lecture 14: bipolar junction...

Department of EECS University of California, Berkeley

EECS 105 Fall 2003, Lecture 14

Lecture 14:

Bipolar Junction Transistors

Prof. Niknejad

Department of EECS University of California, Berkeley

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

Department of EECS University of California, Berkeley

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

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≈ =

Department of EECS University of California, Berkeley

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

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= ≈

Department of EECS University of California, Berkeley

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

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=

Department of EECS University of California, Berkeley

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

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≈

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

BJT Layout

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

Department of EECS University of California, Berkeley

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

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=

Department of EECS University of California, Berkeley

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

BJT Collector Characteristic

� Ground emitter

� Fix VCE

� Drive base with fixed current IB

� Measure the collector current

Department of EECS University of California, Berkeley

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

Collector Characteristics (IB)

Forward ActiveRegion

(Very High Output Resistance)

Saturation Region (Low Output Resistance)

Reverse Active(Crappy Transistor)

Breakdown

Linear Increase

Department of EECS University of California, Berkeley

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

Base-Emitter Voltage Control

Exponential Increase

Forward ActiveRegion

(High Output Resistance)

Reverse Active(Crappy Transistor)

Saturation Region (Low Output Resistance)

~0.3V

Breakdown

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

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

= = =−

Department of EECS University of California, Berkeley

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

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 ≈

Department of EECS University of California, Berkeley

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

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

=

Department of EECS University of California, Berkeley

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

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

= −

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

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=

Department of EECS University of California, Berkeley

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

Ebers-Moll Equivalent Circuit

Building blocks: diodes and I-controlled I sources

Department of EECS University of California, Berkeley

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

Forward Active Region

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

Typical Values:

0.7BEV =

0.2CEV >

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

Analogy from MOSFET s.s. model:

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

Department of EECS University of California, Berkeley

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

Transconductance gm

� The transconductance is analogous to diode conductance

Department of EECS University of California, Berkeley

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

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= =

Department of EECS University of California, Berkeley

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

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= = = × × × =

−

Department of EECS University of California, Berkeley

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

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∂ ∂ ∂

= =∂ ∂ ∂

Department of EECS University of California, Berkeley

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

Small Signal Current Gain

CF

B

i

iβ β∆= =

∆

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

Graphical Interpretation of ro

slope~1/ro

slope

Department of EECS University of California, Berkeley

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

BJT Small-Signal Model

Department of EECS University of California, Berkeley

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

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

Department of EECS University of California, Berkeley

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

Complete Small-Signal Model