EE105 - Fall 2005 Microelectronic Devices and Circuits

Transcription

1 EE5 - Fll 5 Microelectroic evice ircuit Lecture 4 P Juctio Lecture Mteril Lt lecture I mufcturig roce iffuio curret Review of electrottic I ccitor Thi lecture P uctio

2 rrier ocetrtio Potetil I therml equilibrium, there re o eterl fiel we thu eect the electro hole curret eitie to be zero: J q μ E μ oe q q kt o o o kt q o th 3 rrier ocetrtio Potetil We hve equtio reltig the otetil to the crrier cocetrtio kt q If we itegrte the bove equtio we hve l We efie the otetil referece to be itriic Si: th o th i 4

3 rrier ocetrtio eru Potetil The crrier cocetrtio i thu fuctio of otetil e / th i heck tht for zero otetil, we hve itriic crrier cocetrtio referece. If we o imilr clcultio for hole, we rrive t imilr equtio e / th i ote tht the lw of m ctio i uhel / / i e th th e i 5 The oig hge Potetil ue to the log ture of the otetil, the otetil chge lierly for eoetil icree i oig: th l 6m l 6m l log i 6m log 6m log i Quick clcultio i: For -tye cocetrtio of 6 cm -3, the otetil i -36 m -tye mteril hve oitive otetil with reect to itriic Si 6 3

4 P Juctio: Overview 7 P Juctio: Overview 8 4

5 P Juctio: Overview Preet i mot I tructure 9 P Juctio: Overview The mot imortt evice i uctio betwee -tye regio -tye regio Whe the uctio i firt forme, ue to the cocetrtio griet, mole chrge trfer er uctio Electro leve -tye regio hole leve -tye regio Thee mole crrier become miority crrier i ew regio c t eetrte fr ue to recomtio ue to chrge trfer, voltge ifferece occur betwee regio Thi crete fiel t the uctio tht cue rift curret to ooe the iffuio curret I therml equilibrium, rift curret iffuio mut blce -tye A -tye 5

6 P Juctio urret oier the P uctio i therml equilibrium Agi, the curret hve to be zero, o we hve J o qμe q o qμe q o E μ o E μ kt q kt q P Juctio Fiel -tye -tye A E J iff i i E J iff Tritio Regio 6

7 Totl hrge i Tritio Regio To olve for the electric fiel, we ee to write ow the chrge eity i the tritio regio: ρ q I the -ie of the uctio, there re very few electro oly ccetor: ρ q Sice the hole cocetrtio i ecreig o the - ie, the et chrge i egtive: > ρ < < < 3 hrge o -Sie Alogou to the -ie, the chrge o the -ie i give by: q ρ < < The et chrge here i oitive ice: ρ > > i E J iff Tritio Regio 4 7

8 Ect Solutio for Fiel Give the bove roimtio, we ow hve ereio for the chrge eity q ie ρ q / th / th ie o < < < < We lo hve the followig reult from electrottic E ρ otice tht the otetil er o both ie of the equtio ifficult roblem to olve A much imler wy to olve the roblem 5 eletio Aroimtio Let ume tht the tritio regio i comletely elete of free crrier oly immole ot eit The the chrge eity i give by q ρ q o < < < < The olutio for electric fiel i ow ey E E ρ ρ ' ' E Fiel zero outie tritio regio 6 8

9 eletio Aroimtio Sice chrge eity i cott ρ ' q E ' o If we trt from the -ie we get the followig reult ρ ' q E ' E E Fiel zero outie tritio regio q E 7 Plot of Fiel I eletio Regio -tye A eletio Regio -tye q E o q E E-Fiel zero outie of eletio regio ote the ymmetricl eletio with Which regio h higher oig? Sloe of E-Fiel lrger i -regio. Why? Pek E-Fiel t uctio. Why cotiuou? 8 9

10 otiuity of E-Fiel Acro Juctio Recll tht E-fiel iverge o chrge. For heet chrge t the iterfce, the E-fiel coul be icotiuou I our ce, the eletio regio i oly oulte by bckgrou eity of fie chrge o the E-Fiel i cotiuou Wht oe thi imly? q q E E o o q q o o Totl fie chrge i -regio equl fie chrge i - regio! Somewht obviou reult. 9 Potetil Acro Juctio From our erlier clcultio we kow tht the otetil i the -regio i higher th -regio The otetil h to moothly tritio form high to low i croig the uctio Phyiclly, the otetil ifferece i ue to the chrge trfer tht occur ue to the cocetrtio griet Let itegrte the fiel to get the otetil: q o ' q ' ' o o '

11 Potetil Acro Juctio We rrive t otetil o -ie rbolic q o o itegrl o -ie q Potetil mut be cotiuou t iterfce fiel fiite t iterfce q q Solve for eletio Legth We hve two equtio two ukow. We re filly i oitio to olve for the eletio eth q q q q o o o q o q >

12 Sity heck oe the bove equtio mke ee? Let y we oe oe ie very highly. The hyiclly we eect the eletio regio with for the hevily oe ie to roch zero: lim q lim q q Etire eletio with roe cro -regio 3 Totl eletio With The um of the eletio with i the ce chrge regio X q Thi regio i eetilly elete of ll mole chrge ue to high electric fiel, crrier move cro regio t velocity turte ee X q 5 μ E 4 μ cm 4

13 Hve we ivete bttery? we hre the P uctio tur it ito bttery? A A th l l th l i i i? umericl emle: m l 5 6m log 5 6 A i 6m 5 otct Potetil The cotct betwee P uctio crete otetil ifferece Likewie, the cotct betwee two iimilr metl crete otetil ifferece roortiol to the ifferece betwee the work fuctio Whe metl emicouctor uctio i forme, cotct otetil form well If we hort P uctio, the um of the voltge rou the loo mut be zero: m m m m m m 6 3

14 P Juctio citor Uer therml equilibrium, the P uctio oe ot rw y much curret But otice tht P uctio tore chrge i the ce chrge regio tritio regio Sice the evice i torig chrge, it ctig like ccitor Poitive chrge i tore i the -regio, egtive chrge i i the -regio: q q o o 7 Revere Bie P Juctio Wht he if we revere- the P uctio? < Sice o curret i flowig, the etire revere e otetil i roe cro the tritio regio To ccommote the etr otetil, the chrge i thee regio mut icree If o curret i flowig, the oly wy for the chrge to icree i to grow hrik the eletio regio 8 4

15 5 9 9 oltge eeece of eletio With reo the mth but i the e we relize tht the equtio re the me ecet we relce the built-i otetil with the effective revere : q X q q X X 3 3 hrge eru Bi A we icree the revere, the eletio regio grow to ccommote more chrge hrge i ot lier fuctio of voltge Thi i o-lier ccitor We c efie mll igl ccitce for mll igl by brekig u the chrge ito two term J q q Q J J v q Q v Q

16 6 3 3 erivtio of Smll Sigl citce From lt lecture we fou otice tht L J J v Q Q v Q R q Q q q q q q 3 3 Phyicl Iterrettio of eletio otice tht the ereio o the right-h-ie i ut the eletio with i therml equilibrium Thi look like rllel lte ccitor! q X q X

17 A rible citor rctor citce vrie veru : Alictio: Rio Tuer 33 iffuio Reitor -tye iffuio Regio Oie P-tye Si Subtrte Reitor i ccitively ioltio from ubtrte Mut Revere Bi P Juctio! 34 7