Lecture OUTLIE Bc Semcoductor Phycs (cot d) rrer d uo P ucto odes Electrosttcs ctce ot omesto tye semcoductor c be coverted to P tye mterl by couter dog t wth ccetors such tht >. comested semcoductor mterl hs both ccetors d doors. tye mterl ( > ) P tye mterl ( > ) Redg: hter.1. EE15 Srg 8 Lecture 1,, Slde 1 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde Prof. Wu, U Berkeley Tyes of hrge Semcoductor egtve chrges: oducto electros (dety ) Iozed ccetor toms (dety ) Potve chrges: Holes (dety ) Iozed door toms (dety ) The et chrge dety (/cm 3 ) semcoductor s ρ ( + ) EE15 Srg 8 Lecture, Slde 3 Prof. Wu, U Berkeley rrer rft The rocess whch chrged rtcles move becuse of electrc feld s clled. hrged rtcles wth semcoductor move wth verge velocty roortol to the electrc feld. Theroortolty costt s thecrrer moblty. Hole velocty vh Electro velocty EE15 Srg 8 Lecture, Slde 4 Prof. Wu, U Berkeley μ E v μ E otto: μ hole moblty (cm / s) μ electro moblty (cm / s) e EE15 Fll 7 1
elocty Sturto I relty, crrer veloctes sturte t uer lmt, clled the sturto velocty (v st ). rft urret rft curret s roortol to the crrer velocty d crrer cocetrto: Est 4 1 /cm μ μ 1+ be μ vst b μ v E E 1+ μ v st v h t volume from whch ll holes cross le tme t v h t # of holes crosg le tme t v h t chrge crosg le tme t v h chrge crosg le er ut tme hole curret Hole curret er ut re (.e. curret dety), v h EE15 Srg 8 Lecture, Slde 5 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 6 Prof. Wu, U Berkeley oductvty d Restvty I semcoductor, both electros d holes coduct curret: μ E ( μ E), tot, tot,, + oductvty σ μ + μ ( μ + μ ) E σ E μ E + μ E Restvty 1 ρ [Ut: Ω-cm] σ Tycl restvty rge for S: 1 3 ~ 1 3 Ω cm EE15 Srg 8 Lecture, Slde 7 Prof. Wu, U Berkeley [ut: mho/cm S/cm] Restvty Exmle Estmte the restvty of S smle doed wth hoshorus to cocetrto of 1 15 cm 3 d boro to cocetrto of 1 17 cm 3. The electro moblty d hole moblty re 8 cm /s d 3 cm /s, resectvely. EE15 Srg 8 Lecture, Slde 8 Prof. Wu, U Berkeley EE15 Fll 7
Electrcl Restce I + W t homogeeously doed smle L L Restce R ρ I Wt where ρ s the restvty EE15 Srg 8 Lecture, Slde 9 Prof. Wu, U Berkeley _ (Ut: ohms) rrer ffuo ue to thermlly duced rdom moto moble rtcles ted to move from rego of hgh cocetrto to rego of low cocetrto. logy: k drolet wter urret flow due to moble chrge uo s roortol to the crrer cocetrto grdet. The roortolty costt s the uo costt. d EE15 Srg 8 Lecture, Slde 1 Prof. Wu, U Berkeley otto: hole uo costt (cm /s) electro uo costt (cm /s) ffuo Exmles ffuo urret Ler cocetrto rofle costt uo curret x 1 L, d L o-ler cocetrto rofle vryg uo curret, x ex d L d d x ex L L d ffuo curret wth semcoductor costs of hole d electro comoets: d d, tot, ( d ) d The totl curret flowg semcoductor s the sum of curret d uo curret: tot, + +, + EE15 Srg 8 Lecture, Slde 11 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 1 Prof. Wu, U Berkeley EE15 Fll 7 3
The Este Relto The chrcterstc costts for d uo re relted: kt μ The P ucto ode Whe P tye semcoductor rego d tye semcoductor rego re cotct, P jucto dode s formed. + I kt ote tht 6m t room temerture (3K) Ths s ofte referred to s the therml voltge. EE15 Srg 8 Lecture, Slde 13 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 14 Prof. Wu, U Berkeley ode Oertg Regos I order to uderstd the oerto of dode, t s ecessry to study ts behvor three oerto regos: eulbrum, reverse bs, d forwrd bs. rrer ffuo cross the ucto Becuse of the erece hole d electro cocetrtos o ech de of the jucto crrers use cross the jucto: < > otto: electro cocetrto o tye de (cm 3 ) hole cocetrto o tye de (cm 3 ) hole cocetrto o P tye de (cm 3 ) electro cocetrto o P tye de (cm 3 ) EE15 Srg 8 Lecture, Slde 15 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 16 Prof. Wu, U Berkeley EE15 Fll 7 4
eleto Rego s coducto electros d holes use cross the jucto they leve behd ozed dots. Thus, rego tht s deleted of moble crrers s formed. The chrge dety the deleto rego s ot zero. The crrers whch use cross the jucto recombe wth mjorty crrers,.e. they re hlted. ueutrl rego wdthw de ueutrl rego EE15 Srg 8 Lecture, Slde 17 Prof. Wu, U Berkeley The eleto roxmto -b - ρ(x) x I the deleto rego o the de: de ρ Guss s Lw ε ε E ε ( x + b) ε 1 1 F/cm I the deleto rego o the P de: de ρ ε ε E ε ( x) EE15 Srg 8 Lecture, Slde 18 Prof. Wu, U Berkeley b Potetl strbuto I the deleto rego the electrc otetl s udrtc ce the electrc feld s ler The otetl erece betwee the d the P de s clled bult otetl, d E E -b (x) x P ucto Eulbrum I eulbrum, the d uo comoets of curret re blced; therefore the et curret flowg cross the jucto s zero.,, tot, + +, + EE15 Srg 8 Lecture, Slde 19 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde Prof. Wu, U Berkeley EE15 Fll 7 5
Bult Potetl, Becuse of the electrc feld the deleto rego there exsts otetl dro cross the jucto: d d d μe μ d μ d b kt ( b) ( ) l l μ / ( ) kt l EE15 Srg 8 Lecture, Slde 1 Prof. Wu, U Berkeley b (Ut: olts) Bult I Potetl Exmle Estmte the bult otetl for P jucto below. P 1 18 cm -3 1 15 cm -3 18 15 kt 1 1 1 13 ( ) ( ) ( ) l 6m l 6m l 1 kt ote: l(1) 6m.3 6m 6m 13 78m EE15 Srg 8 Lecture, Slde Prof. Wu, U Berkeley P ucto uder Reverse Bs reverse bs creses the otetl dro cross the jucto. s result, the mgtude of the electrc feld creses d the wdth of the deleto rego wdes. W ε 1 1 de + + ( ) R ode urret uder Reverse Bs I eulbrum, the bult otetl effectvely revets crrers from ug cross the jucto. Uder reverse bs, the otetl dro cross the jucto creses; therefore, eglgble uo curret flows. very smll curret flows,, lmted by the rte t whch morty crrers use from the u eutrl regos to the deleto rego. EE15 Srg 8 Lecture, Slde 3 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 4 Prof. Wu, U Berkeley EE15 Fll 7 6
P ucto ctce reverse bsed P jucto c be vewed s cctor. The deleto wdth (W de ) d hece the jucto cctce ( j ) vres wth R. ε j W [F/cm ] de oltge eedet ctce j j j 1+ R 1 ε + ε 1 1 F/cm s the ermttvty of lco EE15 Srg 8 Lecture, Slde 5 Prof. Wu, U Berkeley EE15 Srg 8 Lecture, Slde 6 Prof. Wu, U Berkeley Reverse Bsed ode lcto very mortt lcto of reverse bsed P jucto s voltge cotrolled osclltor (O), whch uses L tk. By chgg R, we c chge, whch chges the oscllto freuecy. 1 1 f res π L EE15 Srg 8 Lecture, Slde 7 Prof. Wu, U Berkeley Summry urret flowg semcoductor s comrsed of d d d uo comoets: tot μ E + μe + rego deleted of moble chrge exsts t the jucto betwee P tye d tye mterls. bult otetl dro ( ) cross ths rego s estblshed by the chrge dety rofle; t ooses uo of crrers cross the jucto. reverse bs voltge serves to ehce the otetl dro cross the deleto rego resultg very lttle () curret flowg cross the jucto. The wdth of the deleto rego (W de ) s fucto of the bs voltge ( ). ε 1 1 kt W + ( ) de l EE15 Srg 8 Lecture, Slde 8 Prof. Wu, U Berkeley EE15 Fll 7 7