We study the electronic properties of GaAs-AlGaAs superlattices with
intentional correlated disorder by means of photoluminescence and vertical dc
resistance. The results are compared to those obtained in ordered and
uncorrelated disordered superlattices. We report the first experimental
evidence that spatial correlations inhibit localization of states in disordered
low-dimensional systems, as our previous theoretical calculations suggested, in
contrast to the earlier belief that all eigenstates are localized.Comment: 4 pages, 5 figures. Physical Review Letters (in press

Bellani, V.

Diez, E.

Dominguez-Adame, F.

Gomez-Alcala, R.

Hey, R.

Parravicini, G. P.

Tarricone, L.

Toni, L.

English

arXiv

© 1999 The American Physical Society.
Work in Italy has been supported by the INFM Network “Fisica e Tecnologia dei Semiconduttori III-V” and in Madrid by the CAM under Project No. 07N/0034/1998. E. D. and F. D.-A. thank A. Sánchez for collaboration on these topics during these years.We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disorder by means of photoluminescence and vertical de resistance. The results are compared to those obtained in ordered and uncorrelated disordered superlattices. We report the first experimental evidence that spatial correlations inhibit localization of states in disordered low-dimensional systems, as our previous theoretical calculations suggested, in contrast to the earlier belief that all eigenstates are localized.CAMDepto. de Física de MaterialesFac. de Ciencias FísicasTRUEpu

Díez Alcántara, Eduardo

Parravicini, G.B.

Domínguez-Adame Acosta, Francisco

Gómez-Alcalá, R.

Docta Complutense

VOLUME 82, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 8 MARCH 1999ainnrderbtaineddenceours areExperimental Evidence of Delocalized States in Random Dimer SuperlatticesV. Bellani,1 E. Diez,2 R. Hey,3 L. Toni,4 L. Tarricone,4 G. B. Parravicini,1F. Domı́nguez-Adame,5 and R. Gómez-Alcalá61INFM-Dipartimento di Fisica “A. Volta,” Universitá di Pavia, I-27100 Pavia, Italy2GISC, Departamento de Matemáticas, Universidad Carlos III de Madrid, E-28911 Leganés, Sp3Paul Drude Institut für Festkörperelektronik, Hausvogteiplatz 5-7, D-10117 Berlin, Germany4INFM-Dipartimento di Fisica, Universitá di Parma, I-43100 Parma, Italy5GISC, Departamento de Fı´sica de Materiales, Universidad Complutense, E-20840 Madrid, Spain6Departamento de Tecnologı´as de las Comunicaciones, Universidad de Vigo, E-36200 Vigo, Spai(Received 21 July 1998; revised manuscript received 17 November 1998)We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disoby means of photoluminescence and vertical dc resistance. The results are compared to those oin ordered and uncorrelated disordered superlattices. We report the first experimental evithat spatial correlations inhibit localization of states in disordered low-dimensional systems, asprevious theoretical calculations suggested, in contrast to the earlier belief that all eigenstatelocalized. [S0031-9007(99)08627-5]PACS numbers: 73.20.Dx, 73.20.Jc, 78.55.–m, 78.66.–wedheeyof5].nionofn-].bysmtntrgead’sk4)esare’s,s.dIn recent years, a number of tight-binding [1–3] ancontinuous [4] models of disordered one-dimension(1D) systems have predicted the existence of setsextended states, in contrast to the earlier belief thatallthe eigenstates are localized in 1D disordered systeThese systems are characterized by the key ingredithat structural disorder is short-rangecorrelated. Becauseof the lack of experimental confirmations, there are stsome controversies as to the relevance of these resand their implications on physical properties. In thcontext, some authors have proposed findingphysicallyrealizable systemsthat allow for a clear cut validation ofthe above-mentioned purely theoretical prediction [5–8Given that semiconductor superlattices (SL’s) have bealready used successfully to observe electron localizatdue to disorder [9–14], these authors have suggesSL’s as ideal candidates for controllable experimenon localization or delocalization and related electronproperties [5–8].To the best of our knowledge, up to now thereno experimental verificationof this theoretical predic-tion owing to the difficulty in building nanoscale materials with intentional and short-range correlated disordeHowever, the confirmation of this phenomenon is impotant both from the fundamental point of view and fothe possibility to develop new devices based on thepeculiar properties. In this work we present anexperi-mental verificationof this phenomenon in semiconductonanoscale materials, taking advantage of the molecubeam epitaxy growth technique, which allows the fabrcation of semiconductor nanostructures with monolaycontrolled perfection.We grew several GaAs-Al 0.35Ga0.65As SL’s and westudied their electronic properties by photoluminescen(PL) at low temperature and dc vertical transportthe dark. Indeed PL has been proven to be a go0031-9007y99y82(10)y2159(4)$15.00dalofms.entillultsis].eniontedtsicis-r.r-rserlari-erceinodtechnique to study the electronic properties of disorderSL’s [9–11], giving transition energies comparable wittheoretical calculations of the electronic levels. Thelectronic states were calculated using a Kronig-Pennmodel that has been shown to hold in this rangewell and barrier thicknesses, with precise results [1This allows the analysis of the experimental transitioenergies for PL and the ascertainment of the localizatand delocalization properties of the SL’s. The detailsthe calculations and a schematic view of the conductioband profiles of the three SL’s can be found in Ref. [7The samples are three undoped SL’s grownmolecular beam epitaxy. All the SL’s have 200 periodand Al0.35Ga0.65As barriers 3.2 nm thick. In theorderedSL all the 200 wells are identical with thickness 3.2 n(hereafter referred to asA wells). In the random SL,58 A wells are replaced by wells of thickness2.6 nm(hereafter referred to asB wells) and this replacemenis done randomly. The so-calledrandom dimerSL isidentical to the random SL with the additional constraithat theB wells appear only in pairs [7]. In the lattesample the disorder exhibits the desired short-ranspatial correlations. In each sample, the SL is clon each side by 100 nm ofn-Al 0.3Ga0.7As, Si dopedto 4 3 1018 cm23, with a 50 nm n-GaAs buffer layer(doped to4 3 1018 cm23) on the substrate and a 3 nmn-GaAs cap layer (doped to6 3 1018 cm23).We measured x-ray diffraction spectra of the SLwith a double-crystal diffractometer, in order to chectheir structural parameters. The diffraction curve at (00symmetric reflections for the two disordered samplshows satellite peaks of order61 lying close to60.8±with respect to the GaAs peak. These satellite peakslocated at identical positions for the two disordered SLshowing that the random SL’s have identical periodTherefore, the dimer constraint intentionally introduce© 1999 The American Physical Society 2159VOLUME 82, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 8 MARCH 1999ess.yeiset1.ethen-sles-nyin,-eni-alofduring sample growth is the only difference betweerandom and random dimer samples.The PL spectra were taken in the11 300 K tempera-ture range with a closed cycle cryostat and were ecited with 514.5 nm light from an Ar1-ion laser (with anexcitation intensity of approximately0.5 Wycm2). Pho-toluminescence was dispersed by a0.46 m Jobin Yvonmonochromator and detected by a cooled photomultiplusing a standard lock-in technique.Figure 1 shows the PL spectra of the three SL’s11 K. We observed the fact that the energy of the neaband edge peaks depends on the sample, but the enshift between them is almost independent of temperaton a wide range, as shown in Fig. 2. The PL pefor the ordered SL, which lies at1.688 eV, is due toa recombination between electrons in the conductiband and heavy holes in the valence band [16]. Wcalculated the miniband structure of this SL with thKronig-Penney model, usingG effective masses (in unitsof free electron mass)mpe ­ 0.067 for GaAs andmpe ­0.096 for Al 0.35Ga0.65As. The expected miniband in theconduction band lies in the range between1.68 and1.76 eV, measured from the (very narrow) heavy hominiband. This calculation is in good agreement withe experimental PL spectrum, with the calculated lowenergy of the miniband being very close to the energywhich PL intensity rises up. Figure 3(a) shows an enerschema of the radiative transitions in the ordered SL.1.65 1.70 1.75GaAs-Al0.35Ga0.65AsSuperlatticesT = 11 K  Ordered-SL  Random-SL  Random dimer-SLPL Intesnity (arb. units)Energy (eV)FIG. 1. PL spectra of the ordered, random, and random dimSL at 11 K.2160nx-ieratr-ergyureakoneeletheratgyerLet us now analyze the spectrum obtained for thrandom SL. The PL peak of this sample shifts towardhigher energies compared with the other two sampleIn the random SL the intentional disorder introduced bthe random distribution of wellsB s2.6 nmd localizesthe electronic states [7]. The calculated energy for thtransition between electron and holes in this case1.72 eV assuming that the exciton binding energy is thsame in the three SL’s. This value is again in excellenagreement with the PL peak, as can be seen in Fig.Figure 3(b) shows a schematic diagram of the radiativtransitions between localized states in the random SL.The PL peak of the random dimer SL is at 1.696 eVand, as can be clearly seen in Fig. 1, is redshifted wirespect to the PL peak for the random SL. As has beshown by Fujiwara [15], the redshift of the PL peak insemiconductor SL’s is due to the formation of a miniband with a tunnel process for carriers between the GaAwells. This result strongly supports previous theoreticapredictions of the occurrence of a band of extended statin random dimer SL’s [7]. We calculated the transmission coefficient for the random dimer SL according toRef. [7] and found that the energy difference betweethe onset for electron delocalization (that is, the energat which transmission suddenly rises, as can be seenFig. 4) and the heavy hole miniband is around 1.70 eVin good agreement with the experimental PL peak energy. Figure 3(c) presents a schematic diagram of thradiative transitions in the random dimer SL.Additionally, the PL linewidth gives support to thesefindings. The PL full width at half maximun of the or-dered SL is 9.1 meV, increasing to 13.2 and 12 meV ithe random SL and random dimer SL, respectively, indcating that these last two samples reflect their intentiondisorder in the optical spectra.0 50 100 150 200 250 3001.581.601.621.641.661.681.701.72 Ordered-SL Random dimer-SL Random-SLPL peak position (eV)Temperature (K)FIG. 2. Temperature dependence of the PL peak positionthe ordered, random, and random dimer SL.VOLUME 82, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 8 MARCH 1999ofiseri-henceara-foron-erncee,x-ithisthea)b)Bloch-likestatesExtendedstatesLocalized statesHHHHHH1.68 eV1.70 eV1.72 eVFIG. 3. Schematic diagram of radiative transitions i(a) ordered SL, (b) random SL, and (c) random dimer SL11 K.To confirm the above interpretation of the PL spectrwe have performed additional measurements of tresistance at low temperatures [17]. The results for ttemperature dependence of the resistance are shoin Fig. 5. The resistance of the random dimer SLvery similar to the resistance of the ordered SL foany temperature below 40 K, and the small differencare due to the different miniband width between botSL’s (see Fig. 3). On the other hand, the randoSL shows a much higher resistance in this rangetemperatures. This is completely consistent with thabove interpretation of the PL spectra and it is cleevidence of the presence of extended states in trandom dimer SL showing transport properties versimilar to an ordered SL. Moreover, the resistancethe random SL still depends on temperature belo30 K, while the resistance of the two other samplereaches a plateau. For low temperatures, transpproperties in the presence of true extended states shobe independent of temperature [17] and, as can be sin Fig. 5, this behavior is observed only in the randomdimer SL and in the ordered SL, which is additionaevidence of the presence of extended states in thesamples.In summary, we have observed the fact that the itroduction of short-range correlations in a disorderesemiconductor SL inhibits localization and gives risto extended states, as expected theoretically [7]. Tpositions of the electronic levels were calculated witthe Kronig-Penney model and the calculations shothat the ordered SL and the random dimer SL ehibit extended electronic states. According to theoretical studies, these extended states in random dimSL’s are not Bloch-like, as occurs in ordered SL’snatahehewnisreshmofearheyofwsortuldeenlsen-dehehwx--er.1.69 1.70 1.71 1.72Energy (eV)0.00.20.40.60.81.0τFIG. 4. Calculated transmission coefficient as a functionthe electron energy in the random dimer SL. Energymeasured from the heavy hole miniband.The PL of the random dimer SL is redshifted withrespect to the PL of the random SL, indicating thformation of delocalized extended states. The expemental PL energies are in very good agreement with tcalculated electronic states. The temperature dependeof the resistance of the random dimer SL is very similto that of the ordered SL. Both SL’s show no temperture dependence below 30 K as should be expectedtransport in the presence of extended states. On the ctrary, the resistance of the random SL is much highfor any temperature and shows temperature dependeas would be expected for localized states. To concludwe have experimentally validated the existence of etended states in low-dimensional random systems wshort-range correlations, where Anderson localizationinhibited.FIG. 5. Temperature dependence of the dc resistance ofordered, random, and random dimer SL.2161VOLUME 82, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 8 MARCH 1999d,rt,.d...ee,Work in Italy has been supported by the INFM Networ“Fisica e Tecnologia dei Semiconduttori III-V” and inMadrid by the CAM under Project No. 07N/0034/1998E. D. and F. D.-A. thank A. Sánchez for collaboration othese topics during these years.[1] J. C. Flores, J. Phys. Condens. Matter1, 8479(1989).[2] D. H. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett65, 88 (1990).[3] P. Phillips and H.-L. Wu, Science252, 1805 (1991).[4] A. Sánchez, E. Maciá, and F. Domı´nguez-Adame, Phys.Rev. B49, 147 (1994).[5] E. Diez, A. Sánchez, and F. Domı´nguez-Adame, Phys.Rev. B50, 14 359 (1994).[6] F. Domı́nguez-Adame, A. Sánchez, and E. Diez, PhyRev. B50, 17 736 (1994).[7] E. Diez, A. Sánchez, and F. Domı´nguez-Adame, IEEE J.Quantum Electron.31, 1919 (1995).2162k.n.s.[8] E. Diez, A. Sánchez, F. Domı´nguez-Adame, and G. P.Berman, Phys. Rev. B54, 14 550 (1996).[9] A. Chomette, B. Deveaud, A. Regreny, and G. BastarPhys. Rev. Lett.57, 1464 (1986).[10] L. Pavesi, E. Tuncel, B. Zimmermann, and F. K. ReinhaPhys. Rev. B39, 7788 (1989).[11] Y. A. Zhang, J. A. Strozier, Jr., and A. Ignatiev, PhysRev. B53, 7426 (1996).[12] G. F. Lorusso, V. Capozzi, and J. L. Staehli, SemiconSci. Technol.11, 308 (1996).[13] K. A. Mäder, L.-W. Wang, and A. Zunger, Phys. RevLett. 74, 2555 (1995).[14] K. A. Mäder, L.-W. Wang, and A. Zunger, J. Appl. Phys78, 6639 (1995).[15] K. Fujiwara, in Semiconductor Superlattices,edited byH. T. Grahn (World Scientific, Singapore, 1995).[16] Exciton binding energies are much smaller than thobserved peak shifts.[17] G. Richter, W. Stolz, P. Thomas, S. W. Koch, K. Maschkand I. P. Zvyagin, Superlattices Microstruct.22, 475(1997).

Physical Review Letters

Experimental evidence of delocalized states in random dimer superlattices

V. Bellani

E. Diez

R. Hey

L. Toni

L. Tarricone

G. B. Parravicini

F. Domínguez-Adame

R. Gómez-Alcalá

Crossref

Experimental Evidence of Delocalized States in Random Dimer Superlattices

We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disorder by means of photoluminescence and vertical dc resistance. The results are compared to those obtained in ordered and uncorrelated disordered superlattices. We report the first experimental evidence that spatial correlations inhibit localization of states in disordered low-dimensional systems, as our previous theoretical calculations suggested, in contrast to the earlier belief that all eigenstates are localized

Experimental evidence of delocalized states in random dimer superlattices

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