Post on 22-May-2020
Institute of Solid State PhysicsTechnische Universität Graz
6. pn - Junctions
Nov. 7, 2018
Institute of Solid State Physics
pn junctions Technische Universität Graz
p n
pn junctions are found in:diodessolar cellsLEDsisolation JFETsbipolar transistorsMOSFETssolid state lasers
pn junction
p-type n-type
Ec
Ev
EF
Ec
Ev
EF
isolated semiconductors
exp v Fv
B
E Ep Nk T
exp F cc
B
E En Nk T
valid for both n and p doping
ln cF c B
D
NE E k TN
ln vF v B
A
NE E k TN
pn junction
p-type
n-typeEc
Ev
EF
Ec
Ev
semiconductors in contactelectrons flow from n to p
ln cF c B
D
NE E k TN
ln v
F v BA
NE E k TN
ln cF v g B
D
NE E E k TN
pn junction semiconductors in contact
Abrupt junction: the doping changes abruptly from p to n
Built-in voltage
FE
bieV
cE
vE
p n
FE
bieV
cE
vE
p n
Built-in voltage Vbi
, , , ,
ln lnc vbi g B B
D n A n A p D p
N NeV E k T k TN N N N
, , , ,
ln c vbi g B
D n A n A p D p
N NeV E k TN N N N
ln vF vp B
A
NE E k TN
ln ccn F B
D
NE E k TN
gE
Vbi
, , , ,
ln c vbi g B
D n A n A p D p
N NeV E k TN N N N
, , , ,2ln D n A n A p D p
bi Bi
N N N NeV k T
n
2ln D Abi B
i
N NeV k Tn
for ND,n - NA,n = ND and NA,p - ND,p = NA
22 exp lng ii v c g B
B v c
E nn N N E k Tk T N N
Vbi
Can Vbi perform work?
p n
E
-
-
-
+
+
+
+
+
+
-
-
-
- - - - -
- - - - + + +
+ + +
p and n profiles
exp F cc
B
E En Nk T
exp v F
vB
E Ep Nk T
p
xn
x
-xp
xn
depletion region
depletion approximation
FE
bieV
cE
vE
p n
space charge
x
-xp
xn
NAxp = NDxn
+
-
eND
eNA
FE
bieV
cE
vE
p n
electric field
x
E-xp xn
E pushes the holes towards p and the electrons towards n
dEdx
Ap
eNE x x
Dn
eNE x x
x
-xp
xn
+
-
eND
eNA
maxA pD n eN xeN xE
E
Gauss's law in 1-D is
potential
x
E-xp xn
dV Edx
2
2
02
02
Ap p
Dn n
eN xV xx x x
eN xV xx x x
Ap
eNE x x
Dn
eNE x x
2 2( ) (0) 0 ( )2 2
A Dp p n n
eN eNV x x V V x x
potential
dV Edx
2 2
2 2A p D n
bi
eN x eN xV
electron energies are plotted in band diagram
Depletion width 2 2
2ln2 2
A p D nB D Abi
i
eN x eN xk T N NVe n
A p D n D p A nN x N x N W x N W x W
D Ap n
A D A D
N W N Wx xN N N N
2
2D A
biD A
N NeV WN N
2 D A bi
D A
N N VW
eN N
light doping => wide depletion width
Depletion width
W
Vbi ~ 1V
W ~ 1m
Emax ~ 104 V/cm
vsat ~ 107 cm/sec
The electric field pushes the electrons towards the n-region and the holes towards the p-region.
Diffusion sends electrons towards the p-region and holes towards the n-region.
linearly graded junction
( ) ( )D Ae N x N x eax
2 22
max 2 2 8ea W eaWE dx x E
2 3
2 2 3ea W xV Edx x
3
12bieaWV
x
ND - NA
W/2-W/2
-W/2 W/2
Area = Vbi
Vbi
EF
Ec
Ev
EgeVbi
http://lampx.tugraz.at/~hadley/psd/L6/linearly_graded.html
Isolation
Solar cell
pn
hf > Eg
Light creates an electron-hole pair in the depletion region. The electric field sweeps the electrons towards the n-region and the holes towards the p-region.
Light emitting diode
pn
hf = Eg
Electrons and holes are injected into the depletion region by forward biasing the junction. The electrons fall in the holes. For direct bandgap semiconductors, photons are emitted. For indirect bandgap semiconductors, phonons are emitted.
Heterojunctions
Bipolar transistor
p
MOSFET
functions as a switch~ 1 billion /chip
Metal Oxide Semiconductor Field Effect Transistor
http://en.wikipedia.org/w
iki/Image:M
osfetlinear.sv
Varactor
nj bi RC V V
abrupt: n = 1/2linearly graded: n = 1/3
n = 1/(m+2)
mD A oN N x x
Capacitance-voltage characteristics
-2 F mjCW
2 D A bi
j D A
N N V VW
C eN N
abrupt junction:
a one sided abrupt junction in reverse bias:
2
21 bi
j D
V VC e N
p+ n
specific capacitance
Capacitance-voltage characteristics
a one sided abrupt junction in reverse bias:
2
21 bi
j D
V VC e N
slope gives impurity concentration and the intercept gives Vbi
p+ n2
1
jC
-V
2slopeDe N
-Vbi
diode fabrication