Lecture 26: Dielectric materials ENGR-1600 Materials Science for Engineers Lecture 26: Dielectric materials

Dielectric Materials A dielectric material is an insulator which contains electric dipoles, that is where positive and negative charge are separated on an atomic or molecular level When an electric field is applied, these dipoles align to the field, causing a net dipole moment that affects the material properties. dipole moment: p = d q dipole “p” d

Resistance and Capacitance Current I ℓ ℓ Capacitance C=Q/V Permittivity Current I

Parallel Plate Capacitor Capacitance is the ability to store charge across a potential difference. Capacitance definition Unit: Farad Capacitance is a device property From capacitance to material property (dielectric constant) permittivity of medium permittivity of a vacuum dielectric constant

Dielectrics or Insulators Q and C depend on the geometry of the plates. C = Q / V = e0 A / l where the proportionality constant e0 is called permittivity of the vacuum. The units of C are 1 Clb/V = 1 Farad (1 F). Hence e0 = 8.85×10-12 F/m. The equation above looks similar to Ohm’s Law: R = V/I and 1/C = V/Q So R of a resistor is to flowing charge I (Clb/s) what 1/C of a capacitor is to static charge Q (Clb).

Dielectrics or Insulators When the space between the two plates of a capacitor is filled with a dielectric material, experiments show that at constant applied voltage V, the charge Q' on the plates is higher than the charge Q before: In this case: C = e A / l = Q’/V where e is the permittivity of the dielectric material. e can be written as e = e0 er with er > 1 The factor er by which the capacitance has been increased due to the material between the plates is called its dielectric constant.

Dielectric Constants for Materials

From Whence Dielectric? Dipole Moment and Polarization Alignment of Dipole p = q d

Remember Weak Secondary Bonding? Temporary Time Average Temporary VdW δ+ δ− δ− δ+ Time Average dipole δ− δ+ O H H O H H H-bond O H

Dielectric Medium in a Capacitor

Team Problem Consider a parallel-plate capacitor having an area of 6.65 x 10-4 m2 and a plate separation of 2 x 10-3 m across which a potential of 10 V is applied. If a material having a dielectric constant of 6.0 is positioned within the region between the plates, compute the following: The capacitance The magnitude of the charge stored on each plate The dielectric displacement The polarization

Origins of Polarization Electronic Polarization Electronic Polarization: Displacement of negative electron “clouds” with respect to positive nucleus. Requires applied electric field. Occurs in all materials. Ionic Polarization: In ionic materials, applied electric field displaces cations and anions in opposite directions Orientation Polarization: Some materials possess permanent electric dipoles, due to distribution of charge in their unit cells. In absence of electric field, dipoles are randomly oriented. Applying electric field aligns these dipoles, causing net (large) dipole moment. Ionic Polarization Orientation Polarization

Frequency Dependence of Dielectric Constant

Dielectrics or Insulators The data for er in the table can be explained roughly in terms of the main applicable polarization mechanism: Mechanism Features Materials Electronic small polarization, fast response gases, non-polar liquids, polymers Ionic medium polarization, medium response ceramics, inorganic glasses Orientational large polarization, slow response polar liquids The response time indicates how er depends on the frequency of the applied field. If tp is a characteristic time for the polarization to change, then the polarization cannot follow an applied electric field which changes in a time shorter than tp, or which has a frequency higher than tp-1.

Dielectrics or Insulators What happens physically to the dielectric is that the applied voltage (or electric field) polarizes the material. This polarization is caused by internal charges being moved slightly off of their normal equilibrium positions. Material er Vacuum 1.0000 Dry air 1.0006 Methane 1.7 Chlorine 2.0 Gasoline HDPE 2.3 PTFE Olive Oil 3.0 PMMA 2.9 PVC 3.1 Quartz 4.7 fused SiO2 3.8 Pyrex glass 5 Diamond 5.0 NaCl 5.9 MgO 9.6 Ethanol 24 Water 80 SrTiO3 300 BaTiO3 1500

Dielectrics or Insulators SrTiO3 and BaTiO3 are “ferroelectric”: very large er is due to permanent internal polarization. SrTiO3 and BaTiO3 are are also “piezoelectric”: polarization changes when mechanically strained. Conversely, if a voltage is applied, the materal expands or contracts. This piezoelectric effect is useful for making electro- mechanical sensors, actuators, and transducers. The material used most often in such applications is lead zirconate titanate (abbreviated PZT), a mixture of PbTiO3 and PbZrO3. PZT can be doped to adjust its piezoelectric and dielectric parameters.

BaTiO4 has a permanent electrical dipole at the unit cell level Ferroelectrics BaTiO4 has a permanent electrical dipole at the unit cell level This effect vanishes above a critical temp (Curie Temp), where the crystal structure converts to cubic

Piezoelectrics In these materials, polarization can be induced by mechanical force Broad Application sensors actuators imaging microphones speakers Compression  (+) electric field Tension  (-) electric field

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Dielectrics or Insulators Optical properties Insulators are optically transparent in single-crystal or amorphous form. Polycrystals may cause light scattering. Wide bandgap insulators Light excites e- from VB to CB when the energy of the photon matches (or exceeds) the Eg electronic and optical properties are intimately related concepts

Dielectrics or Insulators Quantum properties of light A light wave of frequency n and wavelength l consists of small energy packets called photons. A photon with frequency n has an energy Eph of Eph = hn where h is Planck's constant (numerical value: 6.63×10-34 Js). In addition, you should recall that the frequency n and wavelength l of light are related to each other by the equation n × l = c where c is the speed of light (numerical value: 3x108 m/s).

Dielectrics or Insulators Absorption/transmission of light If a photon with frequency n impinges on a material, it can give its energy to an electron in the VB, thus creating an electron-hole pair, if hn > Eg. On the other hand, if hn < Eg, no excitation can take place and the material is transparent. The threshold condition for absorption is Eg = hn = hc/l Þ l = hc/Eg Material Eg (eV) l = hc/Eg Ge 0.67 1.85 µm Si 1.1 1.13 µm GaAs 1.4 0.88 µm

Is there such a thing as a transparent metal? Team Problem Is there such a thing as a transparent metal? Is such a thing theoretically possible? Why or why not?

Solar Cells 6.4×1019 J = annual worldwide electricity consumption (2008) 5.5×1024 J = total energy from the Sun that hits the Earth each year