1 Bipolar Junction Transistor Models Professor K.N.Bhat Center for Excellence in Nanoelectronics ECE Department Indian Institute of Science Bangalore-560.

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Bipolar Junction Transistor Models

Professor K.N.Bhat

Center for Excellence in Nanoelectronics

ECE Department

Indian Institute of Science

Bangalore-560 012

Email: [email protected]

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Bipolar Junction Transistor Modeling

Topics for presentation:

• Merits of BJT

•BJT types and structures

•Current components ,current gain and breakdown voltage

•Ebers –Moll model for BJT and Breakdown voltage

•BJT with non uniform base region doping

•Cut off frequency and effect of base spreading resistance

•Heterojunction Bipolar Transistor and models

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FETs BJTs

Cut-Off Freq and Transit time

Threshold Voltage

Channel Lengthdependent

Base Width dependent

Strongly depends upon doping concentration and thickness of the channel layer

Practically constant (diode cut in voltage) and depends on

the Eg of the

semiconductor

Parameter

ComparativeComparative Merits of FETs and BJTs Merits of FETs and BJTs

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Comparative Merits of FETs and BJTsComparative Merits of FETs and BJTs

FETs BJTsCharge Storage Effects

Trans- Conductance

gm

Minimum – Device is basically fast

charge storage reduces Switching Speed

Depends on

(VGS- VTh), µn,

W, Cox or Cs

and L

Highest in BJT per unit area. Depends upon collector current which exponentially depends on VBE/VT

Parameter

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BJT types

•Alloy Junction – Uniform base (germanium and silicon transistors)

•Planar Junction Transistor-graded base (Silicon transistors)

•Heterojunction Bipolar Transistor-Uniform base and graded base (Transistors using Compound semiconductors- Silicon/ silicon Germanium , AlGaAs/ GaAs)

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Alloy Junction Transistor

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Planar Junction diode

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Planar Junction Transistor

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Monolithic Transistors without Isolation

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BJT in Integrated Circuit with Isolation

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Bipolar Junction Transistor (Uniformly doped regions) Current Components

WE

C pC co

T pE co

T E co

E co

I I I

I I

I I

I I

( )

T is base transport factor

is Emitter efficiency

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Carrier Density Distribution (BJT biased in Active region) E TV V

eo np p e /

E TV Veo pen n e /

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Common Base Characteristics

C E coI I I

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Common Emitter Characteristics

C B coI I I( 1) Change due to Early effect

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Base width Modulation (Early Effect)

Output resistance is reduced

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E T

B ne rec neV V

ne pene eoe e

E E

I I I I

qD n eqD na a

W W

/

E TV Vpb eo pb n

c pc e eqD p qD p e

I I a aW W

/

pb nb E pb i Db Ec

B ne pe ne i Ae

Aepb Ae E pb E

ne Db ne DbB

D p W D n N WI

I D n W D n N W

N dxD N W D

D N W D N dx

2

2

( / )

( / )

Current gain of narrow base transistors

High when total emitter doping is high

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Collector –Base Junction Breakdown Voltage , BVCBO

•Junction breakdown takes place when the carrier multiplication factor ‘M’ becomes infinite.

• ‘M’ depends upon the initiating carrier and is related to the applied voltage, V and the breakdown voltage BVCBO.

n

CBO

MV

BV

1

1

n=6 for PNP transistor

n=4 for NPN transistor

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Maximum sustaining voltage BVCES in the Common emitter configuration

C B coI I I( 1)

At VCES , IC tends to infinity. This is possible when tends to infinity because in CE mode IB is constant

,1

when, 1

T M M0( )

CESAt V M0, 1

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n

CBO

VM gives

M BV0 01

1 , 1

n CBOCES CBO n

BVV BV 1/

0 1/(1 )

(1 )

In high Voltage transistors the is deliberately made small to achieve VCES as close to BVCBO as possible

n

CBO

V

BV 01

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Ebers –Moll Equations for BJT

Transistor Operating modes:

1.Normal mode -active , saturation and cut off .

2. Inverse mode – emitter as collector and collector as emitter

EBERS –MOLL model gives a set of equations encompassing all the four operating regions of operation in circuit simulations

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Transistor operating in Normal Mode or Forward active mode

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Transistor operating in Inverse Mode or Reverse active mode

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Transistor operating in Saturation Mode

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Ebers Moll Equations Valid for all combinations of VEB and VCB

Here we have

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E F I RI I I

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NPN-Transistor having Non-uniformly doped Base P-region (graded base )

Base Region

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The doping gradation gives rise to an electric field E(x) which arises to counter the diffusion of holes. E(x) aids the flow of electrons in the x direction

T A T

A

V dN VE x

N dx L( )

pp p p p

dpJ qp E qD

dx0, In thermal equilibrium

p p

p p

D dpE x

p dx

1( )

pT p A

p

D kTV p N

q,

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•Carrier transport is by drift and diffusion in Graded base transistor

•Velocity of carriers is three to four times higher compared to transistors with uniformly doped base region

•Transit time of carriers ,

•Cut off frequency,

•Smaller base width is required for higher cutoff frequency

tW

velocity

tt

velocity

W

1

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Base spreading resistance

depends upon base region doping concentration NA and base width W

bb br r in figure below' ( )

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For high speed, WB should be reduced . This increases rbb’

affecting the maximum operation

frequency, fm , at which power

gain is unity . fm is given byfTfm C rjc bb'

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Need for modifications in BJT

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Conflicting Requirements for fT and fm

•Cutoff frequency fT can be increased by

reducing base width ‘W’. This increases and lowers fm

•To improve fm , should be reduced

bbr '

bbr '

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r bb’ is the base spreading resistance and is

proportional to the sheet resistance which varies inversely as total integrated doping concentration (= NAW) in the base region.

NA should be increased when WB is reduced so

that rbb’ does not increase . It leads to

(1) increase in CTE , (2) reduction in β and (3) fall

in DnB

These conflicting requirements are met using an emitter region of wider band gap material. This BJT is the Heterojunction Bipolar Transistor (HBT)

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Heterojunction Bipolar Transistor (HBT)

n

E

p

n

n+ collector

GaAs

GaAs

AlGaAs B

C

n-AlGaAs / p-GaAs / n+GaAs HBT

First HBT in the history of BJT

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pb nb E pb ib Db Ec

B ne pe ne ie Ae

pb Ae E ib

ne Db ie

D p W D n N WI

I D n W D n N W

D N W n

D N W n

2

2

2

2

( / )

( / )

For PNP transistor we have seen

Similarly for NPN transistor , we have

c nb De E ib

B pe Ab ie

I D N W n

I D N W n

2

2

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2

nB DTE iB2

pE ATB iE

D N n;

D N n ATB A

Base

N N (x) dx

gB

gE

E kTnB DTE

E kTpE ATB

D N e

D N e

DTE DEmitter

N N (x) dx

g gE gBE E E

gE kTnB DTE

pE ATB

D Ne

D N

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gE kT 5gTypically , E 0.3eV , e 1.63 x 10

DTE nB

ATB pE

N D1When, and 2.5

N 200 D

512.5 x x 1.63 x 10 2038

200

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E

B

C

n-AlGaAs / p-GaAs / n+GaAs HBT

n=1018/cm3

N+GaAs substrate

0.5m GaAs collector

0.15m GaAs base P=1018/cm3

EmitterAlGaAs ND =5x1017/cm30.3m

GaAs0.2m n+ > 1018/cm3

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AlGaAs /GaAs /GaAs HBTs fabricated at BELL Labs showed the following:

•very low values of =30

• Higher values of were observed in Devices with

larger areas.•The increased from 30 t0 about 1800 when the surface of the base region was passivated by chemical treatment to saturate the dangling bonds with sulfur . But the values were unstable .

•Several approaches have been used to stabilize the . The most successful one has been chemical treatment with (NH4)2Sx and protect with PECVD silicon nitride

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n Si

p SiGe

n- Si

n+ Si

WB

• Band gap of Si1-xGex depends upon x.

• Strained layer Si1-xGex without

dislocations can be realized with thin layers of base

Silicon Germanium HBT (SiGe HBT)Silicon Germanium HBT (SiGe HBT)

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Strained Layer EpitaxyStrained Layer Epitaxyfor Lattice mismatched for Lattice mismatched materialsmaterials

Possible means of growing Possible means of growing lattice – mismatched materials.lattice – mismatched materials.

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Solid Line : Calculated thickness above which it becomes energetically favorable to form misfit dislocations in strained layer GeSi grown on Si

Points: experimental data for low temperature MBE growth.

Dashed Line : Trend calculated for simple model of kinetically limited defect formation

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Unstrained Gex Si1-x

Strained Gex Si1-x

on Unstrained

Gex/2 Si1-x/2

Strained Gex Si1-x

on Unstrained Si

Strained Si on

Unstrained Gex Si1-x

Calculations showing the diagrammatic effect of strain upon semiconductor band gaps

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Benefits of SiGe HBT over Si BJTBenefits of SiGe HBT over Si BJT

• Collector Currents IC is larger for a given VBE

BE TB

V VnB iBC W

A

qD ne

N x dx

2

0

gBE kT

iBn e2

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Benefits of SiGe HBT over Si BJT Benefits of SiGe HBT over Si BJT (Contd….)(Contd….)

• IC increase improves

• IC increase decreases the emitter charging time. This improves the switching speed.

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Effect of grading the band gap Effect of grading the band gap in the Base Regionin the Base Region

n p n

x0

Eg(0) Eg(x) Eg(WB)

WB

Eg(x) = Eg(0) - Eg(x)

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Electric Field due to bandgap gradation is

given by . For a linear gradation

g g g B g

B B

dE E E W E

dx W W

0

gdE

q dx

1

For = 0.15 eV and WB = 0.1 mElectric Field = 0.15/10-5 = 15 KV / cm

gE

Cut off frequencies up to 200GHz have been achieved

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Summary

• BJTs are still popular for achieving better driving capability particularly when the load is capacitive.

•Ebers Moll model enables us to estimate the currents for all modes of BJT operation.

•Base region can be reduced and doping concentration in the base can be increased with HBTs.

• Base region with graded doping and graded band gap lead to higher cut of frequencies due to reduction in transit time as a result of the built in electric field