The recombination kinetics in highly doped p- and n-type silicon has been investigated at 77, 300, and 400 K through the radiative band-to-band recombination. The minority-carrier lifetime depends quadratically on the doping concentration as expected for Auger recombination. The Auger coefficients at 300 K for p- and n-type silicon are found to be Cp=9.9×10−32 cm6 s−1 and Cn=2.8×10−31 cm6 s−1. They are nearly independent of temperature in the range investigated. The Auger coefficient in highly excited pure silicon at 4.2 K (electron-hole drops) is essentially the same as in highly doped silicon.

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The lifetimes of excitons bound to the neutral donors Li, P, and As and neutral acceptors B, Al, Ga, and In in silicon are determined by time-resolved photoluminescence measurements a t 4.2 K and a strong dependence on the binding energy of the donor or acceptor is found. This dependence can be understood assuming a localized phononless Auger-process to be the main recombination mechanism. A theoretical calculation using approximate wavefunctions is presented and leads to a very good agreement with the experimental results.Die Lebensdauern gebundener Exzitonen an den neutralen Donatoren Li, P und As sowie den Akzeptoren B, AI, Ga und In in Silizium werden bei 4,2 K mit zeibufgeloster Photolumineszenzspektroskopie gemessen. Es ergibt sich eine starke Abhiingigkeit von der Bindungsenergie der entsprechenden Stdrstelle. Man kann diese Abhangigkeit verstehen, wenn man einen lokalisierten, phononenfreien Auger-Prom6 ale wesentlichen Rekombinationsmechanismus annimmt. Eine theoretische Berechnung der Lebensdauer unter Verwendiing angeniiherter Wellenfunktionen ergibt eine sehr gute Ubereinstimmung mit den experimentellen Ergebnissen.

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ERRATAWe regret that an incorrect version of the Response of Mahler etal. to the Comment by Combescot was published [Phys. Rev. Lett. ^9, 1744]. The correct version follows. Mahler et al. Respond: (1) The nonuniform state of a binary (or multicomponent) system is governed to zero order by the Euler hydrodynamic equations supplemented by the thermodynamic equation of state. The first -order approximation (Enskog) 1 then leads to the irreversible processes of diffusion, heat conduction, and thermal diffusion (neglecting here internal friction) as phenomenologically treated by the Onsager linear transport equations. 2 ' 3 When applied to electronic transport phenomena in solids the binary system is built up by the electrons (and/or holes) and the lattice atoms (where any macroscopic drift of the latter is usually excluded). This is the basis for a large variety of transport effects ranging from Ohm's law to complicated cross effects with or without external fields, including our thermodiffusion model. 4 Alternatively one may try to model the electronhole transport process by a one-component Euler equation to which a phenomenological damping term has been added to simulate the coupling to the lattice. 5 In a way, the resulting equation resembles the Navier-Stokes equation, in which the internal damping term is replaced by an external one, though of different functional dependence.Obviously, these two approaches are by no means equivalent: Combescot 6 just succeeded in proving this for a special case. However, starting from the Euler equation it is certainly not possible to say anything about thermal diffusion, in general, or the sign of the resulting gradients, in particular. This renders Combescot's whole section (1) invalid.(2) First, the condition of vanishing heat current j Q =0 is not essential for obtaining our interesting confinement behavior. The dominant sources for j Q are Auger heating and lattice cooling (through which the bath temperature comes in), with the boundary condition j Q (?c -°°) =0. Only in extreme cases will this lead to a destruction of the confinement, as will be shown in a forthcoming paper.Second, it is textbook knowledge that there exist linear transformations for the currents and forces in the Onsager equations which leave the Onsager reciprocity relations unchanged. 3 The force V(~ MA 1 ), where M is the chemical potential and T the temperature, is the correct force when 3 q is taken to be the heat current while V(-\i) T enters with the so-called reduced heat current (for details see Ref.3).Third, for the {n, T) region we discuss, N =L qq L mm -L qm 2 is certainly positive. N becomes negative in the extreme quantum limit, where not only the present transport theory but any hydrodynamic approach breaks down.(3) Under actual experimental conditions the particle current j m (0) and the initial density n(0) are related to each other. In our approach, however, j m together with the isothermal diffusion constant D only defines the length scale of our profiles, as is easily seen from Eq. (3)...

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