Electrical Engineering Materials PDF

Lecture 1 - Charge Pith ball electroscope one or two balls suspended from threads from a stand. Distance between the rod and the ball is a measure of the magnitude of the force of attraction. Varying the charge on the rod varies the distance before the ball is attracted....

Lecture 1 - Charge Pith ball electroscope one or two balls suspended from threads from a stand. Distance between the rod and the ball is a measure of the magnitude of the force of attraction. Varying the charge on the rod varies the distance before the ball is attracted. ○ The smaller the distance, the weaker the force ○ Distance ∝ Force Charge Like charges repel, opposite charges attract. Objects can be charged or uncharged and hold variable amounts of charge. - The amount of charge can form a new dimension, similar to mass, temperature ect (Difference? Only charge is quantised) The SI unit of charge is the coulomb, C Charge is quantised: integral numbers of ‘q’ q = 1.6 x 10-19 C - Once generated, charge can be stored Capacitors Two parallel conductive plates separated by an insulated material: As one plate is charged, the opposite charges are attracted to the other plate. Moving charge - Once charged the attractive force between the opposite charges will hold the charge in the capacitor. - If the two plates are connected by a wire: The charge will flow from one plate to the other. Moving charges = Currents Current formula: Constant current formula: SI unit of current = Ampere Ampere relationship with the Coulomb and the second: Lecture 2 - Electromagnetism Coulomb’s Law for magnetism: *Considering a long, thin, permanent magnet P1 &p2 are the pole strength of the respective poles R is the distance between them If a permanent magnet is split = two more magnets with N-S poles. Creating a magnetisation field - When a magnetic field H is applied to a material, the material responds with its own magnetic field M - When the initial magnetic field H is removed, some materials retain the magnetisation field M. - The M field is the field that creates the permanent magnet Ferromagnetic materials Ferromagnetic materials Have “remembrance”. Generate their own magnetisation after removal of a magnetic field. Permanent magnetism: retains a magnetic field with no external help. The magnitude of remembrance / retentivity can vary: ○ high remembrance = strong permanent magnet The magnitude of coercivity can vary” ○ High coercivity makes a long-lasting permanent magnet Coercivity: The intensity of the magnetising field (H) needed to demagnetize the magnetic material completely Ferromagnetic materials can demagnetise via ○ Heating past currie temp ○ Mechanical disturbances ○ Magnetic fields with an intensity greater than the coercivity. Curie temperature: Above a certain temperature, ferromagnetic materials lose their permanency: Ferromagnetic materials: Most iron, cobalt and nickel.  - Curie temperature for Iron, cobot and nickel: “Non-Magnetic materials” - All materials are slightly magnetic, however ferromagnetic materials are thousands of times stronger. Paramagnetic Materials Attracted to magnetic fields Become slightly magnetic in the presence of a magnetic field Have no magnetisation in the absence of a magnetic field (no remembrance) Above Curie or Néel temperatures, ferromagnetic, ferrimagnetic and antiferromagnetic materials are paramagnetic. Diamagnetic Materials Repelled form magnetic fields Become slightly magnetic in the presence of a magnetic field Have no magnetisation in the absence of a magnetic field All materials experience diamagnetic effects, however, the force is overcome by other effects in non-diamagnetic materials. Water and pyrolytic carbon are diamagnetic and can cause diamagnetic levitation. To summarise magnetic materials materials response to magnetic fields are complicated and poorly understood. All materials exhibit diamagnetic effects, but are often overcome by other forces. Some materials exhibit “permanent” magnetisation spontaneously or due to external forces. magnetic susceptibility, χ, describes the response of a material to a field: - χ > 0: paramagnetic; - χ < 0: diamagnetic; Electromagnets Moving charges can generate magnetic fields and charges experience forces in magnetic fields. Moving magnetic fields generate currents. We can make electromagnets or magnetic fields due to current. Lecture 3 - Electronic materials classification Classical Electrical Properties of materials Conductivity σ - Ability of a material to conduct a current Permittivity ε - measures the “polarisation” of a material to the field Both properties can vary with temperature, frequency etc. When Conductivity and permittivity are represented together as complex permittivity. complex permittivity: ω = 2πf is the angular frequency Characterisation of Electronic Materials Electrical loss tangent: - tan δe is a measure of how much electrical energy is lost as heat in a dielectric material.  - It is defined as the ratio of the imaginary part (ε'') to the real part (ε') of the complex permittivity(ε). - Real part (ε'): The actual energy storage capability of the material due to polarisation. - The imaginary part (ε''): Represents the energy dispersion or loss within the material in the form of heat. What the ratio of the imaginary and the real part mean in terms of conduction and propagation: Magnetic properties *NOTE: “Permittivity and permeability are two different measures. - Permittivity (ε) measures the ability of a material to store energy within the material. - Permeability (µ) is a measure of a material's ability to support the formation of a magnetic field within the material.” Equivalent property for the “complex permeability” : magnetic loss tangent formula: Free space (Vacuum) Permittivity of free space: Permeability of free space:  Unit is Henry per metre = kg per metre per second squared per ampere squared Speed of light: Relative permittivity (εr) and permeability (µr) are commonly used: Relative permittivity (εr) and relative permeability (µr) Magnetic susceptibility: χ = µr − 1 Previously used “magnetic susceptibility”(‘χ) to characterise if a material was paramagnetic or diamagnetic: (χ>0 paramagnetic, χ>p , electrons carry most charge. Extrinsic silicon (p-type) p>>n, holes carry most charge. Both intrinsic and extrinsic silicon are charge neutral, for extra electrons there is a corresponding proton in the dopant atom and vice versa. (always in pairs) Motion of electrons and holes In the absence of electric field thermal equilibrium, electrons and holes move. This is due to thermal energy being converted into kinetic energy. Random (Brownian) motion of charge carriers - Unpredictable and erratic movement of charged particles. Direction and speed vary, influenced by collisions with other carriers and lattice imperfections. Approximate speed in pure Si at 300K (room temp) = Thermal velocity = vth ≈ 1 × 107 cm/sec Scattering As electrons move, they collide with - crystal defects  - Ions (dopant ions around the crystal) - Unintentional impurities Causing electrons to lose energy (recombine with a hole) or change direction Mean time between collisions in pure Si at 300K is 0.1 ps Drift current of electrons ○ Due to the electric field, electrons moving in the Opposite direction: gain velocity Correct direction: lose velocity Electrons begin to drift in the opposite direction to the field. The net movement of electrons sets up a current flow, The velocity of the electrons is proportional to the magnitude of the electric field. Lecture 5 - Currents in solids Quantifying Currents Current is the net flow of charge, which can often be modelled as I=qnvAE q : the charge on the carrier n : the concentration of carriers in the material v : the velocity of the carrier A : the cross sectional area E : the electric field Drift current of electrons and holes In an electric field, electrons moving in an - opposite direction gain velocity, holes lose velocity - Direction of the field loose velocity, holes gain velocity Electrons begin to drift in the opposite direction to the field. Holes begin to drift in the direction of the field. - The net movement of the electrons makes a current flow. - The net movement of holes makes a current flow. - The respective velocities of the holes and electrons are proportional to the magnitude of the electric field. Quantifying electric drift current for electrons. Indrift = -An(-q)µnE - A: cross-sectional area - n: Density of electrons - q: Charge on the electron (negative) - µn: The mobility of the electron - E: the electric field Quantifying the hole drift current Ipdrift = ApqµpE - A: cross sectional area - p: Density of holes - q: Charge on holes - µp: the mobility of the hole - E: the electric field Combined drift Current: Idrift = AEq(nµn + pµp) The total current ( Idrift ) is the net movement of electrons ( In ) and the net movement of holes ( Ip ). I drift = I drift n + I drift p So combining both formulae: = −n(−q)(µn)EA + p(q)(µp)EA = AEq(nµn + pµp) Resistivity of a semiconductor ρ= EA/I I = σEA (σ is the conductivity) Equal the current formula to fit into our formula for the total drift current: (1) I = AσE (2) I = AEq(nµn + pµp) AEσ = AEq(nµn + pµp) σ = q(nµn + pµp) Therefore, The conductivity of a semiconductor is: σ = q(nµn + pµp) Temperature dependence is an aspect of: - Charge: The charge on the carriers, q, is a fundamental constant. - Concentrations: of electrons, n, and holes, p. - Mobilities: of each carrier µn and µp Thermistors: Temperature-dependant resistors - Normal resistors are designed to minimise the change in resistance due to temperature in their operating range. Thermistors: resistors where the resistance changes with temperature. Thermistors are organised by “temperature coefficient” NCT (negative) resistance decrease with temperature. PTC (positive) resistance increases with temperature. Diffusion current The electron and hole density in a semiconductor is not uniform. - Electrons and holes move away from areas of high concentration and towards areas of low concentration. - Electron diffusion current: Idiffn = A(−q)Dn − (dn(x) / dx) - Hole diffusion current: Idiffp = AqDp − (dp(x) / dx) (the only difference is that the q is positive for the holes) Combined diffusion current = Aq( (Dn. dn(x)/dx) − (Dp. dp(x)/dx) ) Einstein Relations For electrons: Dn/µn = kT/q For holes: Dp/µp = kT/q 2 types of material constants relating to their charge carrier transport for drift and diffusion currents of electrons and holes: 1. Mobility (µn and µp) 2. Diffusivity (Dn and Dp) k ≈ 1.38 J K−1 is Boltzmann’s constant. Barrier potential for an intrinsic x n-type barrier Intrinsic semiconductor at room temp: - Electrically neutral. - Equal number of holes and electrons. p=n=ni N-type at room temp: - Electrically neutral - More free electrons than holes. n = Nd >> ni Recombination of electrons and holes being attracted to each other happens on the barrier Increase in positive ions in n-type and negative in the intrinsic. The material remains neutrally charged but a voltage builds up across the barrier. Barrier potential for a p-n junction P-type at room temp - Electrically neutral - More holes than free electrons - p = Nd>>ni Depletion region formed: - Free electrons diffuse over to the holes, leaving behind positive ions on the n-type diode of the barrier. - Holes diffuse over to n region leaving layers of negative ions on the p-type side. The depletion region will continue to expand until the total negative charge in the depletion region repels any further charge into the p-region from the n-type. Forward bias Positive electric component connected with the n-type and negative electric component with the p-type. The majority charge carriers (electrons) are pushed into the p region and overcome the barrier potential. They then combine with the holes which are moving toward the p-n junction. Lecture 6 - Thermoelectric effects Bond wires Resistivity of Copper - 1.72 x 10-8 Resistivity of gold - 2.44 x 10-8 Resistance of a wire: Temperature difference The change in resistance due to temperature is often approximated as a linear range. This allows change in resistance to be calculated as: Change in resistance: R(T) = R(T0) x (1+ α∆T) If ∆T=T-T0 α - temperature coefficient - Most metals: positive coefficients - Devices (including diodes): negative coefficients. Self Capacitance If an object can be charged, a voltage will build up. If the object is a sphere with radius R: Relationship w/ capacitance, charge, voltage and the physical properties of the capacitor: C = q V = 4πεR Mutual capacitance For two conductors insulated from eachother. The capacitance C relates the charge on each conductor to the voltage between the conductors Capacitance as it relates to charge and the voltage between the conductors C = q/V Parallel plate capacitors If one side of a parallel plate capacitor is free to move with respect to the other - The overlapping area might change - The separation might change  - Application of mutual capacitance - Touch screens - Accelerometers - Pressure transducers Dielectric strength - The voltage at which an insulating material’s insulator properties begin to break down. All insulators have dielectric strength which relates to the breakdown voltage, so do capacitors. Break down voltage for capacitors: Vbd = Edsd E: Electric field strength at breakdown D: separation distance between the capacitor plates. Seebeck Effect This is the basis for the operation of thermocouples in temperature measurements. If you have 2 wires made from 2 different alloys: If you heat one end, and make another cold there will be a voltage generated across the two wires in a loop. If you supply a voltage, one end will heat up and one end will go cool. (Pelteir effect) The open-circuit voltage : ∆V = SAB(TH − TC) - TH : temp at hot junction and - TC : the temp at the cold junction. - SAB: The seebeck coefficient / Thermoelectric sensitivity - Measure of Voltage per unit temperature difference. It's difficult to measure the absolute seebeck coefficient for a metal as it will be in contact with the electrodes used to measure. - Relative seebeck coefficients are measured for metal pairs. - Platinum is often taken as a reference metal. Unit of the seebeck coefficient is listed as µV K−1. Increased thermal carrier generation due to increased temperature. Different concentrations of carriers throughout the materials Diffusion occurs until the electric field generated counteracts the diffusion. Peltier Effect Peltier Effect: If you apply a current to a circuit made of 2 wires of different alloys, a temperature difference will be created. Peltier coefficient: Π Thomson Effect Thomson effect: when an electric current passes through a conductor with a heat gradient along its length, the Thomson elect leads to the heating or cooling of a conductor. - Heating: Travels from cold side to hot side and then the conductor is heated - Positive Thomson coefficient (+K) - Cooling: Travels from hot to cool side and then the conductor is cooled. - Negative Thomson coefficient -(K) Relation between Seebeck, Pelteir and Thomson Equation to relate seebeck, peltier and Thomson: K=dΠ/dt -S Equation including heat added to the resistive heating, and the seebeck. Pelteir and thomson effects: −q˙ ext = J · (ρJ) + ∇ · (K∇T) − TJ · ∇S Lorentz’s Law F = qE + qv x B - F: total force experienced by a charges particle moving in an electric and magnetic field. - E: electric field vector at the location of the charged particle. - B: Magnetic field vector - q: charge on the particle - v: the velocity of the charged particle Hall effect devices Where continuous current I passes through a magnetic field, B, perpendicular to the direction of the current, a voltage develops across the material. The hall voltage: VH = |B| |v| d Both electrons and holes can exhibit a Hall Voltage. Hall voltage for electrons and holes: In a doped material Positive and negative charges are deflected in the same direction. ○ That would lead to opposite polarities as positive and negative charges accumulate in the same place. Hall effect sensors are sensitive to both the magnitude and orientation of the field. Piezoelectric Effect Converts stress to voltage - Certain crystals (mostly quartz) accumulate charge due to rearrangement of the microstructure during stress. - Reversible: structure changes due to applied voltage. Uses: Displacement sensors, vibratory motor, precise actuator Lecture 7