Simulation and Analysis of MEMS Piezoresistive Pressure Sensor

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

BMS College Of Engineering 1


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



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.



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.



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.



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



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,



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



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



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.



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



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.



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.



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



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



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.



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))



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.



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



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.



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



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.



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



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



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.



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.



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.



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.



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.



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



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



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



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



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



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



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



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



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



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



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



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.



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



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



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.



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



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



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.



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


When the simulation is finished,

Click Result…Potential



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.


View the results (Z displacement, Stresses, etc.).



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


When the simulation is finished,

Click Result…Potential

Fig 15: Electrical potential



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



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.



Fig 16: Deflection of the bossed diaphragm to uniform pressure of 11 kPa



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)


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


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



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



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.


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


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



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.



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.



[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).


Documents

Simulation and Analysis of MEMS Piezoresistive Pressure Sensor