Metal–Semiconductor Contacts & Schottky Diodes

When metal meets semiconductor. Learn work function and electron affinity, the ideal Schottky barrier φ_B = φ_m − χ, Fermi-level pinning by interface states, band diagrams under bias, thermionic emission and the Richardson constant, majority-carrier operation (no stored charge), ideality factor, image-force lowering, reverse leakage and its strong temperature dependence, ohmic contacts by heavy doping and tunnelling (specific contact resistivity), Schottky vs PN diodes, power Schottky, SiC Schottky and RF/mixer Schottky diodes — with Python computing Schottky saturation currents, forward drops vs PN diodes and leakage vs temperature.

Every semiconductor device needs metal contacts. Depending on the barrier and doping, the contact either rectifies (Schottky diode) or conducts equally in both directions (ohmic contact).

Schottky diodes conduct by majority carriers flying over the barrier, so they switch almost instantly and have a lower forward voltage than PN diodes — at the cost of higher leakage.

An analogy

A Schottky barrier is a low wall that electrons on the semiconductor side can jump over with enough thermal energy; forward bias lowers the wall from their side. Unlike a PN junction, no 'sponge' of minority carriers is left behind, so switching is instant.

Barrier formation

When a metal with work function larger than the semiconductor's contacts n-type material, electrons flow into the metal until Fermi levels align, leaving a depletion region and a barrier φ_B on the metal side. Interface states (dangling bonds, metal-induced gap states) pin the Fermi level, so real barrier heights depend weakly on the metal — process control (silicides, surface preparation) matters more.

Schottky vs PN diode

Differences:

Power and RF Schottky diodes

Power Schottky: low V_F for low-voltage rectification and freewheeling; trench/JBS (junction-barrier Schottky) structures pinch off leakage with embedded p-regions; SiC JBS/MPS diodes add surge capability. RF Schottky: tiny area, low capacitance for mixers and detectors up to hundreds of GHz; zero-bias detector diodes use very low barriers.

Ohmic contacts in devices

Contact resistance becomes a major part of on-resistance in scaled MOSFETs and power devices. Techniques: heavy surface doping, silicides (NiSi, TiSi₂), low-barrier metals, and for wide-gap materials special stacks (Ti/Al/Ni/Au on GaN, Ni silicide on SiC). Measured by transmission-line (TLM) structures.

Formulas

Worked example: Ideal barrier

Given: Pt φ_m 5.65 eV on n-Si (χ 4.05)

Find: φ_B (ideal).

Answer: 1.6 eV (real ≈ 0.85 eV due to pinning)

Worked example: Leakage scaling

Given: φ_B lowered by 0.1 eV

Find: Leakage factor at 300 K.

Answer: ≈ 48×

Worked example: Forward drop saving

Given: 10 A rectifier, V_F 0.45 vs 0.95 V

Find: Power saved.

Answer: 5 W

Schottky vs ohmic contact

  Schottky (lightly doped n-Si)          Ohmic (n⁺ ≥ 10¹⁹ cm⁻³)
  metal │╲ barrier φ_B                    metal │╲ very thin barrier
  E_F ──│─╲______ E_c                     E_F ──│─╲ ← electrons tunnel through
        │   depletion W (µm)                     │  W ≈ few nm
  Rectifying: thermionic emission         Linear I–V, low ρ_c (10⁻⁷–10⁻⁹ Ω·cm²)

With light doping the depletion region is wide, so electrons must go over the barrier (thermionic emission) — rectifying. With very heavy doping it is only nanometres thick and electrons tunnel through in both directions — an ohmic contact. Silicides (TiSi₂, NiSi) plus heavy doping make IC contacts.

Schottky current, forward drop and leakage

import math
# Schottky (metal-semiconductor) diode: thermionic saturation current, forward drop vs PN, leakage vs temperature
A_star = 112.0                              # Richardson constant for n-Si (A/cm^2/K^2)
area, T = 1e-2, 300.0                        # 1 mm^2
VT = 8.617e-5 * T
for phiB in (0.6, 0.7, 0.8):
    Is = area * A_star * T**2 * math.exp(-phiB / VT)
    VF = VT * math.log(1.0 / Is)             # at 1 A (n = 1, ignoring series resistance)
    print(f"barrier {phiB:.1f} eV: Is = {Is:.2e} A, VF at 1 A = {VF:.3f} V")
Is_pn = 1e-12                                # a comparable PN diode
print(f"PN diode (Is 1e-12 A) at 1 A: VF = {VT*math.log(1/Is_pn):.3f} V")
for T2 in (300, 350, 400):
    VT2 = 8.617e-5 * T2
    Is2 = area * A_star * T2**2 * math.exp(-0.7 / VT2)
    print(f"0.7 eV Schottky leakage at {T2-273:3d} C: {Is2*1e6:.3g} uA")
print(f"ideal barrier Au on n-Si: phi_m - chi = 5.1 - 4.05 = {5.1-4.05:.2f} eV (Fermi-level pinning makes real barriers ~0.8 eV)")
# barrier 0.6 eV: Is = 8.39e-06 A, VF at 1 A = 0.302 V
# barrier 0.7 eV: Is = 1.75e-07 A, VF at 1 A = 0.402 V
# barrier 0.8 eV: Is = 3.66e-09 A, VF at 1 A = 0.502 V
# PN diode (Is 1e-12 A) at 1 A: VF = 0.714 V
# 0.7 eV Schottky leakage at  27 C: 0.175 uA
# 0.7 eV Schottky leakage at  77 C: 11.4 uA
# 0.7 eV Schottky leakage at 127 C: 271 uA
# ideal barrier Au on n-Si: phi_m - chi = 5.1 - 4.05 = 1.05 eV (Fermi-level pinning makes real barriers ~0.8 eV)

Barrier height sets everything: each 0.1 eV lower barrier cuts forward voltage by 0.1 V but multiplies leakage by ~48×. A 0.7 eV Schottky drops ~0.4 V at 1 A versus ~0.71 V for a comparable PN diode, yet its leakage grows from 0.2 µA at 27 °C to 0.27 mA at 127 °C — thermal runaway risk in hot power supplies. Real barriers are pinned near 0.6–0.8 eV regardless of the ideal φ_m − χ.

Common mistakes

Applications

Key takeaways

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