MTLE-6120: Advanced Electronic Properties of Materials - - PowerPoint PPT Presentation

MTLE-6120: Advanced Electronic Properties of Materials Metal-semiconductor junctions: Schottky diodes and Ohmic contacts

Contents: ◮ Contact potential ◮ Depletion region ◮ Debye screening ◮ Schottky diode characteristics ◮ Ohmic contacts Reading: ◮ Kasap 5.9 - 5.10

1

Metal-semiconductor contact potential

Metal Semiconductor Metal Semiconductor

◮ Fermi levels relative to vacuum (Φ) not in same position ◮ Distinction for semiconductor: Φ = work function ◮ Consider case when metal level below n-type semiconductor ◮ Fermi levels line up for equilibrium ◮ Electron transfer to metal in current example ◮ Schottky barrier height ΦB = ΦM − χ ◮ Contact potential: V0 = ΦM − Φn

2

Depletion region

Metal 1 Metal 2

• +

+ + Metal Semiconductor

◮ Region of semiconductor near interface where charge transfer occurs ◮ Number of charge carriers reduce, hence depletion region ◮ In metal-metal case, bands on both sides respond ◮ In metal-semiconductor case, only semiconductor responds: why?

3

Debye screening

◮ Poisson equation for variation of electrostatic potential: ∇2φ( r) = −ρ( r) ǫ0 ◮ Charge density ρ( r) includes external and bound charge ◮ Previously considered bound charge due to P response to E = ∇φ ◮ What if material responds directly to potential as ρ = ρ(φ)? ◮ Specifically consider small change from neutral potential φ0, ρ( r) ≈ ρ′(φ0) (φ( r) − φ0) ◮ Poisson equation becomes (using ǫ to account for dipolar reponse): ∇2(φ − φ0) − −ρ′(φ0) ǫ (φ − φ0) = 0 with 1D solutions of the form φ(x) = φ0 + e±x/λD where λD =

• ǫ/(−ρ′(φ0)) is the Debye screening length

4

Debye screening length

◮ λD =

• ǫ/(−ρ′(φ0)): length scale over which potential restores to neutral

◮ Depletion region non-neutral → becomes neutral over λD length scale ◮ Therefore width of depletion region ∼ λD ◮ In metals, −ρ′(φ0) = e2g(EF ) ◮ Typical λD ∼

• 8.85×10−12 F/m

(1.6×10−19 C)2·1047 J-1m-3 ∼ 0.6 ˚

A ◮ Metals restore potential within an atomic layer! ◮ In semiconductors, −ρ′(φ0) = e2nmaj/(kBT), where nmaj ≈ Na/d = majority carrier density (larger of n, p) ◮ For 1014/cm3 doped Si at room temperature, λD ∼ 400 nm ◮ For 1018/cm3 doped Si at room temperature, λD ∼ 4 nm ◮ In all cases, λD ∝ n−1/2, where n = free carrier density ◮ λD in metals ≪ in semiconductors ⇒ depletion region entirely in semiconductor!

5

Applied bias

Metal Semiconductor Metal Semiconductor

◮ Neutral case: band bending in semiconductor = contact potential V0 ◮ Apply potential bias: change band bending in semiconductor ◮ Forward bias ≡ reduce band bending to V0 − V ◮ Rate of electrons M → SC ∝ exp −φB

kBT

◮ Rate of electrons SC → M ∝ exp −e(V0−V )

kBT

6

Schottky diode: I − V characteristics

◮ Net current density j = j2 exp −e(V0−V )

kBT

− j1 exp −φB

kBT

◮ At equilbrium V = 0, j = 0 ⇒ j2 exp −eV0

kBT = j1 exp −φB kBT = j0 (say)

◮ Therefore: j = j0

• exp eV

kBT − 1

• ◮ Exponentially increasing current in forward bias (V > 0)

◮ Current saturates to −j0 in reverse bias ◮ j0 is given by Richardson-Dushman equation, just different Be!

7

Schottky photovoltaic devices

Metal Semiconductor

◮ Contact potential ⇒ built-in field at interface ◮ Photon absorption → e-h pair, separated by field ◮ In n-type junction, e relaxes to band edge and driven into bulk SC ◮ h recombines at interface (met by e current in metal) ◮ Below band-gap, interfacial generation also possible

8

Ohmic contact

Metal Semiconductor Metal Semiconductor

◮ Similar geometry to Schottky diode, but different level alignment ◮ Consider metal Fermi level lines up inside conduction band (or analogously for p-type material, inside valence band) ◮ Bands bend in opposite direction to equalize Fermi levels ◮ No barrier ΦB any more, electrons free to flow ◮ j(V ) dominated by linear resistance of bulk semiconductor ◮ I-V follows Ohm’s law ⇒ Ohmic contact

9

Peltier effect in Ohmic contacts

◮ Electrons flowing to the left pick up energy Ec − EF ◮ Electrons flowing to the right lose energy Ec − EF ◮ Energy drawn/dissipated from/as thermal energy at junction ◮ Combine p and n-type junctions to get cooling in same metal ◮ Reverse operation: thermoelectric generator (heat to electricity)

Metal Semiconductor 10