Title variants
Languages of publication
Abstracts
Electron dynamics in crystalline semiconductors is described by distinguishing between an instantaneous velocity related to electron's momentum and an average velocity related to its quasi-momentum in a periodic potential. It is shown that the electron velocity used in the theory of electron transport and free-carrier optics is the average electron velocity, not the instantaneous velocity. An effective mass of charge carriers in solids is considered and it is demonstrated that, in contrast to the "acceleration" mass introduced in textbooks, it is a "velocity" mass relating carrier velocity to its quasi-momentum that is a much more useful physical quantity. Among other advantages, the velocity mass is a scalar for spherical but nonparabolic energy bands ϵ(k), whereas the acceleration mass is not a scalar. Important applications of the velocity mass are indicated. A two-band k·p^ model is introduced as the simplest example of a band structure that still keeps track of the periodic lattice potential. It is remarked that the two-band model, adequately describing narrow-gap semiconductors (including zero-gap graphene), strongly resembles the special theory of relativity. Instructive examples of the "semi-relativistic" analogy are given. The presentation has both scientific and pedagogical aspects.
Discipline
- 73.61.Ey: III-V semiconductors
- 72.20.-i: Conductivity phenomena in semiconductors and insulators(see also 66.70.-f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves)
- 71.28.+d: Narrow-band systems; intermediate-valence solids(for magnetic aspects, see 75.20.Hr and 75.30.Mb in magnetic properties and materials)
Journal
Year
Volume
Issue
Pages
132-138
Physical description
Dates
published
2013-01
received
2012-10-03
Contributors
author
- Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warsaw, Poland
References
- [1] E. Schrödinger, Phys. Rev. D 23, 2454 (1981)
- [2] W. Zawadzki, Phys. Rev. B 72, 085217 (2005)
- [3] J. Schliemann, D. Loss, R.M. Westervelt, Phys. Rev. Lett. 94, 206801 (2005)
- [4] W. Zawadzki, T.M. Rusin, J. Phys. Condens. Matter 23, 143201 (2011)
- [5] W. Zawadzki, T.M. Rusin, Phys. Lett. A 374, 3533 (2010)
- [6] R.A. Smith, Wave Mechanics of Crystalline Solids, Chapman and Hall, London 1961
- [7] P.S. Kireev, Semiconductor Physics, MIR Publishers, Moscow 1975
- [8] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)
- [9] N.W. Ashcroft, N.M. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York 1976
- [10] A.I. Anselm, Introduction to the Theory of Semiconductors, Prentice Hall, Englewood 1982
- [11] C. Kittel, Quantum Theory of Solids, Wiley, New York 1963
- [12] C. Aslangul, Mecanique Quantique, Vol. 2, De Boeck, Bruxelles 2008 (in French)
- [13] J.M. Luttinger, W. Kohn, Phys. Rev. 97, 869 (1955)
- [14] J. Zak, W. Zawadzki, Phys. Rev. 145, 536 (1966)
- [15] E.O. Kane, J. Phys. Chem. Solids 1, 249 (1957)
- [16] W. Zawadzki, in: Optical Properties of Solids, Ed. E.D. Haidemenakis, Gordon and Breach, New York 1970, p. 179
- [17] W. Zawadzki, in: High Magnetic Fields in the Physics of Semiconductors II, Eds. G. Landwehr, W. Ossau, World Scientific, Singapore 1997, p. 755
- [18] W. Zawadzki, Phys. Rev. B 74, 205439 (2006)
- [19] G.M. Parker, C.A. Mead, Phys. Rev. Lett. 21, 605 (1968)
- [20] T.M. Rusin, W. Zawadzki, Phys. Rev. B 76, 195439 (2007)
- [21] J.C. Slonczewski, P.R. Weiss, Phys. Rev. 109, 272 (1958)
- [22] C. Kittel, W.D. Knight, M.A. Ruderman, Mechanics, McGraw-Hill, New York 1962
- [23] R. Bowers, Y. Yafet, Phys. Rev. 115, 1165 (1959)
- [24] W. Zawadzki, in: Narrow Gap Semiconductors. Physics and Applications, Ed. W. Zawadzki, Springer, Berlin 1980, p. 85
- [25] W. Zawadzki, Adv. Phys. 23, 435 (1974)
- [26] S. Zukotynski, J. Kolodziejczak, Phys. Status Solidi (b) 3, 990 (1963)
- [27] V.A. Ugarov, Special Theory of Relativity, MIR Publ., Moscow 1977. Supplement by V.L. Ginzburg
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv123n129kz