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MEMS-module 4-5-converted
Electronic and communication (ECE)
Visvesvaraya Technological University
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MODULE 4
SCALING LAWS IN MINIATURIZATION
Syllabus
Scaling Laws in Miniaturization
4 Introduction
4 Scaling in Geometry
4 Scaling in Rigid-Body Dynamics
4 Scaling in Electrostatic Forces
4 Scaling in Fluid Mechanics
4 Scaling in Heat Transfer
4 Introduction to Scaling
- A successful industrial product requires meeting consumer expectations to be intelligent and multifunctional.
- Sensors, actuators, and microprocessors have to be systematically integrated and packaged in these products.
- The constraints on the size and geometry of the products require miniaturization of these components to improve on physical appearance, volume, weight and economy.
- There are two types of scaling laws applicable to design of microsystems.
- The first type of scaling law is dependent on the size of objects- such as geometry.
- Here the behavior of the objects is governed by the law of physics
- Ex. Scaling law include the scaling of rigid-body dynamics and electrostatic and electromagnetic forces.
- The second type of scaling law involves the scaling of phenomenological behavior of microsystems.
- Here both the size and material properties of the system are involved.
- Ex this is used in thermos fluids in microsystems
4 Scaling in Geometry
- Volume and surface are two physical quantities that are frequently involved in micro device design.
- Volume relates to the mass and weight of device components.
- Ex. thermal inertia is related to the heat capacity of the solid which is a measure of how fast we can heat or cool a solid. This is used to design a thermally actuated device.
- Surface properties are related to pressure and the buoyant forces in fluid mechanics and heat absorption or dissipation by a solid in convective heat transfer.
- To minimize a physical quantity, one must weigh the magnitudes of the possible consequences of the reduction on both the volume and surface of the particular device.
- Equal reduction of volume and surface of an object is not normally achievable in a scale down process.
- Consider the example of a solid of rectangular geometry having 3 sides a>b>c.
Solution: the torque required to turn the mirror about the y-y axis is related to mass moment of inertia of the mirror Iyy, expressed as
Where M= mass of the mirror and C= width of the mirror Since the mass of the mirror is M = ρV = ρ(bct), Where ρ= mass density of the mirror material, the mass moment of inertial of the mirror is
The mass moment of inertial of the mirror with a 50 % reduction of the size becomes
A reduction of a factor of 32 is achieved in mass moment of inertia, giving 50% reduction of dimension.
4 Scaling in Rigid-Body Dynamics
Forces are required to make parts move, and power is the source for the generation of forces.
Inertia decides the amount of force required to move a part and how fast movements can be achieved and stopped.
The inertia of a solid is related to its mass and the acceleration required to initiate or stop the motion of a component.
When minimized, the effect of reduction in the size on the power P, force F and pressure p and the time t required to deliver the motion has to be seen
4.3 Scaling in Dynamic Forces
- If a solid moves from one position to another, the distance that the solid travels, S, is S α l, where l stands for the linear scale. The velocity v =s/t
- From particle kinematics, wkt
####### •
4.3 the Trimmer Force Scaling Vector
- Trimmer proposed a Force scaling vector F which is a unique matrix related to parameters of acceleration a, time t and power density P/V 0 required for scaling of systems in motion
####### •
- Using this the scaling laws for rigid body dynamics is established
Ex.
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- This table is useful in scaling down devices in a design process
####### 4 SCALING IN ELECTROSTATIC FORCES
- Consider the configuration of a parallel plate capacitor.
- The electric potential energy induced in the parallel plates is
####### •
####### •
- The above breakdown voltage V varies with the gap between the two plates as per paschen effect.
- Fig 6 shows that the breakdown voltage V drops drastically with increase in d for d<5μ m.
- It decreases after the gap widens from d>5μ m.
- Voltage variation reverses at d ͌ 10μ m.
- The breakdown voltage increases linearly as gap increases.
- We can say that applied voltage Vαd or in scaling Vαl 1 for the working range of d˃ 10 μ m
- The scaling of is neutral, so α
- The electrostatic potential is expressed
####### •
####### •
- Here the gap d is constant and
- Fd α l 2 for the normal force component
- Fw α l 2 for the force component along the width
- FL α l 2 for the normal force component along the length
- So, a reduction by a factor of 10 reduces the electrostatic forces by 100
Basics of fluid mechanics
Many of the MEMS devices involve moving fluids in both liquid and gaseous forms.
- Mechanical designs of these systems requires the application of principles of fluid dynamics and heat transfer.
Fluids in motion are called fluid dynamics and at rest is called fluid statics.
- There are two types of fluids namely non-compressible fluids ex. Liquids and compressible fluids ex. Gases.
Fluids are aggregation of molecules.
- These molecules are closely spaced in solids, widely spaced in liquids and in gases they are loosely spaced.
These molecules are feely moving in liquids unlike solids. So liquids have volume and no shape.
Solids can resist any shear force or shear stress without moving.
Fluids have viscosity that causes friction when they are set in motion.
Viscosity is a measure of fluid’s resistance to shear when the fluid is in motion.
Hence a driving force if needed to make a fluid flow in channels
A continuum fluid is a fluid with its properties continuously varying in space
Fluids can be put into motion even by a slight shear force.
The induced shear strain is expresses as angle θ
This shear deformation is considered possible by a relative motion of a pair of plates placed at the top and bottom of the bulk fluid
####### ER
The relative motion of the plates represents a shear force which causes the fluid flow.
- The associate shear stress τ is considered proportional to the rate of change of induced shear strain θ given by
The proportional constant μ is called the dynamic viscosity of the fluid
Fluids that exhibit such linear relationship are called Newtonian fluids.
6 SCALING IN FLUID MECHANICS
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Fluids flow under the influence of shear forces or shear stresses and the continuum fluid mechanics equations breaks down at submicrometer and nanoscales
The breakdown is due to the capillary effect
Consider the figure 6.
The pressure drop over the length L is computed using Hagen-Poiseuille law as
The rate of volumetric flow of the fluid Q is expressed as
####### •
- The pressure drop for a section of a capillary tube of length L is computed as
####### •
- The scaling laws for fluid flows in capillary tubes are derived as for volumetric flow and
for pressure drop per unit length, whre a is the radius of the tube.
Ex.
Soln: wkt volumetric flow where a is the radius of the tube.
So volumetric flow reduces by 10 4 = 10000 times
Also pressure drop per unit length is so this increases by 10 2 = 100 times.
When the radius of the conduit s very small, capillary effect appears.
This is due to surface tension of the fluids.
The pressure required to overcome the surface tension is
So, the pressure drop per unit length of a liquid is
Ex. What will happen to the pressure drop in the fluid in above ex. If the tube radius is microscale?
Soln: the pressure drop per unit length of the tube, from the scaling law in equation increases 1000 times with a 10 times reduction of the tube radius.
The situation is one order of magnitude more severe than the case in meso or macroscale.
- Due to adverse effect in scaling down, special pumping techniques such as piezoelectric, electro-osmotic, electrohydrodynamic pumping are used
- These are based on surface pumping forces. Ex. Piezoelectric pump.
- Here the forces generated on tube wall is used to drive the fluid flow is used.
- The surface force F, proportional to the surface area of the inner wall of the tube scales favorably.
- This surface area of the inner wall of the tube is S= 2πaL and the volume of the fluid is V= πa 2 L
- The surface area to volume ration S/V = 2/a.
- Scaling down the tube radius will result in the increase of the surface force available for pumping the unit volume of the fluid
####### 6 SCALING IN HEAT TRANSFER
In microsystems, heat transfer is an essential part of the design.
Heat transfer is done by conduction, convection and by radiation in laser treatments.
This heat conduction in solids is governed by the Fourier Law
For one dimensional heat conduction along the x co-ordinate, we have
####### •
- Where qx is the heat flux along x coordinate, k is the thermal conductivity of the solid and T(x,y,z,t)is the temperature field in the solid in a Cartesian coordinate system at time t.
- The heat conduction in a solid is
####### •
- From the above equation, the scaling law for heat conduction for solids in meso and microscales is Qα l 1 (A is replaced by α)
- So the reduction in size leads to the decrease of total heat flow in a solid
6.6.1 Scaling in Termal Conductivity in Submicrometer Regime
Thermal conductivity k in solids is estimated by
Here λ α 1/ρ, where ρ is the mass density of the solid with an order similar to volume i., l 3
The scaling of heat flow in a solid in the sub micrometer regime is obtained by combining the above two equations.
####### •
- So, a reduction in size of 10 would lead to a reduction of total heat flow by 100
6.6.1 Scaling in Effect of Heat Conduction in Solids of Meso and Micro scales
- F 0 is the Fourier number with has no dimension
- It is used to determine the time increments in a transient heat conduction analysis
####### •
- Here α is the thermal diffusivity of the material
- t is the time for heat to flow across the characteristic length L
- Fourier number is the ratio of the rate of heat transfer by conduction to the rate of energy storage in the system.
- From the above equation, the scaling in time for heat conduction in a solid is
####### •
- Where both F 0 and α are constants Ex. Estimate the variation of the heat flow and the time required to transmit heat in a solid with a reduction of size by a factor of 10 Soln: from the equations
and the total heat flow and the time required for heat transmission are both reduced by 10 2 =100 times with a reduction of size by a factor of 10
6.6 Scaling in Heat Convection
- There exists the boundary layers at the interfaces of solids and fluids.
- Heat transfer in fluids is in the mode of convection governed by Newton’s cooling law expressed as
####### •
- Heat transfer h depends on the velocity of the fluid
- This does not play a significant role in scaling the heat flow.
- The total heat therefore depends on the cross-sectional area A, of the order of l 2
- Therefore the scaling of heat transfer in convection is for fluids in meso and micro regimes.
- Consider only the convective heat transfer of gases in the regime
Module 5 Mems and MicroSystems(15EC831)
66
Syllabus
Module 5
OVERVIEW OF MICRO
MANUFACTURING
5 Introduction
5 Bulk Micromanufacturing
5.2 Overview of Etchants
5.2 Isotropic and Anisotropic Etching
5.2 Wet Etchants
5.2 Etch Stop
5.2 Dry Etching
5.2 Comparision of Wet versus Dry Etching
5 Surface Micromachining
5.3 General Description
5.3 Process in General
5.3 Mechanical Problems Associated with Surface Micromachining
5 The LIGA process
5.4 General Description of the LIGA Process
5.4 Materials for substrates and Photoresists
5.4 Electroplating
5.4 The SLIGA Process
5 Summary of Micromanufacturing
5.5 Bulk Micromanufacturing
5.5 Surface Micromachining
5.5 The LIGA Process
Module 5 Mems and MicroSystems(15EC831)
67
5 Introduction
- Traditional fabrication techniques used in the manufacturing are o Machining o Drilling o Milling o Forging o Welding o Casting o Molding o Stamping o Peening
- These traditional fabrication techniques are not used in manufacturing of MEMS and microsystems due to the extreme small size.
- Some of these techniques are used in packaging of MEMS and microsystems products
- The techniques used to produce products like microsensors, accelerometers and actuators are micromachining or micromanufacturing
- There are three micromachining techniques used namely o Bulk manufacturing o Surface micromachining o LIGA process
- LIGA is a German acronym for lithography, electroforming and plastic molding
- New techniques like Laser drilling and machining are also getting popular
5 BULK MICROMANUFACTURING
- Bulk micromanufacturing or micromachining involves the removal of materials from the bulk substrates (silicon wafers) to form 3D geometry of the microstructures
- Physical or chemical techniques either by dry or wet etching are the solutions.
- Orientation-independent isotropic etching or orientation –dependent anisotropic etching is used in bulk micromanufacturing
5.2 Overview of Etching - Etching is the exposure of a substrate covered by an etchant protection mask to chemical etchants as in fig
MEMS-module 4-5-converted
Course: Electronic and communication (ECE)
University: Visvesvaraya Technological University
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