Heterojunctions

An interface where two different SemiconductorMedium materials touch is a heterojunction. Charge simulations detect such interfaces automatically: whenever the two sides differ in band structure (band gap, effective densities of states, band-gap narrowing, or electron affinity), the heterojunction treatment described here is applied by default — no extra configuration is required. Interfaces between identical semiconductor media remain ordinary continuous interfaces.

Note

Heterojunctions that intersect an electrical contact are not currently supported.

Band alignment

Band offsets follow Anderson’s rule from the configured electron affinities \(\chi\) (SemiconductorMedium.electron_affinity) and band gaps \(E_g\):

\[\Delta E_c = \chi_1 - \chi_2, \qquad \Delta E_v = \Delta E_c - E_{g,2} + E_{g,1}.\]

The electrostatic potential is continuous across the interface; the band offsets appear as steps in the conduction and valence band edges, visible in SteadyEnergyBandMonitor data. An unset electron_affinity is treated as 0 eV, so physical alignments require setting the affinity on every semiconductor material of the device.

Interface transport

Carrier transport across the heterojunction is by thermionic emission. Carrier densities are discontinuous at the interface: at equilibrium they differ by the Boltzmann factor of the band offsets, and under bias the interface current is driven by the imbalance of the emission fluxes from the two sides.

The emission rates derive from the per-material Richardson constants SemiconductorMedium.richardson_electron and SemiconductorMedium.richardson_hole. When these are not set, a large default is used that keeps the interface at its local-equilibrium band-offset alignment; set them explicitly to model finite thermionic-emission rates.

Note

Heterojunction support requires the accelerated solver (the default, HeatChargeSimulation.use_accelerated_solver=True). The legacy solver ignores electron_affinity and treats all semiconductor interfaces as continuous.