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[email protected] # 7

SDM 2, Michael Shur 1999-2009

Beta and Alpha

RL

Vcc

~ ~ ~

Rs

vs

Vcc

vs

Rs

RL

RL

VccRs

vs

Common base Common emitter Common collector

Vbe

BJT configurations

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Current Gain Mechanism in CEConfiguration

Each extra hole attracts many electrons

because they are passing through the base

Base

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Common emitter short current gain

o =

DnNdeXe

DpNabW

Electron diffusion current in the base

In ~ Dn /(NabW)

Ip

~ Dp

/(Nde

Xb

)

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Diffusion equation forminority carriers in the base

Dn d2

nbdx2

nb nbonl

= 0

n = Aexpx

Lnb

+Bexp

x

Lnb

n = A +B + A B( ) xLnb

For W

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Diffusion equation again

n = A +B + A B( ) xLnb+ A +B( ) x

2

2Lnb2 + A B( ) x

3

6Lnb3

n = nbe 0( ) nbo[ ] 1xW

2Lnb2

+ x2

2Lnb2

+ x3

6Lnb3

x

Wnbe 0( )

R =2Lnb

2

W2 =

1

o+

1

R

1

=DpNabW

DnNdeXe+

W2

2Lnb2

1

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Common base current gain

=Ic

Ie

=Ic

Ine

Ine

Ie

T

Base transport factor

T = 1 W

2

2Lnb2

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Example

Estimate o and R for the following parameter values,typical for Si BJTs: Nde =10

19cm-3,Nab =2x1017cm-3, n

= 900 cm2/Vs, p = 300 cm2/Vs, W= 0.1 m,Xe = 0.4

m,Lnb = 10 m.

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Solution

o = 600, R = 20,000.

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I-V CharacteristicsCB ConfigurationE B C

Rc

n p n

Forward active mode:Collector current:

CB current gain:

Saturation mode:

Current drops off

owing to opposing

injected currents from

the junctions

Re

Vee Vcc

IcIe

Ib

cboec III +=

1 ec II

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Graded Base Transistors

Modern BJTs have a nonuniform doping in the base, with the

acceptor doping density decreasing towards the collector-basejunction. (Such transistors are called "graded base" transistors.)

The nonuniform doping leads to a non-uniform hole concentration

along the base. Hence, the holes diffuse from the emitter side

of the base toward the collector side of the base. This creates anexcess positive charge at the collector side of the base and an

excess negative charge at the emitter side of the base.

This, in turn, leads to a built-in electric field, which pushes minority

carriers (electrons) injected into the base toward the collector.

As a consequence, the minority carriers take less time to traverse

the base and their recombination is less effective.

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Alpha in graded base transistors

T = 1 W2

2fLnb2

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Alpha and beta

=

1, =

1+

and Ie

=Ic

+IbIc = Ie

Hence,Ie = Ie +Ib,

Divide byIe to obtain

1= + 1/( +1)

Ie

= Ib

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Base modulation

Weff = WXbe Xbc

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Emitter current crowding

Collector contact

n+n

p

n+

Base contact Base contactEmitter contact

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Realistic and idealized doping profiles

. .

0 0.8 1.6 2.4 3.2

Distance (m)

1021

1019

1017

1015

n+ p nConcentration(cm

-3

)

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Circuit diagram

Ib

Vce

+

+Vcc

IcRL

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1/)1(/ >>= bc II

I-V CharacteristicsCE Configuration

Forward active mode:

CE current gain:

Rc

E

B

C

VccRb

Vbb Ie

Ib

Ic

ceobc III +=

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Load line

0 2.0 4.0 6.0-1.0

400

0

600

200

1 A

2 A

3 A

4 A

5 A

Base

current

Collector-emitter voltage (V)

Active forwardSaturation

Cutoff

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I-V Characteristics (transistor NPN BCW82)

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AIMSpice

simulation

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References

I. GETREU, Modeling the Bipolar Transistor, Tektronix, Inc., part no. 062-2841-00 (1970)

K. LEE, M. SHUR, T. A. FJELDLY, AND T. YTTERDAL, Semiconductor DeviceModeling for VLSI, Prentice Hall, Englewood Cliffs, NJ (1993)

M. SHUR, Physics of Semiconductor Devices, Series in Solid State Physical

Electronics, Prentice Hall, Englewood Cliffs, NJ (1990)

S. M. SZE, Physics of Semiconductor Devices, Second Edition, John Wiley& Sons, New York (1981)

S. M. SZE, Semiconductor Devices. Physics and Technology, John Wiley &Sons, New York (1985)

R. M. WARNERAND B. L. GRUNG, Transistors Fundamentals for the Integrated-Circuit Engineer, John

Wiley & Sons, New York (1983)

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Bibliography

B. G. STREETMAN, Solid State Electronic Devices, Fifth Edition, PrenticeHall, Englewood Cliffs, NJ (1995)

Concise and clear undergraduate text on semiconductor devices.

G. W. NEUDECK, The Bipolar Junction Transistors, Addison WesleyModular Series on Solid State Devices, Vol. III, Reading, MA (1983)

Undergraduate text with many examples and problems.

S. K. GHANDHI, VLSI Fabrication Principles, John Wiley & Sons, NewYork (1983)

Detailed description of transistor fabrication technology.

P. M. ASBECK, M. F. CHANG, K. C. WANG AND D. L. MILLER,"Heterojunction Bipolar Transistor Technology," in Introduction toSemiconductor Technology. GaAs and Related Compounds, Cheng T. Wang,Editor, John Wiley & Sons, New York (1990)

good description of HBT technology and device characteristics.

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Summary

Electron concentrations at the boundariesof emitter-base and collector-basedepletion region

nbe = nbo exp Vbe/Vth( )nbc = nbo exp Vbc/Vth( )

Quasineutrality condition in base p n

07 bet alpha

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