On the theory of the electric conductivity of solids in a strong electric field

Abstract

A theory of the electric conductivity is given for a simple semiconductor model in t h e presence of a strong electric field including both the heating of the charge carriers and the field-induced change of the density of states. The conductivity is divided into a n intraband and a n interband part. The intraband part defines the field-dependent plasma frequency. The interband conductivity vanishes in absence of thc strong field and shows a n exponential growth as the field is increased. The connection of this result with the Zener tunneling of electrons between the valence and the conduction bands is discussed.Es wird die elektrische Leitfahigkeit filr einen einfachen Modellhalbleiter in Anwesenheit cines elektrischen Feldes unter Herticksichtigung der Aufheizung der Ladungstrager und der nnderung der Zustandsdichte berechnet. Die Leitfahigkeit wird in einen Tntraband-und einen Interbandanteil aufgespalten. Durch den Intrabandanteil ist insbesondere die feldabhangigc Plasmafrequenz definiert. Der Interbandanteil verschwindet bei Abwesenheit des starkcn elektrischen Feldes uud zeigt einen exponcntiellen Anstieg bei wachsender Feldstarlie. Der Zusammenhang dieses Resultats mit dem Zener-Tunneln der Elektronen zwischen Valenz-und Leitungsband wird disktuiert. IntroductionAs is well known, the application of a sufficiently strong electric field gives rise t o characteristic changes in the optical interband absorption of semiconductors or insulators. This effect, usually called electroabsorption, can be understood as the consequence of a field induced change of the density of thc many-electron states which take part in the optical transition. I n particular this density bccomes different from zero also in the gap region betwccn the ground and the first excited state in presence of the electric field, which results in a n exponential tail in the absorption spectrum of the crystal. The idea underlying the present paper is that the field induced change of the density of states, in analogy to the modification of the optical absorption, should also result in an alteration of the quasistatic electric conductivity.I n evaluating the conductivity in thc presence of a strong electric field we can utilize methods developed in the theory of electroabsorption [l t o 51. There the problem consists in determining the response of a crystal in an electric field to a weak electromagnetic pcrturbation in the optical fcquency region. The calculation of the quasi-static conductivity in the electric field leads to the same problem, the only difference being that the quantum energy of the weak electromagnetic perturbation is much smaller than the energy gap betwccn the ground and the first excited state. Therefore we will start with the general expression for the dielectric tcnsor derived in the electroabsorption theory [3 t o 51. This is done in Section 1 . In Section 2 the Conductivity tcnsor is divided into an intraband

Rigorous theory and simplified model of the band-to-band tunneling in silicon

“…The connection between transmission probability and current density is not necessary, if a macroscopic quantity is calculated which directly determines the band-to-band tunneling current. This was done for the first time by Enderlein and Peuker [37]. They used a Kubo formula [38] for the differential conductivity of a crystal in strong electric fields.…”

“…In this paper we will follow the lines of Enderlein and Peuker [37] and apply the Green's function formalism to the phonon-assisted band-to-band tunneling in silicon. In Section 2 the current density and generation rate are calculated.…”

A new current transport mechanism due to interband tunneling without and with photon assistance

“…Within the p-and n-side of the junction the total current results from the intraband mechanism alone, whereas within the transition region free carriers are not available and, thus, the interband part becomes important.1) I n this paper we are interested in a spatially homogeneous situation. Then both mechanisms occur simultaneously a t each position of the sample as has been shown in [7]. I n this case, however, an immediate experimental observation is hindered until now.…”

“…The outline of the paper is as follows: I n Section 2 we give a reformulation of tunneling transport without photon assistance which makes more clear the separation of the total current density into an intraband and interband part suggested in [7]. Our formulation is based on the direct calculation of the macroscopic current density in contrast to other formulations where quantities, e.g.…”

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields: A rigorous approach

“…In the presence of a non-uniform field however, the WKB approximation can be used provided the applied bias voltage is generating slowly varying potential profiles inside the active device area [5]. The problem of Zener tunneling in an indirect semiconductor was treated earlier by Keldysh [6] and Kane [7], whereas Schenk [8] formulated a model for the tunneling probability in a uniform field using the Kubo formalism [9,10]. Another noteworthy approach is the calculation by Rivas [11] based on a Green's function formulation of Fermi's golden rule to calculate the current through a silicon tunnel diode.…”