P. G. Piva

Optical properties of semiconductors

A power absorption B magnetic field c velocity of light D displacement field d film thickness E applied electric field E c energy , conduction band E e x exciton binding energy E g energy band gap E H hydrogen atom ionization energy 5 13 . 6 eV E electric field E Ú n Landau level energy E y energy , valence band e I ionic charge g * ef fective g-factor K phonon wave vector k extinction coef ficient k B Boltzmann’s constant k electron / hole wave vector L Ú coupled LO phonon – plasmon frequency m * e electron ef fective mass m * h hole ef fective mass

Optoelectronics: Semiconductor heterostructures and quantum wells

Introduction In Chapter 5 we saw that the principal characteristic of a semiconducting material is the existence of forbidden energy bands, or gaps , acting to separate the electronrich valence band from the electron-poor conduction band. Both the bandgap and the energy bands are determined by the bulk potential of the crystalline material. At the basis of bandstructure engineering is the heterojunction , which is obtained by growing one semiconductor layer onto another. For certain carefully selected semiconductors possessing compatible crystal structures and lattice spacings, it is possible to achieve epitaxial growth of one material onto another. In this case, the atomic positions of the second material form a virtually perfect continuation of the underlying substrate lattice. Under carefully controlled conditions, the compositional transition between the two materials can be made almost perfectly abrupt (i.e. with heterointerfaces in many instances being defined on a monolayer scale). Away from the heterojunction, and deep within the bulk of the two materials, the electrons are subject to volumetric potentials (bandgaps and band structures) characteristic of each of the constituent bulk semiconductors. In the vicinity of the heterojunction, the crystal potential changes abruptly from one material to the other. A quantitative description of this change in potential requires that calculations be performed at the atomic level. These calculations (performed numerically on computers) are extremely involved and lie outside the scope of this book. Such calculations indicate, however, that over the scale of a few atomic layers near the interface, there is a transfer of electrical charge.