We have measured the zero-bias differential tunneling conductance of
InAs/AlSb/GaS b/AlSb/InAs heterostructures at low temperatures (1.7K < T < 60K)
and unde r a magnetic field at various angles with the heterostructure's
interfaces. Shubni kov-de Haas oscillations in the magnetoconductance reveal
the two-dimensional (2D) character of the electrons accumulated at the InAs
interfaces and yield their num ber in each of them. The temperature dependence
of the oscillations suggests the f ormation of a field-induced energy gap at
the Fermi level, similar to that observe d before in simpler 2D-2D tunneling
systems. A calculation of the magnetoconductan ce that considers different 2D
densities in the two InAs electrodes agrees with th e main observations, but
fails to explain features that might be related to the pr esence of 2D holes in
the GaSb region.Comment: 4 papes, 3 eps figures. Submit to Phys. Rev. 

González, E. M.

Lin, Y.

Mendez, E. E.

Physical Review B

English

arXiv

©2000 The American Physical Society.
We thank Dr. A. Sacedon for her participation in the early stages of this work, Dr. W. I. Wang for contributing the heterostructures used in it, and Dr. Aleiner for useful discussions. The support of the US Army Research Office and of NATO (E.M.G.) have made this work possible.We have measured the zero-bias differential tunneling conductance of InAs/AlSb/GaSb/AlSb/InAs heterostructures at law temperatures (1.7 K<T<60 K) and under a magnetic field at various angles with the heterostructure's interfaces. Shubnikov-de Haas oscillations in the magnetoconductance reveal the two- dimensional (2D) character of the electrons accumulated at the InAs interfaces and yield their number in each of them. The temperature dependence of the oscillations suggests the formation of a field-induced energy gap at the Fermi level, similar to that observed before in simpler 2D-2D tunneling systems. A calculation of the magnetoconductance that considers different 2D densities in the two InAs electrodes agrees with the main observations, but fails to explain features that might be related to the presence of 2D holes in the GaSb region.NATO (E.M.G.)Depto. de Física de MaterialesFac. de Ciencias FísicasTRUEpu

González Herrera, Elvira María

Docta Complutense

PHYSICAL REVIEW B, VOLUME 63, 033308Magnetotunneling in a two-dimensional electron-hole system near equilibriumE. M. González,* Y. Lin, and E. E. MendezDepartment of Physics and Astronomy, SUNY at Stony Brook, Stony Brook, New York 11794-3800~Received 28 September 2000; published 29 December 2000!We have measured the zero-bias differential tunneling conductance of InAs/AlSb/GaSb/AlSb/InAs hetero-structures at low temperatures (1.7 K,T,60 K) and under a magnetic field at various angles with theheterostructure’s interfaces. Shubnikov–de Haas oscillations in the magnetoconductance reveal the two-dimensional~2D! character of the electrons accumulated at the InAs interfaces and yield their number in eachof them. The temperature dependence of the oscillations suggests the formation of a field-induced energy gapat the Fermi level, similar to that observed before in simpler 2D-2D tunneling systems. A calculation of themagnetoconductance that considers different 2D densities in the two InAs electrodes agrees with the mainobservations, but fails to explain features that might be related to the presence of 2D holes in the GaSb region.DOI: 10.1103/PhysRevB.63.033308 PACS number~s!: 73.40.Gk, 73.50.Jt, 73.50.2hteingewnArosres.AsbsWtroninAthnitextharth2Dtac-atarethersec-heirro-tiesex--on-s.thatofro-ther-Heterostructures based on the InAs-AlSb-GaSb sysare at the heart of low-dimensionality interband tunneldiodes. This system is also attractive from the point of viof basic physics because the unusual ordering of the Iand GaSb energy bands allows to study the tunneling perties of combined two-dimensional electron and hole ga~2DEG and 2DHG, respectively!.Two alternative arrangements are usually consideGaSb/AlSb/InAs/AlSb/GaSb~type A! and InAs/AlSb/GaSb/AlSb/InAs ~type B!, in both of which electrons and holeaccumulate at the InAs and GaSb interfaces, respectivelytype A, when the InAs layer is thin, a quasisquare Inquantum well~QW! for electrons is created between AlSbarriers, and GaSb electrodes behave as sources of holetype B, a thin GaSb central layer forms a quasisquare Qfor holes, whereas the InAs end layers act as elecsources. In either combination, when a voltage~V! is appliedbetween the electrodes, negative differential resista~NDR! appears when the bandgap of GaSb starts blockthe tunneling of electrons from the conduction band of Ininto adjacent layers.1,2Until now, the emphasis has been on the study ofcurrent-voltage (I -V) characteristics, often in connectiowith the materials properties of the heterostructures or wthe details of their band structure.3–8 The wealth of informa-tion available on the InAs-AlSb-GaSb system under anternal bias constrasts with the limited knowledge aboutdetails of the tunneling mechanism when the system isquasiequilibrium, that is, in the zero-voltage limit. Since criers accumulate in quasitriangular wells at the interfaces,fact that tunneling ideally occurs between quantizedstates at the electrodes should be reflected in the conducbehavior.9,10 Moreover, since in both types of heterostrutures vertical transport involves confined valence-band st~holes in GaSb! and conduction band states~electrons inInAs!, one could envision tunneling taking place via2DH~E!G→2DE~H!G→2DH~E!G mechanism, with its ownsignature.The 2D nature of the electronic states at the centralgion, whether it is InAs or GaSb, is unquestioned, butsmall confinement energy at the electrodes in type A hetstructures reduces~if not eliminates altogether! the 2D char-0163-1829/2000/63~ !/033308~4!/$15.00 63 0333msp-esd:In. Inncegseh-ein-encees-eo-acter of the holes.11 In type B structures, however, electronin the quasitriangular accumulation layers at the InAs eltrodes are much more confined, and in a magnetic field tcyclotron energy is large enough to yield a distinct zedimensionality Landau-level spectrum. These propermake InAs-GaSb-InAs based heterojunctions suitable toplore 2DEG→2DHG→2DEG tunneling, which is the objective of this work.We have measured the zero-bias differential magnetocductance~G! of InAs/AlSb/GaSb/AlSb/InAs heterostructuregrown by molecular-beam epitaxy onp1 GaSb substratesThe thickness of the undoped GaSb layer was 60 Å andof each AlSb barrier was 34 Å. Each electrode consisteda 800 Å thick undoped InAs region~residualn2 type dop-ing estimated to be 1 to 331017 cm23) adjacent to AlSb,followed by a thick~3000 Å near the surface, 1mm next tothe substrate! n1 InAs (Nd5231018 cm23) layer.Figure 1 shows the potential energy profile of the heteFIG. 1. Energy-band profile of a type B heterostructure invicinity of the Fermi levelEF . The thickness of each AlSb barrieis 34 Å. E0 and H0 represent the confined levels for twodimensional~2D! electrons in the InAs conduction band~CB! and2D holes in the GaSb valence band~VB!, respectively.©2000 The American Physical Society08-1nAecyebeor oelerhtrlrg-Detn-as2Dth-thd.-rvicthif-snioaafiee028ede-n-eli-di-itsmldsanceofthisofndi-ere-methelf-ouldiedthetheggeorareBRIEF REPORTS PHYSICAL REVIEW B 63 033308structure along the growth direction,z. The overlap betweenthe top of the GaSb valence band and the bottom of the Iconduction band produces a self-limiting transfer of eltrons from GaSb to InAs. As a result, an accumulation lais formed at each InAs/AlSb interface and holes are lefthind in the GaSb quantum well. Ideally the total numberholes is twice that of electrons per interface. The numbetransferred electrons increases with increasing overlapergy and with decreasing barrier thickness. In the figure,E0indicates the ground-state energy for 2D electrons,EF is theFermi level of the system, andH0 represents the heavy-hoground-state energy of the GaSb quantum well. The enevalues have been calculated by solving Poisson and Sc¨-dinger equations self-consistently.The best evidence for the presence of holes in the cenwell is the observation~even at room temperature! of NDRfeatures in theI -V characteristics.2 As the voltage betweenelectrodes is increased, electrons from the emitter tunnethe collector through the two barriers via the small enewindow defined byEF andH0. The tunneling process continues until the voltage is such thatH0 is below the emitter’sE0 level, at which point the tunnel current ceases and Nappears. The shape of theI -V curves and the current-onsvoltage depend on whether the in-plane momentum,ki , isconserved in the tunneling process. A detailed discussiothe similarities and differences between 2DEG→2DEG and2DEG→2DHG is postponed for a future publication. However, it is important to mention now that, in sharp contrwith the former case, tunneling of momentum-conservingelectrons into 2D hole states is possible for all voltages inrange between the threshold~which depends on the difference between the number of 2D electrons and holes! andNDR voltages.We focus here on the quasiequilibrium conductance,is, the slope of theI -V characteristics in theV→0 limit. Themeasurements were done at low temperature (1.7 K,T,60 K) by applying a small ac modulation voltage~200mV) between the electrodes of mesa-defined diodes withmensions of 100mm3100 mm, and a magnetic field B, upto 11 T, forming an anglew with the plane of the interfacesIn Fig. 2~a! we show G~B! for w590° up to B5 11 T.The oscillations in G~B!, discernible even below 0.5 T, exhibit the characteristicB21 periodicity of Shubnikov–deHaas oscillations. They resemble those previously obsein similar measurements on type A heterostructures, whwere explained in terms of the Landau levels formed inInAs quantum well.12 However, there are some notable dferences between the oscillations observed in both typeheterostructures. While at low magnetic fields (B,1 T) theamplitude of the oscillations in type A increases monotocally with increasing field, that of the oscillations in Fig. 2~a!is modulated in a way similar to that observable in a twsubband system. Besides, a second set of oscillations isparent in Fig. 2~a! at intermediate fields (1 T,B,4 T),quite different from the spin-splitting doublets that appearlarger fields in type A. Finally, the oscillations in Fig. 2~a!have an unusual shape at high B (B.4 T).The temperature and angular dependence of the low-oscillations in Fig. 2~a! have elucidated their origin. Th03330s-r-ffn-gyroaltoyRofteati-edheof--p-tldtemperature dependence of the oscillations’ amplitudes~s eFig. 3! yields effective mass values between 0.025 and 0.m0 (m0 is the free-electron mass!. The angular dependencreveals that the positions of the oscillations extrema aretermined not by the total magnetic field but by its perpedicular componentB' , thus proving the 2D character of thcharges involved in magnetotunneling. The low-field amptude modulation and the doublets at intermediate fields incate two different Landau-level ladders, each of them withown B21 periodicity and associated 2D carrier density. Frothe periods of the two oscillations, a simple estimate yieN155.1331011 cm22 andN255.0731011 cm22.These results are consistent with the magnetoconductoscillations being due to tunneling between Landau levelsthe 2D electron gases formed at the InAs electrodes. Inpicture N1 and N2 represent the 2D electron densitiesthose electrodes; the small difference between the two icates that the two interfaces are almost identical and, thfore, that the subband energies,E01 andE02, are almost thesame. Instead, it would be possible to interpretN1 andN2 asthe carrier densities of two electron subbands of the saelectrode, let us say the emitter. But if this were the case,two densities should be quite different; indeed, our seconsistent calculations indicate that a second subband wbe only marginally occupied.The above picture—2D electrons tunneling from occupLandau levels in the emitter to equivalent empty states incollector—is supported by the agreement found betweenexperimental results of Fig. 2~a! and the calculated tunnelinFIG. 2. Differential tunneling conductance in the zero-voltalimit ~V50! it vs a magnetic field perpendicular to the layers, fthe heterostructure to which Fig. 1 refers.~a! Experimental curvemeasured atT51.7 K. ~b! Calculated curve using Eq.~1! in thetext. The indices of the Landau levels in the two InAs electrodesindicated asn andn8.8-2ny;lsextw-atca,veaelter-rs,here-cu-llin-ofablescil-ofnedldfer-erval-detionllyhetwoedtheer-antionldgapier.ant-ra-theeri-ea-delnig--tueteBRIEF REPORTS PHYSICAL REVIEW B 63 033308magnetoconductance shown in Fig. 2~b!. The calculation issimilar to that by Lyo~Ref. 13! for the conductance betweetwo 2D electron gases in a perpendicular fieldB' ,Gzz~B'!}g~B'! (n1 ,n2un1 ,n2~u!2rn1~m!rn2~m2D!, ~1!where g(B')5eB' /p\ is the Landau-level degeneracun1 ,n2(u) is an ‘‘overlap’’ function between Landau leven1 andn2 of the electrodes, which, if the Landau-level indis conserved, is 1 when15n2 and zero otherwise;rni is thedensity of states~DOS! for the Landau level of indexni ; andD is the difference between the subband energies of theelectrodes (D5uE012E02u). We have used the approximation that only Landau levels at the Fermi energym contributesignificantly toGzz(B'), thus reducing the double sum onn1andn2 to n15n1F andn25n2F . We have also assumed ththe value of the overlap function is 1 because since therier densities in the two InAs layers are almost the samepractice, at the Fermi energy the indices of the Landau leof the two electrodes are the same. For the DOS we hused a Gaussian distribution,rn~m!51A2pGexpF2 ~m2«n!22G2G , ~2!FIG. 3. Temperature dependence of the magnetoconductarelative to its zero-field value, for the heterostructure shown in F1. For clarity, the origin is different for each curve. While the amplitude of the low-field~below 3 T! oscillations decreases monotonically with increasingT, that of the high-field~above 4 T!broader oscillations first increases and then decreases. The fealabeled as A, B and C, which are more distinguishable at the lowT, cannot be explained by the simple model described in theand may be related to the 2D holes in the GaSb central well.03330or-inlsvewhere«n5\vc(n11/2) is the energy of the n Landau levand G is the level damping~or broadening!, given by G50.5h\vc /B'1/2 (h is a sample-dependent parameter!. TheFermi energy, which depends on magnetic field, was demined from the condition that the total number of carrie2N05N11N2, be constant:2N05E0`D2D~E! f ~E,m,T!dE, ~3!where f (E,m,T) is the Fermi distribution function, andD2D(E) is the total density of states, which includes tDOS of each accumulation layer. Since the experimentalsults used for comparison were obtained at 1.7 K, in callating m from Eq. ~3! we assumed thatT50 K.As seen in Fig. 2~b!, this simple model reproduces wethe peak positions throughout the entire field range. Ourtention has not been to find systematically a ‘‘best’’ setparameters but rather to illustrate how a set of reasonvalues can explain the observed magnetoconductance olations. The following set has been used in the calculationFig. 2~b!: 0.027 m0 for the electron effective mass,h50.8T1/2 for the parameter related with the broadeningG,N055.731011 cm22 and D54 meV for the misalignmentbetween the two energy subbands,E01 and E02. The valueused for the effective mass is consistent with that determifrom the temperature dependence of the low-fieShubnikov–de Haas oscillations. The subband energy difenceD is less than 10% of any of the two energies; in othwords, the difference betweenN1 andN2 is quite small whencompared to the average density in each electrode. Theues of this difference and of the sum (2N0), although some-what larger than those estimated from the Shubnikov–Haas periods, were chosen so that the calculated G~B! ‘‘fit-ted’’ well the experimental G~B! for the entire magnetic-fieldrange. The small discrepancy may be due to our assumpthatN0 is independent of B, an assumption that is especiaquestionable at high fields, given the physical origin of t2D electrons~the transfer from the GaSb central well!.The different carrier densities of the two~nominally iden-tical! accumulation layers suggest an asymmetry in theAlSb barriers, a fact confirmed by the asymmetry observbetween the two polarities of the diodes’I -V characteristics.If one barrier were thicker or higher than the other, thenintrinsic transfer of electrons from GaSb to each InAs intface would be different. In practice, barrier asymmetry chappen for a number of reasons; for instance, Ga segregaduring the epitaxial growth of the heterostructures woulead to a Ga-rich AlGaSb layer, which has a smaller bandthan AlSb and would present a smaller tunneling barrThis segregation process is known to be the more significthe higher the substrate temperature.3 Since our heterostructures were prepared at 500 °C—a relatively high tempeture for these materials—it would not be surprising thatbarrier asymmetry is caused by that mechanism.In spite of the overall good agreement between the expment and the calculation, at high magnetic fields the msured conductance behaves in a way for which the mocannot account. In Fig. 2~a! there are three peaks~marked byce,.resstxt8-3g.lyfbnlseeme--ntroeaofhenspdnts2D,herthangetheAs-leseiris-tionatan-othiblerlyeus-ofBRIEF REPORTS PHYSICAL REVIEW B 63 033308‘‘A,’’ ‘‘B,’’ and ‘‘C’’ ! that do not have a counterpart in Fi2~b!. Although the fact that they were clearly resolved onat the lowest temperatures~ ee Fig. 3! might suggest spinsplitting effects, the inclusion of spin in the calculation@notshown in Fig. 2~b!# failed to explain both the number opeaks and the fields at which they occur.The temperature dependence of the broader Shukov–de Haas oscillations underlying peaks A, B, and C awarrants a comment. AsT increases, the amplitude of thoscillations increases a bit before it decreases at high tperatures~see Fig. 3!, suggesting a thermally activated bhavior followed by the usualT-induced weakening of quantum effects, whenkBT becomes comparable to the cyclotroenergy and the scattering time is comparable to the cyclotime. Although the low-temperature range investigated his too limited to draw any conclusion, it is quite possible ththe activated behavior is a consequence of the formationfield-induced energy gap at the Fermi level. Such a gapbeen proposed to explain a similar temperature dependof the 2DEG→2DEG conductance in GaAs-GaAlAheterostructures.14 Calculations have shown that the gap apears as a result of the additional energy cost requireextract an electron from the emitter Fermi sea~creating a‘‘vacancy’’! and to inject it into the collector one~creating.i03330i-o-nretaasce-toan ‘‘interstitial’’ ! when many-body effects~for example,Coulomb interactions! become sizeable.15The quasiequilibrium magnetoconductance experimepresented here show unambiguously the participation ofelectrons in the 2DEG→2DHG→2DEG tunneling processbut do not reveal the role of the 2D holes in it. Whether tunaccounted low-temperature peaks~A, B, and C! are evi-dence of the holes we do not know. However, it is wopointing that, based on their shape and the temperature rin which they are most visible, those peaks resemblefeatures found in the in-plane magnetoresistance of InGaSb heterostructures in which 2D electrons and hocoexist.16 Although these features remain unexplained, thconnection with 2D holes is well established, since they dappear when the 2D holes are eliminated by the applicaof hydrostatic pressure.17 It is then reasonable to imagine ththe extra peaks in Fig. 3 are somehow related to the qutized holes in the GaSb quantum well, but more work, btheoretical and experimental, is needed to set this posscorrespondence on a firmer ground.We thank Dr. A. Sacedon for her participation in the eastages of this work, Dr. W. I. Wang for contributing thheterostructures used in it, and Dr. Aleiner for useful discsions. The support of the US Army Research Office andNATO ~E.M.G.! have made this work possible.t,Btt..*Permanent address: Universidad Complutense, Madrid, Spain1J. R. Söderström, D. H. Chow, and T. C. McGill, Appl. Phys.Lett. 55, 1094~1989!.2L. F. Luo, R. Beresford, and W. I. Wang, Appl. Phys. Lett.55,2023 ~1989!.3B. Z. Nosho, W. H. Weinberg, J. J. Zinck, B. V. Shanabrook, BR. Bennett, and L. J. Whitman, J. Vac. Sci. Technol. B16, 2381~1998!.4H. Kitabayashi, T. Waho, and M. Yamamoto, J. Appl. Phys.84,1460 ~1998!.5M. Ogawa, T. Sugano, and T. Miyoshi, Physica E~Amsterdam!7, 840 ~2000!.6T. Takamasu, N. Miura, K. Taira, K. Funato, and H. KawaPhysica B184, 259 ~1993!; 201, 380 ~1994!.7R. R. Marquardt, D. A. Collins, Y. X. Liu, D. Z.-Y. Ting, and T.C. McGill, Phys. Rev. B53, 13 624~1996!; Y. X. Liu, R. R.Marquardt, D. Z.-Y. Ting, and T. C. McGil,ibid. 55, 7073~1997!.8E. E. Mendez, V. V. Kuznetsov, D. Chokin, and J. D. Bruno.,,Physica E~Amsterdam! 6, 335 ~2000!.9E. E. Mendez and L. L. Chang, Surf. Sci.229, 173 ~1990!.10J. P. Eisenstein, T. J. Gramila, L. N. Pfeiffer, and K. W. WesPhys. Rev. B44, 6511~1991!.11E. E. Mendez, J. Nocera, and W. I. 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Magnetotunneling in a two-dimensional electron-hole system near equilibrium

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Magnetotunneling in a Two-Dimensional Electron-Hole System Near Equilibrium

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