Material physics and technologies (2 Modulo) Books, notes and 2023 open questions papers, Sintesi del corso di Fisica Dei Materiali

Scarica Material physics and technologies (2 Modulo) Books, notes and 2023 open questions papers e più Sintesi del corso in PDF di Fisica Dei Materiali solo su Docsity! 18. Electrical property of materials Electric current results from the motion of electrically charged particles in response to forces that act on them from an externally applied electric field. Electronic conduction results from flow of electrons (versus ionic conduction). Ohm’s law: ease by which materials transmit electricity Every material apply some resistance to current flow. Electrical resistivity Electrical conductivity: electrical character of a material Current density where: ε = electric field intensity According to conductivity value materials are classified as: 1. Conductors 2. Semiconductors 3. Insulator POV Atoms: The number of electrons available for electrical conduction in a particular material is related to the arrangement of electron states with respect to energy, and then the manner in which these states are occupied by electrons, namely electronic configuration. Electrons fill only the states having the lowest energies, two electrons of opposite spin per state. POV Molecules: As the atoms come within close proximity of one another, electrons are perturbed, by the electrons and nuclei of adjacent atoms. Each distinct atomic state may split into a series of closely spaced electron states, named electron energy band. The more atom get closer, the broader the energy band is. V = IR ! = R A l = VA Il " = 1 ! J = I A = "# = V l Subshell ( l ) Energy states available in the atom ( from -l to +l ) States in the energy band. N = number of atoms S (0) 1 N P (1) 3 3N D (2) 5 5N F (3) 7 7N Band Structure: A. Conductor: Available electron states above and adjacent to filled states, in the same band. B. Conductor: There is an overlap of filled and empty outer bands. C. Insulators: The filled valence band is separated from the empty conduction band by a relatively large band gap (>2 eV) D. Semiconductor: The band gap is relatively narrow (<2 eV) Fermi’s energy (Ef) : energy corresponding to the highest filled states at 0K Valence Band: energy band completely filled of electrons Conduction band : completely empty energy band Energy band Gap: forbidden energy band. No states cover it Free electron: electrons with energies (greater than the Fermi energy) may be acted on and accelerated in the presence of an electric field. Electrons may be accelerated in opposite direction to the electric field applied. However there exists frictional forces which oppose to the electron motion due to the scattering of electrons resulting from imperfection in the crystal lattice. Electron mobility (μe) indicates the frequency of scattering events, while drift velocity (νd) represents the average speed imposed by the electric field. νd = μe ε where ε = electric field intensity σ = n |e| μe where n = number of free electrons = V l Extrinsic semiconductor behaviour according to temperature variation is divided into three regions: 1. Freeze-out temperature region: at low temperatures electron concentration drops dramatically with decreasing temperature as thermal energy is insufficient to excite electrons. 2. Extrinsic-temperature region: electron concentration is constant as all of the impurities atoms have been excited. 3. Intrinsic temperature region: electron excitations (Intrinsic behaviour) across the band gap completely overwhelm the donor carrier contribution (extrinsic behaviour) with rising temperature. Hall effect is a result of the phenomenon whereby a magnetic field applied perpendicular to the direction of motion of a charged particle exerts a force on the particle perpendicular to both the magnetic field and the particle motion directions deflecting them. VH = hall’s voltage RH = hall’s coefficient (constant for a given material) IX = current intensity BZ = magnetic field d = Material thickness Where: and consequently: • Extrinsic doped semiconductor • Intrinsic doped semiconductor 19. Thermal properties Heat capacity: material’s ability to absorb heat, represented as the amount of energy required to produce a unit temperature rise. per mole of material Specific heat is the heat capacity per unit mass. Cv is heat capacity at constant volume. Cp is heat capacity at constant pressure. Thermal energy is absorbed as vibrational energy of atoms, that in turns are coupled by atomic bonding. Such vibration are coordinated as a the vibration transmission acts with wave nature. Vibrational thermal energy consists of a series of elastic waves and only certain energy values are allowed and such quantum od energy is called phonon. These elastic waves also participate in the transport of energy during thermal conduction known as vibrational contribution. Heat capacity changes according to variation of temperature until the Debye temperature (θD) where Cv become independent from temperature. Electronic contribution consists in electrons whose absorb energy by increasing their kinetic energy. However, this is possible only for free electrons as consequence of excitation above Fermi energy. Thermal expansion: most solid materials expand upon heating and contract when cooled according to the following formula: The same relation can be applied according to volume changes: αV could be anisotropic (depends on the crystallographic direction along which it is measured) or isotropic (do not depends on crystallographic direction and αV = 3αL C = !Q !T !L Lo = $!T !V Vo = $!T Where: αL = linear coefficient of thermal expansion that is a material property that is indicative of the extent to which a material Where: αV =volume coefficient of thermal expansion From an atomic perspective, thermal expansion is reflected by an increase in the average distance between the atoms. This phenomenon can best be understood by consultation of the potential-energy-versus-interatomic- spacing curve. Thermal expansion is really due to the asymmetric curvature. The greater the atomic bonding energy, interatomic separation with a given rise in temperature will be lower. 1. Metals: Intermediate (could be controlled in alloy) expansion behaviour. 2. Ceramics: Strong interatomic bonding lead to ow coefficients of thermal expansion. Anisotropic ceramics may experience fracture as a consequence of nonuniform dimensional changes in what is termed thermal shock. 3. Polymers: Large thermal expansion (it diminishes augmenting cross linking bonds between polymers). Thermal conductivity: Material’s ability to transport heat from high to low temperature regions of substance. Where: k is thermal conductivity constant (minus stands for heat direction from high to low temperature) Heat is transported in solid materials by both lattice vibration waves and free electrons (due to kinetic energy gained from thermal energy): k = kl + ke. 1. Metals: Heat transportation depends on electron mechanism, due to the large availability of free electrons. 2. Ceramics: they are thermal insulators due to their lack large numbers of free electrons. Thus the phonons are primarily responsible for thermal conduction. q = Heat Flu x = " k !T !x Impurities results in a reduction in the thermal conductivity, as they acts as scattering centers, lowering the efficiency of electron motion. Optical properties of metals: Metals are opaque because the incident radiation having frequencies within the visible range excites electrons into unoccupied energy states above the Fermi energy, as a consequence, incident radiation is absorbed. Absorbed radiation is reemitted from the surface which appears as reflected light. Small fraction of energy is dissipated as heat. Refraction: Light transmitted into a transparent material experiences a decrease in velocity due to electronic polarisation. Index of refraction depends on the wave length: Snell law: θ1 = incidence angle θ2 = Transmission angle Generally, the larger an atom, the greater the electronic polarisation, the slower the velocity, and the greater the index of refraction. Total internal reflection: threshold angle in which light is only reflected and not transmitted. the case in which transmission velocity is slow in the first media and very high in the second Reflection: Light is scattered at the interface between the two media having two different index of refraction. Defined as the reduction in reflected power caused by the introduction of an absorbing material. Reflectivity vary with wavelength. Absorption: light radiation is absorbed by electronic polarisation (only for relaxation frequency of atoms) and electron transitions (excitation of an electron from the nearly filled valence band, across the band gap, and into an empty state). Excitation occurs when photon energy is greater than that of the band gap Eg means between 1.8 eV (Gap energy corresponding to maximum λ of visible light) and 3.1 eV (Gap energy corresponding to minimum λ of visible light) If impurities are added, electron levels within the band gap may be introduced, Light radiation may be emitted as a result of electron transitions involving these levels within the band gap. Dissipation of energy absorbed: 1. Electron and hole recombination 2. multiple-step transmission: electron drops from a state in the conduction band to the impurity level and another it decays back into the valence band n = c v Light absorption depends on: and dp (penetration depth) = Where: β = absorption coefficient l = sample thickness Color: consequence of wavelength selectively absorbed (by electron excitation). Color is the result of combination of wavelength that are transmitted and reemitted. Photon are absorbed if ΔE > Eg. Non-absorbed (hence transmitted) visible light consists of photons having energies between about 1.8 and Eg eV. Photons having energies less than the band gap may be emitted as a consequence of electron decay processes involving impurity atoms. Opacity results when the scattering is so extensive that virtually none of the incident beam is transmitted (due to porosity, two phase material, difference between grain boundaries index of refraction). Luminescence: absorbing energy and then reemitting visible light due to electron transitions. Fluorescence: reemitting visible light in less than 1 second Phosphorescence: reemitting visible light in more than 1 second Photoconductivity: charge carriers generated as a consequence of photon-induced electron transitions increase in conductivity. It is direct function of direct function of the intensity of the incident light radiation. Laser: light generated electron transitions initiated by an external stimulus. photons of wavelength 0.56 μm excite electrons into higher energy states. These electrons can decay back in two ways: A. Fall back directly to ground state. B. Decay into a metastable intermediate state (and stay for up 3 ms). The initial spontaneous photon emission by a few of metastable electrons stimulates massive emissions from the remaining electrons in the metastable state. The initial spontaneous photon emission by a few of these electrons is the stimulus that triggers an avalanche of emissions from the remaining electrons in the metastable state 1 & Photonics: Signal transmission by means of optically transparent fibers. Optical fiber: - The information in electronic form must first be digitised into bits. - Convert this electrical signal into an optical (converter is normally a laser that emit a monochromatic light). The output is in form of light binary pulse.ù - Carried through the fiber-optic cable. (Normally for long distances repeaters are required) - Reconversion of signal into electric form. Signal passes through the core (High-purity silica glass), whereas the surrounding cladding constrains the light rays to travel within the core. Internal reflection is accomplished by varying the index of refraction of the core and cladding. Two design: 1. Step-index: Index of refraction of the cladding is slightly lower than that of the core. In this design, output pulse will be broader than the input one as light rays arrive at the output at different times due to different trajectories. 2. Graded-index:impurities are added to silica glass so index of refraction vary parabolically (velocity of light is greater at the periphery than at the center) across the cross section, so that rays comes to the end at the same time.