ECE606: Solid State Devices Lecture 18 Bipolar Transistors a) Introduction b) Design (I) Gerhard Klimeck [email protected] 1 Klimeck – ECE606 Fall 2012 – notes adopted from Alam Background E B C E C Base! Point contact Germanium transistor Ralph Bray from Purdue missed the invention of transistors. http://www.electronicsweekly.com/blogs/david-manners-semiconductor-blog/2009/02/how-purdue-university-nearly-i.html http://www.physics.purdue.edu/about_us/history/semi_conductor_research.shtml Transistor research was also in advanced stages in Europe (radar). Klimeck – ECE606 Fall 2012 – notes adopted from Alam 2 Shockley’s Bipolar Transistors … n+ emitter n+ Double p base n-collector Diffused BJT n+ n+ p n n+ emitter base collector Klimeck – ECE606 Fall 2012 – notes adopted from Alam Modern Bipolar Junction Transistors (BJTs) Base Emitter Collector N+ N- P+ N+ N SiGe intrinsic base P- Dielectric trench Why do we need all these design? Transistor speed increases as the electron's travel distance is reduced SiGe Layer Klimeck – ECE606 Fall 2012 – notes adopted from Alam 4 Symbols and Convention E Symbols Poly emitter N+ NPN PNP Collector B P Low-doped base Collector Base Base N Collector doping optimization Emitter Emitter C IC+I B+I E=0 (DC) VEB +V BC +V CE =0 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 5 Outline 1) Equilibrium and forward band-diagram 2) Currents in bipolar junction transistors 3) Eber’s Moll model 4) Intermediate Summary 5) Current gain in BJTs 6) Considerations for base doping 7) Considerations for collector doping 8) Conclusions REF: SDF, Chapter 10 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 6 Topic Map Equilibrium DC Small Large Circuit signal Signal s Diode Schottky BJT /HBT MOS Klimeck – ECE606 Fall 2012 – notes adopted from Alam 7 Band Diagram at Equilibrium ∇•=( −++ − − ) D qpnND N A Equilibrium ∂n 1 = ∇•J −r + g ∂t q N N N =µ + ∇ J Nqn N E qD N n DC dn/dt=0 Small signal dn/dt ~ jωtn ∂p 1 Transient --- Charge control model =− ∇•J −r + g ∂t q P P P =µ − ∇ J Pqp P E qD P p Klimeck – ECE606 Fall 2012 – notes adopted from Alam 8 Band Diagram at Equilibrium NPN homojunction BJT Emitter Base Collector Vacuum χ2 level χ1 χ3 EC EF EV Klimeck – ECE606 Fall 2012 – notes adopted from Alam 9 Electrostatics in Equilibrium 2kε N 2kε N x= s0 E V x= s0 C V p, BE ()+ bi p, BC ()+ bi q NB N E N B q NB N C N B 2kε N x= s0 B V 2kε N n, E q N() N+ N bi x= s0 B V E B E n, C ()+ bi q NC N C N B Emitter Base Collector Two back to back p-n junction Klimeck – ECE606 Fall 2012 – notes adopted from Alam 10 Outline 1) Equilibrium and forward band-diagram 2) Currents in bipolar junction transistors 3) Eber’s Moll model 4) Intermediate Summary 5) Current gain in BJTs 6) Considerations for base doping 7) Considerations for collector doping 8) Conclusions REF: SDF, Chapter 10 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 11 Topic Map Equilibriu DC Small Large Circuit m signal Signal s Diode Schottk y BJT/HB T MOS Klimeck – ECE606 Fall 2012 – notes adopted from Alam 12 Band Diagram with Bias ∇•=( −++ − − ) D qpnND N A Non-equilibrium ∂n 1 = ∇•J −r + g ∂t q N N N =µ + ∇ J Nqn N E qD N n DC dn/dt=0 Small signal dn/dt ~ jωtn ∂p 1 Transient --- Charge control model = ∇•J −r + g ∂t q P P P =µ − ∇ J Pqp P E qD P p Klimeck – ECE606 Fall 2012 – notes adopted from Alam 13 Electrostatics in Equilibrium 2kε N 2kε N x=s0 E () V − V x=s0 C () V − V p, BE ()+ bi EB p, BC ()+ bi CB q NB N E N B q NB N C N B ε 2ks0 N B 2kε N x=() V − V =s0 B () − n, E ()+ bi EB xn, C Vbi V CB q NE N B N E ()+ q NC N C N B Emitter Base Collector VEB VCB Assume current flow is small… fermi level is flat Klimeck – ECE606 Fall 2012 – notes adopted from Alam 14 Current flow with Bias Input small amount of holes results in large amount of electron output EC-Fn,E V Fp,B -EV EC-Fn,C Klimeck – ECE606 Fall 2012 – notes adopted from Alam 15 Modern MOSFET - “Fundamental” Limit looks similar to BJT Vg S D log I d Metal Oxide Threshold n+p n+ Vg ↑ S≥60 mV/dec 0 Vdd Vg E x Klimeck – ECE606 Fall 2012 – notes adopted from Alam Modern MOSFET - “Fundamental” Limit looks similar to BJT Vg S D log I d Metal Oxide Threshold n+p n+ DOS(E) , log f(E) Vg ↑ S≥60 mV/dec ` Ef 0 Vdd Vg E x Klimeck – ECE606 Fall 2012 – notes adopted from Alam Coordinates and Convention Emitter Base Collector N+ PN X’’ X X’ 0 W = = = NNE DE,,.... NN B AB , ,.... NN C DC , Doping = = = Minority carrier DDEP,........ DD BN ,...... DD CP diffusion = = = nnEp00,....... pp Bn 00 ,...... nn Cp 00 Majority carriers Klimeck – ECE606 Fall 2012 – notes adopted from Alam 18 Carrier Distribution in Base x x ∆nx( ) =+= Ax B C 1 − + D C WB W B D 2 2 ni, B β xni,B β x ∆=n( x ) ()eqV BE −1 1 −+ ()eqV BC −1 NB WB NB W B 2 + ni, B qV β 2 ∆ =()BE − ni, B β n(0) e 1 ∆==qV BC − nxW(B )() e 1 NB NB Assume no recombination. Start from minority carrier VEB VCB Klimeck – ECE606 Fall 2012 – notes adopted from Alam 19 Collector and Emitter Electron Current 2 2 ni, B β xni,B β x ∆=n( x ) ()eqV BE −1 1 −+ ()eqV BC −1 NB WB NB W B 2 2 dn qD n β qD n β J= qD = − n i, B ()eqV BE −1 + n i, B ()eqVBC −1 n, C n dx W N W N WB B B B B VBE VBE dp J= − qD p, E p dx 2 Dp n β = −i ()eqV BE − 1 Wn N D Klimeck – ECE606 Fall 2012 – notes adopted from Alam 20 Current-Voltage Characteristics 2 2 qDniB,β qD n iB , β Normal, Active Region J=−n() eqV BE −+1 n () e qV BC − 1 n, C WN WN EB: Forward biased BB BB BC: Reverse biased JC log 10 JC High-level injection series resistance, etc. IB > 60 mV/dec. VBE VCE W is not independent of bias B same physics of diode , rollover => Early Effect 21 Klimeck – ECE606 Fall 2012 – notes adopted from Alam Outline 1) Equilibrium and forward band-diagram 2) Currents in bipolar junction transistors 3) Eber’s Moll model 4) Intermediate Summary 5) Current gain in BJTs 6) Considerations for base doping 7) Considerations for collector doping 8) Conclusions REF: SDF, Chapter 10 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 22 Ebers Moll Model Hole diffusion in collector 2 2 2 qDniB,β qD n iB ,qD p n iC , β =−nqV BE −+ n +qV BC − IC AeA()1 () e 1 WNBB WNWN BBCC β qV β ≡α Ie()()qV BE −−1 Ie BC − 1 F F0 R 0 IC=Ic,n +Ic,p IF IR E C IE=IE,n +IE,p I β I C =qV BE − IF I F 0 ( e 1) E αRI αFI B β R IB F =qV BC − IR I R 0 () e 1 2 2 2 qD p niE,,qD n iBβ qD n iB, β I =−A +n () eAeqV BE −+1n ()qV BC − 1 E Temperature WNWNEEBB WN EB β β dependent ≡qV BE −−α qV BC − IeF0()()1 R IeR 0 1 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 23 Common Base Configuration IF IR E C E C N PN α I V I I VCB αRIR F F EB E C I I (in) (out) E C B B B CBE CBC IB Junction capacitance and diffusion capacitance How would the model change if this was a Schottky barrier BJT? The original transistor was a metal/ semicond / metal device No minority carriers, no diffusion capacitance but the “rest” about the same. Common base configuration provides power gain, but no current gain. => Emitter and collector current are identical => no current gain => Collector current I C can be driven through large resistor => power gain Is there another configuration that can deliver current gain? Klimeck – ECE606 Fall 2012 – notes adopted from Alam 24 Common Emitter Configuration Cµ IE E C IF CBE IC αRIR B IB P IR N VEC α− α (out) B Cπ FFI RR I VEB α P+ B FI F (in) I β F E E C IR BC αFIF αI α I FF= FF =−()1 α I = I IC β α F F B F F − α 1 F This is a practice problem … Klimeck – ECE606 Fall 2012 – notes adopted from Alam 25 Intermediate Summary • The physics of BJT is most easily understood with reference to the physics of junction diodes. • The equations can be encapsulated in simple equivalent circuit appropriate for dc, ac, and large signal applications. • Design of transistors is far more complicated than this simple model suggests => the next lecture elements • For a terrific and interesting history of invention of the bipolar transistor, read the book “Crystal Fire”. Klimeck – ECE606 Fall 2012 – notes adopted from Alam 26 Outline 1) Equilibrium and forward band-diagram 2) Currents in bipolar junction transistors 3) Eber’s Moll model 4) Intermediate Summary 5) Current gain in BJTs 6) Considerations for base doping 7) Considerations for collector doping 8) Conclusions REF: SDF, Chapter 10 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 27 Ebers Moll Model 2 2 qDpniE,β qD p n iC , β =qV BE −+qV BC − IAB () e1 A() e 1 WNEE WN CC 2 2 2 qDnqD p n β qD n β =−n i,, B + i E ()qV BE −+n i, B ()qV BC − IAEE eA1E e 1 WNWNBB E E WNB B β β =qVBE − − α qV BC − IF 0 () e 1 RI R 0 () e 1 IF IR E C IE IC αRIR αFIF B IB 2 2 2 β qDn ni, B qV β qDn niB, qD n n iC , qV β =qV BE − IAeA=−()BE −+1 + () e BC − 1 IF I F 0 ( e 1) CC C WNBB WNWN BBCC qV β β β =BC − =α qV BE −−qV BC − IR I R 0 () e 1 FIe F0()1 Ie R 0 () 1 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 28 Ebers Moll Model (Basic definition) IC IB saturation active region region V 0 CE The Ebers-Moll model describes both the active and the saturation regions of BJT operation.