University of Zagreb
Faculty of Electrical Engineering and Computing
Department for Electronics, Microelectronics,
Computer and Intelligent Systems
El t
i
Electronics
1
Ž. Butković, J. Divković Pukšec, A. Barić
7 Bipolar Junction Transistors
7.
Bipolar Junction Transistor (BJT)
Three-terminal active device
‰ Input,
Input output and common terminal
‰ Signal on input terminal controls the signal on output terminal
‰ Why bipolar? – charge carriers of both polarities participate in
current conduction process
‰ Application: amplifier, switch
7. Bipolar Junction Transistors (BJTs)
2
Simplified Structures and
Circuit Symbols
Three semiconductor regions
Two types:
npn
pnp
Terminals
‰ emitter → E
‰ base
b
→B
‰ collector → C
Two pn junctions
‰ emitter-base
‰ collector-base
7. Bipolar Junction Transistors (BJTs)
3
Structure
In collector region –
two layers
‰ p-base
b
‰ n+-emitter
discrete transistor – substrate
is part of collector area
integrated transistor –
common substrate for all
devices
Dominant current flow – from
emitter,, through
g base to
collector → intrinsic
transistor
7. Bipolar Junction Transistors (BJTs)
4
Discrete Transistor Example
7. Bipolar Junction Transistors (BJTs)
5
Operation of the npn Transistor
Biasing of pn junctions:
emitter-base → forward-biased,
collector base → reverse-biased
collector-base
reverse biased
→ active mode
Current components:
Injections across emitter-base
junction → currents InE and
IpE
Recombined electrons in base
→ current IR
Electron flow through
collector-base
ll t b
jjunction
ti →
current InC
Saturation current of collectorbase junction → ICBO
7. Bipolar Junction Transistors (BJTs)
6
Energy Band Diagram
Electrons in base are minority carriers
Some of the electrons in base recombine with holes
Most of the electrons pass through collector-base junction → for
electrons as minority carriers no energy barrier is present
7. Bipolar Junction Transistors (BJTs)
7
Transistor Currents
definition: currents flowing into
device are positive
I E + I B + IC = 0
− I E = I nE + I pE
I C = I nC + I CBO
I B = I pE + I R − I CBO
currents: IE < 0, IB > 0, IC > 0
I R = I nE − I nC
7. Bipolar Junction Transistors (BJTs)
8
Emitter Efficiency,
Base Transport Factor
Good transistor – most of the emitter current reaches collector
Emitter efficiency
γ=
I nE
I
= nE
I nE + I pE − I E
good transistor – current IE consists mostly of current InE; γ → 1
Base transport factor
I
I
β * = nC = 1 − R
I nEE
I nEE
good transistor – most of the current InE enters the collector as the current
InC; base recombination is negligible; β* → 1
7. Bipolar Junction Transistors (BJTs)
9
Common-Base Current Gain
Output current is collector current IC, input current is emitter current IE
→ common-base
I C = − γ β * I E + I CBO
Transistor property – forward-biased emitter-base junction controls high current
in adjacent reverse-biased collector-base junction
α = γ β*
I C = − α I E + I CBO
By neglecting saturation current ICBO
I
α= C
− IE
α ≡ common-base current gain
yp
values from 0,98
, to 0,995
,
typical
7. Bipolar Junction Transistors (BJTs)
10
Example 7.1
Bipolar npn transistor is operating in the active region. For every 200 electrons
that pass from emitter to base a 1 hole pass from base to emitter
emitter. From
400 electrons that passed from emitter to base, the 399 reached the
collector. Find the common-base current gain α.
7. Bipolar Junction Transistors (BJTs)
11
Minority Carrier Concentration
Distributions
Carrier concentrations at the edge of the depletion region
⎛U ⎞
nB 0 = n0 B exp ⎜ BE ⎟
⎝ UT ⎠
⎛ U BC ⎞
nBw
=
n
exp
⎜
⎟
B
0B
⎝ UT ⎠
⎛U ⎞
pE 0 = p0 E exp ⎜ BE ⎟
⎝ UT ⎠
⎛U ⎞
pC 0 = p0C exp ⎜ BC ⎟
⎝ UT ⎠
7. Bipolar Junction Transistors (BJTs)
12
Emitter Efficiency
Components InE and IpE → diffusion currents
nB 0 − nBw
n
≈ q S DnB B 0
wB
wB
pE 0 − p0 E
pE 0
=
≈
q
S
D
q
S
D
pE
pE
xE = 0
L ppE
L pE
p
I nE = − I Dn xB = 0 = q S DnB
I pE = − I Dp
γ=
I nE
1
=
=
I nE + I pE 1 + I pE / I nE
ni2
N AB
ni2
p0 E =
N DE
n0 B =
1
D pE wB N AB
1+
DnB L pE N DE
Narrow emitter: instead of LpE → wE
Emitter efficiency factor γ is closer to one as the emitter doping increases
p
to the base doping.
p g
compared
7. Bipolar Junction Transistors (BJTs)
13
Base Transport Factor
Minority-carrier electron concentration profile deviation from linear
approximation
For wB << LnB
1⎛ w ⎞
β* ≈1− ⎜ B ⎟
2 ⎝ LnB ⎠
2
wB – effective width of the base
Factor β* is closer to one as the width wB decreases compared to the diffusion
length
g LnB.
7. Bipolar Junction Transistors (BJTs)
14
Minority Carrier Charge in Base
QnB ≈ q S
QnB
wB2
=
= ttr
I nE 2 DnB
nB 0 wB
2
ttr → forward-base transit time
I R = I nE − I nC = I nE (1 − β * ) = q S
QnB
= τ nB
IR
7. Bipolar Junction Transistors (BJTs)
nB0 wB
2τ nB
15
Example 7.2
Silicon npn transistor has emitter and base homogeneously doped with
concentrations equal to NDE = 2·1017 cm−33 and NAB = 1016 cm−33. Effective
base width is 1 μm, while the widths of emitter and collector are much
larger than minority-carrier diffusion lengths. Transistor area is equal to
1 mm2, and saturation current is equal to ICBO = 0,45 pA. The minority
carrier parameters in emitter are equal to DpE = 8 cm2/s and LpE = 20 μm
and in base are equal to DnB = 10 cm2/s and LnB = 15 μm. Temperature
equals T = 300K. Determine all components of transistor currents, and total
currents of emitter, base and collector by considering following voltages:
a)
UBE = 0,55 V i UCB = 5 V,
b)
UBE = 0,55 V i UCB = 0.
7. Bipolar Junction Transistors (BJTs)
16
Example 7.3
Consider the transistor from Example 7.2 and find the common-base current
gain α for the data given.
given If the emitter width is equal to wE = 3 μm << LpE
recalculate the common-base current gain α.
7. Bipolar Junction Transistors (BJTs)
17
pnp Transistor (1)
Compared to the npn transistor the voltage and current signs are opposite
I E = I pE + I nE
I C = − I pC + I CBO
I B = − I nE − I R − I CBO
I R = I pE − I pC
γ=
I pE
I
= pE
I pE + I nE I E
β* =
currents: IE > 0, IB < 0, IC < 0,
ICBO < 0
7. Bipolar Junction Transistors (BJTs)
I ppC
I
=1− R
I pE
I pE
I C = − α I E + I CBO
18
pnp Transistor (2)
γ=
1
D w N
1 + nE B DB
D pB LnE N AE
Q pB ≈ q S
pB 0 wB
2
1⎛ w ⎞
β* ≈1− ⎜ B ⎟
2 ⎝ LpB ⎠
I pE ≈ q S D pB
I R = I pE − I pC = I pE (1 − β * ) = q S
Q pB
wB2
=
= ttr
I pE 2 D pB
2
pB 0
wB
pB0 wB
2τ pB
Q pB
= τ pB
IR
7. Bipolar Junction Transistors (BJTs)
19
Example 7.4
Bipolar pnp transistor is operating in active region having the emitter current
equal to 10 mA. Emitter efficiency is equal to 0,99
0 99 and the base transport
factor equals 0,998. Determine all components of transistor currents, and
total currents of base and collector. The saturation current ICBO can be
neglected.
7. Bipolar Junction Transistors (BJTs)
20
Example 7.5
The silicon pnp transistor is operating in active region. At the bias point the
stored minority
minority-carriers
carriers charge in the base is equal to 50 pAs, emitter
efficiency equals γ = 0,995, forward-base transit time is equal to ttr = 12,5 ns,
and their lifetime in base is equal to τB = 2 μs. The saturation current
equals ICBO = 0. Determine all components of transistor currents at the bias
point.
7. Bipolar Junction Transistors (BJTs)
21
Basic Bipolar Junction
Transistor Configurations
input
terminal
input
current
input
voltage
common
base
emitter
IE
common
emitter
base
common
collector
base
configuration
7. Bipolar Junction Transistors (BJTs)
output
terminal
output
current
output
voltage
U EB
collector
IC
U CB
IB
U BE
collector
IC
U CE
IB
U BC
emitter
IE
U EC
22
The Common-Base
Configuration
I C = − α I E + I CBO
Neglecting the current ICBO
α=
IC
− IE
Factor α is less than 1 → output current IC is less than input current IE
7. Bipolar Junction Transistors (BJTs)
23
The Common-Emitter
Configuration
pn-junction biases and ratios of the emitter
current IE, base current IB and collector
current IC are the same as in
common-base
I C = − α I E + I CBO = − α ( − I B − I C ) + I CBO
β ≡ common-emitter current gain
t i l values
typical
l
ffrom 50 to
t 200
β=
IC =
I
α
I B + CBO = β I B + I CEO
1−α
1−α
β=
IC
IB
α
1−α
7. Bipolar Junction Transistors (BJTs)
24
The Common-Collector
Configuration
I E = − I C − I B = − ( β + 1) I B − I CEO
β +1=
− IE
IB
Output emitter current IE is larger β + 1 times than input base current IB
7. Bipolar Junction Transistors (BJTs)
25
Saturation Currents
I C = − α I E + I CBO
I C = β I B + I CEO
I CBO = I C
I CEO = I C
for
IE = 0
for
IB = 0
ICBO ≡ collector-base junction saturation current having emitter disconnected
ICEO ≡ collector-emitter jjunction saturation current havingg base disconnected
I CEO =
I CBO
= (1 + β ) I CBO
1−α
7. Bipolar Junction Transistors (BJTs)
26
Example 7.6
Determine common-emitter current gain for the transistor presented in
following figure
figure.
7. Bipolar Junction Transistors (BJTs)
27
Bipolar Junction Transistor
Modes of Operation
Modes of operation:
‰ active region
‰ reverse-active
ti region
i
‰ saturation region
‰ cutoff region
biasing of
pn junctions
collector
-base
emitter-base
forward
reverse
forward
saturation
reverse-active
reverse
active
cutoff
7. Bipolar Junction Transistors (BJTs)
28
Minority-Carrier Electrons Distributions
in Base for Each Mode of Operation
7. Bipolar Junction Transistors (BJTs)
29
Active Region
Emitter-base junction is forward biased.
Emitter injects carriers in base.
Some of carriers are recombined in the base and most of them will be swept
into the collector through the reverse-biased collector-base junction.
Collector current depends on emitter current ii.e.
e on the voltage of the
forward-biased emitter-base junction. Dependency on the voltage of the
reverse biased collector-base junction is negligible.
From the collector terminal point of view the transistor can be represented by
an ideal current source controlled by the input current.
Transistor operating in the active region has significant gain and therefore it is
used in amplifiers.
7. Bipolar Junction Transistors (BJTs)
30
Reverse-Active Region
Similar as the active region but with exchanged roles of the emitter and
collector.
Forward-biased
F
d bi
d collector-base
ll t b
jjunction
ti injects
i j t carriers
i
iin b
base while
hil emitter
itt
collects most of the minority-carriers from base.
In the reverse active region
g
the same q
qualitative description
p
is valid as in the
active region.
αR =
IE
− IC
βR =
IE
αR
=
IB
1 − αR
Transistor is not symmetrical → reverse current gains αR and βR are low;
βR typical values are from 1 to 10.
7. Bipolar Junction Transistors (BJTs)
31
Saturation Region
Both pn junctions are forward-biased and inject the electrons in the base.
Electron current InE is equal to the difference of the electron current that the
emitter injects in the base and the electron current that reaches the emitter
from the collector. Similar explanation can be applied for the current InC.
Transistor operation can be described as the superposition of the operation in
the active region and the reverse-active
reverse active region.
7. Bipolar Junction Transistors (BJTs)
32
Cutoff Region
In the cutoff region both pn junctions are reverse-biased.
Only small saturation currents IEBO and ICBO of the reverse-biased emitter-base
and
d collector-base
ll t b
jjunctions
ti
are flflowing
i iin th
the ttransistor.
i t
Transistor operating in the cutoff or saturation region has no gain.
In the saturation region voltages in input and output side of the transistor are
small and transistor resistances are small resistance. In the cutoff region the
transistor currents are small and resistances are high.
Transistor operating in the cutoff and saturation region represents a switch.
7. Bipolar Junction Transistors (BJTs)
33
Current-Voltage Characteristics
Having three transistor terminals the three currents (IE, IB and IC) and three
voltages (UBE, UBC and UCE) can be measured. From the all possible
combinations following current
current-voltage
voltage characteristics are used mostly:
‰ Input current-voltage characteristics
‰ Output
p current-voltage
g characteristics
Current-voltage characteristics are presented for two basic configurations:
‰ Common-base
‰ Common-emitter.
7. Bipolar Junction Transistors (BJTs)
34
Base-Width Modulation –
The Early Effect
Increasing the voltage UCB of the reverse-biased collector-base junction, the
depletion region is widening and therefore the base width is decreasing.
Having the voltage UBE constant the minority electron concentration gradient in
the base is increasing (currents InE i InC are increasing) and minority
charge storage is decreasing (current IR is decreasing)
charge-storage
7. Bipolar Junction Transistors (BJTs)
35
The Common-Base
Configuration
Input current-voltage characteristics:
I E = f (U EB )UCB
Output current-voltage characteristics:
IC = f (UCB ) I E
7. Bipolar Junction Transistors (BJTs)
36
The Common-Base
Input Characteristics
The characteristics of forward-biased
emitter-base junction
The shift
Th
hift off th
the characteristics
h
t i ti with
ith
respect to voltage UCB →
The Early effect → having the
voltage UEB constant the current IE
is increasing due to the increase of
the base minority carrier
concentration gradient
7. Bipolar Junction Transistors (BJTs)
37
The Common-Base
Output Characteristics
In active region
I C = − α I E + I CBO
current increase → The Early
effect; the current IR is decreasing
and current IC is increasing
Boundary between the active region and the saturation region → UCB = 0
7. Bipolar Junction Transistors (BJTs)
38
The Common-Emitter
Configuration
Input current-voltage characteristics:
I B = f (U BE )UCE
Output current-voltage characteristics:
IC = f (U CE ) I B
7. Bipolar Junction Transistors (BJTs)
39
The Common-Emitter
Input Characteristics
The characteristics
Th
h
t i ti off forward-biased
f
d bi
d
emitter-base junction
The
e sshift o
of the
e ccharacteristics
a ac e s cs with
respect to voltage UCE →
The Early effect → having the
voltage
lt
UEB constant
t t the
th currentt IB
is decreasing due to the decrease
of the minority charge in the base
7. Bipolar Junction Transistors (BJTs)
40
The Common-Emitter
Output Characteristics
In active region
I C = β I B + I CEO
current increase → The Early effect;
the gradient is increasing and the
current IC is increasing
Boundary between the active region and the saturation region → UCE = UBE
7. Bipolar Junction Transistors (BJTs)
41
Example 7.7
Bipolar npn transistor has the current gain factor equal to α = 0,99 and the
collector-base junction saturation current equal to ICBO = 1 nA. The transistor
is operating in the active region having the base current equal to IB = 100 μA.
The voltage between the collector and the base equals 5 V. Sketch the
output current-voltage characteristic and label the bias point if transistor
configuration is:
a) Common-base,
b) Common-emitter.
7. Bipolar Junction Transistors (BJTs)
42
Current Gain Factor
β = f(IC)
‰ Decreasing for low currents →
recombination in the emitter-base
depletion region
‰ Decreasing for high currents →
high injection
β is increasing with temperature →
the collector current IC is increasing
as well as the power dissipation
PT = IC UCE
7. Bipolar Junction Transistors (BJTs)
43
Breakdown
Avalanche breakdown of reverse-biased
collector-base junction
The collector-emitter breakdown
U CE ( PR) =
7. Bipolar Junction Transistors (BJTs)
U CB ( PR )
n
β
44
Dynamic Resistances – Definition
input dynamic resistance
rbe =
d uBE
du
d iB
=
uCE = const
ube
ib
output dynamic resistance
rce =
uce = 0
7. Bipolar Junction Transistors (BJTs)
d uCE
d iC
=
iB = const
uce
ic
ib = 0
45
Input Dynamic Resistance
Total resistance rbe → rbe = rbb' + rb'e
‰ Base series resistance rbb' →
‰ Dynamic resistance of the emitter-base junction rb'e
iB = iPE + iR = q S D pE
⎛u ⎞
⎛u ⎞
p0 E
w n
exp ⎜⎜ B′E ⎟⎟ + q S B 0 B exp ⎜⎜ B′E ⎟⎟
2τ nB
L pE
⎝ UT ⎠
⎝ UT ⎠
1
di
i
= B = B
rb 'e du B′E U T
At the bias point: rb 'e =
UT
IB
7. Bipolar Junction Transistors (BJTs)
46
Output Dynamic Resistance
Model for the slope of the output characteristics in the active region
⎛ u ⎞
iC = β iB ⎜⎜1 + CE ⎟⎟
UA ⎠
⎝
1
di
iC
= C =
rce duCE uCE + U A
rce =
U CE + U A U A
≈
IC
IC
UA ≡ Early voltage
7. Bipolar Junction Transistors (BJTs)
47
The Dynamic
Common-Emitter Current Gain
Models the transistor gain
h fe =
d iC
d iB
=
uCE = konst
ic
ib
From the output characteristics
uce = 0
h fe ≈ β
h fe =
7. Bipolar Junction Transistors (BJTs)
Δ iC
Δ iB
=
uCE = const
ΔiC
I B 2 − I B1
uCE = const
48
Bipolar Junction Transistor
Transconductance
Other parameter for modeling the transistor gain
gm =
gm =
d iC
d u B′E
=
uCE = const
ic
ub′e
uce = 0
h fe
d iC
d i d iB
= C
=
d u B′E d iB d u B′E rb′e
At the bias point:
gm ≈
β
UT / I B
7. Bipolar Junction Transistors (BJTs)
=
IC
UT
49
The Hybrid-π Model
High-frequency hybrid-π model
Capacitances:
Cb'e → the emitter-base junction capacitance; diffusion capacitance
Cb'c → the collector-base junction capacitance; depletion capacitance
7. Bipolar Junction Transistors (BJTs)
50
Low-Frequency Models
Model
M
d l with
ith
transconductance gm
Model with the dynamic
current gain factor hfe
7. Bipolar Junction Transistors (BJTs)
51
Example 7.8
In the output current-voltage characteristics of the npn transistor
measurements are performed at the two bias points
points. At the point A
following values are measured: IBA = 50 μA, ICA = 8 mA and UCEA = 5 V,
and at the point B measured values are: ICB = 8,1 mA and UCEB = 10 V.
Determine dynamical parameters rb'e, rce, hfe and gm at the point A.
Find the Early voltage UA. Consider the room temperature, UT = 25 mV.
7. Bipolar Junction Transistors (BJTs)
52
Summary of Important
Equations (1)
emitter efficiency
γ=
1
D w N
1+ E B B
DB LE N E
or γ =
1
D w N
1+ E B B
DB wE N E
base transport factor
1⎛ w ⎞
β* ≈1− ⎜ B ⎟
2 ⎝ LB ⎠
2
minority carriers charge in base
QB = ttr γ I E = τ B I R
wB2
ttr =
2 DB
7. Bipolar Junction Transistors (BJTs)
53
Summary of Important
Equations (2)
dynamic parameters
input dynamic resistance
rb ' e =
UT
IB
output dynamic resistance
U +UA
⎛ u ⎞
iC = β iB ⎜1 + CE ⎟ → rce = CE
IC
⎝ UA ⎠
transconductance
gm =
I C h fe
=
U T rb′e
7. Bipolar Junction Transistors (BJTs)
54