**Title: Bipolar Junction transistor** ** 1** Bipolar Junction transistor Amplification and switching through 3rd contact

** 2** How can we make a BJT from a pn diode?

Take pn diodeRemember reverse bias characteristicsReverse saturation current I0 ** 3** Test Multiple choice

Why is the reverse bias current of a pn diode small?Because the bias across the depletion region is small. Because the current consist of minority carriers injected across the depletion region. Because all the carriers recombine. ** 4** Test Multiple choice

Why is the reverse bias current of a pn diode small?Because the bias across the depletion region is small. Because the current consist of minority carriers injected across the depletion region. Because all the carriers recombine. ** 5** How can we make a BJT from a pn diode?

Take pn diodeRemember reverse bias characteristicsReverse saturation current I0 Caused by minority carriers swept across the junction ** 6** Test Multiple choice

If minority carrier concentration can be increased what will happen to I0?

Increase Decrease Remain the same ** 7**If minority carrier concentration can be increased near the depletion region edge, then I0 will increase.

** 8** Test True-False pn If we only increase then I0 will still increase.

** 9** How can we increase the minority carrier concentration near the depletion region edge?

Take pn diodeRemember forward bias characteristicsHow can we make a hole injector from a pn diode? By increasing the applied bias, V. By increasing the doping in the p region only By applying a reverse bias. ** 10** Hole injector

Take pn diodeRemember forward bias characteristics p

** 11** Thus A forward biased pn diode is a good hole injector A reverse biased np diode is a good minority carrier collector

Recombination of excess holes will occur and excess will be 0 at end of layer Recombination of excess holes will occur and excess will be large at end of layer No recombination of excess holes will occur. Recombination of excess electrons will occur and excess will be np0 at end of layer ** 12** Thus A forward biased pn diode is a good hole injector A reverse biased np diode is a good minority carrier collector Excess hole concentration reduces exponentially in W to some small value.

** 13** What is the magnitude of the hole diffusion current at the edge xW of the green region?

Magnitude of hole diffusion current at xW is same as at x0 Magnitude of hole diffusion current at xW is almost 0 Magnitude of hole diffusion current cannot be derived from this layer. ** 14** Thus A forward biased pn diode is a good hole injector A reverse biased np diode is a good minority carrier collector Since gradient of dpn _at_ xW is zero, hole diffusion current is also zero

** 15** BJT pnp E emitter VBC EB B base E C C collector C E Common base configuration

** 16** Base Short layer with recombination and no Ohmic contacts at edges. Single junction pno pno npo npo Double junction npo npo pno No Ohmic contact thus minority carrier concentration not

** 17** How will we calculate the minority carrier concentration in the base? Rate equation Steady state General solution of second order differential equation With Ohmic contact C10 C2?0 Without Ohmic contact C1?0 C2?0

** 18** Planar BJT - npn For integrated circuits (ICs) all contacts have to be on the top

** 19** Carrier flow in BJTs IB IB IB IB ICB0

** 20** Control by base current ideal case. Based upon space charge neutrality Base region IE Ip tt transit time tt lt tp Based on the given timescales, holes can pass through the narrow base before a supplied electron recombines with one hole ic/ib tp/tt The electron supply from the base contact controls the forward bias to ensure charge neutrality!

** 21** How good is the transistor?

Wish list C

IEpgtgtIEn or g IEp/(IEn IEp) 1 g emitter injection efficiency

IC IEp or B IC/IEp 1 B base transport factor or a IC/IE 1 a current transfer ratio (1-B) IEp

IB IEn thus b IC/IB a/(1-a) b current amplification factor ICB0 ignored

** 22** Review 1 BJT basics IC Forward active mode (ON) IE VBC V V VBC I I EB E C n p p C E

** 23** Review 1 BJT basics IC Forward active mode (ON) IE VBC V V VBC I I IBIB IB EB E C n p p C E

** 24** Review 2 Amplification? Recombination only case IB, ICB0 negligible ic/ib tp/tt Carriers supplied by the base current stay much longer in the base tp than the carriers supplied by the emitter and travelling through the base tt. b tp/tt But in more realistic case IB is not negligible b IC/IB With IB electrons supplied by base IB In IC holes collected by the collector Ip

** 25** 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. ** 26** Minority carrier distribution

Assume active mode VEBgt0 VBClt0Emitter injects majority carriers into base. dpn(0)pno (exp(VEB/VT)-1)Collector collects minority carriers from base. dpn(Wb)pno (exp(VBC/VT)-1) dp(x) 0

** 27** Currents simplified case

Assume IB0 IBC0 0Then IE total current crossing the base-emitter junctionThen IC IEp gradient of excess hole concentration in the baseIB without recombination is the loss of electrons via the BE junction IBThen IB gradient of excess electron concentration in the emitter ** 28** Narrow base no recombination Ip ? minority carrier density gradient in the base DpE pn0(e eVEB/kT 1) pn0 e eVEB/kT DpC pn0(e eVBC/kT 1) -pn0 Note no recombination

** 29** Collector current Ip Hole current Collector current No recombination, thus all injected holes across the BE junction are collected. Base current??

** 30** Look at emitter In ? minority carrier density gradient in the emitter Dnp np0(e eVEB/kT 1) np0 e eVEB/kT

** 31** Base current In 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 IB0 and no reverse bias electron injection into base ICB00.

** 32** Emitter current The emitter current is the total current flowing through the base emitter contact since IEICIB (current continuity)

** 33** Short layer approach summaryforward active mode dc(x) IE IpEB InEB DpE IC IpBC InBC DnE IC IpBC IpEB IE IB IC x DpC DnC IB IE - IC Wb -Xe Xc 0 IB InEB

** 34** General approach also taking recombination into account.forward active mode dc(x) DpE DnE x DpC -Xe Xc -LpE LpC DnC 0 Wb lt LnB

** 35** Which formulae do we use for the excess minority carrier concentration in each region?forward active mode dc(x) DpE DnE x DpC -Xe Xc -LpE LpC DnC 0 Wb lt LnB Emitter Collector use LONG diode approximation dnpE(x)DnE exp(-(-x)/LpE) dnpC(x)DnC exp(-x/LpC)

** 36** In the base we must take recombination into account ? short diode approximation cannot be used! dp(x) Excess hole concentration dp(x) DpE Exact solution of differential equation x dp(x) C1 ex/Lp C2 e-x/Lp DpC Wb Constants C1, C2 DpE dp(x0) DpC dp(xWb)

** 37** In the base with recombination ? long diode approximation can also not be used! dp(x) Exact solution of differential equation dp(x) C1 ex/Lp C2 e-x/Lp DpE Long diode approximation dp(x) C3 e-x/Lp x Boundary condition at BC junction cannot be guaranteed LnB DpC Wb

** 38** http//www.ecse.rpi.edu/schubert/Course-ECSE-2210 -Microelectronics-Technology-2010/

** 39** Extraction of currents in the general approach.forward active mode dc(x) IE IpEB InEB IC IpBC InBC DpE IC IpBC DnE IE IB IC x IB IE - IC DpC -Xe Xc -LpE LpC DnC 0 Wb lt LnB IB InEB IpEB IpBC - Term due to recombination

** 40** Currents Special case when only recombination in base current is taken into account Approximation IB0 dp(x) B DpE Starting point

Assume IEIEp IBC0 0Then IE Ip(x0) and IC Ip(xWb) x DpC 0 Wb

IBIE - IC IB

** 41** All currents are then determined by the minority carrier gradients in the base. Injection at emitter side DpE pn0(e eVEB/kT 1) Collection at collector side DpC pn0(e eVCB/kT 1) dp(x)

IE Ip(x0) DpE

IC Ip(xWb) B DpC x 0 Wb

** 42** Expression of the diffusion currents Diffusion current Ip (x) -e A Dp ddp(x)/dx Emitter current IE Ip (x0) Collector current IC Ip (xWb) Base current IB Ip (x0) - Ip (xWb) IE e A Dp/Lp (DpE ctnh(Wb/Lp) - DpC csch(Wb/Lp) ) IC e A Dp/Lp (DpE csch(Wb/Lp) - DpC ctnh(Wb/Lp) ) IB e A Dp/Lp ((DpE DpC) tanh(Wb/2Lp) ) Superposition of the effects of injection/collection at each junction! Note only influence of recombination

** 43** Non-ideal effects in BJTs

Base width modulation ** 44** Base width modulation

Early voltage VA iC Wb ideal IB -vCE

** 45** Conclusions

Characteristics of bipolar transistors are based on diffusion of minority carriers in the base. Diffusion is based on excess carrier concentrations dp(x) The base of the BJT is very small dp(x) C1 ex/Lp C2 e-x/Lp Base width modulation changes output impedance of BJT. ** 46** Transistor switching

** 47** p-type material n-type material On Off

** 48** iC iC icbiB -vCE RL iB ECC RS es Es t iE -Es

** 49** iC icbiB iC -vCE RL ECC RS es Es t iE -Es

** 50** iC ic?biB iC -vCE RL ECC RS Ic ECC /RL es Es t iE -Es

** 51** Switching cycle Switch to ON Switch OFF iC ECC /RL -vCE ECC

** 52** Charge in base (linear)

Cut-off VEBlt0 VBClt0 DpE-pn DpC-pnSaturation VEBgt0 VBC0 DpE pn (eeVEB/kT 1) DpC 0 (VBC0) VBCgt0

** 53** Currents - review.forward active mode dc(x) IE IpEB InEB IC IpBC InBC DpE IC IpBC DnE IE IB IC x IB IE - IC DpC -Xe Xc -LpE LpC DnC 0 Wb lt LnB IB InEB IpEB IpBC - Term due to recombination

** 54** Switching cycle - review iB Switch to ON Common emitter cicuit IB IBEs/RS With IBgtICmax/b Over-saturation -IB QB Qs DpE t1 Load line technique t1 ts t2 -pno t0 iC iC ECC /RL IC ICmaxECC/RL ltlt DpE pno -vCE ECC

** 55** Switching cycle - review iB Switch OFF Common emitter cicuit IB iC RL iB -IB -Es/RS dp ECC RS DpE QB t2 DpE es iE ts Es Qs t -Es DpC t3 -pno Load line technique t2 t3 t4 ts 0 t4 x tsd iC iC Wb ECC /RL IC ICECC/RL -vCE ECC

** 56** 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 Qp(t) cannot change immediately ? delay. The additional parameter is the restriction on the maximum collector current imposed by the load. ** 57** ON switching OFF0?ON t0

** 58** Driving off Time to turn the BJT OFF is determined by

The degree of over-saturation (BC junction) 2) The off-switching of the emitter-base diode CASE 2 OFF-IB 0N (saturation)?OFF CASE 1 OFFIB0 0N (saturation)?OFF Qb t

** 59** OFF switching 0N (saturation)?OFF - CASE 1 OFFIB0 RL C p RS vbc ECC e(t) B n veb p t E iC tsd dpnB(x) ICsat tlt0 E B C QB t0 IBtp tsd x WB 0 t t tlt0 tlttsd veb 0.7V (ON)?0V E - p B - n ttsd RS E0V

** 60** 0N (saturation)?OFF - CASE 2 OFF-IB RL C p RS vbc ECC e(t) B n veb p t E iC dpnB(x) ICsat tlt0 E B C QB IBtp x WB 0 t t tlt0 veb 0.7V (ON)?-E E - p B - n tlttsd RS -E ttsd

** 61** 0N (saturation)?OFF - CASE 1 OFFIB0 0N (saturation)?OFF - CASE 1 OFF-IB iC tlttsd iC tsd tlttsd ICsat ICsat ttsd ttsd t t

** 62** Transients Turn-on off to saturation

** 63** Time to saturation ON switching OFF0?ON ttsat tlttsat ttsat

** 64** Transients Turn-on off to saturation ts tp ln(1/( 1 IC/b IB)) ts small when tp small IC small compared to b IB

** 65** Transients Turn-off saturation to off Storage delay time tsd

** 66** Time from saturation 0N (saturation)?OFF - CASE 1 OFFIB0 tlttsd iC tsd ICsat ttsd t

** 67** Transients Turn-off saturation to off Storage delay time tsd tsd tp ln(b IB /IC) tsd small when tp small BUT tsd large when IC small compared to b IB

** 68** Transients Turn-off saturation to off Turn-on off to saturation Storage delay time tsd ts tp ln(1/( 1 IC/b IB)) tsd tp ln(b IB /IC) ts small when tp small IC small compared to b IB tsd small when tp small BUT tsd large when IC small compared to b IB

** 69** Solution to dilemmaThe Schottky diode clamp C C B B E E I V 0.3 0.7 Schottky diode pn diode

** 70** Large signal equivalent circuit

Switching of BJTs LARGE SIGNAL iC RL iB ECC RS es iE iC t

** 71** 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.

** 72** Superposition EB BC influence Take EB BC forward biased. Charge in base negative IE IEN IEI Where IEN, ICI are pn diode currents of EB and BC respectively. IC ICN ICI

** 73** Ebers-Moll equations IE IEN IEI IC ICN ICI IE IES (eeVEB/kT 1) aI ICS (eeVCB/kT 1) IC aN IES (eeVEB/kT 1) ICS (eeVCB/kT 1)

** 74** Ebers-Moll equations IE IEN IEI IC ICN ICI a current transfer factor

** 75** Ebers-Moll equations IE IES (eeVEB/kT 1) aI ICS (eeVCB/kT 1) IC aN IES (eeVEB/kT 1) ICS (eeVCB/kT 1) Where aN IES aI ICS Or IE aI IC (1- aN aI) IES (eeVEB/kT 1) IC aN IE - (1- aN aI) ICS (eeVCB/kT 1) General equivalent circuit based on diode circuit

** 76** Equivalent circuit IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO (eeVCB/kT 1) IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO (eeVCB/kT 1) IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO (eeVCB/kT 1) IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO (eeVCB/kT 1) IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO (eeVCB/kT 1) Valid for all biasing modes

** 77** Description of