Tabulated electron affinities (vacuum level to conduction band minimum) give and

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Semiconductor physics and devices · Surfaces, nanostructures and mesoscopic systems

Solid State Physics, Ch Heterostructures, quantum wells and the two-dimensional electron gas

Problem

Tabulated electron affinities (vacuum level to conduction band minimum) give

\chi(\mathrm{GaAs})=4.07\,\mathrm{eV}

and

\chi(\mathrm{Al_{0.3}Ga_{0.7}As})=3.83\,\mathrm{eV}

. Anderson's rule predicts

\Delta E_C=\chi(\mathrm{GaAs})-\chi(\mathrm{Al_{0.3}Ga_{0.7}As})=0.24\,\mathrm{eV}

, close to the measured

\Delta E_C=243\,\mathrm{meV}

for this pair. Someone argues: "Since aligning the two vacuum levels gave the right answer here, Anderson's rule must be a sound way to get band offsets for any heterojunction pair, and I can use it instead of having the offset measured for a new device." Is this reasoning sound? State what Anderson's rule assumes, and explain, using the range of measured

\Delta E_C:\Delta E_V

splits reported for AlGaAs/GaAs (from 60:40 to 65:35) and what the bonds formed across a real interface do that a free-surface affinity cannot record, why one successful case does not establish the rule's general reliability.

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