CHAPTER 7: Dielectrics … What is a capacitor ? a passive two-terminal electrical component used to store energy in an electric field

Capacitors What is a dielectric material ? an electrical insulator that can be polarized by an applied electric field What are the ways of increasing capacitance? C o + Q ­ E V D i e l c t r ( )

Polarization Polarization … polar molecules vs. non-polar molecules Can non-polar molecules become polar ? Electric Dipole Moment,

Polarization How do dielectrics increase the capacitance of a capacitor ? + Q E ­ V A r e a = p t o l P d ( c ) B u n i z h g s f C o + Q ­ E V D i e l c t r ( ) Polarization,

Polarization Susceptibility, Χe: A proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. (dimesnionless) Permittivity: A measure of how an electric field affects, and is affected by, a dielectric medium. (F/m) polarizability … dielectric constant … are material properties. In a way they are equivalent to what mobility is for conductors and semiconductors.

Polarization Mechanism Dependence of ε’r & ε”r frequency depends on polarization mechanism: Electronic Ionic Interfacial Orientational

POLARIZATION MECHANISMS Ionic: polarization caused by relative displacements between positive and negative ions in ionic crystals (a) A NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion is zero. (b) In the presence of an applied field the ions become slightly displaced which leads to a net average dipole moment per ion.

POLARIZATION MECHANISMS Electronic: the stretching of atoms/electronic clouds under an applied E-field (in covalent solids) (a) Valence electrons in covalent bonds in the absence of an applied field. (b) When an electric field is applied to a covalent solid, the valence electrons in the covalent bonds are shifted very easily with respect to the positive ionic cores. The whole solid becomes polarized due to the collective shift in the negative charge distribution of the valence electrons.

POLARIZATION MECHANISMS Interfacial: charge accumulation at defective interfaces (2 material or 2 regions of same material) leads to the formation of a net polarization vector

POLARIZATION MECHANISMS Orientational (Dipolar): in “rigid polarized molecule” materials, an applied field aligns the permanent dipoles to yield a net polarization vector C l ­ H + p o ( a ) b v = q Q F E t ¹ c d

POLARIZATION MECHANISMS

DIELECTRIC LOSS The dielectric constant is frequency dependent … why ? The polarization process is not instantaneous … i.e. it takes a finite amount of time for the molecules to align themselves. If the applied field is changing so fast that the molecules cannot respond to it at all … then the polarization is … zero! Therefore ε is frequency dependent …

DIELECTRIC LOSS The imaginary part represents dielectric “losses” due to “slow” polarization.

Dielectric Loss per unit volume,

DIELECTRIC LOSS For the dielectric material as in the figure, calculate the loss tangent at 10 MHz frequency. If the parallel plate capacitor is formed with the material, where the separation is 1mm, plate area is 1mm2 and 1V is applied across… Calculate the value of resistance and capacitance. Calculate the power loss per unit volume. =0.5 =1.8x106 ohm =1.7x10-14 F =556 Wcm-3

Matter Polarization & Permittivity Electric Dipole Moment, Spring action Induced Electric Dipole Moment,

Matter Polarization & Permittivity Induced Electric Dipole Moment, Removal of applied E field cause the vibration with a resonant frequency… F=ma Electronic Polarizability Electronic polarization resonance frequency

Permittivity: Electronic Polarization Total Polarization Total Polarization =surface polarization charge density! Also, total polarization

Permittivity: Electronic Polarization before insertion of dielectric medium free surface charge density after insertion of dielectric medium dividing by the area, A

Permittivity: Electronic Polarization Substitution for surface charge density Relative permittivity Relation between polarization mechanism to relative permittivity

Clausius-Mossotti Equation The bulk electric field assumption is not valid in the atomic level Lorentz Field Relation between polarization mechanism to relative permittivity Clausius-Mossotti Equation For electronic polarization

Total Polarization Clausius-Mossotti Equation For ionic polarization Relative permittivity due to ionic and electronic polarization

Total Polarization under dc operation under optical frequency 7.9 Electronic and ionic polarization in KCl KCl has the FCC crystal structure. Lattice parameter is 0.629 nm. The ionic polarizability per ion pair (per K+-Cl- ion) is 4.58 10-40 F m2. The electronic polarizability of K+ is 1.264  10-40 F m2 and Cl- is 3.408  10-40 F m2. Calculate the dielectric constant under dc operation and at optical frequencies. Experimental values are 4.84 and 2.19. FCC… 4 KCl ion pairs per unit cell. The number of ion pairs, or individual ions, per unit volume (N) is: = 1.607  1028 m-3 under dc operation under optical frequency r(op) = 2.18 Example 7.2, 7.3