ECE606: Solid State Devices Lecture 16 p-n diode AC Response

Transcription

1 ECE66: Solid State Devices Lecture 16 - diode C esose Gerhard Klimeck gekco@urdue.edu Klimeck ECE66 Fall 1 otes adoted from lam Toic Ma Equilibrium DC Small sigal Large Sigal Circuits Diode Schottky Diode i o-equilibrium (Eteral DCC voltage alied) BJT/HBT MOSFET Klimeck ECE66 Fall 1 otes adoted from lam

2 Why should we study C esose? Motivatio adio Juctio Caacitace Coductace Series esistace Diffusio Caacitace Klimeck ECE66 Fall 1 otes adoted from lam 3 Outlie 1) Coductace ad series resistace ) Majority carrier juctio caacitace 3) Miority carrier diffusio caacitace 4) Coclusio ef. SDF, Chater 7 Klimeck ECE66 Fall 1 otes adoted from lam 4

3 Forward Bias Coductace o q( S I ) β / m ( 1) I = I e l(i) 1 6,7 3 I Io β l = q( S I ) I m m = G (), diff (1), mbiolar () C J G 5 S 4 m d qβ I I di ( ) o = S 1 g C diff = m qβ ( I I ) S FB Forward Bias Coductace Klimeck ECE66 Fall 1 otes adoted from lam 5 everse Bias Coductace o q( S I ) β / m i ( 1) q B bi q i B bi G I = I e I 1 qi B = g B bi C J 5 4 l(i) 1 6,7 S 3 everse Bias Coductace C diff Klimeck ECE66 Fall 1 otes adoted from lam 6

4 Outlie 1) Coductace ad series resistace ) Majority carrier juctio caacitace 3) Miority carrier diffusio caacitace 4) Coclusio Klimeck ECE66 Fall 1 otes adoted from lam 7 Juctio Caacitace Forward biased diode C sigal Coductace DC F F Juctio Caacitace Series esistace Diffusio Caacitace Deletio width modulatio > Charge modulatio Majority carrier effect < Klimeck ECE66 Fall 1 otes adoted from lam 8

5 Majority Carrier Juctio Caacitace ρ < Juctio Caacitace Coductace Series esistace ρ > Diffusio Caacitace Measure Majority Carrier Juctio Caacitace Ksε Ksε CJ = = W W Ksε Ksε ( bi ) qd q Cj a Klimeck ECE66 Fall 1 otes adoted from lam 9 Measuremet of Built-i Potetial 1 C q ( ) K ε J D s ( ) bi (ssume sigle sided - juctio) measure C J Derive bi from C J measuremets lot C J - bi Klimeck ECE66 Fall 1 otes adoted from lam 1

6 .. d ariable Doig 1 C q ( ) K ε J D s ( bi ) measure C J D ( ) = 1 qksε d(1 CJ ) Measure doig cocetratio as a fuctio of ositio d Charge lot C J - < = > Klimeck ECE66 Fall 1 otes adoted from lam 11 Dielectric elaatio Time (majority side) Majority side J = qµ E qd eglect d 1 dj = G dt q d ( ) 1 ( µ E) DC d d q de = = Dµ dt q d d How log does it take for the sigal to cross the juctio? Ksε =.1 s d σ ery fast -side de q = d k ε ( ) S ( D ) d q Dµ σ = = dt k ε k ε S S σ t k ε t S d ( t) = e = e Klimeck ECE66 Fall 1 otes adoted from lam 1

7 Outlie 1) Coductace ad series resistace ) Majority carrier juctio caacitace 3) Miority carrier diffusio caacitace 4) Coclusio Klimeck ECE66 Fall 1 otes adoted from lam 13 Diffusio Caacitace for Miority Carriers Miority Carrier side J d = qµ E qd d C C 1 dj = r q d g DC DC C jωt jωt jωt dc ac dc ac dc ac = D d ( ) ( ) e d e e Klimeck ECE66 Fall 1 otes adoted from lam 14

8 Diffusio Caacitace for Miority Carriers jωt jωt ( dc ace ) d ( dc ac e ) dc e = D d d d jω = D d d j t dc j t ac dc j t ac ace ω e ω e ω jωt ac d dc dc L L D C : = D = e Be d dc d ac ac ( jω ) d L * L * L * C : = D 1 = Ce De Ce ac ( ) ( ) L = D / 1 jω = / 1 jω * * Klimeck ECE66 Fall 1 otes adoted from lam 15 C Boudary Coditios qdc i kt dc ( = ) = e 1 jωt dc ace q i kt = e 1 jωt ace jωt ( dc ace ) jωt qdc qace i kt kt e e 1 jωt ( dc ace ) Taylor easio q dc jωt i q kt ace e 1 1 kt q q dc ac i kt ac ( = ) = e = C kt Klimeck ECE66 Fall 1 otes adoted from lam 16

9 C Curret ad Imedace q q dc ac i kt ac ( = ) = e kt = C L * L * L * ( ) = Ce De Ce ac Fially d qd q Jac = qd = e d L kt q dc ac ac i kt * = C Curret J q D Yac = = e G qdc ac i kt * 1 ac L kt jω C Imedace Klimeck ECE66 Fall 1 otes adoted from lam 17 Diffusio Coductace ad Caacitace GD ω Y G jωc G jω ac = D D 1 Searate i real & imagiary arts G D G 1/ = 1 ω 1 ωc D G 1/ = 1 ω 1 Product of G D ad C D frequecy-ideedet CD 1/ ω Klimeck ECE66 Fall 1 otes adoted from lam 18

10 Small Sigal -diode Coclusio 1) Small sigal resose relevat for may aalog alicatios. ) Small sigal arameters always refer to the DC oeratig coditios, as such the arameter chages with bias coditio. 3) Imortat to distiguish betwee majority ad miority carrier caacitace. Their relative imortace deeds o secific alicatios. Klimeck ECE66 Fall 1 otes adoted from lam 19 ECE66: Solid State Devices - diode Large Sigal esose Gerhard Klimeck gekco@urdue.edu Klimeck ECE66 Fall 1 otes adoted from lam

11 Equilibrium DC Small sigal Digital Sigals: switch o ad off Large Sigal Toic Ma Circuits Diode Schottky BJT/HBT MOSFET Klimeck ECE66 Fall 1 otes adoted from lam 1 Outlie 1) Large sigal resose ad charge cotrol model ) Tur-off characteristics 3) Tur-o characteristics 4) Other alicatios 5) Coclusio ef. SDF, Chater 8 Klimeck ECE66 Fall 1 otes adoted from lam

12 Digital, Large Sigal licatios :If trasitio is slow, every oit is i quasi-equlibrium treat them like DC 1 :1 :- ---:If trasitio is very fast - to 1 l(i) 1 1 to Klimeck ECE66 Fall 1 otes adoted from lam 3 Closer Look to Fast Trasitio (t) Before trasitio occur costat voltage, curret chage from I F to I t costat curret, voltage chage form 1 to l(i) 1 :1 :- i(t) I F 1 to -.1I - 1 -I t r t s t rr Klimeck ECE66 Fall 1 otes adoted from lam 4

13 Defiitios (t) i(t) -.1I I F t t s Charge storage time t r ecovery time t rr.. everse recovery time -I t r t s t rr Klimeck ECE66 Fall 1 otes adoted from lam 5 Cotiuity Equatios Full aalytical solutio imossible for large sigal. ( D ) D = q 1 = J r g q J 1 = J r g q J = qµ E qd P P P = qµ E qd P P P Klimeck ECE66 Fall 1 otes adoted from lam = i, diff = i, diff Charge cotrol equatios: roimatio whe you have large trasiet resose 6

14 How Does Curret Fli Without oltage Fliig? Where did the charge go? 1. Back to the left-had side. ecombie with the tra ad the majority carrier (,t) forward bias, miority carrier has bee ijected ecombiatio (,t) eoetially dyig out d d (,t) d > d < DC Whe voltage start to chage, (,t) suddely beded dowwards, d/d chage sig ad curret fli from to Klimeck ECE66 Fall 1 otes adoted from lam 7 Large Sigal Charge Cotrol Model 1 dj = r q d g miority carrier d J = qµ E qd d ( ) ( ) d = D t d Klimeck ECE66 Fall 1 otes adoted from lam 8

15 Large Sigal Charge Cotrol Model ( ) ( ) d = D t d (q), itegrate W ( ) d d ( q ) W W W d d (,t) q q d = D d d rea uder the give time Curret goig out ( ) d ( q ) d q = D D d d = W = = idiff Curret comig i ecombiatio W ( ) q d (Total charge that is buildig i)= (et electros flowig i) (recombiatio) Klimeck ECE66 Fall 1 otes adoted from lam 9 Outlie 1) Large sigal resose ad charge cotrol model ) Tur-off characteristics 3) Tur-o characteristics 4) Other alicatios 5) Coclusio Klimeck ECE66 Fall 1 otes adoted from lam 3

16 Tur-off Characteristics: Determie (t s ) IF S 1 F j - P I = idiff i(t) -.1I I F ( ) t < = I F = (Time Ideedet) -I t r Why does the curret remai costat eve with t>? Klimeck ECE66 Fall 1 otes adoted from lam t s t rr 31 Boudary Coditio IF S 1 F j - P I = idiff ( ) t < = I F = ( ) = I = ( ) F ote. For a caacitor, voltage ca ot chage istatly. So charge ca ot chage istatly. Klimeck ECE66 Fall 1 otes adoted from lam 3

17 Tur-off Curret Trasiet IF S F j - P I Sice j ca t be larger tha the bad ga, which is smaller tha, the diode will be forced to suly the egative curret I Klimeck ECE66 Fall 1 otes adoted from lam 33 Tur-off Curret Trasiet IF S (,t) See how the sloe chage F P j - I = idiff roimately costat! t > = I t s I = l I ( ) / ( t ) / s ( ts ) d = I ts ( ) dt Klimeck ECE66 Fall 1 otes adoted from lam 34

18 Storage Time S F IF j - P I to 1 l(i) t I ( ) / I I = l = l I ( t ) / I F s s 1 to (,t) (t s ) Shorte it for fast resose! i Klimeck ECE66 Fall 1 otes adoted from lam 35 Tur-off oltage Trasiet S IF F j - P I a (t) ts t kt (, t) υ ( t) = l q o t / ( ) ( t) = l I ( I I ) e F llows easy calculatio of (,t). Klimeck ECE66 Fall 1 otes adoted from lam (,t) 36

19 ecovery Time erf tr tr e I = 1.1 t I r π F to 1 l(i) 1 to Useful formula erf ( ) = 1 e t r Klimeck ECE66 Fall 1 otes adoted from lam 37 ecovery Time l(i) ef. Sze/g,. 117 to 1 1 to t r t s W I D I F trr = tr t f I I F ( W L ) ( W L ) Klimeck ECE66 Fall 1 otes adoted from lam 38

20 Outlie 1) Large sigal resose ad charge cotrol model ) Tur-off characteristics 3) Tur-o characteristics 4) Other alicatios 5) Coclusio Klimeck ECE66 Fall 1 otes adoted from lam 39 Tur-o Characteristics: Boudary Coditio IF S 1 F j - P I = idiff ( t = ) t = I F ( t = ) = I F Klimeck ECE66 Fall 1 otes adoted from lam 4

21 Tur-o Characteristics S F IF j - P I (,t) time = idiff t > = I F t t ( ) ( ) 1 t = t e = IF 1 e Check: (t=)= (t )=I F Klimeck ECE66 Fall 1 otes adoted from lam 41 Outlie 1) large sigal resose ad charge cotrol model ) tur-off characteristics 3) tur-o characteristics 4) other alicatios 5) coclusio Klimeck ECE66 Fall 1 otes adoted from lam 4

22 Diffusio Time Electros get scattered to the other side, the average time is = idiff ( ) ( t = ) = i diff diff (,t) ( ) recombiatio (, t) = C D' o recombiatio diff () q W ( ) = = i () diff qd W W = D Klimeck ECE66 Fall 1 otes adoted from lam 1 W ~ ( D / W ) Oly half of them goes to the right W Diffusio velocity 43 Two lie derivatio of Steady State Diode Curret = idiff (,t) i diff = diff diff 1 qβ ( 1) i q e W D i = diff W W D q ( β 1) idiff = = q e Eact Eressio! Klimeck ECE66 Fall 1 otes adoted from lam 44

23 Large Sigal -diode Coclusio Large sigal resose of devices of great imortace for digital alicatios. alytical solutio of artial differetial equatio ofte difficult (if ot imossible), therefore aroimate methods like Charge-cotrol aroimatio ofte hel simlify the solutio ad still rovide a great deal of isight ito the dyamics of switchig oeratio. Be careful i usig the boudary coditio which is ofte dictated by eteral circuit coditios. Klimeck ECE66 Fall 1 otes adoted from lam 45