Sc Problems 10

7/22/2019 Sc Problems 10

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Section 1 11. For a uniformly doped n+p+n bipolar transistor in thermal equilib

rium, a sketch the energy-band diagram, b sketch the electricfield through the device, and e repeat parts a and b for thetransistor biased in the forward-active region.

2. Consider a p np bipolar transistor, uniformly doped in each region. Sketch the energy-band diagram for the case when the transistor is a in thermal equilibrium, b biased in the forward-activemode, e biased in the inverse-active region, and d biased in cutoff with both the B-E and B-C junctions reverse biased.

Note: In the following problems, use the transistor geometry shown inFigure 10-7.

PRO L MS

Early effect: Another term for base width modulation.Early voltage: The value of voltage magnitude at the intercept on thevoltage axis obtained by extrapolating the l versus CE curves to zerocurrent.Emitter-base junction capacitance charging time: The time constant describing the time for the B-E space charge width to change with a changein emitter current.Emitter injection efficiency factor: The factor in the common base currentgain that takes into account the injection of carriers from the base into theemitter.Forward active: The bias condition in which the B-E junction is forwardbiased and the B-C junction is reverse biased.Inverse active: The bias condition in which the B-E junction is reversebiased and the B-C junction is forward biased.Output conductance: The ratio of a differential change in collector currentto the corresponding differential change in C-E voltage.Punch-through: The bias condition such that the B-C space charge regionextends completely through the neutral base region to the B-E depletionr ginRcembnation factor: The factor in the common base current gain thataccounts for recombination in the forward-biased B-E junction.Saturation: The bias condition in which both B-E and B-Cjunctions areforward biased and the collector current is no longer controlled by theB-E voltage ..Storage time: The time duration from the point when the input base signalswitches from forward to reverse bias, to the point when the collectorcurrent is reduced to 90 percent of its saturation value. .

Cnapter 10 The Bipolar Transistor


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eDBnBO {. e BE _ e Bc }n XB exp kT exp kTfor XB /LB 1where XB is the neutral base width. h Show that theminority carrier diffusion current in the base is then given by

at x -:- xB /2 for a xB/LB = 0.1 and h xB/LB = 1.0. AssumeVBE kT/e.

7. Consider a pnp bipolar transistor. Assume that the excess minoritycarrier hole concentrations at the edges of the B-E and B-C spacecharge regions are 8PB 0 = 8 x 10 cm and 8PB XB = -2.25 x104cm , respectively. Plot, on the same graph, 8PB X for a theideal case when no recombination occurs in the base, and h thecase when XB = LB 10p,m. What can be said about the slopes ofthe two curves at x Oand x = XB?

8. a A uniformly doped npn bipolar transistor at T 300K is biasedin saturation. Starting with the continuity equation for minority carriers, show that the excess electron concentration in the baseregion can be expressed as

Section 1 23. A uniformly doped silicon npn bipolar transistor is to be biased inthe forward-active mode. The transistor dopings are N 1017cm . NB = 1016 cm , and = 1015 cm . a For T = 300K

calculate the B-E voltage at which the minority carrier electronconcentration at x = is 10percent of the majority carrier holeconcentration. h At this bias, determine the minority carrier holeconcentration at X O e Repeat parts a and h if the temperature is increased to T = 435K

4 Derive the expressions for the coefficients given by Equations(lO-6a) and (l0-6b).5. Derive the expression for the excess minority carrier hole concentrtion in the base region of a uniformly doped pnp bipolar transis

tor operating in the forward-active region.6. The idealized excess minority carrier concentration 8nBO x in thebase of an npn transistor is a linear function of distance through the

base when the transistor is biased in the forward-active region (seeExample 10-6). Using Equation (10-7) for the uniformly doped npndevice, determine

Problems


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Determine a a b Y , e aT d 8, and e {14. Consider a uniformly doped npn bipolar transistor at T3 ) ) O K

with the following parameters:

E = 0.10 mA = 0.20 mAlpeo 0.001 mA

E1.20 mAInc = 1.18mAlo = 0.001 mA

.13. The following currents are measured in a uniformly doped npn bi-polar transistor: ()

Section 1 3

*9. Consider a silicon pnp bipolar transistor at T = 300K with uniformdopings of NE = 5 X 1018cm . NB = 1017 cm , and N= 5 X 1015cm: . Let B = crn-Zsec, XB = 0.7 .tm, and assume XB LBThe transistor is operating in saturation with Jp = 165 A/cm2 andVEB = 0.75 volt. Determine a VCB b VEC(sat), e the /crri2 ofexcess minority carrier holes in the base, and d the /cm2 of excess minority carrier electrons in the long collector. Let Le = 35usn10. An npn silicon bipolar transistor at T300K has uniform dopingsof NE = 1019 cm: , NB = 1017 cm:, and = 7 X 1015 cm='. Thetransistor is operating in the inverse-active mode with VBE = 2volts and VBC 0.565 volt. a Sketch the minority carrier distribution through the device. b Determine the minority carrier concentrations at x = XB and x o .

11. A uniformly doped silicon pnp bipolar transistor at T300Kwithdoping s of NE 5 X 1017 cm=', NB = 1016cm , and = 5 X 1014cm?is biased in the inverse-active mode. What is the maximumB-C voltage so that the low-injection condition applies?

12. Consider a pnp silicon transistor at T = 300oK Assume that thebase doping is NB = 5 X 1016cm: , the neutral base width is XB =1.2 p.m, and the minority carrier diffusion length in the base is LB =10 p.m. a For VEB = VCB O calculate the minority carrier charge(coull cm in the base. (Assume the abrupt junction approximationapplies.) b If the B-C and B-E junctions are reverse biased at 1volt, calculate the minority carrier charge (coul/cm-) in the base.(Assume the neutral base width is unchanged.)

e Show that the total excess minority carrier charge (coul/cm-) inthe base region is given by

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DE 10 cm ZsecB = 1 X 107 cmXB 0.7 J-tmJrO = 2 X 10-9 Azcm?

DB = 25 cm ZsecE 5 X 1018 cme 5 x 1015 cm

TBO = TEO = 10-7 secni1.5 x 1010 cm>h Assuming the base transport and emitter injection efficiencyfactors are unity, plot the common emitter current gain for the conditions in part a . e Considering the results of part h , what canbe said about the recombination factor being the limiting factor inthe common emitter current gain.

18. Consider an npn silicon bipolar transistor at T300K with thefollowing parameters:DB 5 cm-zsec DE = 10 cm-zsecTBO= 10-7 sec TEO = 5 X 10-8 secNB 10]6cm XE 0.5 J-tm

For VBE = 0.60 volt and VCE5 volts, calculate a the currentsJnE JpE Jn and JR and h the current gain factors Y XT 8, cx ,and {3. 5 a Calculate and plot, for a bipolar transistor, the base transport

factor, XT as a function of xBILB) over the range 0.01 xBILB) 10. Use a log scale on the horizontal axis. b Assuming that theemitter injection efficiency and recombination factors are unity, plotthe common ernitter current gain for the conditions in part a .e Considering the results of part h , what can be said about thebase transport factor being the limiting factor in the common emitter current gain?

16. a Calculate and plot the emitter injection efficiency as a functionof the doping ratio, NBINE, over the range 0.01 NBINE 10.Assume that DE = DE, LB = LE, and XB = XE Use a log scale on.. the horizontal axis. Neglect bandgap narrowing effects. h Assuming that the base transport factor and recombination factors areunityplot the cornmon emitter current gain for the conditions inpart a . e Considering the results of part h , what can be saidabout the emitter injection efficiency being the Iimiting factor in thecornmon emitter current gain.

7 a Calculate and plot the recombination factor as a function of theforward-bias B-E voltage for 0.1 VBE 0.6. Assume the following parameters:

1015cmD 2 cm Zsecreo10-7 secJ o 3 X 10-8 l

cm?

NB = 5 X 1016 cmDB = 5 cm ZsecTBO 5 X 10-8 secXB 0.7 J-tm

E 1018 crnDE 8 cm-/secTEO 10-8 secXE 0.8 J-tm

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Section 1 420. A silicon pnp bipolar transistor at T300K has uniformdopingsof NE 1018 cm , NB 1016cm-3, andN1015cm> . The metallurgicalbase width is 1.2 J-tm.Let DB 10 cm-Zsecand TBO 5

10-7 secoAssume that the minority carrier hole concentration in the..base can be approximated by a linear distribution. Let VEB 0.625volt. Determine the hole diffusion current density in the base fora VCB = 5 volts, b VCB10volts, and e VCB15 volts.

*21. In a silicon npn bipolar transistor at T 300oK, the doping concentrations in the emitter and collector are NE 1018 cm?andNc1015cm: , respectively. The netural base width is 0.65 J-tmwhenVBE 0.70 volt and VeB 5 volts. Let DB 25 cm-/sec and TBO5 10- secoThe minority carrier diffusioncurrent in the base is toincrease by no more than 5 percent when VCB increases to 10volts.a Determine the minimumbase doping. b Estimate the Earlyvoltage.

22. Consider a uniformlydoped silicon npn bipolar transistor in whichXE XB, LE LB, and DE DB Assume that Ol.T= a 0.995 andlet NB 1017cm> . Calculate and plot the common ernitter currentgain{3forNE 1017,1018,1019, and 102ocm3 andfor the case awhen the bandgap narrowing effect is neglected, and b when thebandgap narrowing effect is taken into account.

23. A silicon pnp bipolar transistor at T 300K is to be designed sothat the emitter injection efficiencyis Y 0.996. Assume that XE XB, LE LB, DE = DB, and let NE 1019cm: . a) Determine themaximumbase doping, taking into account bandgap narrowing. bIf bandgap narrowing were neglected, what wouldbe the maximumbase doping required?24. A first-approximation type calculation of the current crowding effect can be made using the geometry shown in Figure 10-40. As-

The recombination factor, a has been determined to be a 0.998.Weneed a comrnon emitter current gain of f 120. Assuming thatOl.T Y determine the maximumbase ,width, XB, and the minimumemitter doping, NE to achieve this specification.

19. a The recombination current density, rO in an npn silicon bipolartransistor at T300KisJrO 5 x 10-8 lcm , The uniformdopings are NE 1018 cm , NB 5 X 1016 cm-3, andN 1015cm: .Other parameters are DE 10 cm-/sec , DB 25 cm-/sec, TEO10-8 sec, and TBO 10-7 secoDetermine the neutral base width sothat the recombination factor is a = 0.995 when VBE 0.55 volt. bf JrO remains constant with temperature, what is the value of awhen VBE 0.55 volt for the case when the temperature is T =400K? Use the value of XB determined in part a .

Chapter 10 The Bipolar Transistor


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- a xNB NB O exp ~where a is a constant and is given by

a In NB ONB XB)

a Show that, in thermal equilibrium, the electric fieldin the neutral base region is a constant. h Indicate the direction of the eleetrie field. Does this electric fieldaid or retard the flowof minorityearrier electrons aeross the base? e Derive an expression for thesteady-state minority carrier electron concentration in the base under forward bias. Assume no recombination occurs in the base.Express the electron concentration in terms of the electron currentdensity.

sume that one half of the base current enters from each side of theemitter strip and fiowsuniformly to the center of the emitter. Assume the base is p-type with the followingparameters:

NB 10 cm XB 0.70 J.LmJ.L p 400 cm-/V-sec S 8 J.Lm

Emitter Length, L 100J.Lma Calculate the resistance between x Oand x S/2. p If )IB= 10 J.LA , calculate the voltage drop between x Oand x S/2. e)If VBE 0.6 volt at x O,estimate in percent the number of electrons being injected into the base at x S/2 compared to x O.

25. Consider the geometry shown in Figure 10-40 and the device parameters in problem 24 except the emitter width, S. The emitterwidth S is to be changed so that the number of electrons injeetedinto the base at x S12 is no more than 10percent less than thenumber of electrons injected into the base at x O.Calculate S.*26. The base doping in a diffused npn bipolar transistor can be approximated by an exponential as

x= XB X S/2Figure 10 40 Figure for problems 24 and 25.

Problems


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34. In the Ebers-Moll model, let aF 0.98, lES = 10- A, and les 5x 10- A at T300oK. Plot lc versus VCB for - VBEVCB< 3volts and for VBE0.2, 004,and 0.6 volt. (Note that VCB VBC.What can be said about the base width modulation effect using thismodel?

Section 1 531. The VCE(sat)voltage of a npn transistor in saturation continues todecrease slowly as the base current increases. In the Ebers-Mollmodel, assume aF 0.99, aR 0.20, and lc 1 m A For T 300oK, determine the base current, lB, necessary to give VCE(sat)

0.10 volt.32. Consider an npn bipolar transistor biased in the active mode. Usingthe Ebers-Moll model, derive the equation for the base current, lB,

in terms of aF, aR, lES, CS, and VBE.33. Consider the Ebers-Moll model and let the base terminal be open solB o Show that, when a collector-emitter voltage is applied, wehave

27. Consider a silicon npn bipolar transistor with uniform dopings ofNE = 5 X 108 cm:, NB = 107 cm:, and = 5 X 10 cm=.Assume the c


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Summary and Review,*38. a A silicon npn bipolar transistor at T = 300K is to be designedwith an Early voltage of at least 200 volts and a current gain of at

least 80. h Repeat part a for a pnp bipolar transistor.*39. Design a uniformly doped silicon npn bipolar transistor so that

100 at T300oK. The maximum CE voltage is to be 15 volts andany breakdown voltage is to be at least three times this value. Assume the recombination factor is constant at = 0.995. The transistor is to be operated in low-injection with a maximum collectorcurrent of l = 5 mA. Bandgap narrowing effects and base widthmodulation effects are to be minimized. Let DE = 6 cm-zsec, DB 25 crnZsec TEO = 10-8 sec, and TBO = 10-7 seco Determine dopingconcentrations, the metallurgical base width, the active area, andthe maximum allowable VBE

*40. Design a pair of complementary npn and pnp bipolar transistors.The transistors are to have the same metallurgical base and emitterwidths of WB = 0.75 ,um and XE = 0.5 ,um. Assume that the following minority carrier parameters apply to each device.D = 23 cm zsec TnO = 10-7 secD = 8 cm Zsec TpO = 5 X 10-8 sec

The conector doping concentration in each device is 5 x 1015 cm-3and the recombination factor in each device is constant at =

a Calculate the transit time factors. h Calculate the cutoff andbeta cutoff frequencies, f and f~ respectively.

36. A silicon npn bipolar transistor has a beta cutoff frequency of f~ 100MHz and a common emitter current gain of 125. Assumethat the base transit time and the ernitter base junction chargingtime are equal limiting factors. If lE = mA, determine j XB and[r

37. A silicon npn bipolar transistor at T = 300K has a uniformly dopedbase region. The cutoff frequency is f 500 MHz and is limited bythe base transit time. Estimate the base width. Discuss the variationin f expected as the temperature increases to T400K

j = 0.8 D 25 cm-/secr 30 n = 50

= 0.5 mAXB 0.7 ,umXdc = 2.0 ,umC 0.08

Section 1 635. Consider a silicon npn transistor at T = 300oK. Assume the follow

ing parameters:

Problems


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1 . M ulle r, R . S ., and T . 1. Kamins . D e vic e E le ctr on ic s [ or In te gra te d C irc uits2nd ed . N ew Y ork : W iley , 1986 .

2 . N avon , D . H . S em ic on du cto r M i cr od ev ic es a nd M a te ria ls N ew Y ork :Ho lt, R i ne ha rt Wins ton , 1986 .

3 . N eudeck , G . W . T h e B ip ola r J un ctio n T ra ns is to r Vol . 3 o f the Modu l a rS erie s o n S olid S ta te D evices 2 nd e d. R ea din g, M a ss.: A d diso n-W e sley ,1989 .

4 . R ou lston , D . J. B ip ola r S em ic on du cto r D e vic es N ew Y o rk : M cG raw -H ill,1990 .

* 5 . Shur , M . G aA s D evices a nd C ircu its N ew Y ork : P lenum P ress, 1987 .* 6 . . P hy sics o f S em ic on du cto r D ev ices Eng lewood Cliffs , N J. : P ren-

tic e H a ll, 1990 .7 . S tree tm an , B G . S olid S ta te E le ctro n ic Deoices 3 rd e d. E ng le w oo d C liffs ,

N J.: P ren tice H all, 1990 . '8 . S ze, S . M . P hy sics o j S em ic on du cto r D eo ic es 2nd ed . N ew Y ork : W iley ,

1981 .9 . T iw ari, S .; S . L . W righ t; and A . W . K leinsasser . T ran spo rt and re la tedp ro pe rtie s o f (G a , A I)A s /G aA s d ou ble h ete ro ju nc tio n b ip ola r ju nc tio n tra n

sis tors . IE E E T ra nsa ctio ns o n E lec tro n D ev ic es E D 3 4 (February 1987) ,pp . 185-187 .

*10 . Wang , S . F un da m en ta ls o j S em ico nd ucto r T heo ry a nd D evice P hysics E ng lew oo d C liffs , N J.: P ren tice H all, 1989 .

*11 . Warne r , R . M ., Jr. , and B . L . Grung . T ra ns isto rs : F u nd am en ta ls [ or th eln te g ra te d C i rc u it E ng in e er N ew Y ork : W iley , 1983 .12 . Y ang , E . S . M ic ro e le c tr o n ic De v ic es N ew Y ork : M cG raw -H ill, 1988 .

R E IN G LIS T

0 .9950 . a Des ign , i f p oss ib le , th e d ev ices so th at 1 00 in eachdevice . I f th is is no t po ssib le , how clase a m atch can be ob ta ined?b W ith eq ua l fo rward -b ia s b as e-em itte r v o lta ge s a pp lie d, th e c ollec to r cu rren ts a re to be 5 m A w ith each dev ice opera ting inlow - in je ctio n . De te rm i n e th e a ctiv e c ro s s- se ctio n al a fe as .

C hap ter 1 0 T he B ipo lar T ran sisto r

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Sc Problems 10