Modern Electronics: F3 Bipolar transistor 1

Bipolar Junction Transistors (BJT)

Ideal Transistor

Bipolar Transistor - Terminals

NPN Bipolar Transistor Physics

Large Signal Model

Early Effect

Small Signal ModelReading: (Sedra, Smith, 7th edition)

4.1 - 4.2

6.2.2 (small signal model)

9.2.2 small signal model with

capcitances

Modern Electronics: F3 Bipolar transistor 2

Ideal Transistor - characteristics

Iin Iout

Vin

+

-

Vout

Vout

Iout

kVin

Increasing Vin

Iout independent of Vout!Iin independent of Vout!

Two main transistor types:

Bipolar Transistors (Power

Amplifiers, HighSpeed AD/DA

converters)

Field Effect Transistors (99.999% -

mainly integrated circuits / digital)

current source controlled by a voltage (Vin)

Modern Electronics: F3 Bipolar transistor 3

Bipolar Transistor - npn

Sign convention: Vxy=Vx-Vy

Emitter

Collector

Base

+

-

VBE

VBC

+

-

VCE

+

-

IB

IC

IE

IB – base current

IC – collector current

IE – emitter Current = -(IC+IB)

Modern Electronics: F3 Bipolar transistor 4

Bipolar Transistor - npn in active mode

NEmitter

PBase

NCollector

+-

VBE >0

Forward biased PN junction

VBC <0

Reverse biased PN junction

- +

npn

Modern Electronics: F3 Bipolar transistor

Bipolar transistor: band structure

5

EFneVBE

n=npo×exp(VBE/VT)n ≈ 0

N P N

E B C

Forward biased emitter-base junction injects electrons

Reverse biased base-collector junction sweeps away electrons (independent of VBC)

IC

IB

Modern Electronics: F3 Bipolar transistor

Operating modes

6

N P

N

emitter base collector

Unbiased CutoffEBJ: reverse / CBJ: reverse

ActiveEBJ: forward / CBJ: reverse

SaturationEBJ: forward / CBJ: forward

Modern Electronics: F3 Bipolar transistor

Electron diffusion currents – active mode

7

IC

VCE

Increasing VCE

Incre

asin

g V

BE

Modern Electronics: F3 Bipolar transistor

Currents in active mode

8

NEmitter

PBase

NCollector

+-

VBE >0 VBC <0

- +IC

IB1IB2

IE

IB

IE + IB1 + IB2 + IC = 0

On whiteboard: calculate IC, IB1, IB2 and the gain β

Modern Electronics: F3 Bipolar transistor 9

Large Signal Model – active mode

base collector

emitter

bFIB

IB IC

0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

Vce

(V)

Kolle

kto

rstr

öm

(A

)I C

(A)

VBE < 0.6VVBE > 0.6V

VBC < 0.4V

VCE < VBR

β : current gain

Active

Satu

rati

on

Increasing VBE (IB)

cutoff

F

CB

V

V

SC

II

eII T

BE

b

Modern Electronics: F3 Bipolar transistor 10

Example – typical Si NPN Transistor

NEmitter

PBase

NCollector

ND=1×1019 cm-3 (emitter doping)Dp=1 cm2/s (hole diffusion constant)Lp=0.5µm (diffusion length)

NA=2×1017 cm-3 (base doping)Dn=15 cm2/s (electron diffusion constant)τb=1 µs (minority carrier lifetime)

WB=0.5µm

Area: 200µm2

Calculate b and IS

Modern Electronics: F3 Bipolar transistor

2 min excersise – Early effect (4.2.3)

11

x

np(x

), p

n(x

)

N

emitter

P

base

N

collector

Ideally IC should not increase with VCE, however the width of a pn-junctiondepends on applied voltage!

1. How does the base-collector depletion region change for increasing VCE?2. Sketch the minority carrier distribution in the base with VCE applied?3. How does IC change with VCE in this case?

Modern Electronics: F3 Bipolar transistor 12

Large Signal Model – Early Effect (4.2.3)

basecollector

emitter

bFIB

IBIC

0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

0.12

Vce

(V)

Kolle

kto

rstr

öm

(A

)I C

(A)

F

V

V

A

CES

F

CB

V

V

A

CESC

T

BE

T

BE

eV

VI

II

eV

VII

bb

1

1

VA – Early voltage

15-100V

Modern Electronics: F3 Bipolar transistor 13

Small Signals– Taylor Expansion

...)(

)()(

0

00

xdx

xdfxfxxf

xx

1st order Taylor expansion - linearization

0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

0.12

Vce

(V)

Kolle

kto

rstr

öm

(A

)I C

(A)

t

=+

vBE (t)VBE

vbe (t)

E

B C

VCE

VBE

vbe(t)

iC(t)=IC+ic(t)

iB(t)=IB+ib(t)

VCE (V)

t

=+

iC (t)ICic (t)

vBE(t)=VBE+vbe(t)

ceCECceCEC

bemBECbeBEC

vr

VIvVI

vgVIvVI

0

1

iC

iC

iC

iC

Modern Electronics: F3 Bipolar transistor

capacitances: Cµ, Cje, Cde (9.2.2 (partially))

14

emitter base collector

Cje Cµ

Cje, Cµ : junction capacitances (small).

Cde : diffusion (base charging) capacitance (only forward biased pn-junction). Change in VBE

give change in charge in base (Qn) -> capacitance

Capacitances become important for high-frequencies

Cde

WB

τF: base transit time, average time for a carrier to cross base

τF = WB2/2Dn

x

n

WB

VBE

dQn

VBE+dVBE

np0

𝐶𝑑𝑒 =𝑑𝑄𝑛𝑑𝑣𝐵𝐸

= 𝜏𝐹𝑑𝑖𝐶𝑑𝑣𝐵𝐸

= 𝜏𝐹𝑔𝑚

Modern Electronics: F3 Bipolar transistor 15

(simple) small Signal Model – Active Mode

Transconductance – controls the current source

Input resistance – IB change with VBE

Output resistance – Early effect

Diffusion (base charging) capacitance –forward biased BE junction

+

-

v1rp Cde

r0gmv1

B

E

C

Remember:VT=kT/q

𝐶𝑑𝑒 = 𝜏𝐹𝑔𝑚mFb

Tm

A

C

A

m

F

T

C

m

gC

Vg

V

I

Vr

gr

V

Ig

bp

0

Modern Electronics: F3 Bipolar transistor 16

Example – low f model

rp r0gmv1

+

-

v1

A BJT is biased so that IC=5mA.Low frequency -> capacitances are “open circuit”

Parameters:β= 500VA = 100 VVT = 25.9 mV

Calculate IB and the corresponding small signal model.

ICIB

Modern Electronics: F3 Bipolar transistor 17

Small Signal Model – more advanced

rp

Cp

r0

Cµ

gmv1

rx

- Add junction capacitances Cµ (BC junction) and Cje (BE junction).

- Sum capacitances Cπ=Cje+Cde.

- Add series resistances in base (rx).

Cje Cde+

-

v1

rx, Cje and Cµ: Depends on exact transistor geometry.

B

E

C

Modern Electronics: F3 Bipolar transistor

Summary - BJTs

• NPN or PNP. NPN is faster due to higher electron mobility

• Active mode (used for amplifiers):

– Emitter-base junction is forward biased (injects minority carriers into base)

– Collector-base junction is reverse biased (removes minority carriers from base)

• Early effect: increasing VCE extends the collector-base depletion region narrowing the base resulting in a higher diffusion current IC.

• Small signal model:

– Input resistance (rπ) due change in base current (IB) when changing VBE.

– Output resistance (r0) due to Early effect.

– Base charging capacitance (Cde) due to change in charge in base region when changing VBE.

– Can add more capacitances and resistances to get more accurate (and complicated) model.

18

Modern Electronics: F3 Bipolar transistor 19

State-of-the Art: SiGe Bipolar Transistor

Emitter

Base

Collector

VBR ~ 1.5VVce,sat ~ 0.3VbF ~ 600

ft=300 GHz

- Vertical device

- Not symmetric – high emitter doping, lower in collector

- Heterostructure with graded Eg to enable high dopning in base (low resistance) without backinjection into emitter.