Physics of Electronics:
7. Junction Diodes
July – December 2008
Contents overview
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Current flow in a pn junction with forward bias.
Current flow in a pn junction with reversed bias.
IV characteristics of a junction diode
Electron and hole efficiencies.
Pn junction with finite dimensions.
Depletion-layer capacitance
Small-signal equivalent circuit.
Pn junction with forward bias
• Consider a junction biased with a voltage V:
V (steady state)
V=0
eV0
Same Fermi energy at both sides
e(V0 – V)
Fermi energies separated by eV
Pn junction with forward bias
• Diode equation:
– Continuity eq. for h+ at x ¥ d2
V (steady state)
E =0 E ≠0 E =0
0
p
0
p
h
p
p
h
h
0
• Since E =0, there is only diffusion:
– Continuity eq. for e– at x  d1:
Lh2=τLhDh
Pn junction with reversed bias
• Currents through the junction :
– Applying diode equation (with –V):
I = J0 A
Jhp
Jep
0
Jen
Jhn
0
J = Jhp – Jhn + Jen – Jep º – J0
I = –J0 A
Pn junction with reversed bias
• Decrease of minority carriers:
– As before (with –V):
p(x) = pn{[exp(– eV/kT) – 1] exp(– x/Lh) + 1}
Pn junction with finite dimensions
• Current in a finite junction:
– From the continuity eq. we obtained
E =0
E ≠0 E =0
pp
nn
pn
np
Idem for the electrons. Therefore the
saturation current is:
V
Depletion-layer capacitance
• The depletion layer forms a capacitance (important
for high frequency applications)
E =0
≠0
E =0
++
++
++
II
n
C2 =
x
I
ρp
dp
Applying E =0 at x ¥ dn+dp:
Applying V = V0 at x ¥ dn+dp & using previous
relation:
dn
V0
x
0 dp
Using Poisson relation (
) and
continuity for voltage and its derivative:
I:
II:
ρn
voltage
space-charge density
p
E
–
–
–
dn + dp
Depletion-layer capacitance
• Capacitance of the depletion layer:
– Charge per unit area accumulated at the depletion layer
Vj = V0 ≤ V
– The capacitance per unit area (
) is then:
Vj
V0
Cj-2
Small-AC-signal equivalent circuit
• Reversed biased junction
≡
−V
Jep
e(V0 – V)
rnp: Resistance of the junction @ V=0
Cj(V): Depletion layer capacitance
g:
Conductance of the reverse flow
Jen
Jhp
Jhn
Small-AC-signal equivalent circuit
• Forward biased junction
≡
VV
Jep
e(V0 – V)
rnp: Resistance of the junction @ V=0
Cj(V): Depletion layer capacitance
G:
Conductance of the forward flow
CD: Diffusion capacitance
Jen
Jhp
Jhn
Small-AC-signal equivalent circuit
• Forward biased junction
≡
VVtot
Vtot = V + V1 exp(iω t)
DC
AC
• Therefore we can assume:
DC
AC
Small-AC-signal equivalent circuit
• Forward biased junction
≡
VVtot
– Applying continuity equation:
0
p
p
h
p
h
• But p1(x = 0) = pn0
p
h
Small-AC-signal equivalent circuit
• Forward biased junction
≡
VVtot
– Alternating currents of holes injected into n-region:
1
1
x=0
(1 + i ωτLh)1/2
Lh
– Alternating currents of electrons injected into p-region:
n
e1
e
x=0
(1 + i ωτLe)1/2 np
Le
e
Small-AC-signal equivalent circuit
• Forward biased junction
≡
VVtot
– Total alternating currents of minority injected carriers:
J1 = Jh1 + Je1
– Admittance (Y1 = J1/V1) for ωτ á 1:
2
e
Y1 @
exp
kT
G
CD