ECE606: Solid State Devices Lecture 18 Bipolar Transistors A

Home , Depletion region, Gain (electronics), Leakage (electronics), Schottky barrier

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

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

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

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

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.

> 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

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

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.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 29

Gummel Plot and Output Characteristics

• The simultaneous plot of collector and base current vs. the base-emitter voltage on a semi-logarithmic scale is known as a Gummel Plot.

• This plot is extremely useful in device characterization because it reflects on the quality of the emitter-base junction while the base-collector bias is kept at a constant.

• A number of other device parameters can be ascertained either quantitatively or qualitatively directly from the Gummel plot because of its semi-logarithmic nature − For example the d.c gain β, base and collector ideality factors, series resistances and leakage currents.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 30 Gummel Plot and Output Characteristics

2 2 I qDniB, qD n iB , C ≃ −n(eqVBE / kT −+ 1) n ( e qVBC / kT − 1) AWNBB WN BB

2 I qD p ni, E B =(eqVBE / kT − 1) A WE N E

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

VBE Klimeck – ECE606 Fall 2012 – notes adopted from Alam 31

Current Gain C

Common Emitter current gain .. P+ IC B IB I N β = C DC VEB P I B (in) qDn2 qD n 2 niB,(eqVBE / kT − 1) + n iB , ( e (qVBC / kT ) − 1) E E WN WN D Wn2 N = BB BB ≈ n Ei, B E qD n2 W D n2 N n i, E (eqVBE / kT − 1) B p iE, B WE N E Will examine

C Common Base current gain .. E P+ N P

C I α IE I VCB C IC I C DC VEB α = β = = = (out) DC I DC − −α (in) E IB I E I C 1 DC DC transfer gain B B Properties are related – (transistor did not change ☺) Klimeck – ECE606 Fall 2012 – notes adopted from Alam 32 Current Gain

D Wn2 N β ≈ n Ei, B E DC 2 WB D p n iE, N B =>roll-off Base current Base High High injection does not roll roll not does off collector current collector Klimeck – ECE606 Fall 2012 – notes adopted from Alam 33

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 34 Doping for Gain …

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

N+

NE P

NB N

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 35

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 what’s wrong with the previous recipe? 7) Considerations for collector doping 8) Conclusions

REF: SDF, Chapter 10 Klimeck – ECE606 Fall 2012 – notes adopted from Alam 36 Problem of Low Base Doping: Current Crowding

VBE Double diffused junction configuration: n+ p base Emitter doping must compensate / overcome the base n-collector doping V BE n+ Low doping in base => resistance along the current path => potential drop

2 => Determines the qD n β ∫ n i, B ()eqV 'BE (x ) −1 dx injection I JC ( xdx ) => Spatially β =C =∫ = WB N B 2 dependent I J( xdx ) qD n β B ∫ B p i, E qV'BE ( x ) ∫ ()e−1 dx => More current in WE N E the corners Klimeck – ECE606 Fall 2012 – notes adopted from Alam 37

Low Base Doping: Non-uniform Turn-on

Sketches from text book n+ p base

n-collector n+

Non-uniform current inefficient High current at the edge can cause burn-out E

B Interdigitated designs for almost all high power Klimeck – ECE606 Fall 2012 – notes adoptedtransistors from Alam (E-B distance minimized) 38 Low Base Doping: Current Crowding

n+ p base

n-collector

VBE n+

We talked about how low doping for the base enhances the current gain. But there is a potential downside to this approach

If the base doping is kept to small values, it will have a high resistance: Lesser ability to conduct means higher resistance

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 39

Low Base Doping: Current Crowding

n+ p base

n-collector

VBE n+

Non-zero base resistance results in a lateral potential difference under the emitter region For an n-p-n transistor as shown, the potential decreases from edge of the emitter towards the centre (the emitter is highly doped and can be considered an equipotential region)

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 40 Low Base Doping: Current Crowding

n+ p base

n-collector

VBE n+

The number of electrons injected from emitter to base is exponentially dependent on base-emitter voltage With the lateral drop in the voltage in the base between the edge and centre of emitter, more carriers will be injected at the edge than the emitter centre.

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 41

Low Base Doping: Current Crowding

Key facts: 1. Current crowding is due to 2D nature of BJTs 2. It is a function of the doping concentration 3. As doping concentration increases, resistivity decreases − Consequence: Current gain goes smaller Emitter current injection efficiency decreases

The larger current density near the emitter may cause localized heating and high injection effects

Possible Solution: Emitter widths are fabricated with an inter-digitated design Many narrow emitters connected in parallel to achieve the required emitter area

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 42 Low Base Doping: Non-uniform Turn-on

Sketches from text book n+ p base

n-collector n+

Non-uniform current inefficient High current at the edge can cause burn-out E

B Interdigitated designs for almost all high power Klimeck – ECE606 Fall 2012 – notes adoptedtransistors from Alam (E-B distance minimized) 43

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

Low base doping is not a good idea! Klimeck – ECE606 Fall 2012 – notes adopted from Alam 44 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 45

Problem of Low Base-doping: Early Voltage

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

2 2 qDniB, qDn iB, =−n (/)qVkTBE −+n (/) qVkTBC − In,C ( e 1)( e 1 ) WB 'NB W B ' NB

dI I I IC C= C ≈ C In practice + dVBC V BC V A V A Ideally VBC about 1V VA ideally infinity VBC Jim Early device pioneer VA Klimeck – ECE606 Fall 2012 – notes adopted from Alam 46 The Early Voltage PS1

IC In practice

Ideally

VBC

• 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 . Due to the Early effect, collector current increases with increasing

VCE , for a fixed value of VBE . Klimeck – ECE606 Fall 2012 – notes adopted from Alam 47

The Early Voltage PS2

IC In practice

Ideally

VBC

VA • 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 48 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 49

Outline

REF: SDF, Chapter 10

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 50 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 51

… 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 52 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 53

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 54 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?

Band-gap narrowing reduces gain significantly …

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

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

Klimeck – ECE606 Fall 2012 – notes adopted from Alam 56 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 57