Chp5. pn Junction Electrostatics Part...
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Chp5. pn Junction Electrostatics Part I 119
Transcript of Chp5. pn Junction Electrostatics Part...
Chp5. pn Junction Electrostatics
Part I
119
5.1.1. Junction Terminology
metallurgical junction (not always equal to electrical
junction)
Figure5.1Junction definition : (a) Location of the metallurgical junction, (b) doping profile - a plot of the net doping versus position
5.1 PRELIMINARIES
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Figure reference: “Semiconductor Device Fundamentals”
Robert F. Pierret, Addison-Wesley Publiching Company
5.1.2. Poisson’s Equation
Charge density vs. electric field
3-D
ρ = q (p – n + ND – NA)
full ionization assumed
ρ = 0 for charge neutrality
ρ ≠ 0 in depletion region at junction
Ks : dielectric constant
ε0 : permittivity of free space
ρ : charge density c/cm3
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0
SK
5.1.3. Qualitative Solution
Potential distribution
Electric field
Charge density
at junction under equilibrium
Energy band diagram construction for pn junction diode.
Assume 1-D
step junction
under equilibrium
→ EF constant independent of position
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Step-by-step construction of equilibrium band diagram for pn junction diode
Figure 5.3 Step-by-step construction of the equilibrium energy band diagram for a pnjunction.(a) Assumed step junction profile and energy band diagrams for the semiconductor region far removed from the metallurgical junction. (b) Alignment of the part (a) diagram to the position-independent Fermi level. (c) The completed band diagram.
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Figure reference: “Semiconductor Device Fundamentals”
Robert F. Pierret, Addison-Wesley Publiching Company
General Function Form of Electrostatic Variables in a pn Junction under Equilibrium
Figure 5.4 General functional form of the electrostatic variables in a pn junction under equilibrium conditions. (a) Equilibrium energy band diagram. (b)Electrostatic potential, (c)electric field, and (d)charge density of position
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Figure reference: “Semiconductor Device Fundamentals”
Robert F. Pierret, Addison-Wesley Publiching Company
Conceptual pn junction formation and Associated charge distribution
Figure5.5 Conceptual pn junction formation and associated charge redistribution. (a) Isolated p and n regions. (b) Electrons and holes diffuse to the opposite side of the junction moments after joining the p and n regions. (c) Charge redistribution completed and equilibrium conditions re-established. (d) Previously deduced charge density versus position. ( -holes, -ionized acceptors,
-electrons, and -ionized donors.)
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Figure reference: “Semiconductor Device Fundamentals”
Robert F. Pierret, Addison-Wesley Publiching Company
5.1.4. The Built-in Potential(Vbi)
Consider a non-degenerately-doped pn
junction under equilibrium
metallurgical junction at x = 0
양변 적분
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dx
dV
bipn
xV
xV
x
x
VxVxV
dVdxn
p
n
p
)()(
)(
)(
Under equilibrium,
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0dx
dnqDnqJ NnN
n
dxdn
q
kT
n
dxdnD
n
N //
])(
)(ln[
)(
)(
p
n
xn
xn
x
xbi
xn
xn
q
kT
n
dn
q
kT
dxV
n
p
n
p
Step Junction!
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A
ip
Dn
N
nxn
Nxn
2
)(
)(
qEV
eVV
cmNNqe
n
NN
q
kTV
gbi
bi
DA
i
DAbi
/
6.0
Si 300K, ,10 ..
ln
max,
315
2
Alternative Derivation Based on Energy Band Diagram
(refer to Fig. 5.4)
or
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)()(1
)()(1
)()(
nipi
nCpC
pnbi
xExEq
xExEq
xVxVV
sideniFsidepFibi EEEEq
V )()(1
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q
EV
q
EEEEE
g
bi
g
sideniFsidepFi
)(,)(
2
ln
ln)(
ln)(
i
DAbi
i
DsideniF
i
AsidepFi
n
NN
q
kTV
n
NkTEE
n
NkTEE
5.1.5. The Depletion Approximation
To solve Poisson’s Eq. And obtain closed form
solution!
Consider,
p, n not known for depletion region.
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)( 0
0
AD
S
S
NNnpK
q
Kdx
d
“The approximation”
(1) NA >> np or pn
ρ = -qNA for -xp ≤ x ≤ 0
ND >> nn or pn
ρ = +qND for 0 ≤ x ≤ xn
(2) Charge density ρ = 0 in bulk region
(x > xn , x < -xp)
In summary,
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bulkin 0
reg. dep.in )(0
AD
S
NNK
q
dx
d
Figure 5.6 (a) Pictorial summary of the depletion approximation. (b) Illustration of
the approximation as applied to a step junction.
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Figure reference: “Semiconductor Device Fundamentals”
Robert F. Pierret, Addison-Wesley Publiching Company
