Chapter 5 pn Junctions and Diodes
5.1 Fabrication of pn junction
5.2 Equilibrium conditions
5.3 Forward- and reverse-biased junctions in steady state
5.4 Junction breakdown
5.5 Deviations from the simple theory of junctions
5.6 Transient response
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5.3 Forward- and reverse-biased
junctions in steady state
• Voltage applied (Va) across a pn junction
potential barrier is now changed from the built-in potential V0
Fermi Level on either side of the junction is shifted by an energy in eV
1. only a very tiny fraction drops across the neutral n and p regions. Most of Va appears
across the depletion region.
2. If we take the reference potential to be on the n side of the junction, then the
electrostatic potential of the p side w.r.t. the n side is
Recall:
• The total potential V on the p side:
(a) Forward bias (+’ve on p-side ) :
•
•
•
electrostatic potential (V) of the p side is raised relative to the n side
potential barrier is lowered
𝑉 is reduced W is reduced (narrower) 𝐹0 is reduced
(b) Reverse bias (- ve on p-side) :
•
•
•
electrostatic potential (V) of the p side is lowered relative to the n side
potential barrier is raised
𝑉 is increased W is increased (wider) 𝐹0 is increased
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Separation of the Fermi Level
1. Change in the electrostatic potential across the junction =>corresponding change in
band bending.
2. Deep inside the neutral region on the n side, it must still be true that
where Efn and Ein are respectively the Fermi Level and the intrinsic level deep inside
the neutral region on the n side
Note that
and
(junction in equilibrium)
Va ≠ 0, junction no longer in equilibrium and the Fermi Level
splits apart.
(a) Forward bias : Va > 0, the Fermi Level Efp on the p side
becomes lower than that on the n side Efn, smaller energy
barrier.
(b) Reverse bias : Va < 0, the Fermi Level Efp on the p side
becomes higher than that on the n side Efn, larger energy
barrier.
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Effects of External Bias on Current Flow
1. In equilibrium, no net electron and hole
currents : diffusion and drift components
cancel each other
2. With external bias :
Forward bias : Energy barrier is reduced.
• Less blockage of diffusion current.
• Holes diffuse from the p side to the n side
and electrons diffuse in the opposite
direction.
• Current flows from the p side to the n
side.
Reverse bias : Energy barrier is increased.
• More blockage of diffusion current.
• No current flows across the junction.
Fig. 5-13
Effects of a bias at a p-n junction; transition region
width and electric field, electrostatic potential, energy band
diagram, and particle flow and current directions within W for (a)
equilibrium, (b) forward bias, and (c) reverse bias.
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Carrier Injection /extraction -I
For a junction in equilibrium
(1)
• xpo and xno are the equilibrium separations between
the edges of the depletion region and the junction
Assume no significant generation/recombination in
the depletion region, then Eqn. 1 is also valid in the
presence of an applied bias Va :
(2)
• xp and xn are the corresponding non-equilibrium separation (edges of depletion region)
• V = V0 + Va is the non-equilibrium potential of the p side w.r.t. the n side.
From (1) and (2):
• If majority carrier concentration at the edge of the depletion region is not affected by the
applied bias (LLI) , i.e.
We get
ELEC4510-Semiconductor
Materials
Devices (Fall-2011)
Conclusion : the minority
carrier concentration
is and
significantly
affected by the presence of5 Va
Carrier Injection-II
1. Forward bias :
side to the n side
, holes are said to be “injected” from the p
2. Reverse bias :
, hole carrier concentration at the edge of the
depletion region on the n side is lowered to below its equilibrium value and can be
approached zero for Va sufficiently negative.
3. Excess hole concentration,
, at the edge of the depletion region on the n side :
where pn = p(xno) has been defined as the equilibrium hole concentration on the n side.
4. Similarly, the excess electron concentration,
the p side is
, at the edge of the depletion region on
where np = n(xpo) has been defined as the equilibrium electron concentration on the p side.
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Diffusion Currents due to Injected Carriers
excess hole concentration decays
exponentially as we move away
from the edge of the depletion
region on the n side.
For x > xn on the n side :
where Lp is the hole diffusion length on the n side.
• Similarly for x < xp on the p side :
where Ln is the diffusion length for electrons on the p side
1. hole diffusion
current density (Jp) in
the quasi-neutral
region (x > xn)
2. electron diffusion
current density (Jn) in
the quasi-neutral
region (x < -xp)
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Diffusion Currents and carrier distribution
• Assuming no recombination in the depletion region, then the majority carrier current
densities, Jp(-xp) and Jn(xn), at the edges of the depletion region can be deduced :
and
Forward bias
Total current:
continuity equation and no charge accumulation
Finally
We gate
1. Forward bias:
Reverse bias
2. Reverse bias: Va < 0 such that
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Forward bias
Fig. 5-16 Two methods for calculating
junction current from the excess minority
carrier distributions : (a) diffusion currents at
the edges of the transition region; (b) charge
in the distributions divided by the minority
carrier lifetimes. ( c) the diode equation.
(b)
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“Excess”rriers at Reverse Bias
Recall: excess minority carrier concentrations in the quasi-neutral regions of a “long” pn junction
n side (x > xn) :
p side (x < -xp) :
At the edges of the depletion region
If the applied bias is negative and greater than a few
𝑘𝑇
𝑞
’s,
Hence:
for the n side
for the p side
Conclusion : at a reverse bias of more than a few
𝑘𝑇
𝑞
’s, the minority carrier concentrations at
the edges of the depletion region are essentially zero.
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Reverse bias
The equilibrium minority carrier concentrations are recovered a few diffusion lengths (Lp and
Ln) into the quasi-neutral regions from the edges of the depletion region.
recall the current at reverse bias is given by
the saturation current, 𝐼0 :
Fig.5-18 Reverse-biased pn junction : (a)
minority carrier distribution near the reversebiased junction; (b) variation of the quasiFermi levels.
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