Intrinsic Urbach Rule and Electron—Phonon Interaction in GaAs and Related III‐V Compounds

Abstract

The optical absorption a t the edge of the fundamental absorption band is investigated in highpurity and high-perfection GaAs crystah. The experimental curves show an exponential decay of the absorption coefficient as a function of the photon energy (Urbach's rule) with temperature dependent slope. Since the impurity contribution can be neglected, the data are analyzed within the framework of the polaron model of phonon-assisted transitions. The good agreement obtained between experimental and calculated curves makes it possible to conclude that the interaction of electrons with LO phonons plays a dominant role in shaping the intrinsic Urbach tail in GaAs. The same theoretical model is also applied successfully to I n P and InAs using previously published experimental data.Es wird die optische Absorption an der Kante der Grundgitterabsorptionsbande in hochreinen und hochperfekten GaAs-Kristallen untersucht. Die experimentellen Kurven zeigen einen exponentiellen Abfall des Absorptionskoeffizienten in Abhangigkeit von der Photonenenergie (Urbach'sche Regel) mit temperaturabhangigem Anstieg. Da die Storstellenbeitrage vernachlassigt werden konnen, werden die Daten im Rahmen des Polaronenmodells von phononenassistierten ubergangen analysiert. Die gute Ubereinstimmung zwischen experimentellen und berechneten Kurven macht den SchluB moglich, da13 die Wechselwirkung der Elektronen mit LO-Phononen eine dominierende Rolle fur die Form des Urbachausliufers in GaAs spielt. Dasselbe theoretische Model1 wird erfolgreich auch auf I n P und InAs unter Benutzung fruherer experimenteller Daten angewendet.

Ultrafast Electron Dynamics in GaAs and InP Studied by Time-Resolved Terahertz Emission Spectroscopy

“…This energy region corresponds to the Urbach tail. [37][38][39][40] The present experimental results show that the electrons excited in the Urbach tail region (Urbach electrons) do not contribute to the macroscopic current immediately after the excitation, and that a transition to a mobile state occurs in 1-2 ps. We believe that the present results are the first experimental observation of the ultrafast dynamics of Urbach electrons.…”

“…Studies on the absorption edge of GaAs and InP have shown that the Urbach tail of these crystals should be attributed to LO phonon scattering and/or crystal randomness. 33,35,[37][38][39][40]…”

Chirp Control of Free Carrier Injection in GaAs Using Femtosecond Optical Pulses

“…Only the spatial distribution of the carrier density depends on the chirp of the pump pulse. A considerable portion of the spectrum of the probe pulse, on the other hand, is also absorbed within the sample, and only the spectral portion below the band gap energy (1.428 eV), i.e., that in the Urbach tail region, [9][10][11][12][13][14] can be transmitted through the sample. The spectra of the incident and transmitted light are plotted in Fig.…”

The Pulsed Nonresonant Optical Stark Effect and the Urbach Tail in Semiconductors

“…The interaction of the exciton with the longitudinal optical phonons will give rise to a frequency-dependent self-energy Z:(o), so that the Green's function is given by -1m ,Z:(w) = y(o), (5) so that one can write approximately the retarded Green's function as 1…”

“…I I I I I I I I I I I I I I I I I I I I I I Better results are obtained by a cumulant expansion [4] in the time representation of the retarded exciton Green's function, which is for a crystal in its ground state simply I I I I I I I I I I I I 1 CdS Here T is the time ordering operator and W, are the 2n-th order perturbational terms. The perturbational expansion (7) can be rewritten in terms of a cumulant expansion res) according to [5], [ti], and [7], respectively Because all matrix elements (Is[ H , In, k) are known analytically, both for the bound and ionized exciton states, the first cumulant and the resulting absorption spectrum can be evaluated very precisely [4]. It turns out that the main contribution to F1 is the x-intraband (1s -+ 1s) scattering, while the interband scattering is energetically less favourable.…”