Physica E 2 (1998) 282—286

Ballistic electron transport in vertical biased superlattices

C. Rauch!,*, G. Strasser!, K. Unterrainer!, W. Boxleitner!, K. Kempa", E. Gornik!

! Solid State Electronics, TU Vienna, Floragasse 7, A-1040 Wien, Austria" Department of Physics, Boston College, Chestnut Hill, MA 02167, USA

Abstract

We present direct evidence for the breakdown of coherent transport through an undoped biased GaAs/AlGaAssuperlattice using the technique of hot electron spectroscopy. A three terminal device is used to inject an energy tunableelectron beam via a tunneling barrier into a biased superlattice structure. A significant decrease of the total minibandtransmission, related to the localization of the superlattice states with increasing electric field is observed. The measuredtransfer characteristics are compared to the results of a theoretical calculation based on a transfer matrix method usingan envelope function approximation. The calculated localization of the electron wave functions and the shift of thesuperlattice states agrees well with the measured tunneling data. ( 1998 Elsevier Science B.V. All rights reserved.

Keywords: Superlattice; Stark localization; Transport; Tunneling

Decreasing the barrier thickness of multiplequantum-well structures leads to a stronger coup-ling between the degenerate eigenstates in thewells and thus to the formation of superlatticeminibands. The application of an external electricfield parallel to the growth axis quantizes the en-ergy continuum associated with the miniband dis-persion into a Stark ladder [1] of discrete energylevels, and transforms the extended Bloch wavesinto strongly localized wave functions. The energyspectrum is given by E

0#neFd where E

0is the

eigenenergy of an isolated quantum well, F is theapplied electric field and d the period of the crystal.Under strong localization coherence will be re-

*Corresponding author. Tel.: #43 1 5045525 14; fax: #431 50455259; e-mail: crauch@fkeserver.fke.tueirn.ac.at.

duced to a few periods and in the limit, to a singlequantum well.

The presence of extended states is essential forthe realization of devices which are based on super-lattice transport. Therefore, the study of the extentof the coherent superlattice wave function is ofgreat relevance.

Transport and optical properties of biased super-lattices have been the object of intense investiga-tions in the last three decades. The first experi-mental observation of the Stark ladder formationin superlattices was reported by Mendez et al. [2].In photoluminescence and photocurrent experi-ments they clearly demonstrated the splitting ofthe optical transitions. After these early experi-ments there has been a great deal of work onthe Stark ladder in superlattices. Using differentoptical techniques like electroreflectance [3], optical

1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reservedPII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 0 5 9 - 9

absorption [4], resonant Raman scattering [5],and differential photocurrent spectroscopy [6], sev-eral III—V semiconductor superlattices have beeninvestigated.

England et al. [7] described tunneling measure-ments of electronic states of superlattices in whichan electric field destroys the miniband structure.Current resonances appear for specific alignmentsof neighboring Wannier—Stark states.

Transport measurements of n—i—n superlatticestructures were extensively reported as well. Theobserved experimental I—V characteristics can befitted with a self-consistent solution of Poisson andBolzmann equation using semiclassical field velo-city relations in accordance inspired with the orig-inal work by Esaki and Tsu [8]. However, it turnsout that the experimental study of electronic prop-erties of a biased superlattice is hindered by theinterdependence of the intensity of the current in-jected and the field present in the superlattice [9].At high electric fields the large current densitiesmake the field in the superlattice nonuniform andcauses the formation of high-field domains [10]and leads to thermal saturation of miniband trans-port [11].

In the present paper we describe experimentsof hot electron transport in an undoped, biasedGaAs/Ga

0.7Al

0.3As superlattice, where the influ-

ence of electron—electron and electron impurityscattering can be neglected. A three-terminal deviceis used to probe the superlattice transmittance. Anenergy tunable hot electron beam is generated bya tunneling barrier, passes the superlattice aftertraversing a thin, highly doped n-GaAs base layerand an undoped drift region. The measured collec-tor current reflects the probability of an injectedhot electron to cross the superlattice. Having thepossibility to drive the injected current indepen-dently from the superlattice bias voltage, the trans-mittance of the superlattice can be measured dir-ectly at given superlattice bias conditions.

The structure was grown by molecular beamepitaxy on a semiinsulating GaAs substrate. Thegrowth started with a highly doped n`-GaAs col-lector contact layer (n"1]1018 cm~3) followedby a superlattice and the drift regions that areslightly n-doped (n&5]1014 cm~3) in order toavoid undesired band bending. To reduce quantum

mechanical confining effects originating from thequantum well formed by the emitter barrier and bythe superlattice the drift region is chosen to be atleast 200 nm in width. This is followed by a highlydoped (n"2]1018 cm~3) n`-GaAs layer (base) of13 nm width. As found in previous experiments[12], about 75% of the injected electrons traversethe base ballistically. On top of the base layera 13 m undoped Ga

0.7Al

0.3As barrier is grown fol-

lowed by a spacer and a n`-GaAs layer, nominallydoped to n"3]1017 cm~3, in order to achieve anestimated narrow normal energy distribution of theinjected electrons of about 20 meV. It should benoted that the half-width of the injected electronbeam limits the energy resolution of the experi-ment. Finally, a n`-GaAs contact layer (n"1]1018 cm~3) is grown on top of the heterostruc-ture to form the emitter.

The superlattice under investigation consists of10 periods of 2.5 nm Ga

0.7Al

0.3As barriers and

6.5 nm GaAs wells. The layer structure was verifiedby using transmission electron microscopy (TEM),the doping profile was measured using a CV-etchprofiler. For these parameters a simple Kronig—Penny calculation gives one miniband lying between46 and 68 meV, and a second one between 182 and276 meV. The calculated equilibrium C-point con-duction energy diagram including band bending isshown in Fig. 1 for typical biasing conditions.

The device was fabricated using wet etching of20]20 lm2 Mesas. The ohmic contacts are formedusing standard AuGe/Ni alloy.

Fig. 1. Schematic band diagram of a three terminal device withnegative bias applied to the superlattice. The miniband positionsare indicated by shaded areas.

C. Rauch et al. / Physica E 2 (1998) 282—286 283

Fig. 2. Transfer ratio a versus injection energy at different col-lector base voltages. The solid line represents the transfer ratiounder flat band condition (º

BC"0).

The static transfer ratio a"IC/I

Eis measured as

a function of negative emitter bias ("injectedelectron energy) at 4.2 K in a common base config-uration [15].

In Fig. 2 the transfer ratio a versus injectionenergy is shown for different collector biases. Nocollector current is observed up to the first trans-parent state of the first miniband, indicating thatthere is no significant leakage current between baseand collector. The solid line represents the transferratio at flat band condition (º

BC"0). The sharp

increase of the transfer ratio at about 45 meV co-incides very well with the lower edge of the firstminiband which is calculated to be 46 meV. Thepeak due to ballistic transport through the firstminiband is broader than the expected minibandwidth (22 meV) since the injected hot electron dis-tribution is about 20 meV in width. A referencesample contains a resonant tunneling diode in thedrift region [13] instead of the superlattice andallows the measurement of the hot electron distri-bution [14] of the injected electrons. The shape ofthe electron distribution is slightly asymmetricshowing the peak at the high-energy side.

The second observed peak is shifted 36 meV tohigher injection energies and is ascribed to the first

longitudinal optical (LO) phonon emission replica(hu

LO"36 meV). With the longitudinal optical

phonon scattering time at 100 meV in undopedGaAs in the order of 200 fs and the electron velo-city of 7.2]105 m/s, about 75% of the injectedelectrons are scattered by longitudinal opticalphonons and loose 36 meV in energy. A rate equa-tion is used to predict the transfer ratio due toinjected electrons at higher energies which includethe part of the distribution which is generated byone consecutive phonon-emission process. Thisresults in a non-vanishing transfer ratio betweenthe peaks since the full-width at half-maximum(FWHM) of the injected electron distribution(20 meV) plus the width of the first miniband(22 meV) is greater than the LO-phonon energy.Superposition of the transfer ratio of the replicasand the non-scattered electrons leads to the ob-served behavior as evident in the experiment(Fig. 2). The increase at about 180 meV is due totransport through the second superlatticeminiband.

The superlattice states are calculated based ona self-consistent Schroedinger solution assumingthat the Fermi level is pinned at the collector side inthe negative bias case. In the case of positive collec-tor bias, the Fermi level is pinned at the base side.No voltage drop is expected over these regions. InFig. 3, the positions of the superlattice states form-ing the first miniband with respect to the Fermilevel of the base are plotted versus electric field.A clear shift to higher energies due to the voltagedrop along the drift region and a broadening of theminiband with the applied electric field can be seen.The insets show the squared electron wave func-tions. At 3 kV/cm, the electron wave function of thelowest superlattice state is highly localized, whilethe electron wave function of the middle state is stillextended over the total dimension of the superla-ttice and transparent for ballistic electrons.

Based on a transfer matrix method using anenvelope function approximation, we have cal-culated the transmission of each superlattice stateas a function of electric field. This transmissionmultiplied by the linewidth is considered to beproportional to the current. In Fig. 4 it can be seenthat the transmission of the lowest and uppermoststates already vanishes for very low applied electric

284 C. Rauch et al. / Physica E 2 (1998) 282—286

Fig. 3. The energy position of the superlattice electron stateswith respect to the Fermi level at the base are plotted against theapplied electric field. The inset show the squared wave functionsof electron states.

Fig. 4. Theoretical transmittance of superlattice states versuselectric field. The calculation is based on a transfer matrixmethod.

fields, while the center states stays transparent upto much higher electric fields. If the transmissiontimes linewidth is less than a certain limit, the statesare localized and will not contribute to the ballisticcoherent transport. The hatched region of Figs. 3

Fig. 5. Measured total miniband transmission versus appliedelectric field. The full curve represents the result of a calculationof the transmittance for negative bias.

and 4 indicate the superlattice states which aretransparent for ballistic electrons.

Fig. 5 shows the total miniband transmissionversus electric field in the superlattice. The totalminiband transmission is defined as the integralover the deconvoluted transfer ratio of the firstpeak. This represents the transport through the firstminiband not taking into account electrons whichhave lost an LO phonon. This transmission isa measure of the transmittance of the superlattice atdifferent biases. It can be seen that the transmit-tance is vanishing for an applied electric field ex-ceeding 4 kV/cm for negative bias. This is in goodagreement with the simple estimate for the localiza-tion length j"D/eF (D is the miniband width, andF the applied electric field) which corresponds toabout 60% of the superlattice length at this bias.With reducing the electric field (below 4 kV/cm) thesuperlattice states extend successively one after theother over the total superlattice dimension andbecome transparent which leads to an increase inthe current. At zero bias the total miniband trans-mission has its maximum since all states are ex-tended and contribute to the collector current.For positive collector bias we observe a relativelyweak decay of the total miniband transmission. An

C. Rauch et al. / Physica E 2 (1998) 282—286 285

approximately constant transmittance is observedup to 1 kV/cm for positive bias which is followed bya sharp drop at about 2 kV/cm. The asymmetryseems to be an indication of an electric field addi-tional current which is compensating the field loc-alization.

The full curve in Fig. 5 represents the result ofa calculation based on a transfer matrix methodusing an envelope function approximation. Sinceno scattering of the injected electrons within thesuperlattice is included in the theoretical approach,the curve is well above the measured result. How-ever, it is evident that the total miniband trans-mission, in particular, the quenching of minibandconduction at about 4 kV/cm is in good qualitativeagreement with the experiment.

We have shown the controlled decrease of super-lattice conduction in a superlattice with bias usingthe technique of hot electron spectroscopy. Forelectric fields higher than 4 kV/cm (D/eFNd"0.6)the superlattice becomes non-transparent. Theexperimental results are in good agreementwith a calculation based on a transfer matrixmethod.

This work has been partly supported by theAustrian Federal Ministry of Science, the Society

for Microelectronics (GMe, Austria), and the U.S.Army Research Office.

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