Institute of Solid State Physics. Technische Universität Graz. Exam. Feb 2, 10:00-11:00 P2

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1 Technische Universität Graz nstitute of Solid State Physics Exam Feb 2, 10:00-11:00 P2

2 Exam Four questions, two from the online list. Calculator is ok. No notes. Explain some concept: (tunnel contact, indirect band gap, thermionic emission, inversion, threshold voltage,...) Perform a calculation: (concentration of minority carriers, integrate charge density to find electric field,...) Explain how a device works: (JFET, MESFET, MOSFET, laser diode, bipolar transistor, LED, Schottky diode, Heterojunction bipolar transistor,...)

3 Technische Universität Graz nstitute of Solid State Physics bipolar transistors npn transistor collector base emitter n p n + lightly doped p substrate Used in front-end high-frequency receivers (mobile telephones).

4 bipolar transistors

5 ρ de dx E = ρ ε dv dx = E abrupt junction + -x p - en A x n en D x A E = ( x+ xp ) -x p x n ε x ev bi NDN A = kt ln 2 ni n p ktln ktln n0 p0 = = n p0 pn0 en en = ε ( ) D E x xn x > x> 0 0 > x> x 2 en A x V = + xxp xp > x > 0 ε 2 2 en D x V = xxn 0 > x > x ε 2 p n n

6 Forward bias, V > 0 n p (0) p n (0) + Minority electrons are injected into the p-region Minority holes are injected into the n-region Electrons and holes are driven towards the junction. The depletion region becomes narrower ev ( bi V) np(0) = nn0 exp kt ev ( bi V) pn(0) = pp0 exp kt np(0) ev exp pn(0) ev exp = np0 kt = pn0 kt

7 Reverse bias, V < 0 Electrons and holes are driven away from the junction. The depletion region becomes wider n p (0) p n (0) n p p n (0) exp = np0 kt (0) exp ev ev = pn0 kt + Minority electrons are extracted from the p-region by the electric field Minority holes are extracted from the n-region by the electric field

8 pnp transistor, no bias

9 pnp transistor, forward active bias The base-emitter voltage controls the minority carriers injected from the emitter to the base. These diffuse to the base-collector junction and are swept into the collector. Always dissipate power due to the forward bias

10 Long/Short diode Long diode d n >> L p p n (0) p n0 p n (x) n-type d n dp J = ed = ed dx diff, p p p x Short diode d n << L p Metal contact is much closer to the depletion region than the diffusion length J diff, p = ( p (0) p ) n d n n0 dp edp dx

11 Minority carrier concentration contact p emitter (n+) base (p) collector (n) exp ev be nb0 ev kt kt e0 exp be contact n b0 p c0 p exp ev bc nb0 e0 kt x e We W eb W x bc c = ea D Ep be p = ea D En be n b0 p evbe / kt ( e ) e0 1 W eb x evbe / kt evbc / kt ( ) n e e W bc e W be W c p ev kt c0 exp bc

12 Emitter current ea D p ea D n e ea D n e be bc ( 1) ( 1) be p e 0 be n b0 ev / k T be n b0 ev / k T E = En + Ep = + Web xe Wbc Wbe Wbc Wbe evbe / kt / ( 1 evbc kt ) α ( 1 ) = e e E ES R CS p ev kt e0 exp be n ev kt b0 exp be p e0 n b0 exp ev bc nb0 kt x e We W eb W x bc W c c p c0

13 Collector current contact p emitter (n+) base (p) collector (n) exp ev be nb0 ev kt kt e0 exp be contact n b0 p c0 p exp ev bc nb0 e0 kt x e We W eb W bc W x c c evbc / kt pc0 ( e 1) exp ev bc pc0 kt cp = eabc Dp x W = ea D cn bc n b0 c evbe / kt evbc / kt ( ) n e e W bc W c eb

14 Collector current = + ea D n = ea D p ea D n + evbe ( / kt bc p c0 evbc 1) ( / kt 1) bc n b0 bc n b0 c cp cn e e Wbc Wbe xc Wc Wbc Wbe evbe / kt / ( 1 evbc kt ) ( 1 ) = + = α e e c cp cn F ES CS p ev kt e0 exp be n ev kt b0 exp be p e0 n b0 exp ev bc nb0 kt x e We W eb W x bc W c c p c0

15 Not an npn transistor contact p e0 exp be emitter (n+) base (p) collector (n) exp ev be nb0 ev kt kt contact n b0 p c0 p exp ev bc nb0 e0 kt x e We W eb W x bc c W c p ev kt c0 exp bc

16 Ebers-Moll model evbe / kt / ( 1 evbc kt ) α ( 1 ) = e e E ES R CS evbe / kt / ( 1 evbc kt ) ( 1 ) = α e e C F ES CS = E C E α α R F F R C F evbe / kt evbc / kt = ES ( 1) R = CS ( e 1) e

17 Emitter efficiency γ = e En En + Ep for npn = ea D Ep be p = ea D En be n b0 p evbe / kt ( e ) e0 1 W eb x evbe / kt evbc / kt ( ) n e e W bc e W be For γ e ~ 1, W bc - W be << L b, W eb - x e and n b0 >> p e0 n N Small base width and heavy emitter doping 2 i Ab n N 2 i De

18 Emitter efficiency γ = e En En + Ep 1 γ e = ev k T D p e W W p 1 D n e e W x be / e0 ( 1)( bc be ) evbe / kt evbc / kt ( )( ) n b0 eb e = ea D Ep be p p evbe / kt ( e ) e0 1 W eb x e = ea D En be n b0 evbe / kt evbc / kt ( ) n e e W bc W be Small base width and heavy emitter doping

19 ase transport factor = c En ratio of the injected current to the collected current recombination in the base would reduce the base transport factor A thin base with low doping results in a base transport factor ~ 1

20 Current transfer ratio α C = = E γ e α ~ 1 for a good JT

21 Transistor modes 1. Forward active: emitter-base forward, base-collector reverse 2. Saturation: emitter-base forward, base-collector forward 3. Reverse active: emitter-base reverse, base-collector forward 4. Cut-off: emitter-base reverse, base-collector reverse

22 Common base configuration evbe / kt / ( 1 evbc kt ) α ( 1 ) = e e E ES R CS solve for V be = α e e evbe / kt / ( 1 evbc kt ) ( 1 ) c F ES CS saturation active cutoff E < 0

23 Common base configuration c C ~ E buffer circuit: the output current is constant over a wide range of output voltages

24 Common emitter configuration evbe / kt / ( 1 evbc kt ) α ( 1 ) = e e E ES R CS evbe / kt / ( 1 evbc kt ) ( 1 ) = α e e c F ES CS current amplification ~100 = E C

25 Current amplification factor β = h = fe C = E C 1 = 1 α C C = α E C α γ e β = = = 1 α 1 γ e β ~

26 The Art of Electronics Horowitz and Hill for common emitter configuration

27 Transconductance g m = V C be evbe / kt / ( 1 evbc kt ) ( 1 ) = α e e c F ES CS At a typical operating point, the first term usually dominates α e c F ES ev be / k T g m eα e eβ kt kt kt be = e = F ES ev / k T C The transconductance can be very high.

28 Early effect Ebers - Moll: evbe / kt / ( 1 evbc kt ) α ( 1 ) = e e E ES R CS evbe / kt / ( 1 evbc kt ) ( 1 ) = α e e c F ES CS = E C ES ea D p ea D n = + W x W W be p e0 be n b0 eb e bc be CS ea D p ea D n = + x W W W bc p c0 bc n b0 c c bc be ES and CS are treated as constants but the depletion widths W bc, W be, W c, and W e depend on the voltages. p ev kt e0 exp be n ev kt b0 exp be n b0 p c0 p exp evbc nb0 e0 kt x e W e W eb W x bc W c c p ev kt c0 exp bc

29 Punchthrough: The neutral base width goes to zero and all gain is lost. Lightly dope the collector -> voltage drops in collector. Makes circuit slower. Early effect Common emitter configuration ase width modulation: smaller width increases the diffusion current and increases the gain.

30 Common emitter configuration C ~ β amplifier

31 Small signal response i = βi = βg v c E E transistor man input conductance: g E i = v E transconductance: g m i = v c E

32 Small signal response α β = 1 α f β ( 1 α ) = f ft = α0 0 α f α

33 Heterojunction bipolar transistors

34 Heterojunction bipolar transistor small emitter-base capacitance to increase speed

35 HT current gain C = β α β = 1 α n p 0 E0 (npn) Higher doping in the emitter makes the minority carrier concentration lower in the emitter. n 0 p E0 2 n NC NV exp( Eg / kt ) i = = NA NA 2 n N C N V exp( EgE / kt ) i = = N N D f the emitter and the base have different band gaps NE NN E c v g β = exp N NN c v kt D

36 HT current gain A HT has an emitter bandgap of 1.62 and a base bandgap of A JT has an emitter bandgap of 1.42 and a base bandgap of oth have an emitter doping of cm -3 and a base doping of cm -3. How much larger is the gain in the HT? ( ) ( ) β HT Eg = exp = exp = 2257 β JT kt

37 HT Trade off gain for higher speed Higher base doping lower base resistance reduced Early effect less trouble with punch through base can be made thinner -> faster transistors ecause of higher base doping, a higher collector doping is possible without punch through lower collector resistance

38 HT current gain band discontinuity reduces emitter efficiency Graded layer emitter and base improve performance Si/SiGe AlnAs/nGaAs

39 Heterojunction bipolar transistors Fastest np/ngaas HT's have an f T of 710 GHz. Higher doping in the base allows for a thinner base without punch through and lower base resistance and thus higher frequency operation

40 nterdigitated contacts in power transistors