Solid state electronic devices streetman pdf 6th is mathematically represented by a density distribution and it is generally an average over the space and time domains of the various states occupied by the system. A high DOS at a specific energy level means that there are many states available for occupation. A DOS of zero means that no states can be occupied at that energy level.
The DOS is usually represented by one of the symbols g, ρ, D, n, or N. Generally, the density of states of matter is continuous. In isolated systems however, like atoms or molecules in the gas phase, the density distribution is discrete like a spectral density.
If the DOS of an undisturbed system is zero, the LDOS can locally be non-zero due to the presence of a local potential. For example, in some systems, the interatomic spacing and the atomic charge of a material could allow only electrons of certain wavelengths to exist. In other systems, the crystalline structure of a material could allow waves to propagate in one direction, while suppressing wave propagation in another direction. Often, only specific states are permitted.
Thus, it can happen that many states are available for occupation at a specific energy level, while no states are available at other energy levels . For example, the density of states of electrons at the bandedge between the conduction band and the valence band in a semiconductor is shown in orange in Fig. For an electron in the conduction band, an increase of the electron energy causes more states to become available for occupation. Alternatively, the density of state is discontinuous for an interval of energy, which means that there are no states available for electrons to occupy within the bandgap of the material.
This also means that an electron at the conduction band edge must lose at least the bandgap energy of the material in order to transition to another state in the valence band. Depending on the QM system, the density of states can be calculated for electrons, photons, or phonons, and can be given as a function of either energy or the wave vector k.
To convert between the DOS as a function of the energy and the DOS as a function of the wave vector, the system-specific energy dispersion relation between E and k must be known. In general, the topological properties of the system have a major impact on the properties of the density of states. Quantum Hall effect system in MOSFET type devices, have a 2-dimensional Euclidean topology. Even less familiar are Carbon nanotubes, the quantum wire and Luttinger liquid with their 1-dimensional topologies.
Systems with 1D and 2D topologies are likely to become more common, assuming developments in nanotechnology and materials science proceed. There are a large variety of systems and types of states for which DOS calculations can be done. Some condensed matter systems possess a symmetry of its structure on its microscopic scale which simplifies calculations of its density of states. In spherically symmetric systems, the integrals of function are one-dimensional because all variables in the calculation depend only on the radial parameter of the dispersion relation.