The coefficient of thermal expansion (α) at 300K is 2.616.
Thermomechanics relates mechanical effects (stresses, strains, and deformation) induced by thermal forces (temperature difference or heat flow) – common phenomena in microsystems.
Linear Elastic Fracture Mechanics (LEFM) is a theory developed in 1963 by the US naval research institute to assess the integrity of structures by formulating the stress/strain fields near tips of cracks in elastic solids.
An ion is an electrically charged atom or molecule.
Doping is the process of turning semiconductors into electrically conducting materials by altering the number of electrons in their atoms through the implantation of foreign materials called dopants.
Dissociation is when a molecule of the medium breaks down into smaller fragments, with or without ionization.
An n-type semiconductor is created by doping silicon with elements like arsenic or phosphorus, which have five electrons in their outer orbit, resulting in an extra electron and increased conductivity.
Electro-osmotic Pumping is used to move electrically neutral fluids through channels of extremely small cross sections. The condition is that the walls of the conduit or channel must have attached, immobile charges. The gradient of the concentration of electric charges decreases toward the center of the conduit, forming a dual layer of fluid with varying concentration of charges. The charges in the double layer can be moved with the applied electric charges along the longitudinal direction.
The approximate electrical resistivity of Germanium (Ge) is 10^1.5 Ω-cm.
Smaller and more elements in a discretized model produce better results because the model is closer to the original continuum.
A bi-atom molecule involves two different kinds of atoms. An example is a water molecule (H2O).
Plasma is used to 'knock out' substrate materials at desired localities in a 'dry etching process' or to carry chemicals in the chemical vapor deposition (CVD) process.
These films usually are in the order of sub-micrometer or a few micrometers thick.
In the electrolysis of NaCl, the chemical reaction 2NaCl → 2Na + Cl2 occurs, where positively charged Na ions move toward the negatively charged electrode (cathode) and negatively charged Cl ions move toward the positively charged electrode (anode).
Common geometries of MEMS components include beams, plates, tubes, and channels.
The maximum deflection in the silicon square plate is 43 μm.
The approximate electrical resistivity of Silver (Ag) is 10^-6 Ω-cm.
The mass of a proton is 1.67x10^-24 g.
A donor is an atom that gives up electrons during the doping process, making the semiconductor more conductive.
During Excitation, the molecules hold together but absorb energy from the fast electrons present in the chamber, raising them to an excited electronic state.
An electrolyte is a solution that conducts electric current.
A bi-metallic strip will bend into a curved shape when subjected to a temperature rise if t2 > t1 and α2 > α1.
Micro valves are designed using Computational Fluid Dynamics (CFD).
The term for the deflection of a plate in static bending analysis is w(x,y).
Channels of square, rectangular, and trapezoidal cross-sections.
The coefficient of linear thermal expansion (α) is a material property that measures the fractional change in length of a material per degree change in temperature.
The formula for the maximum radial stress (σrr) is (σrr)max = 3W / (4πh^2).
The formula for the maximum deflection (wmax) is wmax = α(pb^4 / Eh^3).
The specific heat (c) of a material at 400K is 0.785 J/g-K.
Some commercial FEM codes used in stress analysis include ANSYS, ABAQUS, COMSOL, IntelliSuites, and MEMCad.
The diameter of the outer orbit of an atom is approximately 1 to 3x10^-10 m, or 0.1 to 0.3 nm.
The results from individual elements are 'assembled' to give results of the overall structure.
A common practice in MEMS and microsystems fabrication is to deposit thin films of a variety of materials onto the surface of silicon substrates.
Intrinsic stresses in thin films are normally determined by empirical means.
The radius of curvature (ρ) of a bi-metallic strip can be obtained using the expression: 1/ρ = 6(1 + m²)(α1 - α2)∆T / [h³(3(m + 1)² + (1 + mn)m² + 1/mn)], where m = t1/t2 and n = E1/E2.
The maximum stress (σmax) in a square plate with fixed edges is given by the formula: σmax = 0.308 * (p * a^2 / h^2).
The expression for the bending moment Mx in a thin plate is Mx = -D (∂²w/∂x²) + ν (∂²w/∂y²).
Component geometry unique to MEMS and microsystems includes multi-layers with thin films of dissimilar materials.
Thermomechanics is the study of the effects of temperature on the mechanical behavior of materials, which is crucial in the design of microsystems that operate under varying thermal conditions.
The diameter (D) of the circular diaphragm is 600 μm.
Intermolecular forces are forces between molecules in a matter that can be either attractions or repulsions, determined by the distances between the molecules. They are often referred to as Van der Waals forces and are chemical and electrostatic in nature.
No, silicon and silicon compounds have strong creep resistance and do not have a creep problem.
An Electron Gun, consisting of a cathode heater, anode, and electrode, releases electrons to ionize a medium such as H2 or He gas.
An anion is an atom that receives extra electrons during the doping process, becoming negatively charged.
Recombination is the process where electrons and positive ions combine to form a molecule.
The two principal applications are electrolysis in electroplating, electroforming, and electrochemical machining, and electrohydrodynamics for pumping fluids in microfluidics.
Electrohydrodynamics (EHD) is the principle of moving fluids in micro channels or passages by ionizing the fluid first using electric potential, causing the ionized fluid to move in the direction of the preferred electrodes, achieving a pumping effect.
The Navier-Stokes equations are used for fluid dynamics analysis.
The moment of inertia for strip 1 is I1 = t1³/12 and for strip 2 is I2 = t2³/12.
Examples include microrelays, gripping arms in a micro tong, and beam springs.
The strain (ε) at the center of a square plate with fixed edges is given by the formula: ε = (1 - 3ν) * σ / E.
Thermal conductivity (k) is a material property that measures a material's ability to conduct heat.
The expression for the maximum stress σrr in a circular plate with edge fixed is σrr_max = 3W/(4πh²).
The modulus of elasticity (E) of silicon used is 190,000 MPa.
The geometry of the plate significantly affects the induced maximum stresses and deflections. For example, a circular plate has a maximum stress of 7000 MPa and deflection of 55.97 μm, a rectangular plate has a maximum stress of 7293 MPa and deflection of 21.76 μm, and a square plate has a maximum stress of 9040 MPa and deflection of 43.00 μm.
Polymer materials and many solder alloys commonly have a creep problem.
Ionization is the process of producing ion beams, which can be achieved by electrolysis or electron beams.
Diffusion processes may take place in gas-gas (e.g., gas mixing and air pollution), liquid-liquid (e.g., spread of a drop of ink in a pot of clear water), gas-solids (e.g., oxidation of metal), and liquid-solids (e.g., corrosion of metal in water).
The purpose of developing an FE mesh is to discretize the structure.
An electrolytic cell is the vessel that holds the electrolyte.
The maximum deflection (wmax) is calculated using the formula: wmax = -α * (p * b^4 / E * h^3). For the given values, wmax = -0.0277 * (20x10^-6) * (376x10^-6)^4 / (190000x10^6) * (13.887x10^-6)^3 = -21.76x10^-6 m.
Bending induced deformation generates signals for sensors and relays using beams and plates.
Mass density (ρ) is a material property that measures the mass per unit volume of a material.
Static Bending of Thin Plates refers to the deformation of thin, flat materials under static loads, which is important in the structural analysis of microsystems.
The formula for the maximum circumferential stress (σθθ) is (σθθ)max = 3W / (4πh^2).
The coefficients α and β are used to determine the maximum deflection and maximum stress in a rectangular plate with fixed edges.
Temperature affects Young’s modulus (E), plastic yield strength (σy), ultimate tensile strength (σu), thermal conductivity (k), specific heat (c), and the coefficient of thermal expansion (α).
Creep deformation is when a structure changes its shape with time without an increase in mechanical load.
A positive ion is an atom with more protons than electrons.
A single atom molecule is made up of only one type of atom. An example is a silicon (Si) molecule.
General information required includes the profile of the structure geometry and the establishment of coordinates.
Electrochemistry is the study of chemical reactions caused by the passage of an electric current.
Electro-osmosis is a process used for driving capillary flow of fluids in microfluidic systems.
Newton’s law is used for dynamic and vibration analysis.
Solids expand when they are heated up and contract when they are cooled down.
Pressure sensors using beams vibrating at resonant frequencies.
The shear modulus of elasticity (G) is a material property that describes the material's response to shear stress. It is defined as the ratio of shear stress to the shear strain.
The expression for the bending moment My in a thin plate is My = -D (∂²w/∂y²) + ν (∂²w/∂x²).
Electrochemistry and Electrolysis involve the study of chemical processes that cause electrons to move, which is essential in applications like battery technology and material deposition.
The expression for the maximum deflection wmax in a circular plate with edge fixed is wmax = (3W(m² - 1)a²)/(16πDm²h²).
The calculated minimum thickness (h) of the circular diaphragm is 13.887 x 10^-6 m.
The three serious effects are: 1. Effect on Material Properties, 2. Creep Deformation, 3. Thermal Stresses.
The three types of engineering materials frequently used are electrical conducting materials, electrical insulation or dielectric materials, and semiconducting materials.
Ionization is the process of producing ions.
The diffusion process is the introduction of a controlled amount of foreign material into selected regions of another material.
Doping can alter a semiconductor's resistance to chemical or physical etching, which is a common technique in microfabrication.
Plasma is produced in a plasma generator.
Electrolysis is the process involving the production of chemical changes in a chemical compound or solution by oppositely charged constituents moving in opposite directions under an electric potential difference.
The linear theory of elasticity is used for stress analysis.
The formula for flexural rigidity (D) of a thin plate is D = Eh³ / 12(1-ν²), where E is Young’s modulus and ν is Poisson’s Ratio.
Proper functioning of microsystems requires the application of engineering mechanics principles.
Examples include diaphragms in pressure sensors and plate-springs in microaccelerometers.
Ultimate strength (σu) is the maximum stress that a material can withstand while being stretched or pulled before breaking.
Specific heat (c) is a material property that measures the amount of heat required to change the temperature of a unit mass of the material by one degree Celsius.
The yield strength of silicon (σy) used is 7000 MPa.
The formula for the minimum thickness (h) is h = 3W / (4π(σy)).
The maximum stress in the silicon square plate is 9040 MPa.
Fracture mechanics was first introduced by Griffith in 1921 in the study of crack propagation in glasses using the energy balance concept.
A negative ion is an atom with more electrons than protons.
Continuum mechanics theories and principles are applied to individual elements.
Plasma is a gas containing high energy ions that carries electrical charges, containing approximately equal numbers of electrons and positively charged ions, making it a mixture of neutral ionized gas.
Another major source that induces stresses in thin films is 'residual stresses' resulting from fabrication processes.
Fourier's law is applied for heat conduction analysis.
Young’s modulus (E) is used to calculate the flexural rigidity (D) of thin plates.
The maximum stress (σyy)max is calculated using the formula: (σyy)max = β * (p * b^2 / h^2). For the given values, (σyy)max = 0.4974 * (20x10^6) * (376x10^-6)^2 / (13.887x10^-6)^2 = 7292.8x10^6 Pa.
The stress (σ) at the center of a square plate with fixed edges is given by the formula: σ = 6 * p * (m + 1) * a^2 / (47 * m * h^2).
Doping of Semiconductors is the process of adding impurities to semiconductor materials to change their electrical properties.
The expression for the maximum bending stress σyy in a thin plate is σyy_max = 6(My_max)/h².
Fracture Mechanics is the study of the propagation of cracks in materials, which is essential for predicting failure in microsystems.
The formula for the maximum stress (σyy) is (σyy)max = β(pb^2 / h^2).
Electrophoretic Pumping is a method used to separate minute foreign particles from the bulk fluid, widely used in biomedical and pharmaceutical industries. The movement of ions of the particles in a heterogeneous medium is prompted by an applied high voltage electric field. The ions with different charges move in opposite directions along the channel in the separation process. When the flow is fully developed, the ions in the stream can automatically separate themselves by their inherent electro-osmotic mobility under the influence of the applied electric field.
The approximate electrical resistivity of Oxide Glass is 10^9 Ω-cm.
A molecule is a particle made of atoms interconnected by deformable bonds. Molecules can consist of single atoms or multiple kinds of atoms.
The major applications of diffusion in microfabrication include doping of semiconducting materials to produce p-n junctions and the production of piezoresistors, oxidation of semiconducting materials, and chemical vapor deposition processes.
The user usually specifies the desirable density of nodes and elements in specific regions, placing denser and smaller elements in parts of the structure with abrupt changes in geometry where high stress/strain concentrations exist.
The two principal applications of Electrohydrodynamics (EHD) are electro-osmotic pumping and electrophoretic pumping.
The governing differential equation for the induced deflection, w(x,y), of thin plates is: ∂²/∂x² + ∂²/∂y² ∂²w/∂x² + ∂²w/∂y² = p/D.
Mechanics is a branch of engineering science that studies the relationship between the applied forces and the resulting motions.
Poisson's ratio (v) is a material property that describes the ratio of the transverse strain to the axial strain in the material when it is stretched.
Capillary tubes in microfluidic network systems with electro-kinetic pumping, such as electro-osmosis and electrophoresis.
Plasma Physics and Its Applications study the properties of plasma, a state of matter similar to gas but with charged particles, and its use in various technologies including microfabrication.
Thin-Film Mechanics involves the study of mechanical properties and behaviors of thin layers of material, which are often used in microsystems and microelectronics.
The Poisson's ratio (ν) of silicon used is 0.25.
The Finite Element Method (FEM) is a powerful tool in stress analysis of MEMS and microsystems of complex geometry, loading, and boundary conditions. It involves discretizing a structure made of continuum into a finite number of 'elements' interconnected at 'nodes.'
The mass of an electron is 9.11x10^-28 g.
Ionization is the process where an electron is knocked loose from the atom of the medium, resulting in a positively charged molecule or ion.
A p-type semiconductor is created by doping silicon with an element like boron, which has three electrons in its outer orbit, resulting in an electron deficit and the creation of a 'hole' for an electron.
The imbalance of electrons in a doped semiconductor facilitates the flow of electrons, thereby increasing the material's conductivity.
The total stress in thin films is expressed as: σ = σ_th + σ_m + σ_int, where σ_th = thermal stress, σ_m = due to mechanical loads, and σ_int = intrinsic stresses.
Fick’s law is used for diffusion analysis.
Poisson’s Ratio (ν) represents the ratio of transverse strain to axial strain in the material of the thin plate.
Young's modulus (E) is a material property that measures the stiffness of a solid material. It is defined as the ratio of stress to strain in the linear elasticity regime of a uniaxial deformation.
Yield strength (σy) is the stress at which a material begins to deform plastically. Beyond this point, the material will deform permanently and will not return to its original shape.
Diffusion Processes in Microfabrication involve the movement of particles from regions of high concentration to regions of low concentration, which is crucial in the manufacturing of microscale devices.
Von Mises stress is a scalar stress value derived from the stress tensor that is used to predict yielding of materials under complex loading conditions. It is often compared with the yield strength (σy) for plastic yielding and with the ultimate strength (σu) for predicting rupture.
Quantitative assessment of induced stresses in thin films is difficult because the films are so thin that unusual forces such as molecular forces (or van der Waals forces) become dominant, and there is no reliable way to assess such forces quantitatively at the present time.
A key advantage of electrohydrodynamic pumping is that it involves no moving mechanical parts such as rotating impellers, making it effective for moving fluids in extremely small channels.
Thermal stress (σT) in solids with both ends fixed is given by the formula -EƐT = -αE∆T, where E is Young's modulus, ƐT is thermal strain, ∆T is the temperature rise from reference (room) temperature, and α is the coefficient of thermal expansion.
Motion can either involve rigid body motion or deformation of solids.
The maximum deflection (wmax) at the center of a square plate with fixed edges is given by the formula: wmax = -0.0138 * (p * a^4 / E * h^3).
The study of Atomic and Molecular Structure of Matter involves understanding the arrangement and interactions of atoms and molecules in materials.
The expression for the maximum bending stress σxx in a thin plate is σxx_max = 6(Mx_max)/h².
The expression for the maximum stress σθθ in a circular plate with edge fixed is σθθ_max = 9W/(4πh²).
The successful design of Microsystems requires knowledge of Mechanical, Electrical, Materials and Chemical Engineering, Physics, Chemistry and Biology, and Micromanufacturing processes.
The expression for the bending moment Mxy in a thin plate is Mxy = D(1 - ν) (∂²w/∂x∂y).
The expression for the maximum bending stress σxy in a thin plate is σxy_max = 6(Mxy_max)/h².
The applied pressure (p) used is 20 MPa.
