Holes and electrons determine device characteristics. Three terminal device Control of two terminal currents. Bipolar Junction transistor. Amplification and switching through 3 rd contact. V. I. p. n. I. V. I 0. How can we make a BJT from a pn diode?.
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determine device characteristics
Three terminal device
Control of two terminal currents
Amplification and switching through 3rd contact
I
p
n
I
V
I0
How can we make a BJT from a pn diode?Why is the reverse bias current of a pn diode small?
Why is the reverse bias current of a pn diode small?
I
e
p
n
h+
I
V
I0
How can we make a BJT from a pn diode?I
e
p
n
h+
I
np and/or pn
V
I0
Test: Multiple choice
can be increased what will happen to I0?
V
I
e
p
n
h+
I
V
I0
can be increased near the depletion region edge, then I0 will increase.
I
h+
p
n
e
How can we increase the minority carrier concentration near the depletion region edge?I
h+
p
n
e
I
V
If
Hole injector
p+
V
I0
I
h+
p+
n
e
n
p
e
h+
If W large, then?
W
Thus:
A forward biased p+n diode is a good hole injector
A reverse biased np diode is a good minority carrier collector
V
I
I0
dpn
h+
p+
n
e
n
p
e
x
h+
Lp
If W large → holes
recombine
W
Thus:
A forward biased p+n 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.
V
I
I0
dpn
h+
p+
n
e
n
p
e
x
h+
Lp
W
What is the magnitude of the hole diffusion current at the edge
x=W of the “green” region?
V
I
I0
dpn
h+
p+
n
e
n
p
e
x
h+
Lp
if W large → holes
recombine
W
Reduce W
Thus:
A forward biased p+n diode is a good hole injector
A reverse biased np diode is a good minority carrier collector
Since gradient of dpn @ x=W is zero, hole diffusion current is also zero
Single junction
pno
pno
npo
npo
Double junction
npo
npo
pno
No Ohmic contact thus minority carrier concentration not
Rate equation
Steady state
General solution of second order differential equation
With Ohmic contact C1=0
C2≠0
Without Ohmic contact C1≠0
C2≠0
pwell for base
p+ Si
Ohmic contact
n+ Si
ohmic contact
device insulation
psubstrate
nwell for collector
B
C
E
n+ Si
p+ Si
p+ Si
p Si
n Si
p Si
Planar BJT  npnFor integrated circuits (ICs) all contacts have to be on the top
B
C
IE
IC
p+
n
p
holes
e gain, reverse bias
holes
IE
IC
ICB0
I’B
I”B
Recombination
e loss
e loss, forward bias
IB
Carrier flow in BJTsIB
IB = I’B + I”B – ICB0
h+
e
tp
recombine with
Wb << Lp
Control by base current : ideal case.Based upon space charge neutrality
Base region
IE = Ip
tt transit time
tt < 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!
IC
IEp
B
equilibrium
Injection of carriers
e
VBE>0
Wb < Lp
x
h+
No amplification!
IEn
Amplification!
How good is the transistor?C
or g = IEp/(IEn + IEp) ≈ 1
g: emitter injection efficiency
or B= IC/IEp≈ 1
B: base transport factor
or a= IC/IE≈ 1
a: current transfer ratio
+ (1B) IEp
thus b= IC/IB= a/(1a)
b: current amplification factor
ICB0 ignored
Forward biased p+n junction is a hole injector
Reverse biased np junction is a hole collector
B
E
W < Lp
Review 1 – BJT basicsIC
Forward active mode (ON)
IE
VBC
V
V
VBC
I
I
EB
E
C
p+
n
p
C
E
Forward biased p+n junction is a hole injector
Reverse biased np junction is a hole collector
B
E
W < Lp
Review 1 – BJT basicsIC
Forward active mode (ON)
IE
VBC
V
V
VBC
IB=I’B
+I”B
I
I
EB
E
C
p+
n
p
C
E
Amplification?
Recombination only case: I’B, ICB0negligible
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: I’Bis not negligible
b = IC/IB
With IB electrons supplied by base = I’B = In
IC holes collected by the collector = Ip
B
C
p(x)
B
DpE
Without recombination
pn0
With recombination
pn0
DpC
x
0
Wb
Minority carrier distributiondp(x)
0
B
DpE
DpC
x
0
Wb
See expressions for diode current for short diode
Currents: simplified caseAssume I”B=0 & IBC0= 0
DpE
Linear variation of excess carrier concentration:
DpC
x
0
Wb
Narrow base: no recombination: Ip→minority carrierdensity gradient in the base
DpE = pn0(e eVEB/kT – 1) ≈pn0 e eVEB/kT
DpC = pn0(e –eVBC/kT – 1) ≈ pn0
Note: no recombination
Hole current:
Collector current
No recombination, thus all injected holes across the BE junction are collected.
Base current??
Dnp
Linear variation of excess carrier concentration:
0
x
xe
0
Look at emitter: In→ minority carrier density gradient in the emitter
Dnp = np0(e eVEB/kT – 1) ≈np0 e eVEB/kT
Base current:
The base contact has to resupply only the electrons that are escaping from the base via the baseemitter junction since no recombination I”B=0 and no reverse bias electron injection into base ICB0=0.
Current gain:
Emitter current
The emitter current is the total current flowing through the base emitter contact since IE=IC+IB (current continuity)
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
Xe
Wb
Xc
0
IB
=
InEB
General approach also taking recombination into account.forward active mode
dc(x)
DpE
DnE
x
Xe
DpC
Xc
LpE
LpC
DnC
0
Wb
< LnB
Which formulae do we use for the excess minority carrier concentration in each region?forward active mode
dc(x)
DpE
DnE
x
Xe
DpC
Xc
LpE
LpC
DnC
0
Wb
< LnB
Emitter
Collector
use LONG diode approximation
dnpE(x)=DnE exp((x)/LpE)
dnpC(x)=DnC exp(x/LpC)
dp(x)
Excess hole concentration dp(x):
DpE
Exact solution of differential equation:
x
dp(x) = C1 ex/Lp + C2 ex/Lp
DpC
Wb
Constants C1, C2:
DpE = dp(x=0)
DpC = dp(x=Wb)
dp(x)
Exact solution of differential equation:
dp(x) = C1 ex/Lp + C2 ex/Lp
DpE
Long diode approximation:
dp(x) = C3 ex/Lp
Boundary condition at BC junction cannot be guaranteed
x
LnB
DpC
Wb
http://www.ecse.rpi.edu/~schubert/CourseECSE2210MicroelectronicsTechnology2010/http://www.ecse.rpi.edu/~schubert/CourseECSE2210MicroelectronicsTechnology2010/
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
Xe
DpC
Xc
LpE
LpC
DnC
0
Wb
< LnB
IB
=
InEB
+
IpEB

IpBC
Term due to recombination
dp(x)
B
DpE
Starting point:
x
DpC
0
Wb
=I”B
Injection at emitter side: DpE = pn0(e eVEB/kT – 1)
Collection at collector side: DpC = pn0(e eVCB/kT – 1)
dp(x)
DpE
B
DpC
x
0
Wb
Diffusion current: Ip (x) = e A Dp ddp(x)/dx
Emitter current: IE ≈ Ip (x=0)
Collector current: IC ≈ Ip (x=Wb)
Base current: IB ≈ Ip (x=0)  Ip (x=Wb)
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
BE
E
C
p+
n
p
C
E
B
Original base width
V
V
I
I
Depletion width changes with VBC
Effective base width
Metallurgic junction
Nonideal effects in BJTsIB
IB≈Es/RS
iC
RL
iB
IB
dp
ECC
RS
DpE
QB
t2
es
iE
ts
Qs
DpC
DpE
t1
Es
t1
ts
t2
t’s
0
t
Es
x
pn
DpE
tsd
t0
Wb
iC
IC≈ECC/RL
IC
Switching cycleSwitch to ON
Switch OFF
iC
ECC /RL
vCE
ECC
VEB<0 & VBC<0
DpE=pn & DpC=pn
Saturation
VEB>0 & VBC≥0
DpE = pn (eeVEB/kT – 1)
DpC = 0 (VBC=0)
dp
dp
DpE
DpE
pn
DpC
x
Wb
x
Wb
Charge in base (linear)VBC>0
Currents  review.forward active mode
dc(x)
IE
=
IpEB
+
InEB
IC
=
IpBC
+
InBC
DpE
IC
≈
IpBC
DnE
IE
=
IB
+
IC
x
IB
=
IE

IC
Xe
DpC
Xc
LpE
LpC
DnC
0
Wb
< LnB
IB
=
InEB
+
IpEB

IpBC
Term due to recombination
RL
iB
dp
ECC
RS
DpE
t2
es
iE
ts
DpC
Es
0
t
Es
x
DpE
Wb
Switching cycle  reviewiB
Switch to ON
Common emitter cicuit
IB
IB≈Es/RS
With IB>ICmax/b
Oversaturation
IB
QB
Qs
DpE
t1
Load line technique
t1
ts
t2
pno
t0
iC
iC
ECC /RL
ICmax≈ECC/RL
IC
<< DpE
pno
vCE
ECC
iB
Switch OFF
Common emitter cicuit
IB
iC
RL
iB
IB
≈Es/RS
dp
ECC
RS
DpE
QB
t2
DpE
es
iE
t’s
Es
Qs
t
Es
DpC
t3
pno
Load line technique
t2
t3
t4
t’s
0
t4
x
tsd
iC
Wb
iC
ECC /RL
IC≈ECC/RL
IC
vCE
ECC
C
p
RS
vbc
e(t)
ECC
B
n
veb
p
t
E
iC
ICsat
dpnB(x)
E
B
C
QB
IBtp
Qsat
IB
IB
IB
IB
IB
tsat
t
0
WB
x
tsat
t
t<0
t<tsat
veb
= 0→ON≈0.7V
E  p
B  n
t≥tsat
RS
+E>>0.7V
ON switching
OFF=0→ON
t≥0
IB
IB
t
IB
t
Qb
IBtp
IBtp
Qs
t
Qs = ICtt
iC
iC
ib
IBtp
t
tsd
tsd
IC
IC
t
Driving offTime to turn the BJT OFF is determined by:
2) The offswitching of the emitterbase diode
CASE 2: OFF=IB
0N (saturation)→OFF
CASE 1: OFF=IB=0
0N (saturation)→OFF
Qb
t
tsd
Qsat
IB
tsd
tsd
OFF switching
0N (saturation)→OFF  CASE 1: OFF=IB=0
RL
C
p
RS
vbc
e(t)
ECC
B
n
veb
p
t
E
iC
tsd
dpnB(x)
ICsat
t<0
E
B
C
QB
t≥0
IBtp
tsd
t
0
WB
x
t
t<0
t<tsd
veb
= 0.7V (ON)→0V
E  p
B  n
t≥tsd
RS
E=0V
t≥0
IB
tsd
tsd
Qsat
IB
tsd
tsd
0N (saturation)→OFF  CASE 2: OFF=IB
RL
C
p
RS
vbc
e(t)
ECC
B
n
veb
p
t
E
iC
dpnB(x)
ICsat
t<0
E
B
C
QB
IBtp
t
0
WB
x
t
t<0
veb
= 0.7V (ON)→E
E  p
B  n
t<tsd
RS
E
t≥tsd
STORAGE DELAY TIME: tsd
tsd
tsd
shorter delay
0N (saturation)→OFF  CASE 1: OFF=IB=0
0N (saturation)→OFF  CASE 1: OFF=IB
iC
t<tsd
iC
t<tsd
tsd
ICsat
ICsat
t≥tsd
t≥tsd
t
t
C
p
RS
vbc
e(t)
ECC
B
n
veb
p
t
E
iC
ICsat
QB
IBtp
Qsat
tsat
t
tsat
t
Time to saturation
ON switching
OFF=0→ON
t≥tsat
t<tsat
t=tsat
ts
iC
IC≈ECC/RL
IC
oversaturation
TransientsTurnon: off to saturation
ts = tp ln(1/( 1 – IC/b IB))
ts small when:
tp small
IC small compared to b IB
EB diode
toff
t’s
iC
IC ≈ ECC/RL
IC
NO oversaturation
TransientsTurnoff: 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
EB diode
t
ts
toff
t’s
iC
iC
IC ≈ ECC/RL
IC≈ECC/RL
IC
IC
oversaturation
NO oversaturation
TransientsTurnoff: saturation to off
Turnon: 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
Not examinable
Is valid for all bias conditions.
The excess at the BC is taken into account what is essential for saturation operation and offcurrents.
dp
dp
DpE
DpE
DpC
DpC
IEN
ICN
IEI
ICI
Wb
x
Wb
x
Wb
x
SuperpositionEB & BC influenceTake 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
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)
IEI = aI ICI
ICN = aN IEN
IE = IES (eeVEB/kT –1) – aI ICS (eeVCB/kT –1)
IC = aN IES (eeVEB/kT –1) – ICS (eeVCB/kT –1)
EbersMoll equationsIE = IEN + IEI
IC = ICN + ICI
a: current transfer factor
IE = aI IC + IEO (eeVEB/kT –1)
IC = aN IE  ICO (eeVCB/kT –1)
ICO
EbersMoll equationsIE = 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
C
IE
IC
IB
B
Equivalent circuitIE = 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
VBE<0 & VCB<0
Active
VBE>0 & VCB<0
E
E
C
C
IE
IE
IC
IC
IB
IB
B
B
IC
IE
VCB
Small!
IC0, IE=0
Description of different transistor regimesIC = IC0 + aN IE
IE = (1aN) IES
IC = (1aI) ICS
Cj,BC
C
B
Cj,BE
Cd,BE
npn
Rp
gmvbe
Ro
vbe
E
Cj,BE
Depletion capacitance
Cd,BE
Diffusion capacitance
See SG on pndiode
Cj,BC
C
B
Cj,BE
Cd,BE
Rp
gmvbe
Ro
E
Cj,BC
Depletion capacitance
Miller capacitance: feedback between B & C
Cj,BC
C
B
Cj,BE
Cd,BE
Rp
gmvbe
Ro
E
Circuit analysis
Max gain
ib
Cj,BC
C
B
Cj,BE
Cd,BE
vbe
Rp
gmvbe
Ro
E
t total transit time
Base transit time
BaseEmitter charging time
for p+n
Note: this approach ignores delay caused by BC junction (see 3rd year)
Commonemitter connection
Active mode:
BE: forward, BC: reverse.
ic
E
C
i’e
re
rc
ai’e
Cdif
CjE
CjC
B
Small signal equivalent circuit when other biasing connection is madeCommonbase connection
Active mode:
BE: forward, BC: reverse.