MetalSemiconductor Interfaces MetalSemiconductor contact Schottky BarrierDiode Ohmic Contacts

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( s-c) = EC – EF = k. Tln(NC/ND) for n-type = EG – k. Tln(Nv/NA) for p-type ECE 663

Energy band diagram of a metal-n semiconductor contact in thermal equilibrium. q Bn = q ms + k. Tln(NC/ND) ECE 663

Measured barrier height fms for metal-Si and metal-Ga. As 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 = ms (Doping does not matter!) Bn = ms + k. Tln(NC/ND) electric-field distribution E(x) = q. ND(x-W)/Kse 0 Em = q. NDW/Kse 0 W (Vbi-V) = - ∫E(x)dx = q. NDW 2/Kse 0 0 ECE 663

Depletion width Charge per unit area q ECE 663

Capacitance Per unit area: Rearranging: Or: ECE 663

1/C 2 versus applied voltage for W-Si and W-Ga. As diodes ECE 663

1/C 2 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 thermionic emission process Thermal equilibrium forward bias reverse bias J = Js m(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 • 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 !! -(E -E )/k. T Js m = 2 q f(Ek-EF)vx = 2 q dkxdkydkzvxe k F vx > vmin, vy, vz (2 p)3/W Vbi - V V>0 Ek-EF = (Ek-EC) + (EC -EF) EC - EF = q( Bn-Vbi) Ek - EC = m(vx 2 + vy 2 + vz 2 )/2 m*vmin 2/2 = q(Vbi – V) kx, y, z = m*vx, y, z/ħ ECE 663

This means… Js m ∞ ∞ ∞ 2/2 k. T 2 -m*v /2 k. T dvxvxe-m*vx 2/2 k. T dvze z = q(m*)3 W/4 p 3ħ 3 dvye y -∞ -∞ v min x e-q( Bn-Vbi)/k. T (2 pk. T/m*) (k. T/m*)e-m*vmin 2/2 k. T = (k. T/m*)e-q(Vbi-V)k. T ∞ -x 2/2 s 2 = s 2 p dxe -∞ ∞ -x 2/2 s 2 = s 2 e-A 2/2 s 2 dx xe A = qm*k 2 T 2/2 p 2ħ 3 e-q( Bn-V)k. T = A*T 2 e-q( Bn-V)k. T A* = 4 pm*qk 2/h 3 = 120 A/cm 2/K 2 ECE 663

J = A*T 2 e-q BN /k. T (eq. V/k. T-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