nearly-free electron model
E645945
The nearly-free electron model is a quantum mechanical approximation in solid-state physics that describes how electrons move in a weak periodic potential within a crystal lattice, leading to the formation of electronic band structures.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
quantum mechanical approximation
ⓘ
theoretical model in solid-state physics ⓘ |
| appliesTo |
electrons in crystalline solids
ⓘ
metals ⓘ semiconductors ⓘ |
| approximationType |
perturbative treatment of lattice potential
ⓘ
weak-potential approximation ⓘ |
| assumes |
electrons move almost freely in a crystal lattice
ⓘ
independent electrons neglecting electron–electron interactions ⓘ weak electron–lattice interaction ⓘ weak periodic potential from ions ⓘ |
| basedOn |
Bloch theorem
NERFINISHED
ⓘ
Schrödinger equation in a periodic potential ⓘ |
| category |
electronic structure model
ⓘ
model of electrons in periodic potentials ⓘ |
| comparesWith |
free electron gas model
ⓘ
nearly localized electron picture ⓘ |
| contrastsWith | strongly bound electron models ⓘ |
| describes |
electronic band structure in crystals
ⓘ
electrons in a weak periodic potential ⓘ |
| explains |
deviation from free-electron parabolic dispersion near zone boundaries
ⓘ
formation of band gaps at Brillouin zone boundaries ⓘ formation of energy bands ⓘ |
| field |
condensed matter physics
ⓘ
solid-state physics ⓘ |
| goal |
calculate electronic band structure
ⓘ
understand conduction properties of solids ⓘ |
| historicalContext | developed in early quantum theory of solids ⓘ |
| leadsTo |
energy level splitting at degeneracy points
ⓘ
zone-folding of free-electron dispersion ⓘ |
| mathematicalFormulation | Schrödinger equation with periodic potential V(r) ⓘ |
| predicts |
effective mass of electrons in bands
ⓘ
energy dispersion relations E(k) ⓘ opening of band gaps at zone boundaries ⓘ |
| relatedTo |
band theory of solids
ⓘ
free electron model ⓘ tight-binding model ⓘ |
| requires |
periodic crystal lattice
ⓘ
translational symmetry ⓘ |
| usedFor |
qualitative understanding of band formation
ⓘ
simple analytic band-structure calculations ⓘ |
| usedIn | introductory solid-state physics courses ⓘ |
| usesConcept |
Brillouin zone
NERFINISHED
ⓘ
Fourier expansion of periodic potentials ⓘ perturbation theory ⓘ plane-wave basis ⓘ reciprocal lattice ⓘ |
Referenced by (1)
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