# Materials Science and Engineering/Progression of Topics

## The Electron

### The Electron as a Particle

#### Conductivity

Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density ${\displaystyle \mathbf {J} }$  to the electric field strength ${\displaystyle \mathbf {E} }$ :

${\displaystyle \mathbf {J} =\sigma \mathbf {E} }$

##### Ohm's Law

Ohm's law states that,at constant temperature in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them.

The mathematical equation that describes this relationship is:

${\displaystyle I={\frac {V}{R}}}$

where I is the current in amperes, V is the potential difference between two points of interest in volts, and R is a circuit parameter, measured in ohms (which is equivalent to volts per ampere), and is called the resistance. The potential difference is also known as the voltage drop, and is sometimes denoted by U, E or emf (electromotive force) instead of V.

##### The Hall Effect

The Hall effect refers to the potential difference (Hall voltage) on the opposite sides of an electrical conductor through which an electric current is flowing, created by a magnetic field applied perpendicular to the current. Edwin Hall discovered this effect in 1879.

### The Electron

#### The Electron in a Potential

##### Particle in a Box

Finite Potential

Infinite Potential

## Model of the Atom

### Models Before 1920

#### Cubical Atom (1902)

The cubical atom was an early atomic model in which electrons were positioned at the eight corners of a cube in a non-polar atom or molecule.

#### Plum-Pudding Model (1904)

In this model, the atom is composed of electrons (which Thomson still called "corpuscles," though G.J. Stoney had proposed that atoms of electricity be called electrons in 1894), surrounded by a soup of positive charge to balance the electron's negative charge, like negatively-charged "plums" surrounded by positively-charged "pudding".

#### Rutherford Model (1913)

The Rutherford model or planetary model was a model of the atom devised by Ernest Rutherford.

#### Bohr Atom (1913)

In atomic physics, the Bohr model depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus — similar in structure to the solar system, but with electrostatic forces providing attraction, rather than gravity.

#### Sommerfeld Model

Several enhancements to the Bohr model were proposed; most notably the Sommerfeld model or Bohr-Sommerfeld model, which suggested that electrons travel in elliptical orbits around a nucleus instead of the Bohr model's circular orbits.

## Collections of Atoms

### Arrangement in Bulk

#### Types of Materials

##### Glasses

Glass in the common sense refers to soda-lime glass, or any similar substance: a hard, brittle, transparent solid made by fusing soda with lime and cooling rapidly. In the technical sense, glass is any amorphous solid, i.e., any non-crystalline solid.

##### Metals

In chemistry, a metal (Greek: Metallon) is an element that readily loses electrons to form positive ions (cations) and has metallic bonds between metal atoms. Metals form ionic bonds with non-metals. They are sometimes described as a lattice of positive ions surrounded by a cloud of delocalized electrons. The metals are one of the three groups of elements as distinguished by their ionization and bonding properties, along with the metalloids and nonmetals. On the periodic table, a diagonal line drawn from boron (B) to polonium (Po) separates the metals from the nonmetals. Most elements on this line are metalloids, sometimes called semi-metals; elements to the lower left are metals; elements to the upper right are nonmetals.

##### Ceramics

The word ceramic is derived from the Greek word κεραμικός (keramos). The term covers inorganic non-metallic materials which are formed by the action of heat. Up until the 1950s or so, the most important of these were the traditional clays, made into pottery, bricks, tiles and the like, along with cements and glass.

##### Polymers

A polymer is a substance composed of molecules with large molecular mass composed of repeating structural units, or monomers, connected by covalent chemical bonds. The word is derived from the Greek, πολυ, polu, "many"; and μέρος, meros, "part". Well known examples of polymers include plastics, DNA and proteins.

##### Ionic Crystals

An ionic crystal is a crystal consisting of ions bound together by their electrostatic attraction. Examples of such crystals are the alkali halides, including potassium fluoride, potassium chloride, potassium bromide, potassium iodide, sodium fluoride, and other combinations of sodium, caesium, rubidium, or lithium ions with fluoride, bromide, chloride or iodide ions.

##### Intermetallics

Intermetallics or intermetallic compounds is a term that is used in a number of different ways. Most commonly it refers to solid state phases involving metals. There is a "research definition" adhered to generally in scientific publications, and a wider "common use" term. There is also a completely different use in coordination chemistry, where it has been used to refer to complexes containing two or more different metals. Although the term intermetallic compounds, as it applies to solid phases, has been in use for many years, its introduction was regretted, for example by Hume-Rothery in 1955.

##### Semiconductors

A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically. Semiconductors are tremendously important in technology.

##### Composite materials

Composite materials (or composites for short) are engineered materials made from two or more constituent materials with significantly different physical or chemical properties and which remain separate and distinct on a macroscopic level within the finished structure.

#### Bravais Lattice

##### Lattice Centerings
• Primitive centering (P): lattice points on the cell corners only
• Body centered (I): one additional lattice point at the center of the cell
• Face centered (F): one additional lattice point at center of each of the faces of the cell
• Centered on a single face (A, B or C centering): one additional lattice point at the center of one of the cell faces.

### Arrangement of Electrons

• Bloch Theory
• Kronig-Penney Model
• Nearly-free electron approximation
• Tight-binding model
• Density-functional theory
• Triclinic
• Monoclinic
• Orthorhombic
• Tetragonal
• Rhombohedral
• Hexagonal
• Cubic

### Arrangement on Surface

#### Texture

Texture is the distribution of crystallographic orientations of a sample.

#### Surface Reconstruction

Surface reconstruction refers to the process by which atoms at the surface of a crystal assume a different structure than that of the bulk.

## Properties of Atoms

### Electrical Properties

Brillouin Zones

#### Density of States

In statistical and condensed matter physics, density of states (DOS) is a property that quantifies how closely packed energy levels are in a quantum-mechanical system.

#### Resistivity

The electrical resistivity ρ (rho) of a material is given by

${\displaystyle \rho =R{\frac {A}{\ell }}}$

where

ρ is the static resistivity (measured in ohm metres, Ω-m);
R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω);
${\displaystyle \ell }$  is the length of the piece of material (measured in metres, m);
A is the cross-sectional area of the specimen (measured in square metres, m²).

Electrical resistivity can also be defined as

${\displaystyle \rho ={E \over J}}$

where

E is the magnitude of the electric field (measured in volts per metre, V/m);
J is the magnitude of the current density (measured in amperes per square metre, A/m²).

### Mechanical Properties

#### Stress Terms

${\displaystyle \sigma ={\frac {F}{A}}}$

##### Compressive Stress

The stress state when the material (compression member) tends to compact. A simple case of compression is the uniaxial compression induced by the action of opposite, pushing forces. Compressive strength for materials is generally higher than that of tensile stress, but geometry is very important in the analysis, as compressive stress can lead to buckling.

##### Tensile Stress

Tensile stress is a loading that tends to produce stretching of a material by the application of axially directed pulling forces. Any material which falls into the "elastic" category can generally tolerate mild tensile stresses while materials such as ceramics and brittle alloys are very succeptable to failure under the same conditions. If a material is stressed beyond its limits, it will fail. The failure mode, either ductile or brittle, is based mostly on the microstructure of the material.

##### Shear Stress

Shear stress is caused when a force is applied to produce a sliding failure of a material along a plane that is parallel to the direction of the applied force

#### Strength Terms

##### Yield Strength

Yield strength is the lowest stress that gives permanent deformation in a material. In some materials, like aluminium alloys, the point of yielding is hard to define, thus it is usually given as the stress required to cause 0.2% plastic strain.

##### Compressive Strength

Compressive strength is a limit state of compressive stress that leads to compressive failure in the manner of ductile failure (infinite theoretical yield) or in the manner of brittle failure (rupture as the result of crack propagation, or sliding along a weak plane - see shear strength).

##### Tensile Strength

Tensile strength or ultimate tensile strength is a limit state of tensile stress that leads to tensile failure in the manner of ductile failure (yield as the first stage of failure, some hardening in the second stage and break after a possible "neck" formation) or in the manner of brittle failure (sudden breaking in two or more pieces with a low stress state). Tensile strength can be given as either true stress or engineering stress.

##### Fatigue Strength

Fatigue strength is a measure of the strength of a material or a component under cyclic loading, and is usually more difficult to assess than the static strength measures. Fatigue strength is given as stress amplitude or stress range (Δσ = σmax − σmin), usually at zero mean stress, along with the number of cycles to failure.

##### Impact Strength

Impact strength, it is the capability of the material in withstanding by the suddenly applied loads in terms of energy. Often measured with the Izod impact strength test or Charpy impact test, both of which measure the impact energy required to fracture a sample.

#### Engineering Strain

when a uniaxial tensile force is applied to a rod, it causes rod to elongated in the direction of the force such a displacement is called strain.

##### Deformation

Deformation of the material is the change in geometry when stress is applied (in the form of force loading, gravitational field, acceleration, thermal expansion, etc.). Deformation is expressed by the displacement field of the material.

##### Strain

Strain or reduced deformation is a mathematical term to express the trend of the deformation change among the material field. For uniaxial loading - displacements of a specimen (for example a bar element) it is expressed as the quotient of the displacement and the length of the specimen. For 3D displacement fields it is expressed as derivatives of displacement functions in terms of a second order tensor (with 6 independent elements).

##### Deflection

Deflection is a term to describe the magnitude to which a structural element bends under a load.

#### Stress-Strain Relations

##### Elasticity

Elasticity is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress and the resulting strain is directly proportional (up to a certain limit), and a graph representing those two quantities is a straight line.

The slope of this line is known as Young's Modulus, or the "Modulus of Elasticity." The Modulus of Elasticity can be used to determine stress-strain relationships in the linear-elastic portion of the stress-strain curve. The linear-elastic region is taken to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.

##### Plasticity

Plasticity or plastic deformation is the opposite of elastic deformation and is accepted as unrecoverable strain. Plastic deformation is retained even after the relaxation of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low stress. Materials such as metals usually experience a small amount of plastic deformation before failure while soft or ductile polymers will plasticly deform much more.

### Thermodynamic Properties

• T temperature [K]
• ρ density [kg/m3]
• cp specific heat at constant pressure [J/(kg·K)]
• cv specific heat at constant volume [J/(kg·K)]
• μ dynamic viscosity [N/(m²·s)]
• ν kinematic viscosity [m²/s]
• k thermal conductivity [W/(m·K)]
• α thermal diffusivity [m²/s]
• β volumetric thermal expansion coefficient [K-1]
• H enthalpy [J/kg]
• S entropy [J/(kg·K)]
• G gibbs free energy [J/kg]
• p pressure [N/m²]

### Magnetic Properties

#### Diamagnetism

Diamagnetism is a weak repulsion from a magnetic field. It is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. It results from changes in the orbital motion of electrons. Applying a magnetic field creates a magnetic force on a moving electron in the form of F = Qv × B. This force changes the centripetal force on the electron, causing it to either speed up or slow down in its orbital motion. This changed electron speed modifies the magnetic moment of the orbital in a direction opposing the external field.

#### Paramagnetism

Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility). The force of attraction generated by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect. Unlike ferromagnets paramagnets do not retain any magnetization in the absence of an externally applied magnetic field, because thermal motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop to zero when the applied field is removed. Even in the presence of the field there is only a small induced magnetization because only a small fraction of the spins will be oriented by the field.

#### Ferromagnetism

Ferromagnetism is the "normal" form of magnetism with which most people are familiar, as exhibited in horseshoe magnets and refrigerator magnets. It is responsible for most of the magnetic behavior encountered in everyday life. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, and to us today," according to a classic text on ferromagnetism.

#### Antiferromagnetism

In materials that exhibit antiferromagnetism, the spins of electrons align in a regular pattern with neighboring spins pointing in opposite directions. This is a different manifestation of magnetism. Generally, antiferromagnetic materials exhibit antiferromagnetism at a low temperature, and become disordered above a certain temperature; the transition temperature is called the Néel temperature. Above the Néel temperature, the material is typically paramagnetic.

#### Ferrimagnetism

In physics, a ferrimagnetic material is one in which the magnetic moment of the atoms on different sublattices are opposed, as in antiferromagnetism; however, in ferrimagnetic materials, the opposing moments are unequal and a spontaneous magnetization remains.

#### Metamagnetism

Metamagnetism is a physical state of matter characterized by a superlinear increase of magnetization over a narrow range of applied magnetic field.

## Material Processes

### Diffusion

Diffusion is the spontaneous net movement of particles from an area of high concentration to an area of low concentration in a given volume of fluid (either liquid or gas) down the concentration gradient. For example, diffusing molecules will move randomly between areas of high and low concentration but because there are more molecules in the high concentration region, more molecules will leave the high concentration region than the low concentration one. Therefore, there will be a net movement of molecules from high to low concentration. Initially, a concentration gradient leaves a smooth decrease in concentration from high to low which will form between the two regions. As time progresses, the gradient will grow increasingly shallow until the concentrations are equalized.

#### Fick's Law

##### Fick's First Law

Fick's first law is used in steady-state diffusion, i.e., when the concentration within the diffusion volume does not change with respect to time (${\displaystyle \,J_{\mathrm {in} }=J_{\mathrm {out} }}$ ). In one (spatial) dimension, this is

${\displaystyle J=-D{\frac {\partial \phi }{\partial x}}}$

##### Fick's Second Law

Fick's second law is used in non-steady or continually changing state diffusion, i.e., when the concentration within the diffusion volume changes with respect to time.

${\displaystyle {\frac {\partial \phi }{\partial t}}=D\,{\frac {\partial ^{2}\phi }{\partial x^{2}}}\,\!}$

## Processing Materials

### Towards Creation of Electronic, Magnetic, and Optical Devices

#### Deposition

##### Sputtering

Sputtering is a process whereby atoms are ejected from a solid target material due to bombardment of the target by energetic ions. It is commonly used for thin-film deposition, etching and analytical techniques.

##### ALD

Atomic Layer Deposition (ALD) is a gas phase chemical process used to create extremely thin coatings. The majority of ALD reactions use two chemicals, typically called precursors. These precursors react with a surface one-at-a-time in a sequential manner. By exposing the precursors to the growth surface repeatedly, a thin film is deposited.

##### Evaporation

Evaporation is a common method of thin film deposition. The source material is evaporated in a vacuum. The vacuum allows vapor particles to travel directly to the target object (substrate), where they condense back to a solid state. Evaporation is used in microfabrication, and to make macro-scale products such as metallized plastic film.

##### CVD

Chemical vapor deposition (CVD) is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer (substrate) is exposed to one or more volatile precursors, which react and/or decompose on the substrate surface to produce the desired deposit. Frequently, volatile byproducts are also produced, which are removed by gas flow through the reaction chamber.

Types of CVD

Classified by operating pressure

• Atmospheric pressure CVD (APCVD) - CVD processes at atmospheric pressure.
• Low-pressure CVD (LPCVD) - CVD processes at subatmospheric pressures. Reduced pressures tend to reduce unwanted gas-phase reactions and improve film uniformity across the wafer. Most modern CVD process are either LPCVD or UHVCVD.
• Ultrahigh vacuum CVD (UHVCVD) - CVD processes at a very low pressure, typically below 10-6 Pa (~ 10-8 torr). Caution: in other fields, a lower division between high and ultra-high vacuum is common, often 10-7 Pa.

Classified by physical characteristics of vapor

• Aerosol assisted CVD (AACVD) - A CVD process in which the precursors are transported to the substrate by means of a liquid/gas aerosol, which can be generated ultrasonically. This technique is suitable for use with involatile precursors.
• Direct liquid injection CVD (DLICVD) - A CVD process in which the precursors are in liquid form (liquid or solid dissolved in a convenient solvent). Liquid solutions are injected in a vaporization chamber towards injectors (typically car injectors). Then the precursors vapours are transported to the substrate as in classical CVD process. This technique is suitable for use on liquid or solid precursors. High growth rates can be reached using this technique.

• Microwave plasma-assisted CVD (MPCVD)
• Plasma-Enhanced CVD (PECVD) - CVD processes that utilize a plasma to enhance chemical reaction rates of the precursors. PECVD processing allows deposition at lower temperatures, which is often critical in the manufacture of semiconductors.
• Remote plasma-enhanced CVD (RPECVD) - Similar to PECVD except that the wafer substrate is not directly in the plasma discharge region. Removing the wafer from the plasma region allows processing temperatures down to room temperature.
• Atomic layer CVD (ALCVD) – Deposits successive layers of different substances to produce layered, crystalline films. See Atomic layer epitaxy.
• Hot wire CVD (HWCVD) - Also known as Catalytic CVD (Cat-CVD) or hot filament CVD (HFCVD). Uses a hot filament to chemically decompose the source gases.[1]
• Metalorganic chemical vapor deposition (MOCVD) - CVD processes based on metalorganic precursors.
• Hybrid Physical-Chemical Vapor Deposition (HPCVD) - Vapor deposition processes that involve both chemical decomposition of precursor gas and vaporization of solid a source.
• Rapid thermal CVD (RTCVD) - CVD processes that use heating lamps or other methods to rapidly heat the wafer substrate. Heating only the substrate rather than the gas or chamber walls helps reduce unwanted gas phase reactions that can lead to particle formation.
• Vapor phase epitaxy (VPE)

#### Etching

##### Reactive Ion Etching

Reactive ion etching (RIE) is an etching technology used in microfabrication. It uses chemically reactive plasma to remove material deposited on wafers. The plasma is generated under low pressure (vacuum) by an electromagnetic field. High-energy ions from the plasma attack the wafer surface and react with it.

##### Deep Reactive Ion Etching

Deep reactive-ion etching (DRIE) is a highly anisotropic etch process used to create deep, steep-sided holes and trenches in wafers, with aspect ratios of 20:1 or more. It was developed for microelectromechanical systems (MEMS), which require these features, but is also used to excavate trenches for high-density capacitors for DRAM.

## Devices

### Electronic Devices

#### Capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called "plates"). The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate.

##### Properties of Capacitor

The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates:

${\displaystyle C={Q \over V}}$

The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates.

The capacitance of a parallel-plate capacitor is given by:

${\displaystyle C\approx {\frac {\varepsilon A}{d}};A\gg d^{2}}$

#### Transistor

A transistor is a semiconductor device, commonly used to amplify or switch electronic signals.

##### Bipolar Junction Transistor

A bipolar junction transistor (BJT) is a type of transistor. It is a three-terminal device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons and holes. A bipolar (junction) transistor (BJT) is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons and holes. Charge flow in a BJT is due to bidirectional diffusion of charge carriers across a junction between two regions of different charge concentrations. This mode of operation is contrasted with unipolar transistors, such as field-effect transistors, in which only one carrier type is involved in charge flow due to drift. By design, most of the BJT collector current is due to the flow of charges injected from a high-concentration emitter into the base where they are minority carriers that diffuse toward the collector, and so BJTs are classified as minority-carrier devices.

Introduction NPN BJT with forward-biased E–B junction and reverse-biased B–C junction

An NPN transistor can be considered as two diodes with a shared anode. In typical operation, the emitter–base junction is forward biased and the base–collector junction is reverse biased. In an NPN transistor, for example, when a positive voltage is applied to the base–emitter junction, the equilibrium between thermally generated carriers and the repelling electric field of the depletion region becomes unbalanced, allowing thermally excited electrons to inject into the base region. These electrons wander (or "diffuse") through the base from the region of high concentration near the emitter towards the region of low concentration near the collector. The electrons in the base are called minority carriers because the base is doped p-type which would make holes the majority carrier in the base.

To minimize the percentage of carriers that recombine before reaching the collector–base junction, the transistor's base region must be thin enough that carriers can diffuse across it in much less time than the semiconductor's minority carrier lifetime. In particular, the thickness of the base must be much less than the diffusion length of the electrons. The collector–base junction is reverse-biased, and so little electron injection occurs from the collector to the base, but electrons that diffuse through the base towards the collector are swept into the collector by the electric field in the depletion region of the collector–base junction. The thin shared base and asymmetric collector–emitter doping is what differentiates a bipolar transistor from two separate and oppositely biased diodes connected in series. 

##### Heterojunction Bipolar Transistor

The heterojunction bipolar transistor (HBT) is an improvement of the bipolar junction transistor (BJT) that can handle signals of very high frequencies up to several hundred GHz.

##### MOSFET

The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is by far the most common field-effect transistor in both digital and analog circuits. The MOSFET is composed of a channel of n-type or p-type semiconductor material (see article on semiconductor devices), and is accordingly called an NMOSFET or a PMOSFET (also commonly nMOSFET, pMOSFET).

##### JFET

The junction gate field-effect transistor (JFET or JUGFET) is the simplest type of field effect transistor. Like other transistors, it can be used as an electronically-controlled switch.

### Optical Devices

#### Solar Cells

A solar cell or photovoltaic cell is a device that converts solar energy into electricity by the photovoltaic effect.

#### Laser

A laser is an electronic-optical device that produces coherent light radiation.

#### LED

A light-emitting diode, usually called an LED, is a semiconductor diode that emits incoherent narrow-spectrum light when electrically biased in the forward direction of the p-n junction, as in the common LED circuit.

#### Photoresistor

A photoresistor or LDR is an electronic component whose resistance decreases with increasing incident light intensity.

#### Photodiode

A photodiode is a type of photodetector capable of converting light into either current or voltage, depending upon the mode of operation.

### Magnetic Devices

#### Inductor

An inductor is a passive electrical device employed in electrical circuits for its property of inductance.