1:DielectricResponse,ChargeInjectionandtransport,DoallquestionsandallpartsforfullDescribewhathappenswhenanidealdielectriciscedinanelectric[Answer]Intheidealsituation,whenweceanidealdielectricinelectricitcannotconduct,butthechargerequiredbytheelectrodeswillincreasetokeepthevalueofelectricfieldinthedielectriccomparedtothechargerequiredwhentheelectrodesareseparatedbyspace.ExinwhythedielectricresponsechangeswiththefrequencyofanappliedACelectricfield[Answer]Weknowdielectrichaspermanentdipoles,andwhendipolesrotateaneworientation.NowweconsiderACelectricfieldsituation,timeallowedbytheelectricfielddecidetheamountofrotationbeforeitreversesdirection.Thedielectricspermittivitychangeswiththefrequencyoftheelectricfieldpointedoutbytheelectricphysicstheory.Therealcomponentofthedielectricspermittivityisproportionaltothecapacitivelystoredchargeatfrequency.Theimaginarycomponentofthedielectricspermittivitydefinesaccurrentdensityatfrequency.Wehave??(??)=?(??)??(??); ??()=??[??()]/????.Firstdefineg(t)asthepolarizationresponsetoaunitfieldimpulseatt=0,andpolarizationattimetduetoacontinuouslyappliedfieldisthesumofalltheimpulseresponsesoverthewholetimerange.P(t)

g(tt')E(t')dtForAC-field,we

??()=??()=?e χ*(ω)g(z)e0

Nowwecanfindthattheresponsechangeswiththefrequencyfromthecalculation,thisresponseisdefinedbyrelaxationandoscillator.ThefrequencydependentdielectricpermittivityofapolymerisgiveninFigure1forarangeoftemperatures.(i)DrawanArrheniusplotofthepeakfrequencyofthetwopeaksandworkouttheiractivationenergies.(ii)Drawaplotofthethesusceptibilitymagnitudeofthe'alpha'processasfunctionoftemperature,temperature,andstatewhat lsusaboutthematerial,(ii)estimatesusceptibilityofthe'beta'processat346K.(iv)SaywhatthestateofthematerialisatT<333K,(v)Statewhetherthematerialwouldbegoodasacapacitorcapacitororasaninsulator,and inyourWeknow

1/exp(-/kT)ln(1/)=(-Fromthefigure1wecanchoose75℃and1/T1=1/(75+273)=1/348,ln(1/1)=ln(10^-0.75)=-1/T2=1/(90+273)=1/363,ln(1/2)=So,theslope(4.03+1.73)/(1/363-1/348)=--/k=-48508, =6.69×10?19FIGURETheconductivityisgivenby=en. inwhatnand[Answer]Firstweknowtheformula??=????.Thisformuladefinestheconductivity??.ItisamaterialpropertyconsideringameasuredtyJ(thecurrentdensity)andthecontrolparameterE(theelectricfield).WedefinethecurrentdensityJandtheelectricfieldEintermsofthecurrentpassingthroughasampleofmaterialwhenapotentialdifferenceisappliedbetweentheends.fromtheformula??=????=??????(????+????)??,weknowmobility??=????+????,isthemobilityofthecarriers.WhenanelectricfieldEisappliedacrossasampleofmaterial,theelectronswillrespondbymovingwithanaveragevelocity.Wecallitdriftvelocity????.Thentheelectronmobilityμisdefinedasthevelocityofmigrationcorrespondingtounitfieldstrength(1V/cm)withtheformulaμ=ECarrierconcentration??=????=???????????{?????/2????}and????iselectronenergywhenjumpfromvalencestatestoconductionband.Exinwherechargecarrierscomefrom:i)atlowfieldsii)athighAtlowfields,itisaohmicregion,weneedtoconsiderthreewhenbandgapseg≥5ev,thereisnointrinsiccarriersionisableimpuritiesgivecarriers----donorsdonatenegativecarriers(electrons),acceptorsacceptelectronsfromvalencebondsandcreatemovablepositive‘holes’chargeatelectrodesproducedbycontactbetweendissimilarmaterials---salimitedamountofchargecarriersathighfields,thecurrentisnon-linearinelectricfield.Thecarrierconcentrationdependsontheamountofinjection.JJ ExinwhythemobilitymeasuredforpolyethyleneatT=300Kis10-14m2/Vsalthoughthemobilityofachargecarrierinanextendedstateisabout10-3[Answer]Becausetypicalmobilityisjustonecarrierfromevery2×104lamella,i.e.10-3c/m3ofchargecarriersandimcounterions.Butastotheextendedstate,forpolymerstheirregularstructure(macroscopicallynon-periodic)meansthatstatesonlyextendoverlimitedregionsofspace.Sothemobilityinextendedstateismuchhigher.Thetimetakentoreleaseachargecarrierfromatrapisgivenby-1exp(/kT),withk=86.2x10-6eV/Kandtheattemptfrequencyforcarrierreleasegivenby=6.25x1012s-1atT=300K.Thetimetakenforachargecarriertocross1mmofpolyethyleneinafieldof106V/mis105s.Exinw eansthatchargecarrierdoesnotentertrapswithadepthgreaterthan1.06eVonits[Answer]Becausewhenthetimetakentoreleaseachargecarrierislessthan105s,thechargecarrierwouldnotenterthetraps.Soγ?1eΔ/kT>Nowwecansubstitutethenumberintothisformulafromtheinformation,wecanfindout Δ>1.06????thismeansthatthechargecarrierdoesnotentertrapswithadepthgreaterthan1.06eVonitspath.Describewhatismeantbytheterm'dynamicequilibrium'forthecurrentswhenafieldisappliedtoasystemofdielectricandelectrodes,andstatehowthisisdifferenttoathermodynamicequilibrium.[Answer]Thesystemisinatransient ernedbythedynamicstrap,de-trap,injection,extraction,andgeneration(ionizationandionseparation)whenafieldisappliedtoasystemofdielectricandelectrodes.Sowhenitreachesthesteadystate,therewillbeaequilibrium,wecallitdynamicequilibrium.Thismaybedifferentfromathermaldynamicequilibrium.Ifathermalequlibriumisreached,chargecarrierswillbedistributedbetweentrapstatesandtransportstatesaccordingtotheboltzmandistribution.Thismeans,inthermalequilibriumtherearealwayssomecarriers,whichmightbedifferentfromthedynamicequilibrium.Exinhowanappliedfieldaffectstheinjectioncurrentfromthe[Answer]Whenafieldisapplied,theconcentrationofcarriersisincreasedfield-reductionofbarrierforchargereleasefromaneutralentityand/orseparationofionicspecies.Carrierscanbeinjectedfromelectrodesathighfields--excesscarrierscontributetoconductionIonspresentinthepolymercanbeseparatedathighfields--neutralmoleculesareinchemicalequilibriumwithdissociatedions:AB?A-+B+AndconcentrationsofionsA-&B+dependupontemperatureandverylittleuponfielduntilexceptionallyhighfieldvalues.Sothecurrentincreaseswhenthereishighfield.Exinhowanappliedfieldaffectsthecurrentinsidethedielectricwhenitiscontrolledbyhopbetweenneutraltraps.[Answer]外施電場的作用將使陷阱的勢壘發(fā)生傾斜。即具有正電荷的施主能級上所捕獲的電子，脫陷時所需克服的勢壘高度降低，使得注入到介內(nèi)的電流增加，稱為普爾-凱爾效應。Whenahighfieldisapplied,fieldincreasestransferratebetweentrapsites.Asshownfromthegraphandtheformula,thefieldlowersbarrierforforwardtransferandincreasesbarrierforreversetransfer.So,theeffectoffieldistoincreasecarriermobility,whichmeanstoincreasethecurrent.-

(x)e/(4netchargeflow=forwardsrate–reverseTherefore,thechargetransportcontrolledbyhopofinjectedcarriersbetweenneutraltrapswouldincreasethecurrentinthehighfieldfromtheformula??=??????.TheinjectioncurrentdensityintoamaterialisgivenbyJ=1.8375x10-2exp(6.82x10-24E0.5/kT),withk=1.381x10-23J/KandEisthemeasuredelectrodefieldinV/m.StatehowyouknowthatthisisaSchottkyinjectioncurrent.ThebulktransportcurrentisgivenbyJ=(3.275x10-13/E)sinh(1.59335x10-6E/kT),withk=1.381x10-23J/K.WhenafieldofE=3x107V/misappliedatT=300Kthesetwocurrentsarenotequal.ExinwhathappenstobringthesystemintodynamicDefinethetermspacechargeandstatehowitaffectstheelectricfieldSpacechargeisaconceptinwhichexcesselectricchargeistreatedasacontinuumofchargedistributedoveraregionofspaceratherthandistinctpoint-likecharges.Thenetchargeinaregionofspaceiscalledspacecharge,definedby=

risthespacechargedensityspacechargeisgeneratedwhenthereisacurrent?J/?x+?/?t=JandarefunctionsofbothpositionxandtimeSpacechargemodifiesthelocalfieldandaltersJlocallysoastoremovethecurrentgradientsteadystateequilibriumoccurswhen?J/?x=0.Thatmeanselectrodecurrentadjuststoequalbulkcurrenttogivesteadystate,whichwillchangethedistributionofthefield.Forexample,inacableasAtinnerconductor(anode),theappliedfieldisthehighest.J(Eapp)initiallyreducesalongradialvector:?J/?r<Theinnerconductor(anode)ishotterthanouter.Jisinitiallylargestclosetoinnerconductor:?J/?r<Wecangetthefigurebelow.SpacechargereducesfieldnearanodeincreasesfieldnearcathodeequalisescurrentdensityacrosstheinsulationDrawadiagramshowingthedependenceofthefielduponpositionwhenthereisheterochargeneartotheanode.Whenthereisheterochargeneartotheanode,spacechargeincreaseselectrodefieldandreducesbulkfield.Itcanincreaseinjectioncurrentandreducesbulkcurrenttobringequality.Wecanfindoutthefollowingfigure.Exinwhyitisimportanttousethemeasuredlocalfieldandlocalcurrentswhentestingproposedmechanismsforthecurrentdensityfielddependence.Becausespacechargeisgeneratedwhenthereisacurrentgradient.Fieldandtemperaturegradientsacrosscablesgivecurrentgradientsandspacecharge.spacechargemodifiesthelocalfieldandaltersjlocallysoastoremovethecurrentgradientsteadystateequilibriumoccurswhen?j/?x=0.Theywillaffecteachother,soitisimportanttousethemeasuredlocalfieldanFigure2givesthespacechargeasafunctionoftimeafterthevoltagehasbeenremoved.Calculatetheminimum(min)and um(max)trapdepths(ineV)forthepositivespacechargeinthetrapsthatareemptiedduringtheexperiment(thesecontainabout3x10-8Cofcharge).Calculatethenumberoftrapsperm3,pereV,assumingthatthisvalueisconstantfortheenergyrangemaxtomin.Theattemptfrequencyforcarrierrelease)isgivenbykT/h(T=absolutetemperature,k=86.210-6eV/K,h=4.136x10-15eVs),andthechargeontheelectronis1.602x10-19C.Unstressed,NegativeUnstressed,NegativechargedataPositivechargedataPositivechargefitNegativechargefitSpaceChargeSpaceCharge10-410-310-210-1100101102103104105106Log-TimeFromthetrelease=-1Withtwotimevalueswehad,wecanSo,thetotalnumberofthetraps3x108C/(1.602x10-Therangemax-Thenumberoftrapsperm3,pereV=totalnumberoftraps/(volum