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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