ECE 663

Metal-Semiconductor Interfaces

• Metal-Semiconductor contact

• Schottky Barrier/Diode

• Ohmic Contacts

• MESFET

ECE 663

Device Building Blocks

Schottky (MS) p-n junction

HBT MOS

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Energy band diagram of an isolated metal adjacent to an isolated n-type semiconductor

q(s-) = EC – EF = kTln(NC/ND) for n-type = EG – kTln(Nv/NA) for p-type

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Energy band diagram of a metal-n semiconductor contact in thermal equilibrium.

qBn = qms + kTln(NC/ND)

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Measured barrier height ms 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

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Energy band diagrams of metal n-type and p-type semiconductors under forward bias

Energy band diagrams of metal n-type and p-type semiconductors under reverse bias

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Charge distribution

electric-field distribution

Em = qNDW/Ks0

E(x) = qND(x-W)/Ks0

(Vbi-V) = - ∫E(x)dx = qNDW2/Ks0

0

W

Vbi = ms (Doping does not matter!)Bn = ms + kTln(NC/ND)

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Dbis qNVVW /)(2

)(2 VVNqWQNQ biDsD

Depletion width

Charge per unit area

Depletion

q

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Capacitance

WVVNq

VQ

C s

bi

Ds

2Per unit area:

Ds

bi

NqVV

C

21

2

Rearranging:

Or:

dV

Cdq

Ns

D/1

12

2

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1/C2 versus applied voltage for W-Si and W-GaAs diodes

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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

i

Dn

binBn

nN

qkT

V

VV

ln

ECE 663

Current transport by the thermionic emission process

Thermal equilibrium forward biasreverse bias

J = Jsm(V) – Jms(V) Jms(V) = Jms(0) = Jsm(0)

• 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

Note the difference with p-n junctions!!

• 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)

In both cases, we’re modulating the population of backflowing electrons, hence the Shockley form, but…

V > 0

V < 0

V > 0V < 0

ECE 663

Let’s roll up our sleeves and do the algebra !!

Jsm = 2qf(Ek-EF)vxvx > vmin,vy,vz

dkxdkydkzvxe-(Ek-EF)/kT(2)3/

= 2q

Ek-EF = (Ek-EC) + (EC -EF)

EC - EF = q(Bn-Vbi)

Ek - EC = m(vx2 + vy

2 + vz2 )/2

m*vmin2/2 = q(Vbi – V)

kx,y,z = m*vx,y,z/ħ

V > 0

Vbi - V

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This means…

Jsm = q(m*)3/43ħ3 dvye-m*vy2/2kT

∞

-∞dvze-m*vz2/2kT

∞

-∞dvxvxe-m*vx2/2kT

∞

vmin

x e-q(Bn-Vbi)/kT

(2kT/m*) (2kT/m*) (kT/m*)e-m*vmin2/2kT

= (kT/m*)e-q(Vbi-V)kT

= qm*k2T2/22ħ3e-q(Bn-V)kT

= A*T2e-q(Bn-V)kT

A* = 4m*qk2/h3

= 120 A/cm2/K2

dxe-x2/22 = 2

∞

-∞

dx xe-x2/22 = 2e-A2/22

∞

A

J = A*T2e-qBN

/kT(eqV/kT-1)

In regular pn junctions, charge needs to move throughdrift-diffusion, and get whisked away by RG processes

MS junctions are majority carrier devices, and RG is notas critical. Charges that go over a barrier already have high velocity, and these continue with those velocities togive the current

ECE 663

Forward current density vs applied voltage of W-Si and W-GaAs diodes

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Thermionic Emission over the barrier – low doping

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Tunneling through the barrier – high doping

Schottky barrier becomes Ohmic !!

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