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Due to the influence of a strong electromagnetic field an induced gap is expected to orcur in the band structure of a semiconductor. I n this paper the influence of the damping by electron-phonon collisions and by recombination on the new band structure is investigated. Taking into account damping kinetic equations for the electrons are derived and discussed with the help of calculations.Unter dem EinfIuR eines starken elektromagnetischen Feldes kommt es in der Bandstruktur eines Halbleiters zur Ausbildung eines Zusatzgaps. In dieser Arbeit wird der EinfluB der Dilmpfung durch Elektron-PhononstBBe und Rekombination auf die neue Bandstruktur untersucht. Weiterhin werden kinetische Gleichungen unter Beriicksichtigung der Dilmpfung abgeleitet und an Hand von numerischen Berechnungen diskutiert. 1, IntroductionThe ground state of an intrinsic semiconductor is characterized by filled valence bands and empty conduction bands, the ground state and the excited states being separated by the energy gap E,. If light of the energy ho > E , is absorbed, electron-hole pairs are produced. Conventional optical experiments apply weak light intensities and, consequently, the electron-hole density remains small -there is practically no change in the state of the system, so it is the ground state which is studied in the linear response regime.With increasing, but not too high light intensities, however, band filling effects will be important. Under such conditions two times are of interest, the relaxation time trel and the recombination time trec ; zr,l characterizes the scattering process which tends t o establish equilibrium within the bands, t,,, measures the lifetime of the excited carriers. Because trel<< z , , , is fulfilled in most cases a quasi-equilibrium situation is established. On the other hand, on a very short time scale, the quasiequilibrium concept surely fails.A t higher light intensities of excitation no quasi-equilibrium concept is applicable independently of the pulse duration because the band structure is modified by the radiation field. Under such conditions highly excited semiconductors have to be treated as true nonequilibrium systems. Therefore, in the present contribution we shall use the nonequilibrium Green function formalism which has been introduced by Keldysh and others [l, 21. This formalism allows a consistent calculation of the single particle energies and of the carrier distribution function. An important advantage is that the Keldysh formalism provides us with strict diagrammatic rules for the calculation of higher-order many-body contributions under nonequilibrium conditions.
Due to the influence of a strong electromagnetic field an induced gap is expected to orcur in the band structure of a semiconductor. I n this paper the influence of the damping by electron-phonon collisions and by recombination on the new band structure is investigated. Taking into account damping kinetic equations for the electrons are derived and discussed with the help of calculations.Unter dem EinfIuR eines starken elektromagnetischen Feldes kommt es in der Bandstruktur eines Halbleiters zur Ausbildung eines Zusatzgaps. In dieser Arbeit wird der EinfluB der Dilmpfung durch Elektron-PhononstBBe und Rekombination auf die neue Bandstruktur untersucht. Weiterhin werden kinetische Gleichungen unter Beriicksichtigung der Dilmpfung abgeleitet und an Hand von numerischen Berechnungen diskutiert. 1, IntroductionThe ground state of an intrinsic semiconductor is characterized by filled valence bands and empty conduction bands, the ground state and the excited states being separated by the energy gap E,. If light of the energy ho > E , is absorbed, electron-hole pairs are produced. Conventional optical experiments apply weak light intensities and, consequently, the electron-hole density remains small -there is practically no change in the state of the system, so it is the ground state which is studied in the linear response regime.With increasing, but not too high light intensities, however, band filling effects will be important. Under such conditions two times are of interest, the relaxation time trel and the recombination time trec ; zr,l characterizes the scattering process which tends t o establish equilibrium within the bands, t,,, measures the lifetime of the excited carriers. Because trel<< z , , , is fulfilled in most cases a quasi-equilibrium situation is established. On the other hand, on a very short time scale, the quasiequilibrium concept surely fails.A t higher light intensities of excitation no quasi-equilibrium concept is applicable independently of the pulse duration because the band structure is modified by the radiation field. Under such conditions highly excited semiconductors have to be treated as true nonequilibrium systems. Therefore, in the present contribution we shall use the nonequilibrium Green function formalism which has been introduced by Keldysh and others [l, 21. This formalism allows a consistent calculation of the single particle energies and of the carrier distribution function. An important advantage is that the Keldysh formalism provides us with strict diagrammatic rules for the calculation of higher-order many-body contributions under nonequilibrium conditions.
In the present paper the Green's function approach to nonequilibrium quasi-free charge carriers in highly excited semiconductors is applied. I n doing this a system of kinetic equations for generalized Wigner distributions of renormalized quasi-electrons and holes is obtained, that takes into account (additionally to well-known published results) the interaction of the longitudinal optical phonons and the intraband interaction of the radiation field with the electron-hole plasma. Thus, utilizing the corresponding field equations and the suitable boundary conditions, relaxation processes in the semiconductor after excitation by a short laser pulse and a laser probe beam experiment may be described.I n der Arbeit wird die Methode der Green'schen Funktionen fur das Nichtgleichgewicht auf das Verhalten quasifreier Ladungstrager in hochangeregten direkten Halbleitern im nichtstationiiren Bereich angewendet. Dabei wird ein System von kinetischen Gleichungen fur verallgemeinerte Wigner-Verteilungen renormierter Quasi-Elektronen und Locher erhalten, welches gegenuber den aus der Literatur bekannten auch die Wechselwirkung mit longitudinalen optischen Phononen und die Intraband-Wechselwirkung mit dem Strahlungsfeld einschliel3t. Zusammen mit den entspreclienden Feldgleichungen und unter geeigneten Randbedingungen konnen somit Relaxationsprozesse im Halbleiter nach Anregung durch einen kurzen Laserimpuls und deren Austesten mittels eines Teststrahlexperimentes beschrieben werden.
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