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The Elliott formula describes analytically, or with few adjustable parameters such as the dephasing constant, the light absorption or emission spectra of solids. It was originally derived by Roger James Elliott to describe linear absorption based on properties of a single electron–hole pair.〔 Kuper, C. G.; Whitfield, G. D. (1963). ''Polarons and Excitons''. Plenum Press. LCCN (63021217 ). 〕 The analysis can be extended to a many-body investigation with full predictive powers when all parameters are computed microscopically using, e.g., the semiconductor Bloch equations (abbreviated as SBEs) or the semiconductor luminescence equations (abbreviated as SLEs). ==Background== One of the most accurate theories of semiconductor absorption and photoluminescence is provided by the SBEs and SLEs, respectively. Both of them are systematically derived starting from the many-body/quantum-optical system Hamiltonian and fully describe the resulting quantum dynamics of optical and quantum-optical observables such as optical polarization (SBEs) and photoluminescence intensity (SLEs). All relevant many-body effects can be systematically included by using various techniques such as the cluster-expansion approach. Both the SBEs and SLEs contain an identical homogeneous part driven either by a classical field (SBEs) or by a spontaneous-emission source (SLEs). This homogeneous part yields an eigenvalue problem that can be expressed through the generalized Wannier equation that can be solved analytically in special cases. In particular, the low-density Wannier equation is analogous to bound solutions of the hydrogen problem of quantum mechanics. These are often referred to as exciton solutions and they formally describe Coulombic binding by oppositely charged electrons and holes. The actual physical meaning of excitonic states is discussed further in connection with the SBEs and SLEs. The exciton eigenfunctions are denoted by is the crystal momentum of charge carriers in the solid. These exciton eigenstates provide valuable insight to SBEs and SLEs, especially, when one analyses the linear semiconductor absorption spectrum or photoluminescence at steady-state conditions. One simply uses the constructed eigenstates to diagonalize the homogeneous parts of the SBEs and SLEs.〔 Kira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. ISBN 978-0521875097. 〕 Under the steady-state conditions, the resulting equations can be solved analytically when one further approximates dephasing due to higher-order many-body effects. When such effects are fully included, one must resort to a numeric approach. After the exciton states are obtained, one can eventually express the linear absorption and steady-state photoluminescence analytically. The same approach can be applied to compute absorption spectrum for fields that are in the terahertz (abbreviated as THz) range〔 Lee, Y.-S. (2009). ''Principles of Terahertz Science and Technology''. doi:(10.1007/978-0-387-09540-0 ). ISBN 978-0-387-09539-4. 〕 of electromagnetic radiation. Since the THz-photon energy lies within the meV range, it is mostly resonant with the many-body states, not the interband transitions that are typically in the eV range. Technically, the THz investigations are an extension of the ordinary SBEs and/or involve solving the dynamics of two-particle correlations explicitly.〔 Kira, M.; Koch, S.W. (2006). "Many-body correlations and excitonic effects in semiconductor spectroscopy". ''Progress in Quantum Electronics'' 30 (5): 155–296. doi:(10.1016/j.pquantelec.2006.12.002 ) 〕 Like for the optical absorption and emission problem, one can diagonalize the homogeneous parts that emerge analytically with the help of the exciton eigenstates. Once the diagonalization is completed, one can then compute the THz absorption analytically. All of these derivations rely on the steady-state conditions and the analytic knowledge of the exciton states. Furthermore, the effect of further many-body contributions, such as the excitation-induced dephasing, can be included microscopically〔 Jahnke, F.; Kira, M.; Koch, S. W.; Tai, K. (1996). "Excitonic Nonlinearities of Semiconductor Microcavities in the Nonperturbative Regime". ''Physical Review Letters'' 77 (26): 5257–5260. doi:(10.1103/PhysRevLett.77.5257 ) 〕 to the Wannier solver, which removes the need to introduce phenomenological dephasing constant, energy shifts, or screening of the Coulomb interaction. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elliott formula」の詳細全文を読む スポンサード リンク
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