Digital Integrated CircuitDesign

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1 Digital Integrated CircuitDesign Lecture 5a Bipolar Transistor Dep. Region Neutral Base n(0) b B C n b0 P C0 P e0 P C xn 0 xp 0 x n(w) b W B Adib Abrishamifar EE Department IUST

2 Contents Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 2/26

3 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 3/26

4 Minority Carrier Concentration Two Basic Assumptions Low level injection in base region All terminal voltages appear across the junction depletion region The concentration of minority at interface n ( o) = n exp( V V ) b bo BE T n ( W) = n exp( V V ) = n exp( V V ) b bo BC T bo CB T V >> V n ( W) o CB T b W << L negligible recombination b 4/26

5 Minority Carrier Concentration The width of the neutral emitter and collector regions is much greater than the diffusion length The minority carrier concentration shows an exponential slope Dep. Region Neutral Base n(0) b B C n b0 P C0 P e0 P C xn 0 xp 0 x n(w) b W B 5/26

6 Minority Carrier Concentration Some important device equations (excess carrier Concentration) n ( x) = n ( x) n b b b Excess minority carrier concentration at the collector junction [ n b ( W )] is less than 0, but the analysis is simplified by assuming b IE = IC = qadb dx n ( W ) o dn b x = o dn b n b( o) n b( W ) = dx W qadn b b( o) qadn b bo IC = = V BE VT 1 W W 6/26 [ exp( ) ]

7 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 7/26

8 Dynamic Properties of BJT (Charge Control) QF= excess minority carrier charge 2 qawn b( o) qaw WIC W Q = Q = =. I 2 2 qad 2D F F C b b Q= It Q = τ I τ = F W 2D 2 F F C b 8/26

9 Dynamic Properties of BJT (Charge Control) For high speed digital circuit we require to be as short as possible Then W must be reduced Example ( ) W = 0.5 µ md, b = 7 cm /sec τf = = 0.18nsec 2 7 τ F 9/26

10 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 10/26

11 The Base Current I BB = the minority carrier diffuse across the base from the emitter to the collector, some do not reach the collector and recombine with the majority carriers β F I = I C B I = I + I + I B BB BE BC I E E B I BB C I C W nb ( x) IBB = qa dx τ o b ( ) normally V < o I >> I + I BC BC BE BB IBE IBC N P N 0 WB I B V BE V CB 11/26

12 Terminal Currents All of current is reversed for pnp transistor B C n p n E B C n n E p D C D E B V BC + C V + BE E I C I E B I DC I DE C V BC + + V BE E I C I E αfide α R I DC 12/26

13 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 13/26

14 Terminal Currents VBE VT I = I ( e 1) DE VBC VT I = I ( e 1) DC I, I Saturation current for emitter and collector ES CS ES CS I = I α I E DE R DC I = α I I C F DE DC B I DC I DE C V BC + + V BE E I C I E αfide α R I DC 14/26

15 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 15/26

16 The Ebers-Moll Equations VBE VT VBC VT I = I ( e 1) α I ( e 1) E ES R CS VBE VT VBC VT I = α I ( e 1) I ( e 1) C F ES CS Then we have four parameters: I ES, I CS, α, and two F αr variables: Emitter and Collector junction voltages VBE VT I = I ( e 1) DE VBC VT I = I ( e 1) DC ES CS B I DC I DE C V BC + + V BE E I C I E αfide α R I DC 16/26

17 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 17/26

18 Reciprocity Theorem For ideal transistor the four parameters are related by reciprocity theorem α I = α I F ES R CS Typical value ( nonideal transistor) α 0.99, α 0.66, I 10 AI, 10 A F R ES CS 18/26

19 Bipolar Transistor Minority Carrier Concentration Dynamic Properties of BJT (Charge Control) The Base Current Terminal Currents The Ebers-Moll Equations Reciprocity Theorem Modes of Operation Forward Active Mode Reverse Active Mode Cut off Mode Saturation Mode Summary 19/26

20 Modes of Operation Emitter Junction Collector Junction Mode of Operation Forward Reverse Forward active Reverse Forward Reverse active Reverse Reverse Cut off Forward Forward Saturation 20/26

21 Forward Active Mode V 4V, V 4V BE T BC T I = I exp( V V ) + α I E ES BE T R CS I = α I exp( V V ) + I C F ES BE T CS By substitution for IES exp( V BE VT ) I = α ( I α I ) + I = α I + I ( 1 αα ) = α I + I C F E R CS CS F E CS F R F E CO αf I = I + I, = β 1 α E B C F F 21/26

22 Reverse Active Mode Similar as previous V 4V, V V BE T BC T I = I exp( V V ) + α I C CS BC T IR ES I = α I exp( V V ) + I E IF CS BC T ES I = α ( I α I ) + I = α I + ( 1 α α ) I E IF C IR ES ES IF C IF IR ES 22/26

23 Cut off Mode ( V, V ) 4V BE BC T I = I + α I E ES R CS I = α I + I C F ES CS By reciprocity theorem I I = I ( 1 α ) E ES F = I ( 1 α ) C CS R 23/26

24 Saturation Mode ( V, V ) 4V BE BC T I = I exp( V V ) α I exp( V V ) (I) E ES BE T R CS BC T I = α I exp( V V ) I exp( V V ) (II) C F ES BE T CS BC T V = V V CE ( sat) BE ( sat) BC ( sat ) α R Multiply (II) by and subtract from (I) I α I = I ( 1 αα )exp( V V ) E R C ES F R BE T I = I + I I + I ( 1 α ) = I ( 1 αα )exp( V V ) E B C B C R ES F R BE T I + I ( 1 α ) V = V Ln, I = I ( 1 αα ) B C R BE ( sat) T EO ES F R I EO 24/26

25 Saturation Mode By similar method α I I ( 1 α ) V = V Ln, I = I ( 1 αα ) F B C F BC ( sat) T CO CS F R I CO I + I ( 1 α ) I VCE ( sat) = VTLn α I I ( 1 α ) I ICO ICS αf = = I I α EO ES R B C R CO F B C F EO 1 IC 1 + ( ) α I β α α V = V Ln, β =, β = ( ) I B β F R B R R F CE ( sat) T R F IC αr 1 αf 25/26

26 Summary In this lecture the operation of the bipolar transistor was first described in physical terms The fundamental Ebers-Moll equation was described The four modes of BJT ( Cut off, Forward active, Reverse active, Sat.) were described 26/26

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