pn Junctions, Heterojunctions, and Built-In Electrostatics
The pn Junction
Built-in potential
When p-type and n-type regions are brought into contact, diffusion of majority carriers leaves behind ionized dopants and creates a depletion region. The built-in potential is approximately for an abrupt junction under ideal assumptions.
Model assumption
The depletion approximation works best when the depletion width is much larger than the Debye length and when free-carrier density inside the space-charge region is small.
Depletion Width and Junction Capacitance
Space-charge region
For an abrupt one-sided junction, the depletion width depends on doping asymmetry and applied bias. Junction capacitance arises from the bias-dependent depletion width and is central to diode switching, varactors, and charge sensing.
What is the main physical origin of the depletion region in a pn junction?
Carrier diffusion leaves fixed space charge that generates the internal electric field.
Correct answer: Diffusion of majority carriers followed by uncovered ionized dopants
Write the ideal abrupt-junction built-in potential formula.
This is the standard equilibrium result under nondegenerate conditions.
Correct answer:
Heterojunction Band Alignment
Anderson model and real interfaces
In heterojunctions, differences in electron affinity and band gap produce conduction- and valence-band offsets. These offsets govern carrier confinement, tunneling, and injection. Real interfaces can deviate from ideal alignment due to interface states, strain, dipoles, and chemical intermixing.
Junction types
| Type | Key feature | Typical use |
|---|---|---|
| Homojunction | Same material, different doping | Diodes, BJTs |
| Type-I heterojunction | Both carriers confined in same layer | Lasers, LEDs, quantum wells |
| Type-II heterojunction | Electrons and holes separated spatially | Photovoltaics, charge separation |
| Graded junction | Composition varies continuously | Field management, reduced barriers |
A type-II heterojunction is especially useful when one wants to:
Type-II alignment places electrons and holes in different materials or spatial regions, aiding separation.
Correct answer: Maximize carrier spatial separation
Why do interface states matter in heterojunctions?
Interface chemistry can dominate over ideal bulk alignment.
Correct answer: They can trap carriers, pin the Fermi level, modify band bending, and reduce ideal band-offset behavior.