Skip to main content
SpringerLink
Log in

Band structure and optical properties of graphite and of the layer compounds GaS and GaSe

Зонная стуку ура и оптические свойства графита и слоистых соединений GaS и GaSe

  • Published:
Il Nuovo Cimento B (1965-1970)

Summary

The band structure of graphite and of the layer compounds GaS and GaSe is computed by using the tight-binding approach in a semi-empirical way. The band structure is related to the basic properties of these compounds and some features of the optical excitation spectrum are explained. We show that the reason why graphite is a semi-metal and GaS and GaSe are semiconductors can be understood in the two-dimensional approximation and is due to the existence of the inversion symmetry in the former case. The absorption edge in GaS corresponds to indirect transitions between the statesΓ +1 andP +1 , while in GaSe it corresponds to direct transitions between the statesΓ +1 andΓ +3 . Sharp peaks inε 2(0,ω) are attributed to saddle point singularities in the joint density of states. The effect on the optical properties produced by a change in the polarization of light is discussed.

Riassunto

La struttura a bande della grafite e dei composti lamellari GaS e GaSe è ottenuta usando l’approssimazione dell’elettrone fortemente legato in forma semi-empirica. La struttura a bande è messa in relazione con le proprietà fondamentali di tali composti ed alcune caratteristiche dello spettro di eccitazione ottica vengono spiegate. Si è mostrato che la ragione per la quale la grafite è un semimetallo, mentre GaS e GaSe sono semiconduttori, può essere capita nella approssimazione bidimensionale; essa è dovuta alla presenza, nel caso della grafite, della simmetria di inversione. Lo spigolo di assorbimento del GaS corrisponde a transizioni indirette tra gli statiΓ +1 eP +1 , mentre nel GaSe esso corrisponde a transizioni dirette tra gli statiΓ +1 eΓ +3 . Picchi nella funzione dielettricaɛ 2(0,ω) sono attribuiti a singolarità nella densità di stati in corrispondenza a punti di sella. L’effetto di un cambiamento della direzione di polarizzazione della luce sulle proprietà ottiche viene discusso.

Реэюме

Вычисляется эонная структура графита слоистых соединений GaS и GaSe, причем, полузмпирически испольэуется приближение плотной свяэи. Зонная структура свяэывается с основными свойствами зтих соединений, и общясняются некоторые особенности спектра оптических воэбуждений. Мы отмечаем, что причину того, почему графит является полуметаллом, а GaS и GaSe являются полупрово-дниками, можно понять иэ двумерного приближения, и зто обусловлено сушество-ванием обратной симметрии в первом случае. Край поглошения в GaS соответствует непрямым переходам между состояниямиΓ +1 иP +1 , тогда как в GaSe край поглошения соответствует прямым переходам между состояниямиΓ +1 иP +3 . Острые пики вɛ 2 (0,ω) относятся эа счет сингулярностей седловых точек в сочленной плотности состояний, обсуждается зффект для оптических свойств, который обусловлен иэменением поляриэации света.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Haering andS. Mrozowski:Progress in Semiconductors,5, 273 (1960), and quoted references are suggested to the reader.D. E. Soule, J. W. McClure andL. B. Smith:Phys. Rev.,134, A 453 (1964);S. J. Williamson, S. Foner andM. S. Dresselhaus:Phys. Rev.,140, A 1429 (1965).

    Google Scholar 

  2. G. Fischer andJ. L. Brebner:Journ. Phys. Chem. Solids,23, 1363 (1962);R. Fivaz andE. Mooser:Phys. Rev.,136, A 833 (1964);R. Fivaz:Helv. Phys. Acta,39, 247 (1966).

    Article  ADS  Google Scholar 

  3. W. S. Boyle andP. Nozieres:Phys. Rev.,111, 782 (1958);S. P. F. Humphreys-Owen andL. A. Gilbert:Industrial Carbon and Graphite (London, 1958), p. 37;S. Ergun andJ. T. Mc-Cartney:Proceedings of the Fifth Conference on Carbon, vol. 2 (London, 1963);G. R. Hennig:Journ. Chem. Phys.,43, 1201 (1965);J. B. Yasinsky andS. Ergun:Carbon,2, 355 (1965);J. G. Carter, R. H. Huebner, R. N. Hamm andR. D. Birkhoff:Phys. Rev.,137, A 639 (1965);E. A. Taft andH. R. Philipp:Phys. Rev.,138, A 197 (1965).

    Article  ADS  Google Scholar 

  4. P. Fielding, G. Fischer andE. Mooser:Journ. Phys. Chem. Solids,8, 434 (1959);J. L. Brebner andG. Fischer:Proc. Intern. Conf. on the Physics of Semiconductors (Exeter, 1962), p. 760;J. L. Brebner:Journ. Phys. Chem. Solids.,25, 1427 (1964);F. Bassani, D. L. Greenaway andG. Fischer:Proc. Intern. Conf. on the Physics of Semiconductors, (Paris 1964), p. 51;J. L. Brebner andJ. A. Deverin:Helv. Phys. Acta,38, 650 (1965);P. C. Leung, G. Andermann, W. G. Spitzer andC. A. Mead:Journ. Phys. Chem. Solids,27, 849 (1966).

    Article  ADS  Google Scholar 

  5. T. Sagawa:Journ. Phys. Soc. of Japan,21, 49 (1966).

    Article  ADS  Google Scholar 

  6. P. R. Wallace:Phys. Rev.,71, 622 (1947).

    Article  ADS  Google Scholar 

  7. C. A. Coulson andH. Taylor:Proc. Phys. Soc. London, A65, 815 (1952);W. M. Lomer:Proc. Roy. Soc., A227, 330 (1955).

    Article  ADS  Google Scholar 

  8. F. J. Corbato:Proceedings of the Third Conference on Carbon (London, 1959), p. 173.

  9. G. Fischer:Helv. Phys. Acta,36, 317 (1963).

    Google Scholar 

  10. J. W. McClure:Phys. Rev.,108, 612 (1957).

    Article  ADS  Google Scholar 

  11. D. F. Johnston:Proc. Roy. Soc., A227, 349 (1955).

    Article  ADS  Google Scholar 

  12. J. C. Slonczewski andP. R. Weiss:Phys. Rev.,109, 272 (1958).

    Article  ADS  Google Scholar 

  13. G. Dresselhaus andM. S. Dresselhaus:Phys. Rev.,140, A 401 (1965).

    Google Scholar 

  14. G. F. Koster:Solid State Phys.,5, 173 (1957).

    Google Scholar 

  15. H. Hahn andG. Frank:Z. Inorg. Chem.,278, 340 (1955);K. Shubert, E. Dörre andZ. Kluge:Z. Metallkunde,46, 216 (1955). The authors are indebted to Dr.G. Fisher, who called their attention to the above papers.

    Google Scholar 

  16. R. Fivaz:Theory of Layer Structures (to be published).

  17. J. Callaway:Energy Band Theory (New York, 1964);J. C. Slater:Quantum Theory of Molecules and Solids, vol.2 (New York, 1965);F. Bassani:Methods of Band Calculation Applicable to III-V Compounds, inThe Physics of III-V Compounds, vol.1, edited byR. Willardson andA. Beer (New York, 1966).

  18. E. Mooser andW. B. Pearson:Progr. in Semiconductors,5, 103 (1960).

    Google Scholar 

  19. F. Bassani, R. S. Knox andW. B. Fowler:Phys. Rev.,137, A 1217 (1965);D. J. Olechna andR. S. Knox:Phys. Rev.,140, A 986 (1965).

  20. J. C. Slater andG. F. Koster:Phys. Rev.,94, 1498 (1954).

    Article  ADS  Google Scholar 

  21. W. H. Harrison:Pseudopotentials in the Theory of Metals (New York, 1966).

  22. T. L. Gilbert:Molecular Orbits in Chemistry, Physics and Biology (New York, 1964), p. 405.

  23. A. J. Freeman:Phys. Rev.,91, 1410 (1953);A. J. Freeman andR. E. Watson:Phys. Rev.,123, 521 (1961);124, 1117 (1961);F. Herman andS. Skillman:Atomic Structure Calculations (New York, 1963).

    Article  ADS  Google Scholar 

  24. F. Bassani:Rendiconti SIF, XXXIV Course (New York, 1966), p. 33.

  25. L. Van Hove:Phys. Rev.,89, 1189 (1953).

    Article  ADS  Google Scholar 

  26. D. Brust, J. C. Phillips andF. Bassani:Phys. Rev. Lett.,9, 94 (1962);D. Brust:Phys. Rev.,134, A 1337 (1964).

    Article  ADS  Google Scholar 

  27. J. C. Phillips:Phys. Rev.,104, 1263 (1956).

    Article  ADS  MathSciNet  Google Scholar 

  28. H. Kamimura andK. Nakao: to be published.

  29. J. L. Brebner:Journ. Phys. Chem. Solids,25, 1427 (1964). We are grateful to Dr.Mooser for having brought this point to our attention.

    Article  ADS  Google Scholar 

  30. R. S. Pease:Acta Cryst.,5, 356 (1952). We are grateful to Dr.Mooser for having brought this point to our attention.

    Article  Google Scholar 

  31. D. Greenaway andG. Harbecke: to be published. We are grateful to Dr.Greenaway and Dr.Harbecke for having communicated us their results prior to publication.

  32. F. Aymerich andF. Bassani:Nuovo Cimento,48 B, 358 (1967).

    Article  ADS  Google Scholar 

Download references

Author information

Author notes

  1. F. Bassani & G. Pastori Parravicini

    Present address: Instituto di Fisica dell’Università, Pisa

Authors and Affiliations

  1. Istituto di Fisica dell’Università, Messina

    F. Bassani & G. Pastori Parravicini

  2. Gruppo Nazionale di Struttura della Materia del CNR, Italy

    F. Bassani & G. Pastori Parravicini

Authors
  1. F. Bassani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Pastori Parravicini
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Based on work performed with the assistance and co-operation of the «Istituto di Fisica Nucleare Sezione Siciliana».

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bassani, F., Parravicini, G.P. Band structure and optical properties of graphite and of the layer compounds GaS and GaSe. Nuovo Cimento B (1965-1970) 50, 95–128 (1967). https://doi.org/10.1007/BF02710685

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02710685

Keywords

Search

Navigation