Effective mass (solid-state physics)

About: Effective mass (solid-state physics) is a research topic. Over the lifetime, 12539 publications have been published within this topic receiving 295485 citations.

Twisted boundary conditions and effective mass in Heisenberg-Ising and Hubbard rings.

Abstract: We identify the boundary energy of a many-body system of fermions on a lattice under twisted boundary conditions as the inverse of the effective charge-carrying mass, or the stiffness, renormalizing nontrivially under interactions due to the absence of Galilean invariance. We point out that this quantity is a sensitive and direct probe of the metal-insulator transitions possible in these systems, i.e., the Mott-Hubbard transition or Density-wave formation. We calculate exactly the stiffness, or the effective mass, in the 1D Heisenberg-Ising ring and the 1D Hubbard model by using the ansatz of Bethe. For the Hubbard ring we also calculate a spin stiffness by extending the nested ansatz of Bethe-Yang to this case.

Low Effective Mass Leading to High Thermoelectric Performance

Abstract: High Seebeck coefficient by creating large density of state (DOS) around the Fermi level through either electronic structure modification or manipulating nanostructures, is commonly considered as a route to advanced thermoelectrics. However, large density of state due to flat bands leads to large effective mass, which results in a simultaneous decrease of mobility. In fact, the net effect of high effective mass is a lower thermoelectric figure of merit when the carriers are predominantly scattered by acoustic phonons according to the deformation potential theory of Bardeen-Shockley. We demonstrate the beneficial effect of light effective mass leading to high power factor in n-type thermoelectric PbTe, where doping and temperature can be used to tune the effective mass. This clear demonstration of the deformation potential theory to thermoelectrics shows that the guiding principle for band structure engineering should be low effective mass along the transport direction.

Transport properties of a many-valley semiconductor

Abstract: The simple model of a semiconductor, based on a single effective mass for the charge carriers and a spherical shape for the surfaces of constant energy, is now known to be inadequate for most of the semiconductors which have been extensively studied experimentally. However, some of these do correspond to what may be called the “many-valley” model, a model for which the band edge occurs at a number of equivalent points K(i) in wave number space, and for which the surfaces of constant energy are multiple ellipsoids, one centered on each of these points. This paper develops, for models of this type, the theory for: mobility (Section 2) and its temperature dependence (Section 3); thermoelectric power (Section 4); piezoresistance (Section 5); Hall effect (Sections 6 and 9); high-frequency dielectric constant (Section 7); and magnetoresistance (Sections 8 and 9). These phenomena are treated, for cases to which Maxwellian statistics apply, on the assumption that the scattering of the charge carriers is describable by a relaxation time which depends on energy only, but is otherwise unrestricted. This assumption can be shown to be justified in a large class of cases, although for some cases it fails, notably when ionized impurity scattering predominates and at the same time the effective mass is very anisotropic. Special attention is given to the role of inter-valley lattice scattering, i.e., to processes whereby a charge carrier is scattered from the neighborhood of one of the band edge points

Self-Trapping of an Electron by the Acoustical Mode of Lattice Vibration. I

Abstract: The importance of the acoustical mode of lattice vibration for self- trapping of an electron is shown. It is shown that when the coupling constant between the electron and the acoustical mode vibration exceeds a certain critical value, the effective mass of the electron changes discontinuously to such an enormous value that the electron is practically allowed to take a localized self- trapping state as an eigenstate. This model is in contrast with the case of the pelaron, in which the effective mass changes continuously with coupling constant. This difference is attributed to the different force range of electron-lattice interaction in the two cases. (auth)

Band Structure and Electron Transport of GaAs

Abstract: Existing experimental data on GaAs are reviewed and analyzed to yield the band structure in the vicinity of the band edges as well as the parameters characterizing the bands summarized in Fig. 1 of this paper. On the basis of presently existing experimental evidence, chiefly the behavior of the optical band gap in Ga(As, P) alloys and the deduced pressure shift and density of states effective mass, it is thought likely that the subsidiary conduction band minima lie along [100] directions. Analytical expressions including nonparabolic effects are given for the energy and density of states of the [000] conduction band and used to obtain a better value of the effective mass from optical reflectivity data. The experimentally observed structure in the Hall effect in $n$-type material at elevated temperatures is shown to result from excitation of carriers into the subsidiary conduction band. Changes of resistivity with pressure are explained on the basis of an increase of the [000] effective mass at low pressures and the transfer of carriers to the subsidiary minima at higher pressures. The scattering mechanisms, which are important in connection with transport phenomena, are shown to be polar lattice scattering and charged impurity scattering in the highest mobility samples. The transport calculations leading to the mobility and thermoelectric power as a function of temperature and impurity concentrations are performed using variational techniques, and shown to agree well with experiment. The apparently low mobility in the subsidiary minima is attributed at least in part to the large effective mass and relatively small anisotropy ratio. An estimate shows scattering between the two conduction bands probably to be unimportant.