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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

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