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

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

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 ECE 663 Theory still evolving (see review article by Tung)

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

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

Depletion Depletion width Charge per unit area q ECE 663

Capacitance Per unit area: Rearranging: Or: ECE 663

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

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

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

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

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

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

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

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