The approach taken is to study means of varying the average effective mass of the carriers. For example, the bare mass at the band edge of insb and gaas decreases from 0. Ravindran, phy02e semiconductor physics, 30 january 20. These masses are related but, as explained in the previous sections, are not the same because the weightings of various directions and wavevectors are different. Complete set of video lessons and notes available only at learn how the mass of electrons. The effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a parabola. In a simple approximation the heavy hole and light hole bands can. Pdf effectivemass theory of metalsemiconductor contact. Properties of the iivi compound semic0nductors author d. Using the above results, the effective mass of charge carriers can be calculated in the extended and tail states in any asemiconductor. While this concept is simple enough the issue turns out to be substancially more complex due to the multitude and the occasional anisotropy of the minima and maxima. Optical conductivity and optical effective mass in a high. An additional method for the estimation of the effective. The effective mass is inversely proportional to the curvature of the energy band.
Effective mass of an electron in a band bgu physics department. Indeed, the hole effective mass values for zno range from 0. Comparing free ein vacuum in an electric field mo9. In solid state physics, a particles effective mass often denoted m. Most actual band structures for semiconductors have ellipsoidal energy surfaces which require longitudinal and transverse effective masses in place of the three principal effective masses figure 11.
Effective mass approximation for two extreme semiconductors. Ravindran, phy02e semiconductor physics, autum 20 17 december. In many cases they are much smaller than the freeelectron mass. Introduction the effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a paraboloid. Exploring the effective mass of semiconductors using infrared faraday rotation haifengqiao16andfrankc. The effective mass may be anisotropic, and it may even be negative. Currently crystal, vasp, castep are supported, quantum espresso is coming. The effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a. The important point is that the electron in a periodic potential is accelerated relative to the lattice in an applied electric or magnetic field as if its mass is equal to an effective mass. Chaotic dynamics in terahertzdriven semiconductors with.
In addition there are three band maxima of interest. Pdf conduction electron effectivemass in a field of. Electrons strongly absorb microwaves of that frequency. Cao state key laboratory of functional materials for informatics, shanghai institute of metallurgy, chinese academy of sciences, 865 changning road, shanghai, 200050, peoples republic of china.
Bandgap than it is to measure the effecitve mass k. Conductivity effective mass of holes m c m l m t 1 2 3 1 1 m e m 22 2 2 2 66 mm. These semiconductors are in our cell phones, in our opticalfiber communications systems, in our cd and dvd players, and soon in our home and office lights. As you can see its obvious that for bigger dimension bigger than 2. Introduction the effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a parabola. A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic copper, and an insulator, such as glass. The effective mass of electrons and holes in the material. The ek diagram for direct band gap semiconductors will be studied and the hole. Effects of effective mass anisotropy and effective mass. Effective mass calculator for semiconductors github. Exploring the effective mass of semiconductors using.
Its conducting properties may be altered in useful ways by introducing impurities doping into the crystal structure. A particles effective mass is the mass it appears to carry in transport in a crystal. An additional method for the estimation of the effective mass band gap in nonparabolic semiconductors u. Conduction electron effectivemass in a field of excitons in semiconductors. In most semiconductors the effective mass is a tensor quantity. Introduction of the concepts of hole and effective mass. The effective mass is used in transport calculations, such as transport of electrons under the influence of fields or carrier gradients, but it also is used to calculate the carrier density and density of states in semiconductors. The conduction and valence bands in semiconductors consist of a. In this presentation, the effective mass theory emt for the electron in the crystal lattice will be introduced. Most semiconductors can be described as having one band minimum at k 0 as well as several equivalent anisotropic band minima at k. Leads us to, the action of the hamiltonian on the bloch amplitude. In crystals with ionic binding a moving electron polarizes the ions.
In this paper the possibility of using other band structure properties to produce negative resistance effects is considered. Excitons with anisotropic effective mass radiative. Therefore, the densityofstates effective mass is expressed as 3 1 2 d l m t 11. Related content radiative properties of semiconductors. Semiconductor bands effective mass holes in semiconductors semiconductor alloys. Effective mass calculator emc implements calculation of the effective masses at the bands extrema using finite difference method not the band fitting method. Chaotic dynamics in terahertzdriven semiconductors with negative effective mass j. We analyze the effects of effective mass anisotropy and the effective mass difference between electrons and holes on the electronhole e h bcs state in highly excited semiconductors at various temperatures. Effectivemass theory of metalsemiconductor contact resistivity walter a. The quasifree electron and electron effective mass, m. Questions you should be able to answer by the end of todays lecture. This is given by the curvature of each of the bands. Looks like newtons law if we define the mass as follows dynamical effective mass mass changes with kso it changes with time according to k.
Ravindran, phy02e semiconductor physics, autum 20 17. So with this alone, you can easily see why a semiconductor will have a very different effective mass than metals, considering that the charge carrier in a semiconductor tends to be at the bottom of the conduction band for electrons, and at the top of the valence band for holes. Variation of effective mass with diameter of nano particles this equation is a damping one, which increasing of r will results in moving the eve towards to 21, which is the effective mass of the bulk substance zns. In a solid, the electron hole effective mass represents how electrons move in an applied field. The effective mass reflects the inverse of the band curvature. Peirisdepartmentofphysics,kenyoncollege,gambier,oh43022abstract due to the influence of the crystal in which an electron inhabits, its. Negative resistance in semiconductors semiconductors.
Considering, for example, the density of weak bonds contributing to the tail states as 1 at. Nc is called the effective density of states of the conduction band. Fissan department of electrical engineering and information. Easily doped p type, low hole effective mass, transparent. The present analysis is based on the bcslike pairing theory for finite temperatures.
Chapter 2 energy bands and effective mass semiconductors, insulators and metals prof. Weakly for semiconductor with wurtzite structure, such as gaas. Intrinsic and extrinsic semiconductors effective mass at k0, the e,k relationship near the minimum is usually parabolic. Effective masses in semiconductors the effective mass is defined as. Similarly, for the valence band one get, v ev k ev k kv mh k k 1 2 2 1.
Phadke department of physics, indian institute of technology, new delhi. For this reason and because of its good transparency, there have been continuous. Note that the masses differ considerably from the freeelectron mass. Note that the top of the valence band is often degenerate, with heavy and light holes and a splitoff hole band. Energy momentum dispersion is only parabolic for small kvalues. The dynamics of the electron in free space and in the lattice will be compared. This diagram indicates diagramatically how the actual electron states are equally spaced in kspace. The table also shows that the wider the gap, the greater the mass of the electron.