lecture 14: bipolar junction...

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 14

Lecture 14:

Bipolar Junction Transistors

Prof. Niknejad


EECS 105 Fall 2003, Lecture 14 Prof. A. Niknejad

Lecture Outline

� Diode Small Signal Model

� Diode Charge Storage (6.4.4)

� Diode Circuits

� The BJT (7.1)

� BJT Physics (7.2)

� BJT Ebers-Moll Equations (7.3)

� BJT Small-Signal Model



Diode Small Signal Model

� The I-V relation of a diode can be linearized

( )

1d d d dq V v qV qv

kT kT kTD D S SI i I e I e e

+ + = − ≈

1 dD D D

qvI i I

kT + ≈ + +

�

2 3

12! 3!

x x xe x= + + + +�

DD d d d

qIi v g v

kT≈ =



Diode Capacitance

� We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field. the capacitance in forward bias is given by

� But another charge storage mechanism comes into play in forward bias

� Minority carriers injected into p and n regions “stay” in each region for a while

� On average additional charge is stored in diode

01.4Sj j

dep

C A CX

ε= ≈



Charge Storage

� Increasing forward bias increases minority charge density

� By charge neutrality, the source voltage must supply equal and opposite charge

� A detailed analysis yields:

p side n side

-Wp Wn xn -xp

( )

0

d dq V v

kTnp e

+

0np0pn

( )

0

d dq V v

kTpn e

+

1

2d

d T

qIC

kTτ=

Time to cross junction(or minority carrier lifetime)

Extra chargeStored in diode

1

2d d TC g τ=



Ideal BJT Structure

� NPN or PNP sandwich (Two back-to-back diodes)

� How does current flow? Base is very thin.

� A good BJT satisfies the following

Base (P)

Collector (N)

Emitter (N)

CI

BI

EI−BEV

+

−

CEV

+

−Base (N)

Emitter (P)

Collector (P)

EI

BICI−

EBV

+

−ECV

+

−

C EI I≈ −

C BI I>>BEqV

kTC SI I e≈



Actual BJT Cross Section

� Vertical npn sandwich (pnp is usually a lateral structure)

� n+ buried layout is a low resistance contact to collector

� Base width determined by vertical distance between emitter diffusion and base diffusion



BJT Layout

� Emitter area most important layout parameter� Multi-finger device also possible for reduced base resistance



BJT Schematic Symbol

� Collector current is control by base current linearly

� Collector is controlled by base-emitter voltage exponentially

BI

EI−BEV

+

−

CEV

+

−BV

CV

EV

BEqV

kTC SI I e≈

C BI Iβ=



BJT Collector Characteristic

� Ground emitter

� Fix VCE

� Drive base with fixed current IB

� Measure the collector current



Collector Characteristics (IB)

Forward ActiveRegion

(Very High Output Resistance)

Saturation Region (Low Output Resistance)

Reverse Active(Crappy Transistor)

Breakdown

Linear Increase



Base-Emitter Voltage Control

Exponential Increase

Forward ActiveRegion

(High Output Resistance)

Reverse Active(Crappy Transistor)

Saturation Region (Low Output Resistance)

~0.3V

Breakdown



Transistor Action

� Base-emitter junction is forward biased and collector-base junction is reverse biased

� Electrons “emitted” into base much more than holes since the doping of emitter is much higher

� Magic: Most electrons cross the base junction and are swept into collector

� Why? Base width much smaller than diffusion length. Base-collector junction pulls electrons into collector

Base (p)

Emitter (n+)

Collector (n)

0BEV

+>

−

0CBV

+>

−

e

he h h

recombination



Diffusion Currents

� Minority carriers in base form a uniform diffusion current. Since emitter doping is higher, this current swamps out the current portion due to the minority carriers injected from base



BJT Currents

C F EI Iα= −

Collector current is nearly identical to the (magnitude)of the emitter current … define

Kirchhoff: E C BI I I− = +

DC Current Gain:

( )C F E F B CI I I Iα α= − = +

1F

C B F BF

I I Iα β

α= =

−

.999Fα =

.999999

1 .001F

FF

αβα

= = =−



Origin of αF

Base-emitter junction: some reverse injection of holes into the emitter � base current isn’t zero

E B C

Typical:

Some electrons lost due to recombination

.99Fα ≈ 100Fβ ≈



Collector Current

Diffusion of electrons across base results in

0BEqV

p n pBdiff kTn n

B

dn qD nJ qD e

dx W

= =

BEqV

kTC SI I e=

0n pB ES

B

qD n AI

W

=



Base Current

Diffusion of holes across emitter results in

0 1BEqV

p nEdiff nE kTp p

E

qD pdpJ qD e

dx W

= − = −

0 1BEqV

p nE E kTB

E

qD p AI e

W

= −



Current Gain

0

0

n pBo E

pBBC n EF

p nEo EB p nE B

E

qD n A

nWI D WqD p AI D p W

W

β

= = =

2

0 , ,2

0 ,

,

i

pB A B D E

inE A B

D E

nn N N

np NN

= =

Minimize base width

Maximize doping in emitter



Ebers-Moll Equations

Exp. 6: measure E-M parametersDerivation: Write emitter and collector currents in terms

of internal currents at two junctions

( ) ( )/ /1 1BE th BC thV V V VE ES R CSI I e I eα= − − + −

( ) ( )/ /1 1BE th BC thV V V VC F ES CSI I e I eα= − − −

F ES R CSI Iα α=



Ebers-Moll Equivalent Circuit

Building blocks: diodes and I-controlled I sources



Forward Active Region

B-C junction is not forward-biased � IR is very small

Typical Values:

0.7BEV =

0.2CEV >



Simplified Ebers-Moll

Forward-Active Case:

Saturation: both diodes are forward-biases � batteries

0.7BEV = C F BI Iβ=

BIB C

E

CI

0.7BEV =

BIB C

E

0.1CEV =

CI



Analogy from MOSFET s.s. model:

( )BSDSGSD vvvfi ,,= ( )CEBEC vvfi ,=



Transconductance gm

� The transconductance is analogous to diode conductance



Transconductance (cont)

� Forward-active large-signal current:

/ (1 )BE thv VC S CE Ai I e v V= +

• Differentiating and evaluating at Q = (VBE, VCE )

/ (1 )BEqV kTCS CE A

BE Q

di qI e V V

dv kT= +

C Cm

BE Q

di qIg

dv kT= =



Comparison with MOSFET

� Typical bias point: drain/coll. current = 100 µA;

Select (W/L) = 8/1, µnCox = 100 µA/V2

� BJT:

� MOSFET:

100µ4mS

25mC

mth

Ig

V= = =

2 Dm

GS T

Ig

V V=

−

C Cm

th

qI Ig

kT V= =

22 2 100µ 8 100µ 400µD

m ox DGS T

I Wg C I S

V V Lµ= = = × × × =

−



BJT Base Currents

Unlike MOSFET, there is a DC current into thebase terminal of a bipolar transistor:

( ) / (1 )BEqV kTB C F S F CE thI I I e V Vβ β= = +

To find the change in base current due to changein base-emitter voltage:

1B B Cm

BE C BEQ QQ

i i ig

v i v β∂ ∂ ∂

= =∂ ∂ ∂



Small Signal Current Gain

CF

B

i

iβ β∆= =

∆



Input Resistance rπ

( ) 1 1 C mB

BE BEQ Q

i gir

v vπ β β− ∂∂= = =

∂ ∂

In practice, the DC current gain βF and the small-signalcurrent gain βo are both highly variable (+/- 25%)

Typical bias point: DC collector current = 100 µA



Output Resistance ro

Why does current increase slightly with increasing vCE?

Model: math is a mess, so introduce the Early voltage

)1(/ACE

VvSC VveIi thBE +=

Base (p)

Emitter (n+)

Collector (n)

BW



Graphical Interpretation of ro

slope~1/ro

slope



BJT Small-Signal Model



BJT Capacitances

Base-charging capacitance Cb: due to minority carrier charge storage (mostly electrons in the base)

Fmb gC τ=

Base-emitter depletion capacitance: CjE= 1.4 CjEo

Total B-E capacitance: Cπ = CjE + Cb



Complete Small-Signal Model

lecture 14: bipolar junction...

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