lecture 17 dielectric materials - home | center for … 17 dielectric...a hysteresis loop is...
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Lecture17:DielectricMaterialsTheyareofgreatimportanceinelectronicsindustry.‐Howdowedefineaninsulator?• Energygapof≈2.5eV• Materialsinwhichelectron‐holesareless,notcreatedbyvisiblelight(400nm‐700nm)≈ 3𝑒𝑉
‐Whatisthereasonbehindwidegap??DielectricConstant(ℰ):
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Example:WhenyouapplyavoltagetotwoparallelplatesseparatedbydistanceL,theresultingelectricchargesremainontheplatesevenafterremovingthevoltage,Wedefinethatby
C =Qv
C=capacitanceC→abilitytostoreelectriccharge
𝐶 ∝𝐴𝐿
ItalsodependsonthematerialbetweentheplatesInvacuum,𝐶 = ℰ0
𝐴𝐿(eq1)
ℰ!:Permittivityoffreespace(universalconstant)=8.85 ∗ 10!!" F mInthepresenceofdielectricmaterial𝐶 = ℰ𝑟ℰ0
𝐴𝐿(eq2)
ℰ! :Dielectricconstant(relativepermittivity)
Usingeq1&eq2:
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Thecapacitanceincreasedafteradielectricmaterialisintroduced.Explain:
Theatomisrepresentedbyapositivelychargedcoreandanegativelychargedelectroncloud.Byapplyingelectricfield,thechargesaredisplaced →FormationofanelectricdipoleTheelectricdipolemoment
𝑃 = 𝑄 ∙ 𝛿Polarization:Theprocessofformationofanelectricdipole(oralignmentofanexistingdipole)undertheinfluenceofanexternalelectricfield.Thiscausesredistributionofcharges.
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Looktothedirectionoftheexternalelectricfieldandthedirectionofpolarization,itisclearthatEhasbeendecreasedbypolarization:
𝐸 =E!"#$$%
ℰ E:afterdielectricmetalℰ:DielectricconstantTypeofPolarization1.Electricpolarization2.Molecularpolarization3.Dipolarpolarization4.Spacechargepolarization:longrangechargemigrationTheireffectscanbeaddedNote:DielectricconstantisfrequencydependentFrequencyDependence:Relaxationtime:Reorientationofthedipoleinresponsetoanelectricfieldischaracterizedbyrelaxationtime (𝜏):• Electricpolarization:𝜏issmall‐fastresponse
• Ionicpolarization:Slow
• MolecularPolarization:Muchslower
• Spacechargepolarization:Veryslow(𝜏verylarge)
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𝛼:standsforpolarization‐ Whenrelaxationtime𝜏ismuchfasterthanthefrequencyoftheappliedelectricfield,polarizationoccursinstantaneously.
‐ When𝜏ismuchslowerthanthefrequency,nopolarizationoccurs.
‐ When𝜏andthefrequencyoftheappliedfieldarethesame,adielectricionwillhappen(excitationenergyisabsorbed)
Note:Itisveryimportanttoknowthefrequencyfordielectricionsforthematerial
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Ferroelectric
Inmostdielectricmaterials(insulatingdensesolids)thepolarizationiseitherionicorelectronic.Ferroelectricmaterial:Ioniccontributionisthelargestandithastwoofthefollowingconditions1. Containsionsdisplaceinresponsetoanelectricfield
2. Thedisplacementslineupinthesamedirection3. Thedisplacementsdonotdisappearafterremovingtheelectricfield
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‐Someferroelectricmaterialsdevelopaspontaneouspolarizationwithoutanexternalappliedelectricfield.‐Insomematerials,polarizationdoesnotvanishafterremovingtheelectricfield(remnantpolarization).Itcanonlyremainremovedbyinvertingtheelectricfield,ahysteresisloopisobtained.Whatistheimplicationofthat?
Note:DirectionofpolarizationisreversibleNote:Ferroelectricsdonotusuallycontainiron.Whyaretheycalledferroelectric?CriticalTemperature(Curie):similartoferromagnetic.Abovethecriticaltemperature,ferroelectriceffectsaregoneandthematerialbecomesdielectric.RangeofCurietemperature:
−200℃ to 640℃Useofferroelectrics‐Multilayercapacitors‐RandomAccessMemoryExample:Materialexhibitsaspontaneouspolarization:BaTiO3(BariumTitanate)
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Whythesematerialspossesspontaneouspolarizations?Intheircrystalstructure,thepositiveandnegativeionsareslightlydisplacedfromtheirsymmetricalpositions,whichleadtoapermanentionicdipolemoment.Alargenumberofthesedipoleslineup.
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IonicConductionsThemovementofsomenegativeandpositivechargedions(jumpfromlatticesitetoanotherlatticesiteundertheinfluenceofanelectricfield).Conductivity𝜎:𝜎!"# = 𝑁!"#𝑒𝜇!"#Itdependsonvacancyconcentrations,soionscanjump:(Mobility)μ!"# =
!"!!!
(EinsteinRelation)D:Diffusioncoeff.T:temperatureK!:Boltzmanconstant