pn-junctions - zid: lampx web serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g b dn...
TRANSCRIPT
![Page 1: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/1.jpg)
Institute of Solid State PhysicsTechnische Universität Graz
pn-junctions
![Page 2: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/2.jpg)
Institute of Solid State Physics
pn junctions Technische Universität Graz
p n
pn junctions are found in:diodessolar cellsLEDsisolation JFETsbipolar transistorsMOSFETssolid state lasers
![Page 3: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/3.jpg)
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
![Page 4: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/4.jpg)
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
![Page 5: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/5.jpg)
pn junction semiconductors in contact
Abrupt junction: the doping changes abruptly from p to n
Built-in voltage
FE
bieV
cE
vE
p n
![Page 6: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/6.jpg)
FE
bieV
cE
vE
p n
Built-in voltage Vbi
, , , ,
ln lnc vbi v g B v B
D n A n A p D p
N NeV E E k T E 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 v B
A
NE E k TN
ln cF v g B
D
NE E E k TN
![Page 7: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/7.jpg)
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
![Page 8: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/8.jpg)
Vbi
Can Vbi perform work?
p n
E
-
-
-
+
+
+
+
+
+
-
-
-
- - - - -
- - - - + + +
+ + +
![Page 9: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/9.jpg)
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
![Page 10: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/10.jpg)
space charge
x
-xp
xn
NAxp = NDxn
+
-
eND
eNA
FE
bieV
cE
vE
p n
![Page 11: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/11.jpg)
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
![Page 12: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/12.jpg)
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
![Page 13: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/13.jpg)
potential
dV Edx
2 2
2 2A p D n
bi
eN x eN xV
electron energies are plotted in band diagram
![Page 14: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/14.jpg)
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
![Page 15: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/15.jpg)
D Ap n
A D A D
N W N Wx xN N N N
2 D A bi
D A
N N VW
eN N
2lnB D Abi
i
k T N NVe n
![Page 16: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/16.jpg)
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.
![Page 17: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/17.jpg)
![Page 18: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/18.jpg)
![Page 19: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/19.jpg)
![Page 20: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/20.jpg)
p and n profiles (again)
exp c Fc
B
E En Nk T
exp F vv
B
E Ep Nk T
p
xn
x
-xp
xn
depletion region
Knowing the voltage profile we can calculate n and p.
FE
bieV
cE
vE
p n
![Page 21: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/21.jpg)
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
![Page 22: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/22.jpg)
Isolation
![Page 23: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/23.jpg)
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.
![Page 24: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/24.jpg)
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.
![Page 25: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/25.jpg)
Heterojunctions
![Page 26: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/26.jpg)
Bipolar transistor
p
![Page 27: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/27.jpg)
MOSFET
functions as a switch~ 1 billion /chip
Metal Oxide Semiconductor Field Effect Transistor
http://en.wikipedia.org/w
iki/Image:M
osfetlinear.sv
![Page 28: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/28.jpg)
Varactor
nj bi RC V V
abrupt: n = 1/2linearly graded: n = 1/3
n = 1/(m+2)
mD A oN N x x
![Page 29: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/29.jpg)
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
![Page 30: pn-junctions - ZID: LampX Web Serverlampx.tugraz.at/~hadley/psd/lectures17/nov15.pdfln cv bi g B Dn An Ap D p NN eV E k T NN N N ,, , , 2 ln Dn An Ap D p bi B i NN N N eV k T n 2 ln](https://reader036.vdocuments.us/reader036/viewer/2022081607/5eca088ee6fffa22096b08a9/html5/thumbnails/30.jpg)
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