Lecture 4. Electrons and Holes in Semiconductors

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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 Faha Raa 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 Glde Rule f Thumb: Whe yig udead emicduc device alway fi ee wha he miiy caie ae dig C 35 Sig 2005 Faha Raa Cell Uiveiy

Geeai ce: Geeai ad Recmbiai i Semicduc Recmbiai ce: + Rae = G + We ca wie he fllwig euai f he caie deiie: G R G R Thee euai ell hw he elec ad hle deiie chage i ime a a eul f ecmbiai ad geeai cee Rae = R C 35 Sig 2005 Faha Raa Cell Uiveiy Geeai ad Recmbiai i Themal uilibium Fm he fi lecue i hemal euilibium: The ecmbiai ae R k eual he geeai ae G i.e. G R The i hemal euilibium: G G R R 0 0 C 35 Sig 2005 Faha Raa Cell Uiveiy 2

Ligh Abi i Semicduc Geeai 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 bke bd (e elec ad e hle) C 35 Sig 2005 Faha Raa Cell Uiveiy Geeai ad Recmbiai Ou f Themal uilibium ) Cide a P-ded lab f Silic: lec-hle ecmbiai ae i hemal euilibium R k eual he geeai ae 2 G k i 2) Nw u ligh a ime = 0: C 35 Sig 2005 Faha Raa Cell Uiveiy Ligh beak he Si-Si cvale bd ad geeae ece elec-hle ai The e geeai ae w becme: G G G L 3) Mahemaical mdel f he abve iuai: P-ded P-ded ' ' ( ) ad () ae he ece elec ad hle deiie I mu be ha: ' We al aume ha: ' ' ' ligh ea a 3

Geeai ad Recmbiai Ou f Themal uilibium We ca ue he euai: G R G R ' ' Geeai ae: G G G L Recmbiai ae: R k k ' ' ' k k k ' ' R Aumi: ' ' k i he lifeime f he miiy caie (i.e. elec) The euai f ece miiy caie (i.e. elec) becme: ' G R ' G GL R The ece ecmbiai ae i ial he ece MINORITY caie deiy ' G L ' C 35 Sig 2005 Faha Raa Cell Uiveiy Geeai ad Recmbiai Ou f Themal uilibium ' ' GL Slui wih he buday cdii ' 0 0 i: ( ) ligh ued- a = 0 ' G L e ce hle deiy i f cue : ' ' G L 0 A he ece elec ad hle deiie each a eady ae value ' ' GL GL ad GL GL C 35 Sig 2005 Faha Raa Cell Uiveiy 4

Geeai ad Recmbiai 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 : ' GL ' GL ad G L L G ( ) 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 Raa Cell Uiveiy Geeai ad Recmbiai Ou f Themal uilibium We ca ue he euai: ' G R G R ' Geeai ae: G G Recmbiai ae: R k Aumi: ' ' k ' ' k ' k k ' ' The ece ecmbiai ae i ial R he ece MINORITY caie deiy The euai f ece miiy caie (i.e. elec) becme: ' G R ' G R ' ' GL C 35 Sig 2005 Faha Raa Cell Uiveiy 5

Geeai ad Recmbiai 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 Raa 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 Geeai ad Recmbiai i Ded Semicduc Wheeve yu have fid a eei f R ue he fllwig ecie: If i i a -ded emicduc: R R ' i he miiy caie lifeime If i i a -ded emicduc: R R ' i he miiy caie lifeime The ece ecmbiai ae (i.e. R - R ) i alway ial he ece MINORITY caie deiy C 35 Sig 2005 Faha Raa Cell Uiveiy 6

lec ad Hle Cue Deiy uai Fm la lecue D d d D d d 2 Thee ae w f Shckley euai! Shckley Badee ad Baai fm Bell Lab wee awaded he Nbel Pize f iveig he emicduc ai William Shckley h Badee Wale Baai C 35 Sig 2005 Faha Raa Cell Uiveiy lec ad Hle Cue Ciuiy uai Yu have aleady ee he euai: G R G R 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 Raa Cell Uiveiy 7

8 C 35 Sig 2005 Faha Raa 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: R G C 35 Sig 2005 Faha Raa Cell Uiveiy lec ad Hle Cue Ciuiy uai - III Oe ca d he ame f elec a well R G S w we have w ew euai R G R G 3 4 Thee ae w me f Shckley euai!

Gau Law ad lecaic The e chage deiy i a emicduc i N N d a Gau Law i diffeeial fm: Nd Na 5 Thi i he fifh ad he la f he Shckley euai! 8.85 0 8.85 0 2 4 Faad/m Faad/cm F Silic:. 7 C 35 Sig 2005 Faha Raa Cell Uiveiy The Five Shckley uai d D d D G R G R d d Nd Na 3 4 2 5 Uig hee euai e ca udead he behavi f emicduc micelecic device!! C 35 Sig 2005 Faha Raa Cell Uiveiy 9

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 Le 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 Gau law): N-ded C 35 Sig 2005 Faha Raa 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 ake a ime f he de f he dielecic elaai ime d : 5 3 d ~ 0 0 Secd C 35 Sig 2005 Faha Raa Cell Uiveiy 0

C 35 Sig 2005 Faha Raa Cell Uiveiy Aedi: Reai f Quai-Neualiy N-ded. Fm Gau 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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