Bipolar Junction transistor

1
Bipolar Junction transistor
Amplification and switching through 3rd contact
2
How can we make a BJT from a pn diode?

• Take pn diode

• Remember reverse bias characteristics

• Reverse saturation current I0

3
Test Multiple choice

• Why is the reverse bias current of a pn diode
  small?

1. Because the bias across the depletion region is
   small.
2. Because the current consist of minority carriers
   injected across the depletion region.
3. Because all the carriers recombine.

4
Test Multiple choice

• Why is the reverse bias current of a pn diode
  small?

1. Because the bias across the depletion region is
   small.
2. Because the current consist of minority carriers
   injected across the depletion region.
3. Because all the carriers recombine.

5
How can we make a BJT from a pn diode?

• Take pn diode

• Remember reverse bias characteristics

• Reverse saturation current I0
• Caused by minority carriers swept across the
  junction

6
Test Multiple choice

• If minority carrier concentration

can be increased what will happen to I0?

1. Increase
2. Decrease
3. Remain the same

7

• If minority carrier concentration

can be increased near the depletion region edge,
then I0 will increase.
8
Test True-False
pn
If we only increase
then I0 will still increase.
9
How can we increase the minority carrier
concentration near the depletion region edge?

• Take pn diode

• Remember forward bias characteristics

• How can we make a hole injector from a pn diode?
  

1. By increasing the applied bias, V.
2. By increasing the doping in the p region only
3. By applying a reverse bias.

10
Hole injector

• Take pn diode

• Remember forward bias characteristics

p
11
Thus
A forward biased pn diode is a good hole injector
A reverse biased np diode is a good minority
carrier collector

1. Recombination of excess holes will occur and
   excess will be 0 at end of layer
2. Recombination of excess holes will occur and
   excess will be large at end of layer
3. No recombination of excess holes will occur.
4. Recombination of excess electrons will occur and
   excess will be np0 at end of layer

12
Thus
A forward biased pn diode is a good hole injector
A reverse biased np diode is a good minority
carrier collector
Excess hole concentration reduces exponentially
in W to some small value.
13
What is the magnitude of the hole diffusion
current at the edge xW of the green region?

1. Magnitude of hole diffusion current at xW is
   same as at x0
2. Magnitude of hole diffusion current at xW is
   almost 0
3. Magnitude of hole diffusion current cannot be
   derived from this layer.

14
Thus
A forward biased pn diode is a good hole injector
A reverse biased np diode is a good minority
carrier collector
Since gradient of dpn _at_ xW is zero, hole
diffusion current is also zero
15
BJT pnp
E emitter
VBC
EB
B base
E
C
C collector
C
E
Common base configuration
16
Base Short layer with recombination and no Ohmic
contacts at edges.
Single junction
pno
pno
npo
npo
Double junction
npo
npo
pno
No Ohmic contact thus minority carrier
concentration not
17
How will we calculate the minority carrier
concentration in the base?
Rate equation
Steady state
General solution of second order differential
equation
With Ohmic contact C10 C2?0
Without Ohmic contact C1?0 C2?0
18
Planar BJT - npn
For integrated circuits (ICs) all contacts have
to be on the top
19
Carrier flow in BJTs
IB
IB IB IB ICB0
20
Control by base current ideal case.
Based upon space charge neutrality
Base region
IE Ip
tt transit time
tt lt tp
Based on the given timescales, holes can pass
through the narrow base before a supplied
electron recombines with one hole ic/ib tp/tt
The electron supply from the base contact
controls the forward bias to ensure charge
neutrality!
21
How good is the transistor?

• Wish list

C

• IEpgtgtIEn

or g IEp/(IEn IEp) 1
g emitter injection efficiency

• IC IEp

or B IC/IEp 1
B base transport factor
or a IC/IE 1
a current transfer ratio
(1-B) IEp

• IB IEn

thus b IC/IB a/(1-a)
b current amplification factor
ICB0 ignored
22
Review 1 BJT basics
IC
Forward active mode (ON)
IE
VBC
V
V
VBC
I
I
EB
E
C
n
p
p
C
E
23
Review 1 BJT basics
IC
Forward active mode (ON)
IE
VBC
V
V
VBC
I
I
IBIB
IB
EB
E
C
n
p
p
C
E
24
Review 2
Amplification?
Recombination only case IB, ICB0 negligible
ic/ib tp/tt
Carriers supplied by the base current stay much
longer in the base tp than the carriers supplied
by the emitter and travelling through the base
tt.
b tp/tt
But in more realistic case IB is not negligible
b IC/IB
With IB electrons supplied by base IB In IC
holes collected by the collector Ip
25
Currents?

• In order to calculate currents in pn junctions,
  knowledge of the variation of the minority
  carrier concentration is required in each layer.
• The current flowing through the base will be
  determined by the excess carrier distribution in
  the base region.
• Simple to calculate when the short diode
  approximation is used this means linear
  variations of the minority carrier distributions
  in all regions of the transistor. (recombination
  neglected)
• Complex when recombination in the base is also
  taken into account then exponential based
  minority carrier concentration in base.

26
Minority carrier distribution

• Assume active mode VEBgt0 VBClt0

• Emitter injects majority carriers into base.
• dpn(0)pno (exp(VEB/VT)-1)

• Collector collects minority carriers from base.
• dpn(Wb)pno (exp(VBC/VT)-1)

dp(x)
0
27
Currents simplified case

• Assume IB0 IBC0 0

• Then IE total current crossing the base-emitter
  junction

• Then IC IEp gradient of excess hole
  concentration in the base

• IB without recombination is the loss of electrons
  via the BE junction IB

• Then IB gradient of excess electron
  concentration in the emitter

28
Narrow base no recombination Ip
? minority carrier density gradient in the base
DpE pn0(e eVEB/kT 1) pn0 e eVEB/kT
DpC pn0(e eVBC/kT 1) -pn0
Note no recombination
29
Collector current Ip
Hole current
Collector current
No recombination, thus all injected holes across
the BE junction are collected.
Base current??
30
Look at emitter In
? minority carrier density gradient in the emitter
Dnp np0(e eVEB/kT 1) np0 e eVEB/kT
31
Base current In
Base current
The base contact has to re-supply only the
electrons that are escaping from the base via the
base-emitter junction since no recombination
IB0 and no reverse bias electron injection into
base ICB00.
32
Emitter current
The emitter current is the total current flowing
through the base emitter contact since IEICIB
(current continuity)
33
Short layer approach summaryforward active mode
dc(x)
IE

IpEB

InEB
DpE
IC

IpBC

InBC
DnE
IC

IpBC

IpEB
IE

IB

IC
x
DpC
DnC
IB

IE
-
IC
Wb
-Xe
Xc
0
IB

InEB
34
General approach also taking recombination into
account.forward active mode
dc(x)
DpE
DnE
x
DpC
-Xe
Xc
-LpE
LpC
DnC
0
Wb
lt LnB
35
Which formulae do we use for the excess minority
carrier concentration in each region?forward
active mode
dc(x)
DpE
DnE
x
DpC
-Xe
Xc
-LpE
LpC
DnC
0
Wb
lt LnB
Emitter Collector
use LONG diode approximation
dnpE(x)DnE exp(-(-x)/LpE)
dnpC(x)DnC exp(-x/LpC)
36
In the base we must take recombination into
account ? short diode approximation cannot be
used!
dp(x)
Excess hole concentration dp(x)
DpE
Exact solution of differential equation
x
dp(x) C1 ex/Lp C2 e-x/Lp
DpC
Wb
Constants C1, C2 DpE dp(x0) DpC dp(xWb)
37
In the base with recombination ? long diode
approximation can also not be used!
dp(x)
Exact solution of differential equation
dp(x) C1 ex/Lp C2 e-x/Lp
DpE
Long diode approximation
dp(x) C3 e-x/Lp
x
Boundary condition at BC junction cannot be
guaranteed
LnB
DpC
Wb
38
http//www.ecse.rpi.edu/schubert/Course-ECSE-2210
-Microelectronics-Technology-2010/
39
Extraction of currents in the general
approach.forward active mode
dc(x)
IE

IpEB

InEB
IC

IpBC

InBC
DpE
IC

IpBC
DnE
IE

IB

IC
x
IB

IE
-
IC
DpC
-Xe
Xc
-LpE
LpC
DnC
0
Wb
lt LnB
IB

InEB
IpEB
IpBC
-

Term due to recombination
40
Currents Special case when only recombination in
base current is taken into account
Approximation IB0
dp(x)
B
DpE
Starting point

• Assume IEIEp IBC0 0

• Then IE Ip(x0)
• and IC Ip(xWb)

x
DpC
0
Wb

• IBIE - IC

IB
41
All currents are then determined by the minority
carrier gradients in the base.
Injection at emitter side DpE pn0(e
eVEB/kT 1)
Collection at collector side DpC pn0(e eVCB/kT
1)
dp(x)

• IE Ip(x0)

DpE

• IC Ip(xWb)

B
DpC
x
0
Wb
42
Expression of the diffusion currents
Diffusion current Ip (x) -e A Dp ddp(x)/dx
Emitter current IE Ip (x0)
Collector current IC Ip (xWb)
Base current IB Ip (x0) - Ip (xWb)
IE e A Dp/Lp (DpE ctnh(Wb/Lp) - DpC
csch(Wb/Lp) ) IC e A Dp/Lp (DpE csch(Wb/Lp) -
DpC ctnh(Wb/Lp) ) IB e A Dp/Lp ((DpE DpC)
tanh(Wb/2Lp) )
Superposition of the effects of
injection/collection at each junction!
Note only influence of recombination
43
Non-ideal effects in BJTs

• Base width modulation

44
Base width modulation

• Early voltage VA

iC
Wb
ideal
IB
-vCE
45
Conclusions

• Characteristics of bipolar transistors are based
  on diffusion of minority carriers in the base.
• Diffusion is based on excess carrier
  concentrations
• dp(x)
• The base of the BJT is very small
• dp(x) C1 ex/Lp C2 e-x/Lp
• Base width modulation changes output impedance of
  BJT.

46
Transistor switching
47
p-type material
n-type material
On
Off
48
iC
iC
icbiB
-vCE
RL
iB
ECC
RS
es
Es
t
iE
-Es
49
iC
icbiB
iC
-vCE
RL
ECC
RS
es
Es
t
iE
-Es
50
iC
ic?biB
iC
-vCE
RL
ECC
RS
Ic ECC /RL
es
Es
t
iE
-Es
51
Switching cycle
Switch to ON
Switch OFF
iC
ECC /RL
-vCE
ECC
52
Charge in base (linear)

• Cut-off
• VEBlt0 VBClt0
• DpE-pn DpC-pn

• Saturation
• VEBgt0 VBC0
• DpE pn (eeVEB/kT 1)
• DpC 0 (VBC0)

VBCgt0
53
Currents - review.forward active mode
dc(x)
IE

IpEB

InEB
IC

IpBC

InBC
DpE
IC

IpBC
DnE
IE

IB

IC
x
IB

IE
-
IC
DpC
-Xe
Xc
-LpE
LpC
DnC
0
Wb
lt LnB
IB

InEB
IpEB
IpBC
-

Term due to recombination
54
Switching cycle - review
iB
Switch to ON
Common emitter cicuit
IB
IBEs/RS
With IBgtICmax/b
Over-saturation
-IB
QB
Qs
DpE
t1
Load line technique
t1
ts
t2
-pno
t0
iC
iC
ECC /RL
IC
ICmaxECC/RL
ltlt DpE
pno
-vCE
ECC
55
Switching cycle - review
iB
Switch OFF
Common emitter cicuit
IB
iC
RL
iB
-IB
-Es/RS
dp
ECC
RS
DpE
QB
t2
DpE
es
iE
ts
Es
Qs
t
-Es
DpC
t3
-pno
Load line technique
t2
t3
t4
ts
0
t4
x
tsd
iC
iC
Wb
ECC /RL
IC
ICECC/RL
-vCE
ECC
56
Calculating the delays

• Since the currents and minority carrier charge
  storage are determined by the pn diodes, the
  delays are calculated as in the pn diode.
• Knowledge of current immediately before and after
  switch
• Stored minority carrier charge Qp(t) cannot
  change immediately ? delay.
• The additional parameter is the restriction on
  the maximum collector current imposed by the load.

57
ON switching
OFF0?ON
t0
58
Driving off
Time to turn the BJT OFF is determined by

1. The degree of over-saturation (BC junction)

2) The off-switching of the emitter-base diode
CASE 2 OFF-IB 0N (saturation)?OFF
CASE 1 OFFIB0 0N (saturation)?OFF
Qb
t
59
OFF switching
0N (saturation)?OFF - CASE 1 OFFIB0
RL
C
p
RS
vbc
ECC
e(t)
B
n
veb
p
t
E
iC
tsd
dpnB(x)
ICsat
tlt0
E
B
C
QB
t0
IBtp
tsd
x
WB
0
t
t
tlt0
tlttsd
veb
0.7V (ON)?0V
E - p
B - n
ttsd
RS
E0V
60
0N (saturation)?OFF - CASE 2 OFF-IB
RL
C
p
RS
vbc
ECC
e(t)
B
n
veb
p
t
E
iC
dpnB(x)
ICsat
tlt0
E
B
C
QB
IBtp
x
WB
0
t
t
tlt0
veb
0.7V (ON)?-E
E - p
B - n
tlttsd
RS
-E
ttsd
61
0N (saturation)?OFF - CASE 1 OFFIB0
0N (saturation)?OFF - CASE 1 OFF-IB
iC
tlttsd
iC
tsd
tlttsd
ICsat
ICsat
ttsd
ttsd
t
t
62
Transients
Turn-on off to saturation
63
Time to saturation
ON switching
OFF0?ON
ttsat
tlttsat
ttsat
64
Transients
Turn-on off to saturation
ts tp ln(1/( 1 IC/b IB))
ts small when tp small IC small compared to b
IB
65
Transients
Turn-off saturation to off
Storage delay time tsd
66
Time from saturation
0N (saturation)?OFF - CASE 1 OFFIB0
tlttsd
iC
tsd
ICsat
ttsd
t
67
Transients
Turn-off saturation to off
Storage delay time tsd
tsd tp ln(b IB /IC)
tsd small when tp small BUT tsd large when IC
small compared to b IB
68
Transients
Turn-off saturation to off
Turn-on off to saturation
Storage delay time tsd
ts tp ln(1/( 1 IC/b IB))
tsd tp ln(b IB /IC)
ts small when tp small IC small compared to b
IB
tsd small when tp small BUT tsd large when IC
small compared to b IB
69
Solution to dilemmaThe Schottky diode clamp
C
C
B
B
E
E
I
V
0.3
0.7
Schottky diode
pn diode
70
Large signal equivalent circuit

• Switching of BJTs
• LARGE SIGNAL

iC
RL
iB
ECC
RS
es
iE
iC
t
71
Ebers-Moll large signal circuit model for large
signal analysis in SPICE
Not examinable
Is valid for all bias conditions. The excess at
the BC is taken into account what is essential
for saturation operation and off-currents.
72
Superposition EB BC influence
Take EB BC forward biased.
Charge in base


negative
IE IEN IEI
Where IEN, ICI are pn diode currents of EB and
BC respectively.
IC ICN ICI
73
Ebers-Moll equations
IE IEN IEI
IC ICN ICI
IE IES (eeVEB/kT 1) aI ICS (eeVCB/kT 1) IC
aN IES (eeVEB/kT 1) ICS (eeVCB/kT 1)
74
Ebers-Moll equations
IE IEN IEI
IC ICN ICI
a current transfer factor
75
Ebers-Moll equations
IE IES (eeVEB/kT 1) aI ICS (eeVCB/kT 1) IC
aN IES (eeVEB/kT 1) ICS (eeVCB/kT 1)
Where aN IES aI ICS
Or
IE aI IC (1- aN aI) IES (eeVEB/kT 1) IC
aN IE - (1- aN aI) ICS (eeVCB/kT 1)
General equivalent circuit based on diode circuit
76
Equivalent circuit
IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO
(eeVCB/kT 1)
IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO
(eeVCB/kT 1)
IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO
(eeVCB/kT 1)
IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO
(eeVCB/kT 1)
IE aI IC IEO (eeVEB/kT 1) IC aN IE - ICO
(eeVCB/kT 1)
Valid for all biasing modes
77
Description of different transistor regimes

• Cut-off
• VBElt0 VCBlt0

• Active
• VBEgt0 VCBlt0

IC IC0 aN IE
IE -(1-aN) IES IC (1-aI) ICS
78
BJT small signal equivalent circuit
79
Now

• Amplification and maximum operation frequency
• SMALL SIGNAL equivalent circuit

Cj,BC
C
B
Cj,BE
Cd,BE
npn
Rp
Ro
gmvbe
vbe
E
80
Definition of circuit elements

• Transconductance

Cj,BC
C
B
Cj,BE
Cd,BE
Rp
Ro
gmvbe
E
81

• Base input resistance

Cj,BC
C
B
Cj,BE
Cd,BE
Rp
Ro
gmvbe
E
82

• Base-emitter input capacitances

Cj,BE
Depletion capacitance
Cd,BE
Diffusion capacitance
See SG on pn-diode
Cj,BC
C
B
Cj,BE
Cd,BE
Rp
Ro
gmvbe
E
83

• Base-collector capacitance

Cj,BC
Depletion capacitance
Miller capacitance feedback between B C
Cj,BC
C
B
Cj,BE
Cd,BE
Rp
Ro
gmvbe
E
84

• Output resistance

Cj,BC
C
B
Cj,BE
Cd,BE
Rp
Ro
gmvbe
E
85
Current gain - frequency

• Small signal current gain

Circuit analysis
Max gain
ib
Cj,BC
C
B
Cj,BE
Cd,BE
vbe
Rp
Ro
gmvbe
E
86
Transit frequency fT

• Small signal current gain1

t total transit time
Base transit time
Base-Emitter charging time
87
Transit frequency fT

• Base transit time

for pn
Note this approach ignores delay caused by BC
junction (see 3rd year)
88
Simplified small signal equivalent circuit
Common-emitter connection Active mode BE
forward, BC reverse.
89
Small signal equivalent circuit when other
biasing connection is made
Common-base connection Active mode BE forward,
BC reverse.
90
Conclusion

• Delays in BJTs are a result of the storage of
  minority carriers.
• Main delay in common BJTs is due to the base
  transit time tt.