# Effective Mass

Also found in: Wikipedia.

## effective mass

[ə¦fek·tiv ′mas]
(solid-state physics)
A parameter with the dimensions of mass that is assigned to electrons in a solid; in the presence of an external electromagnetic field the electrons behave in many respects as if they were free, but with a mass equal to this parameter rather than the true mass.

## Effective Mass

a quantity that has dimensions of a mass and that characterizes the dynamic properties of quasiparticles. For example, the motion of a conduction electron in a crystal under the action of an external force F and the forces within the crystal lattice can be described as the motion of a free electron under the action of force F alone (Newton’s law) but with an effective mass m* that differs from the mass m of the free electron. This difference reflects the interaction of the conduction electron with the crystal lattice. Effective mass is defined by the relation

where ℰ is the energy and p is the quasimomentum of the conduction electron. If the relation ℰ(p) is anisotropic (law of dispersion), then the effective mass is a tensor (inverse mass tensor):

This means that, in general, the direction of acceleration of an electron in a crystal lattice is not parallel to the external force F. The acceleration may even be directed antiparallel to F, which corresponds to a negative value of effective mass. The properties of electrons with negative effective mass differ from those of ordinary particles to such an extent that it has been found to be more convenient to deal with positively charged holes with positive effective mass.

The cyclotron effective mass of electrons and holes is used in studying galvanomagnetic phenomena:

where S is the area of the intersection of the constant energy surface ℰ(p) by a plane perpendicular to the magnetic field H. Methods like cyclotron resonance and the measurement of electron heat capacity are the most important techniques for determining the effective mass of conduction electrons and holes.

In the theory of quantum fluids for the quasiparticles fermions with isotropic law of dispersion, the effective mass is the ratio

(4) m* = p0/v0

where p0 and v0 are the absolute values of the momentum and velocity of the quasiparticles at a temperature of absolute zero that correspond to the Fermi level. The effective mass of an atom of liquid 3He is m* = 3.08m0, where m0 is the mass of a free atom of 3He.

The concept of effective mass has been extended to such quasiparticles as phonons, rotons, and excitons. Relation (1) is valid for all these cases.

M. I. KAGANOV

References in periodicals archive ?
In all likelihood, Karachi will be unable to have an effective mass transit system by 2030.
An effective mass transport system between Metro Manila and Central Luzon is badly needed and long overdue, said Frank Villanueva, Philippine Chamber of Commerce and Industry governor in Central Luzon.
Objective: Enhanced personal locator beacon (plb), Embedded egnss receiver, And meolut, Implementing innovative technologies complying with the cospas-sarsat standards yet significantly improving the localization of slow-moving beacons and on-land activated beacons with restricted sky visibility, Paving the way to effective mass market terrestrial search and rescue services based on sar/galileo.
Theresa May is a weak leader, and her party has scarcely been so divided; an effective mass movement involving workers, trade unions, young people, community groups, anti-cuts campaigners and other concerned parties could hand Mrs May her P45 for real.
In particular, we should encourage construction that takes advantage of the most effective mass transit technology yet devised: the elevator.
Chandrababu Naidu had a review meeting with Andhra Pradesh Capital Region Development Authority (CRDA) officials, discussing the cost effective mass transit systems, on Wednesday.
This successfully implemented model at CMH QTA and our recommendations may become the backbone for developing national level guidelines for effective mass casualty management.
Quantitative imaging of cell membrane-associated effective mass density using Photonic Crystal Enhanced Microscopy (PCEM)," Progress in Quantum Electronics, 2016; 50: 1 DOI: 10.
Engineering, technology, and management specialists from Europe and the US discuss recent trends and success factors in mass customization, including the design of production systems and assembly lines, and the need for a functioning and effective mass customization information system; complexity drivers, including the impact of complexity on the human operator in assembly-oriented manufacturing, alternative assembly supply chain structures, variety-induced complexity metrics, and a method to determine the more suitable degree of customization for a specific product design platform; and product configuration management and its approaches, including an interactive product configurator, web-based sales configurators, product configurator application, and sustainability issues.
if the kinetic energy of the vacuum wave is significantly less than its effective mass energy.
Effective mass casualty response is founded on the principle of triage--the system of sorting and prioritizing casualties based on the tactical situation, mission, and available resources.
This could then lead to easier urban-rural development, as well as urban land reform, including socialized housing, and development of an effective mass transport system that will ease the urban traffic situation.

Site: Follow: Share:
Open / Close