WAVEFUNCTION DELOCALIZATION OF STRONGLY- LOCALIZED STARK-LADDER STATES IN A GaAs/AlAs SUPERLATTICE M. ANDO 1 , M. NAKAYAMA 1 , H. NISHIMURA 1 , M. HOSODA 2 , N. OHTANI 3 , N. EGAMI 3 and K. FUJIWARA 4 1 Department of Applied Physics, Faculty of Engineering, Osaka City University, Sugimoto, Sumiyoshi- ku, Osaka, 558, Japan 2 ATR Optical Radio Communications Research Laboratories, Hikaridai, Seika-cho, Soraku-gun, Kyoto, 619-02, Japan 3 ATR Adaptive Communications Research Laboratories, Hikaridai, Seika-cho, Soraku-gun, Kyoto, 619-02, Japan 4 Department of Electrical Engineering, Kyushu Institute of Technology, Tobata-ku, Kitakyushu, 804, Japan AbstractÐWe have investigated the wavefunction-localization properties as a function of electric ®eld from 0 30 to 0 300 kV/cm in a GaAs(6.8 nm)/AlAs(0.8 nm) superlattice by using electrore¯ectance spec- troscopy to observe Stark-ladder transitions. It has been found from the electric-®eld dependence of the electrore¯ectance spectra that the electron wavefunctions are delocalized after they are fully localized in individual quantum wells in a high electric-®eld regime. We conclude that the wavefunction delocaliza- tion results from the tunneling eect induced by the interaction between the spatially-separated ®rst and second Stark-ladder states from the analysis of the eigenstates based on a transfer-matrix method in the framework of an envelope-function approximation. # 1998 Elsevier Science Ltd. All rights reserved 1. INTRODUCTION In the past one decade, there has been considerable interest in the Wannier±Stark (WS) localization in semiconductor superlattices (SLs) from the fundamental and device-application aspects[1±3]. This phenomenon corresponds to the electric-®eld- induced localization of miniband wavefunctions which are delocalized under a ¯at band condition. In the WS localization, the minibands are split into a set of localized states with an equidistant energy spacing eFD, so-called Stark-ladder states, where F is the electric ®eld, and D is the SL period. Experimentally, the WS localization manifests itself by the appearance of the optical transitions with the energy of E 0 2meFD (m=0, 1, 2, ... ), where E 0 is the transition energy in individual quantum wells (QWs), the integer m is called a Stark-ladder index. When we observe the Stark-ladder transitions up to the m max index, m max D corresponds to the wavefunction-localization length. Therefore, we can measure the localization properties from the obser- vation of the Stark-ladder transitions. From this scenario, several works[4±8] were reported on exper- imental results of the electric-®eld dependence of the wavefunction localization. In the previous works[5±8], a one-band nearest-neighbor tight-bind- ing model[9,10], which is called hereafter one-band TB model, has been used for the analysis of the localization properties. On the basis of the one- band TB model, the probability density of the loca- lized wavefunction in the mth nearest neighbor QW, P m , is given by the following Bessel-function form: P m  J 2 m D=eFD, 1 where D is one half of the total energy width of the miniband. This equation provides a simple picture of the enhancement of the wavefunction localization with the increase of electric ®eld F: under the full localization condition, P 0 =1 and P m$0 =0. In the present work, we have systematically measured the electrore¯ectance (ER) spectra of a GaAs(6.8 nm)/AlAs(0.8 nm) SL embedded in a p±i±n structure at 77 K to investigate the wavefunction-localization properties as a function of electric ®eld. We have found that the electron wavefunctions are delocalized after they are fully localized in individual QW's in a high electric-®eld regime. This is never expected within the framework of the one-band TB model. It should be noted that there exist multiple minibands in the SL, so that the interactions between the dierent-quantum- number Stark-ladder states are not negligible. We discuss the electric-®eld dependence of the wave- function localization obtained from the ER spectra on the basis of the energies and wavefunction forms of the Stark-ladder states calculated by a transfer- matrix (TM) method[11,12] in the framework of an Solid-State Electronics Vol. 42, No. 7±8, pp. 1499±1503, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0038-1101/98 $19.00 + 0.00 PII: S0038-1101(98)00057-4 1499