Valence and conduction bands and the bandgap in between these bands determine the electronic properties of solids. For semiconductors, the band structure of the conduction band and the valence bands near the edge to the fundamental bandgap is of particular interest. Both the band structure and bandgap are influenced by external parameters such as temperature and pressure and can also be changed by alloying and heavy doping.In low-dimensional semiconductors like superlattices and quantum wells, quantum wires and quantum dots anisotropic carrier confinement occurs. The effective gap and energies in conduction and valence bands can be varied by changing spatial dimensions and barrier height of the low-dimensional structure. The bands in amorphous semiconductors near the band edge are ill-defined since long-range periodicity is missing. Still the density-of-state distribution shows significant similarities to that of the same material in the crystallite state.
Valence and Conduction BandsThis chapter outlines the most important bands in semiconductors, the valence and conduction bands, and their dependence on various material and external parameters.A set of bands (subbands), created by the splitting and hybridization (see below) of the ground state of valence electrons, taken together are referred to as the valence band. The number of states contained in this band is given by the multiplicity of its atomic state (typically 4 for sp 3 hybridization), multiplied by the number of atoms creating this band, e.g., the number of atoms in an entire ideal crystal.
1The formation of such bands is often shown as it evolves from the spectrum of isolated atoms when they are brought together to form the crystal lattice. Their levels split with decreasing interatomic distance, as shown in Fig. 1 and discussed in Section "1" of chapter "▶ The Origin of Band Structure". There are several possibilities for the energy and electron distribution over these levels, depending on the crystal bonding and structure. Three relatively simple examples are given in Fig. 1. Figure 1a shows the splitting and overlap of the s and p bands of a main-group metal. The atomic states remain nearly unchanged when the atoms approach each other (here s and p bands do not mix) to form a metal.*Email: pohl@physik.tu-berlin.de 1 In a real crystal this number is reduced since electron scattering limits the coherence length of the electron wave (i.e., the length in which quantum-mechanical interaction can take place). With a mean free path l the number of atoms responsible for the band-level splitting is of the order of (l/a) 3 for a primitive cubic lattice with lattice constant a. Each of these levels is broadened by collision broadening; therefore, even for l approaching a, the result is still bands rather than discrete levels.Semiconductor Physics
