Basics of Envelope-Function Theory

Author(s):  
Vurgaftman Igor

The chapter shows how the bulk theory described in Part I can be generalized within the envelope-function framework to model the band structure of layered materials with quantum confinement of carriers such as quantum wells or superlattices. In practice, the approach amounts to substituting derivatives for wavevector components in suitably chosen Hamiltonians as well as augmenting them with interface terms. It also discusses the spin splitting of the states of the quantum structures that arises from structural and intrinsic asymmetries.

Author(s):  
Vurgaftman Igor

This chapter presents a detailed development of several numerical methods for calculating the band structure of semiconductor quantum wells and superlattices. These include the transfer-matrix method, the finite-difference method, and the reciprocal-space approach. The relative merits and drawbacks of each approach are briefly considered. It is pointed out that real-space methods often introduce spurious states for the most common forms of the Hamiltonian. The chapter also discusses how the tight-binding and pseudopotential methods can be applied to model quantum structures.


2020 ◽  
pp. 649-698
Author(s):  
Sandip Tiwari

This chapter brings together several themes and perspectives by exploring them in quantum-confined conditions or in monolayer crystals. In it, confinement of electrons and holes at heterostructure interfaces, in inversion layers, in quantum wells and in superlattices is analyzed using the envelope function to illustrate the variety of interactions that must be properly accounted for. The formation of subbands in confinement, minibands in superlattices, and transmission, reflection and resonance at confined barriers and wells is discussed. Propagation, screening, scattering and the behavior of shallow dopants are discussed to illustrate changes with reduction of dimensions. Particular emphasis is placed on optical transitions to illustrate the changes in selection rules for interband and intraband transitions. Confined semiconductors are contrasted with monolayer semiconductors, using graphene and nanotubes as examples whose analysis and electronic properties are discussed, to compare them with the semiconductor discussions in earlier chapters.


2003 ◽  
Vol 150 (1) ◽  
pp. 25 ◽  
Author(s):  
X. Marie ◽  
J. Barrau ◽  
T. Amand ◽  
H. Carrère ◽  
A. Arnoult ◽  
...  

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