Heterostructures such as resonant tunneling diodes, quantum well photodetectors and lasers, and cascade lasers break the symmetry of the crystalline lattice. Such break in lattice symmetry causes a strong interaction of heavy-, light- and split-off hole bands. The bandstructure of holes and the transport through these states is of very current interest to the semiconductor industry. As semiconduction devices are scaled down to a nanometer level and as holes are confined to very thin triangular or square quantum wells.
A resonant tunneling diode is used as a vehicle to study the bandstructure in thin quantum wells and hole transport in heterostructures including the subband dispersion transverse to the main transport direction. Four key findings are demonstrated: (1) the heavy and light hole interaction is shown to be strong enough to result in dominant current flow off the Gamma zone center (more holes flow through the structure at an angle than straight through), (2) explicit inclusion of the transverse momentum in the current integration is needed, (3) most of the current flow is due to injection from heavy holes in the emitter, and (4) the dependence on the angle φ of the transverse momentum k is weak. Two bandstructure models are utilized to demonstrate the underlying physics: (1) independent/uncoupled heavy-, light- and split-off bands, and (2) second-nearest neighbor sp3s* tight-binding model. Current–voltage (I–V ) simulations including explicit integration of the total energy E, transverse momentum |k| and transverse momentum angle φ are analyzed. Three independent mechanisms that generate off-zone-center current flow are identified: (1) nonmonotonic (electron-like) hole dispersion, (2) different quantum well and emitter effective masses, and (3) momentum-dependent quantum well coupling strength.
The methodologies and physical mechanism explained here provide a critical guidance to the treatment of hole transport in ultra-thin bodies or shallow channel transistors. Since the tight binding model intrinsically comprehends strain and crystal distortions, the methodology is immediately applicable to strain engineering methods.
- Understand the approximate construction of hole dispersions in quantum wells from simple effective mass theories.
- Understand the consequences of band mixing in full band theories.
- Understand the correlation between transverse dispersion in a quantum well and transmission coefficents.
- Understand physical mechanisms that can cause hole transport to be highly momentum dependent.
- Appreciate the relevance to modern ultra-thin body devices.
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Università di Pisa, Pisa, Italy
- course lecture
- band structure
- quantum mechanics
- quantum transport
- quantum wells
- I-V curves