The junctions between a metal and a semiconductor. The third important class of junctions consist of those between two lattice matched semiconductors with different band gaps (heterojunctions).
When semiconductors of different band gaps, work functions, and electron affinities are brought together to form a junction, we expect discontinuities
in the energy bands as the Fermi levels line up at equilibrium (Fig. given below).
- The discontinuities in the conduction band ΔEC and the valence band ΔEv accommodate the difference in band gap between the two semiconductors ΔEg.
- In an ideal case, ΔEC would be the difference in electron affinities q(x2 - X1), and ΔEv would be found from ΔEg - ΔEC .
- This is known as the Anderson affinity rule.
- In practice, the band discontinuities are found experimentally for particular semiconductor pairs.
- For example, in the commonly used system GaAs-AlGaAs, the direct band gap difference ΔEg. between the wider band gap AlGaAs and the narrower band gap GaAs is apportioned approximately 2/3 in the conduction band and 1/3 in the valence band for the heterojunction.
- The built-in contact potential is divided between the two semiconductors as required to align the Fermi levels at equilibrium.
- The resulting depletion region on each side of the heterojunction and the amount of built-in potential on each side (making up the contact potential V0) are found by solving Poisson's equation with the boundary condition of continuous electric flux density, at the junction.
- The barrier that electrons must overcome in moving from the n side to the p side may be quite different from the barrier for holes moving from p to n.
- The depletion region on each side is analogous except that we must account for the different dielectric constants in the two semiconductors.
- To draw the band diagram for any semiconductor device involving homojunctions or heterojunctions, we need material parameters such as the band gap and the electron affinity which depend on the semiconductor material but not on the doping, and the work function which depends on the semiconductor as well as the doping.
- The electron affinity and work function are referenced to the vacuum level.
- The true vacuum level (or global vacuum level), Evac,is the potential energy reference when an electron is taken out of the semiconductor to infinity, where it sees no forces.
- Hence, the true vacuum level is a constant (Fig. above).
- That introduces an apparent contradiction, however, because looking at the band bending in a semiconductor device, it seems to imply that the electron affinity in the semiconductor changes as a function of position, which is impossible because the electron affinity is a material parameter.