VBIC. SPICE Gummel-Poon. (Bipolar Junction Transistor, BJT) Gummel Poon. BJT (parasitic transistor) (avalance mutliplication) (self-heating)

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1 page 4 VBC SPCE Gummel-Poon (Bipolar Junction Transistor, BJT) 1970 Gummel Poon GP BJT (parasitic transistor) (avalance mutliplication) (self-heating) (qusai-saturation) Early GP BJT (Heter-junction Bipolar Transistor HBT) Vertical Bipolar nter-company (VBC) VBC Gummel-Poon page 4

2 page 5 Gummel-Poon GP VBC.1 VBC Gummel-Poon VBC BJT Gummel-Poon VBC 1. (Base width modulation) BJT HBT GP VA(Early voltage). (parasitic PNP) 3. Kull (quasi-saturation) (distributed base) (current crowding effect) 7. epi-layer 8. (self-heating) 9. (weak avalanche breakdown) 10. (excess phase shift) page 5

3 page 6 NPN VBC -1 Gummel-Poon NPN Gummel-Poon PNP R C Q BCX Q BC BE BEX BC gc BC C BEO C BCO Double Poly-Silicon BJT (poly-silicon base) R B R BP (normalized base charge qb qbp) (DC AC Transient) VBC Weil-McNamee RLC (thermal network) page 6

4 page 7 S C si R S C BCO R CX tfp trp bp BCP Q BCP R BP q bp cx BEP Q BEP Q BCX R C ci B R BX Q BEX bx bex R B q b Q BC Q BE bc bi be gc ei txf tzr C BEO R E E dt F lxf xf xf 1 tzf RTH CTH tzf Q cxf 1Ω t 1 page 7

5 Chap. VBC page (cc) CC (Transport current) tzf tzr s V bei V bci cc = tzf tzr = exp 1 exp 1 q b NF V th NR V th (.1a) V th k T q = (.1b) Vth (Thermal voltage) k q T ( K) q b ( ) qb q S q S q S q je q jc q1s 1 VER VEF s V bei s V bci qs = exp 1 exp 1 KF + N FV tv KR NR V tv = + + (.a) = + + (.b) (.c) q 1S (Base-width modulation) q S (High Level injection effect) q je q jc C JE C JC.1. ( be, bc ) VBC ( ) ( Recombination) V bei V bei BE = WBE BE exp 1 + BEN exp 1 NE V th N EN V th (.3a) page 8

6 page 9 V bei V bei BEX = ( 1 WBE ) BE exp 1 + BEN exp 1 NE V th NEN V th V bci V bci BC = BC exp 1 + BCN exp 1 NCV th NCN V th (.3b) (.3c) BE BC - - NE NC - - (emission coefficient) BEN BCN NEN NCN W BE (ntrinsic) (extrinsic).1.3 (Weak Avalanche Effect) BC BC ( i ) ( ) d ε qe i = d εi P = exp = exp λ qeλ (mean free path) gc α n b n gc = n xd Emax exp (.4a) b E n max n = cc bc (.4b) gc BC x d E max BC n ( NPN ) gc << n page 9

7 page 10 CJC C jc = (.5a) MC VBC 1 PC ε xd = (.5b) C x d jc PC V Emax = 1 MC BC (.5c) C BC CJC BC PC jc BC (Built-in potential) MC BC (Grading coefficient) BC (.4a) AVC igc = ( cc BC ) AVC1 ( PC Vbci ) exp ( ) 1 MC PC Vbci αn 1 AVC1 = b 1 MC ( 1 MC ) εbn AVC = CJC PC n MC (.6) AVC1 AVC VBC Gummel-Poon.1.4 (Quasi-saturation effects) Kirk Effect ( β ) (f T ) ( ρ c ) page 10

8 Chap. VBC page 11 ( C R ), BC V V ( R R ) = + BCi BC C CX C VBC BC BC - ci cx contact BE SCR BC SCR Emitter Base Collector Sub collector contact ci cx R C R CX [11] rci rci K Vrci + VthK bci Kbcx ln K = Vrci RC 1+ VO bci bcx (.7) RC VO GAMM VBC. VBC CC( ) GCTC (Global Communication Technology Coporation) ngap/gaas HBT VBC page 11

9 page 1-3 Emitter n + n + ngaas GaAs Ledge n ngap Ledge Base p + GaAs Collector n GaAs Subcollector n + GaAs Semi nsulator Substrate..1-1 VBC (R E ) (R CX ) page 1

10 page 13 (R B ) (R BX )..1.1 RE-flyback RC-flyback -4 HP 414 R E (E) (ei) C ( ) V CE R E V CE B R E -4(a) B + V CE = 0 ~ 10mA = 0A step 100uA C B + V EC = 0 ~ 0mA 0 E = A step 100uA (a) (b) RE-flyback(a) RCX-flyback(b) R E 1 = V B CE (.8).8 page 13

11 page VCE (V) Linear fit of RE VCE (V) B (ma) VCE (V) Linear fit of RCX 0.4 VEC (V) B (ma) page 14

12 page VBC (R BX R B ) (1). (R BX ) (). (R B ) (.8) (Early Effect) VBC (emitter current crowding effect) RB WBE R B R B = RBX + (.8) qb ( ) ( 1 β ) R + R i + R + + R C π BX B b π ac E ( ) R + R i + R BX B b E optimized -1 ngap/gaas HBT (N B >>N E,N C ) R B 0 page 15

13 Chap. VBC page 16 j * MAG + ( ) + + ( ) + + ( 1+ β ) R R i R BX B b E R R i R R BX B b π ac E REAL frequency RBX RB R E ( ) R CX ( ) R BX ( ) R B ( ) Gummel plot ngap/gaas HBT pnp pnp VBC page 16

14 Chap. VBC page 17 Gummel plot Gummel plot Gummel plot (Diode) V E 0 V B V C V B V C -8 ( B ) ( BE N E ) ( BEN N EN ) V BE (Recombination) kt V BE (R E ) - ( C ) KF KF B C NF 1 RE NE BEN S BE NEN V BE page 17

15 page 18 B E KR NC NR 1 RCX BCN BC NEN S V BC Gummel plot -10 ( S ) ngap/gaas HBT Gummel kt Gummel HBT ngap/gaas HBT KF 1 - Gummel plot page 18

16 page x10-4 C E 1x10-5 C & E V BE &V CE x10-4 C & B (A) 1x V BE (V) c Simulation b Simulation b Measurement c Measurement page 19

17 Chap. VBC page x10-4 E & B (A) 1x B Sim (A) E Sim (A) B Mea (A) E mea (A) V BC (V) S(Amp.) 1.58E-5 BE(Amp.) 8.63E-6 BC(Amp.) 4.31E-15 NF 1.03 NE 1.11 NC 1.98 NR 1.01 BEN(Amp.) 1.00E-19 BCN(Amp.) 1.00E-19 KF 1 NEN NCN KR 1.86E (Base Width Modulation Effect) ngap/gaas HBT V EF V ER page 0

18 Chap. VBC page (Quasi-saturation) VBC R C G AMM V O H RCF Q CO R C G AMM V O R C G AMM (epi) V O H RCF Q CO ngap/gaas (mobility) -4 page 1

19 page RC = 500 RC = 1500 C C GAMM = 100 p GAMM = 0 V C V C RC V GAMM V C VO =100 VO = 10 R C 1 G AMM 5.00E-15 V O 100 H RCF 0.1 V C Q CO 1.00E-15 VO V page

20 page measurement data simulation Jc (ma/um ) Vc (V) Measurement Data Simulation Jc (ma/um ) Vc (V) page 3

21 Chap. VBC page 4..5 ngap/gaas HBT VBC 3 1. GaAs pnp. (N B >>N E N C ) V EF V ER 0 3. GaAs (epi-layer) VBC ngap/gaas HBT ngap/gaas HBT S(Amp.) 1.58E-5 BE(Amp.) 8.63E-6 BC(Amp.) 4.31E-15 NF 1.03 NE 1.11 NC 1.98 NR 1.01 BEN(Amp.) 1.00E-19 BCN(Amp.) 1.00E-19 KF 1 NEN NCN KR 1.86E-07 WBE 1 R C 1 R E ( ) 19. VEF 0 G AMM 5.00E-15 R CX ( ) 7 VER 0 V O 100 R BX ( ) 31.4 RTH 4.4K H RCF 0.1 R B ( ) 0 CTH 1.00E-09 Q CO 1.00E-15 page 4

22 Chap. VBC page 5.3 VBC.3.1 VBC VBC (Q BE ) (Q BEX ) - (Q BC ) (Q BCX ) VBC (CBEO) (CBCO) (space charge) (deplete) VBC SGP FC smooth AJ Q, = CJE qj( Vbei, PE, ME, FC, AJE) BE dep C BE QBE, dep qj( Vbei, PE, ME, FC, AJE) = = CJE Vbei Vbei 1 CJE for Vbei < FC PE ME Vbei 1 PE CJE Vbei 1 FC 1 ( 1 ME) ME for Vbei FC PE ME FC PE ( 1 ) (.9) PE - (built-in potential) ME - (0.5, for uniform doped base) - CBE - CBC (1). (). (1). - Q BE page 5

23 page 6 Q = Q + Q BE BE, dep BE, duf = CJE WBE qje + TFF tzf (.10a) tzf V bci TFF = TF( 1+ QTFq1 ) 1 + XTF exp tzf + TF 1.44 VTF (.10b) CJE - WBE TFF VBC (transit time) (). - Q BEX = ( ) = ( ) (.11) QBEX QBE, dep 1 WBE CJE 1 WBE qj( Vbex, PE, ME, FC, AJE) 0<WBE<1 V BEX VBC Vbx-Vei (3). - QBC Q = Q + Q + Q BC BC, dep BC, duf epi, in = CJC qjc + TR qb + QCO K tzr bci (.1) V bci Kbci = 1+ GAMM exp Vth QCO Kbci (base pushout Kirk Effect) (4). - QBCX Q BCX = QCO K (.13a) bcx page 6

24 page 7 K bcx V bcx 1 GAMM exp V = + (.13b) th.3. HP 8510 S S de-embedding Pad de-embedding dummy open S Y S mea Y Y open Y deivce pad page 7

25 page 8 S S S S S 11, open 1, open S 1, open, open S 11, mea 1, mea S 1, mea, mea Y Y Y Y Y 11, open 1, open Y 1, open, open Y 11, mea 1, mea Y 1, mea, mea Y11, device Y1, device Y11, mea Y1, mea Y11, open Y1, open Y Y = Y Y Y Y 1, device, device 1, mea, mea 1, open, open -18 Port 1 Port Ca C c Cb C C C a b c mag ( Y11, device + Y1, device ) = (.14a) mag π f ( Y, device + Y1, device ) = (.14b) -mag π f ( Y1, device ) = (.14c) π f CV C BE V c 0 V b (.14) page 8

26 page 9 Port Port 1 Vb = 5 ~ 1V step 0.V Vc = 0V C BE Port Port 1 Vc = 1 ~ 7.5V step 0.45V Vb = 0V C BC -1 - ngap/gaas HBT page 9

27 page CBE Measurement CBE Simulation 8 CBE (ff) VBE (V) C BE CBC (ff) Measurement Data Simulation VBC (V) C BC page 30

28 page 31 C JE (ff) 7.5 C JC (ff) 10. P E 1.35 P C 1.09 M E 75.01m M C 481.m A JE 1m A JC 1m F C f t (unit current gain frequency) VBC (.15) TFF = 1 π f T tzf V bci TFF = TF( 1+ QTFq1 ) 1 + XTF exp tzf + TF 1.44 VTF (.15) TF XTF TF QTF TF TF TF VTF TF VBC Gummel- Poon VBC VTF VBC S de-embbeding H H 1 page 31

29 page 3 f t H 1-0dB/decade DC~0GHz S H GHz -3 Port Port 1 Vc = 1 ~ 3V step 0.5V Vb = 1. ~ 1.5V step 0.01V ngap/gaas HBT QTF 0 C-CAP -4-7 page 3

30 page Ft (GHz) Measurement Simulation 1x10-5 1x c (A) Ft (GHz) Measurement Simulation c (ma) VBC page 33

31 page 34 VBC TF(psec) 3.01 TF 0.61m QTF 0 VTF 0 XTF TR 0 VBC V BC VBC - (BC) - Kirk Effect VBC V CE (V BC ).3.4 S S TD ADS VBC S S page 34

32 page 35 ngap/gaas HBT VBC C JE (ff) 7.5 C JC (ff) 10. P E 1.35 P C 1.09 M E 75.01m M C 481.m A JE 1m A JC 1m F C 0.9 TF(psec) 3.01 TF 0.61m QTF 0 VTF 0 XTF TR 0 S11 Mag. (db) Qx4 b =15µA V c =V VBC Model Measurement Data(Mag.) S11 Phase(degree) -6-7 VBC Model Measurement Data (Phase) Freq. (GHz) ngap/gaas HBT S VBC (S11) page 35

33 page 36 S1 Mag. (db) VBC Model Measurement Data (Phase) Qx4 b =15µA V c =V VBC Model Measurement Data (Mag.) S1 Phase (degree) Freq. (GHz) ngap/gaas HBT S VBC (S1) S1 Mag. (db) Qx4 b =15µA V c =V VBC Model Measurement Data (Mag.) S1 Phase(degree) - VBC Model Measurement Data (Phase) Freq. (GHz) ngap/gaas HBT S VBC (S1) page 36

34 page 37 S Mag. (db) Qx4 b =15µA V c =V VBC Model Measurement Data (Mag.) S Phase (degree) VBC Model Measurement Data (Phase) Freq. (GHz) ngap/gaas HBT S VBC (S).4 ngap/gaas HBT.3.3 GP VBC BiCMOS HBT f t C V CE V CB TF XTF VTF TF Q GP VBC f C S dq f d C HBT - HBT page 37

35 Chap. VBC page Middle current region 30 V ce 5 Low current region Ft (GHz) High current region 0 1x10-5 1x c (A) Ft c contact BE SCR BC SCR Emitter Base Collector Sub collector contact high current density w E w B w C w BE w BC ngap/gaas HBT page 38

36 Chap. VBC page (Neutral Base Region) w B Q nb ζ ζ w ( ζ 1) e + 1 B wb e 1 i (.16) = + ζ µ V ζ e v e ζ ζ nb T c T µ nb (drift factor) E w V n B ζ = (.17) th ζ wb ( N B ) (intrinsic) ( n i ) En E n V dn V dn = n + N dx n dx T B T i B i (.18) ( n i ) (SiGe) band-gap grading (.16) / ( v c ) (Kirk Effect ) w B v c - vbci ζ ζ dq ( 1) e 1 nb w ζ + B wb e 1 = = + = + (.19) Bf ζ ζ Bfd Bfv dt µ nbvt ζ e vc e ζ page 39

37 page 40 w B v c c ζ bias Bfd Bfv ( ) w 1 1 B = wb 0 kb c (.0) w w ( V ) = = k b - B0 B BCi 0 c = C jci0 C jci Bfd Bfd 0 b k ( c ) ζ ( ζ ) e = 1 1 w B Bfd 0 = ζ µ nbvt ζ e (.1) E n = 0 ζ w ( ζ 1) e + 1 B wb = = Bfd 0 ζ µ nbvt ζ e µ nbvt Bfv u Vlim vs v = c vs, E lim 1+ u = w = c µ nc 0 (.) u E ( v, i ) / Elim = jc BCi T BC lim E µ nc 0 Bfv ζ wb 0 1+ u e 1 kb ( c 1) v ζ s u e = ζ 1 (.3) page 40

38 page 41 ζ e ζ 1 ζ BC e 1 1+ u u 1 1 kb ( c 1) > 1 BC 1+ u u > 1 1 kb ( c 1) 1 BC Bfd 1+ u u 1 kb ( c 1) u ζ wb 0 e ζ 1 Bfv0 u0 Bfv = 1 Bfv0 1 ζ + = + vs e 1 u 1+ u0 u w e ζ 1 ζ B0 Bfv0 = 1+ ζ vs e 1 u0 (.4) V = 0 u 0 u 1 c Bfv0 BCi.4. - (BC Space Charge Region) - wbc BC = (.5) v c w BC v c - BC (punch-through) ε A C jcip C = w C C jcip jcip BC = BCP = BCP c (.6) C jci C jci0 page 41

39 Chap. VBC page 4 punch-through wc BCP = v c.4.3 (Neutral Emitter Region) w E pe0 pe 0 = dqpe we we d = v + µ V (.7) B ke pe T v ke (contact recombination velotcity) µ pe C β 0 = dc db Ef pe0 = (.8) β 0 0 ( C, Low ) β V = 0 β 0 BCi Ef β ( C Low ) 0, = Ef 0 (.9) β ( V ) 0 C, BCi (ntegral Charge-Control Relation) page 4

40 page 43 β β 0 ( C Low ) g E 0, T 1+ (.30) (, V ) C BCi CK g E CK.4.5 Ef Q Ef g E T Ef = Ef 01 + CK g E Q = 1 + i T Ef Ef 0 T CK (.31) (BE Space Charge Region) - V T v BEi QBE = qae wbe ni exp 1 (.3) PE VT w BE - n i - PE BE BE vbei qae wbeni exp V T 1 = g PE m C (.33) g m g m C BE page 43

41 page (Neutral Collector Region) - (Sub-Collector) Kir-effect Krik-effect f T CK CK v 1 ceff x + x + 10 = 1 + r Ci0 1+ ( vceff Vlim ) 3 (.34a) x v V ceff lim = (.34b) V PT x V PT punchthrough V lim ( v < Vlim ) CK ( V lim V PT ) ceff rci 0 v ceff r Ci0 w qa µ = C (.35a) N E nc 0 C v ceff vcei v CEs = VT ln 1+ exp V T (.35b) v CEs CE CK page 44

42 page 45 v CEi T = ( ) CK Q pc pcs ( ) QpC = pcsit wi wc wc pcs = 4µ nc 0VT (.36) w w ( 1 i ) = Q pc i C CK T T < CK pc Q + + = = + + i = 1 CK it w i i a i hc w w C 1 1 ahc (.37) a hc > 0 pc pc dq w 1 pc CK = = pcs + di C it i + ahc (.38).4.6 page 45

43 Chap. VBC page 46 (1). drift Ef - BC - BE = << 1 ( c ) Bfd 0kb 1 = f 0 Bfd Bfv BC Ef BE ( ) [ ] ( c 1) [ u u 1 ] / sqrt( i ) ( c 1) [ 1 c 1 ] / sqrt( i ) = 0 + BCP C jcip C jci0 Bfd 0kb c 1 + Bfvl u0 u 1 + BE0 / sqrt( it ) (.39) = h Bfvl 0 BE0 T h Bfvl BE0 T 0 Ef 0 Bfd 0 Bfv0 BCP ( C jcip C jci0 ) = V = 0 0h - Early Effect Bfvl T C BCi (). Ef Bf pc Ef = g E ( i ) ( 1 ) Ef Ef 0 T CK Q = i + g Ef Ef T E (.40) Bf pc [11] page 46

44 page 47 fh = hcsw 1+ Q = w i fh hcs T it i ahc w w e ζ w hcs = Bfvs + pcs = + µ 1 4µ CK + ζ Bm C C ζ nc 0VT e nc 0VT (.41) Ef 0 g E hcs a hc V BCi = 0 V BE ( V = 1.5V ) 1 π f CE je jc ( V ) = (.4) ', f CE C T C + C g m 0h matlab Bfvl BE0 r Ci0 = wc 75 qa µ N Ω (.43a) E nc 0 C VPT V (.43b) E lim V v w µ lim s = = lim c nc 0 vs V = wc 0.V (.43c) µ nc 0 w C N C V PT CV matlab page 47

45 page 48 ngap/gaas HBT f 0 (psec).6 Ef rci h (psec) 1.3 g E.7 VPT.5 Bfvl (psec) 0.01 hcs (psec) 5 Vlim 0.34 BE0 5.5e-14 a hc 0.65 VCEs Measurement Simulation 5 Ft (GHz) x10-5 1x c (A) (log) page 48

46 page Ft (GHz) Measurement Simulation c (ma) (lin) page 49