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Metal-Semiconductor Interfaces

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Metal-Semiconductor Interfaces
• Metal-Semiconductor contact
• Schottky Barrier/Diode
• Ohmic Contacts
• MESFET
ECE 663
Device Building Blocks
Schottky (MS)
HBT
p-n junction
MOS
ECE 663
Energy band diagram of an isolated metal adjacent
to an isolated n-type semiconductor
q(fs-c) = EC – EF = kTln(NC/ND) for n-type
= EG – kTln(Nv/NA) for p-type
ECE 663
Energy band diagram of a metal-n semiconductor contact
in thermal equilibrium.
qfBn = qfms + kTln(NC/ND)
ECE 663
Measured barrier height
fms
for metal-Si and metal-GaAs contacts
Theory still evolving (see review article by Tung)
ECE 663
Energy band diagrams of metal n-type and p-type semiconductors
under thermal equilibrium
ECE 663
Energy band diagrams of metal n-type and p-type semiconductors
under forward bias
ECE 663
Energy band diagrams of metal n-type and p-type semiconductors
under reverse bias
ECE 663
Charge distribution
Vbi = fms (Doping does not matter!)
fBn = fms + kTln(NC/ND)
electric-field
distribution
E(x) = qND(x-W)/Kse0
Em = qNDW/Kse0
W
(Vbi-V) = - ∫E(x)dx = qNDW2/Kse0
0
ECE 663
Depletion
Depletion width
W пЂЅ
2 e s (V bi пЂ­ V ) / qN D
Charge per unit area
q DW пЂЅ
Q пЂЅ QN
2 q e s N D (V bi пЂ­ V )
ECE 663
Capacitance
Per unit area:
Rearranging:
C пЂЅ
Q
qe s N D
пЂЅ
V
1
C
Or:
ND
2
2 пЂЁV bi пЂ­ V пЂ©
пЂЅ
2 пЂЁV bi пЂ­ V
пЂЅ
es
W
пЂ©
qe s N D
пѓ©
пЂ­1
пѓЄ
пЂЅ
q e s пѓЄ d 1 2 / dV
пѓ«
C
2
пЂЁ
пЂ©
пѓ№
пѓє
пѓє
пѓ»
ECE 663
1/C2 versus applied voltage for W-Si and W-GaAs diodes
ECE 663
1/C2 vs V
•If straight line – constant doping profile –
slope = doping concentration
•If not straight line, can be used to find profile
•Intercept = Vbi can be used to find fBn
f Bn пЂЅ V n пЂ« V bi
пѓ¦ ND пѓ¶
Vn пЂЅ
ln пѓ§
пѓ·
q
пѓЁ ni пѓё
kT
ECE 663
Current transport by the thermionic emission process
Thermal equilibrium
forward bias
reverse bias
J = Jsпѓ m(V) – Jmпѓ s(V)
Jmпѓ s(V) = Jmпѓ s(0) = Jsпѓ m(0)
ECE 663
Note the difference with p-n junctions!!
In both cases, we’re modulating the population
of backflowing electrons, hence the Shockley
form, but…
V>0
V<0
V>0
V<0
• Barrier is not pinned
• Barrier from metal side is pinned
• Els with zero kinetic energy can slide
down negative barrier to initiate current
• Els from metal must jump over barrier
• Current is limited by how fast minority
carriers can be removed (diffusion rate)
• Current is limited by speed of jumping
electrons (that the ones jumping from
the right cancel at equilibrium)
• Both el and hole currents important
(charges X-over and become min. carriers)
• Unipolar majority carrier device, since
valence band is entirely inside metal band
Let’s roll up our sleeves and do the algebra !!
dkxdkydkzvxe-(Ek-EF)/kT
Jsпѓ m = 2qf(Ek-EF)vx = 2qпѓі
пѓµ
vx > vmin,vy,vz
(2p)3/W
Vbi - V
V>0
Ek-EF = (Ek-EC) + (EC -EF)
EC - EF = q(fBn-Vbi)
Ek - EC = m(vx2 + vy2 + vz2 )/2
m*vmin2/2 = q(Vbi – V)
kx,y,z = m*vx,y,z/Д§
ECE 663
This means…
Jsпѓ m
в€ћ
в€ћ
в€ћ
2/2kT
2
-m*v
-m*v
/2kT
пѓі
пѓіdvze z
пѓіdvxvxe-m*vx2/2kT
= q(m*)3W/4p3Д§3пѓµdvye y
пѓµ
пѓµ
-в€ћ
-в€ћ
v
min
x e-q(fBn-Vbi)/kT
пѓ–(2pkT/m*)
пѓ–(2pkT/m*)
(kT/m*)e-m*vmin2/2kT
= (kT/m*)e-q(Vbi-V)kT
в€ћ
пѓі
-x2/2s2 = sпѓ–2p
dxe
пѓµ
-в€ћ
в€ћ
пѓі
-x2/2s2 = s2e-A2/2s2
dx
xe
пѓµ
A
= qm*k2T2/2p2Д§3e-q(fBn-V)kT
= A*T2e-q(fBn-V)kT
A* = 4pm*qk2/h3
= 120 A/cm2/K2
ECE 663
J = A*T2e-qf
BN
(eqV/kT-1)
/kT
In regular pn junctions, charge needs to move through
drift-diffusion, and get whisked away by RG processes
MS junctions are majority carrier devices, and RG is not
as critical. Charges that go over a barrier already have
high velocity, and these continue with those velocities to
give the current
Forward current density vs applied voltage of W-Si and W-GaAs diodes
ECE 663
Thermionic Emission over the barrier – low doping
ECE 663
Tunneling through the barrier – high doping
Schottky barrier becomes Ohmic !!
ECE 663
ECE 663
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