The light emission of ZnO under high one- and two-quantumexcitation is investigated in the temperature region from 4 to 300 K. Emission bands are observed which can be attributed to the interactions of free excitons with phonons, free excitons and free electrons, and of bound excitons with phonons and free and bound electrons.



Die Lichtemission von ZnO-Kristallen bei starker Bin- und Zweiquantenanregung wird im Temperaturbereich von 4 bis 300 K untersucht. Dabei werden Emissionsbanden beob-achtet, die zuruckgefuhrt werden konnen auf die Wechselwirkungen von freien Exzitonen mit Phononen, freien Exzitonen und freien Elektronen und von gebundenen Exzitonenmit Phononen und freien und gebundenen Elektronen.

The Luminescence of ZnO under High One‐ and Two‐Quantum Excitation

Optical properties of highly excited direct gap semiconductors

The dispersion of excitons, polaritons and biexcitons in direct-gap semiconductors

For more than 40 years it was thought that polaron- and exciton-phonon systems exhibited unexpected localization properties. Particular attention was paid to the so-called phonon-induced self-trapping transition, which, it was believed, should manifest itself as a point of nonanalyticity in the ground-state energy as a function of the electron-phonon coupling parameter. It will be demonstrated for a large class of (generalized Fr\"ohlich) models that no such transition exists. The dimensionality of space has no qualitative influence; insofar, an application of the authors' results to problems in lower dimensions (e.g., polarons in quantum wells) is straightforward. The same holds true if homogeneous external fields are involved; for example, a discontinuous mass stripping for magnetopolarons can be excluded. On the other hand, a phase-transition-like behavior will be found, if a polaron or exciton is exposed to a short-range potential, allowing a so-called pinning transition. The authors emphasize, however, that even in this case the transition is only modified, and not induced, by phonons.

Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

The binding energy of the excitonic molecule, a complex consisting of two electrons and two positive holes, is calculated as a function of the mass ratio m e / m h by avariational method. It is shown that the excitonic molecule is stable for any value of the mass ratio. For m e = m h , the binding energy is estimated to be 0.00684 $m_{\text{e}}e^{4}/{\varepsilon_{0}}^{2}\hbar^{2}$. Some results about the wave function are also presented.

Excitonic Molecule. I. : Calculation of the Binding Energy

Binding energies, interparticle distances, oscillator strengths, and exchange corrections are calculated for the three-particle complex corresponding to an exciton bound to an ionized donor. The results are given as functions of the mass ratio of the electron and hole. Binding of the complex is obtained for mass ratios up to 0.426. The interparticle distances are up to 50 times larger than the corresponding exciton radius. The oscillator strengths are about ${10}^{4}$ times greater than those of free excitons, while the exchange corrections for the complex are comparable to those of free excitions. The results are applied to CdS and ZnO and compared with experimental results on these.

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Properties of Excitons Bound to Ionized Donors

Binding energy of the biexcitons

Effective Hamiltonian for few-particle systems in polar semiconductors

The dependence of the binding energy W of the biexciton on the electronhole mass ratio σ is discussed. The bounds from above and from below on the possible curves y = W (σ) have been obtained. In particular, the upper bound implies a positive binding of the biexcitons in the whole interval of the parameter σ. The bounds on W (σ) have been compared with experimental results on biexcitons in semiconductors.

M. Suffczyński

Papers

Properties of Excitons Bound to Ionized Donors

Binding energy of the biexcitons

Effective Hamiltonian for few-particle systems in polar semiconductors

Binding energy of the biexcitons in isotropic semiconductors

Dependence of the exchange splitting in excitons on the interatomic distance