Summary
A pseudopotential approach to the calculation of the conduction band structure of ionic crystals is proposed along the lines suggested by Heine and Abarenkov. An improved model potential originally suggested by Griuliano and Ruggeri is adopted and discussed in connection with other choices of the potential. Detailed calculations are performed in LiCl, NaCl and KC1, and the results are similar to those obtained with the KKR and the OPW methods, but are more free electronlike, as suggested by Phillips. The minimum of the conduction band is F1 in NaCl and KC1 andL 1 in LiCl. The lowest conduction band is nondegenerate and overlaps very little with the higher conduction bands. In the case of KC1 a well-defined secondary minimum exists atX 3, while in LiCl and NaClX 3 is more likely a saddle point. The strong absorbtion peak above ionization in KC1 is attributed to a resonant exciton associated to the minimum atX 3, rather than to a peak in the density of states. The electron-hole interaction should be taken into account to interpret the entire optical excitation spectrum.
Riassunto
Si propone un metodo a pseudopotenziale per il calcolo delle bande di conduzione dei cristalli ionici lungo le linee indicate da Heine e Abarenkov. Si usa un potenziale modello proposto da Giuliano e Ruggeri, che presenta notevoli vantaggi sui potenziali comunemente usati negli alogenuri alcalini. Si eseguono calcoli dettagliati in LiCl NaCl e KC1, e i risultati sono abbastanza simili a quelli ottenuti con i metodi KKR e OPW, ma nel nostro caso gli elettroni di conduzione tendono ad essere più simili ad elettroni liberi, come proposto da Phillips. Il minimo della banda di conduzione eF 1 in NaCl e KC1 eL 1 in LiCl. La banda di conduzione a energia inferiore è non degenere e si sovrappone poco con le bande di conduzione ad energia superiore. Nel caso di KC1 un minimo secondario ben definite esiste aX 3 mentre in LiCl e NaClX 3 sembra più probabilmente un punto di sella. II forte picco di assorbimento in KC1 sopra la ionizzazione è attribuito a un eccitone risonante dovuto al minimoX 3 piuttosto che a un picco nella densità di stati. Si dovrebbe tener conto dell’interazione buca-elettrone per interpretare lo spettro di eccitazione ottica.
Резюме
Следуя Гейне и Абарен кову, предлагается псевдопотенциальны й подход к вычислению с труктуры зоны провод имости ионных кристаллов. Вы бирается улучшенная модель по тенциала, первоначал ьно предложенная Джулиа но и Руджери.
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Bassani, F., Giuliano, E.S. Pseudopotential approach to the band structure of alkali halides. Nuov Cim B 8, 193–222 (1972). https://doi.org/10.1007/BF02743516
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DOI: https://doi.org/10.1007/BF02743516