Lec 2 - Electrical Conductors Definition, Types and Properties PDF

Electric Properties of Material Band Energy Theory & Electrical Conductors Dr. Sameh Mustafa  ENERGY BAND STRUCTURES IN SOLIDS The electrical conductivity is strongly dependent on the number of electrons available to participate in the conduction process. However, n...

Electric Properties of Material Band Energy Theory & Electrical Conductors Dr. Sameh Mustafa  ENERGY BAND STRUCTURES IN SOLIDS The electrical conductivity is strongly dependent on the number of electrons available to participate in the conduction process. However, not all electrons in every atom accelerate in the presence of an electric field. The number of electrons available for electrical conduction in a particular material is related to the arrangement of electron states or levels with respect to energy A solid may be consisting of a large number—say, N—of atoms initially separated from one another that are brought together and bonded to form the crystalline material. At relatively large separation distances, each atom is independent of all the others and has the atomic energy levels and electron configuration as if isolated. However, as the atoms come within close proximity of one another, electrons are acted upon, or perturbed, by the electrons and nuclei of adjacent atoms  ENERGY BAND STRUCTURES IN SOLIDS This influence is such that each distinct atomic state may split into a series of closely spaced electron states in the solid to form what is termed an electron energy band. Within each band, the energy states are discrete, yet the difference between adjacent states is exceedingly small. ENERGY BAND STRUCTURES IN SOLIDS  ENERGY BAND STRUCTURES IN SOLIDS The electrical properties of a solid material are a consequence of its electron band structure—that is, the arrangement of the outermost electron bands and the way in which they are filled with electrons.  ENERGY BAND STRUCTURES IN SOLIDS The energy corresponding to the highest filled state at 0 K is called the Fermi energy Ef, only electrons with energies greater than the Fermi energy may be acted on and accelerated in the presence of an electric field. These are the electrons that participate in the conduction process, which are termed free electrons. CONDUCTION IN TERMS OF BAND AND ATOMIC BONDING MODELS (1) Conductors (Metals): For an electron to become free, it must be excited or promoted into one of the empty and available energy states above Ef. the energy provided by an electric field is sufficient to excite large numbers of electrons into these conducting states  CONDUCTION IN TERMS OF BAND AND ATOMIC BONDING MODELS (2)  ENERGY BAND THEORY OF SOLIDS  A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials, where the available energy states form bands.  Crucial to the conduction process is whether or not there are electrons in the conduction band.  The conduction band is the band of electron orbitals that electrons can bounce up into from the valence band when energized.  The energy distinction between the highest occupied energy state of the valence band and the least abandoned condition of the conduction band is known as the bandgap and is demonstrative of the electrical conductivity of a material.  ENERGY BAND THEORY OF SOLIDS  In insulators the electrons in the valence band are separated by a large gap from the conduction band.  In insulators, the conduction band is completely empty. So even if an electric field is applied there are no electrons to move and so no conduction can take place.  The valence electrons cannot move because the valance band is tightly packed, so the insulator refuses to let any electrons move when we apply an electric field 11 12 Silicon Atomic number (14) 13  Electrical Conductors Electrical conduction involves the motion of charges in a material under the influence of an applied electric field. a conductor contains a large number of “free” or mobile charge carriers. In metals, due to the nature of metallic bonding, the valence electrons from the atoms form a sea of electrons that are free to move within the metal and are therefore called conduction electrons. Electrical conductors are usually metals, such as copper, silver, gold, aluminum, and iron. Electrical conductors are used for making wires, cables, circuits, and other devices that carry electric current. have high conductance and low resistance. Electrical conductors may be metals, metal alloys, electrolytes, or some non-metals like graphite and conductive polymers. Electrical Conductors Electrical Conductors CLASSICAL THEORY: THE DRUDE MODEL  Drift of Electrons Without applicatio n of electric field With applicatio n of electric field Electrons Drift Velocity  Drift Velocity  crystal will not be perfect and the atoms will not be stationary. There will be crystal defects, vacancies, dislocations, impurities, etc., which will scatter the conduction electrons.  More importantly, due to their thermal energy, the atoms will vibrate about their lattice sites (equilibrium positions)  An electron will not be able to avoid collisions with vibrating atoms; consequently, it will be “scattered” from one atom to another.  In the absence of an applied field, the path of an electron may be visualized as illustrated in Figure.  the electrons therefore show no net displacement in any one direction. Absence of Electric Field Drift Velocity When the conductor is connected to a battery and an electric field is applied to the crystal, as shown in Figure , the electron experiences an acceleration in the x direction in addition to its random motion, so after some time, it will drift a finite distance in the x direction.  The electron accelerates along the x direction under the action of the force e*Ex, and then it suddenly collides with a vibrating atom and loses the gained velocity. Therefore, there is an average velocity in the x direction. Presence of Electric Field  Electrons Drift Velocity (vdx)  The average velocity of the electrons in the x direction at time t is denoted vdx(t).  This is called the drift velocity, which is the instantaneous velocity vx in the x direction averaged over many electrons (perhaps, ∼1028 m−3); that is:  Suppose that n is the number of electrons per unit volume in the conductor (n = N/V ).  In time Δt, electrons move a distance Δx = vdx.Δt, so the total charge Δq crossing the area A is Δq =e*n*A Δx. Electrical Conductors CLASSICAL THEORY: THE DRUDE MODEL Drift Velocity  The current density in the x direction is  The average velocity at one time may not be the same as at another time, because the applied field. May be changing with time.  To relate the current density Jx to the electric field Ex, we must examine the effect of the electric field on the motion of the electrons in the conductor. Calculation of Drift Velocity  To calculate the drift velocity vdx of the electrons due to applied field Ex, we first consider the velocity vxi of the ith electron in the x direction at time t.  Suppose its last collision was at time ti; therefore, for time (t − ti), it accelerated free of collisions, as indicated in Figure. Calculation of Drift Velocity  Let uxi be the velocity of electron i in the x direction just after the collision.  We will call this the initial velocity. Since e*Ex/me is the acceleration of the electron, the velocity vxi in the x direction at time t will be:  We need the average velocity vdx for all such electrons along x.  We assume that immediately after a collision with a vibrating ion, the electron may move in any random direction; that is, it can just as likely move along the negative or positive x. Calculation of Drift Velocity  Thus the drift velocity is  where (t − ti) is the average free time for N electrons between  Suppose that 𝜏 is the mean free time, or the mean time between collisions. collisions (also known as the mean scattering time). Or relaxation time  Calculation of Drift Velocity  We can express the drift velocity as  The drift velocity increases linearly with the applied field. The constant of proportionality (eτ/me) has been given a special name and symbol.  It is called the drift mobility μd, which is defined as the ability of free charges to move in the material  Ohm’s Law  From the expression for the drift velocity vdx, the current density Jx follows immediately as: J= σ * E  Therefore, the current density is proportional to the electric field and the conductivity σ is the term multiplying Ex, that is,  Deformation ‫تشوه‬ Effect of temperature on Resistivity  When the conduction electrons are only scattered by thermal vibrations of the metal ions, then τ in the mobility expression μd = eτ/me refers to the mean time between scattering events by this process.  The resulting conductivity and resistivity are denoted by σT and ρT, where the subscript T represents “thermal vibration scattering.”  To find the temperature dependence of σ, we first consider the temperature dependence of the mean free time τ, since this determines the drift mobility  An electron moving with a mean speed u is scattered when its path crosses the cross sectional area S of a scattering centre, as depicted in the Figure  The scattering centre may be a vibrating atom, impurity, vacancy, or some other crystal defect.  Since τ is the mean time taken for one scattering process, the mean free path ℓ of the electron between scattering processes is u*τ.  Effect of temperature on Resistivity  If Ns is the concentration of scattering centres, then in the volume S*ℓ, there is one scattering centre, that is, (S*u*τ)Ns = 1. Thus, the mean free time is given by  Mean free time between collisions  The thermal vibrations of the atom can be considered to be simple harmonic motion, much the same way as that of a mass M attached to a spring.  The average kinetic energy of the oscillations is ¼* M*a2*ω2, where ω is the oscillation frequency.  From the kinetic theory of matter, this average kinetic energy must be on the order of ½* kT. Effect of temperature on Resistivity  Therefore,  so a2 ∝ T. Intuitively, this is correct because raising the temperature increases the amplitude of the atomic vibrations.  Thus,  where C is a temperature-independent constant. Effect of temperature on Resistivity  Substituting for τ in μd = eτ/me, we obtain  that is,ρT = AT ,where A is a temperature-independent constant.  This shows that the resistivity of a pure metal wire increases linearly with the temperature, and that the resistivity is due simply to the scattering of conduction electrons by the thermal vibrations of the atoms.  We term this conductivity lattice-scattering-limited conductivity Assignme nt  Conduction materials Conduction materials include metals, electrolytes, superconductors, semiconductors, plasmas and some nonmetallic conductors such as graphite and conductive polymers. Copper has a high conductivity. Annealed copper is the international standard to which all other electrical conductors are compared The main grade of copper used for electrical applications, such as building wire, motor windings, cables and busbars Silver is 6% more conductive than copper, but due to cost it is not practical in most cases. However, it is used in specialized equipment, such as satellites, and as a thin plating to mitigate skin effect losses at high frequencies.  Several electrically conductive metals are less dense than copper, but require larger cross sections to carry the same current and may not be usable when limited space is a major requirement.Aluminium has 61% of the conductivity of copper. The cross sectional area of an aluminium conductor must be 56% larger than copper for the same current carrying capability. The need to increase the thickness of aluminium wire restricts its use in many applications, such as in small motors and automobiles. However, in some applications such as aerial electric power transmission cables, aluminium predominates, and copper is rarely used.  Report: (Pay attention for a Discussion) Properties of conducting materials (Definitions – comparison bet Copper –Aluminum – Silver) Conductivity Mechanical strength Modulus of elasticity Heat expansion coefficient Cost Tensile strength Ductility Creep Resistance Corrosion resistance Thermal conductivity Solderability Ease of installation 1. Introduction to Crystals and Energy Bands Crystals are solid materials in which atoms are arranged in a highly ordered, repeating pattern extending in all three spatial dimensions. This regular arrangement of atoms or ions is known as a crystal lattice. The study of crystals and their properties, including the interaction of atoms, forms the foundation of materials science, particularly when analyzing electrical properties in materials. In crystalline solids, the energy of electrons is restricted to specific ranges, and the concept of energy bands becomes critical. Electrons in an atom occupy discrete energy levels; when atoms come together to form a solid, their outermost energy levels overlap to create bands of allowed energy states for electrons. These bands are crucial for understanding the electrical properties of materials. The energy band theory explains the behavior of electrons in solids and their ability to conduct electricity. There are three types of energy bands in materials: 1. Valence Band: The highest range of electron energies in which electrons are normally present at absolute zero temperature. 2. Conduction Band: The range of energy higher than the valence band where free electrons can move through the material, allowing for electrical conductivity. 3. Band Gap: The energy difference between the valence band and the conduction band. The size of the band gap determines whether a material behaves as a conductor, semiconductor, or insulator. Metals have overlapping valence and conduction bands, resulting in high conductivity. Insulators have large band gaps, preventing electron flow, while semiconductors have smaller gaps that can be bridged under certain conditions, such as temperature or doping. Understanding crystals and energy bands is essential in semiconductor physics, where the control of electron movement between these bands determines the functionality of electronic devices like transistors and diodes. Furthermore, manipulating the structure of crystals through techniques like doping allows for enhanced control over electrical conductivity, making materials more suitable for specific applications in electronic devices. 2- Charge Carriers in Semiconductors In semiconductors, charge carriers are particles that carry electrical charge and are responsible for the flow of electric current. There are two primary types of charge carriers in semiconductors: 1. Electrons: Negatively charged particles that occupy the conduction band. 2. Holes: Positively charged "vacancies" in the valence band, where an electron is absent. These holes behave as positively charged particles since nearby electrons can move into the vacancy, creating the illusion of positive charge moving through the material. The intrinsic behavior of semiconductors relies on the natural thermal excitation of electrons from the valence band to the conduction band, leaving behind holes. This process generates electron-hole pairs, which contribute to electrical conductivity. Charge carriers are significantly influenced by temperature, doping (the introduction of impurities), and external electric fields. Semiconductors like silicon or germanium can be "doped" with other elements to increase their electrical conductivity: n-type Semiconductors: Doping with elements that have extra electrons (e.g., phosphorus in silicon) increases the number of free electrons in the conduction band. p-type Semiconductors: Doping with elements that have fewer valence electrons (e.g., boron in silicon) creates more holes in the valence band. The behavior and mobility of these charge carriers are essential in determining the overall performance of semiconductor devices, which include diodes, transistors, and photovoltaic cells. 3. Carrier Concentrations Carrier concentration refers to the number of free electrons and holes per unit volume in a semiconductor material. This concentration is critical for determining the conductivity and overall behavior of semiconductors. The carrier concentration in intrinsic semiconductors (pure materials) is a function of temperature, as higher temperatures provide more energy for electron excitation from the valence band to the conduction band. In n-type semiconductors, electrons are the majority carriers, while holes are the minority carriers. Conversely, in p-type semiconductors, holes are the majority carriers, and electrons are the minority carriers. The carrier concentration depends on: Intrinsic Carrier Concentration (ni): The number of electrons or holes generated in an undoped semiconductor due to thermal excitation. Doping Levels: Introducing impurities (dopants) can significantly increase the carrier concentration. For example, in n-type materials, the concentration of electrons increases due to the addition of donor atoms, while in p-type materials, the concentration of holes increases due to the addition of acceptor atoms. Carrier concentration also affects the resistivity of the material, and it can be adjusted to create specific behaviors in semiconductor devices. By controlling doping levels and manipulating the carrier concentrations, engineers can design semiconductors with desired electrical properties for use in various electronic applications. 4. Drift of Carriers in Electric and Magnetic Fields Drift is the motion of charge carriers (electrons and holes) in response to an applied electric field. When an electric field is applied to a semiconductor, free carriers experience a force that causes them to accelerate in the direction of the field (for holes) or opposite to the field (for electrons). This net movement of carriers constitutes an electric current, and the phenomenon is described by Ohm's Law: where is the current density, is the electrical conductivity, and is the applied electric field. In the presence of a magnetic field, the motion of charge carriers is influenced by the Lorentz force, which acts perpendicular to both the velocity of the carriers and the magnetic field. This results in the Hall Effect, where charge carriers accumulate on one side of the material, creating a potential difference across the material. This phenomenon is used to measure carrier concentrations and mobilities in semiconductors. The drift of carriers is characterized by the mobility of the charge carriers, which defines how quickly they respond to the electric field. High mobility materials are preferred for applications requiring fast electronic responses, such as transistors in microprocessors.