PHILOSOPHICAL MAGAZINE B, 1994, VOL. 70, No. 3,481492 zyxw Evolution of the electronic states of In,Ga, -,As/GaAs superlattices in the presence of an external d.c. electric field By FERNANDO CERDEIRA and EVALDO RIBEIRO Instituto de Fisica ‘Gleb Wataghin’, Universidade Estadual de Campinas, Unicamp, 13083-970 Campinas, zyxwvu SPo Paulo, Brazil ABSTRACT We discuss recent measurements of photomodulated and electromodulated spectroscopy zyxwvuts (77 K) as well as photoexcitation luminescence (2 K) in some &Gal -,As/GaAs superlattices. Our results show clear evidence of Franz- Keldysh and Stark-Wannier regimes for different samples and field values. In one of the samples, light and heavy holes are shown to be in different field regimes simultaneously. These studies support the idea that band line-up at the heterojunc- tion is always such that the light holes are essentially unconfined. zyxwv 5 zyxwvuts 1. INTRODUCTION The effect of an external electric field F on the electronic states of a semiconductor can be formulated in relatively simple terms in two extreme cases (Franz 1958, Keldysh 1958, Wannier 1960, 1962). For fields sufficiently weak that the effective- mass approximation is valid, the eigenstates are represented by Airy functions. These functions are delocalized and have a continuous energy spectrum. The oscillatory nature of the Airy functions results in the appearance of oscillations in the frequency dependence of the absorption coefficient and other related quantities (Lederman and Dow 1976, Aspnes 1980). These Franz-Keldysh (FK) oscillations appear above the energy gap and their period scales with electric field as zyxwv F2I3. The effective-mass approximation breaks down when the electron (hole) is capable of gaining energies from the electric field which are comparable with, or greater than, the bandwidth A of the zero-field energy band. In this case a tight-binding approach is a better starting point for discussing the problem. Within this picture the eigenstates are discrete and localized on a length scale L=A/eF. This localization manifests itself by the appearance of a series of equally spaced peaks in the optical constants known as Stark-Wannier (SW) ladders (Ermin and Hart 1987, Mendez and Agull6-Rueda 1989). The validity of each approximation is best discussed in terms of an effective electric field eFD D A 1’ f=-=- where D is the lattice period along the electric field direction. Thus the FK regime should appear for f 4 1, whereas for f x 1 the SW picture should be appropriate to describe the electronic states of the solid. In bulk semiconductors (A x 1 eV; D x 6 A) enormous fields (Fz 106Vcm-’) would be required to attain the fx 1 condition. Hence, no clear evidence of SW ladders exists for these materials, while the FK regime has been amply documented (Aspnes and Studna 1973, Lederman and Dow 1976, Aspnes 1980, Sydor et al. 1989). On the other hand, in semiconductor superlattices, periods and bandwidths can be tailored in such a way thatfx 1 for relatively modest applied fields ( F x 104-105 Vcm-I). Following the first reports of SW ladder forma- tion in Al,Ga, -&/GaAs superlattices (Bleuse, Bastard and Voisin 1988, Mendez, 0141-8637/94 $1oal~ 1994 Taylor zyxwvut & Francis Ltd