ECE606: Solid State Devices Lecture 19 Bipolar Transistors Design

1 Klimeck – ECE606 Fall 2012 – notes adopted from Alam

Outline

1) Current gain in BJTs 2) Considerations for base doping 3) Considerations for collector doping 4) Intermediate Summary 5) Problems of classical transistor 6) Poly-Si emitter 7) Short base transport 8) High frequency response 9) Conclusions REF: SDF, Chapter 10

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 2 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

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

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 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 5

Gummel Plot and Output Characteristics

I β = C DC I B β Common emitter DC Current Gain

D Wn2 N VBE β ≈ n Ei, B E DC 2 WB D p n iE, N B

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 6 How to make a Good Silicon Transistor

For a given Emitter length ~1, same material primarily determined by bandgap D Wn2 N β ≈ n Ei, B E DC 2 WB D p n iE, N B

Make-Base short … (few mm in 1950s, 200 A now) Emitter doping higher Want high gradient of carrier density than Base doping

Base doping hard to control Emitter doping easier

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 7

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 8 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 9

Problem of Low Base Doping: Punch-through

N+ N

ε ε 2ks0 N C 2ks0 N E =() − =() − xp, BC Vbi V BC xp, BE Vbi V BE ()+ ()+ q NB N C N B q NB N E N B V is negative (reverse bias) VBE is positive (forward bias) BC => xp,BC grows Low base doping is not a good idea! Klimeck – ECE606 Fall 2012 – notes adopted from Alam 10 Problem of low Base -doping: Base Width Modulation Electrical base region is smaller than the metallurgical region! 2 D WnE i, B N β ≈ n E DC − − 2 WB x pB, xDn pc , p i, E N B NE

2kε N N x=s0 E () V − V C p, BE ()+ bi BE q NB N E N B

2kε N x=s0 C () V − V p, BC ()+ bi BC q NB N C N B + N N P

Gain depends on collector voltage (bad ) … Depletion region width modulation Klimeck – ECE606 Fall 2012 – notes adopted from Alam 11

The Early Voltage

IC In practice Device Pioneer Jim Early Ideally

VBC VBC about 1V VA VA ideally infinity • The collector current depends on VCE :

• For a fixed value of VBE , as VCE increases, the reverse bias on the collector-base junction increases, hence the width of the depletion region increases. − The quasi-neutral base width decreases collector current increases .

collector current increases with increasing VCE , for a fixed value of VBE . Gain depends on collector voltage (bad ) … Depletion region width modulation Klimeck – ECE606 Fall 2012 – notes adopted from Alam 12 The Early Voltage

IC In practice Device Pioneer Jim Early Ideally

VBC VBC about 1V VA VA ideally infinity • The Early voltage is obtained by drawing a line tangential to the transistor I-V characteristic at the point of interest. • The Early voltage equals the horizontal distance between the point chosen on the I-V characteristics and the intersection between the tangential line and the horizontal axis. • Early voltage is indicated on the figure by the horizontal dotted line

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 13

Problem of Low Base-doping: Early Voltage

IC In practice Device Pioneer Jim Early Ideally

VBC VBC about 1V VA VA ideally infinity dI I I C= C ≈ C + dVBC V BC V A V A

2 D Wni, B N β ≈ n E E DC − − 2 WB xpB. xDn pC . p iE , N B

2 2 qD niB, qD n iB, =−n (/)qVBE kT −+n (/) qVBC kT − In,C ( e 1)( e 1 ) WB 'NB W B ' NB Klimeck – ECE606 Fall 2012 – notes adopted from Alam Punch-through and Early Voltage

dI I I C= C ≈ C + dVBC V BC V A V A

CCB IC I C dI dI d (qN W ) − ≈ C= C B B qN W V () B B A dVBC dqN B W B dV BC qN W 1 dI   dQ  ⇒ V = − B B → ∞ = C  B  A CCB qN B dWB   dV BC  I  = − 1 C   CCB qNB WB  Need higher N B and WB or …

2 2 ξ  ζ qDniB,β qD n iB , β dI d =nqV BE −+ n qV BC − C = = − IC () e1() e 1   2 WN WN dWB dW BB W  W B ξBB BB I = = − C WB W Klimeck – ECE606 Fall 2012 – notes adopted from Alam B 15

Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 16 Collector Doping

D Wn2 N β ≈ n Ei, B E − − 2 WB x pB, x pC , DnN piE , B

NE qN W κ ε = − B B = s 0 VA C NB C CB + CB xnC, x pB ,

NC Base-Collector in reverse bias ⇒Majority carriers only ⇒No diffusion capacitance ⇒Reduce capacitance

+ ⇒Increase xnC N N P If you want low base doping then reduce collector doping even more to increase Collector depletion….. Klimeck – ECE606 Fall 2012 – notes adopted from Alam 17

… but (!) Kirk Effect and Base Pushout

n-Collector p-Base p-Base n-Collector n+ n+ = υ Nc Nc JC q sat n + x x Additional charge! Space-Charge Density Space-Charge Space-Charge Density Space-Charge - Can be large NB NB compared to low C WB WC WB W doping = ( +) =( − ) NxBB Nx CC NB nx B' N C nx C ' q q −=()() ++−2 2  − =2 + 2  VVbiBC Nnx B B' Nnx C C '  VVbi BC NxNx B B C C  2κ ε 2κ ε s 0 s 0 n J 1+ 1+ C N qυ N x' = xB = x sat B C Cn C J 1− 1 − C υ NC q sat N C Klimeck – ECE606 Fall 2012 – notes adopted from Alam 18 Kirk Effect and Base Pushout

n+ p n n+ emitter base collector

n+ p-Base n-Collector n+ p-Base n-Collector p-Base n-Collector n+ Nc Nc x x x Space-Charge Density Space-Charge Space-Charge Space-Charge WCI nc-Nc NB NB B WS C WB WC WB WC WB WC E

⇒Increase ⇒Junction lost bias & current ⇒High current dominates Klimeck – ECE606 Fall 2012 – notes adopted from Alam collector doping 19

Kirk Effect and Base Pushout

J 1+ C qυ N x' = x sat B C C J 1− C υ qsat N C

=υ ≡ JCcrit, qN sat C J K

Can not reduce collector doping arbitrarily without causing base pushout

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 20 Kirk Effect

The Kirk effect occurs at high current densities in a bipolar transistor. The effect is due to the charge density associated with the current passing through the base-collector region. As this charge density exceeds the charge density in the depletion region the depletion region ceases to exist. Instead, there will be a build-up of majority carriers from the base in the base-collector depletion region. The dipole formed by the positively and negatively charged ionized donors and acceptors is pushed into the collector and replaced by positively charged ionized donors and a negatively charged electron accumulation layer, which is referred to as base push out. This effect occurs if the charge density associated with the current is larger than the ionized impurity density in the base-collector depletion region. Assuming full ionization, this translates into the following condition on the collector current density.

Key point : Under high current and low collector doping the depletion approximation is invalid in the C-B junction!

Klimeck – ECE606 Fall 2012 – notes adopted from Alam

Perhaps High Doping in Emitter?

2 − D W n N Eg ,B / kT n E i, B E DW N N e N −∆ E/ kT N β ≈ = nE C V E ≈ g E 2 −E / kT e WB D p n iE, N B g, E WB D pNCN V e N B NB

Very high doping can narrow the bandgap of a semiconductor!

If the emitter is extremely highly doped, then the bandgap in the emitter may be smaller than the base

=> Reduction in gain

Band-gap narrowing reduces gain significantly …

22 Klimeck – ECE606 Fall 2012 – notes adopted from Alam Perhaps High Doping in Emitter?

(Easki-like) Tunneling cause loss of base control …

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 23

Intermediate Summary

While basic transistor operation is simple, its optimum design is not.

In general, good transistor gain requires that the emitter doping be larger than base doping, which in turn should be larger than collector doping.

If the base doping is too low, however, the transistor suffers from current crowding, Early effects. If the collector doping is too low, then we have Kirk effect (base push out) with reduced high-frequency operation and if the emitter doping is too high then the gain is reduced.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 24 Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 25

Doping for Gain

Emitter doping: As high as possible without band gap narrowing D Wn2 N β ≈ n Ei, B E Base doping: As low as possible, without dc 2 WB D p n iE, N B current crowding, Early effect

Collector doping: Lower than base doping without Kirk Effect NE Base Width: As thin as possible without NB punch through

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 26 How to make better Transistor

D Wn2 N β ≈ n Ei, B E 2 WB D p n iE, N B

Graded Base transport

Polysilicon Emitter Classical Shockley Transistor

Hetero-junction Bipolar Transistor

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 27

Poly-silicon Emitter

Base Emitter Collector

N+N+ N- P+ N+ N SiGe intrinsic base P- Dielectric trench

emitter + N N P

Poly-silicon

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 28 Poly-silicon Emitter

2 qD ni, B β =n ≡qV BE − In, E nn 1 1 () e 1 poly WB N B + P N

p υ × vs Infinite at metal 1 s DpW E p2 I =−qυ p =− qp Finite at poly v p,, E p ol y s 2 1 +υ s Dp W E s I = − q(D W ) p WE p,E , si p E 1 p − p I υ I=− qD 1 2 =− q υ p p, E , poly = s p, E , pol y p W s 2 +υ E I p, E , si Dp WE s p D W Question: Why does poly only suppress 2 = p E +υ the hole current, not electron current? p1 DpW E s Ans. Polysilicon is not a ohmic contact and acts as rectifying contact. It blocks the easy passage of holes but lets electron29 s Klimeck – ECE606 Fall 2012 – notes adopted from Alam pass through

Gain in Poly-silicon Transistor

υ × D W I= −q p s p E = I p,, E poly 1+υ p ,, B pol y Dp WE s = − I p,E , si q(Dp WE ) p 1

Iυ I p, B , poly= s ≃ B , poly +υ Ip, B , s iDp WE s I B , s i

I I  I  D Wn2 N  D W +υ  β =C = C  × B, si  ≈n Ei, B E  × p E s  poly   2  υ IB, polyI B, si   I B , poly  WB D p n iE, N B  s 

D n2 N 1 →ni, B E ×(∵υ << D W ) 2 υ s p E WB n i, E N B s Poly suppresses base current, increases gain … Klimeck – ECE606 Fall 2012 – notes adopted from Alam 30 Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 31

How to make better Transistor

DWn2 N D n 2 N 1 β ≈nEiE, E → n iB , E × 2 2 υ WDnBpiB, N B Wn BiE , N B s

Polysilicon Emitter

Graded Base transport Classical Shockley transistor

Heterojunction bipolar transistor

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 32 Short-base Quasi-ballistic Transistor

n − n =−1 2 =− υ In,E qDn q th n2 WB

n D W I υ 2 = n B n, E , ballistic = th +υ +υ n1 Dn W B th In, E , s i Dn WB th

n1 n2 ∆n υ th + P N

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 33

Gain in short-base Poly-silicon Transistor

Iυ I I υ p, B , poly= s ≃ B , poly n, E , ballistic = th +υ +υ Ip, B , s iDp WE s I B , s i In, E , s i D n W B th

I I  II    β =C, ballistic = C , ballistic ×× C ,, si B si poly, ballistic      IBpoly, I Csi ,  II Bsi ,,   Bpoly 

υ  D Wn2 N  D W +υ  ≈th ×n Ei, B E  × p E s +υ  2 υ  DWnBth   WDnN BpiE, B  s  Assume small v Compared to 2 υ s ni, B N → ×E × th vs Assume small diffusion velocity 2 υ ni, E N B s Large devices, dinite diffusion length => small diffusion velocity => thermal velocity is large => neglect diffusion velocity Quasi-Ballistic transport in very short base limits the gain … Klimeck – ECE606 Fall 2012 – notes adopted from Alam 34 Outline

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 35

Topic Map

Equilibrium DC Small Large Circuits signal Signal Diode

Schottky

BJT/HBT

MOS

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 36 Small Signal Response

β log10

P+ IC B IB ω β() ω ≈ β β N VEC DC (out) ω VE P B (in)

E E 1 log10 f

fβ fT

Desire high f 1 W2 W  kT T =++B BC  B C + C  ⇒High IC π υ j, BC j , BE  ⇒ 2fT 2 D n 2 sat  qI C Low capacitances ⇒Low widths

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 37

Frequency Response

The gain of an amplifier is affected by the capacitance associated with its circuit. This capacitance reduces the gain in both the low and high frequency ranges of operation. The reduction of gain in the low frequency band is due to the coupling and bypass capacitors selected. They are essentially short circuits in the mid and high bands. The reduction of gain in the high frequency band is due to the internal capacitance of the amplifying device, e.g., BJT, FET, etc. This capacitance is represented by capacitors in the small signal equivalent circuit for these devices. They are essentially open circuits in the low and mid bands. Klimeck – ECE606 Fall 2012 – notes adopted from Alam 38 Small Signal Response (Common Emitter) From Ebers Moll Model DC Circuit => AC small signal Circuit Cµ BC In reverse bias, I R=0

Cµ C I IC B IB IR α− α P+ IC FFI RR I B IB N VEC Cπ r Cπ πππ g V VEB P (out) (1−α ) I m BE (in) F F

E E IE ( −α )  1 dI d 1 FI F q I 1 qI = B =  = B = C β rπ dVBE dVBE k B T DCk B T I= I( e qVBE / kT − 1) d(α I ) qI F F 0 =F F = C gm dVBEk B T δ(α ) = δ = υ FI F gm V B E gm BE

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 39

Short Circuit Current Gain

υ + ω υ i g j Cµ β (f ) =C = m BE CB C i   B µ C B 1 υ+ ωυ + ω υ BEj Cπ BE  j C µ BC rπ 

rπ Cπ υ g g − jω Cµ g m BE β (f ) ≡1 =m T ≈ m T   jω () C+ C 1 +ω + ω T π µ jT Cπ  j C µ E rπ 

1 1 Cπ+ C µ kT kT ≡= =B ()CC ++B () CC + ω π jBC,, j BE dB ,,C d BE T 2 fT gmqI C qI C k TC dQ B =d, BC = B Cd, BC qIC dIdV C BE dI C

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 40 Base Transit Time

Ref. Charge control model ∆n n1 + P N

1 q nW 2 dQ Q 1 B W Base B= B =2 = B dI I n 2D transit time C C q 1 n WB

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 43

Collector Transit Time

Electrons injected into collector depletion region – very high fields more than diffusion => drift => acceleration of carriers Charge imaged in collector + P N W τ = BC ? υ sat

i τ t

q τ W 1 τ = = = BC ×i ×τ = q eff, BC υ 2 i 2 2 sat Klimeck – ECE606 Fall 2012 – notes adopted from Alam 44 Putting the Terms Together

Collector transit time Kirk Current log 10 fT Base transit time

1 W2 W  =B + BC + π υ  2fT 2 D n 2 sat  k T B +  Cj, BC C j , BE  qI C log I I K 10 C Junction charging time

Do you see the motivation to reduce WB and W BC as much as possible? What problem would you face if you push this too far ?

Increasing I C too high reduces W BC and increases the overall capacitance => frequency rolls off…. Klimeck – ECE606 Fall 2012 – notes adopted from Alam 45

High Frequency Metrics

(current-gain cutoff frequency, fT) 1 W2 W kTq τ = =B + BC + B ()C+ C + ()R + R C π υ jBE, jBC , ex c cb 2fT 2 D n 2 satI C

(power-gain cutoff frequency, fmax ) f f = T max π 8 RbbCcbi

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 46 Summary

We have discussed various modifications of the classical BJTs and explained why improvement of performance has become so difficult in recent years.

The small signal analysis illustrates the importance of reduced junction capacitance, resistances, and transit times.

Classical homojunctions BJTs can only go so far, further improvement is possible with heterojunction bipolar transistors.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 47