Abstract
A new method of developing an "effective-mass" equation for electrons moving in a perturbed periodic structure is discussed. This method is particularly adapted to such problems as arise in connection with impurity states and cyclotron resonance in semiconductors such as Si and Ge. The resulting theory generalizes the usual effective-mass treatment to the case where a band minimum is not at the center of the Brillouin zone, and also to the case where the band is degenerate. The latter is particularly striking, the usual Wannier equation being replaced by a set of coupled differential equations.
Keywords
Brillouin zonePhysicsElectronEffective mass (spring–mass system)Degenerate energy levelsCyclotron resonanceDifferential equationSemiconductorWannier functionCenter of mass (relativistic)Equations of motionMotion (physics)Bloch waveQuantum mechanicsElectronic band structureCyclotronQuantum electrodynamicsClassical mechanicsEnergy–momentum relation
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Publication Info
- Year
- 1955
- Type
- article
- Volume
- 97
- Issue
- 4
- Pages
- 869-883
- Citations
- 3041
- Access
- Closed
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Cite This
J. M. Luttinger,
W. Kohn
(1955).
Motion of Electrons and Holes in Perturbed Periodic Fields.
Physical Review
, 97
(4)
, 869-883.
https://doi.org/10.1103/physrev.97.869
Identifiers
- DOI
- 10.1103/physrev.97.869