Bipolar Junction transistor Holes and electrons determine device characteristics Three terminal device Control of two terminal currents Amplification and switching through 3 rd contact

How can we make a BJT from a pn diode? Take pn diode pn Remember reverse bias characteristics V I I V I0I0 Reverse saturation current: I 0

Test: Multiple choice Why is the reverse bias current of a pn diode small? 1.Because the bias across the depletion region is small. 2.Because the current consist of minority carriers injected across the depletion region. 3.Because all the carriers recombine.

Test: Multiple choice Why is the reverse bias current of a pn diode small? 1.Because the bias across the depletion region is small. 2.Because the current consist of minority carriers injected across the depletion region. 3.Because all the carriers recombine.

How can we make a BJT from a pn diode? Take pn diode pn Remember reverse bias characteristics V I I V I0I0 Reverse saturation current: I 0 Caused by minority carriers swept across the junction e-e- h+h+ n p and p n low I 0 small

If minority carrier concentration pn V I I V I0I0 e-e- h+h+ n p and/or p n can be increased what will happen to I 0 ? Test: Multiple choice 1.Increase 2.Decrease 3.Remain the same

If minority carrier concentration pn V I I V I0I0 e-e- h+h+ If n p and p n higher |I 0 | larger n p and p n can be increased near the depletion region edge, then I 0 will increase.

If we only increase pn V I I V I0I0 e-e- h+h+ pnpn then |I 0 | will still increase. Test: True-False

How can we increase the minority carrier concentration near the depletion region edge? Take pn diode pn Remember forward bias characteristics V I h+h+ e-e- How can we make a hole injector from a pn diode? 1.By increasing the applied bias, V. 2.By increasing the doping in the p region only 3.By applying a reverse bias.

Take pn diode pn Remember forward bias characteristics V I I V h+h+ e-e- When using a p + n junction diode current I f ≈ hole current IfIf Hole injector I p p no (e eV/kT -1) I n n po (e eV/kT -1) Since N A >> N D n p << p n →I p >> I n p +

p+p+ n V I h+h+ e-e- pn V I0I0 e-e- h+h+ Thus: A forward biased p + n diode is a good hole injector A reverse biased np diode is a good minority carrier collector W If W large, then? 1.Recombination of excess holes will occur and excess will be 0 at end of layer 2.Recombination of excess holes will occur and excess will be large at end of layer 3.No recombination of excess holes will occur. 4.Recombination of excess electrons will occur and excess will be n p0 at end of layer

p+p+ n V I h+h+ e-e- pn V I0I0 e-e- h+h+ Thus: A forward biased p + n diode is a good hole injector A reverse biased np diode is a good minority carrier collector W If W large → holes recombine pnpn x LpLp Excess hole concentration reduces exponentially in W to some small value.

p+p+ n V I h+h+ e-e- pn V I0I0 e-e- h+h+ What is the magnitude of the hole diffusion current at the edge x=W of the “green” region? W pnpn x LpLp 1.Magnitude of hole diffusion current at x=W is same as at x=0 2.Magnitude of hole diffusion current at x=W is almost 0 3.Magnitude of hole diffusion current cannot be derived from this layer.

p+p+ n V I h+h+ e-e- pn V I0I0 e-e- h+h+ Thus: A forward biased p + n diode is a good hole injector A reverse biased np diode is a good minority carrier collector W if W large → holes recombine pnpn x LpLp Since gradient of  p x=W is zero, hole diffusion current is also zero Reduce W

V I V I p+p+ np BJT p + np W < L p E C B E: emitter B: base C: collector E C EB V BC ICIC IEIE

Base: Short layer with recombination and no Ohmic contacts at edges. Single junction Double junction n po p no n po p no n po No Ohmic contact thus minority carrier concentration not p no

How will we calculate the minority carrier concentration in the base? Rate equation Steady state General solution of second order differential equation With Ohmic contactC 1 =0 C 2 ≠0 Without Ohmic contact C 1 ≠0 C 2 ≠0

p + Si p Si n Si n + Si E B C p Si p + Si Ohmic contact Planar BJT - npn For integrated circuits (ICs) all contacts have to be on the top p-substrate n-well for collector p-well for base n + -well for emitter device insulation n + Si ohmic contact

EBC p+p+ np IEIE ICIC Carrier flow in BJTs holes IBIB IEIE ICIC I CB0 IBIB I’ B I” B I B = I’ B + I” B – I CB0 e - loss, forward bias e - gain, reverse bias Recombination e - loss

Control by base current : ideal case. Based upon space charge neutrality Base region I E = I p h+h+ Electrostatically neutral e-e-  t transit time W b << L p  t <  p pp recombine with Based on the given timescales, holes can pass through the narrow base before a supplied electron recombines with one hole: i c /i b =  p /  t The electron supply from the base contact controls the forward bias to ensure charge neutrality!

How good is the transistor? Wish list: h+h+ e-e- equilibrium EB V BE >0 I Ep >>I En or  = I Ep /(I En + I Ep ) ≈ 1  : emitter injection efficiency CI Ep Injection of carriers x W b < L p ICIC I C ≈ I Ep or B= I C /I Ep ≈ 1 B: base transport factor or  = I C /I E ≈ 1  : current transfer ratio No amplification! I B ≈ I En I CB0 ignored I En + (1-B) I Ep thus  = I C /I B =  /(1-  )  : current amplification factor Amplification!

Review 1 – BJT basics V I V I np W < L p E C B E C EB V BC Forward biased p + n junction is a hole injector Reverse biased np junction is a hole collector p+p+ Forward active mode (ON) ICIC V BC IEIE E

Review 1 – BJT basics V I V I np W < L p E C B E C EB V BC Forward biased p + n junction is a hole injector Reverse biased np junction is a hole collector p+p+ Forward active mode (ON) ICIC V BC IEIE E I B =I’ B +I” B

Review 2 Amplification? I B = I’ B + I” B – I CB0 Recombination only case: I’ B, I CB0 negligible i c /i b =  p /  t Carriers supplied by the base current stay much longer in the base:  p than the carriers supplied by the emitter and travelling through the base:  t.  =  p /  t But in more realistic case: I’ B is not negligible  = I C /I B WithI B electrons supplied by base = I’ B = I n I C holes collected by the collector = I p

Currents? In order to calculate currents in pn junctions, knowledge of the variation of the minority carrier concentration is required in each layer. The current flowing through the base will be determined by the excess carrier distribution in the base region. Simple to calculate when the short diode approximation is used: this means linear variations of the minority carrier distributions in all regions of the transistor. (recombination neglected) Complex when recombination in the base is also taken into account: then exponential based minority carrier concentration in base.

Minority carrier distribution Assume active mode: V EB >0 & V BC <0 Emitter injects majority carriers into base.  p n (0)=p no (exp(V EB /V T )-1) Collector collects minority carriers from base.  p n (W b )=p no (exp(V BC /V T )-1) EBC pCpC pEpE B p(x) x p n0 0WbWb Without recombination With recombination  p(x) p n0 0

Currents: simplified case Assume I” B =0 & I BC0 = 0 Then I C = I Ep gradient of excess hole concentration in the base I B without recombination is the loss of electrons via the BE junction: I’ B See expressions for diode current for short diode B  p(x) x pCpC pEpE 0WbWb Then I B = gradient of excess electron concentration in the emitter Then I E = total current crossing the base-emitter junction

Narrow base: no recombination: I p → minority carrier density gradient in the base  p E = p n0 (e eV EB /kT – 1) ≈ p n0 e eV EB /kT  p C = p n0 (e –e|V BC |/kT – 1) ≈ -p n0 pEpE pCpC  p(x) x 0 WbWb Linear variation of excess carrier concentration: Note: no recombination

Collector current: I p Diffusion current: Hole current: Base current?? Collector currentNo recombination, thus all injected holes across the BE junction are collected.

Look at emitter: I n → minority carrier density gradient in the emitter  n p = n p0 (e eV EB /kT – 1) ≈ n p0 e eV EB /kT npnp 0  n(x) x 0 xexe Linear variation of excess carrier concentration:

Diffusion current: Base current: The base contact has to re-supply only the electrons that are escaping from the base via the base-emitter junction since no recombination I” B =0 and no reverse bias electron injection into base I CB0 =0. Base current: In

Current gain: Emitter current The emitter current is the total current flowing through the base emitter contact since I E =I C +I B (current continuity) Emitter current:

Short layer approach – summary forward active mode pCpC  c(x) x 0 WbWb pEpE nEnE nCnC -X e XcXc IEIE =I pEB +I nEB ICIC =I pBC +I nBC ICIC ≈I pBC =I pEB IEIE =IBIB +ICIC IBIB =IEIE -ICIC IBIB =I nEB

General approach also taking recombination into account. forward active mode pCpC  c(x) x 0WbWb pEpE nEnE nCnC -X e XcXc -L pE L pC < L nB

Which formulae do we use for the excess minority carrier concentration in each region? forward active mode pCpC  c(x) x 0WbWb pEpE nEnE nCnC -X e XcXc -L pE L pC < L nB use LONG diode approximation  n pE (x)=  nE exp(-(-x)/L pE )  n pC (x)=  nC exp(-x/L pC ) Emitter Collector

In the base we must take recombination into account → short diode approximation cannot be used!  p E pCpC Excess hole concentration  p(x):  p(x) = C 1 e x/L p + C 2 e -x/L p Constants C 1, C 2 :  p E =  p(x=0)  p C =  p(x=W b )  p(x) x From: Exact solution of differential equation: WbWb

In the base with recombination → long diode approximation can also not be used!  p E pCpC  p(x) = C 1 e x/L p + C 2 e -x/L p  p(x) x Exact solution of differential equation: WbWb  p(x) = C 3 e -x/L p Long diode approximation: L nB Boundary condition at BC junction cannot be guaranteed

Extraction of currents in the general approach. forward active mode pCpC  c(x) x 0WbWb pEpE nEnE nCnC -X e XcXc -L pE L pC < L nB IEIE =I pEB +I nEB ICIC =I pBC +I nBC ICIC ≈I pBC IEIE =IBIB +ICIC IBIB =IEIE -ICIC IBIB =I nEB I pEB I pBC -+ Term due to recombination

Currents: Special case when only recombination in base current is taken into account: Approximation: I B ’=0 Assume I E =I Ep & I BC0 = 0 B  p(x) x pCpC pEpE 0 WbWb Then I E = I p (x=0) and I C = I p (x=W b ) I B =I E - I C Starting point: =I” B

All currents are then determined by the minority carrier gradients in the base. Injection at emitter side:  p E = p n0 (e eV EB /kT – 1) Collection at collector side:  p C = p n0 (e eV CB /kT – 1) B  p(x) x pEpE 0 WbWb I E = I p (x=0) I C = I p (x=W b ) pCpC

Expression of the diffusion currents Diffusion current: I p (x) = -e A D p d  p(x)/dx Emitter current: I E ≈ I p (x=0) Collector current: I C ≈ I p (x=W b ) I E ≈ e A D p /L p (  p E ctnh(W b /L p ) -  p C csch(W b /L p ) ) I C ≈ e A D p /L p (  p E csch(W b /L p ) -  p C ctnh(W b /L p ) ) I B ≈ e A D p /L p ((  p E +  p C ) tanh(W b /2L p ) ) Superposition of the effects of injection/collection at each junction! Base current: I B ≈ I p (x=0) - I p (x=W b ) Note: only influence of recombination Hyperbolic functions

Non-ideal effects in BJTs Base width modulation E V I V I p+p+ np C B E C BE V BC Metallurgic junction Original base width Depletion width changes with V BC Effective base width

Base width modulation iCiC -v CE Early voltage: V A ideal base width modulated VAVA IBIB WbWb

Conclusions Characteristics of bipolar transistors are based on diffusion of minority carriers in the base. Diffusion is based on excess carrier concentrations: –  p(x) The base of the BJT is very small: –  p(x) = C 1 e x/L p + C 2 e -x/L p Base width modulation changes output impedance of BJT.

Transistor switching IcIc t

eses iBiB iCiC iEiE RLRL E CC RSRS eses t iCiC -v CE E CC /R L E CC Off On p-type material n-type material ibib i b higher

iCiC iEiE RLRL E CC RSRS eses t EsEs -E s iBiB iCiC -v CE ic=iBic=iB

iCiC iEiE RLRL E CC RSRS eses t EsEs -E s iCiC -v CE ic=iBic=iB

iCiC iEiE RLRL E CC RSRS eses t EsEs -E s iCiC -v CE ic≠iBic≠iB I c =  CC /R L

Switching cycle eses iBiB iCiC iEiE RLRL E CC RSRS iBiB QBQB iCiC pp x WbWb -p n t0t0 pEpE 0 tsts pEpE pCpC t2t2 -I B QsQs t sd ICIC I C ≈E CC /R L t EsEs -E s t1t1 tsts t2t2 t’ s pEpE t1t1 IBIB I B ≈E s /R S Switch to ON Switch OFF iCiC -v CE E CC /R L E CC

Charge in base (linear) Cut-off –V EB <0 & V BC <0 –  p E =-p n &  p C =-p n Saturation –V EB >0 & V BC ≥0 –  p E = p n (e eV EB /kT – 1) –  p C = 0 (V BC =0) pp x WbWb -p n pp x WbWb pEpE pEpE pCpC V BC >0

Currents - review. forward active mode pCpC  c(x) x 0WbWb pEpE nEnE nCnC -X e XcXc -L pE L pC < L nB IEIE =I pEB +I nEB ICIC =I pBC +I nBC ICIC ≈I pBC IEIE =IBIB +ICIC IBIB =IEIE -ICIC IBIB =I nEB I pEB I pBC -+ Term due to recombination

Switching cycle - review eses iBiB iCiC iEiE RLRL E CC RSRS iBiB QBQB iCiC pp x WbWb -p no t0t0 pEpE 0 tsts pEpE pCpC t2t2 -I B QsQs ICIC I C max ≈E CC /R L t EsEs -E s t1t1 tsts t2t2 pEpE t1t1 IBIB I B ≈E s /R S Switch to ON iCiC -v CE E CC /R L E CC Common emitter cicuit Load line technique With I B >I C max /  Over-saturation p no  p E

Switching cycle - review eses iBiB iCiC iEiE RLRL E CC RSRS iBiB QBQB iCiC pp x WbWb -p no t4t4 pEpE 0 t’ s pEpE pCpC t2t2 -I B QsQs t sd ICIC I C ≈E CC /R L t EsEs -E s t2t2 t’ s t3t3 IBIB ≈-E s /R S Switch OFF iCiC -v CE E CC /R L E CC Common emitter cicuit Load line technique t3t3 t4t4

Calculating the delays Since the currents and minority carrier charge storage are determined by the pn diodes, the delays are calculated as in the pn diode. –Knowledge of current immediately before and after switch –Stored minority carrier charge Q p (t) cannot change immediately → delay. The additional parameter is the restriction on the maximum collector current imposed by the load.

 p nB (x) xWBWB 0 EBC IBIB p p n RLRL RSRS E CC t e(t) E B C v eb v bc OFF=0→ON t≥0 QBQB t E - pB - n +E>>0.7V RSRS v eb = 0→ON ≈0.7V IBIB IBIB IBIB IBIB Q sat t sat IBpIBp iCiC t t<0 t<t sat t≥t sat t sat I Csat ON switching

Driving off Time to turn the BJT OFF is determined by: 1)The degree of over-saturation (BC junction) 2) The off-switching of the emitter-base diode t ibib IBIB iCiC t ICIC QbQb t Q s = I C  t IB pIB p t sd iCiC ICIC ibib IBIB t -I B QbQb CASE 1: OFF=I B =0 0N (saturation)→OFF CASE 2: OFF=-I B 0N (saturation)→OFF t t QsQs IB pIB p -I B  p

 p nB (x) xWBWB 0 EBC IBIB p p n RLRL RSRS E CC t e(t) E B C v eb v bc 0N (saturation)→OFF - CASE 1: OFF=I B =0 QBQB t E - pB - n E=0V RSRS v eb = 0.7V (ON)→0V Q sat t sd IBpIBp iCiC t t<0 t≥t sd t<t sd t sd I Csat t sd t<0 I B =0 t sd t≥0t≥0 OFF switching

 p nB (x) xWBWB 0 EBC IBIB p p n RLRL RSRS E CC t e(t) E B C v eb v bc 0N (saturation)→OFF - CASE 2: OFF=-I B QBQB t E - pB - n -E RSRS v eb = 0.7V (ON)→-E Q sat t sd IBpIBp iCiC t t<0 t≥t sd t<t sd t sd I Csat t sd t<0 t sd t≥0t≥0 -I B

iCiC t t≥t sd t<t sd t sd I Csat t sd iCiC t I Csat t sd 0N (saturation)→OFF - CASE 1: OFF=I B =00N (saturation)→OFF - CASE 1: OFF=-I B t≥t sd t<t sd STORAGE DELAY TIME: t sd shorter delay

Transients Turn-on: off to saturation iCiC ICIC I C ≈E CC /R L t tsts

p p n RLRL RSRS E CC t e(t) E B C v eb v bc OFF=0→ON QBQB t Q sat t sat IBpIBp iCiC t t<t sat t≥t sat t sat I Csat ON switching Time to saturation t=t sat

Transients Turn-on: off to saturation iCiC ICIC I C ≈E CC /R L t tsts t s =  p ln(1/( 1 – I C /  I B )) t s small when:  p small I C small compared to  I B oversaturation

Transients Turn-off: saturation to off Storage delay time: t sd iCiC ICIC I C ≈ E CC /R L t off t’ s

iCiC t t≥t sd t<t sd t sd I Csat t sd 0N (saturation)→OFF - CASE 1: OFF=I B =0 Time from saturation

Transients Turn-off: saturation to off Storage delay time: t sd iCiC ICIC I C ≈ E CC /R L t off t’ s t sd =  p ln(  I B /I C ) t sd small when:  p small BUT t sd large when: I C small compared to  I B NO oversaturation Determined by EB diode

Transients Turn-on: off to saturation iCiC ICIC I C ≈E CC /R L t tsts t s =  p ln(1/( 1 – I C /  I B )) t s small when:  p small I C small compared to  I B oversaturation Turn-off: saturation to off Storage delay time: t sd iCiC ICIC I C ≈ E CC /R L t off t’ s t sd =  p ln(  I B /I C ) t sd small when:  p small BUT t sd large when: I C small compared to  I B NO oversaturation Determined by EB diode

Solution to dilemma The Schottky diode clamp B C E B C E I V B C B metal pn diode Schottky diode

Large signal equivalent circuit Switching of BJTs –LARGE SIGNAL eses iBiB iCiC iEiE RLRL E CC RSRS iCiC t

Ebers-Moll large signal circuit model for large signal analysis in SPICE Not examinable Is valid for all bias conditions. The excess at the BC is taken into account what is essential for saturation operation and off- currents.

Superposition EB & BC influence Take EB & BC forward biased. Charge in base: xWbWb pp pEpE pCpC xWbWb pp pEpE xWbWb pp pCpC =+ I EN I CN I EI I CI negative I E = I EN + I EI I C = I CN + I CI Where I E N, I C I are pn diode currents of EB and BC respectively.

Ebers-Moll equations I E = I ES (e eV EB /kT –1) –  I I CS (e eV CB /kT –1) I C =  N I ES (e eV EB /kT –1) – I CS (e eV CB /kT –1) I E = I EN + I EI I C = I CN + I CI Diode currents

Ebers-Moll equations I E = I EN + I EI I C = I CN + I CI Collected currents I EI =  I I CI I CN =  N I EN I E = I ES (e eV EB /kT –1) –  I I CS (e eV CB /kT –1) I C =  N I ES (e eV EB /kT –1) – I CS (e eV CB /kT –1)  : current transfer factor

Ebers-Moll equations I E = I ES (e eV EB /kT –1) –  I I CS (e eV CB /kT –1) I C =  N I ES (e eV EB /kT –1) – I CS (e eV CB /kT –1) Where:  N I ES =  I I CS I E =  I I C + (1-  N  I ) I ES (e eV EB /kT –1) I C =  N I E - (1-  N  I ) I CS (e eV CB /kT –1) Or: I EO I CO I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) General equivalent circuit based on diode circuit

Equivalent circuit I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) E B C IEIE ICIC IBIB I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) I E =  I I C + I EO (e eV EB /kT –1) I C =  N I E - I CO (e eV CB /kT –1) Valid for all biasing modes

Description of different transistor regimes Cut-off –V BE <0 & V CB <0 Active –V BE >0 & V CB <0 E B C IEIE ICIC IBIB I E = -(1-  N ) I ES I C = (1-  I ) I CS Small! E B C IEIE ICIC IBIB I C = I C0 +  N I E ICIC -V CB IEIE I C0, I E =0

BJT small signal equivalent circuit

Now Amplification and maximum operation frequency –SMALL SIGNAL equivalent circuit B C E RR C j,BE C d,BE C j,BC RoRo g m v be npn v be

Definition of circuit elements Transconductance B C E RR C j,BE C d,BE C j,BC RoRo g m v be

Base input resistance B C E RR C j,BE C d,BE C j,BC RoRo g m v be

Base-emitter input capacitances B C E RR C j,BE C d,BE C j,BC RoRo g m v be C j,BE C d,BE Depletion capacitance Diffusion capacitance See SG on pn-diode

Base-collector capacitance B C E RR C j,BE C d,BE C j,BC RoRo g m v be C j,BC Depletion capacitance Miller capacitance: feedback between B & C

Output resistance B C E RR C j,BE C d,BE C j,BC RoRo g m v be iCiC -v CE ideal VAVA IBIB

Current gain - frequency Small signal current gain B C E RR C j,BE C d,BE C j,BC RoRo g m v be ibib v be Max gain Circuit analysis

Transit frequency f T Small signal current gain=1  total transit time Base-Emitter charging time Base transit time

Transit frequency f T Base transit time for p + n Note: this approach ignores delay caused by BC junction (see 3 rd year)

Simplified small signal equivalent circuit Common-emitter connection Active mode: BE: forward, BC: reverse.

Small signal equivalent circuit when other biasing connection is made Common-base connection Active mode: BE: forward, BC: reverse. E B C C dif C jE rere C jC rcrc  i’ e ieie i’ e icic

Conclusion Delays in BJTs are a result of the storage of minority carriers. Main delay in common BJTs is due to the base transit time  t.