P-N Junctions Physical aspects of pn junctions Mathematical models • Depletion capacitance • Breakdown characteristics • Basis for other devices Circuit Symbol + V -
Dec 28, 2015
P-N Junctions
Physical aspects of pn junctions
Mathematical models
• Depletion capacitance• Breakdown characteristics
• Basis for other devices Circuit Symbol
+ V -
PHYSICAL ASPECTS OF THE PN JUNCTION
Metallurgical Junction
p-type semiconductor n-type semiconductor
iD+ -vDDepletion region
x
p-type semicon- ductor
n-type semicon- ductor
iD+
-W1 0
W
-Dv -
W2Fig. 1.2-1
P-N Junctions
N-typeN
D
P-typeN
A
P-N Junctions
N-typeN
D
P-typeN
A
P-N Junctions
N-typeN
D
P-typeN
A
Depletion Layer or Region
P-N Junctions
N-typeN
D
P-typeN
A
Depletion Layer or Region
ChargeDensity
qND
-qNA
P-N Junctions
N-typeN
D
P-typeN
A
Depletion Layer or Region
ChargeDensity
qND
-qNA
BandDiagram
Electrostatics in PN Junction
ChargeDensity
qND
-qNA
x
Q = x
Electrostatics in PN Junction
ChargeDensity
qND
-qNA
x
xElectric Field
Gauss' Law in 1 Dimension: Electric Field = Q /
Q = x
Electrostatics in PN Junction
Vbi = Built
in Voltage
ChargeDensity
qND
-qNA
x
x
x
Electric Field
ElectronPotential
Gauss' Law in 1 Dimension: Electric Field = Q /
Q = x
Why is this the Equilibrium Condition?
Vbi = built-in voltage
= kT ln ( )NAN
D
ni2
Why is this the Equilibrium Condition?
Vbi = built-in voltage
= kT ln ( )NAN
D
ni2
Too much Vbi
Too little Vbi
P-N Junctions --- Diodes
N-typeN
D
P-typeN
A
First-Principles Model
P-N Junctions --- Diodes
N-typeN
D
P-typeN
A
First-Principles Model
P-N Junctions --- Diodes
N-typeN
D
P-typeN
A
First-Principles Model
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40
10
20
30
40
50
60
70
80
90
100
Diode voltage (V)
Dio
de
cu
rre
nt
(nA
)
P-N Junctions --- Diodes
N-typeN
D
P-typeN
A
First-Principles Model
Applying Voltage to a Diode
- V +F
P
FN
Forward Bias
Forward Bias
Applying Voltage to a Diode
- V ++ V -F
P
FN
FN
FP
Forward Bias
Reverse Bias
Capacitance in pn Junctions
W1 =
2si(o-vD)NDqND(NA+ND)
W2 = 2si(o-vD)NAqND(NA+ND)
o = kTq ln
NAND
ni2 = UT ln
NAND
ni2
Capacitance in pn Junctions
W1 =
2si(o-vD)NDqND(NA+ND)
W2 = 2si(o-vD)NAqND(NA+ND)
o = kTq ln
NAND
ni2 = UT ln
NAND
ni2
Cj = AsiqNAND2(NA+ND)
1o-vD
= Cj0
1 - vDo
Capacitance in pn Junctions
W1 =
2si(o-vD)NDqND(NA+ND)
W2 = 2si(o-vD)NAqND(NA+ND)
o = kTq ln
NAND
ni2 = UT ln
NAND
ni2
Cj = AsiqNAND2(NA+ND)
1o-vD
= Cj0
1 - vDo
-3 -2.5 -2 -1.5 -1 -0.5 0 0.50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Diode voltage (V)
Ca
pa
cita
nce
(fF
) Cj0
Breakdown Voltage
Breakdown Voltage
Caused byAvalancheMultiplication
Due to reachinga critical electric field