SOLID STAT LTROI DVIS 339 Å gstrom..., 3 ccetor toms... 7 lloye jucto... 3 lh...16 morhous... gstrom..., 3 gulr mometum... 5 elg... 3 vlche brekow...14 Avogro's umber...3 Blmer... 4 b grm...1 b g... 6 b-beg...18 bse trsort fctor...16 bse-to-collector curret mlfcto fctor...17 bet...17 BJTs...16 Bohr moel... 5 Boltzm costt...3 Boltzm strbuto... 6 boury wth...1, 11 Brvs lttce... brekow...14 cctce...1, c see of lght...3 cctce jucto...1 cctce of - juctos...1 crrer cocetrto t equlbrum... 7 temerture eeece7 cthoolumescece... 3 chel... chrge cross jucto...11 chrge esty...1 chrge esty trsto rego...11 chrge storge cctce1 j jucto cctce.. 1, 13 commo-bse curret g16 commo-emtter curret g...17 couctvty... 7 costts...3 cotct otetl...1 cross rouct...3 csch...3 cth...3 curret esty... 8 ffuso... 8 oe...1 r... rft... 8 reverse sturto...1 trsstor...15, 16, 17 curret trsfer rto...16 cutoff...17 egeerte...14 el... esty of sttes... 6 eeet wve fucto.. 4 eleto chrge... eleto lyer cctce...1 eleto lyer wth...1 ffuse jucto... 3 ffuso...16 ffuso cctce...1 ffuso coeffcet... 9 ffuso curret... 8 ffuso equto...9, 16 ffuso legth... 9 oe equto...1 oes...14 D ffuso coeffcet... 9 oor toms... 7 oor bg eergy... 5 og... gs ffuso...11 lyer ffuso...1 ot rouct...3 D ffuso coeffcet... 9 r curret... rft curret... 8 rft velocty... 8 oor bg eergy... 5 () electrc fel...8, 11 bers-moll equtos...17 c coucto b eergy level... 6 erm eergy level... 6 effectve esty of sttes. 6 effectve mss... 5 g eergy b g... 6 ste relto... 7 electrc fel...8, 11, 1 electrolumescece... 3 electro bog... 7 cetretl force... 4 effectve mss of... 5 eergy... 4 trsc cocetrto of6 moblty...8, 9 orbt rus... 5 electro mss...3 electro volt... 3 electro-hole rs... 9 electrosttc otetl...1 emtter jecto effcecy17 eergy b g... 6 eergy g... ety... equllbrum...1 uler's equto... IDX ev electro volt...3, 3 v vlece b eergy level... 6 ecess crrers... 9 ecess hole cocetrto. 9 esos...3 etrsc..., 6 f() erm-drc strbuto fucto... 6 erm eergy level... 6 erm-drc strbuto fucto... 6 flt-b voltge...19 flourescece... 3 flu esty... 9 g fctor...17 gte voltge...18 gr oertor... grow jucto... 3 h Plck's costt...3 hyerbolc fuctos...3 hν hoto... 3 I reverse sturto curret...1 I D r curret... terfce chrge... terfce voltge...19 trsc..., 6 trsc to erm otetl...19, verso...1 verso chrge... verte moe...17 o mltto... 3 I t trsmtte lght testy... 8 J curret esty... 8 JT...18 k Boltzm costt...3 Llc...3 lght... 3 lght trsmsso... 8 L ffuso legth... 9 log fucto... L ffuso legth... 9 lumescece... 3 Lym... 4 m* effectve mss... 5 m electro mss...3 metl semcouctor work fucto...19 mscelleous... MOST...18 cctce... chrge esty...1 curret... eleto lyer...1 esg cosertos.. electrc fel...1 electrosttc otetl..1 el...18 rel...18 og gret fctor.13 equlbrum free electro cocetrto... 7 volume murty cocetrto...11 A Avogro's umber...3 bl oertor... turl log... c totl esty of sttes, coucto b... 6 trsc cocetrto. 6 (T) temerture-eeet crrer cocetrto... 7 orml ctve moe...17 orml moe...17 S re surfce murty cocetrto...1 v totl esty of sttes, vlece b... 6 + - jucto...13 + -- trsstor...15, 16 equlbrum hole cocetrto... 7 Psche... 4 ermttvty of free sce.. 5, 3 hoto oe...14 hotoelectrc... 4 hotolumescece... 3 hoto... 3 ch-off voltge...18 Plck's costt...3 - juctos... 3 - ste jucto...1 olycrystlle... otetl brrer heght...14 uch through...14 Q chrge cross jucto11 Q chrge esty, MOST...1 q elemetry chrge...3 Q eleto chrge... Q terfce chrge... Q verso chrge... Q s surfce chrge... qutum mechcs... 3 r electro orbt rus... 5 R Ryberg costt...3 recombto... 9 rect...13 rect...13 recombto lfetme... 9 reltve ermttvty... 5 reverse sturto curret 1 Ryberg costt...3 sturto...17 Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 1 of 3
sturto velocty... 8 Schröger wve equto5 sech...3 solr cells...14 sce chrge...11 sce chrge eutrlty... 7 sce ervtve... see of lght...3 stey stte cocetrtos13 ste jucto...1 strog verso...1 surfce chrge... surfce otetl... th...3 threshol voltge.19, 1, justg...19 totl cctce... trsstor bsg...15 curret flow...15, 16, 17 ffuso...16 ffuso equto...16 eergy bs...15 ecess crrers...15 ecess hole strbuto17 oertg moes...17 trsto rego...1, 11 trsto rego cctce...1 trg...13 trgoometrc ettes... tuel oe...14 uts... 3 V cotct otetl...1 vrctor...14 vector fferetl equto... V B flt-b voltge...19 V G gte voltge...18 V terfce voltge...19 V ch-off voltge...18 v s sturto velocty... 8 V T threshol voltge...19 v rft velocty... 8 W boury wth...1 W eleto lyer wth..1 wve equto... 5 wve fucto... 5 wve fucto, eeet. 4 wve mechcs... 3 wvelegth... 3 work fucto...4, 19 trsto rego...11 trsto rego...11 zeer...14 Φ work fucto...4, 19 Φ B otetl brrer heght...14 Φ m(φ) eeet wve fucto... 4 Ψ() wve fucto... 5 α bsorto coeffcet... 8 α curret trsfer rto...16 β g fctor...17 δ ecess hole cocetrto... 9 ε ermttvty of free sce...3 ε r reltve ermttvty... 5 φ erm otetl...19 φ flu esty... 9 φ S surfce otetl... γ emtter jecto effcecy...17 λ wvelegth... 3 µ electro moblty... 8 µ hole moblty... 8 ρ gulr mometum... 5 σ couctvty... 7 τ electro recombto lfetme... 9 τ hole recombto lfetme... 9 el... Llc...3 ITRODUTIO (see lso PerocTbleAAtoms.f) I crystl, toms re rrge eroc rry clle lttce structure. Some tyes of lttce structure re 1) smle cubc hvg oe tom t ech corer of cube for totl terl cotet of 1 tom/cube, ) boy-cetere cubc hvg tol tom the ceter of the cube, toms/cube, 3) fce-cetere cubc hvg tom t ech corer other the ceter of ech outer fce, 4 toms/cube, 4) mo hvg fcecetere structure wth 4 tol terl toms, 8 toms/cube. The legth of ech se of the cube s the lttce costt, eote by, eresse uts of gstroms (1Å 1-8 cm). We re sometmes tereste the erest eghbor stce, the ceter-to-ceter stce betwee the two closes toms cube, eresse terms of. I the mo lttce, ths s ¼ the legth of the gol coectg the most stt oosg corers of the cube, 3 / 4. rystls re tlore orer to cotrol 1) electro trsort, ) bsorto rto of lght. lemetl semcouctors hve mo lttce structure. Bry comous comose of 3-lyer close-cke le combtos from grous II-V II-VI hve zc blee structure smlr to mo structure. Slco s ot metl becuse there s g betwee the bog sttes the o-bog sttes. Two sttes of the sme eergy re s to be egeerte. Semcouctors hve smll eergy g. Isultors hve lrge eergy g. I metls there s overl betwee bog sttes. Itrsc semcouctors such s ure S Ge, hve etcl umber of electros the coucto b holes the vlece b. At K, ll electros retur to the vlece b. Dog s the cotrolle troucto of murtes to ure substce. Ths geerlly results etrsc semcouctor,.e. mterl hvg ether surlus of electros (-tye) or surlus of holes (-tye). Sgle crystl mes tht the toms re rrge sgle rry. Polycrystlle mes tht toms re multle rrys, hvg gr boures betwee them. Amorhous mes the toms re rrge wth o efte form. Brvs (br-vay) s lttce wth oe tom er cell. A cubc close-cke le hs lyers of toms rrge 3 offset rrys s show the llustrto t rght. ty s the techque of growg orete, sglecrystl lyer o substrte lyer hvg etcl or smlr lttce structure. ty methos clue 1) VD hemcl Vor Deosto (lso use for olycrystle morhous eosto), ) LP Lqu-Phse ty - growth from melt, 3) MB Moleculr Bem ty - elemets re evorte vcuum. Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge of 3
Qutum mechcs s theory of mtter tht s bse o the cocet of the ossesso of wve roertes by elemetry rtcles, tht ffors mthemtcl terretto of the structure terctos of mtter o the bss of these roertes, tht corortes wth t qutum theory the ucertty rcle clle lso wve mechcs. LIGHT Lumescece the roerty of lght emsso Photolumescece rto resultg from the recombto of crrers ecte by hoto bsorto. Some mterls rect rly to the ectto beg ture off; ths rocess s clle fluorescece. I other mterls, emsso cotues log fter ectto s remove; these rocesses re clle hoshorescece, the mterls re hoshors. thoolumescece rto resultg from the recombto of ecte crrers crete by hgheergy electro bombrmet. lectrolumescece rto resultg from the recombto of crrers ecte by the troucto of curret to the smle. The jecto electrolumescece effect occurs whe electrc curret cuses the jecto of morty crrers to regos of the semcouctor crystl where they c recombe wth mjorty crrers, resultg recombto rto use LDs. P- JUTIO ABRIATIO Grow A jucto s crete by brutly chgg the og urg the growth of the crystl. Alloye A ellet o oe mterl s melte to oostely-oe mterl regrow crystl rego forms t the jucto. Dffuse The crystl s hete to bout 1º cusg toms to move out of ther lttce ostos. Dog toms gseous stte outse the mterl move to the vcte ostos by ffuso. Ths methos offers recso s mlemete tegrte crcut fbrcto. Io Imltto A bem of murty os s ccelerte to ketc eergy the rge of severl KeV to severl MeV fre to the crystl. The eth t whch the os come to rest c be cotrolle by the ketc eergy level. Use tegrte crcuts. Dmge to the lttce cuse by o collsos c be rere by elg, or hetg of the crystl. B ARUL WITH UITS! I ths course, eergy s usully eresse ev rther th J, stce s ofte cm rther th m. Be sure to be cosstet wth uts formul, yg tteto to the uts of costts s well. Some formuls just o ot work wth uts of ev; clculte eergy J covert to ev. PHOTO The qutty of eergy ge or lost whe electro moves from oe eergy level to the et, qutze ut of lght eergy whose mgtue s eeet uo frequecy. The mout of eergy s equl to Plk's costt multle by the rto frequecy. 1hoto hν [J] v LTRO VOLT The eergy ge whe electro moves to ot wth 1 volt greter otetl [1.6 1-19 J]. To covert from joules to electro volts, ve J by q. c λν 1Å 1-1 m WAVLGTH c see of lght.998 1 8 m/s λ wvelegth [m] ν (u) rto frequecy [Hz] Å (gstrom) ut of stce equl to 1-1 m m (meters) WAVLGTH SPTRUM BAD MTRS AGSTROMS Logwve ro 1-1 km 1 13-1 15 Str Brocst 1-1 m 1 1-1 13 Shortwve ro 1-1 m 1 11-1 1 TV, M.1-1 m 1 9-1 11 Mcrowve 1-1 mm 1 7-1 9 Ifrre lght.8-1 µm 8-1 7 Vsble lght 36-69 m 36-69 volet 36 m 36 blue 43 m 43 gree 49 m 49 yellow 56 m 56 orge 6 m 6 re 69 m 69 Ultrvolet lght 1-39 m 1-39 X-rys 5-1, m.5-1 Gmm rys 1-5 fm.1 -.5 osmc rys < 1 fm <.1 1 Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 3 of 3
PHOTOLTRI T I orer to esce from metl beg bombre by lght, electro requres mout of eergy qφ emts eergy hν. The work fucto Φ, s the mmum mout of eergy eee to cuse electro to leve the metl. It s costt for ech metl. Tugste: 4.5 ev. m hν qφ (must kow) m mmum eergy of emtte electros [J] h Plck's costt, 6.63 1-34 J-s ν (u) frequecy [Hz] q electro chrge 1.6 1-19 [c] qφ (hee) the work fucto of the metl [ev] The electrosttc force betwee electro ts ucleus equls the cetretl force. q Kr TRIPTAL OR mv r q v Kħ q electro chrge 1.6 1-19 c K 4πε [4π 8.85 1-1 /m] r orbtl rus [m] m electro mss [9.11 1-31 kg], relce wth effectve mss m* crystle structures v electro velocty [m/s] orbt of the electro [teger] ħ Plck's costt ve by π [J-s] LTRO RGY 4 1 mq K.. mv K ħ 4 q mq P.. mv Kr K ħ 4 mq K.. + P.. K ħ K.. ketc eergy [J] P.. otetl eergy [J] totl eergy of electro the th orbt [J] m electro mss [9.11 1-31 kg] for the hyroge tom; for other roblems use m *, the effectve mss tycl of the semcouctor use. v velocty [m/s] K 4πε for the hyroge tom or 4 πε εr for other toms where ε r s the reltve electrc costt of the semcouctor mterl [/m] h Plck's costt, 6.63 1-34 J-s q chrge o the electro 1.6 1-19 [c] orbt of the electro [teger] ħ Plck's costt ve by π [J-s] LYMA, BALMR, & PASH SRIS Descrbe grous of les tht er emssos sectrum. Lym: Blmer: 1 1 cr,, 3, 4, 1 ν 1 1 cr, 3, 4, 5, ν 1 1 Psche: ν cr, 4, 5, 6, 3 ν (u) frequecy [Hz] c see of lght.998 1 1 cm/s R Ryberg costt, 19,678 cm -1 Φ m f- DPDT WAV UTIO Φ (ee) work fucto 1 jmφ otetl [V] ( φ) e φ (fee) otetl [V] π m qutum umber [teger] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 4 of 3
BOHR MODL els Bohr costructe moel for the hyroge tom bse o the mthemtcs of letry systems. He me the followg ostultes: 1. lectros est cert stble, crculr orbts bout the ucleus.. The electro my shft to orbt of hgher or lower eergy, gg or losg mout of eergy equl to the fferece eergy levels by bsorbg or emttg 1 hoto of eergy hν. 3. The gulr mometum r q of the electro orbt s lwys tegrl multle of Plck's costt ve by π. ρ h/π ħ. BOHR LTRO ORBIT RADIUS The electro of the hyroge tom my occuy oe of severl orbts of rus r. rm* q 4πε ε r ħ r orbt rus [m] m* effectve mss of the semcouctor mterl [kg] q electro chrge 1.6 1-19 [] ε ermttvty of free sce [/m] ε r reltve ermttvty of the mterl [costt] orbt, 1 s grou stte [teger] ħ Plck's costt ve by π [J-s] e r RLATIV PRMITTIVITY The rto of the ermttvty of the mterl to the ermttvty of free sce (ε 8.85 1-1 /m). The ermttvty of the mterl s the ε ε r. The reltve ermttvtes of some commo mterls re: S 11.8, Ge 16, GAs 13. SHRÖDIGR WAV QUATIO I three mesos: where ħ m ħ Ψ Ψ + VΨ j t Ψ Ψ Ψ Ψ + + y z ħ Plck's costt ve by π [J-s] m qutum umber [teger] totl eergy of electro the th orbt [J] Ψ() the wve fucto, hvg sce tme eeeces j 1 t tme [s],y,z osto coortes [m] refer to Wvequto.f for more formto TIV MASS O A LTRO The effectve mss of electro s smly justmet to the str electro mss tht ccouts for the fluece of the lttce structure. Ths ebles the sme formuls to work for fferet elemets. m* effectve mss of electro (), hole (). [kg] ħ Plck's costt ve by ħ m* π [J-s] / k ervtve electro eergy scle [J] k wve vector [m -1 ] The effectve mss for severl semcouctors s gve below terms of the free electro rest mss m. These re verge vlues rorte for esty of sttes clcultos oly. * m * m Ge S GAs.55m 1.1m.67m.37m.56m.48m DOOR BIDIG RGY The mout of eergy requre to ecte oor electro to the coucto b. oor bg eergy [J] m* effectve mss of the 4 semcouctor mterl [kg] m* q q electro chrge 1.6 1-19 [] 8( εε r ) h ε ermttvty of free sce [/m] ε r reltve ermttvty of the mterl [costt] h Plck's costt, 6.63 1-34 J-s Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 5 of 3
ITRISI OTRATIO O HOLS AD LTROS A trsc semcouctor s erfect semcouctor crystl (o murtes). The umber of electros the coucto b equls the umber of holes the vlece b. At K, ll electros retur to the vlece b there re o ecess crrers. The ooste of trsc s etrsc s cheve by og. c v e cocetrto of holes the vlece b t equlbrum [cm -3 ] Ths vlue s ofte tke to be equl to, the ccetor og cocetrto, sce t room temerture t my be ssume tht ech ccetor wll host electro from the vlece b. cocetrto of electros the coucto b t equlbrum [cm -3 ] Ths vlue s ofte tke to be equl to, the oor og cocetrto, sce t room temerture t my be ssume tht ech oor hs cotrbute electro to the coucto b. trsc cocetrto of electros the coucto b (costt for rtculr mterl t temerture) [cm -3 ] c effectve esty of sttes the coucto b [cm -3 ] v effectve esty of sttes the vlece b [cm -3 ] g b g eergy [ev] k Boltzm s costt 8.6 1-5 ev/k T bsolute temerture [K] kt costt (.586 whe T 3 k s ev/k) Some trsc cocetrtos @ 3K: S: 1.5 1 1 cm -3 Ge:.5 1 13 cm -3 GAs: 1 6 cm -3 g RGY BAD GAP The fferece otetl betwee the coucto b the vlece b electro volts ev. The eergy b gs of selecte semcouctor mterls re lste below: S Ge AlAs GP GAs 1.11 ev.67 ev.16 ev.6 ev 1.43 ev GSb IP IAs ISb ZS.7 ev 1.35 ev.36 ev.18 ev 3.6 ev ZSe S Se PbS PbSe g / kt.7 ev.4 ev 1.73 ev.37 ev.7 ev f() RMI-DIRA DISTRIBUTIO UTIO or trsc mterls (such s ure S crystl wth ll vlece electros covletly boe) the erm level s er the ceter of the eergy b g. or -tye mterl the erm level s off-ceter towr the coucto b for -tye mterl the erm level s off-ceter towr the vlece b. 1 1+ e f ( ) / kt f() erm-drc strbuto fucto, the strbuto of electros over rge of llowe eergy levels t therml equlbrum, hvg vlue from to 1. vlble eergy stte [ev] erm level the eergy level t the ceter of strbuto of the free electro oulto [ev] k Boltzm s costt 8.6 1-5 ev/k T bsolute temerture [K] kt costt (.586 whe T 3 k s ev/k) c the eergy level t the coucto b [ev] v the eergy level t the vlece b [ev] c v Itrsc semcouctor c v -tye semcouctor c v -tye semcouctor TH BOLTZMA DISTRIBUTIO or two screte eergy levels 1 wth > 1 : 1 umber of toms stte 1 ( 1 ) kt e / umber of toms stte kt costt (.586 whe 1 T 3 k s ev/k) c, v TIV DSITY O STATS The effectve esty of sttes s the cocetrto of loctos tht my host free electros the coucto b (c) or free holes the vlece b (v) uts of cm -3. Ths shoul ot be cofuse wth the esty of sttes whch re ctully occue, clle the crrer cocetrto or. c v πm * kt h 3/ 3/ πm * kt h m* effectve mss of electro [kg] h Plck's costt, 6.63 1-34 J-s k Boltzm s costt 1.38 1-3 J/K T 3 K t room temerture Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 6 of 3
, QUILIBRIUM ARRIR OTRATIO The cocetrto of free electros ( ) or holes ( ) t the ege of the coucto b (), or vlece b () uts of [cm -3 ] t equlbrum: e c e ( )/ kt c ( )/ kt ( )/ kt v e v ( )/ kt e cocetrto of electros the coucto b t equlbrum [cm -3 ] trsc cocetrto of electros the coucto b (costt for rtculr mterl t temerture) [cm -3 ] cocetrto of holes the vlece b t equlbrum [cm -3 ] c effectve esty of sttes the coucto b [cm -3 ] v effectve esty of sttes the vlece b [cm -3 ] c the coucto b eergy level [ev] the trsc eergy level [ev] erm level the eergy level whch s the ceter of strbuto of the free electro oulto [ev] kt costt (.586 whe T 3 k s ev/k) SPA HARG UTRALITY The sum of the holes ( ) oze oor toms ( + ) equls the sum of the egtve chrges ( ) oze ccetor toms ( - ). It s eecte tht ll oors ccetors re oze t room temerture. + + + ert techques re emloye whe workg wth ths equto, e.g. f the mterl s -tye, the the vlue of + wll be hgh c be tke to be zero. Also, the relto c be use to reuce the umber of ukows. LTRO BODIG I SMIODUTORS Where there re four erest eghbors the lttce structure, toms from grou IV of the eroc tble, such s S Ge, hvg 4 electros the outer (vlece) b, form strog (covlet) bos by shrg these electros wth ther eghbors. Whe the mterl s oe wth (oor) toms hvg more th 4 electros the vlece b, the ecess electros whch o ot become covletly boe re free to rtcte coucto. oversely, whe the mterl s oe wth (ccetor) toms hvg fewer th 4 electros the vlece b, holes uboe electros re vlble for coucto. TMPRATUR DPD O ARRIR OTRATIOS π ( T) h 3/ kt * g kt ( m m ) 3/ 4 / * e trsc cocetrto of electros the coucto b (costt for rtculr mterl t temerture) [cm -3 ] k Boltzm s costt 8.6 1-5 ev/k T bsolute temerture [K] h Plck's costt, 6.63 1-34 J-s or 4.14 1-15 ev m * effectve mss of electro [kg] m * effectve mss of hole [kg] g b g eergy [J, ev] D kt µ q σ qµ TH ISTI RLATIO D ffuso coeffcet [cm /s] µ electro or hole moblty [cm /V-s] 8. kt/q costt [V] (.586 V whe T 3 k s J/K) q electro chrge 1.6 1-19 [] s ODUTIVITY σ (sgm) couctvty [(Ω-cm) -1 ] q electro chrge 1.6 1-19 [] cocetrto of electros [cm -3 ] cocetrto of holes [cm -3 ] µ electro moblty [cm /V-s] 8. µ hole moblty [cm /V-s] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 7 of 3
m LTRO MOBILITY AD DRIT lectro moblty s the ese wth whch electros rft the mterl, or the verge rtcle rft velocty er ut of electrc fel (cm/s/v/cm cm /V-s). There s uer lmt to the velocty, clle sturto velocty v s, tht s cuse by sctterg, bout 1 7 cm/s for slco. See ISTI RLATIO 7. qt µ v m * q electro chrge 1.6 1-19 [] µ electro moblty [cm /V-s] µ hole moblty [cm /V-s] electrc fel le the -recto [V/cm] v verge rtcle rft velocty [cm/s] m [cm /V-s] m [cm /V-s] Slco S 135 48 Germum Ge 39 19 Gllum Arsee GAs 85 4 J URRT DSITY J qµ + µ σ If electrc fel s reset to to the crrer gret, the curret estes wll ech hve rft comoet ffuso comoet: () J() qµ () + qd rft ffuso () J() qµ () qd J, J curret esty ue to electros, holes [A/cm ] q electro chrge 1.6 1-19 [], cocetrto of electros, holes [cm -3 ] µ, µ electro moblty, hole moblty [cm /V-s] 8. electrc fel the -recto [V/cm] D, D ffuso coeffcet for electros, holes [cm /s] σ (sgm) couctvty [(Ω-cm) -1 ] I t ITSITY O LIGHT TRASMITTD THROUGH A SMIODUTOR I t testy of trsmtte lght [wtts or hotos/cm -s] αl I lght source testy [wtts or I e hotos/cm -s] α bsorto coeffcet [cm -1 ] l smle thckess [cm] DRIT AD DIUSIO URRTS The two bsc rocesses of curret coucto re ffuso ue to crrer gret, rft electrc fel. hrge crrers (electros or holes) move by ffuso from res of hgh crrer cocetrto to res of low crrer cocetrto. Sce the mout of curret s roortol to the crrer gret rther th the umber of crrers, morty crrers my cotrbute sgfctly to the ffuso curret. The recombto of electros holes s crrers ss through mterl c crete crrer gret rouce ffuso curret. Drft curret s the result of electros rom moto beg fluece by electrc fel. Although electros re movg my rectos, the et movemet wll be gst the electrc fel, holes move wth the fel. The result s curret flow wth the electrc fel. Drft curret flows resose to le voltge. () LTRI ILD The electrc fel () s equl to the chge voltge the -recto. A electrc fel occurs whe there s gret the og cocetrto, s relte to the chge the trsc eergy level of the semcouctor mterl. The recto of electrc fel s uhll b grm. lectros rft ow the sloe, whle holes rft the fel recto. A electrc fel my lso be the result of semcouctor jucto, see ge 11. V() 1 () q D µ 1 v () () electrc fel s fucto of locto [V/cm] V voltge [V] q electro chrge 1.6 1-19 [] the trsc eergy level [ev] D ffuso coeffcet for holes [cm /s] µ hole moblty [cm /V-s] 8. P() strbuto of holes [cm -3 ] c Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 8 of 3
D, D DIUSIO OIIT The et moto of electros (or holes) ue to ffuso s the recto of ecresg electro (or hole) cocetrto. see ISTI RLATIO 7. D ffuso coeffcet for electros [cm /s] l D l the me free th; fferetl t stce [cm] t the me free tme; fferetl tme [s] DIUSIO OIIT LTRO MOBILITY for trsc semcouctors D (cm /s) D (cm /s) µ (cm /V-s) µ (cm /V-s) Ge 1 5 39 19 S 35 1.5 135 48 GAs 1 85 4 DIUSIO QUATIO or electros: δ δ δ D t τ or holes: δ δ δ D t τ δ, δ ecess electro, hole cocetrto [cm -3 ] D, D ffuso coeffcet for electros, holes [cm /s] stce the (ooste) mterl, [cm] τ, τ recombto lfetme for electros, holes (les to morty crrers oly) [s] The geerl soluto for the ffuso equto for holes s: / L / L δ e + e 1 Sce ll holes evetully combe ( we -rego), δ t so 1. At, δ by efto, so. Therefore the fl soluto s: (see XSS ARRIRS) / δ e L f LTRO LUX DSITY The rte of electro flow er ut re. φ ( ) ( ) φ l t 1 D cocetrto of electros [cm -3 ] l the me free th the recto [cm] t the me free tme [s] D ffuso coeffcet for electros [cm /s] XSS ARRIRS cess crrers re chrge crrers (holes or electros) ecess of quttes fou t therml equlbrum. They my be crete by otcl ectto, electro bombrmet, or jecte wth le voltge. / L δ e δ ecess hole cocetrto [cm -3 ] ecess hole cocetrto t the trsto [cm -3 ] stce log the jucto [cm] L ffuso legth; the verge stce hole, or electro, ffuses before recombg; the stce t whch the ecess hole strbuto s reuce to 1/e of ts vlue t the ot of jecto (crrer jecto lwys mles morty crrers) [cm] (t) ROMBIATIO O XSS LTRO-HOL PAIRS (HPs) t / δ t e τ δ(t) ecess crrer cocetrto t tme t [cm -3 ] ecess crrer cocetrto t t [cm -3 ] t tme [s] τ recombto lfetme (les to morty crrers oly) [s] L DIUSIO LGTH D τ L D τ L, L ffuso legth; the verge stce hole, or electro, ffuses before recombg; the stce t whch the ecess hole (or electro) strbuto s reuce to 1/e of ts vlue t the ot of jecto (crrer jecto lwys mles morty crrers) [cm] D, D ffuso coeffcet for electros, holes [cm /s] τ recombto lfetme (les to morty crrers oly) [s] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 9 of 3
V OTAT POTTIAL The fferece trsc eergy levels the regos. kt V l V q, equlbrum cocetrto of holes the boury rego of the mterl, of the mterl [cm -3 ]. or the mterl, ths mght just be the trsc cocetrto, uless there re lso ccetors reset. I the mterl ths coul just be the ccetor cocetrto A, ssumg tht the trsc cocetrto s smll comrso there re o oor toms tht woul gve u electros to the ccetors. kt/q costt (.586 whe T 3 k s J/K) (refer to JUTIO secto, ge 1.) - STP JUTIO or ste jucto ( brut trsto), the oors ccetors gve u ll of ther oor electros holes to the jcet rego so tht. The effect of ccetor cocetrto the rego s to brg the erm eergy level close to the vlece b, the effect of oor cocetrto the rego s to brg the erm level close to the coucto b. Whe the regos re brought together, the erm levels must be equl t equlbrum. See B Dgrm below. ( )/ kt e e ( )/ kt qv / kt e cocetrto of holes the boury rego of the mterl [cm -3 ] cocetrto of electros the boury rego of the mterl [cm -3 ] trsc cocetrto of electros [cm -3 ], trsc eergy level the rego, rego [ev], erm eergy level the rego, rego [ev] kt costt (.586 whe T 3 k s ev/k) cocetrto of ccetors (toms tht my g electro) [cm -3 ] cocetrto of oors (toms tht my lose electro) [cm -3 ] V cotct otetl [ev] QUILIBRIUM BAD DIAGRAM I - jucto t equlbrum, the erm eergy level of the -mterl s equl to the erm eergy level of the -mterl. Refer to the reltos uer STP JUTIO V OTAT POTTIAL bove to clculte b g vlues show. c v -mterl jucto -mterl qv c v c the -mterl coucto b eergy level [ev] the -mterl trsc eergy level [ev] the erm eergy level [ev] v the -mterl vlece b eergy level [ev] c the -mterl coucto b eergy level [ev] the -mterl trsc eergy level [ev] v the -mterl vlece b eergy level [ev] W BOUDARY WIDTH A - jucto s show wth >, hece the trsto rego (lso clle the eleto rego) etes further to the mterl. W - εv + W q εkt l q - - - - - - - - - - - - - - - - 1/ 1 + + + + + + + + + + + + + + + + 1 + εv q 1/ 1 1 + W boury wth, wth of the trsto rego [cm] ε ermttvty [/cm] cocetrto of ccetors (toms tht my g electro) [cm -3 ] cocetrto of oors (toms tht my lose electro) [cm -3 ] V cotct otetl [ev] q electro chrge 1.6 1-19 [] 1/ Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 1 of 3
HARG DSITY WITHI TH TRASITIO RGIO The umber of chrges the rego s equl to the umber of chrges the rego ue to sce chrge eutrlty. If the mgtue of the chrge esty s greter the mterl (.e. there s hgher og cocetrto the mterl), the the trsto rego etes further to the mterl orer to blce the chrge, s llustrte the grm below. (comre wth W BOUDARY WIDTH secto revous) hrge esty/cm 3 - + q (-) W (+) q ā Dstce cm LTRI ILD STRGTH WITHI TH TRASITIO RGIO (refer to W BOUDARY WIDTH secto revous) The totl re boue by the fucto the -s s equl to -V. - Dstce cm q q ε ε mmum vlue of the electrc fel (occurs t the W jucto) [V/cm] () electrc fel [V/cm] q electro chrge 1.6 1-19 [], cocetrto of oors, ccetors [cm -3 ] o, o eetrto of the trsto re to the rego, rego [cm] W BOUDARY WIDTH WITH BIAS ε W ( V V ) q + 1/ (refer to W BOUDARY WIDTH secto revous), PTRATIO O TH TRASI- TIO ARA ITO TH & RGIOS + + εv W q εv W q W + ( + ) ( + ) o eetrto of the trsto re to rego [cm] o eetrto of the trsto re to rego [cm] (refer to W BOUDARY WIDTH secto. 1) 1/ 1/ Q TOTAL HARG AROSS TH JUTIO There must be equl umber of chrges o ether se of the jucto wth the trsto re. Ths s clle sce chrge eutrlty. Sce the chrge crrers re quckly swet cross the jucto by the electrc fel, chrges the trsto re re ue rmrly to ucomeste oors ccetors. (refer to W BOUDARY WIDTH secto. 1) Q qa qa Q + A the jucto re [cm ] q electro chrge 1.6 1-19 [] o eetrto of the trsto re to the rego [cm] (,t) DOPIG BY DIUSIO (GAS) The murty cocetrto s hel costt t the surfce urg the ffuso rocess. t (,) erfc Dt (,t) the murty strbuto [cm -3 ] volume cocetrto of murtes mte outse the surfce of the mterl urg ffuso [cm -3 ] erfc somethg clle the comlemetry error fucto eetrto level the mterl [cm] (tyclly coverte to µm) D the ffuso coeffcet for the murty [cm /s] t the urto of the ffuso rocess [s] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 11 of 3
(,t) DOPIG BY DIUSIO LAYR A lyer of murtes s le to the surfce before ffuso. o murtes esce from the mterl urg the ffuso rocess. s ( / Dt ) t (,) e π Dt S re cocetrto of murtes the surfce lyer [toms/cm ] see bove for other vrble eftos D I qa L I DIOD QUATIO D + L qv / kt qv / kt ( e 1) I ( e 1) qv / kt for the o-el oe: I I ( e 1) I oe curret [A] q electro chrge 1.6 1-19 [] A the jucto re [cm ] D, D ffuso coeffcet for holes, electros [cm /s] L, L ffuso legth; the verge stce hole, or electro, ffuses before recombg; the stce t whch the ecess hole (or electro) strbuto s reuce to 1/e of ts vlue t the ot of jecto (crrer jecto lwys mles morty crrers) [cm] cocetrto of holes the boury rego of the mterl [cm -3 ] cocetrto of electros the boury rego of the mterl [cm -3 ] kt costt (.586 whe T 3 k s ev/k) I sturto curret [A] elty fctor < < 1 I RVRS SATURATIO URRT D D I qa + L L APAITA O P- JUTIOS There re bsclly two tyes of cctce ssocte wth jucto: 1. jucto cctce or trsto rego cctce or eleto lyer cctce. Ths s the cctce ue to the ole the trsto rego (the re cotg two oostely chrge regos mergg t the jucto). Ths tye s omt uer reverse-bs cotos. ctce vres wth voltge sce the wth of the trsto rego vres wth voltge. 1/ j εa q εa W ε( V V) +. chrge storge cctce or ffuso cctce. Ths s the cctce ue to the lggg beh of voltge s curret chges. Ths tye s omt uer forwr-bs cotos. hrge storge cctce c be serous lmtto hgh frequecy crcuts volvg forwr-bse - juctos. Store chrge: ctce ue to smll chges the store chrge,.e. chrge storge cctce: Q Iτ qa L s qal e qv / kt Q q AL e V kt q I τ kt qv / kt j JUTIO APAITA The cctce of symmetrclly oe jucto s eterme by oly oe of the og cocetrtos. j s voltge-vrble cctce. j A qε V V 1/ or + - jucto, <<, W j jucto cctce [] A the jucto re [cm ] q electro chrge 1.6 1-19 [] ε ermttvty [/cm] V cotct otetl [ev] (V V) brrer heght [ev] cocetrto of oors (toms tht my lose electro) [cm -3 ] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 1 of 3
TH + - JUTIO The mterl s more hevly oe so tht the eleto lyer wth W etes rmrly to the se. j V r for V r >> V m G 1 /( m + ) <<, W j jucto cctce [] og gret fctor 1/3 for lerly gre jucto 1/ for brut jucto > 1/ for hyerbrut jucto for vrcter evce G costt V r V cotct otetl [ev] cocetrto of oors (toms tht my lose electro) [cm -3 ] DIRT ROMBIATIO The rect recombto of electro hole rs occurs whe electros fll from the coucto b to emty holes the vlece b. Lght s rouce. The et rte of chge the coucto b electro cocetrto s the therml geerto rte mus the recombto rte: ( t) α r α r( t) ( t) t α r costt of recombto roortolty [cm -3 ] trsc cocetrto of electros the coucto b [cm -3 ] cocetrto of electros [cm -3 ] cocetrto of holes [cm -3 ] If ecess crrer cocetrtos re smll the mterl s etrsc, we c sy: δ( t) α r δ( t), t α r t t / τ where δ( t) e e τ α r 1 r ( + ) ( α ) 1 δ(t) cocetrto of ecess electros [cm -3 ] cocetrto of ecess electros t t [cm -3 ] τ recombto lfetme,.e. the verge tme electro ses the eergy b before recombto [s] The ecess mjorty crrers ecy t the sme rte s the morty crrers, so τ τ. If, the δ(t) δ(t). IDIRT ROMBIATIO, TRAPPIG The mjorty of recombto evets rect mterls, such s colum IV semcouctors, occur v recombto levels wth the b g. These eergy levels re clle trg ceters my be eote by r. The rocess of recombto through cremetl stes through the eergy b s clle rect recombto. The eergy loss ue to recombto of electro/hole rs s gve u mostly s het (rther th lght). The rocess of rect recombto s more comle th rect recombto sce crrers tht hve shfte to trg eergy level my retur to ther orgl eergy level wthout recombg. The rte of recombto my be mesure by motorg the couctvty of smle. σ ( t ) q ( t) µ + ( t) µ ] [ σ (sgm) couctvty [(Ω-cm) -1 ] q electro chrge 1.6 1-19 [] cocetrto of electros [cm -3 ] cocetrto of holes [cm -3 ] µ electro moblty [cm /V-s] 8. µ hole moblty [cm /V-s] STADY STAT LTRO AD HOL OTRATIO The stey stte coto s whe the rte of geerto of electro hole rs equls the recombto rte. cocetrto of electros [cm -3 ] cocetrto of holes [cm -3 ] ( ) trsc cocetrto of / kt e electros the coucto b [cm -3 ] ( )/ kt e δ δ g o τ trsc eergy level [J, ev], qus erm eergy level for electros, holes [J, ev] δ, δ ecess crrer cocetrto [cm -3 ] g o otcl electro hole r geerto rte [cm -3 -s -1 ] τ recombto lfetme (les to morty crrers oly) [s] Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 13 of 3
B POTTIAL BARRIR HIGHT The Schottky otetl brrer heght for electro jecto from the metl to the semcouctor coucto b s qφ B otetl brrer heght qφb qφm qχ [ev] qφ m metl work fucto [ev] qχ electro ffty [ev] uch through A occurrece of brekow below the eecte brekow voltge cuse by the trsto rego eteg cross the etre wth of the lyer. Ths c be roblem short, lghtlyoe regos. vlche brekow A hgh-eergy electro s rve from the -rego to the trsto rego by eterlly le voltge. It colles wth the lttce, cretg electro-hole r. The two electros re swet towr the -rego whle the hole s swet towr the -rego uer r ccelerto ue to strog electrc fel. Wth suffcet eergy, these rtcles rtcte tol lttce collsos wth the trsto rego, cusg the creto of tol electrohole rs. Hgh reverse-bs voltge hgh - rego og cocetrtos cotrbute to the effect, but the zeer (tuelg) effect tkes over t very hgh og cocetrtos. Zeer effect The - -regos of brut - jucto must both be hevly oe. The jucto s reverse-bse to the etet tht the eergy bs cross, tht s, the eergy level of the -mterl coucto b s below tht of the -mterl vlece b. These. cotos ermt electros to tuel from v to c curret flows from to s llustrte the lower grm t rght. ote tht the mterls the grm t rght s egeerte tye mterl, meg tht the og cocetrto s so hgh tht the erm level les wth the vlece b of the - mterl wth the coucto b of the - tye mterl. c v c v -mterl e- jucto -mterl c v v Tuelg wth forwr bs (to) reverse bs (bottom) e- c DIODS Tuel oe The tuel oe oertes ( cert regos of ts I-V chrcterstc) by the qutum mechcl tuelg of electros through the otetl brrer of the jucto. or reverse curret, ths s essetlly the zeer effect but requres oly smll reverse bs. Alctos clue hgh-see swtchg logc crcuts. Photo oes, solr cells The jucto s oerte the fourth qurt of ts I-V chrcterstc. The voltge rouce s restrcte to vlues less th the cotct otetl, tyclly less th 1V. My comromses re me solr cell esg. Jucto eth the mterl must be less th L to llow holes geerte er the survce to ffuse to the jucto before they recombe. I orer to hve hgh cotct otetl V, hevg og s requre. Solr cells re eesve to fbrcte rouce oly moest mouts of ower. My surfce cotct trces re requre to collect curret from ths th lyer ue to ts hgh resstce. But these trces block comg lght. To hve log lfetmes, og must be reuce. Sulght my be cocetrte to crese outut but effcecy s lost. GAs relte comous c be use t the hgher temertures. Photo oes, hotoetectors The jucto s oerte the thr qurt of ts I-V chrcterstc. I ths rego, curret s essetlly eeet of voltge but roortol to the otcl geerto rte, mkg the evce useful mesurg llumto levels or covertg tme-vryg otcl sgls to electrcl sgls. It s usully esrble for these evces to ct quckly, so the trsto rego W s me lrge. Whe HP s geerte ths rego, the electrc fel quckly swees the electro to the se the hole to the se. Vrctor oe Ths evce emloys the voltgevrble cctce chrcterstc of reversebse - jucto. I gre jucto, the reltosh betwee cctce voltge s j V r for V r >> V or lerly gre jucto, the vlue of s ½. The vlue creses wth more brut juctos. Zeer oe The zeer oe s brekow oe esge to brek ow brutly t rtculr voltge. Although me for the zeer or tuelg brekow mechsm, the vlche effect s ctully the more commoly use brekow mechsm zeer oes. A commo lcto s voltge regultor. Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 14 of 3
BJTs TH + -- TRASISTOR The emtter ( + ) s more hevly oe so tht the eleto rego etes rmrly to the bse rego. 5 + 4 3 emtter bse collector (1) jecte holes lost to recombto the bse () holes tht fl to be recombe the bse re swet cross the reverse-bse collector jucto by the electrc fel (3) thermlly geerte electros holes re swet cross the B jucto by the electrc fel mke u the reverse sturto curret of the collector jucto (4) electros sule by the bse cotct recombe wth holes from (1), hece (1) (4) re equl mgtue (5) electros jecte cross the forwr-bse emtter jucto; ths curret s smll ue to the hevly oe emtter or -- trsstor, smly reverse the roles of electros holes. 1 ORMAL BIASIG I TH + -- TRASISTOR orml bsg the -- trsstor mes tht the emtter-bse jucto s forwr-bse the collector-bse jucto s reverse-bse. orml bsg results reuce wth of the emtter-bse trsto rego crese wthof the collectorbse trsto rego. + forwr bs emtter + I I B bse W b + reverse bs I collector ( qv B / kt e 1), ( qv B / kt e 1), ecess hole cocetrto t the ege of the emtter ( ) collector ( ) eleto regos [cm -3 ] V B, V B emtter to bse voltge, ormlly ostve (V B ), collector to bse voltge, ormlly egtve (V B ) [V] W b the wth of the eutrl bse rego; very mortt to the see effcecy of the trsstor; ths rego s short so tht most of the jecte holes ss through to the collector (ssste by the electrc fel t the B jucto) wthout recombg the bse. [cm] RGY BAD DIAGRAMS OR TH + -- TRASISTOR t equlbrum c + qv B + orml bs q( V B + V B) v c q( V B -V B) v emtter emtter bse collector bse collector Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 15 of 3
TH DIUSIO QUATIO AD TH + -- TRASISTOR Refer to the revous rwg. The ffuso equto: The ffuso equto soluto: ( ) Boury cotos: Solvg for 1 : Wb/ L e 1 Wb / L Wb / L δ δ L / L / L 1 δ e + e ( ) 1 δ + b Wb/ L Wb/ L 1 δ W e + e W / L b e Wb / L Wb / L e e e e, ecess hole cocetrto t the ege of the emtter ( ) collector ( ) eleto regos [cm -3 ] W b the wth of the bse rego ot tke u by trsto regos [cm] L ffuso legth; the verge stce hole ffuses before recombg [cm] D DIUSIO I TH BAS RGIO The followg s lcble to -- trsstor; these vlues re use other equtos. The symbol usully ctes fferece betwee two vlues; ths cse t woul be the fferece betwee the totl umber of holes those ot vlble for coucto, two vlues whch we re ot tereste. D ecess hole cocetrto t the boury of the emtter-bse eleto rego [cm -3 ] D ecess hole cocetrto t the boury of the collector-bse eleto rego ( - whe the collector s strogly reverse-bse) [cm -3 ] ( qv B / kt e 1) ( qv B / kt e 1) cocetrto of ecess holes the bse rego [cm -3 ] q electro chrge 1.6 1-19 [] V B emtter-to-bse voltge [V] V B collector-to-bse voltge [V] I, I, I B TRASISTOR URRTS ote: cth s 1/th, csch s 1/sh. D W W I cth b csch b qa L L L D W W I csch b cth b qa L L L D W b IB qa + th L L I the hole comoet of the emtter curret [A] I collector curret [A] I B bse curret [A] q electro chrge 1.6 1-19 [] A cross-sectol jucto re (uform for both juctos) [cm ] D ffuso coeffcet for holes [cm /s] L ffuso legth; the verge stce hole ffuses before recombg [cm] cocetrto of ecess holes t the boury of the emtter-bse eleto rego [cm -3 ] ( qv B / kt 1) e cocetrto of ecess holes t the boury of the collector-bse eleto rego ( - whe the collector s strogly reverse-bse) [cm -3 ] qv B e / kt 1 W b wth of the bse rego [cm] URRT TRASR RATIO The rto of collector to emtter curret, or commobse curret g. To mke α close to 1, mke the bse rrow so ot my holes recombe the bse. I α I b BI β Bγ I + I β+ 1 (qad /L ) cth(w b/l ) b (qad /L ) csch(w b/l ) B c/ b, the bse trsort fctor, the frcto of jecte holes tht mke t cross the bse to the collector I emtter curret ue to holes [A] I emtter curret ue to electros [A] γ emtter jecto effcecy Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 16 of 3
b GAI ATOR The rto of collector to bse curret, or bse-tocollector curret mlfcto fctor, or commoemtter curret g. I BI Bγ α β I I + 1 B I 1 Bγ 1 α B (see revous for escrto of vrbles) g MITTR IJTIO IIY γ 1 s the emtter curret ue etrely to hole jecto (crrer jecto lwys mles morty crrers). To mke γ s lrge s ossble, mke the emtter hevly oe. The suerscrts cte whch se of the emtter-bse jucto s beg referre to. 1 1 µ W L b µ µ µ L γ 1+ th 1+ L L L I I + I L, L ffuso legth; the verge stce hole, or electro, ffuses before recombg; the stce t whch the ecess hole (or electro) strbuto s reuce to 1/e of ts vlue t the ot of jecto [cm] cocetrto of holes the boury rego of the mterl [cm -3 ] cocetrto of electros the boury rego of the mterl [cm -3 ] W b bse wth BJT, mesure betwee the eges of the emtter collector jucto eleto regos [cm] µ electro moblty [cm /V-s] 8. µ hole moblty [cm /V-s] I, I BRS-MOLL QUATIOS These equtos for trsstor curret llow for symmetry betwee the juctos. I I + I I qvb / kt qvb / kt ( 1) ( 1) qvb / kt ( 1) I e α I e S I S α I I e I O I I + I I qvb / kt qvb / kt ( 1) ( 1) qvb / kt ( 1) α I e I e S S α I I e O (e1) (e) (e3) (c1) (c) (c3) To mesure the curret, use equtos e c. To get I S, mesure I wth the collector oe the B jucto B / reverse-bse. Tht wy, qv kt e s very smll. To get I, mke V B lrge egtve (reverse-bse), the α I - I /I. To get, mke V B lrge egtve (reversebse), the α -I /I. To get I S, mesure I wth the emtter oe the B jucto reverse-bse. Ths formto comes from The Physcs of Semcouctor Devces, D.A. rser,. 11, my ot be correct vrbles were me fferetly. I emtter curret wth V B,.e. B shorte [A] I I α I I I emtter curret, verte moe (egtve vlue) I S emtter sturto curret wth V B [A] I O emtter sturto curret wth collector oe [A] α I, α curret trsfer rto, verte/orml moes I collector curret wth V B,.e. B shorte [A] I I collector curret, verte moe (egtve vlue) [A] I S collector sturto curret wth V B [A] I O collector sturto curret wth emtter oe [A] orml moe mes orml bsg verte moe mes verte bsg,.e. reverse-bse emtter forwr-bse collector, mkg I I jecte curret I I collecte curret. TRASISTOR OPRATIG MODS cutoff the off stte. I B s zero or egtve. orml ctve emtter jucto s forwr-bse; collector jucto s reverse-bse. oertg ot s o the lo le. sturto collector jucto voltge s zero or forwr-bse cess Hole Dstrbuto the -- Bse Begg of Sturto δ orml Actve Sturto W b utoff Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 17 of 3
JTs JUTIO ILD T TRASISTOR gte r + + gte + V G - source V P PIH-O VOLTAG eleto rego chel The JT bs voltge V gs tht just cuses the eleto regos to meet er the r, essetlly hltg further creses r curret. q electro chrge 1.6 1-19 [] chel hlf-wth [m] q V P cocetrto of oors (toms ε tht my lose electro) [cm -3 ] ε ermttvty of the mterl [/cm] MOSTs MTAL OXID SILIO ILD T TRASISTOR + r reverse bs gte source metl + V G - slco oe + forwr bs verso lyer eleto rego substrte IDAL MOS AT QUILIBRIUM I el MOS, 1) Φ M Φ,.e. there s o bbeg t equlbrum, ) there s o chrge S the oe rego or t the oe/semcouctor terfce. m erm level of the metl [ev] qφ m mofe work fucto, eergy b eteg from the metl erm level to the coucto b of the slco oe [ev] qφ s work fucto, for the semcouctor lyer [ev] qφ how much lower the erm level s th the trsc eergy level. Ths vlue ctes how strogly -tye (chel MOST) the semcouctor s. [ev] RMI POTTIAL.19. A brek s show the eergy b of the oe sultor becuse ts b g s much greter th tht of slco. m -chel MOST Metl qφ m qφ s RAL MOS AT QUILIBRIUM Tre chrges the SO lyer, s well s chrges ue to the SO s/s terfce, rouce lyer of ostve chrge Q the SO mterl er the substrte boury. Ths rouces comlemetry egtve chrge Q the substrte. These bult- chrges cuse bbeg to occur the substrte t equlbrum. m Metl qφ m Oe qφ c s v Semcouctor Oe qφ s Semcouctor c s v V G GAT VOLTAG The gte voltge c be broke ow to comoets of the voltge ro cross the terfce, the voltge ro cross the eleto rego, the voltge requre to cheve flt-b cotos. VG V +φ s + VB Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 18 of 3
V T THRSHOLD VOLTAG The mmum gte voltge of MOST requre to uce the chel. -chel MOST: V T s ostve or slghtly egtve becuse the frst two terms (wth ther oertors) re egtve the lst two ostve. Whe -chel MOST hs egtve V T t mes tht the chel s me (the MOST coucts) utl egtve gte voltge s le. -chel MOST: V T s egtve becuse ll terms (wth ther oertors) re egtve. V Q Q T Φms + φ φ kt l q Φ ms metl semcouctor work fucto otetl fferece [V] Q terfce chrge er ut re [/cm ].. Q eleto rego chrge er ut re [/cm ].. terfce cctce er ut re [/cm ].. φ erm otetl;, [V].19. ADJUSTIG V T BY IO IMPLATATIO The threshol voltge c be me less egtve/more ostve by mltg boro ccetors just below the S surfce er the gte both - chel -chel MOSTs. V q V + B T( ew) T( org.) B boro og cocetrto er ut re [cm - ] terfce cctce er ut re [/cm ].. V B LAT BAD VOLTAG The egtve voltge requre to strghte the eergy bs. Tre chrges the SO lyer, s well s chrges ue to the SO s /S terfce, rouce lyer of ostve chrge Q the SO mterl er the substrte boury (-chel -chel MOSTs). Ths rouces comlemetry egtve chrge Q the substrte. Whe the (egtve) flt b voltge s le to the gte, electrc fel s set u betwee the ostve chrges the SO lyer the egtve chrges o the gte, elmtg the egtve chrges Q the substrte. V B Φ ms Q Φ ms metl semcouctor work fucto voltge [V] Q effectve MOS terfce chrge er ut re; the turlly occurrg chrge the SO lyer. Dr. Kwog refers to cll ths Q o. [/cm ] terfce cctce er ut re [/cm ].. V ITRA VOLTAG The voltge ro cross the SO sultor. Dr. Kwog refers to cll ths V o. V Q s ε Q φ s surfce otetl [V].. Q s the egtve chrge esty o the semcouctor [/cm ] thckess of the sultor [cm] V G gte voltge [V] terfce cctce er ut re [/cm ].. ε ermttvty of the terfce lyer, 3.9ε /1 for SO [/cm] ms MTAL SMIODUTOR WORK UTIO [V] The metl semcouctor work fucto s the voltge otetl betwee the metl gte the semcouctor boy. Work fucto voltges vry wth the mterl the og cocetrto. Also, see llustrto t RAL MOS AT QUILIBRIUM.18. Φ ms Φm Φ s Φ m work fucto voltge of the metl gte (hgh) [V] Φ s work fucto voltge of the semcouctor (low) [V] Φ ms (V) -. -.4 -.6 -.8-1. 1 1 s 14 1 1 16 1 18, Al to -tye S Al to -tye S (cm-3 ) f RMI POTTIAL [V] φ s the otetl betwee the trsc eergy level the erm level. It s relte to how strogly oe the semcouctor s. -chel: φ -chel: φ kt q e φ l q / kt kt q l -chel MOST oe semcouctor qφ c v Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 19 of 3
f S SURA POTTIAL [V] φ S s the voltge ro cross the eleto rego of the semcouctor,.e. how fr the eergy bs re bet. φ S s comoet of the gte voltge: V V +φ + V G s B t verso: φ φ S -chel MOST oe qφ S semcouctor qφ Q IVRSIO HARG [/cm ] Q s the (vrble) chrge er ut re resultg from the eleto of holes the -tye substrte ue to ostve gte voltge. See MOS HARG DSITY.1. Qs Q + Q c Q s surfce chrge; the totl chrge esty the substrte [/cm ] Q eleto chrge esty [/cm ] Q DPLTIO HARG [/cm ] Q s the (fe) chrge esty the eleto rego ue to Q the terfce (SO ) rego. See MOS HARG DSITY.1. See lso LAT BAD VOLTAG,. 19. -chel (-tye substrte): Q q W m ε ε q φ -chel (-tye substrte): Q q W ε ε m r r q φ q electro chrge 1.6 1-19 [] cocetrto of ccetors (toms tht my g electro) [cm -3 ] W m mmum wth of the eleto rego [cm].1. ε ε r ermttvty of the mterl [/cm] φ erm otetl;, [V].19. Q ITRA HARG [/cm ] Q s (vrble) ostve chrge esty the SO mterl er the substrte boury (-chel -chel MOSTs) comose of tre chrges the SO lyer, s well s chrges ue to the SO s /S terfce. Wth the lcto of ostve gte voltge, the terfce chrge c be swet out of the sultor rego by the electrc fel. Dr. Kwog refers to cll ths Q o. v Q s SURA HARG [/cm ] Q s s the (vrble) totl chrge esty the eleto rego of the semcouctor. Qs Q + Q Q verso chrge esty [/cm ] Q eleto chrge esty [/cm ] I D DRAI URRT whe V D s smll: more ccurtely: µ Z 1 ID ( VG VT ) VD VD L µ Z 1 εsq 3/ 3/ ID VG VB φ VD VD ( VD+φ ) ( φ) L 3 µ surfce electro moblty [cm /V-s] 8. Z eth of the chel [cm] terfce cctce er ut re [/cm ].. L legth of the chel [cm] V G gte voltge [V] V T threshhol voltge, the voltge t whch the chel begs to couct [V] V D r voltge (r-to-source) [V],, APAITA [/cm ] The totl cctce s the sum of the terfce cctce the eleto cctce. ε A geerl eresso for cctce [] + εs W ε A re [cm ] ε s ermttvty of the substrte, 11.8ε /1 for S [/cm] ε ermttvty of the terfce lyer, 3.9ε /1 for SO [/cm] serto stce [cm] totl cctce; seres cctce er ut re ue to the SO sultor the eleto cctce [/cm ] terfce cctce; (fe) cctce er ut re ue to the SO sultor [/cm ] eleto cctce; cctce er ut re ue to the eleto lyer (vres wth the gte voltge) [/cm ] W wth of the eleto rego [cm].1. Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge of 3
W, W m DPLTIO LAYR WIDTH The wth of the eleto lyer wth the substrte, clug the wth of the verso lyer, f reset. The wth grows wth crese gte voltge utl rechg mmum t the oset of strog verso (.1). urther creses voltge cuse stroger verso rther th more eleto. 1/ 1/ εφ W s s εsktl / Wm q q ε s ermttvty of the substrte, 11.8ε /1 for S [/cm] φ s surfce otetl [V].. q electro chrge 1.6 1-19 [] trsc cocetrto of electros the coucto b, 1.5 1 1 for S [cm -3 ] ccetor cocetrto the substrte [cm -3 ] STROG IVRSIO Whe ostve gte voltge s le, bbeg tkes lce. Whe the gte voltge V G reches the threshol voltge V T, the trsc eergy b hs bet ow below the erm level by stce equl to the serto of the trsc erm eergy bs, the chel re becomes s strogly -tye s the rest of the substrte s - tye, tht s, the free electro cocetrto equls the ccetor og cocetrto. Ths coto s clle strog verso t ths ot the chel coucts. s e ( )/ kt Strog Iverso: q φ φ φ s s A oe semcouctor qφ qφ s surfce cocetrto of crrers (electros) the substrte t the semcouctor/so trsto [cm -3 ] trsc cocetrto of electros the coucto b, 1.5 1 1 for S [cm -3 ] the trsc eergy level t fty (fr wy from the semcouctor/so terfce) [ev] the trsc eergy level t the semcouctor/so terfce [ev] φ s surfce otetl [V].. φ erm otetl;, [V].19. ccetor cocetrto the substrte [cm -3 ] c v MOS HARG DSITY Q m gte chrge esty, ue to the ostve gte Q voltge [/cm ] m Q eleto rego chrge esty [/cm ] Q verso chrge esty, resultg from the eleto of holes ue to the ostve gte voltge [/cm ] MOS LTRI ILD The electrc fel of el MOST verso: W chel wth; corresos to where b-beg tkes lce [cm].1. εφ W s s q 1/ Q (chrge er ut re) Q W W Q MOS LTROSTATI POTTIAL V V V +φ (el) V G s Q s ε Q V G gte voltge [V] V terfce voltge; voltge ro cross the SO terfce [V] φ s surfce otetl [V].. Q s surfce chrge; the totl chrge esty the substrte [/cm ].. s V V G gte SO sultor eleto rego W see ITRA VOLTAG 19. φ s Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge 1 of 3
HAL Whe the gte voltge V G reches the threshol voltge V T, the trsc eergy b hs bet ow below the erm level by stce equl to the serto of the trsc erm eergy bs (strog verso), orto of the the eleto rego becomes s strogly -tye s the rest of the substrte s -tye. Ths re s clle the chel s the couctve th betwee the r source of the MOST. The chge voltge ro cross the eleto rego s you move log the -s s equl to the r curret tmes the chge resstce s you move log the - s cross the wth of the chel. source y z V L I R Aother wy to stte ths s: the chge curret the eleto rego s you move log the -s (there s't y chge) s equl to the couctvty of secto tmes the voltge ro t tht ot. I uzq V D 1 Q VG VB φ V qεs φ + V where: We woul't wt to ss u oortuty to tegrte: L I uz Q V D V D The result s the log eresso from Dr urret o ge. D r V voltge cross the eleto rego t some ot log the legth of the chel [V] Pot of cofuso: Here, the legth of the chel (L) s wht s referre to elsewhere t the mmum wth (W m) of the eleto rego. I D r curret [A] R the chge the resstvty, whch s roortol to the chge re [Ω/m] 1 1 R σ A σ zy σ (sgm) couctce [Ω -1 ] σ qµ A re [m ] u electro moblty er the surfce [cm /V-s] 8. z chel eth (see llustrto) [m] V B flt-b voltge [V] 19. ccetor cocetrto the substrte [cm -3 ] φ erm otetl;, [V].19. MOST DSIG OSIDRATIOS Substrte: Lght og hels gur gst brekow t the r jucto. Dog er the terfce by o mltto justs Q. ms c be reuce by usg hevly-oe olycrystlle slco for the gte mterl. Icresg by usg ther oe lyer or fferet mterl, reuce the mgtue of V T. MISLLAOUS ATURAL LOG b e l b ULR'S QUATIO j e φ cosφ+ js φ TRIGOOMTRI IDTITIS e j + e cos θ + jθ θ + jθ jθ e e js θ j e ±θ cosθ± js θ ABLA, DL OR GRAD OPRATOR omre the oerto to tkg the tme ervtve. Where / t mes to tke the ervtve wth resect to tme trouces s -1 comoet to the uts of the result, the oerto mes to tke the ervtve wth resect to stce ( 3 mesos) trouces m -1 comoet to the uts of the result. terms my be clle sce ervtves equto whch cots the oertor my be clle vector fferetl equto. I other wors, A s how fst A chges s you move through sce. rectgulr A A A coortes: A ˆ + yˆ + zˆ y z cylrcl ˆ 1 coortes: A rˆ A +φ A + zˆ A r r φ z shercl ˆ 1 ˆ 1 coortes: ˆ A r A A +θ +φ A r r θ rs θ φ Tom Peck tomz@ee.com www.tecotrols.com/otes 1/14/1 Pge of 3