Calculation of the spectrum of quasiparticle electron excitations in organic molecular semiconductors
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ONIC PROPERTIES OF SOLID
Calculation of the Spectrum of Quasiparticle Electron Excitations in Organic Molecular Semiconductors E. V. Tikhonova*, Yu. A. Uspenskiib, and D. R. Khokhlova a
b
Moscow State University, Moscow, 119991 Russia Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia *email: [email protected] Received December 22, 2014
Abstract—A quasiparticle electronic spectrum belongs to the characteristics of nanoobjects that are most important for applications. The following methods of calculating the electronic spectrum are analyzed: the Kohn–Sham equations of the density functional theory (DFT), the hybrid functional method, the GW approximation, and the Lehmann approximation used in the spectral representation of oneelectron Green’s function. The results of these approaches are compared with the data of photoemission measurements of ben zene, PTCDA, and phthalocyanine (CuPc, H2Pc, FePc, PtPc) molecules, which are typical representatives of organic molecular semiconductors (OMS). This comparison demonstrates that the Kohn–Sham equa tions of DFT incorrectly reproduce the electronic spectrum of OMS. The hybrid functional method correctly describes the spectrum of the valence and conduction bands; however, the HOMO–LUMO gap width is sig nificantly underestimated. The correct gap width is obtained in both the GW approximation and the Leh mann approach, and the total energy in this approach can be calculated in the local density approximation of DFT. DOI: 10.1134/S1063776115050210
1. INTRODUCTION The spectral properties of semiconductor nanoob jects differ strongly from those of the corresponding bulk semiconductors. One of the main causes of this difference is the enhancement of multielectron effects that is induced by weak screening of Coulomb interac tion. This cause has a universal character and is char acteristic of a wide class of nanoobjects, such as semi conductor nanoclusters and quantum dots and organic molecular semiconductor (OMS) molecules. As a matter of fact, the spatial redistribution of elec trons in nanoobjects is substantially restricted, which significantly weakens the electronic response and the effective permittivity of the system. For example, we have εeff ≈ 1.3–1.4 in silicon clusters about 1 nm in diameter [1–5] and ε0 = 11.6 in bulk silicon. Unfortu nately, it is rather difficult to exactly measure the dependence of the spectra of semiconductor nano clusters, quantum dots, and other artificial objects on their sizes. The point is that nanoclusters (or quantum dots), even those synthesized in one experiment, exhibit a significant scatter of their sizes, shapes, and (sometimes) chemical compositions. Therefore, their measured spectral characteristics correspond to a mix ture of various clusters rather than to one type of clus ters, which strongly hinders the interpretation of experimental results. OMS molecules are a more convenient object for studying the electronic spectrum of nanoobjects, since
they can be formed i
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