ideal currents in a pn junction
DESCRIPTION
Ideal currents in a pn Junction. Debye length. +. -. +. +. +. +. +. +. +. +. -. -. -. -. -. -. -. -. +. Debye length. +. -. +. +. +. +. +. +. +. +. -. -. -. -. -. -. -. -. +. Transient sheath in ion acoustic wave experiments in a plasma. Charge neutrality. - PowerPoint PPT PresentationTRANSCRIPT
Debye length2 vV
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V
x
2
2
d V
dx i en n e
eV0TB e
n e1 e
0B e
eV1 1 n e
T
Debye length
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+
V
x
2
2
d V
dx
0B e
eV1 1 n e
T
20
B e
n e V
T
x
TB e2n e0
0V V e
B eD 2
0
T
n e
Transient sheath in ion acoustic wave experiments in a plasma
02
20
1 expB e
eVn e
Td V
dx
2
2
dVU
dx
d V dU dV dUU
dx dV dx dV
dVE
dx
0
0
1 expB e
eVn e
TUdU dV
0
0
1 expB e
eVn e
TUdU dV
20
10
exp2
B e
B e
n e TU eVV C
e T
01
0
2expB e
B e
n e TdV eVU V C
dx e T
00 1
0
2expx B e
appliedB e
n e T eVV V V C dx
e T
0
0
1 expB e
eVn e
TUdU dV
1applied
B e
eV
T
2
2 20
02 2 B e
dVn e Vdx
T
0
0
1 1B e
eVn e
TUdU dV
20
0 B e
n edVdx
V T
20 0
0
exp
B e
x
V V n e
T
20
0 B e
n ew
T
1applied
B e
eV
T
01
0
2expB e
B e
n e TdV eVU V C
dx e T
0
0
2n eVdVU
dx
00
00
2applied
w
V
n edVdx
V
0
0
2 appliedVw
n e
MATLAB calculation
Basic model
p n
aN
dNhole diffusion
electron diffusion
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Basic model
p n+-
space charge region
negative chargeaN positive chargedN
Basic model – thermal equilibriumno applied bias voltage
FE
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p n
cE
cE
vE
vE
FiEbi biE eV
FiEbi biE eV
bi biE eV
FneVFpeV
Reverse biased PN junction- - - - - -
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p n
bias RV Vtotal bi RV V V
WW
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p n
2 s bi R a d
a d
V V N NW
e N N
bi Rmax
2 V VE
W
Reverse biased PN junctionenergy diagram
cE
cEvE
vE
FiE
FiE
FnE
FpE
ReV
totaleV
Forward biased PN junction- - - - - -
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p n
W
bias FV V
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p n
W
- +
Forward biased PN junctionenergy diagram
cEcE
vEvE
FnEFpE bi Fe V V
-
+
Schottky barrier junctionThermal equilibrium
cE
vE
FiE
FE
nx
W
bi biE eVSchottky barriermetal surface
FE -
Schottky barrier junction
cE
vE
FiEFE
nx
FE
bias RV V
cE
vE
FiEFE
nx
FEcE
vE
FiEFE
nx
FE
biasV 0bias FV V
Characteristics of a Schottky diode and a PN junction diode
VDVT
D sI I e 1
reverse
saturation current
thermal potential
BT
TV
e
Basic assumptions
p n
aN
dNhole diffusion
electron diffusion
Maxwell Boltzmann distributions
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p n+-
acceptor density in p regionp0 ap N
donor density in n regionn0 dn N
sharp boundaries
Basic assumptions
px nx0
hole concentration in n region2i
n0d
np N
electron concentration in p region2i
p0a
nn N
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p n
Basic assumptions
px nx0
total minority carrier hole densitynp total minority electron densitypn
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p n
Basic assumptions
excess minority carrier hole densityn n n0p p - p
-
excess minority electron density
p p p0n n n
px nx0
total minority carrier hole densitynp total minority electron densitypn
excess minority carrier hole densityn n n0p p - p
-
excess minority electron density
p p p0n n n
acceptor density in p regionp0 ap N donor density in n regionn0 dn N
hole concentration in n region2i
n0d
np N
electron concentration in p region2i
p0a
nn N
Electron energy profile- - - - - -
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p n
px nx0
where a d Bbi T T2
i
N N TV V ln V
en
Charge concentration- - - - - -
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p n
px nx0
where a d Bbi T T2
i
N N TV V ln V
en
VbiVa d T
2i
N Ne
n
eVbiTBe
n0 dn N
2i
p0a
nn
N
eVbiTB
p0 n0n n e
Charge concentration- - - - - -
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p n
px nx0eVbi
TBp0 n0n n e
n0 dn N
2i
p0a
nn
N
Forward biased PN junction- - - - - -
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p n
W
bias FV V
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p n
W
due to space chargeE
due to applied potentialE
Forward biased PN junction- - - - - -
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p n
bias FV V
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p n
W
e V Vbi appliedTB
p n0n n e
eVappliedTB
p0n e
Forward biased PN junction- - - - - -
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p n
bias FV V
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p n
W
eVappliedTB
p p0n n e
eVappliedTB
n n0p p e
Forward biased PN junction- - - - - -
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p n
bias FV V
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p n
W
eVappliedTB
p p0n n e
eVappliedTB
n n0p p e
Forward biased PN junction- - - - - -
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p n
bias FV V
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p n
W
eVappliedTB
p p0n n e
eVappliedTB
n n0p p e
Evolution of the density perturbations
n
2n n nn
p p2p0
x x
p p ppD E g'
x tx
2p p p0L D
2n n
2 2p
d p p0
dx L
Drift due to the electric field
Diffusion of the perturbation
Generation of additional perturbationCollision lifetimeSteady-stateNeglect drift and generation
Evolution of the density perturbations
2
n nn2 2
p
d p p0 x x
dx L
eVappliedT nB
n n0p
x xp p e 1 exp
L
2p p p0L D
Evolution of the density perturbations
eVappliedT pB
p p0n
x xn n e 1 exp
L
2
p pp2 2
n
d n n0 x x
dx L
2
n n n0L D
Currents – sum of hole and electron diffusion currents
eVappliedT pB
p p0n
x xn n e 1 exp
L
np n p
x xn
dpJ x eD
dx
eVappliedT nB
n n0p
x xp p e 1 exp
L
pn p n
x xp
dnJ x eD
dx
Currents – sum of hole and electron diffusion currents
np n p
x xn
dpJ x eD
dx
pn p n
x xp
dnJ x eD
dx
The Cowasaki gets excellent gas mileage.
Simple three-dimensional unit cell
a
b
c
