Energy momentum dispersion is only parabolic for small kvalues. An additional method for the estimation of the effective. Conduction electron effectivemass in a field of excitons in semiconductors. An additional method for the estimation of the effective mass band gap in nonparabolic semiconductors u. Ravindran, phy02e semiconductor physics, autum 20 17 december. Pdf effectivemass theory of metalsemiconductor contact. 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. Ravindran, phy02e semiconductor physics, 30 january 20. Excitons with anisotropic effective mass to cite this article. Electrons strongly absorb microwaves of that frequency.
Negative resistance in semiconductors semiconductors. This is given by the curvature of each of the bands. 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. The effective mass reflects the inverse of the band curvature. 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. The ek diagram for direct band gap semiconductors will be studied and the hole. The conduction and valence bands in semiconductors consist of a. In most semiconductors the effective mass is a tensor quantity. Optical conductivity and optical effective mass in a high. 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. 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.
Weakly for semiconductor with wurtzite structure, such as gaas. Effectivemass theory of metalsemiconductor contact resistivity walter a. In solid state physics, a particles effective mass often denoted m. Currently crystal, vasp, castep are supported, quantum espresso is coming. 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. Considering, for example, the density of weak bonds contributing to the tail states as 1 at. 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. The effective mass is inversely proportional to the curvature of the energy band. Review of effective mass theorem impurity states in semiconductors fermi surfaces in metals fermi level, chemical potential intrinsic semiconductors extrinsic semicondutors outline march 31, 2004 without explicitly knowing the bloch functions, we can solve. In many cases they are much smaller than the freeelectron mass.
Similarly, for the valence band one get, v ev k ev k kv mh k k 1 2 2 1. In this presentation, the effective mass theory emt for the electron in the crystal lattice will be introduced. 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. Therefore, the densityofstates effective mass is expressed as 3 1 2 d l m t 11. Nc is called the effective density of states of the conduction band. Ravindran, phy02e semiconductor physics, autum 20 17. In most semiconductors, as the temperature is increased, the band gap decreases so that the effective mass decreases. 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. Density of charge carriers in intrinsic semiconductors. The present analysis is based on the bcslike pairing theory for finite temperatures. In a solid, the electron hole effective mass represents how electrons move in an applied field. For this reason and because of its good transparency, there have been continuous. Quantum size effects on effective mass and band gap of. The effective mass may be anisotropic, and it may even be negative.
Why is the effective mass of electron different for metals. Effects of effective mass anisotropy and effective mass. A particles effective mass is the mass it appears to carry in transport in a crystal. In a simple approximation the heavy hole and light hole bands can. Note that the masses differ considerably from the freeelectron mass. Leads us to, the action of the hamiltonian on the bloch amplitude.
Note that the top of the valence band is often degenerate, with heavy and light holes and a splitoff hole band. In crystals with ionic binding a moving electron polarizes the ions. Pdf conduction electron effectivemass in a field of. Fissan department of electrical engineering and information. Semiconductor physics electron and hole effective masses in.
The dynamics of the electron in free space and in the lattice will be compared. 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. 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. Semiconductor bands effective mass holes in semiconductors semiconductor alloys. The quasifree electron and electron effective mass, m. 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. Effective mass of an electron in a band bgu physics department. 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. In this paper the possibility of using other band structure properties to produce negative resistance effects is considered. Comparing free ein vacuum in an electric field mo9. For example, the bare mass at the band edge of insb and gaas decreases from 0.
Effective mass calculator emc implements calculation of the effective masses at the bands extrema using finite difference method not the band fitting method. Properties of the iivi compound semic0nductors author d. Indeed, the hole effective mass values for zno range from 0. The effective mass of electrons and holes in the material. Most semiconductors can be described as having one band minimum at k 0 as well as several equivalent anisotropic band minima at k. The approach taken is to study means of varying the average effective mass of the carriers. The ek diagram for direct band gap semiconductors will be studied and. Exploring the effective mass of semiconductors using infrared faraday rotation haifengqiao16andfrankc. Questions you should be able to answer by the end of todays lecture. 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.
Introduction of the concepts of hole and effective mass. Phadke department of physics, indian institute of technology, new delhi. Excitons with anisotropic effective mass radiative. Chaotic dynamics in terahertzdriven semiconductors with negative effective mass j. Using the above results, the effective mass of charge carriers can be calculated in the extended and tail states in any asemiconductor. Chapter 11 density of states, fermi energy and energy bands. Effective mass approximation for two extreme semiconductors.
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. Chapter 2 energy bands and effective mass semiconductors, insulators and metals prof. Intrinsic and extrinsic semiconductors effective mass at k0, the e,k relationship near the minimum is usually parabolic. 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. Chaotic dynamics in terahertzdriven semiconductors with. In addition there are three band maxima of interest. Easily doped p type, low hole effective mass, transparent.
A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic copper, and an insulator, such as glass. Complete set of video lessons and notes available only at learn how the mass of electrons. Related content radiative properties of semiconductors. Effective masses in semiconductors the effective mass is defined as. This diagram indicates diagramatically how the actual electron states are equally spaced in kspace. Exploring the effective mass of semiconductors using. Bandgap than it is to measure the effecitve mass k. The table also shows that the wider the gap, the greater the mass of the electron. Its conducting properties may be altered in useful ways by introducing impurities doping into the crystal structure.
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