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UVA MSE 2090 - Electrical properties

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11MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityElectrical properties¾ Electrical conduction • How many moveable electrons are there in a material (carrier density)? • How easily do they move (mobility) ?¾ Semiconductivity• Electrons and holes• Intrinsic and extrinsic carriers• Semiconductor devices: p-n junctions and transistors¾ Conduction in polymers and ionic materials¾ Dielectric behaviorOptional reading: 18.14, 18.15, 18.21, 18.23-18.252MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityBasic laws and electrical properties of metals (I)When an electrical potential V [volts, J/C] is applied across a piece of material, a current of magnitude I [amperes, C/s] flows. In most metals, at low values of V, the current is proportional to V, and can be described by Ohm's law: I = V/Rwhere R is the electrical resistance [ohms, Ω, V/A]. R depends on the intrinsic resistivity ρ of the material [Ω-m] and on the geometry (length l and area A through which the current passes): R = ρl/AIn most materials (e.g. metals), the current is carried by electrons (electronic conduction). In ionic crystals, the charge carriers are ions (ionic conduction).3MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityBasic laws and electrical properties of metals (II)The electrical conductivity (the ability of a substance to conduct an electric current) is the inverse of the resistivity:σ = 1/ρSince the electric field intensity in the material is E = V/l, Ohm's law can be rewritten in terms of the current density J = I/A as: J = σ EElectrical conductivity varies between different materials by over 27 orders of magnitude, the greatest variation of any physical propertyMetals: σ > 105(Ω.m)-1Semiconductors: 10-6 < σ < 105(Ω.m)-1Insulators: σ < 10-6(Ω.m)-1σ (Ω.cm)-14MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity25MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures in Solids (I)In an isolated atom electrons occupy well defined energy states, as discussed in Chapter 2.When atoms come together to form a solid, their valence electrons interact with each other and with nuclei due to Coulomb forces. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same energy.As a result of these effects, the valence electrons of atoms form wide electron energy bands when they form a solid. The bands are separated by gaps, where electrons cannot exist. 6MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and ConductivityThe highest filled state at 0 K Fermi Energy (EF)The two highest energy bands are:¾ Valence band – the highest band where the electrons are present at 0 K¾ Conduction band - a partially filled or empty energy band where the electrons can increase their energies by going to higher energy levels within the band when an electric field is appliedEnergyconduction bandvalence bandunfilled bandsfilled bandsband gap7MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and Conductivity (metals)In metals (conductors), highest occupied band is partially filled or bands overlap.Conduction occurs by promoting electrons into conducting states, that starts right above the Fermi level. The conducting states are separated from the valence band by an infinitesimal amount. Energy provided by an electric field is sufficient to excite many electrons into conducting states. Cu Mg1s22s22p63s21s22s22p63s23p63d104s1filled bandEnergypartly filled band empty bandGAPfilled statesPartially filled bandEnergyfilled bandfilled band empty bandfilled statesOverlapping bands8MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and Conductivity(semiconductors and insulators)In semiconductors and insulators, the valence band is filled, no more electrons can be added (Pauli's principle). Electrical conduction requires that electrons be able to gain energy in an electric field. To become free, electrons must be promoted (excited) across the band gap. The excitation energy can be provided by heat or light.Insulators:wide band gap (> 2 eV)Energyfilled bandfilled valence bandfilled statesGAPemptybandconductionSemiconductors:narrow band gap (< 2 eV)Energyfilled bandfilled valence bandfilled statesGAP?emptybandconduction39MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and Conductivity (semiconductors and insulators)¾ In semiconductors and insulators, electrons have to jump across the band gap into conduction band to find conducting states above Ef¾ The energy needed for the jump may come from heat, or from irradiation at sufficiently small wavelength (photoexcitation).¾ The difference between semiconductors and insulators is that in semiconductors electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot.¾ The probability that an electron reaches the conduction band is about exp(-Eg/2kT) where Egis the band gap. If this probability is < 10-24one would not find a single electron in the conduction band in a solid of 1 cm3. This requires Eg/2kT > 55. At room temperature, 2kT = 0.05 eV ⇒ Eg> 2.8 eV corresponds to an insulator.¾ An electron promoted into the conduction band leaves a hole (positive charge) in the valence band, that can also participate in conduction. Holes exist in metals as well, but are more important in semiconductors and insulators.10MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and Bonding (metals, semiconductors, insulators)Relation to atomic bonding:¾ Insulators – valence electrons are tightly bound to (or shared with) the individual atoms – strongest ionic (partially covalent) bonding.¾ Semiconductors - mostly covalent bonding somewhat weaker bonding.¾ Metals – valence electrons form an “electron gas” that are not bound to any particular ion. 11MSE 2090: Introduction to Materials Science Chapter 18, Electrical ConductivityEnergy Band Structures and Conductivity(metals,


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