CHAPTER 3 DIODES. NTUEE Electronics L.H. Lu 3-1

Transcription

1 CHPTER 3 OES Chater Outlie 3.1 The deal iode 3. Termial Characteristics of Juctio iodes 3.3 Modelig the iode Forward Characteristics 3.4 Oeratio i the Reverse Breakdow Regio-Zeer iodes 3.5 Rectifier Circuits 3.6 imitig ad Clamig Circuits 3.7 Physical Oeratio of iodes 3.8 Secial iode Tyes TUEE Electroics.H. u 3-1

2 deal iode Characteristics diode is a two-termial device: ode: the ositive termial Cathode: the egative termial For ositive termial voltage short For egative termial voltage oe Circuit licatios 3.1 THE E OE Rectifier iode logic gates Y B C Y B C TUEE Electroics.H. u 3-

3 3. TERM CHRCTERSTCS OF JUCTO OES - Characteristics of Juctio iodes 1. The forward-bias regio, determied by v >.. The reverse-bias regio, determied by v <. 3. The breakdow regio, determied by v < ZK Forward-bias regio v/ T i S ( e 1 S (saturatio curret: roortioal to diode area. T (thermal voltage 5 m at room temerature. (ideality factor: betwee 1 ad. circuit aalysis, the simlified forward-bias - relatioshi: v / i T i Se v T l S ue to the eoetial - relatioshi i for v <.5 (cut-i voltage Fully coductio for.6 < v <.8 o.7 Temerature deedece S doubles for every 5 C rise i temerature. v decreases m/ C for a give i. i icreases with temerature for a give v. TUEE Electroics.H. u 3-3

4 Reverse-Bias Regio i S deally, the reverse curret is ideedet of reverse bias. reality, reverse curret is larger tha S ad also icreases somewhat with the icrease i the reverse bias. Temerature deedece: reverse curret doubles for every 1 C rise i temerature. Breakdow Regio The kee of the - curve is secified as breakdow voltage ZK for Zeer breakdow mechaism. The reverse curret icreases raidly with the associated icrease i voltage dro beig very small. ormally, the reverse curret is secified by eteral circuitry to assure the ower dissiatio withi a safe rage (o-destructive oeratio. TUEE Electroics.H. u 3-4

5 Circuit alysis 3.3 Modelig the iode Forward Characteristics To aalyze a diode circuit, we eed to determie the diode curret ad voltage. The equatio required for the aalysis: 1. S e( / T doide - characteristics.. ( /R Kirchhoff loo equatio. Grahical aalysis Plot the two equatios i the same coordiatio (i-v. The straight lie is kow as load lie. The itersect (Q of the two curves is the values of ad oeratig oit. terative aalysis 1. set iitial value 1.7. ( /R obtai 1 3. T l ( / S obtai 4. after iteratio (, coverges ad the oeratig oit ca be obtaied. 1 1 TUEE Electroics.H. u 3-5

6 The eed for Raid alysis Raid aalysis usig simlified models for iitial desig. ccurate aalysis (iterative aalysis or comuter rogram for fial desig. Raid aalysis (: ideal-diode model Oe circuit if v < ad short circuit if v >. The most simlified model for a diode i circuit aalysis. t is ormally used for suly voltage much higher tha diode dro. i i v ideal v Raid aalysis (: costat-voltage-dro model Oe circuit if v <.7 ad short circuit if v >.7. The costat-voltage-dro model is the oe most frequetly i i v ideal used i iitial hases of aalysis ad desig. v Raid aalysis (: simlified diode model (iecewise-liear The eoetial curve is aroimated by two straight lies. i for v.7. i (v /r for v >. i sloe r v i v ideal r TUEE Electroics.H. u 3-6

7 Small-gal roimatio v ( t i ( t v ( t d v / T Se ( vd / T S / T S vd / T associates with dc oeratig oit Q. i d associates with v d small sigal resose. The diode ca be aroimated as a liear device uder small-sigal coditios (v d 1m. iode small-sigal resistace ad coductace at oeratig oit Q: i i d vd gdvd vd / rd g d [ ] i T T v T i r d 1/[ ] i v The iode Small-gal Model e Uder small-sigal coditio: v d / T «1 vd i ( t (1 vd id T T e vd / T arge-sigal model is used to obtai the oeratio oit Q. The small-sigal model is determied oce Q is rovided. The small-sigal model is used for circuit aalysis whe the diode is oeratig aroud Q. e e arge-sigal model ideal r Small-sigal model r d TUEE Electroics.H. u 3-7

8 Circuit alysis Techiques Elimiate all the time varyig sigals (ac voltage ad curret sources for oeratio oit aalysis. Use raid aalysis or accurate aalysis to obtai dc voltage ad curret at oeratig oit Q. etermie the arameters of small-sigal models from Q. Relace the devices with small-sigal models ad elimiate all the dc sources. Circuit aalysis uder small-sigal aroimatio. The comlete resose (ac dc of the circuit is obtaied by suerositio of the dc ad ac comoets. The High-Frequecy Small-gal Model r d C d C j Forward-biased diode r d C C d j T T τ C / j / T τ / r T d Reverse-biased diode r d C C d j C ( 1 m j / / For high-frequecy aalysis, caacitace C j ad C d should be icluded i the small-sigal model. C j (juctio caacitace: to reflect the charge i deletio regio with resect to the chage of v. Uder forward bias, C j icreases due to small w de, ad it is ormally aroimated by C j. C d (diffusio caacitace: to reflect the forward-bias miority carrier storage i eutral regio. The diffusio caacitace is large uder forward bias, but is egligible uder reverse bias. TUEE Electroics.H. u 3-8

9 3.4 OPERTO THE REERSE BREKOW REGO-ZEER OE Symbol ad Circuit Model for the Zeer iode s the reverse bias R icreases beyod the kee voltage ZK, large reverse curret coductig associates with small icrease i the reverse bias. The curret i breakdow regio is aroimated as Z Z r z z. Z r Z Temerature Effect of Zeer iode Zeer diode is widely used as a voltage referece. voltage referece requires a costat voltage (ideedet of T temerature coefficiet (TC. Zeer diode with Z < 5ehibit a egative TC. Zeer diode with Z > 5ehibit a ositive TC. The TC of a Zeer diode with a Z about 5 ca be made zero by oeratig the diode at a secified curret. other commoly used techique is to coect a Zeer diode i series with a forward-coductig diode: Z.7 Zeer diode (TC m/ C Forward-biased diode (TC m/ C oltage referece with zero TC TUEE Electroics.H. u 3-9

10 Block iagram of a C Power Suly 3.5 RECTFER CRCUTS C ower suly Geerate a dc voltage from ac ower sources. The ac iut is a low-frequecy large-sigal voltage. Power trasformer Ste the lie voltage dow to required value ad rovides electric isolatio. iode rectifier Coverts the iut siusoidal to a uiolar outut. Ca be divided to half-wave ad full-wave rectifiers. Filter Reduces the magitude variatio for the rectifier outut. Equivalet to time-average oeratio of the iut waveform. oltage Regulator Further stabilizes the outut to obtai a costat dc voltage. Ca be imlemeted by Zeer diode circuits. TUEE Electroics.H. u 3-1

11 The Half-Wave Rectifier oltage trasfer curve: v < v S S v v O O R R r ( v S may alicatios, r << R v O v S. Rectifier diode secificatios: Curret-hadlig caability: the largest curret the diode is eected to coduct. Peak iverse voltage (P: the largest reverse voltage the diode ca stad without breakdow. P s i half-wave rectifier ad the diode breakdow voltage is selected at least 5% higher. TUEE Electroics.H. u 3-11

12 The Full-Wave Rectifier (Ceter-Taed Trasformer v v v S S S < v v O O v O R R r ( v R R r S ( v S Positive cycle 1 R v o egative cycle 1 R v o Trasformer secodary widig is ceter-taed. Peak iverse voltage (P s. Rectified outut waveform for both ositive ad egative cycles. TUEE Electroics.H. u 3-1

13 Full-Wave Rectifier (Bridge Rectifier B v o v s v v v S S S < v v O O v R R r O ( v R R r S ( v S Positive Cycle egative Cycle B v o 1 o 3 4 off 1 R B v o 3 4 o 1 off 3 4 R oes ot require a ceter-taed trasformer, resultig i half of turs for the secodary widig. Higher tur-o voltage (. Peak iverse voltage (P s. Most oular rectifier circuit cofiguratio. TUEE Electroics.H. u 3-13

14 Uloaded Half-Wave Peak Rectifier with deal iode iode turs off after the first cycle. o discharge ath outut remais o eak value. oaded Half-Wave Peak Rectifier with deal iode iode turs off aroud the eak iut value (t. i ad caacitor C discharges through load R. v O decreases eoetially with a time costat RC. iode turs o whe the iut v equals the eoetially decayig outut (t T t. The diode oly coducts for a brief iterval ( t. urig this iterval, outut (v O follows iut waveform (v, chargig the caacitor C. TUEE Electroics.H. u 3-14

15 Circuit alysis of oaded Half-Wave Peak Rectifier with deal iode The iut siusoid is give as v (t cos ω t. Tyically, the RC time costat is chose to be greater tha the siusoid eriod: RC >> T. The diode coducts oly for a short eriod of time t withi oe siusoidal eriod ( t << T. iode cut-off eriod iode-off eriod ( t T t: caacitor C is discharged through R. v equals to v O at the ed of the off eriod diode starts to coduct. v ( t e O t / RC iode coductig eriod v ( t T t e O ( T t/ RC T / RC (1 T / RC r T / RC / frc v ( t T t v ( t T t cosω( T t cosω t (1.5ω t O t ( r / / ω r iode-o eriod (T t t T: caacitor C is charged by the iut. v O equals to v durig this eriod of time. Cr ωcr icav t Qlost Cr icav π / r where t r / dvo i C ma C t T t ω C siω t ω C t π / r dt i i av ma i Cav i C ma (1 π (1 π / r / r e TUEE Electroics.H. u 3-15 r / R ad π r / ωrc

16 Circuit alysis of oaded Full-Wave Peak Rectifier with deal iode Rile frequecy is twice of the iut frequecy. ischarge eriod is reduced to T/ ad r /frc. iav (1 π / r i ma (1 π / r For the same coditio, caacitor eeded is oly half the size of that required i the half-wave rectifier. Rectifier alysis with iode oltage ro Relace with i above aalysis for half-wave rectifier ad full-wave rectifier usig a cetertaed trasformer. Relace with i above aalysis for bridge-rectifier case. TUEE Electroics.H. u 3-16

17 esig of the Zeer Shut Regulator R s Z o oad Z s s,ma s,mi Z o deal case s Z R Z r Z o t R rz RrZ O Z S R rz R rz R rz ie regulatio O rz S R rz oad regulatio O RrZ R r Z t ie regulatio ad load regulatio should be miimized. For r Z «R, lie regulatio ca be miimized by choosig small r Z. oad regulatio ca be miimized by choosig small r Z ad large R. However, there is a uer limit o the value of R to esure sufficietly high curret Z (r z icreases if Z is too low. R should be selected from S mi Z rz Z mi R Z mi ma TUEE Electroics.H. u 3-17

18 3.6 MTG CMPG CRCUTS imiter Trasfer Fuctio ad Outut Waveform Hard limiter Soft limiter ariety of Basic imiter Circuits TUEE Electroics.H. u 3-18

19 The Clamed Caacitor (C Restorer Caacitor Proerties The voltage across a caacitor results from charge accumulatio at both of the lates. The amout of charge accumulate at the two lates of a caacitor are equal with oosite olarity. With fiite chargig/dischargig curret, the voltage across a caacitor ca ot chage value abrutly. Circuit Oeratio v O > : the diode is off ad o curret ath to charge/discharge C v C will ot chage. v O < : the diode is o ad C is coected to groud v O will be clamed to zero. For a caacitive couled system, dc comoet is lost durig trasmissio. The use of clamed caacitor ca restore the dc comoet, which is etremely imortat for duty cycle measuremet. For arbitrary iut waveform, the lowest eak will always be clamed to zero at the outut. v v O t t clamed to TUEE Electroics.H. u 3-19

20 The Clamed Caacitor with oad Resistace v O > : the diode is off C is discharged by curret through R v O eoetially decays with a time costat RC v O < : the diode is o C is charged by curret through the diode ad R v O icreases toward zero oltage oubler clam ad a eak rectifier i cascade voltage doubler TUEE Electroics.H. u 3-

21 trisic Semicoductor Covalet bod 3.7 PHYSC OPERTO OF OES Each valece electro of a silico atom is shared by oe of its four earest eighbors. Electros served as covalet bods are tightly boud to the ucleus (ot free to cotribute to coductio. Electro-hole air t K, o free carriers are available behaves as a isulator. t room temerature, a small amout of covalet bod will be broke by the thermal eergy free carriers. Electros i the valece bad are ecited to the coductio bad ad leave holes i valece bad electro-hole air geeratio. Both electros ad holes are free to move ca cotribute to coductio. Carrier cocetratio i itrisic semicoductor For itrisic semicoductor at thermal equilibrium. i (itrisic carrier cocetratio i i (T BT 3 eeg /kt s T icreases, i icreases. Coductio bad Eergy ga (E g alece bad Coductio bad Eergy ga (E g electro (e hole (h s T decreases, i decreases. alece bad TUEE Electroics.H. u 3-1

22 Etrisic Semicoductor Etrisic semicoductor itrisic semicoductor imurities ccordig to the secies of imurities, etrisic semicoductor ca be either -tye or -tye. -tye semicoductor tom Free electro The door imurities have 5 valece electros are added ito silico. P, s, Sb are commoly used as door. lico atom dislaced by a door atom. oor ios are bouded i the lattice structure ad thus doate free electros without cotributig holes. By addig door atoms ito itrisic semicoductor, the umber of electros icreases ( > -tye semicoductor. Majority carrier: electro Miority carrier: hole oor Covalet Bod E d E c E i E v TUEE Electroics.H. u 3-

23 -tye semicoductor The accetor imurity has 3 valece electro (Boro. lico atom dislaced by a trivalet imurity atom. The boro lacks oe valece electro. t leaves a vacacy i the bod structure. This vacacy ca accet electro at the eese of creatig a ew vacacy. ccetor creates a hole without cotributig free electro. By addig accetor ito itrisic semicoductor ( > -tye semicoductor. Majority carrier: hole Miority carrier: electro Hole tom ccetor Covalet Bod E a E c E i E v TUEE Electroics.H. u 3-3

24 Carrier Cocetratio Charge eutrality: Particles with ositive charge: : hole cocetratio (mobile : door cocetratio (immobile Particles with egative charge: : electro cocetratio (mobile : accetor cocetratio (immobile ocal charge desity: ρ v q ( Charge eutrality (ositive charge egative charge: Mass-actio law i for semicoductor uder thermal equilibrium For -tye semicoductor i [1 1 ( i i / ] if» i i / For -tye semicoductor i [1 1 ( ] i i / if» i i / TUEE Electroics.H. u 3-4

25 Free Carriers i Semicoductors Free Carrier Mobile articles with ositive or egative charges: electros ad holes The trasortatio of carriers results i curret coductio i semicoductors. rift 1. Thermal motio i the absece of electric field: The directio of flight beig chaged at each collisio with the heavy, almost statioary ios. Statistically, a electro has a radom thermal motio i the crystal structure. et dislacemet over a log eriod of time is zero o et curret flow (.. Thermal motio uder electric field E: The combied motio of electro uder electric field has a radom comoet ad a drift comoet. Still, o et dislacemet due to radom motio comoet over a log eriod of time. The drift comoet rovides the electro a et dislacemet Seed (istataeous > elocity (average E rift comoet due to electric field TUEE Electroics.H. u 3-5

26 Mobility F qe a F /m * (m * is the effective mass of electro ssume the time iterval betwee collisio is t coll ad the drift velocity immediately after the collisio is. The the average velocity of the electro due to the electric field is: atcoll qe vd ( drift tcoll µ E * m µ v E d µ (electro mobility is very imortat i aalyzig electro coductio. Mobility idicates how fast a electro ca move uder certai electric field itesity. Curret Time iterval for electros flowig across : T /v d (sec Total charge: Q q (Coulomb Curret Q /T q /T qv d ( Curret desity J / qv d qµe σe (/cm Coductivity σ qµ (Ωcm 1 Ohm s ow qt m coll * (cm /sec J σe σ / /R ( R /σ ρ / (Ω v d : area (cm : legth (cm : electros desity (cm -3 v d : drift velocity (cm/sec TUEE Electroics.H. u 3-6

27 iffusio Carrier diffusio iffusio is a maifestatio of the thermal radom motio of articles. Sectio : total # 6 (3 movig to the left ad 3 movig to the right Sectio : total # 4 ( movig to the left ad movig to the right et flu: 1 movig across the iterface from sectio to sectio. a ihomogeeous material, statistically more articles will cross the iterface from high cocetratio side to low cocetratio side tha the reverse directio. ( Eistei Relatio J Hole diffusio rift ad diffusio are both maifestatios of radom thermal motio of carriers, ad the relatio betwee µ ad is give by: /µ /µ kt/q T (thermal voltage. Total diffusio curret desity Both electro ad hole diffusio cotribute to coductio curret. d d Total diffusio curret desity: J diff J ( diff J ( diff q q d d ( J Electro diffusio d q d d q d TUEE Electroics.H. u 3-7 J J ( diff ( diff : diffusio costat (diffusivity of e : diffusio costat (diffusivity of h

28 Graded Semicoductor For a o-uiform semicoductor, the doig cocetratio is rereseted as (. The mobile carrier will diffuse due to the o-uiform distributio. The ucomesated sace charge will build u a field (otetial for the system to reach equilibrium. o et curret flows at ay oit uder equilibrium. ( Therefore, the built-i otetial ca be derived uder thermal equilibrium Electro diffusio betwee oits with differet doig cocetratio. Built-i otetial from hole cocetratio d J qµ E q d d µ E d T d d E d d d d T T l e 1 1 / T Built-i otetial from electro cocetratio J µ E T d E d d q µ T d e E q d d d d d d 1 1 T l 1 1 / T 1 ( E TUEE Electroics.H. u 3-8 ( ( E Electro drift Electro diffusio ecess ositive fied charge ecess egative mobile charge

29 Carrier Geeratio ad Recombiatio Geeratio (G: electros are ecited from valece to coductio bad geerates electro-hole airs. Carrier recombiatio (R β : electros move back to valece bad elimiates electro-hole airs. Thermal equilibrium: E c i Geeratio rate recombiatio rate R th β β i G th o-equilibrium: Wheever thermal equilibrium is disturbed, rocesses eist to restore the system to equilibrium. f < i, G (geeratio rate > R (recombiatio rate to restore equilibrium. f > i, G (geeratio rate < R (recombiatio rate to restore equilibrium. ow-level ijectio coditio: Equilibrium is disturbed due to carrier ijectio ( ( > i ow-level ijectio is secified uder the coditio i << << (or. Recombiatio: R β β ( ( et recombiatio: U R G β β i -tye: U ( /τ where τ (ecess-miority-carrier lifetime for hole 1/β -tye: U ( /τ where τ (ecess-miority-carrier lifetime for electro 1/β E v G R otatio -tye -tye (equilibrium -tye -tye (equilibrium Electro cocetratio Hole cocetratio TUEE Electroics.H. u 3-9

30 TUEE Electroics.H. u 3-3 Curret i semicoductors rift curret: J drift qµ E qµ E iffusio curret: J diff q (d/d q (d/d Total curret: J J J (qµ E q (d/d (qµ E q (d/d Cotiuity equatio * rea d J ( J (d d G R The rate of chage i carrier umber: carrier flowig i the sectio carrier flowig out the sectio carrier geeratio withi the sectio carrier recombiatio withi the sectio ( 1 ( 1 R G J q t R G J q t G E E t τ µ µ d R G q d J q J d t ( ] ( ( [ G E E t τ µ µ E e h J J

31 Juctio Uder Zero-Bias Coditios solated, eutral regio of -tye ad -tye semicoductor -tye ( E F T l i E c E i E v i -tye ( E F T l i E c E i E v i -tye ad -tye semicoductor i cotact P-tye ( -tye ( Majority carrier i -tye: electro Miority carrier i -tye: hole Majority carrier i -tye: hole Miority carrier i -tye: electro Majority carriers are crossig the iterface (diffusio ad recombied i the other side of the juctio. eavig ucomesated sace charges ad deletio regio. deletio regio, electric field (otetial builds u due to the ucomesated sace charges. The built-i otetial behaves as a eergy barrier, resultig i reductio of the majority carrier diffusio. This field will also result i miority carrier drift across the iterface i the oosite directio to diffusio. TUEE Electroics.H. u 3-31

32 juctio formatio (thermal equilibrium eletio regio icreases due to majority carrier diffusio across the juctio. The built-i otetial from ucomesated sace charge icreases, resultig i reductio of diffusio. Miority carriers are swet across the juctio i the resece of the built-i field drift curret. Equilibrium is reached whe J diff ad J drift are equal i magitude ad oosite i directio. o et curret flows across the juctio. -tye ( E -tye ( hole diffusio hole drift electro diffusio electro drift J J eutral Regio eletio Regio eutral Regio -tye -tye T l T l T l i TUEE Electroics.H. u 3-3

33 The deletio regio Ste graded juctio (abrut juctio is used for aalysis. Carriers are fully deleted i the deletio regio. eutral regio i -tye ad -tye outside deletio regio. Built-i otetial: T l ( / i. Poisso s equatio: q w q Carrier distributio d d (Poisso's equatio: E w (Poisso's equatio: w de ρ ν d ε ( ρ / ε v eutral -tye regio: Majority carrier Miority carrier i / Ed d E E ma ma q ( w w / ε q w / l ε ε ε de w w q( q ( q T w / ε ( / i charge desity (ρ v q w w q electric field (Ε w w E ma electrostatic otetial ( otetial of electro w w w Carrier cocetratio 1 18 w eutral -tye regio: Majority carrier Miority carrier i / eletio regio: TUEE Electroics.H. u 3-33

34 Juctio Uder Forward-Bias Coditios lyig forward bias to the juctio -tye ( E -tye ( -tye -tye F F F hole diffusio hole drift J -tye -tye electro diffusio electro drift J Forward bias F reduces the deletio regio ad the eergy barrier. Majority carrier diffusio across the juctio icreases due to the reductio of eergy barrier. The drift curret of miority carrier i the oosite directio is almost costat. et curret flows from -tye side to -tye side. This forward curret deeds strogly o the value of the forward bias. TUEE Electroics.H. u 3-34

35 Miority carrier distributio ssume all voltage dro takes lace across the deletio o voltage dro i eutral regio (E ;. The miority carrier cocetratio ear the edge of the deletio will be raised due to F : ( e[q( /kt] e(q/kt ( e[q( /kt] e(q/kt By solvig the cotiuity equatio, the miority carrier distributio are: ( ( ( e ( e q / kt q / kt 1 e 1 e ( / ( / τ (τ : ecess-miority-carrier lifetime; ( : diffusio legth J( J ( J ( J ( J ( J ( J ( J J ( J ( q ( Forward curret across the juctio ssume o carrier geeratio ad recombiatio withi the deletio regio: J ( J ( ad J ( J ( J i -tye side ad J i -tye side ca be obtaied by: d q q / kt J ( q ( e 1 d d q q / kt J ( q ( e 1 d τ τ q q / kt q / kt ( e 1 J s( e 1 TUEE Electroics.H. u

36 Juctio Uder Reverse-Bias Coditios lyig reverse bias to the juctio -tye ( E -tye ( -tye -tye R R R hole diffusio hole drift electro diffusio electro drift J J -tye -tye Miority carrier distributio ad reverse curret Reverse bias R wides the deletio regio, resultig i a higher barrier. Majority carrier diffusio decreases due to the eergy barrier. Miority carrier drift i the oosite directio does ot chage sigificatly. The equilibrium is disturbed ad a small et curret (reverse curret flows from -tye side to -tye side R R s the reverse bias icreases, the reverse curret remais almost costat reverse saturatio curret S. TUEE Electroics.H. u 3-36

37 TUEE Electroics.H. u 3-37 Juctio - Characteristics aw of the juctio: ( e(/ T ad ( e(/ T The distributio of miority carriers deeds o diffusivity ad ecess-miority-carrier lifetime: The - characteristics of the juctio diode (icludig ideality factor is give by: deality factor ( 1 is icluded to accout for o-ideal roerties of the juctio diode. iffusio Caacitace Ecess miority carrier stored i eutral regio will chage with the termial voltage caacitace. By itegratio the ecess miority carriers at both sides: Small-sigal diffusio caacitace: C d is large uder forward bias coditios. C d is eglected uder reverse bias coditios. / ( / / ( / 1 ( ( 1 ( ( kt q kt q e e e e τ τ [ ] 1 ( 1 ( ( ( ( / / T T s e e q q J J Q Q Q T τ τ τ d dq C e e Q T T d s T kt q s T T T ( / / τ τ τ τ

38 TUEE Electroics.H. u 3-38 Juctio Caacitace The deletio width is cotrolled by the termial voltage. The chage of termial voltage (d will result i dq at the edge of the deletio regio caacitace. The juctio caacitace due to sace charge is C j dq/d R. C j ca also be estimated by a arallel-late caacitor: Uder forward bias coditios, w de reduces larger C j. Uder forward bias coditios, w de icreases smaller C j. Geeral formula for deletio caacitace for arbitrary doig rofile: ( q C C q w C q w j R j R de j R de ε ε ε ε ( R R R j q d w q d d dq C ( ε m R j j C C (1

39 Juctio i the Breakdow Regio Breakdow voltage Whe reverse bias eceeds the breakdow voltage, a large reverse curret flows with small icrease of R. For breakdow voltage < 5 Zeer breakdow. For breakdow voltage > 5 avalache breakdow. Juctio breakdow is ot a destructive rocess if the maimum secified ower dissiatio is ot eceeded. Zeer breakdow The electric field i the deletio regio icreases to the oit where it ca break covalet bods ad geerate electro-hole air. Geerated electros are swet ito the side ad holes are swet ito the side reverse curret. ormally, zeer breakdow takes lace for juctio with high doig cocetratio. electric field (Ε E c E w w E v E critical E ma Shaded area termial voltage E c E v TUEE Electroics.H. u 3-39

40 valache breakdow The miority carriers that cross the deletio regio uder the ifluece of the electric field gai sufficiet kietic eergy to be able to break covalet bods i atoms with which they collide. The geerated carriers (from collisio will be further accelerated ad break other covalet bods after gai sufficiet kietic eergy avalache reactio. ormally, avalache takes lace first for juctio with low doig cocetratio. electric field (Ε E E c w w E v E ma Ecritical E c Shaded area termial voltage E v TUEE Electroics.H. u 3-4