ch1 4 pn iv characteristics
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8/11/2019 Ch1 4 PN IV Characteristics
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Current-Voltage Characteristics
Qualitative Analysis: Thermal Equilibrium
Diffusion
- electron diffusion from n-side to p-side
- most will be reflected- few electrons will have enough energy
and overcome the barrier height
Drift
- Electron drift from p-side to n-side
- few electrons will be drifted (e- isminority carriers in p-side)
- at thermal equilibrium, diffusion and
drift are balanced
Net electron current = 0
Similar, net hole current=0
Thus, the total current=0
Electrons
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Current-Voltage Characteristics
Qualitative Analysis: Forward Bias (V A
>0)
More electron diffusion from n-side to p-side
due to lowering of barrier height
Electrons drift from p-side to n-side remains
same (minority concentration unchanged)
Electron diffusion dominates
Diffusion current increases exponentiallywith V A
potential barrier (Vbi-V A) linearly
decrease with V A,
plus electron concentration (in n-side,majority carrier) above the barrier
height increases exponentially when
the energy level moves upward
Electrons
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Current-Voltage Characteristics
Qualitative Analysis: Forward Bias (V A>0)
Similar analysis applied to holes
The total current is dominated by both
electron and hole diffusion and given
as
JF=JN, F+JP, F
Forward current increasesexponentially with V A
Particle Flow
Hole diffusion
Current
Hole drift
electron
diffusion
electron drift
Will V A be larger than Vbi?
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Current-Voltage Characteristics
Qualitative Analysis: Reverse Bias (V A<0)
- Very few electron diffusion from n-side to
p-side due to increased barrier height
- Electrons drift from p-side to n-side
remains same (minority concentration
unchanged)
- Electron current is dominated by drift- Thus electron current is very small
Similar analysis applied to holes
So, the total reverse current dominated byboth electron and hole drift currents
Reverse currents are very small and nearly
independent with V A value
Electrons
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Current-Voltage Characteristics
Qualitative Analysis: I-V Characteristics
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Assumptions
(1) The diode is being operated under steady state conditions
(2) A non-degenerately doped step junction models the doping profile(3) The diode is one dimensional
(4) Low level injection prevails in the quasineutral regions
(5) There are no processes other than drift, diffusion, and thermal R-G (with
negligible) taking place inside the diode.
Thus, the current can be calculated as
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Current-Voltage Characteristics
Quanti tative Analysis: I-V Characteristics
Quasi-neutral regions
- The minority carrier diffusion equations are
E0E0
-x p xn
Depletion
region
Quasi-neutral
regions
P-region N-region
E≠0
n
p
nnP
p
n
p p
N
x x p
dx
pd D
x xn
dx
nd D
2
2
2
2
0
0
From the above two equations (plus boundary
condition, will be discussed later),
both and
can be obtained
pn n p
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Quasi-neutral regions
- Since low level injection (E≈0) and 000
dx
dp
dx
dn
Thus, current density in these two quasi-neutral region
can be calculated as
dxnd qD x J
p
N N )(
dx
pd qD x J n
PP
)(
For x ≤ -xp
For x ≥ xn
Recall:
pqD pE q J J J p pdiff pdrift p p ,,
nqDnE q J J J nndiff ndrift nn ,,
Thus, we are able to calculate the current density (diffusion current)
at quasi-neutral regions!!!
Since low-level injection,
the majority carrier
concentration remains
same within quasi-neutral
regions, thus the E-field isalmost zero
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Depletion region
E0E0
-x p xn
Depletionregion
Quasi-neutral
regions
P-region N-region
E≠0G R
P
G R N
t
p
dx
dJ
q
t
n
dx
dJ
q
|1
0
|1
0- Recall
- From assumption (5), we have
0|
0|
G R
G R
t
p
t
n
- Then, we have0
dx
dJ N
0dx
dJ P
- Which mean that JN and JP are constant within depletion region
)()(
)()(
nPn pP
p N n p N
x J x x x J
x J x x x J
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Depletion region
E0E0
-x p xn
Depletionregion
Quasi-neutral
regions
P-region N-region
E≠0
- Since JN and JP are constant within depletion
region
)()(
)()(
nPn pP
p N n p N
x J x x x J
x J x x x J
- The total current density can be given asbelow
)()()()( nP p N P N x J x J x J x J J
Thus, the total current density can be calculated as the sum of
diffusion currents at both depletion edges JN(-xp) and JP(xn)!!!
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Current-Voltage Characteristics
Quanti tative Analysis: I-V Characteristics
Boundary Conditions
At the Obmic contacts
- Consider long “wide” base diode, which
means the diode has contacts which are
larger than the minority carrier diffusion
lengths, the contacts can be viewed at
- So, the boundary conditions are
x
0)(
0)(
xn
p
x pn
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Boundary Conditions
At Depletion Region Edges
- Introducing “quasi-Fermi level” FN and FP
(FN-FP=V A), inside depletion region, we have
- So, the boundary conditions are
kT E F
ii N enn
/)(
kT F E
iPien p /)(
recall
kT qV
i Aennp
/2
kT qV
A
i p p
Ae N
n xn
/2
)( A p p N x p )(
)1()( /2
kT qV
A
i
p p
Ae N
n xn
at x = -xp
Dnn N xn )( kT qV
D
inn
Ae N
n x p
/2
)(
)1()( /2
kT qV
D
i
nn Ae
N
n x p
at x = xn
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Calculation of Current JP(xn)
xn-x p
x
x’0
(1) Shift the origin of coordinates to xn
(2) the equation and boundary conditions are
(3) Solving the above equations, we have
Lp xkT qV
D p
pn pP ee
N L
n Dq
dx pd qD x J Ai /'/
2
)1('
)'(
(4) So, JP(xn) can be given as
)1()0'()( /
2
kT qV
D p
p
PnP Ai e
N L
n Dq x J x x J
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Current-Voltage Characteristics
Quantitative Analysis: I-V Characteristics
Calculation of Current
(1) Similarly, JN(-x
p) can be obtained as follow
)1()( /
2
kT qV
An
n
p N Ai e
N L
n Dq x x J
(3) A useful and important equation
)1)(( /22
kT qV
A N
n
DP
p Aii e
N L
n D
N L
n DqA AJ I
(2) So, the total current
)(
)1(22
0
/0
A N
n
DP
p
kT qV
N L
n D
N L
n DqA I
e I I
ii
A
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Current-Voltage Characteristics
Some Useful Discussions
IV Characteristics (Ideal)
(i) For reverse biases greater than a few
kT/q,
(ii) For forward biasing larger than a few
kT/q,
(iii) In forward bias conditions, I-V alwaysplotted as semilog scale since
(iv) Saturation current
- depends on intrinsic concentration
- depends on doping concentration
0 I I
)/exp(0 kT qV I I A
AV kT
q I I )ln()ln( 0
)(22
0
A N
n
DP
p
N L
n D
N L
n DqA I ii
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Current-Voltage Characteristics
Some Useful Discussions
Carrier Current Components
Think Again: How we calculate the current?
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Current-Voltage Characteristics
Some Useful Discussions
Carrier Concentrations (Forward bias)
- Carriers are injected into other side by
diffusion and become minority
carriers.
- The excess minority carriers are
eliminated by recombination during
diffusion deeper into the regions
- Thus, there is a build-up of minority
carrier in the quasinetural regionsimmediately adjacent to the edges of
the depletion regions.
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Current-Voltage Characteristics
Some Useful Discussions
Carrier Concentrations (Reverse bias)
- The depletion region acts like a “sink”for minority carriers, draining the carriers
from the adjacent quasineutral region.
- A reverse bias of a few kT/q effectively
reduces the minority carrier concentrations
to zero at the edges of the depletion
region.
- Larger reverse biases have little effecton the carrier concentration (consistent
with the saturation current in reverse
bias).
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