Notes1 - ECE215B/Materials206B Fundamentals of Solids for...

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ECE215B/Materials206B Fundamentals of Solids for Electronics E.R. Brown/Spring 2008 1 NOTES 1: Electrostatic Behavior of Solids#1 Solids are good at storing mechanical potential energy associated with the microscopic forces between atom (ionic or covalent bonds). A small compression of expansion of the solid entails a big change of energy. Solids are also good at storing other forms of potential energy, especially in electric and magnetic fields. We start with a look at electrostatic energy and the forces associated with it. This is one of the oldest branches of physics and engineering, and fundamental to the understanding of solid-state electronics. Energy and electric fields In presence of externally applied electric field, E 0 G , there are two terms that contribute to electrical potential energy inside a solid: (a) Work done by external field alone 2 0 0 (| |) 2 E Wd U d Ed V ε δ == G where U E is the energy stored per unit volume. (b) Potential energy from alignment of microscopic dipoles ( ) E G G in e P V = ⋅⋅ where G e P polarization per unit volume, E G in electric field inside solid For the purpose of solid-state analysis, we can subtract out the first term since it is there even without the solid present. The 1 st law of thermodynamics then becomes () in e dU TdS PdV E d P V =− + G G i By definition: 1 || G in e U E V P = intensive variable derivative taken along G e P direction and we have a susceptibility (thermodynamic) 0 e VP E χ = G G electric susceptibility The more common electrical susceptibility is given by
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ECE215B/Materials206B Fundamentals of Solids for Electronics E.R. Brown/Spring 2008 2 0 00 || e e VP E χ ε =≡ G G ε 0 permittivity of vacuum G in E and G e P are to be thought of as macroscopic averages over a volume much larger than the atoms but smaller than the solid itself. Solids generally form dipoles in 3 different ways (a) Microscopic dipoles are induced by applied field (b) Permanent internal dipoles are aligned by applied field (c) Free carriers (as in metals or semimetals) displace to create a large induced dipole extending over the entire solid sample. Independent of the type of atomic dipole, the response mechanism is the same and can be drawn graphically as shown below: Net positive charge 0 applied EE →→ 1 response E E So by linear superposition: 0 1 E E E in G G K + = (Note: Kittel defines G G in = ) The physics of dielectrics is largely the study of G e P and how it depends on: (a) geometrical (i.e., shape) effects of the solid sample (b) microscopic nature of the solid Before getting into these effects, we need one important result from electrostatics 1 E + p + p + p + p + p + p + p + p + p ˆ n
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ECE215B/Materials206B Fundamentals of Solids for Electronics E.R. Brown/Spring 2008 3 Polarization Theorem The distribution of microscopic dipoles shown in the above figure leads to a simple relation between the polarization vector and the microscopic dipole moment: e Pn p =⋅ G G . It is assumed that e P G
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Notes1 - ECE215B/Materials206B Fundamentals of Solids for...

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