Institute of Solid State PhysicsTechnische Universität Graz
13. Bipolar transistors
Jan. 15, 2019
Institute of Solid State Physics
bipolar transistorsTechnische Universität Graz
collector base emitter
np
n+
lightly doped p substrate
npn transistor
Used in front-end high-frequency receivers (mobile telephones).
p+n+
bipolar transistors
p+
abrupt junction
x
E-xp xn
Ap
eNE x x
Dn
eNE x x
x
-xp
xn
+
-
eND
eNA
2
2
02
02
Ap p
Dn n
eN xV xx x x
eN xV xx x x
0
0
p
n
x x
x x
2ln D Abi B
i
N NeV k Tn
dEdx
dV Edx
Forward bias, V > 0
Electrons and holes are driven towards the junction.The depletion region becomes narrower
Minority electrons are injected into the p-regionMinority holes are injected into the n-region
np(xp) pn(xn)
+
0
0
( ) exp
( ) exp
p p pB
n n nB
eVn x nk T
eVp x pk T
0 exp bee
B
eVpk T
Reverse bias, V < 0
Electrons and holes are driven away from the junction.The depletion region becomes wider
Minority electrons are extracted from the p-region by the electric fieldMinority holes are extracted from the n-region by the electric field
+
np(xp) pn(xn)
0
0
( ) exp
( ) exp
p p pB
n n nB
eVn x nk T
eVp x pk T
pnp transistor, no bias
pnp transistor, forward active bias
The base-emitter voltage controls the minority carriers injected from the emitter to the base. These diffuse to the base-collector junction and are swept into the collector.
Always dissipate power due to the forward bias
Long/Short diode
n-type
,diff p pdpJ eDdx
0,
( )n n ndiff p p p
n
p x pdpJ eD eDdx d
pn(xn)
pn0
dn x
pn(x)Short diode
dn << Lp
Metal contact is much closer to the depletion region than the diffusion length
Long diode dn >> Lppn(xn)
Minority carrier concentration
emitter (n+) base (p) collector (n)contact contact
pe0
nb0 pc0
/0 1be BeV k T
eEp be p
e e
p eI eA D
W x
xe We Web WbcxcWc
/ /0
be B bc BeV k T eV k Tb
En be nbc be
n e eI eA D
W W
0 exp beb
B
eVnk T
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp bcc
B
eVpk T
Emitter current
0 / /0 01 1be B bc Bbe p e eV k T eV k Tbe n b be n bE En Ep
eb e bc be bc be
eA D p eA D n eA D nI I I e eW x W W W W
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
pe0
nb0 pc0
xe We Web WbcxcWc
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp beb
B
eVnk T
Collector current
emitter (n+) base (p) collector (n)contact contact
/0 1bc BeV k T
ccp bc p
c c
p eI eA D
x W
/ /0
be B bc BeV k T eV k Tb
cn bc nbc eb
n e eI eA D
W W
pe0
nb0 pc0
xe We Web WbcxcWc
0 exp beb
B
eVnk T
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp bcc
B
eVpk T
Collector current
0/ /0 01 1be B bc Bbc p ceV k T eV k Tbc n b bc n bc cp cn
bc be c c bc be
eA D peA D n eA D nI I I e eW W x W W W
/ /1 1be B bc BeV k T eV k Tc cp cn F ES CSI I I I e I e
pe0
nb0 pc0
xe We Web WbcxcWc
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp beb
B
eVnk T
Ebers-Moll model
/ /1 1be B bc BeV k T eV k TC F ES CSI I e I e
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
IE
IB
IC
/ 1be BeV k TF ESI I e / 1bc BeV k T
R CSI I e
R RI F FI
B E CI I I
emitter (n+) base (p) collector (n)contact contact
pe0
nb0 pc0
xe We Web WbcxcWc
0 exp beb
B
eVnk T
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp bcc
B
eVpk T
Not an npn transistor
Emitter efficiency
/0 1be BeV k T
eEp be p
eb e
p eI eA D
W x
/ /0
be B bc BeV k T eV k Tb
En be nbc be
n e eI eA D
W W
For e ~ 1, Wbc - Wbe << Lb, Web - xe and nb0 >> pe0
Small base width and heavy emitter doping
for npn
2i
De
nN
2i
Ab
nN
11 /
Ene
En Ep Ep En
II I I I
neutral base width
Base transport factor
c
En
IBI
ratio of the injected current to the collected current
recombination in the base would reduce the base transport factor
A thin base with low doping results in a base transport factor ~ 1
Current transfer ratio
Ce
E
I BI
~ 1 for a good BJT
Transistor modes
1. Forward active: emitter-base forward, base-collector reverse2. Saturation: emitter-base forward, base-collector forward3. Reverse active: emitter-base reverse, base-collector forward4. Cut-off: emitter-base reverse, base-collector reverse
Ebers-Moll model
/ /1 1be B bc BeV k T eV k TC F ES CSI I e I e
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
IE
IB
IC
/ 1be BeV k TF ESI I e / 1bc BeV k T
R CSI I e
R RI F FI
B E CI I I
Common base configuration
/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
solve for Vbe
saturation
active
cutoff IE < 0
http://lamp.tu-graz.ac.at/~hadley/psd/L13/commonbase/pnp_current.html
0 0
0
be p e be n bES
eb e bc be
be n bR CS
bc be
eA D p eA D nIW x W WeA D nIW W
Ebers - Moll Model
0
0 0
bc n bF ES
bc be
bc p c bc n bCS
c c bc be
eA D nIW W
eA D p eA D nIx W W W
Common emitter configuration
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e
B E CI I I
http
://la
mp.
tu-g
raz.
ac.a
t/~ha
dley
/psd
/L13
/com
mon
emitt
er.p
hp
current amplification ~100
Current amplification factor
Cfe
B
IhI
B E CI I I
1 1B CI I
1 1C e
B e
I BI B
~ 50 - 500
C EI I
for common emitter configuration
The Art of ElectronicsHorowitz and Hill
Transconductance
Cm
be
IgV
The transconductance can be very high.
/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e
/be BeV k TF ES C Bm
B B B
e I eI e Ig ek T k T k T
The first term depends on Vbe
Early effect
/ /1 1be B bc BeV k T eV k Tc F ES CSI I e I e
/ /1 1be B bc BeV k T eV k TE ES R CSI I e I e
B E CI I I
Ebers - Moll:
0 0be p e be n bES
eb e bc be
eA D p eA D nIW x W W
0 0bc p c bc n bCS
c c bc be
eA D p eA D nIx W W W
IES and ICS are treated as constants but the depletion widths Wbc, Wbe, Wc,and We depend on the voltages.
pe0
nb0 pc0
xe We Web WbcxcWc
0 exp beb
B
eVnk T
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp bcc
B
eVpk T
Minority carrier concentration
pe0
pc0
xe xc
0 exp beb
B
eVnk T
0 exp bcb
B
eVnk T
0 exp bee
B
eVpk T
0 exp bcc
B
eVpk T
xn1 xp1 xn2xp2
Early effect
Common emitter configurationBase width modulation: smaller width increases the diffusion current and increases the gain.
Punchthrough: The neutral base width goes to zero and all gain is lost.Lightly dope the collector -> voltage drops in collector. Makes circuit slower.
http
://la
mpx
.tugr
az.a
t/~ha
dley
/psd
/L13
/com
mon
_e_e
arly
.php
IC ~ IB
Common emitter configuration
IC ~ IB amplifier
Small signal response
Low input impedance amplifier
Vcc
VresistorVtransistor
Small signal response
input conductance: cm
EB
igv
transconductance:
c B EB EBi i g v transistor man
BEB
EB
igv
Small signal response
01f f 0Tf f
1
Heterojunction bipolar transistors