Lecture 4. Electrons and Holes in Semiconductors
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1 ecue 4 lec ad Hle i Semicduc I hi lecue yu will lea: eeai-ecmbiai i emicduc i me deail The baic e f euai gveig he behavi f elec ad hle i emicduc Shcley uai Quai-eualiy i cducive maeial C 35 Sig 2005 Faha aa Cell Uiveiy Majiy ad Miiy Caie I N-ded Semicduc: lec ae he majiy caie Hle ae he miiy caie I P-ded Semicduc: Hle ae he majiy caie lec ae he miiy caie lde ule f Thumb: Whe yig udead emicduc device alway fi ee wha he miiy caie ae dig C 35 Sig 2005 Faha aa Cell Uiveiy
2 eeai ce: eeai ad ecmbiai i Semicduc ecmbiai ce: + ae = + We ca wie he fllwig euai f he caie deiie: Thee euai ell hw he elec ad hle deiie chage i ime a a eul f ecmbiai ad geeai cee ae = C 35 Sig 2005 Faha aa Cell Uiveiy eeai ad ecmbiai i Themal uilibium Fm he fi lecue i hemal euilibium: The ecmbiai ae eual he geeai ae i.e. The i hemal euilibium: 0 0 C 35 Sig 2005 Faha aa Cell Uiveiy 2
3 igh Abi i Semicduc eeai f elec ad hle by h i emicduc: Ph g A efec ilic cyal laice Negaively chaged fee elec Piively chaged hle + A ilic cyal laice wih e be bd (e elec ad e hle) C 35 Sig 2005 Faha aa Cell Uiveiy eeai ad ecmbiai Ou f Themal uilibium ) Cide a P-ded lab f Silic: lec-hle ecmbiai ae i hemal euilibium eual he geeai ae 2 i 2) Nw u ligh a ime = 0: ligh igh bea he Si-Si cvale bd ad geeae ece elec-hle ai The e geeai ae w becme: 3) Mahemaical mdel f he abve iuai: ( ) ad () ae he ece elec ad hle deiie I mu be ha: We al aume ha: C 35 Sig 2005 Faha aa Cell Uiveiy ea a 3
4 4 C 35 Sig 2005 Faha aa Cell Uiveiy eeai ae: Aumi: i he lifeime f he miiy caie (i.e. elec) We ca ue he euai: The euai f ece miiy caie (i.e. elec) becme: eeai ad ecmbiai Ou f Themal uilibium ecmbiai ae: The ece ecmbiai ae i ial he ece MINOITY caie deiy C 35 Sig 2005 Faha aa Cell Uiveiy Slui wih he buday cdii i: 0 0 e 0 ( ) ligh ued- a = 0 ce hle deiy i f cue : eeai ad ecmbiai Ou f Themal uilibium A he ece elec ad hle deiie each a eady ae value ad
5 eeai ad ecmbiai Ou f Themal uilibium Nw ue ha ligh had bee ued- f a vey vey lg ime ad i wa ued-ff a ime = 0 A ime = 0 : ad ( ) ligh ued-ff a = 0?? 0 Sice ad he caie deiie ae eual hei hemal euilibium value. Themal euilibium mu ge eed ice he ligh ha bee ued-ff Quei: Hw de hemal euilibium ge eed?? C 35 Sig 2005 Faha aa Cell Uiveiy eeai ad ecmbiai Ou f Themal uilibium We ca ue he euai: eeai ae: ecmbiai ae: Aumi: The ece ecmbiai ae i ial he ece MINOITY caie deiy The euai f ece miiy caie (i.e. elec) becme: C 35 Sig 2005 Faha aa Cell Uiveiy 5
6 eeai ad ecmbiai Ou f Themal uilibium Slui i: 0 e ce elec deiy decay eeially ze fm i iiial value ( ) ligh ued-ff a = 0 0 The ece hle deiy will al decay i he ame way: A 0 0 C 35 Sig 2005 Faha aa Cell Uiveiy The ece caie deiie decay wih ime ad hemal euilibium value f caie deiie ae eed 0 he elec ad hle deiie each hei euilibium value: ad e eeai ad ecmbiai i Ded Semicduc Wheeve yu have fid a eei f ue he fllwig ecie: If i i a -ded emicduc: i he miiy caie lifeime If i i a -ded emicduc: i he miiy caie lifeime The ece ecmbiai ae (i.e. - ) i alway ial he ece MINOITY caie deiy C 35 Sig 2005 Faha aa Cell Uiveiy 6
7 lec ad Hle Cue Deiy uai Fm la lecue D d d D d d 2 Thee ae w f Shcley euai! Shcley Badee ad Baai fm Bell ab wee awaded he Nbel Pize f iveig he emicduc ai William Shcley h Badee Wale Baai C 35 Sig 2005 Faha aa Cell Uiveiy lec ad Hle Cue Ciuiy uai Yu have aleady ee he euai: Thee euai ell hw he elec ad hle deiie chage i ime a a eul f ecmbiai ad geeai cee. Caie deiie ca al chage i ime if he cue deiie chage i ace!!! C 35 Sig 2005 Faha aa Cell Uiveiy 7
8 8 C 35 Sig 2005 Faha aa Cell Uiveiy lec ad Hle Cue Ciuiy uai Cide he ifiieimal i bewee ad + The diffeece i hle flue a ad + mu eul i ilig u f hle i he ifiieimal i. Ne ha i he hle chage deiy Nw add ecmbiai ad geeai he abve euai: C 35 Sig 2005 Faha aa Cell Uiveiy lec ad Hle Cue Ciuiy uai - III Oe ca d he ame f elec a well S w we have w ew euai 3 4 Thee ae w me f Shcley euai!
9 au aw ad lecaic The e chage deiy i a emicduc i N N d a au aw i diffeeial fm: Nd Na 5 Thi i he fifh ad he la f he Shcley euai! Faad/m Faad/cm F Silic:. 7 C 35 Sig 2005 Faha aa Cell Uiveiy The Five Shcley uai d D d D d d Nd Na Uig hee euai e ca udead he behavi f emicduc micelecic device!! C 35 Sig 2005 Faha aa Cell Uiveiy 9
10 Quai-Neualiy Maeial wih lage cduciviie ae uai-eual Quai-eualiy imlie ha hee ca be lage chage deiie elecic field iide a cducive maeial e ee why hi i ue..ad hw deviai fm uai-eualiy diaea. Cide a ifiie ad cducive N-ded emicduc wih a e chage deiy a ime =0: N-ded Chage deiy The chage deiy will geeae elecic field (by au law): N-ded C 35 Sig 2005 Faha aa Cell Uiveiy Quai-Neualiy The elecic field will geeae elecical cue: N-ded The elecical cue will ile elec f he chage deiy ad eualize i ad he hee i chage deiy lef i he medium N-ded Thi whle ce ae a ime f he de f he dielecic elaai ime d : 5 3 d ~ 0 0 Secd C 35 Sig 2005 Faha aa Cell Uiveiy 0
11 C 35 Sig 2005 Faha aa Cell Uiveiy Aedi: eai f Quai-Neualiy N-ded. Fm au law: Ue he ciuiy euai f chage: d d 0.. Cue euai: Slui: d e 0 Chage deiy i a cducive medium diaea a ime cale f d
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Lecue 4 lec ad Hle i Semicduc I hi lecue yu will lea: Geeai-ecmbiai i emicduc i me deail The baic e f euai gveig he behavi f elec ad hle i emicduc Shckley uai Quai-eualiy i cducive maeial C 35 Sig 2005
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