Lecture 17. Dielectric Materials

Transcription

1 Lecture 17 Dielectric Materials

2 3/ 3 3 3/ 3/ 4 4 exp = = = e R R B B e B v c B g v c e k k k k E π π π Dielectric aterials play a large rle in electrnics. One exaple was te xide in te MOS structures. Als listed as insulatrs. S, wen is it an insulatr and n lnger a seicnductr? 1) Sufficiently large energy gap f re tan.5 ev r 100 Ges k B at r teperature. ) Electrn le pairs cannt be created by visible ligt (400 n t 700 n) r 140 ev/(400 t 700)= (3.10 t 1.77) ev 3) erally excited electrn le pairs in intrinsic aterial plays virtually n rle. 3/ 4 3/ 3/ exp = = e R R B B g i k k E π = ) ( exp ) ( 3/ 3 10 Si E E K c R g g e i ev 1/c 3 i (1/c 3 ) E g (ev) Si At R = 300K

3 Defining prperty: w parallel cnducgng (etal) plates f area A, separated by distance d. Separated by vacuu. Define te capacitance as te aunt f carge n eac place wen a bias U is applied. e capacitance is te ability t stre carge. Q C = U A cnducgve places d It is prprgnal t te area A f te capacitr and inversely t te separagn f te plates. dielectric C = Q U A d And te capacitance depends n te ediu in between. Fr vacuu tis is te periyvity f space, a universal cnstant. ε Q A C = = ε ε = U d Wit actual aterials between te plates, re carge can be stred, i.e. te dielectric prperty (te dielectric cnstant r relagve periyvity) plays a rle. A Cater = ε r ε d Here, is te relagve periyvity r dielectric cnstant. ε r 1 F F is te unit f capacitance in Farad. As 1 F = 1 V

4 e intrducgn f a dielectric aterial (anyting but a cnductr) increases te capacitance ver te vacuu level. Eac at cnsists f tw parts: 1) a rater stagnary (really eavy) in tat is fixed in te layce f te aterial, and ) a clud f ving and bile electrns. As te external bias is applied and an electric field is establised. Wrk is carried ut t si^ te negagve electrn clud and ffset it fr te ins by a sall distance. A diple is created. In rder fr te sae bias t build up (i.e. wrk carried ut), extra carge ust be added t te plates f te capacitr. e electric diple ent P is a funcgn f te ved carge Q and teir separagn δ. P = Qδ Plariza(n is te prcess f fring te electric diple r its alignent wit exisgng ter diples in te presence f an external electric field. Carge redistribugn is te cnsequence.

5 PsiGve egagve e addign f te plarized aterial eans tere are carges. e ptengal steps dwn in te aterial. e residual electric field is lwer. Electric field, n dielectric Electric field, wit dielectric at ends vacuu r E dielectric E ε 1 =

6 PlarizaGn is caused by: 1) Electric plarizagn (external electric fields) ) Mlecular plarizagn 3) Diple rientagnal plarizagn 4) Space carge plarizagn All effects are addigve. If te applied electric field (tat generates te plarizagn) varies wit a frequency f, tere will be a crigcal frequency at wic te bile carges can n lnger respnd. e dielectric cnstant depends nt nly n te aterial but als n te frequency f te applied electric field. ere is a relaxagn Ge: is is te Ge scale during wic te carges respnd t te applied field. 1) electrns: very fast, sall relaxagn Ges. ) Ins: slw 3) Mlecules: uc slwer 4) Space carge: very slw wit very large relaxagn Ges.

7 Water: refracgve index n=1.3: =1.7; Radi freq.: =80 ε r ε r Radi Micrwave Radar visible If relaxagn Ge τ is uc srter tan te excitagn frequency f te applied electric field, te plarizagn ccurs instantaneusly (fr all pracgcal purpses). Wen τ is uc larger tan te frequency, n plarizagn ccurs. Wen 1/ τ and te frequency are te sae, resnances ccur. ExcitaGn energy is absrbed. e caracterisgc resnance frequencies are f crucial iprtance.

8 Piezelectrics: A strain results in a sall electric ptengal (diples are created). Exaple: quartz Pyrelectrics: ese are a subclass f piezelectric aterials. Hwever, tey exibit a spntaneus diple. eir teperature dependence akes te useful. Exaple: cigareie ligters Ferrelectrics: A subclass f pyrelectrics. ese als ave a spntaneus plarizagn. Hwever, te direcgn f te plarizagn ay be reversed by an external electric field.

9 In st aterials (i.e. dense slids knwn as insulatrs) te plarizagn is eiter electrnic (by electrns) r inic. Ferrelectrics: In ferrelectric aterials te inic cntribugn is te largest cpnent. 1) ere are ins tat are displaced in respnse t an electric field. ) All te inic displaceents ccur in te sae direcgn (i.e. are addigve) Wen te external field is switced ff, te displaceent is aintained. ere is ysteresis.

10 Ferrelectrics: In se aterials te displaceent ccurs spntaneusly. PlarizaGn exists witut any external field being applied. In ters te created plarizagn can nly reved by reversing te external field. IplicaGns: OE: e plarizagn is reversible. OE: Ferrelectrics usually d nt cntain any irn (Fe). Wy are tey called ferrelectric anyway? ere is a crigcal teperature (Curie teperature): Very uc like in ferragnegs, abve tis crigcal teperature c, te ferrelectric effect vanises. e aterials bece standard dielectrics. ypical Curie teperatures are: Uses are fr ulglayer capacitrs and rand access ery (nn vlagle). Exaples: Bariu Gtanate (BaiO 3 ) 00 C t 640 C

11 As illustrated fr BaiO 3 ne in is sligtly displaced fr its syetric lcagn. A sall separagn f inic carge ccurs. w terwise idengcal displaceent direcgns exist. A bistable cndign is present. If all displaceents r a ajrity line up in te sae direcgn, a peranent inic diple ent is establised.

12 e crystalline structure influences te dielectric cnstant. Different structures are stable in different teperature regies. A brad range f applicagns ave been realized. VibraGns, aka. sund, ve ats. e dielectric prperges cange. Pressure as siilar effect. is wrks in bt direcgns.

13 Inic cnducgn: e veent f negagve r psigve ins as tey jup fr ne layce site t anter under te influence f electric fields cntributes t verall current. It is uc weaker tan electrn currents (r les), i.e. nt bvius in cnductrs r seicnductrs. e inic cnducgvity depends n σ = q µ. in in It is a funcgn f te cncentragn f vacancies. ese prvide r fr te ins t jup. Here te bility is te effect f te diffusin cefficient D and te teperature. e Einstein relagn states k D = µ B in q in

14 Dielectric aterials are used t excite, r prbe te envirnent