniques and are subjected to tensile stress,
and the resulting load versus strain curve results in the determination of E from the slope. The challenge here is to accurately measure the small force and deflection in the micron-
sized specimen, and techniques such as interferometry must be used. The advantage of
this technique is that it can be extended to measure the fracture strength of the specimen
without any modifications. Similarly, E can be determined from the load versus
deflection curve of cantilever beams, subject to load from a stylus [16-18]. This type of
testing can also be extended to fracture strength determination; however, it is also faced
with the same difficulty as tensile testing.
Table 1.1 Survey of existing literature on Young’s modulus
of polycrystalline silicon films
(GPa) Reference Method ESi
†*tensile test with interferometry for strain measurement 120 – 170 
tensile testing of micromachined specimen 172 ? 7  tensile testing with interferometry for strain measurement 170 
*beam deflection by profilometer 173 ? 20 
bulge testing of square and rectangular membrane 162 ? 4 
bulge testing of square and rectangular membrane 160 
lateral resonance structures ~150 [21,22]
comb drive lateral resonance structures ~150 – 155 
‡comb drive lateral resonance structures ~167 – 163 
* Part of a study which tested the same film using different testing methods  † Found to increase with film thickness, from 120 GPa at 1.5 ?m to 170 GPa at 3.5 ?m. ‡ Found to decrease monotonically with temperature, from 167 GPa at room temperature to 163 GPa at
Another well-documented testing technique is the bulge-testing of thin film membranes
[19,20]. In this technique, a large (~mm) membrane of thin film material is fabricated,
typically by depositing the film on Si substrate and etching the substrate away to create a
window. A pressure is applied to one side of the film, which results in the bulging of
membrane to the side with lower pressure. The deflection of the membrane, often
measured by interferometry, is a function of the Young’s modulus. This method is often
used to measure E and the Poisson’s ratio.
One of the most commonly used technique is the measurement of resonance frequency of
specially-designed structures [21-24]. The resonance frequency of the structures are
functions only of structure geometry, density, and the Young’s modulus. This method
allows determination of E that is independent of other mechanical properties; however,
the accurate determination of density and geometry of the specimen are often difficult.
All of above referenced studies were done at room temperature, with the exception of the
for temperatures up to 500 ºC. Most of the work by Kahn, et.al , which studied ESi
techniques mentioned above cannot be used at high temperature due to the delicate and
elaborate equipments involved, resulting in a lack of study done on the temperature-
dependence of film properties. There is a great need of mechanical characterization of
thin films at high temperatures as MEMS applications extend to high-temperature range.
A less studied property, but equally important in the analysis of T-MEMS, is the thermal
?) of thin film materials. Determination of ? is necessary not expansion coefficient (
only for T-MEMS, but for other MEMS applications and the microelectronics industry as
well. Thermal strain at layer interfaces cause high stress, deformation, and possibly
fracture in the structure, and measurement of ? for various thin film materials are a
requirement in preventing high levels of thermal strain. The difficulty in measuring the
property comes from the coupled nature of E and ? in the mechanical behavior of
materials; it is difficult to find the value of one without the knowledge of the other.
Furthermore, thermal expansion coefficient by definition must be studied at high
temperatures, and experimental design and implementation have proven to be very
In addition to performing as temperature sensors, T-MEMS can also be used to determine
the thermal expansion coefficient of thin films at high temperature. The thermally
induced curvature of multilayered structures is a well-understood phenomena for which a
numerical model has been developed by Townsend, et.al . This model will be
presented in Chapter 3. The thicknesses of the T-MEMS layers are such that the
Young’s modulus of the layers have little effect on the overall curvature of the beams.
Consequently, the thermal expansion coefficients of the layers can be studied
independently of E (that is, the error due to assuming published values for E is very
small). Furthermore, since the beams were designed to function as temperature sensors,
they can be used to find the properties at corresponding high temperatures. In order to
find the properties of beams from beam curvature, the beams are heated to a known
temperature and the curvature monitored. The thermal expansion coefficients are then extracted by comparing experimental curvature data to numerical model of the curvature,
? at room temperature. Furthermore, by adjusting the as well as published results of
layer thicknesses so that Young’s modulus play a strong role in the curvature, these structures can be used to determine E as a function of temperature for thin film materials.
In the following chapters, T-MEMS design will be described in more detail, as well as the experimental apparatus developed to monitor the beam curvature at high temperatures. The numerical model is presented for beam curvature, as well as heat transfer models used to characterize the behavior of T-MEMS under radiant heating. This is a concern because the thin films and other microstructures that comprise the T-MEMS result in microscale radiative effects which alter the radiative properties of T-MEMS. In order to function properly as non-intrusive temperature sensors, T-MEMS must be designed so that the effect on surrounding wafer temperature is minimized. Finally, results of material property determination and heat transfer analysis are combined to evaluate the T-MEMS performance as temperature sensors.