1. Chapter 5 Conductors, Dielectrics and Capacitance Current and Current Density

3. Example D5.1

4. Continuity of Current This equation indicates that the current diverging from a small volume per unit volume is equal to the time rate of decrease of charge per unit volume at every point

5. Conductors, Dielectrics, Semiconductors The Energy Band Structure in Three Different Types of Materials at 0K a)The conductor exhibits no energy gap between the valence and conduction bands. b)The Insulator shows a large energy gap c)The semiconductor has only a small energy gap

6. Table 2.1 Electrical Classification of Solid Materials MaterialsResistivity (  -cm) Insulators10 5 <  <  Semiconductors10 -3 <  < 10 5 Conductors  < 10 -3 Conductors, Dielectrics, Semiconductors

7. Metallic Conductors In a conductor, electric current can flow freely, in an insulator it cannot. Metals such as copper typify conductors, while most non-metallic solids are said to be good insulators, having extremely high resistance to the flow of charge through them. "Conductor" implies that the outer electrons of the atoms are loosely bound and free to move through the material. Most atoms hold on to their electrons tightly and are insulators. In copper, the valence electrons are essentially free and strongly repel each other. Any external influence which moves one of them will cause a repulsion of other electrons which propagates, "domino fashion" through the conductor

8. Metallic Conductors

9. Conductor Properties and Boundary Conditions Boundary Conditions Conductor-free space boundary in electrostatic 1 – The static electric field intensity inside a conductor is zero 2 – The static electric field at the surface of a conductor is everywhere directed normal to that surface 3 – The conductor surface is an equipotential surface E=0 within the conductor

11. The Method of Images

14. Semiconductors Conductivity is a function of both hole and electron concentrations and mobility

15. Semiconductor Materials SemiconductorBandgap Energy E G (eV) Carbon (Diamond)5.47 Silicon1.12 Germanium0.66 Tin0.082 Gallium Arsenide1.42 Indium Phosphide1.35 Boron Nitride7.50 Silicon Carbide3.00 Cadmium Selenide1.70 Conductors, Dielectrics, Semiconductors

17. Two-dimensional silicon lattice with shared covalent bonds. At temperatures approaching 0 K, all bonds are filled, and the outer shells of the silicon atoms are completely full. Conductors, Dielectrics, Semiconductors

18. An electron-hole pair is generated whenever a covalent bond is broken Conductors, Dielectrics, Semiconductors

21. A silicon crystal is somewhat different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a "hole". If a voltage is applied, then both the electron and the hole can contribute to a small current flow. The term intrinsic here distinguishes between the properties of pure "intrinsic" silicon and the dramatically different properties of doped n-type or p-type semiconductors. Semiconductors

22. The Nature of Dielectric Materials Most solid materials are classified as insulators because they offer very large resistance to the flow of electric current. Metals are classified as conductors because their outer electrons are not tightly bound, but in most materials even the outermost electrons are so tightly bound that there is essentially zero electron flow through them with ordinary voltages. Some materials are particularly good insulators and can be characterized by their high resistivities: Resistivity (ohm) Glass10 ^12 Mica9 x 10 ^13 Quartz (fused)5 x 10 ^16 Resistivity (ohm) Copper1.7 x 10 ^-8 -Dielectric in an electric field can be viewed as a free-space arrangement of microscopic electric dipoles which are composed of positive and negative charges whose centers do not quite coincide. Not free charges - They bound charges They are sources of electrostatic fields Model – Polarization P and Permittivity

23. If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. An applied electric field will polarize the material by orienting the dipole moments of polar molecules. This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure. The dielectric must be a good electric insulator so as to minimize any DC leakage current through a capacitor. Polar molecules have a permanent displacement existing between the centers of gravity of the positive and negative charges, and each pair of charges acts as a dipole. Dipoles are oriented randomly. A non-polar molecule does not have this dipole arrangement until a field is applied. A dipole may be described by its dipole moment p p = Qd where d is the vector from the negative to the positive charge. p are in coulomb-meters P = Polarization The Nature of Dielectric Materials

24. Electrical Properties ASTM Standard UnitTeflon ® PTFE Powder Paste Disper. Powder Paste Disper. Teflon ® FEP FEP Teflon ® PFA PFA Tefzel Tefzel ® Dielectric ConstantD1501 MHz2.1 2.6 Dissipation FactorD1501MHz<0.00010.00060.00010.007 Arc ResistanceD495sec>300 >180122 Volume ResistivityD257ohm·cm>10 18 >10 17 Surface ResistivityD257ohm·sq>10 18 >10 16 >10 17 >10 15 The Nature of Dielectric Materials

25. Electrical Properties of Kapton® Type HN Polyimide Film The Nature of Dielectric Materials Property Property Value--Film Thickness, mil (µm) 0.30 (7.6) 0.50 (12.7)* 1.00 (25.4)* 2.00 (50.8)* 3.00 (76.2)* 5.00 (127)* Dielectric Strength, AC V/mil (kV/mm), min. 3,000 (118) 6,000 (236) 5,000 (197) 4,500 (177) 3,000 (118) Volume Resistivity, ohm-cm at 200°C (392°F), min. 10 12 Dielectric Constant at 1 kHz, max. 4.0 3.9 Dissipation Factor at 1 kHz, max. 0.00700.00500.0036

26. The Nature of Dielectric Materials

27. Boundary Conditions For Perfect Dielectric Materials

29. The Nature of Dielectric Materials

30. Capacitance Capacitance of two conductor systems as the ratio of the magnitude of the total charge on either conductor to the ratio of the potential difference between conductors

31. Capacitance

32. Several Capacitance Examples Coaxial Cable Two concentric spheres Parallel-plate capacitor – two dielectrics

33. Capacitance of A Two-Wire Line

34. Coil Modeling - Parameter Computation

35. Simplified Frequency Model of Coil

36. Capacitance

37. Capacitance – Zero-Potential Conducting Plane and Conducting Cylinder