A New Approach to Auger Reconibination Application to Lead Chalcogenides 0. ZIEP and M. MOCKER BY The Auger transition rate derived b y means of Green's functions is formulated in terms of exchange of energy and wave vector of the corresponding transitions. Hereby the transition probabilities are modified b y dynamical corrections. This treatment allows t o calculate the Auger coefficient in lead chalcogenides with sufficient accuracy. As a consequence Auger recombination in PbSe has t o be considered.Die Ubergangsrate fur Augerrekombination wird mit Hilfe Greenscher Funktionen hergeleitet und in AbhBngigkeit von Energie-und Impulsaustausch der einzelnen Rekombinationsakte angegeben. Dabei modifizieren dynamische Korrekturen die Wahrscheinlichkeit der Ubergange. In dieser Formulierung der Augerrekombination wird der Augerkoeffizient fur die Bleisalze mit hinreichender Genauigkeit berechnet. Augerrekombination in PbSe ist danach nicht vernachlissigbar.
I n semiconductors with PbSnTe-like band structure the Auger coefficient C, is investigated for most probable eeh transitions taking into account a nonparabolic approximation (NPA). Considering mirror-symmetric hyperbolic bands, singularities in the so-called "activation energy" appear which are removed if deviations from the hyperbolicity are included. At high temperatures T I the value of C , in NPA has the same order of magnitude as the value Czm proposed by Emtage and is nearly independent of temperature; if TI < 77 K the value of C, strongly decreases and differs by orders of magnitude from C:". The obtained results are compared with experimental data.Der Augerkoeffizient C , fur Halbleiter mit PbSnTe-iihnlicher Bandstruktur wird unter Beriicksichtigung von deren Nichtparabolizitiit (NPA) fur die statistisoh wahrscheinlichsten eeh Prozesse untersucht. Setzt man spiegelsymmetrische hyperbolische Biinder voraus, treten Singularitiiten in der sogenannten ,,Aktivierungsenergie" auf, die bei nichthyperbolischen Biindern verschwinden. Fur hohe Temperaturen 2' 1 liegt der Wert von C, in der gleichen GroSenordnung wie der von Emtage vorgeschlagene ( 7 : " und ist ebenfalls schwach temperaturabhiingig; fiir TI < 77 K nimmt C, stark ab und unterscheidet sich um einige GroSenordnungen von C:". Die erhaltenen Werte werden mit experimentellen Ergebnissen verglichen.
A transport equation for ballistic charge carriers which contains the influence of strong and spatially inhomogeneous electric fields in the collision integral is derived by use of Airy functions. A simple analytical expression for the scattering rate due to electron-phonon interaction is obtained including the intra-collisional field effect. Near the threshold energies for several electronphonon interaction mechanisms strong modifications of the corresponding scattering rates are calculated whereas the field-induced change of the scattering rate is negligible for high-energetic carriers.Eine Transportgleichung fur ballistische Ladungstrager, die den EinfluD starker und raumlich inhomogener elektrischer Felder im StoDterm berucksichtigt, wird unter Verwendung von AiryFunktionen abgeleitet. Es wird ein einfacher analytischer Ausdruck fur die StoDzahl infolge Elektron-Phonon-Streuung unter Einbeziehung des ,,intra-collisional field-effects" angegeben. In der Nahe der Schwellenergien werden fur verschiedene Elektron-Phonon-Streumechanismen starke Modifikationen der StoBzahl berechnet, wiihrend fur hochenergetische Ladungstrager die feldinduzierte h d e r u n g der StoBzahl vernachlassigbar ist.
In a wide range of temperature and doping level the small signal lifetime for Auger recombination, spontaneous emission of radiation, and for spontaneous emission of plasmons is calculated in the compounds Pb0.78Sno. 22Te and Pb0.91Sno0.09Se. In the calculation degeneracy of the carrier gas and anisotropy of band structure is taken into account. At donor concentrations ND > 1019 cm−3, recombination by emission of plasmons dominates. For ND < 5 ×1016 cm−3 radiative recombination dominates in Pb0.78. Sno22Se up to temperatures TL < 180 K, in Pb0.09Se, however, up to 230 K.
The disagreement is stronger for the six-band model. The temperature-and composition-dependence of K near the absorption edge are described better by the two-band than by the six-band model.
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