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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
1. INTRODUCTION TO MEMS
MEMS is an integration of mechanical elements, sensors, actuators and
electronics on a common silicon substrate through micro fabrication technology. The
acronym MEMS stands for “Microelectromechanical Systems”. These systems have
become increasingly popular in many areas of science and engineering. The field of
MEMS has evolved because of the fact that silicon and other semiconductors can be
used to fabricate not only integrated electronic circuits, but also transducers and other
devices by the use of similar lithographic and other micro fabrication techniques.
These techniques that are used to carry out fabrication of MEMS devices are referred
to as “micro machining”.
Microelectromechanical Systems (MEMS) is an emerging, cutting-edge
technology that relies on the micro fabrication of small-scale mechanical components
like actuators, sensors and mirrors and the integration of these components with on-
board electronic processing.
MEMS promises to revolutionize nearly every product category, thereby,
making the realization of complete system-on-a-chip.
In Microsystems, microelectronic integrated circuits (ICs) can be thought of as
the “brains” of system and MEMS augment this decision-making capability with
“eyes” and “arms”, to allow Microsystems to sense and control the environment. The
sensor gathers the information from the environment through measuring mechanical,
thermal, biological, chemical, optical, and magnetic phenomena. While the electronics
process the information derived from the sensors and through some decision making
capability direct the actuators to response by moving, positioning, regulating,
pumping, and filtering, thereby, controlling the environment for some desired
outcome or purpose.
MEMS is a new manufacturing technology, a new way of making complex
electromechanical systems using batch fabrication techniques similar to the way
integrated circuits are made and making these electromechanical elements along with
electronics. Since MEMS devices are manufactured using batch fabrication
techniques, similar to ICs, unprecedented levels of functionality, reliability, and
sophistication can be placed on a small silicon chip at a relatively low cost. MEMS
technology is enabling new discoveries in science and engineering such as the
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
polymerize chain reaction (PCR) Microsystems for DNA amplification and
identification, the micro machined scanning tunnelling microscopes (STMS), biochips
for detection of hazardous and selection. In the industrial sector, MEMS devices are
emerging as product performance differentiates in numerous markets with a projected
market growth of over 50% per year. As a breakthrough technology, allowing
unparalleled synergy between hitherto unrelated fields of endeavour such as biology
and microelectronics, many new MEMS applications will emerge, expanding beyond
that which is currently identified or known.
MEMS is an extremely diverse technology that potentially could significantly
impact every category of commercial and military products. The nature of MEMS
technology and its diversity of useful applications make it potentially a far more
pervasive technology than even integrated circuits microchips. MEMS blur the
distinction between complex mechanical systems and integrated circuit electronics.
Historically, sensors and actuators are the most costly and unreliable part of a macro
scale sensory-actuator-electronics system. In comparison, MEMS technology allows
these complex electromechanical systems to be manufactured using batch fabrication
techniques allowing the cost and reliability of the sensors and actuators to be put into
parity with that of integrated circuits. Interestingly, even though the performance of
MEMS devices and systems is expected to be superior to macro scale components and
systems, the price is predicted to be much lower.
MEMS is believed to become a hallmark 21st-century manufacturing
technology with numerous and diverse applications having a dramatic impact on
everything from aerospace technology to biotechnology. The MEMS technology now
being forged in R&D labs will generate new technological capabilities for society,
tremendous economic growth through countless commercial opportunities, many of
new products, and thousands of high-paying, high quality jobs. As breakthrough
technology allowing unparalleled synergy between hitherto unrelated fields of
endeavour such as biology and microelectronics, MEMS is forecasted to have a
commercial and defence market growth similar to its parent IC technology. The
United States, Japan as well as many Europe governments have used huge amount of
investment for the research, development and commercial application of MEMS
devices.
MEMS is inevitably the next step in the silicon revolution involving the integrated
circuit and the need and desire of making things smaller, like in mini robots. Thanks
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
to the 3 decades long research and development of higher performance IC chips,
today, the world is equipped with almost all the necessary equipment and procedures
needed in the successful making of MEMS devices. Hence making the research and
development work into the micro domain relatively easier and economical. In fact,
most of the equipment used today in the making of micro-machines is actually
obsolete equipment formally used in making IC chips. Thus MEMS offers a second
chance to extend the life of aging IC fabrication facilities. Since they are made by
exploiting the existing integrated circuit manufacturing infrastructure, MEMS-based
devices can be made cheaply. The usual process involves the successive deposition,
photo patterning, and etching of thin films on silicon. For the case of integrated
circuits, these patterns are formed to create small electrical devices. For the case of
MEMS, these same fabrication sequences are used to create mechanical structures.
The advances in the last few years in the field of micro devices show the
immense potential of MEMS. These devices have the ability to perform a variety of
functions like physical and chemical sensing, actuation, steering light and
communication. Much interest in the MEMS devices centres around its 2 main
characteristic,
(a) The very small size
(b) The promise of very low cost of production which is really the driving
force for MEMS-based devices.
MEMS are constructed to achieve a certain engineering function by micro
fabrication methods. The core element in MEMS generally consists of two principal
components: a sensing or actuating element and a signal transduction unit. Sensors are
used to measure parameters of the environment, while actuators modify this
environment. A sensor is a device that converts one form of energy into another and
provides the user with a usable energy output in response to a specific measurable
input.
Micro sensors are interesting because their small physical size allows them to
be less intrusive. Micro actuators are useful when small and very precise displacement
is needed. Micro sensors are built to sense the existence and the intensity of certain
physical, chemical, or biological quantities, such as pressure, force, humidity, light,
temperature, nuclear radiation, magnetic flux, and chemical composition. Micro
sensors have the advantage of being sensitive and accurate with minimal amount of
required sample substance.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Numerous Micro machined Sensors have been developed so far and this has
been possible mainly because of the fact that silicon possesses remarkable mechanical
properties. These sensors have a wide range of applications: pressure measurement,
optical interconnects in VLSI technology, micro fluidic systems, inertial sensing and
RF devices. A market study by System Planning Corporation (SPC (1999)) indicates
that Pressure Sensors dominate over other MEMS applications.
MEMS have been used to describe micro miniature systems that are
constructed with both integrated circuit (IC) based fabrication techniques and other
mechanical fabrication techniques. In most cases, an emphasis has been placed on
having the techniques compatible with IC techniques to ensure the integration of
related electronics on the same chip. Integration has the advantage of picking up less
electrical noise thereby improving the precision and sensitivity of the sensor. IC
fabrication can be used to fabricate hundreds of devices on the same wafer and batch
processing of wafers is possible. This mass production greatly reduces the cost of
each individual device. Hence MEMS devices are less expensive than their macro-
world counterparts.
This project aims at designing, simulating and analysis of a MEMS Pressure
sensor for general use in industries.
The transducing element in the sensor is a piezoresistive device fabricated on a
silicon diaphragm that senses pressure in terms of change in resistance. The pressure
displaces the diaphragm and this in turn causes a stress in the piezoresistive element
changing the value of its original resistance. If the sensor is calibrated then the stress
can be measured in terms of change in resistance of the piezoresistive elements.
1.1 Applications of MEMS
The greatest impact of MEMS is likely to be in the medical field. A true MEMS
medicine dispenser (sensor, actuator, and control) should allow the treatment of
patients to improve substantially. The ability to monitor and dispense medicine as
required by the patient will improve the treatment of both chronic and acute
conditions. Within the next ten years, MEMS will find applications in a variety of
areas, including.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
a) Remote environmental monitoring and control, which can vary from sampling,
analyzing, and reporting to doing on-site control. The applications could range from
building environmental control to dispensing nutrients to plants,
b) Dispensing known amounts of materials in difficult-to-reach places on an as
needed basis, which could be applicable in robotic systems,
c) Automotive applications will include intelligent vehicle highway systems and
navigation applications,
d) Consumer products will see uses that allow the customer to adapt the product to
individual needs. This will range from the automatic adjustment of a chair contour to
measuring the quality and taste of water, and compensating for the individual
requirements at the point of use.
e) Medical applications include blood pressure measurement, intrauterine and
intracardiac applications.
1.2 Literature review
MEMS based silicon piezoresistive pressure sensors have attained high performance
and are widely used in industry applications. Low pressure sensing for biomedical
applications like intrauterine and intracardiac applications impose hard constraints on
size, accuracy and sensitivity. One of the main sources of error, resulting in reduced
accuracy, is non-linearity. Even though piezoresistive sensors are much more linear
than counterparts based on capacitive detection, a non-negligible non-linearity
appears when high sensitivity and accuracy are simultaneously required.
Michael Kraft [9] in “Mechanical Microsensors” has clearly described about
different shapes of diaphragm. Thimoshenko and Krieger [4], “Theory of plates and
shells” have depicted various types of diaphragm analysis and the assumptions to be
made during diaphragm analysis.
Tai-Ran Hsu [1] in his book “MEMS and MicroSystems, Design and
Manufacture has covered about the piezoresistive and capacitive sensors along with their
advantages and disadvantages. He has also covered the piezoresistive effect in silicon.
Tai-Ran Hsu [1] has also covered design of silicon die for a low pressure sensor
and fabrication techniques used for manufacturing of MEMS devices. He has also
mentioned about doping concentration of semiconductors.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
The optimum shape, plane of diaphragm and the optimum direction of
piezoresistors are analyzed by taking into account the large deflection of diaphragm. The
information on these aspects is clearly mentioned by James J. Allen [11] in Micro
Electro Mechanical System Design.
1.3 Motivation And Problem Definition
As stated earlier Microelectromechanical Systems (MEMS) is an emerging, cutting-
edge technology that relies on the micro fabrication of small-scale mechanical
components like actuators, sensors and mirrors and the integration of these
components with on-board electronic processing. Micro pressure sensors are the most
widely used MEM devices today. Low-pressure sensors are originally intended to find
its application in intrauterine and intracardiac applications where these sensors are
used to measure the blood pressure of the foetus and this motivated us to take up this
problem and analyze the behavior of the low-pressure sensor.
The Dimensions of the diaphragm as in a typical application [10] of low pressure
sensor are: 600 μm long, 600 μm wide and 5 μm thick. The boss at the centre of the
diaphragm is 120 x 120 x 30 μm. The resistors are to be designed so as to get
maximum output. The position of the resistors is to be found by considering the
maximum stressed region in the bossed structure using a MEMS package
INTELLISUITETM.
Taking a = 600 μm, h=5µm, b=60µm, isotopic material properties of silicon (silicon is
anisotropic material but still for diaphragm analysis it is assumed as isotropic), Elastic
modulus as 169 GPa and Poisson’s ratio as 0.23.
2. MICROMACHINING TECHNIQUE
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
In this section, the techniques for the fabrication of Microelectromechanical devices
are briefly introduced. The processes for the fabrication of Microelectromechanical
devices are as follows:
1. Bulk micromachining,
2. Surface micromachining,
3. LIGA (Lithographie, Galvanoformung, Abformung) micromachining.
2.1 Bulk micromachining
Bulk micromachining is a fabrication technique which builds mechanical elements by
starting with a silicon wafer, and then etching away unwanted parts, and being left
with a useful mechanical device. Typically, the wafer is photo patterned, leaving a
protective layer on parts of the wafer that you want to keep. The wafer is submersed
into liquid etchant, like potassium hydroxide, which eats away any exposed silicon.
This is relatively and inexpensive fabrication technology, and is well suited for
applications which do not require much complexity and which are price sensitive.
Today almost all pressure sensors are built with bulk micromachining. Bulk
micro machined pressure sensors offer several advantages over traditional pressure
sensor. They cost less, are highly reliable, manufacturable, and there is very good
repeatability between devices.
All new cars on the market today have several micromachined pressure
sensors, typically used to measure manifold pressure in the engines.
The small size and high reliability of micromachined pressure sensors make
them ideal for a variety of medical applications as well.
2.2 Surface micromachining
While Bulk micromachining creates devices by etching into a wafer, Surface
Micromachining builds devices up from the wafer layer-by-layer.
A typical Surface Micromachining process is a repetitive sequence of depositing thin
films on a wafer, photo patterning the films, and then etching the patterns into the
films. In order to create moving, functioning machines, these layers are alternating
thin films of a structural material (typically silicon) and a sacrificial material
(typically silicon dioxide). The structural material will form the mechanical elements,
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
and the sacrificial material creates the gaps and spaces between the mechanical
elements. At the end of the process, the sacrificial material is removed, and the
structural elements are left free to move and function.
For the case of the structural level being silicon, and the sacrificial material being
silicon dioxide, the final "release" process is performed by placing the wafer in
Hydrofluoric Acid. The Hydrofluoric Acid quickly etches away the silicon dioxide,
while leaving the silicon undisturbed.
The wafers are typically then sawn into individual chips, and the chips packaged in an
appropriate manner for the given application.
Surface Micromachining requires more fabrication steps than Bulk Micromachining,
and hence is more expensive. It is able to create much more complicated devices,
capable of sophisticated functionality. Surface Micromachining is suitable for
applications requiring more sophisticated mechanical elements.
2.3 LIGA micromachining
A technique that overcomes the two-dimensionality of surface micromachining is the
LIGA (Lithographie, Galvanoformung, and Abformung) process. It is able to produce
a microstructure with a height ranging from a few microns to hundreds of microns,
and like bulk and surface micromachining relies on lithographic patterning. But
instead of ultraviolet light streaming through a photolithographic mask, this process
utilizes high-energy x-ray that penetrates several hundred microns into a thick layer of
polymer. Exposed areas are stripped away with a developing chemical, leaving a
template that can be filled with nickel or another material by electrode position.
Template may be either a structural element or the master for a moulding process. As
with surface micromachining, LIGA structures can be processed to etch away an
underlying sacrificial layer, leaving suspended or movable structures on a substrate.
The entire process can be carried out on the surface of a silicon chip, giving LIGA a
degree of compatibility with microelectronics.
3. MEMS Based Pressure Sensor
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Pressure sensor represents one of the greatest successes of the micromachining
technology. They have been benefited from developments in this field for about four
decades, in which time both commercially available and research-oriented devices
have been developed for a variety of automobile, biomedical and industrial
applications.
In the long history of the use of micromachining technology for pressure sensor,
device designs have evolved as the technology has progressed, allowing pressure
sensor to serve as a technology demonstrator vehicle in some sense. A number of
sensing approaches that offer different relative merits have evolved (mainly
peizoresistive and capacitive), and there has been a steady march towards improving
performance parameters such as sensitivity, resolution and dynamic range.
Although multiple options exist, silicon has been popular choice for the
structural material of micromachined pressure sensor partly because its material
properties are adequate and partly because significant manufacturing capacity and
know-how can be borrowed from the integrated circuit industry
It is without doubt one of the most successful application areas, accounting for
a large portion of the MEMS market. The suitability of MEMS to mass-produced
miniature high-performance sensors at low cost has opened up a wide range of
applications. Examples include automotive manifold air and tire pressure, industrial
process control, hydraulic systems, microphones, and intravenous blood pressure
measurement. Normally the pressurized medium is a fluid, and pressure can also be
used to indirectly determine a range of other measurands such as flow in a pipe,
volume of liquid inside a tank, altitude, and air speed.
3.1 Types of pressure sensor
There are basically three types of pressure sensors used in common application:
1. Absolute pressure sensor
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
2. Gauge pressure sensor
3. Differential pressure sensor
3.1.1 Absolute Pressure sensor
Fig 1: Absolute Pressure
Absolute pressure does include atmospheric pressure, and is measured relative to
vacuum (0 psi). For an absolute pressure sensor, the reference side of the pressure-
sensing diaphragm is isolated from the local environment, being hermetically sealed
in a vacuum. (Absolute pressure sensors are thus not only isolated from
environmental contaminants, but—theoretically—have better thermal performance
than sealed gage units, because there is no trapped volume of gas to expand and
contract with ambient temperature changes.) The transducer will then indicate a
pressure of 14.696 pounds per square inch at sea level, when it is not connected to the
process pressure of interest, but with the sensing element exposed to atmospheric
pressure. Absolute pressure is always the sum of the local "gage" pressure (induced
by some source) and the atmospheric pressure at the location of the measurement.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
3.1.2 Gauge pressure sensor
Fig 2: Gauge Pressure
Gauge pressure is pressure measured relative to ambient atmospheric pressure
(approximately 14.7 psi). That is, a gage pressure measurement does not include
atmospheric pressure itself. For a gage pressure transducer, one side of the pressure-
sensing diaphragm must be vented to the local environment. The transducer will then
indicate a pressure of "zero" when it is not connected to the process pressure of
interest, but while the sensing element is still exposed to atmospheric pressure. Gage
pressure is actually a kind of differential pressure. It always equals the difference
between the local absolute pressure and the local atmospheric pressure.
3.1.3 Differential pressure sensor
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 3: Differential Pressure
Differential pressure is pressure measured relative to a specific reference pressure.
If the reference pressure is one atmosphere, the differential pressure equals the gage
pressure. Normally, a differential pressure transducer will have two pressure ports,
and its pressure reading is generated by subtracting the pressure at the low port
from that at the high port. One port may be "dry" and the other "wet" or both may
be "wet" or both may be "dry." Differential pressure may be either absolute or gage,
as long as pressure is being measured in the same units at both ports.
3.2 Transduction Mechanisms
Transduction is the means by which one form of energy is transformed into another.
An example is strain gauge, which transforms strain into a change of electrical
resistance. There are various transduction methods like Piezoresistance, capacitance,
piezoelectric, bimorphs, shape memory alloys, optical etc. In pressure sensors
piezoresistive and capacitive transduction methods are commonly used.
3.2.1 Piezoresistance
Piezoresistance is the property of material, which causes the change in resistivity due
to applied strain. The resistivity change is generally linear with strain. While
piezoresistivity is present in most metals, the effect in semiconductors is up to two
orders of magnitude stronger. The larger effect in silicon and germanium is due to
electronic band deformation and redistribution of carriers within the various
conduction and valence bands. Thus when load is applied on diaphragm it deflects
and stresses are induced, due to the stress there is change in resistivity and hence
resistance of a piezoresistor. The resistors are placed in a Wheatstone bridge, hence
when load is applied the bridge is unbalanced; the output voltage is proportional to
applied pressure load. Piezoresistive theory in more detail is explained later section.
Advantages
1. The Resistor Bridge presents very low impedance; this permits the reminder of
sensing circuit to be located at some distance from diaphragm and no
deleterious effects from parasitic capacitance in capacitive sensor.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
2. Good linearity over wide dynamic range, which is a very important parameter
of the pressure sensor.
3. Relative freedom from hysteresis and creep.
Disadvantages:
1. Temperature sensitive as peizo coefficients decrease with increase in
temperature.
2. Resistors present scaling limitation for the pressure sensor. As the length of a
resistor is decreased the resistance decreased and power consumption rises,
which is not favorable. As width of the resistor is decreased, the minute
variations that may occur because of nonideal lithography or other process
limitations will have more significant impact on the on the resistor. This issues
constraints how small a resistor can be made.
3. Resistor scaling also imposes the size limitation on the diaphragm, or else will
lead to stress averaging effect and then the sensitivity has to be compromised.
3.2.2 Capacitance
In capacitive pressure sensor the flexible diaphragm serves as one electrode of a
capacitor, where the other electrode is located on a substrate beneath it. As the
diaphragm deflects in response to applied pressure, the average gap between the
electrodes changes, leading to change in the capacitance.
Advantages of capacitive pressure sensor:
1. The resistors do not have to be fabricated on the diaphragm, so scaling down of
device dimensions is easier because the concerns about stress averaging and
resistors tolerance are eliminated.
2. The full-scale output swing can be 100% or more in comparison to about 2%
for piezoresistive sensing.
Disadvantages:
1. The capacitance changes nonlinearly with diaphragm displacement and applied
pressure sensor.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
2. Even though the fractional change in the sense capacitance may be large, the
absolute change is small and considerable caution must be exercised in
designing the sense of the circuit.
3. The output impedance of the device is large, which also affects the interface
circuit design, and the parasitic capacitance between the interface circuit and
the device output can have a significant negative impact on the readout, which
means that the circuit must be placed in close proximity to the device in a
hybrid or monolithic implementation.
4. In the case of absolute pressure sensor the cavity beneath the diaphragm must
be sealed in vacuum, transferring the signal at the counter electrode out of the
cavity in manner that retains the hermetic seal can present a substantial
manufacturing challenge.
3.3 Type of pressurization
There are two different ways to apply pressure to diaphragm
Back Side Pressurization
Front Side Pressurization
With backside pressurization, there is no interference with the signal transducer such
as piezoresistor that is normally implanted at the top surface of diaphragm. The other
way of pressurization i.e. front-side pressurization is used only under very special
circumstances because of interfacing of pressurizing medium with the signal
transducer. The signal transducers are rarely placed on the back surface the diaphragm
because of the space limitation as well as awkward access for interconnects
3.4 Pressure Sensor Layout
The basic structure of a piezoresistive pressure sensor consists of four sensing elements in
a Wheatstone bridge configuration to measure stress in a thin, crystalline silicon
membrane. The stress is a direct consequence of the membrane deflection in response to
an applied pressure. The thickness and geometrical dimensions of the membrane affect
the sensitivity and consequently, the pressure range of the sensor
In the case of single crystal piezoresistive pressure sensor design layout on 100
substrates, the four ion implanted piezoresistive sense elements are placed at the locations
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
of high stress which occur at the centre of the membrane edge as shown in figure 4(a).
Here the two piezoresistors R1 and R3 are placed parallel to opposite edges of the
membrane, and the other two are placed perpendicular to the other two edges. When the
membrane deflects downwards, causing tensile stress at the edges of the membrane
surface, the parallel resistors R1 and R3 are under lateral stress and show a decrease in
resistance while the perpendicular ones R2 and R4 are under longitudinal stress and show
an increase in resistance. If the resistors are correctly positioned with respect to the stress
field over the membrane, the absolute value of the four resistance changes can be made
equal. The resistors are connected in a Wheatstone bridge, as shown schematically in
figure 4(b). When pressure is applied on the diaphragm, it gives rise to non-zero output
voltage from the bridge. It is necessary that the four piezoresistors have identical
resistances in the absence of applied pressure. Any mismatch in resistance, even one
caused by temperature, brings an imbalance in the Wheatstone bridge. The resulting
output reading is known as zero offset, and is undesirable.
Fig 4: (a) Schematic representation of the positions of four piezoresistors on a
membrane. (b) Wheatstone bridge configuration of the four piezoresistors
The Wheatstone bridge configuration has some distinct advantages. It converts the
resistance change directly to a voltage signal. It can be easily show that the
differential output voltage (Vo) of an ideally balanced bridge with assumed identical
(but opposite in sign) resistance changes ΔR, in response to a differential pressure
change ΔP on a sensor, is given by
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Here R is the zero-stress resistance and VIN is the bridge supply voltage. The pressure
sensitivity (S) is then defined as the relative change of output voltage per unit of
applied differential pressure. This is expressed in mV/V-bar
In the ideal case, the total resistance of each half-bridge and, thus, of the total bridge
is independent of pressure since the resistance changes cancel one another. Moreover
common-mode effects, in particular temperature influences, are not felt at the
differential bridge output. Indeed, a temperature rise increases the resistance of all
piezoresistors equally, so that the output of the bridge remains zero. This is the case
only for a perfectly balanced bridge. It is also interesting to notice that at constant
bridge voltage, the total current will vary with the temperature. On the other hand, for
a constant-current bridge supply, the total bridge voltage will vary.
3.5 Terminology of Pressure sensor
There are several MEMS companies manufacturing pressure sensors for various
applications. Their data sheets contain the specification of pressure ranges and types
of devices available. It is important for customers, to choose the system by comparing
the specification of different sensors. There are no standards for specifying sensors,
each manufacturer writes in his own format. Sensor specifications are given as
absolute numbers- milli volts, volts, psi, and ohms or as % of full scale (FS).
The following are the terms related with specification of pressure sensor:
1. Pressure Range: The pressure range given on the data sheet is the pressure at
which the device has been calibrated and tested i.e. pressure range in which sensor
should work.
2. Pressure type: Absolute pressure, gauge pressure or differential pressure.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
3. Accuracy: It is a figure of merit how accurately the sensor can measure the
unknown pressure. It may be referring to linearity, hysteresis and may be
repeatability. Temperature effects are added to the basic accuracy numbers to give the
overall accuracy.
4. Span: The device output signal over the pressure range is called span. also known
as output span voltage.
5. Sensitivity: Is defined as the ratio electrical output to its mechanical input. In
piezoresistive pressure sensor it is expressed as Voltage per unit of pressure at the
rated excitation.
Here R is the zero-stress resistance and Vb is the bridge supply voltage, Vo change in
output voltage due to change in pressure ΔP
6. Resolution: The maximum change in pressure required to give a specified change
in output.
7. Linearity: Linearity defines how closely the output of the sensor approximates a
straight line when a linear pressure is applied. The non-linearity is measured and
expressed as linearity. The deviation of sensor calibration curve from a straight line is
expressed as a percent of full scale (% FSO).
There are three accepted ways to express linearity: Independent, terminal based and
zero-based. If data sheet does not specify a testing procedure for linearity,
independent linearity is assumed. (Figure 5(a))
8. Pressure Hysteresis: Is the maximum difference in output, at any pressure, when
the pressure level is approached with increasing and then with decreasing pressure.
Because of excellent elastic characteristic of silicon, the Hysteresis of these gauges is
usually quite small, most of time under 0.1 % FSO (Figure 5(b))
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 5: a) Linearity curve b) Hysteresis curve
9. Zero Measurand output (offset voltage): Zero balance or Zero pressure output is
expressed in mill volts at the output of the transducer under room conditions with full
rated excitation but no pressure is applied to the transducer. Although the resistance in
the bridge is closely matched and compensated during manufacture, slight difference
in resistance exists.
10. Resonant Frequency: Resonant frequency is the frequency of pressure
application at which the transducer responds with maximum output amplitude. Peak
pressure greater than the specified range should not be applied at frequencies greater
than 30% of resonance frequency. The resultant mechanical amplification effect near
the resonant frequency may cause erroneous data, or in extreme cases may burst the
diaphragm
11. Over pressure: The maximum specified pressure, which may be applied to the
sensing element without causing a permanent change in output characteristics. It is
generally taken as three times the rated pressure range.
12. Burst pressure: The maximum pressure that can be applied to a transducer
without rupture of either sensing element or transducer casing.
13. Excitation Voltage: It is the external voltage applied to the transducer for its
operation within specified tolerances.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
14. Temperature range: The range over which the device operates safely.
15. Chip size: Chip size may also be one of the specifications from customer for the
customized application depending upon external environment.
3.6 Theory of Sensor Design
A major difference between mechanical engineering design of Microsystems and that
of other products is that the design of Microsystems requires the integration of the
related manufacturing and fabrication processes. Mechanical engineering design of
traditional products and systems rarely requires the consideration of the consequences
of the manufacturing process. In Microsystems which involve MEMS components,
however, the situation is quite different. Components for MEMS are fabricated by
various physical-chemical means. These fabrication and manufacturing processes
often involve high temperature and harsh physical and chemical treatments of delicate
materials used for the components. These processes can have serious repercussions in
the performance of Microsystems and hence must be taken into design considerations.
Tolerance of the finished components, and the intrinsic effects such as residual
stresses and strains inherent from micro fabrication processes are just two obvious
examples of such repercussions.
In general, Microsystems design involves three major tasks that are mutually coupled:
1. Process flow design,
2. Electromechanical and structural design, and
3. Design verifications that include packaging, and testing.
In this work, emphasis is laid on the second part i.e. on the Electromechanical and
structural design.
The design analysis can be carried out on the initial configurations and can be
compared so as to make an optimum design, which satisfies the specification set
initially. Once the optimum design is done, process design can be done so as to make
the prototype.
Prototypes fabricated can be tested and verified with the design being carried out. If
there is large variation between the test results and design results, the original design
and process is to be studied again so as to trace the cause for difference. Once the
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
cause is traced it is to be redesigned until the test and design results agree with each
other. When the results are validated then product can be mass fabricated. Figure 6
illustrates the design methodology adopted to design a typical pressure sensor.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 6: Sensor Design flow
3.7 Technical specifications for mems based pressure sensor
Table 1: Data Sheet
DESCRIPTION SPECIFICATION
Pressure Range (kPa) 11-18
Pressure Type Absolute
Output Span Voltage (mV) 0-24
Excitation Voltage(V) 3
Sensitivity (mV/V*psi) 3
3.8 Membrane Design
Understanding the deflection behaviour of the diaphragm is the first step in designing
of a pressure sensor. A Piezoresistive pressure sensor, which is the focus of this work,
measures deflection and diaphragm stress and converts them into output voltage.
Hence a careful study and analysis of the diaphragm is of importance.
3.8.1 Silicon as a substrate material
Single crystal silicon is the most widely used substrate material for MEMS and
Microsystems.
The popularity of silicon for such application is primarily due to the following
reasons.
1. It is mechanically stable and it can be integrated into electronics on the same
substrate. Electronics for signal transduction, such as p- or n-type
piezoresistor can be readily integrated with the Si substrate.
2. Silicon is almost an ideal structural material. It has about the same Young’s
modulus as steel (about 2 x 105 MPa, but is as light as aluminium, with a mass
density of about 2.3g/cm3. Materials with high Young’s modulus can better
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
maintain a linear relationship between the applied load and the induced
deformations.
3. It has a high melting point at 1400 0C, which is twice as high as that of
aluminium. This high melting point makes silicon dimensionally stable even at
elevated temperature.
4. Its thermal expansion coefficient is about 8 times smaller than that of steel, and
is more than 10 times smaller than that of aluminium.
5. Silicon shows virtually no mechanical hysteresis. It is thus an ideal material for
sensors and actuators.
3.8.2 Design considerations
Silicon dice are key components in micro sensors. Proper mechanical design is
necessary to ensure the proper functioning of the sensor. The design depends on the
specification required. The typical specification of a pressure sensor are listed in
Table 1.The diaphragm structure plays a major role in deciding the pressure range,
sensitivity, non-linearity, frequency response etc.
3.8.3 Diaphragm shape
Fig 7: Comparison of various shapes of diaphragm of similar width.
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Figure 7 illustrates the performance of diaphragms of different shapes, but of same
width. Comparison of these diaphragm shapes at pressure ratio of 100 reveals that
round diaphragm deflects approximately 0.78 of its thickness, the square diaphragm
deflects approximately 0.95 of its thickness, and the rectangular diaphragm deflects
approximately 1.25 of its thickness.
A comparison of stress ratios reveal also a significant difference in stress levels at the
same pressure ratio. Thus for the round diaphragm the stress ratio is approximately
18, for square diaphragm the stress ratio is approximately 27, and for rectangular
diaphragm the stress ratio increases even more to approximately 35 almost double that
of round diaphragm.
Thus for same width it is clear that square diaphragm gives better deflection and stress
characteristic over rectangular or circular diaphragm. The advantage of square
diaphragm over rectangular is that stress along all the four edges is almost similar and
it becomes easier to place the resistor over the four edges, so that they experience
almost equal stress and show equal change in resistance. The advantage of square
diaphragm over circular is the maximum stress is 1.64 times as large as that of the
circular diaphragm when the diaphragm thickness is same. This means that better
characteristics are obtained in a square than in a circular diaphragm.
3.8.4 Bossed diaphragm
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In this work based on advantages stated in previous sections of this chapter, square
plate is selected to act as the diaphragm. It has been stated that the design of
diaphragm is very critical as it decides many parameters as sensitivity, linearity etc.
The parameter on which the diaphragm is designed will vary according to one’s
needs. In this work a low-pressure sensor in the range of 12-18 kPa is desired.
Sensitivity is proportional to (a/h)2. Thus sensitivity can be increased using greater
(a/h) ratio. However, the nonlinearity error increases with this ratio at a much faster
rate. Hence a high sensitivity may involve a non-tolerable error. The nonlinearity
caused by the large deflection can be overcome by local stiffening of the diaphragm
using a bossed structure, while keeping the resistors in the thinner areas. The boss
should be a minimum of six times thicker than the diaphragm and the ratio of (b/a)
should be greater than 0.15 for the boss to be effective. In this work, diaphragm is
designed so as to get optimum linearity and sensitivity. The governing equations for
such bossed diaphragms are as follows
Where
Here P is the applied pressure, E is the young’s modulus and v is the poisson’s ratio
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
The maximum radial bending stress occurs at the outer perimeter where the
diaphragm is clamped and the inner perimeter where the boss begins. The stress on
the outer perimeter is equal and opposite to that occurring at the inner. The radial
stress is given by
Considering the deflections to be very small compared to the diaphragm thickness the
membrane can be classified as a thin plate with small deflection and can be analyzed
using Classical thin plate theory. The assumptions, which have to be taken care during
design according to the above theory, are
1. The material is isotropic and homogenous
2. The maximum deflection due to applied pressure should be small – not more
than 30% of the thickness of the plate.
3. All forces, loads and reactions are applied normally to the plane of the plate.
4. The plate deflection is mostly due to bending; therefore the median plane of plate
endures no stresses.
The pressure deflection relationship for a loaded diaphragm is linear for only small
deflections. At large deflections tensile stress begins to appear and as the load
continues to increase the deflection increases at slower rate and load deflection
relationship becomes nonlinear. Hence the problem of sensitivity and linearity appear
and both contradict each other. If a linearity of 0.20% is expected, then the diaphragm
must not be deflected more than 12% of its thickness, on the other hand if linearity of
2% is permissible, a deflection of 30% of thickness can be tolerated. So as to get a
better accuracy along with good linearity in this work the thickness of diaphragm is
calculated such that at rated pressure the maximum deflection is 20% to 25% of
thickness of diaphragm. Thus the percentage of deflection with respect to diaphragm
thickness is analyzed to finally freeze the diaphragm thickness. In depth analysis is
done using IntelliSuite software, which is a tool for MEMS design.
Based on equation 3.1, taking a = 600 μm, Rated Pressure (P) = 18 kPa, isotopic
material properties of silicon (silicon is anisotropic material but still for diaphragm
analysis it is assumed as isotropic, as explained in chapter , Elastic modulus as 169
GPa and Poisson’s ratio as 0.23.
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3.9 Piezoresistive Effect in Silicon
It is the fractional change in bulk resistivity induced by small mechanical stresses
applied on material. Lord Kelvin discovered the piezoresistive effect in 1856. Most
materials exhibit some piezoresistive effect.
In 1954, C. S. Smith discovered that silicon and germanium (semiconductors) had a
much greater piezoresistive effect than metals. This discovery enabled the first
silicon-based sensors. Silicon is particularly well suited for Piezoresistance
measurement on membrane for several reasons:
1. The measured effect in semiconductor is up to two orders of magnitude higher
than that of metals.
2. The integration of gauge and membrane eliminates hysteresis and creep
3. The strain is transmitted perfectly from the membrane to the gauge.
4. The resistors are limited to the surface of the element in bending or torsion
where the stresses are maximal.
5. Good matching of resistors can be achieved which is particularly useful if
Wheatstone bridge is used.
Metal undergoes a change in electrical resistance when subjected to mechanical strain.
The Physics of this phenomenon is different in semiconductors. In semiconductors the
conductivity (C) which is reciprocal of resistivity (ρ) is related to carrier concentration
(p) as
C = p * μ * q (3.8)
The applied stress varies the conductivity either by affecting the charge carrier
concentration or the mobility of carriers (μ) or both. ‘q’ is the charge.
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3.9.1 Gauge Factor
The piezoresistive effect can be quantified using the gauge factor. The general
definition for the gauge factor begins with the relationship between resistance R and
resistivity ρ.
The resistance R of a rectangular conductor is expressed by
Where ρ is the resistivity and l, w, and t are the length, width, and thickness of the
conductor, respectively. When the resistor is subjected to strain, the relative change in
resistance is given by
Where Δl, Δw, Δt and Δρ are the changes in the respective parameters due to the
strain. Introducing Poisson’s ratio ν, where
The gauge factor G (strain sensitivity) is given by
Where is the strain. The first two terms in Eqn. (3.12) represent the change in
resistance due to dimensional changes, and are dominant in metal gauges, while the
last term is due to the change in resistivity. In semiconductor gauges, the resistivity
change is larger than the dimensional change by a factor of about 50, and the
dimensional change is generally neglected.
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Table 2: Gauge Factor for different strain Gauge
Type of Strain gauge Gauge Factor
Metal foil 1 to 5
Thin film Metal ≈ 2
Diffused Semi-Conductor 80 to 200
Polycrystalline Silicon ≈ 30
3.9.2 Piezoresistive in single crystal silicon
The fact that silicon crystal, whether it is p type or n type, is anisotropic has made the
relation between the resistance and the existent stress field more complex. This
relationship is shown below:
Where represents the change of
resistance in an infinitesimally small cubic Piezoresistance crystal element with
corresponding stress components . Of the six
independent stress components in the stress tensor σ, there are three normal stress
components, σ xx, σ yy, and σzz, and three shearing stress components, σxy, σxz, and
σyz. The vector [π] in equation 3.13 is referred to as Piezoresistive co-efficient
matrix. It has the following form.
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We notice from equation 3.14 that only three co-efficients π11, π12, and π44 appear in
the matrix by expanding the matrix in the equation 3.13, with the appropriate
Piezoresistive co-efficient in equation 3.14, we will have the following relations:
ΔRxx = π 11 σxx + π12 (σyy + σzz)
ΔRyy = π11 σyy + π12 (σxx + σzz)
ΔRzz = π11 σzz + π12 (σxx + σyy)
ΔRxy = π44 σxy
ΔRxz = π44 σxz
ΔRyz = π44 σyz
It is thus apparent that the co-efficient π 11, π12 are associated with normal stress
components, where as the co-efficient π44 is related to shearing stress components.
The actual values of these three co-efficients depend on the angles of the piezoresistor
with respect to the silicon crystal lattice. The values of these co-efficient at room
temperature are given in table 3
Table 3: Piezoresistive coefficients at room temperature
Material ρ (Ω-cm) π 11 π 12 π 44
(10^-11 Pa-1)
p-type 7.8 6.6 -1.1 138.1
n-type 11.7 -102.2 53.4 -13.6
Equation 3.13 represents general case of Piezoresistive crystal in 3D geometry. In
almost all applications in MEMS and microsystems, silicon piezoresistors exist in the
form of thin strips. In such cases only the in-plane stresses in the X and Y directions
need to be accounted for.
We will realize form table 3 that the maximum Piezoresistive co-efficient for p-type
silicon is π44 = +138.1*10^-11 Pa-1, and the maximum co-efficient for the n-type
silicon is π11 = -102.2*10^-11 Pa-1. Thus, many silicon piezoresistors are made of p-
type material with boron as the dopant.
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The value of πL denotes the Piezoresistive co-efficient along the longitudinal direction
whereas πT represent the Piezoresistive co-efficient in tangential direction. The change
of electrical resistance in silicon Piezoresistance gauge can thus be expressed as:
In which ΔR and R are respectively change of resistance and the original resistance of
silicon piezoresistors. The value of original resistance R in equation 3.15 can be
obtained by using the formula R = ρ * L / A, in which ρ is the resistivity of the
piezoresistor, L and A are respective length and cross sectional area of the
piezoresistor. The stress components in longitudinal and tangential directions, σL and
σT, are the stresses that cause the change of resistance in the piezoresistor.
3.9.3 Resistance change as a Function of stress
The resistance change can be calculated as a function of the membrane stress.
Assuming that the mechanical stress is uniform over the resistor, the total resistance
change is given by
The surface of silicon wafer is usually a <100> plane and the orientation of the
piezoresistor with respect to the silicon crystal is (110).
For p type resistors π44 is more important than other two coefficients. Thus the above
equation is approximated for p-type resistor by
For n-type resistor π44 can be neglected and we obtain
The above equations are only valid for uniform stress fields or if resistor dimensions are
small compared to the membrane. For small sensors the stress will vary across the resistor
and have to be integrated, which can be done most conveniently by computer simulations.
3.9.4 Design Rules for Piezoresistor
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Most sensors with square membrane have four resistors deposited on four edges of the
membrane, however the exact layout varies. The resistors are connected in
Wheatstone bridge, as shown in Figure 4.
The following parameters are to be considered in design of piezoresistor.
1. Size (Geometrical design)
2. Location
3. Orientation.
Certain design rules or constraints are to be followed, to make a efficient design and
finally come up with the sensitive sensing element for a pressure sensors.
Constraints 1:
All the resistors are chosen to have the same initial value. This implies that each
resistor has the same length, width and thickness. i.e. they have same volume.
Constraints 2:
The size and orientation of resistors should be such that the change in resistance of
parallel and perpendicular piezoresistors should be equal and opposite to get
maximum sensitivity.
Constraint 3:
The locations of the resistors on the diaphragm should be chosen such that the stress
acting on the resistor is maximum. The resistors are located as close to the centre of
the membrane edges where the stresses are maximum.
Constraint 4:
In order to maximize the output voltage of the Wheatstone bridge, ΔR/R for adjacent
arms of the bridge must have to be opposite in sign.
Constraints (1) and (2) determine the dimensions of the Piezoresistors, constraints (3)
& (4) determines the location of the resistors.
3.9.5 Piezoresistors Design
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P-type silicon is used as diffused resistors in the pressure sensors because they are
compatible with the electrochemical etch-stop technique, and also p-type material has
a higher piezoresistive coefficient in the (110) direction than n-type material
Geometry of piezoresistors
From the diaphragm analysis it is evident that the maximum stressed area is around
600 μm X 600 μm. Therefore the resistor dimensions were arbitrarily selected as 600
X 8 μm.
Thickness of Piezoresistor
The thickness of the resistor mainly depends upon two conditions. They are
1. Stability
2. Sensitivity
The buried Piezoresistors are used for high stability because they are passivated by an
epitaxial layer grown on top. However the sensitivity of such devices is lower
comparatively.
The surface piezoresistors are used for higher sensitivity, but with a compromise of
reduced long-term stability. The reason being, stress in the membrane is higher near
the surface than into the bulk. However the danger of delamination of resistors causes
these sensors to be less stable.
With this inference and also the process capability, we have decided to keep the
thickness of the resistor to be 2 μm.
Now the resistivity, which is the key parameter in the INTELLIFAB simulations, can
be calculated using the relation,
Where, L, W, T is the length, width and the thickness of the resistor respectively. And
ρ is the electrical resistivity of the resistor.
Therefore
This is an input parameter for simulation in IntellisuiteTM.
4. INTELLISUITE SOFTWARE
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IntelliSuite is a complete integrated design environment for MEMS process
modeling, device layout and device analysis. IntelliSuite comes with completely
coupled electrical, piezo-electrical, mechanical and thermal analysis tools for
executing linear or non-linear static or transient analysis. The IntelliMask design tool
allows us to capture the MEMS design at the mask level with an easy-to-use editor,
which includes a built-in scripting language to automate the creation of complex
geometries. IntelliSuite also includes a wide range of parametric elements such as
comb drives, springs, beams and test structures.
The 3D Builder tool provides 3D model creation and meshing capabilities. Automatic
meshing tools can generate near optimal meshes while interactive tools enable us to
further refine the mesh. 3D Builder allows us to work in polar or rectilinear
coordinates to help you quickly generate 3D meshes.
IntelliSuite includes a comprehensive set of analysis tools. The Thermo-Electro-
Mechanical analysis tool provides fully coupled static, dynamic, transient and contact
analysis. The piezoelectric and piezoresistive analysis tool is for the design of peizo-
sensing or peizo-actuation mechanisms. IntelliSuite also comes with analysis tools for
die-level and board-level packaging enabling packaging stresses, shock effects,
effects of packaging pressure on device damping etc. to be investigated.
Additional optional modules are available for Electromagnetic and RFMEMS analysis
and BioMEMS and Microfluidics analysis used by MEMS professionals worldwide
for design, development and manufacturing of MEMS, IntelliSuite has firmly
established itself as industry’s standard tool. As such, IntelliSuite provides MEMS
companies and individual users with a complete living design environment.
IntelliSuite is a tightly integrated design environment that will link your entire MEMS
organization together. Built to scale from a point tool to an organization-wide tool,
IntelliSuite unifies various engineering and manufacturing tasks into a single living
design environment. Designed around collaboration, IntelliSuite allows the design and
process teams collaborate on MEMS devices that can be prototyped and manufactured
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
with less costly iteration. IntelliSuite starts the design process from fabrication
machine settings, rather than device geometry — an approach that helps create highly
accurate models. In turn, this demonstrates that device geometry and behavior are a
direct result of process conditions. Which means that IntelliSuite optimizes MEMS
designs prior to fabrication, which reduces prototype development cycle time and cuts
manufacturing costs
4.1 Process modeling modules
4.1.1 AnisE (Si Wet Anisotropic Etch)
AnisE is an easy-to-use anisotropic etch process simulation tool for MEMS design
and process control
Demystifying etch behavior
Anisotropic etching is one of the most difficult silicon micro-machining processes to
model, often considered in the realm of the “black arts.” It can be challenging to grasp
intuitively due to the complex nature of evolving etch fronts. In fact, many companies
have developed closely guarded etch secrets through trial-and-error experimentation.
Well, those days have ended. AnisE simplifies the process of accurately simulating
etch behavior. Import the mask, choose the wafer orientation and the process
parameters, and then watch the etch progress online before our eyes.
Sophisticated controls
AnisE comes with built-in etch databases for KOH and TMAH. It automatically
updates the etch rates as a function of temperature and concentration.
With AnisE, you can simulate single or double-sided <100> and <110> etching. We
can incorporate multiple etch stops, steps or anything else you can do in the real
world. In addition, one can study the effect of mask misalignment, the effect of
combining RIE etching with anisotropic etching and many other real- world
conditions.
4.1.2 Intelli FAB
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IntelliFAB allows us to debug the process flow
and the mask set even before we enter the clean
room. It allows you to make a virtual prototype
to save fabrication mistakes. Until now, MEMS
costly designers have typically focused purely
on geometric representation of the device in
order to analyze device behavior. The drawback
of this
Methodology is that process induced effects may vary the geometry of the structure
significantly. For example, the boron diffusion as an etch stop layer for bulk silicon
processing may overstress the structure, strain gradients in poly-silicon structures can
distort features, or an anodic bonding process may break down protective oxide films.
IntelliFAB allows designers to takes a different approach. Process flow forms the
basis of creating your devices. Our comprehensive process simulation modules
incorporate deposition, etching, bonding, doping, electroplating, liftoff, and other
process steps common in MEMS design. Other process-induced effects, such as
micro-assembly, are also addressed to generate accurate geometric models for the
complete range of MEMS devices.
IntelliFAB is directly linked with MEMaterial, a MEMS process database that stores
material properties as a function of machine settings. By developing the fabrication
process in conjunction with the analysis model, IntelliSuite enables engineers to
perform more accurate device physics analysis and produce manufacturable devices
faster.
4.2 Design Tools
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4.2.1 IntelliMask
IntelliMask incorporates MEMS-specific design
features unavailable in standard electronics and
mechanical layout tools. Thanks to IntelliMask’s
comprehensive design environment, one can
take designs from process definition to mask
layout to device analysis. Along with this there
are several features specifically for MEMS
designers. Arcs,
Splines, wires and curves are standard features, rather than afterthoughts patched onto
an IC layout tool. Control the grid down to a nanometer or create complex shapes
easily with our built-in Boolean operations. We can create scaled, rotated and arrayed
instances of a cell — and the changes propagate without a hitch. IntelliMask is a
powerful, yet easy to use mask editor developed specifically for the MEMS
community.
Within a single unified design environment. The IntelliMask can be used to
• Create complex MEMS curvilinear and non-Manhattan masks with ease
• Geometric Boolean operations.
• Create masks with cell based hierarchy.
• Import/Export GDS/DXF files.
• Automate mask creation through
Scripting or use the parametric element library to quickly create typical structures
4.2.2 IntelliMask Pro
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IntelliMask Pro has additional features, which
make it easy to manage masks on a work group
level. Hierarchical shared libraries make enable
an entire organization to share mask templates.
Process control features, alignment marks and custom test features. IntelliMask Pro is
a production ready mask making environment. IntelliMask Pro is available as a paid
upgrade to existing IntelliMask/ IntelliSuite users. IntelliMask Pro takes Boolean
support to the next level. While IntelliMask provides simple support for Boolean
operations, IntelliMask Pro can perform Boolean operations between cells and layers.
This can be very useful in version control; for instance, you can differentiate between
two cells to see what the changes are. The possibilities are endless IntelliMask pro
gives you additional production ready capabilities such as
• Import and export of additional formats (CIF, Gerber, RS 274, Electromask,
PostScript)
• Ability to perform complex Boolean operations between entire layers or cells.
• Full layer transparency support.
• Workgroup features such as hierarchical shared libraries.
#D
4.2.3 3D Builder
3D Builder is a powerful tool to create and
refine structured or unstructured grids.
IntelliSuite gives as much control over the
device meshing process as we need. On one
hand, automatic meshing tools can generate near
optimal meshes while, on the other, interactive
tools allow us to further refine With 3D
Builder, IntelliSuite gives unparalleled control over the mesh creation and refinement
process. 3D Builder allows us to import structured and unstructured grids in a variety
of formats (ANSYS, ABAQUS, PATRAN neutral file, IntelliSuite). 3D Builder
simplifies the creation of optimal meshes. While automated meshing methods are
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
convenient, they have been known to produce too many elements. 3D Builder allows
you to create rectilinear or polar meshes with ease. What’s more, regions can be sliced
(sub-divided) using a number of algorithms. Popular refinement techniques, such as
spider-web meshes, corner frame meshes or zippered slicing can be applied with a
simple click of the mouse. Think of it as the Tiptronic™ of meshing tools enabling to
switch from automatic to manual gears.
With 3D Builder we can:
• Import/Export grids in a variety of formats (ABAQUS, ANSYS, PATRAN etc)
• Work with Polar or rectilinear grids
• Snap-to grid and snap-to point (mid-points, intersections, refinement cues) features
• Use GDS/DXF mask layouts as mesh cues.
• Easy creation and manipulation of entities
4.3 Analysis Modules
4.3.1 Fully coupled ThermoElectroMechanical analysis
The Thermo-Electro-Mechanical (TEM)
analysis module allows us to perform
fully coupled thermal, electrical and
electrostatic and mechanical analysis.
TEM allow us to perform fully coupled
static, dynamic, harmonic, transient,
contact and post contact analyses on
linear or non-linear systems.
Use TEM for analyzing a wide range of devices based on electrostatic, thermal or
Electro thermal principles. Based on a custom version of the leading nonlinear FEM
solver from ABAQUS, TEM allows you to tackle large highly non-linear problems.
TEM incorporates many custom MEMS algorithms that are unmatched by other tools.
Full dynamics capability (all other tools are limited to quasi-static
approximations)
Exposed Face Mesh algorithms: No need to mesh the air gaps. Decouple
mechanical and Electrical meshes to solve large problems
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Optimized Squeeze Film damping module for Fluid structure interaction (15X
faster than typical Navier-Stokes based solvers).
4.3.2 Thermal Analysis
IntelliSuite gives a full range of tools to model
heat transfer phenomena. Designing a thermal
actuator or a bolometer is easier and to calculate
thermal stresses during packaging and even to
model Joule heating or heat flux. This tool does
it all. Or we can use the tool in conjunction with
other analysis modules to calculate the
temperature coefficient and response of the
device.
4.3.3 Electrostatic Analysis
The electrostatic module of IntelliSuite is
designed from the ground up for real world
MEMS problems, like a 200-finger radial comb
drive or a corrugated RFMEMS device. Other
CAD tools run into severe limitations while
solving real world problems and have to use
reduced toy models but not IntelliSuite. The
innovative Exposed Face Meshing algorithm can
solve extremely large problems up to 90% Faster than other tools on the market. In
fact, now one can even investigate second order effects such as levitation due to the
ground plane (important in most comb drive structures), temperature coefficients of
your capacitors, and charge buildup that can cause potential arcing. Multi-dielectric
problems, dielectric discontinuities, and parasitic capacitance can all be modeled
accurately without resorting to costly trial and error in the fab.
4.3.4 Mechanical Analysis
One of the strong suits of IntelliSuite is its
unparalleled capability in mechanical analysis
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
and its integration with the thermal and
electrostatic modules to perform fully coupled
analyses. IntelliSuite comes with a full featured
mechanical module that can solve the most
complex linear or non-linear, transient or steady
state, static or dynamic problems. Stress and
strain calculations,
Modal and buckling analysis and frequency response can all be performed with ease.
Full squeeze film damping, dynamic response to complex vibration inputs, shock
analysis, and Q factor calculations are equally easy to derive. Difficult problems such
as the shift of natural frequency due to voltage or stress loading or the effect of
residual processing stresses on device performance are likewise easy to analyze.
4.3.5 Contact Analysis and micro assembly
IntelliSuite really shines when it comes to
contact, post contact, and micro-assembly
analysis. Other MEMS CAD tools are limited to
analyzing single dielectric layers with artificial
air stops, and make you specify contact faces a
priori. IntelliSuite avoids such limitations.
IntelliSuite proprietary
Algorithms take into account multi-dielectric moving or deformable boundaries and
help to locate the exact point of contact. IntelliSuite's contact analysis goes way
beyond the reduced order models and other gross simplifications and can help us to
model complex post-contact phenomenon such as hysteresis. Micro-assembly
techniques such as stress release, pop-up structures, latching mechanisms, and bi-
stable and multi-stable elements can also be modeled with IntelliSuite.
4.3.6 Piezoelectric and piezoresistive Analysis
IntelliSuite ships with the most sophisticated
piezoelectric and piezoresistive modeling
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
capabilities in the industry. If we are considering
peizo actuation for our MEMS device then
IntelliSuite can handle the needs such as time
varying loading; steady state, mode based or
direct integration transient analysis of your
device. In addition, we can look at a floating
conductor voltage as a function of time varying
loading which is important for acoustic
transducer and microphone design
4.3.7 RF and Micro Wave MEMS
The IntelliSuite electromagnetic analysis module
is specifically designed to address the needs of
researchers in RF MEMS, microwave, and
Optical MEMS by providing fast, accurate, cost-
effective solutions for electromagnetic and RF
associated phenomena. Whether we are
designing an RF Switch, a tunable capacitor, a
VCSEL, an antenna, or a waveguide, we will
find IntelliSuite indispensable.
Electromagnetic module is the only fully integrated high frequency solver available
for MEMS simulation. Traditional high frequency tools are designed for planar or
quasi-planar structures, not for the high aspect ratio structures of MEMS. These tools
also fail badly when it comes to highly resonant mechanical structures.
This engine overcomes these obstacles, and is in fact the only tool that can truly tackle
RF MEMS modeling additionally, more limitations found in most other high
frequency tools were removed by adding support for lossy conductors and dielectric
discontinuities. Best of all, it tightly integrates with the IntelliSuite environment,
providing us with all the tools for your MEMS needs. This software has full support
for multiple dielectrics with gaps and lossy conductors allowing us to model devices
in full 3d. No more limitations to quasi-planar structures. The algorithms are designed
to give accurate results for even the most highly resonant structures.
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4.3.8 BioMEMS and Microfluidics analysis
Most Computational Fluid Dynamics (CFD)
tools available on the market were designed for
either aircrafts or automobiles, or for flow in
pipes. They are not optimized for Microfluidics
or bioMEMS. IntelliSuite is a full solver
optimized for MEMS applications from the
ground up. At the same time it goes way beyond
the existing code bases by adding support for
electrokinetic phenomenon, Red-Ox reactions, acids, bases, ampholytes, and fluid-
structure interaction. To top it off there is a few Added advanced visualization
algorithms to look at cross sectional profiles, velocity vectors, and transients. The
code base is not only faster at solving Microfluidics problems but is the only MEMS
tool for problems ranging from electrophoresis to isoelectric focusing. This module is
fine tuned for real world.
4.3.9 Packaging analysis
IntelliSuite solves most complex
packaging problems involving linear and
non-linear, static, frequency, and
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dynamic behavior. Stress, strain and
warpage calculations, modal and
buckling analysis, and the Thermal-
electrical (joule heating) response
of packaged devices can all be performed with ease. Users can model the dynamic
response of packaged devices to complex vibration inputs, perform shock analysis,
incorporate convective heat losses, and calculate Q factors. Fully coupled squeeze
film damping modeling allows you to determine device performance as a function of
package pressure. This allows you to perform JEDEC, MIL STD, or Belcore tests on
packaged devices before costly device fabrication. One of our dictums has been to
concurrently design the MEMS and packaging. In fact, far too many MEMS projects
fail due to the lack of packaging considerations upfront. IntelliSuite is at its best in
demystifying packaging of MEMS devices. Packaging related stresses, thermal
gradients, and the temperature response of a device can all be modeled without
needing to purchase yet another tool. IntelliSuite gives the tools to perform die level
and board level packaging thermo-mechanical and high frequency analysis.
5. METHODOLOGY
5.1 Simulation Using IntelliSuite
IntelliSuite has been used to design the pressure sensor. It is special software for
MEMS and not just for Microfluidics design and analysis, it’s even for RF devices
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etc. Physical design starts with a 2-D layout representing the MEMS geometry. The
layout together with the process description is used to build a 3-D model. This model
is meshed and then simulations are run using the available 3-D physics solvers.
Results can be viewed in tables, graphs or colour counter mapped onto the 3-D model.
5.2 Piezoresistive Pressure Sensor Simulation.
This problem models a piezoresistive pressure sensor using the Mechanical analysis
module of IntelliSuite. The device consists of a membrane, fixed around the edges,
with a trace wire on the surface. The wire is made of a piezoresistive material (a
material whose resistance is a function of strain). When a pressure is applied to the
top of the membrane, the membrane (and the wire on it) deform, changing the
resistance of the wire. By measuring the resistance of the wire, one can measure the
pressure causing the deformation.
5.2.1 Mask Layout
Click Start…Programs…IntelliSuite…IntelliMask
The mask editor will appear. The fig below shows the mask editor window with the
final mask.
Fig 8: IntelliMask window
5.2.2 Build and visualize the MEMS structure based on process
A MEMS 3D solid model can be built in IntelliSuite by defining a list of the process
steps used for manufacturing. This process sequence is referred to as a Process Table.
IntelliSuite provides Process Table templates to users, or they make their own by
accessing the IntelliSuite database of individual process steps.
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5.2.2.1 Building the process table
1. Click Start…Programs…IntelliSuite…IntelliFab
2. Click File…Open Database
Fig 9: Process Flow
3. Click Construct……. Visualize
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Fig 10: Pressure Sensor Model
5.2.3 ANALYSIS
Click Start…Programs…IntelliSuite…ThermoElectroMechanical
Click File…Open
Select prsnsrboss.save from the Training\prsnsrboss directory. Click Open.
5.2.3.1 Simulation Setting
Click Simulation…Simulation Setting
Set the Calculation Type to Static and the Analysis Type to Stress/Displacement. In
the Piezo section of the window, check the box next to Piezoresistive – Transducer
Assembly.
5.2.3.2 Boundary Conditions
Click Boundary…Fixed
Select the bottom face of the model.
5.2.3.3 Material properties
The resistivity values of the membrane and the resistor must be adjusted.
Click Material…Check/Modify
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Select the green (membrane) entity
Double Click RESIST
Set the resistivity to 2.5 ohm.cm. Click OK twice.
The initial resistivity of the wire must then be set. Select the yellow (resistor) entity
Double Click RESIST
Set the resistivity to 5e-5 ohm.cm. Click OK twice.
Piezoresistive properties must now be applied to the resistor wire to define how the
wire resistance will change as a function of strain.
Click Material…Define Piezo-resistive Material
Select the yellow (resistor) entity. Click OK to accept the default values.
Fig 11: Piezoresistive properties dialog box
5.2.3.4 Transducer analysis (pressure = 0)
For the initial simulation, no pressure will be applied, so that the baseline electrical
response of the wire can be measured. The stresses in the full transducer model must
be calculated first (even if there will be no external loading applied).
Click Analysis…Start Static Analysis
All results should be zero (0).
5.2.3.5 Prepare resistor sub model
The piezoresistive analysis can now be set up.
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Click Mesh…Extract Resistor Mesh
Only the resistor wire should now be shown in the software window, as in Figure 16.
Fig 12: Piezoresistor model
Refine the resistor mesh
Click Mesh…Auto
Enter a maximum mesh size of 5 μm.
Apply electro thermal loads
Click Loads…Current…Face
Select the left (input) electrical contact face and enter a value of 1e-3 A/μm2. This
corresponds to a 5 mA current.
Click Loads…Voltage…Face
Select the right (output) electrical contact face and enter a value of 0 V. This will
serve as the reference voltage for the solution.
Click Loads…Temperature…Face
Select the bottom face of the wire and enter a value of 20 deg C. This represents a
“heat sink” boundary condition, in which the wire sits on the membrane, which is
always at 20 deg C.
5.2.3.6 Resistor analysis
Click Analysis…Start Static Analysis
When the simulation is finished,
Click Result…Potential
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 13: Electrical potential
The potential at the input is 1.18892V. As the current was 5 mA, this corresponds to a
resistance of 237.784 Ohm.
5.2.3.7 Transducer analysis (pressure = 11 kPa)
The second simulation will use the same model and properties, this time with a 11 kPa
pressure load applied to the top of the membrane. To return to the model of the entire
device,
Click Simulation…Piezo-resistive…Show Transducer
Click Simulation…Simulation Setting
Set the Analysis Type to Stress/Displacement. Click OK.
Loads
Click Loads…Pressure…Face
Select the top face of the model and enter a pressure of 11 kPa.
Click Analysis…Start Static Analysis
View the results (Z displacement, Stresses, etc.).
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 14: Z-displacement results
The piezoresistive analysis must now be set up again with the new stresses.
5.2.3.8 Resistor analysis
We can now run the piezoresistor analysis again without any additional setup
required.
Click Simulation…Piezo-resistive…Show Resistor
Click Analysis…Start Static Analysis
When the simulation is finished,
Click Result…Potential
Fig 15: Electrical potential
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
The potential at the input is 1.18915 V. As the current was 5 mA, this corresponds to
a resistance of 237.83 Ohm.
6. RESULTS AND DISCUSSIONS
6.1 Diaphragm Analysis Using TEM Solver
Finite Element Analysis was performed for the square diaphragm structure, which is
of interest in this work. Diaphragm 600 μm long and 600 μm wide was considered. A
boss at the centre of the diaphragm with 120 x 120 x 30 μm was also considered as
required for low-pressure to maintain linearity.
6.1.1 Boundary Conditions
The Boundary conditions imposed for FEA are.
1. Fixing the Bottom face of the Die.
2. Applying pressure load at the top of the diaphragm
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6.1.2 Material properties
Isotropic material properties were used for all the TEM simulations on diaphragm.
This can be justified for the silicon substrate, as illustrated by Chen et.al. There is
only 3 % difference in stress between the results of isotropic and anisotropic
modelling on (100) silicon substrate. It was hence concluded that isotropic material
properties are a good approximation for modelling (100) silicon. For this analysis
Young’s Modulus of 169 GPa and a Poisson’s ratio of 0.23 was used for silicon.
The sidewall angle formed due to anisotropic etching on silicon during bulk
micromachining is ignored during simulations. As stated in Table 1, the diaphragm
structure is designed for the 11-18 kPa pressure range. Analysis was performed even
for higher pressure to determine the over pressure performance of the structure. The
uniform pressure load was applied on the Diaphragm.
6.2 Results
6.2.1 Deflection and Stress
The following are the results for 600 * 600 μm square diaphragm, 5 μm thick and a
boss
of 120 x 120 x 30 μm for uniform pressure load of 11 kPa.
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Fig 16: Deflection of the bossed diaphragm to uniform pressure of 11 kPa
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 17: 3-D Result plot of Stress along XX
The deflection and stress in X-direction of the diaphragm for the given
range of pressures is tabulated in Table 4.
Sl. No. Load Applied
(kPa)
Deflection in
microns
Stress in x-
direction(MPa)
1 11 0.6554 39.04
2 12 0.72009 41.98
3 13 0.76582 46.904
4 14 0.8247 50.51
5 15 0.88363 54.12
6 16 0.94254 57.78
7 17 1.0014 61.33
8 18 1.06037 64.944
Table 4: Results of deflection and stress of bossed diaphragm for various
pressures (sensor output).
Table 5: Results of deflection and stress of bossed diaphragm for various pressures
(Ideal)
Sl. No. Load Applied
(kPa)
Deflection in
microns
Stress in x-
direction(MPa)
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Deflection vs Pressure
0.5
0.6
0.7
0.8
0.9
1
1.1
11 12 13 14 15 16 17 18
Pressure (kpa)
Def
lect
ion
(m
icro
ns)
ideal
sensor output
Stress vs Pressure
0
10
20
30
40
50
60
70
11 12 13 14 15 16 17 18
Pressure (kpa)
Str
ess
(Mp
a)
ideal
sensor output
Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
1 11 0.6614 36.288
2 12 0.716 38.88
3 13 0.771 41.472
4 14 0.826 44.06
5 15 0.8819 46.656
6 16 0.9371 49.248
7 17 0.9923 51.84
8 18 1.047 54.432
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 18: Deflection and Stress Vs Applied pressure
6.2.2 Modal Analysis
Modal analysis determines the vibration characteristics (natural frequencies and mode
shapes) of a structure or a machine component while it is being designed. It also can
be a starting point for another, more detailed, dynamic analysis, such as a transient
dynamic analysis, a harmonic response analysis.
Fig 19: Modal Values
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Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Fig 20: First 4 modes shapes of Bossed diaphragm
6.3 Voltage output calculations
Output voltage can be calculated by standard equations. Assuming an average stress
of σmax/4 over the resistor area, the corresponding value of strain can be calculated
using
Where and E = 169 GPa.
A gauge factor of 80 for diffused silicon (refer table 4) is considered to calculate
ΔR/R
The full-scale output is given by,
Where V is the applied voltage. The output voltage calculations were made by
applying a supply voltage of 3 volts.
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Output Voltage vs Applied Pressure
10
12
14
16
18
20
22
24
11 12 13 14 15 16 17 18
Pressure (kpa)
Ou
tpu
t V
olt
age
(mV
)
Series1
Simulation and Analysis of MEMS Piezoresistive Pressure Sensor
Table 6: Results of output voltage Vs Applied Pressure
Pressure
(Kpa)
σ
(MPa)
σ/4
(MPa)
strain ε
(x 10^-5)
ΔR/R Output
voltage
(mV)
11 39.04 9.76 5.775 0.00462 13.86
12 41.9855 10.496 6.2106 0.004984 14.95
13 46.9044 11.726 6.938 0.0055 16.50
14 50.51 12.627 7.4716 0.00597 17.91
15 54.1205 13.53 8.0059 0.0064 19.20
16 57.728 14.43 8.5396 0.006831 20.49
17 61.3365 15.334 9.073 0.00725 21.75
18 64.9446 16.236 9.607 0.007685 23.05
Fig 21: Output Voltage Vs Applied Pressure
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6.4 Sensitivity of sensor
Sensitivity of a sensor can be calculated using a relation,
S = (6.5)
Where P is the pressure applied.
By substituting the values in the above equation, we get the sensitivity as
CONCLUSION
Micro pressure sensors are the most widely used MEM devices today. A micro
pressure sensor is a device that converts mechanically induced diaphragm
deformations and stresses into electrical signal output. Low-pressure sensors are
originally intended to find its application in intrauterine and intracardiac applications
where these sensors are used to measure the blood pressure of the foetus.
The analysis of MEMS based Low-pressure piezoresistive sensor with bossed
structure was carried out using INTELLISUITETM software. The Dimensions of
diaphragm of final design are: 600 μm long, 600 μm wide and 5 μm thick. The boss at
the centre of the diaphragm is 120 x 120 x 30 μm. The resistors where designed so as
to get maximum output. The position of the resistors was found by considering the
maximum stressed region in the bossed structure.
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Also the resistors of suitable dimensions where designed so that they experience the
maximum stress inducted by the diaphragm into them. The dimensions of resistors
were 600x 8 x 2 μm. The designed pressure sensor satisfies all the specifications that
were initially selected.
In the future work the complete design of the piezoresistors can be done using the
Piezoresistive Analysis module of INTELLISUITETM. Various layout designs can be
simulated to get the maximum output.
REFERENCES
[1] Tai Ran Hsu, “MEMS and Microsystems Design and Manufacture”, Tata Mc-
Graw Hill Edition, Tata Mc-Graw Hill, 2002.
[2] Duane Tandeske, “Pressure Sensors Selection and application”, Marcel Dekker
Inc, 1991
[3] Gad-El-Hak, “MEMS Handbook”, CRC Press, 2002
[4] Thimoshenko and Krieger, “Theory of plates and shells”
[5] Stephen D. Senturia, “Microsystem Design”, Kluwer Academic Publishers, 2001.
[6] IntelliSuite User Training Manual v8.1
[7] “Intellifab Reference Guide” – Manual
[8] “Intellisuite ThermoElectroMechanical Reference Guide” – Manual
[9] Stephen Beeby & Michael Kraft,“ Mechanical Microsensors”, Artech House.
[10] Thesis on Design of Piezoresistive pressure sensor & Development of
Electrochemical Etch stop Technique, Chandrasekar Raju K K, MSRIT.
[11] James J Allen, “Micro Electro Mechanical System Design”, CRC Press, 1999.
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[12] http://mems.sandia.gov/scripts/index.asp
[13] http://www.mems-exchange.org/
[14] http://www.memsnet.org/
[15] IEEE/ASME Journal of MEMS this journal originally edited by W. Trimmer, is
arguably one of the best journal in the field of MEMS
(http://www.ieee.org/organizations/pubs/transactions/jms.htm).
[16]Journal of Microlithography, Micro fabrication, and Microsystems A recent
(2002) Journal from the SPIE (http://www.spie.org/app/Publications/ index.cfm?
fuseaction=journals&type=jm3).
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