1. Metal-Semiconductor Interfaces
Metal-Semiconductor contact
Schottky Barrier/Diode
Ohmic Contacts
MESFET
ECE 663

2. Device Building Blocks
Schottky (MS)
p-n junction
ECE 663
HBT
MOS

3. 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

4. Energy band diagram of a metal-n semiconductor contact in thermal equilibrium.
qfBn = qfms + kTln(NC/ND)
ECE 663

5. Measured barrier height fms for metal-Si and metal-GaAs contacts
ECE 663
Theory still evolving (see review article by Tung)

6. Energy band diagrams of metal n-type and p-type semiconductors under thermal equilibrium
ECE 663

7. Energy band diagrams of metal n-type and p-type semiconductors under forward bias
ECE 663

8. Energy band diagrams of metal n-type and p-type semiconductors under reverse bias
ECE 663

9. Vbi = fms (Doping does not matter!) fBn = fms + kTln(NC/ND)
Charge distribution
Vbi = fms (Doping does not matter!)
fBn = fms + kTln(NC/ND)
electric-field distribution
Em = qNDW/Kse0
E(x) = qND(x-W)/Kse0 W
(Vbi-V) = - ∫E(x)dx = qNDW2/Kse0
ECE 663

10. Depletion
Depletion width
Charge per unit area q
ECE 663

11. Capacitance
Per unit area:
Rearranging:
Or:
ECE 663

12. 1/C2 versus applied voltage for W-Si and W-GaAs diodes
ECE 663

13. If straight line – constant doping profile –
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 Bn
ECE 663

14. Current transport by the thermionic emission process
Thermal equilibrium
forward bias
reverse bias
J = Jsm(V) – Jms(V)
Jms(V) = Jms(0) = Jsm(0)
ECE 663

15. 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
Els with zero kinetic energy can slide
down negative barrier to initiate current
Current is limited by how fast minority
carriers can be removed (diffusion rate)
Both el and hole currents important
(charges X-over and become min. carriers)
Barrier from metal side is pinned
Els from metal must jump over barrier
Current is limited by speed of jumping
electrons (that the ones jumping from
the right cancel at equilibrium)
Unipolar majority carrier device, since
valence band is entirely inside metal band

16. Let’s roll up our sleeves and do the algebra !!
Jsm = 2qf(Ek-EF)vx
dkxdkydkzvxe-(Ek-EF)/kT  
(2p)3/W
= 2q
vx > vmin,vy,vz
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/ħ
ECE 663

17. This means… Jsm = q(m*)3W/4p3ħ3 dvye-m*vy2/2kT   ∞ -∞
dvze-m*vz2/2kT
dvxvxe-m*vx2/2kT
vmin
(2pkT/m*)
(kT/m*)e-m*vmin2/2kT
= (kT/m*)e-q(Vbi-V)kT
x e-q(fBn-Vbi)/kT
dxe-x2/2s2 = s2p ∞ -∞  
dx xe-x2/2s2 = s2e-A2/2s2 A
= qm*k2T2/2p2ħ3e-q(fBn-V)kT
= A*T2e-q(fBn-V)kT
A* = 4pm*qk2/h3
= 120 A/cm2/K2
ECE 663

18. J = A*T2e-qfBN/kT(eqV/kT-1)

19. 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

20. Forward current density vs applied voltage of W-Si and W-GaAs diodes
ECE 663

21. Thermionic Emission over the barrier – low doping
ECE 663

22. Tunneling through the barrier – high doping
Schottky barrier becomes Ohmic !!
ECE 663

23. ECE 663