The electron-phonon interaction in solids is important for many interesting properties of solids, among them the critical temperature of phonon-mediated superconductors, the effective electron mass in metals and semiconductors, and the carrier dynamics in semiconductors. Modern density-functional techniques have made it possible to perform $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations of the electron-phonon interaction. This review explains these techniques and discusses their applications.

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Electron-phonon interactions from first principles

Halide semiconductors stand at the very beginning of semiconductor science and technology. CuI was reported as the first transparent conductor, and the first field effect transistor was made from KBr. Although halogens are frequently used in semiconductor preparation, little use is currently made from halide semiconductors in electronics and photonics. We review past reports on the metal halide semiconductor CuI and related alloys and discuss recent progress with regard to this material including its use in organic electronics and solar cells as well as our own work on fully transparent bipolar heterostructure diodes (p-CuI/n-ZnO) with high rectification of several 107 and ideality factors down to 1.5. 

γ-CuI(111) thin film on glass (1 × 1 cm2) and IV-characteristics of p-CuI/n-ZnO/a-Al2O3 bipolar heterojunction diode.

Cuprous iodide – a p‐type transparent semiconductor: history and novel applications

Recently, lead halide perovskite quantum dots have been reported with potential for photovoltaic and optoelectronic applications due to their excellent luminescent properties. Herein excitonic photoluminescence (PL) excited by two-photon absorption in perovskite CsPbBr3 quantum dots (QDs) has been studied at a broad temperature range, from 80 to 380 K. Two-photon absorption has been investigated and the absorption coefficient is up to 0.085 cm/GW at room temperature. Moreover, the PL spectrum excited by two-photon absorption shows a linear blue-shift (0.32 meV/K) below the temperature of 220 K. However, for higher temperatures, the PL peak approaches a roughly constant value and shows temperature-independent chromaticity up to 380 K. This behavior is distinct from the general red-shift for semiconductors and can be attributed to the result of thermal expansion, electron–phonon interaction and structural phase transition around 360 K. The strong nonlinear absorption and temperature-independent chromaticity of CsPbBr3 QDs observed in temperature range from 220 to 380 K will offer new opportunities in nonlinear photonics, light-harvesting, and light-emitting devices.

Temperature-dependent excitonic photoluminescence excited by two-photon absorption in perovskite CsPbBr 3 quantum dots.

The semi-local Becke-Johnson (BJ) exchange-correlation potential and its modified form proposed by Tran and Blaha (TB-mBJ) have attracted a lot of interest recently because of the surprisingly accurate band gaps they can deliver for many semiconductors and insulators. In this work, we have investigated the performance of the TB-mBJ potential for the description of electronic band structures in a comprehensive set of semiconductors and insulators. We point out that a perturbative use of the TB-mBJ potential can give overall better results. By investigating a set of IIB-VI and III-V semiconductors, we point out that although the TB-mBJ approach can describe the band gap of these materials quite well, the binding energies of semi-core d-states in these materials deviate strongly from experiment. The difficulty of the TB-mBJ potential to describe the localized states is likely the cause for the fact that the electronic band structures of Cu2O and La2O3 are still poorly described. Based on these observations, we propose to combine the TB-mBJ approach with the Hubbard U correction for localized d∕f states, which is able to provide overall good descriptions for both the band gaps and semi-core states binding energies. We further apply the approach to calculate the band gaps of a set of Ti(IV)-oxides, many of which have complicated structures so that the more advanced methods like GW are expensive to treat directly. An overall good agreement with experiment is obtained, which is remarkable considering its little computational efforts compared to GW.

Band gaps from the Tran-Blaha modified Becke-Johnson approach: a systematic investigation.

Anatase TiO2 is among the most studied materials for light-energy conversion applications, but the nature of its fundamental charge excitations is still unknown. Yet it is crucial to establish whether light absorption creates uncorrelated electron-hole pairs or bound excitons and, in the latter case, to determine their character. Here, by combining steady-state angle-resolved photoemission spectroscopy and spectroscopic ellipsometry with state-of-the-art ab initio calculations, we demonstrate that the direct optical gap of single crystals is dominated by a strongly bound exciton rising over the continuum of indirect interband transitions. This exciton possesses an intermediate character between the Wannier-Mott and Frenkel regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional lattice. The nature of the higher-energy excitations is also identified. The universal validity of our results is confirmed up to room temperature by observing the same elementary excitations in defect-rich samples (doped single crystals and nanoparticles) via ultrafast two-dimensional deep-ultraviolet spectroscopy.Here the authors combine steady-state angle-resolved photoemission spectroscopy, ellipsometry and ultrafast two-dimensional ultraviolet spectroscopy to examine the role of many-body correlations in anatase TiO2, revealing the existence of strongly bound excitons in single crystals and nanoparticles.

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Strongly bound excitons in anatase TiO2 single crystals and nanoparticles.

We have theoretically investigated, by ab initio techniques, the phonon properties of several semiconductors with chalcopyrite structure. Comparison with experiments has led us to distinguish between materials with d electrons in the valence band (e.g., CuGaS2, AgGaS2) and those without d electrons (e.g., ZnSnAs2). The former exhibit a rather peculiar nonmonotonic temperature dependence of the energy gap which, so far, has resisted cogent theoretical description. We analyze this nonmonotonic temperature dependence by fitting two Bose-Einstein oscillators with weights of opposite sign leading to an increase at low temperatures and a decrease at higher temperatures and find that the energy of the former correlates well with characteristic peaks in the phonon density of states associated with low-energy vibrations of the d-electron elements. We hope that this work will encourage theoretical investigations of the electron-phonon interaction in this direction, especially of the current ab initio type.

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A. Mu ~{n}oz

Papers

Temperature dependence of band gaps in semiconductors: Electron-phonon interaction