5.1 Introduction 5.2 Equilibrium condition Contact potential Equilibrium Fermi level Space charge at a junction 5.

Transcription

1 5.1 troductio 5.2 Equilibrium coditio Cotact otetial Equilibrium Fermi level Sace charge at a juctio 5.3 Forward- ad Reverse-biased juctios; steady state coditios Qualitative descritio of curret flow at a juctio Carrier ijectio Reverse bias 5.4 Reverse-bias breakdow Zeer breakdow Avalache breakdow Rectifiers The breakdow diode 1

2 For almost all calculatios it is valid to assume that a alied voltage aears etirely across the trasitio regio ad ot i the eutral ad regios. 2

3 Forward- ad Reverse-biased Juctio Forward bias: The alied electric field is i the oosite directio of the built-i electric field Bias field Reverse bias: The alied electric field is i the same directio of the builti electric field Bias field For almost all calculatios it is valid to assume that a alied voltage aears etirely across the trasitio regio ad ot i the eutral ad regios. 3

4 4

5 Bad Diagrams of Biased Juctios 5

6 Forward bias Particle Flow Schematics electro hole ( V 0) Equilibrium ( V 0) Reverse bias ( V 0) 6

7 Bad Diagrams of Biased Juctios Forward bias (V 0) Equilibriu m (V 0) Reverse bias (V 0) V f V r W E C E C E C E C E C E V E V E V E V E C E V E V 7

8 Particle Flow Schematics 8

9 E C E C E C E C E V E V E C E V E C E V E V E V E C E C E V E V 9

10 Particle Flow ad Curret Directio 10

11 The drift curret is relatively isesitive to the height of the otetial barrier. The drift curret is limited ot by how fast carriers are swet dow the barrier, but rather how ofte. The drift curret is ot sesitive to electric field, as we ormally thik. 11

12 Costructio of the Bad Diagram uder Forward Bias Equilibrium ( V 0) Forward bias ( V 0) E C E C E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. Raise the levels of side util the Fermi level searatio reaches qv f. 3. Move the levels of side close to those of side util frot eds of the levels touch the origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o -V f ). 12

13 Costructio of the Bad Diagram uder Forward Bias Equilibrium ( V 0) Forward bias ( V 0) E C E C qv f E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. Raise the levels of side util the Fermi level searatio reaches qv f. 3. Move the levels of side close to those of side util frot eds of the levels touch the origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o -V f ). 13

14 Costructio of the Bad Diagram uder Forward Bias Equilibrium ( V 0) Forward bias ( V 0) E C E C qv f E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. Raise the levels of side util the Fermi level searatio reaches qv f. 3. Move the levels of side close to those of side util frot eds of the levels touch the origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o -V f ). 14

15 Costructio of the Bad Diagram uder Forward Bias Equilibrium ( V 0) Forward bias ( V 0) E C E C E C E C qv f E V E V E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. Raise the levels of side util the Fermi level searatio reaches qv f. 3. Move the levels of side close to those of side util frot eds of the levels touch the origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o -V f ). 15

16 Costructio of the Bad Diagram uder Reverse Bias Equilibrium ( V 0) Reverse bias ( V 0) E C E C E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. ower the levels of side util the Fermi level searatio reaches qv r. 3. Move the levels of side away from those of side util frot eds of the levels touch the extesio of origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o +V r ). 16

17 Costructio of the Bad Diagram uder Reverse Bias Equilibrium ( V 0) Reverse bias ( V 0) E C EV E C qvr E V 1. Redraw the ad bads but without the trasitio ortio. 2. ower the levels of side util the Fermi level searatio reaches qv r. 3. Move the levels of side away from those of side util frot eds of the levels touch the extesio of origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o +V r ). 17

18 Costructio of the Bad Diagram uder Reverse Bias Equilibrium ( V 0) Reverse bias ( V 0) E C EV E C qv r r E V 1. Redraw the ad bads but without the trasitio ortio. 2. ower the levels of side util the Fermi level searatio reaches qv r. 3. Move the levels of side away from those of side util frot eds of the levels touch the extesio of origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o +V r ). 18

19 Costructio of the Bad Diagram uder Reverse Bias Equilibrium ( V 0) Reverse bias ( V 0) E C E C E V E C E V E C qv r E V E V 1. Redraw the ad bads but without the trasitio ortio. 2. ower the levels of side util the Fermi level searatio reaches qv r. 3. Move the levels of side away from those of side util frot eds of the levels touch the extesio of origial sloe lies coectig both sides. 4. Coect the ad sides. The otetial barrier is labeled as q(v o +V r ). 19

20 Diode Equatio (ge.) ( e qv / kt 1) V o ( e qv / kt 1) qa( D D ) ( e qv / kt 1) Will be derived later. 20

21 x 0 0 x0 V (x) x V (x o ) = e qv/kt V x 21

22 Deletio model of - Juctio e e e e e e e h h h h h h h regio eutral regio eutral regio delet No free charges i deletio regio, oly immobile ios remai. 22

23 Fid (V V ) relatio with doig: From with V q kt q kt V ( x) q[ μ dv ( x) E( x) dx dv dx V V J dv kt q l ( x) Ε( x) D 1 d ( x) 1 d( x) ( x) dx ( V o ) ad D d( x) ] 0 dx kt q E( x) D V 1 d( x) ( x) dx x 0 0 x0 V (x) x V x Voltage offset is determied by itegratio of iverse of hole cocetratio across the deletio regio. Sice dv ( x) E( x) dx ad D kt q relatioshis still hold everywhere over the - juctio eve whe voltage bias is alied, the itegratio relatioshi should still hold regardless if the voltage offset is chaged by the alied bias. 23

24 tye Miority jectio tye Electro coc. Hole coc. ( x o ) e qv kt Electro coc. Hole coc. x 0 0 x0 x 24

25 Miority Carrier jectio tye tye Hole coc. Electro coc. ( x o ) e qv kt Electro coc. Hole coc. x 0 0 x0 x 25

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27 Quasi-Fermi evel ad Doig Desity E F E F E E i i kt l kt l o i o i htt://ecee.colorado.edu/~bart/book/extrisi.htm 27

28 o o ad Geeral Equatios for Carrier Cocetratio N N c v e e -( E E c -( E E F F v ) / ) / N c : Effective desity of state at bottom of C.B. N v : Effective desity of state at to of V.B. o : Cocetratio of electros i the coductio bad (extrisic or doed semicoductor) o : Cocetratio of holes i the valece bad (extrisic or doed semicoductor) i : Cocetratio of electros i the coductio bad (itrisic or udoed semicoductor) i : Cocetratio of holes i the valece bad (itrisic or udoed semicoductor) E c : Coductio bad edge E v : Valece bad edge E F : Fermi level E i : Fermi level for the udoed semicoductor (itrisic) kt kt i i N N c v e e -( E E c -( E E (geeral) (itrisic) o o i i o o i e i e ( E E F ( E E i i F ) / kt ) / kt where i v i ) / ) / i i kt kt Same equatios used for defiig quasi-fermi levels. 28

29 Forward-biased juctio: (a) miority carrier distributios o the two sides of the trasitio regio ad defiitios of distaces X ad X measured from the trasitio regio edges; (b) 29 variatio of the quasi-fermi levels with ositio.

30 Miority Carrier jectio ito the Neutral Regios 30

31 Quiz Whe - juctio is forward biased by voltage V, the miority carrier cocetratios will be icreased above the equivalet value at the eutral regios. Please write dow the exressios for the followig arameters. Give that x is a coordiate of x-axis with directio away from the - juctio ad with the origi located at the iterface of delete/eutral regios. (1) (x =0) (2) (3) (x )itermsof (4) (x )itermsof (5) ( ) Please also draw the diagram of (X ) ad idicate,,,ad( ). 31

32 Calculatio of Juctio Curret 32

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34 Juctio Curret by Electros ad holes 34

35 Total Juctio Curret 35

36 Calculatio of Juctio Curret (method ) 36

37 37 Total Juctio Curret ) ( 0) ( 0) ( qa x x qa x 0) ( qa x 0) ( 1) )( ( kt qv e qa radom walk D D D D 1) )( ( kt qv e D D qa

38 Diode Equatio qv kt o ( e 1) ( x 0) ( x 0) qa ( ) qa qv kt ( )( e 1) qv kt o ( e 1) where o qa D D ( ) 38

39 Diode Equatio V 1) ( (ge.) / kt qv e 1) ( / kt qv o e 1) ( ) ( / kt qv e D D qa 39

40 Examle 5-3 Fid a exressio for the electro curret i the -tye material of a forward-biased - juctio. 40

41 (x o ) = e qv/kt 41

42 Diode Equatio at Reverse Bias o kt qv o kt qv o e e r 1) ( 1) ( / / V 42 ) ( o D D qa where

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44 Miority Carrier Extractio from the Neutral Regios 44

45 Forward bias Particle Flow Schematics electro hole ( V 0) Equilibrium ( V 0) Reverse bias ( V 0) 45

46 Tyical -V curve of a Diode htt:// D forward reverse bias forward bias 0.7 V V D reverse 46

47 Examle 5-4 A abrut Si - juctio (A = 10-4 cm 2 ) has the followig roerties at 300 K: side N a =10 17 cm -3 = 0.1 s = 200 cm 2 /(Vs) = 700 cm 2 /(Vs) side N d =10 15 cm -3 =10s =450cm 2 /(Vs) = 1300 cm 2 /(Vs) The juctio is forward biased by 0.5 V. What is the forward curret? What is the curret at a reverse bias of -0.5 V? 47