8 Biasd - Juctio Solid Stat Dvic Fudamtals 8. Biasd - Juctio ENS 345 Lctur Cours by Aladr M. Zaitsv aladr.zaitsv@csi.cuy.du Tl: 718 98 81 4N101b Dartmt of Egirig Scic ad Physics
Biasig uiolar smicoductor 8 Biasd - Juctio V E = 0 E 0 E 0 E E 0 Coductio bad E F Valc bad No bias Uiform smicoductor Highly rsistiv smicoductor btw two low rsistiv os Wh biasig a o-uiformly coductiv smicoductor, th most of bias is alid to th most rsistiv rgio. Th highst lctric fild is dvloig i th most rsistiv rgio. Dartmt of Egirig Scic ad Physics
Biasig - juctio 8 Biasd - Juctio E F CB V=0 ΔE C -V ΔE C +V VB de B d 0 de B d 0 de B d 0 de F d 0 de F d 0 de F d 0 At ay bias, th gradit of th rgy bads dos ot chag its sig, whras th gradit of Frmi lvl may b ositiv (gativ bias), or ositiv (gativ bias). Dartmt of Egirig Scic ad Physics 3
Rvrs (gativ) bias of - juctio 8 Biasd - Juctio V + Assum o currt flows udr tral rvrs bias V, th: W d s ottial barrir N Φ j Φ bi V E c E F E v bi V = 0 E c E F E v E ma N D s W d N A s s ( bi V ) 1 N s A A ( Φbi V ) N N N A D 1 N N D D E c E c bi + V V E F E v Th dltio layr wids with icrasig rvrs bias: W d V E F E v rvrsbiasd Currt flow through gativly biasd - juctio is gligibl Dartmt of Egirig Scic ad Physics 4
8 Biasd - Juctio Homwork 1. Calculat width of th dltio rgio i silico ad grmaium - juctios for doig coctratios 10 17 cm -3 ad 10 18 cm -3 of doors ad acctors rsctivly.. Fid th maimum lctric fild i ths - juctios. Dartmt of Egirig Scic ad Physics 5
Caacitac of - juctio 8 Biasd - Juctio N N d N a P A Rvrs biasd - juctio is a caacitor. Coductor Isulator Coductor W d A C d s A W d C d ca b lowrd by rducig th juctio ara ad icrasig W d. W d dcrass with rductio of th doig coctratio(s) ad/or with icrasig rvrs bias. Tyically, C d 1fF/μm for W d = 0.1μm. Dartmt of Egirig Scic ad Physics 6
8 Biasd - Juctio Homwork 1. Calculat/stimat caacitac of a - silico diod of a ara of 1 mm th - ad -ty rgios of which hav rsistivity of 10 ohm.cm ad ohm.cm rsctivly.. Calculat caacitac of th dltio layr i th diod dscribd abov udr rvrs bias 10V. Dartmt of Egirig Scic ad Physics 7
Juctio brakdow 8 Biasd - Juctio At a high rvrs bias, - juctio rics brakdow. Two mchaisms causig th brakdow ar: 1. Avalach multilicatio of charg carrirs.. Quatum tulig of charg carrirs through th badga. Nithr of th two brakdow mchaisms is dstructiv. Howvr hatig causd by th larg brakdow currt ad high brakdow voltag may caus dstructio ulss sufficit hat sikig is rovidd. Dartmt of Egirig Scic ad Physics 8
8 Biasd - Juctio Pak lctric fild ad brakdow voltag Nutral Rgio icrasig N+ rvrs bias P E E N a 0 (a) icrasig rvrs bias (b) E V brakdow N E ( ) =0 bi Vr s secrit N - bi 1/ Dartmt of Egirig Scic ad Physics 9
8 Biasd - Juctio Brakdow voltag of Si - juctio Brakdow voltag ad brakdow fild vs. doig dsity for a abrut - juctio at room tmratur. Dartmt of Egirig Scic ad Physics 10
Tulig brakdow 8 Biasd - Juctio Filld Stats - Emty Stats E c E E crit 10 6 V/cm E v Brakdow I V Tulig is th domiat brakdow mchaism wh N is vry high ad V B is quit low (blow a fw volts). 11 Dartmt of Egirig Scic ad Physics
Avalach brakdow 8 Biasd - Juctio E c E F E v origial lctro Imact ioizatio ad ositiv fdback avalach brakdow Brakdow lctro-hol air gratio I V E c E F E V V V B B secrit N 1 N 1 N a 1 N Avalach brakdow is th domiatig mchaism of - diod brakdow at highr V B. d Dartmt of Egirig Scic ad Physics 1
8 Biasd - Juctio Homwork Calculat brakdow voltag Si ad G - juctios th - ad - ty rgios of which hav rsistivity of 5 ohm.cm ad 0 ohm.cm rsctivly. Dartmt of Egirig Scic ad Physics 13
8 Biasd - Juctio Forward bias charg carrir ijctio V = 0 I = 0 V + E c bi E F Ev E F bi V V E c E F bi V E v Drift ad diffusio cacl out Miority carrir ijctio Dartmt of Egirig Scic ad Physics 14
8 Biasd - Juctio Coctratio of ijctd charg carrirs ( ) N c -( E c -E F )/ kt N c -( E c -E F )/ kt ( E F -E F )/ kt 0 [( E F -E F )/ kt ] 0 [ V / kt ] E f F E c E c E F f E v E v Th miority carrir dsitis ar raidly raisig with voltag by (V / kt). Which sid of - juctio 0 N 0 P grats mor charg carrirs? Dartmt of Egirig Scic ad Physics 15
Ijctio of css charg carrirs 8 Biasd - Juctio ( ) 0 V ) 0 ( V kt kt Ecss coctratio of ijctd carrirs V kt ( ) ( ) - 0 0( -1) Total coctratio of ijctd carrirs E c E F V E F E v V kt ( ) ( ) - 0 0( -1) Dartmt of Egirig Scic ad Physics 16
8 Biasd - Juctio Eaml: A silico - juctio has N A =10 19 cm -3 ad N D =10 16 cm -3. Th alid forward voltag is 0.6 V. - Fid miority carrir coctratios at th dltio-rgio dgs. Solutio: qv kt 0.6 0.06 11-3 ( P) P0 10 10 cm ( ) N qv kt 4 0.6 0.06 14-3 N 0 10 10 cm - What ar th coctratios of th css miority carrirs? Solutio: 11 11-3 ( P) ( P) - P0 10-10 10 cm 14 4 14-3 ( N ) ( N ) - N 0 10-10 10 cm Dartmt of Egirig Scic ad Physics 17
8 Biasd - Juctio Homwork A grmaium - juctio has N A =10 17 cm -3 ad N D =10 18 cm -3. Th alid forward voltag is 0.7 V. - Fid miority carrir coctratios at th dltio-rgio dgs. - Fid ar th css miority carrir coctratios. Dartmt of Egirig Scic ad Physics 18
Currt cotiuity quatio 8 Biasd - Juctio A J ( ) A J ( ) A J () ara A J ( + ) - J ( ) - J ( ) Volum = A - dj d Dartmt of Egirig Scic ad Physics 19
8 Biasd - Juctio Currt cotiuity quatio - D dj d d d Miority drift currt is gligibl: J = D d/d d d D L d d L L ad L ar th diffusio lgths: L D L D Dartmt of Egirig Scic ad Physics 0
8 Biasd - Juctio Distributio of css charg carrirs P N d d L P - N 0 Solutio: ( ) A / L B -/ L Boudary coditios: ( ) ( ) 0 V / kt 0( -1) ( ) 0 ( V / kt -1) - - / L, Dartmt of Egirig Scic ad Physics 1
Distributio of css charg carrirs 8 Biasd - Juctio ( ) ( ) 0 0 ( ( V / kt V / kt -1) - -1) - - / L / L,, 1.0 P-sid N a = 10 17 cm -3 P ' /L 0.5 N-sid N d = 10 17 cm -3 N ' /L 3L L L 0 L L 3L 4L L D 3610-6 85 μm Dartmt of Egirig Scic ad Physics
8 Biasd - Juctio Eaml: Carrir distributio i forward-biasd - diod N-ty N d = 5 cm -3 D =1 cm /s = 1 s P-ty N a = 10 17 cm -3 D =36.4 cm /s = s ( P ) 0 qv kt i qv/ kt 10 0.6 0.06 13-3 P0( -1) ( -1) 10 cm 17 Na 10 -sid 10 13 cm -3 ( = ) -sid ( = ) Dartmt of Egirig Scic ad Physics 3
Distributio of currt i - diod 8 Biasd - Juctio J total J total J = J total J J = J total J P-sid J P 0 J N N-sid J P P-sid 0 J N N-sid J J N P d( ) qv kt -qd q N 0( -1) d L d( ) D D qv kt qd q P0( -1) d L - - P L - N L J total J N D D V kt ( N ) J P ( P ) N 0 P0 ( -1) L L J at all Dartmt of Egirig Scic ad Physics 4
Currt-Voltag charactristic of - diod 8 Biasd - Juctio I V kt I0( -1) Rvrs saturatio currt: I 0 A i D LN D D L N A -EG kt i NC NV I AN C N V L D N D D L N A EG -V - kt What causs th IV-curvs to shift to lowr V at highr T? Dartmt of Egirig Scic ad Physics 5
Currt-Voltag charactristic of - diod 8 Biasd - Juctio Forward currt I 0 V kt Rvrs (lakag) currt - I 0 Dartmt of Egirig Scic ad Physics 6
Homwork 8 Biasd - Juctio Fid coctratio of css miority charg carrirs at a distacs 10 ad 100 micros from - juctio ad currt dsity of a grmaium diod at forward voltag 0.7 V at room tmratur. How ths aramtrs chag wh tmratur is icrasd to 100 C? Th doig, diffusio ad rcombiatio aramtrs of th diod is giv i th tabl blow: N-ty N d = 5 cm -3 D =1 cm /s = 1 s P-ty N a = 10 17 cm -3 D =36.4 cm /s = s Dartmt of Egirig Scic ad Physics 7