EE105 – Fall 2014
Microelectronic Devices and Circuits
Prof. Ming C. Wu
wu@eecs.berkeley.edu
511 Sutardja Dai Hall (SDH)
Lecture 10: BJT Physics
1
NPN Bipolar Junction Transistor (BJT)
Forward
Bias
Hole
Flow
•  3 layers of semiconductors
–  Emitter (N-type), Base (P-type),
Collector (N-type)
Emitter (E)
–  B-E junction forward-biased
N
–  B-C junction reverse-biased
•  Two important criteria
–  Emitter more heavily doped than base
N Collector (C)
•  Much more electrons injected into
base than holes into emitter
–  Base very thin
•  Most electrons travel through
base and reach collector
Reverse
Bias
P Base (B)
Electron
Flow
Note: BJT is NOT 2 back-to-back
junction diodes.
Lecture 10: BJT Physics
•  Current gain
–  Small base current controls large
collector current
2
1
Physical Construction of BJT
•  The transistor is usually planar
–  All contacts are on the front
side
•  Emitter and base are created by
“ion implantation”
•  To facilitate electrons travel to
collector contact, an n+ buried
layer is usually employed to
reduce collector resistance.
•  Typical doping
–  NE > 1018 cm-3
–  NB ~ 1016 cm-3
–  NC ~ 1015 cm-3
Lecture 10: BJT Physics
3
npn Transistor
Forward Characteristics
Collector current:
(
!v $ +
iC = I S *exp # BE & −1" VT % ,
)
kT
VT =
(26mV at room temp)
q
I S : BJT saturation current
(note: different from pn junction's I S )
Base current:
iB =
iC
βF
! 1
$
i
Emitter current: iE = iB + iC = # +1& iC = C
αF
" βF %
β F : current gain (typical value: ~ 100)
αF =
Lecture 10: BJT Physics
βF
: typical value 0.95 to 0.99
β F +1
4
2
npn Transistor Reverse Characteristics
(Low Gain, Used Rarely in This Mode)
βR is the reverse common-emitter current
gain. βR is typically small, even smaller than
1, because the doping profile is optimized for
forward active gain.
Collector current iC is given by
iC = iB − iE =
Emitter current iE is
)
vBC &( ,.
−1
V ( .
$ T '€ .#
iE = −iR = IS ++exp%%
+*
αR is the reverse common-base current gain
αR =
Base current iB is given by
€
€
iB =
iR
βR
=
IS
βR
*
,
,
,+
I S * $ vBC ' ,exp&
) −1/
α R + % VT ( .
βR
β R +1
vBC &( -/
−1
V ( //.
$ T '
#
exp%%
Lecture 10: BJT Physics
5
npn Transistor
Complete Transport Model - Valid for Any Bias
(
!v $
! v $+ I (
!v $ +
iC = I S *exp # BE & − exp # BC &- − S *exp # BC & −1" VT %
" VT %, β R )
" VT % ,
)
(
!v $
! v $+ I (
!v $ +
iE = I S *exp # BE & − exp # BC &- + S *exp # BE & −1" VT %
" VT %, β F )
" VT % ,
)
!v $ + I (
!v $ +
I (
iB = S *exp # BE & −1- − S *exp # BC & −1β F ) " VT % , β R ) " VT % ,
First term in both emitter and collector current expressions gives
current transported completely across base region.
Symmetry exists between base-emitter and base-collector voltages in
establishing dominant current in bipolar transistor.
Lecture 10: BJT Physics
6
3
pnp Transistor Structure
•  Voltages vEB and vCB are positive when they forward bias
their respective pn junctions.
•  Collector current and base current exit transistor terminals
and emitter current enters the device.
Lecture 10: BJT Physics
7
pnp Transistor
Forward Characteristics
Collector current iC equals the
forward transport current is
(
!v $ +
iC = iF = I S *exp # EB & −1" VT % ,
)
Base current iB is given by
iB =
iC
βF
Emitter current iE is given by
iE = iC + iB =
Lecture 10: BJT Physics
iC
αF
8
4
Transport Model Circuit Representations
In npn transistor (expressions are analogous for pnp transistors),
the total current traversing base is modeled by a current source
given by:
(
"v %
" v %+
iT = iF − iR = I S *exp $ BE ' − exp $ BC '# VT &
# VT &,
)
Diode currents correspond directly to the two components of base
current.
iB =
!v $ + I (
!v $ +
IS (
*exp # BE & −1-− S *exp # BC & −1β F ) " VT % , β R ) " VT % ,
Lecture 10: BJT Physics
9
i-v Characteristics
Collect current
increases
exponentially
with VBE
•  Flat part of the i-v curves is
called “forward active” region.
Saturation
Collect current
increases
linearly with IB
•  The non-flat part is called
“saturation” region
•  Please note Saturation in BJT
and MOSFET refers to
opposite regions
Lecture 10: BJT Physics
Forward
Active
10
5
Operation Regions of Bipolar Transistors
Base-Emitter
Junction
Base-Collector Junction
Reverse Bias
Forward Bias
Reverse Bias
Lecture 10: BJT Physics
Forward Bias
Forward-Active
Saturation
Region
Region
(Good Amplifier) (Closed Switch)
Cutoff Region
(Open Switch)
Reverse-Active
Region
(Poor Amplifier)
Binary Logic
States
11
Example 1
•  Problem: Estimate transistor terminal currents and base-emitter
voltage
•  Given data: IS =10-16 A, αF = 0.95, VBC = VB - VC = -5 V, IE = 100 µA
•  Assumption: BJT in forward-active
•  Analysis:
I C = α F I E = 0.95 (100µ A) = 95 µ A
βF =
αF
0.95
=
= 19
1− α F 1− 0.95
I C 95µ A
=
= 5 µA
βF
19
"I %
VBE = VT ln $ C ' = 0.689 V
# IS &
IB =
Lecture 10: BJT Physics
12
6
Example 2
•
•
•
•
Problem: Estimate terminal currents and voltages
Given data: IS = 10-16 A, αF = 0.95, VC = +5 V, IB = 100 µA
Assumptions: BJT in forward active
Analysis:
βF =
αF
0.95
=
= 19
1− α F 1− 0.95
I C = β F I B = 19 (100µ A) = 1.90 mA
I E = ( β F +1) I B = 20 (100µ A) = 2.00 mA
"I %
" 1.9mA %
VBE = VT ln $ C ' = 0.025V ln $
' = 0.764 V
# 0.1 fA &
# IS &
VBC = VB −VC = VBE −VC = 0.764 − 5 = −4.24 V
Lecture 10: BJT Physics
13
Simplified Circuit Model
Forward-Active Region
•  Current in base-emitter diode is amplified by common-emitter
current gain βF and appears at collector; base and collector
currents are exponentially related to base-emitter voltage.
•  Base-emitter diode is replaced by constant voltage drop model (VBE
= 0.7 V) since it is forward-biased in forward-active region.
•  dc base and emitter voltages differ by 0.7-V diode voltage drop in
forward-active region.
Lecture 10: BJT Physics
14
7
Simplified Forward-Active Region Model
Example 3
•
•
•
•
Problem: Find transistor Q-point
Given data: βF = 50, βR = 1
Assumptions: Forward-active region of operation, VBE = 0.7 V
Analysis:
VBE + 8200I E −VEE = 0
9 − 0.7 V
= 1.01 mA
8200 Ω
I
1.01mA
IB = E =
= 19.8 µ A
β F +1
51
∴ IE =
I C = β F I B = 50 (19.8µ A) = 0.990 mA
VCE = VCC − I C RC − (−VBE )
VCE = 9 − 0.99mA ( 4.3K ) + 0.7 = 5.44 V
Forward-active region is correct.
Lecture 10: BJT Physics
15
Simplified Circuit Model
Saturation Region
•  In the saturation region, both junctions are forward-biased,
and the transistor operates with a small voltage between
collector and emitter. vCESAT is the saturation voltage for the
npn BJT.
!V $ I
!V $
!V $ I
!V $
I
I C = I S exp # BE & − S exp # BC &
I B = S exp # BE & + S exp # BC &
βF
" VT % α R
" VT %
" VT % β R
" VT %
(
+
IC
*! $ 1+ β +1 I 1
(
)
R
B
- for I B ≥ I C
VCESAT = VBE −VBC = VT ln *# &
*" α R % 1− I C
βF
*)
-,
β I
Simplified Model
F B
No simplified expressions exist for
terminal currents other than iC + iB = iE.
Lecture 10: BJT Physics
16
8