X– indirect intersubband transitions in type II GaAs/AlAs superlatticesA. Fenigstein, E. Finkman, G. Bahir, and S. E. Schacham

Citation: Applied Physics Letters 69, 1758 (1996); doi: 10.1063/1.117476 View online: http://dx.doi.org/10.1063/1.117476 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/69/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hotelectron power loss in a doped GaAs/AlGaAs superlattice at intermediate temperature studied by infrareddifferential spectroscopy Appl. Phys. Lett. 69, 2528 (1996); 10.1063/1.117728 Evidence of –X sequential resonant tunneling in GaAs/AlAs superlattices Appl. Phys. Lett. 69, 520 (1996); 10.1063/1.117773 Current selfoscillations in photoexcited typeII GaAsAlAs superlattices Appl. Phys. Lett. 69, 500 (1996); 10.1063/1.117766 Fouriertransform infrared and Raman spectroscopies of plasmon anisotropy in heavily doped GaAs/AlAssuperlattices J. Appl. Phys. 79, 8024 (1996); 10.1063/1.362354 Pseudonegative photocurrent spectroscopy in GaAsAlAs superlattices J. Appl. Phys. 79, 4197 (1996); 10.1063/1.361877

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X–G indirect intersubband transitions in type II GaAs/AlAs superlatticesA. Fenigstein, E. Finkman,a) and G. BahirDepartment of Electrical Engineering and Solid State Institute, Technion Israel Institute of TechnologyTechnion City, Haifa 32000, Israel

S. E. SchachamDepartment of Electrical and Electronic Engineering, College of Judea and Samaria, Ariel, Israel

~Received 13 February 1996; accepted for publication 9 July 1996!

Intersubband transitionsindirect in both real and momentum spaces were observed in GaAs/AlAstype II short period superlattices. Significant absorption of normal incident radiation, with‘‘forbidden’’ polarization was measured, in addition to absorption in the ‘‘allowed’’ configuration.The transition energy shows a strong temperature dependence. This absorption is attributed toX–Gtransition. Both doped and undoped samples were investigated. Normal incidence absorption isstronger for the doped superlattices. Simulations using a two band model show good agreement toexperimental data. ©1996 American Institute of Physics.@S0003-6951~96!02638-1#

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Conventional GaAs/GaAlAs heterostructures are of tyI, in which both electrons and holes are confined in the salayer, here the GaAs layers. However, in short period suplattices~SPS! of GaAs/AlAs in which the GaAs layer thick-ness is below 35 Å, the lowestG level in the GaAs is‘‘pushed’’ higher than the lowestX level in the AlAs. Thus,the system becomes a type II structure, i.e., one in whelectrons and holes are located in separate layers. Furmore, this structure is indirect both in real and in momentuspaces. The energy band structure of such SPS is presein Fig. 1.

Indirect interband transitions in type II short perioGaAs/AlAs superlattices, were observed by means of pholuminescence and excitation photoluminescence.1,2 Thesetransitions were investigated by many authors~see review inRef. 3!. The interpretations of these direct transitions abased on the assumption that the superlattice structure mtheX valley states with theG states. The origin of this bandmixing is not completely clear, and various models wesuggested.4,5 Intersubband transitions in type II heterostrutures were observed as well.6–8 In these structures, howevethe transitions weredirect, between subbands belongingthe same Bloch state, and in the same layer. The worksscribed in Refs. 6 and 7 involveG–G transitions, as wasevident by the polarization selection rule, i.e., the respowas sensitive toP-polarized light. The carriers were resonantly coupled into theX valley states in the adjacent layereither due to tunneling6 or due to mixing,7 as manifested bytheir contribution to the conduction. The paper by Waet al.8 describesdirect X–X transitions. The unpolarized nature of the absorption in this case was attributed to the efftive mass anisotropy of electrons in the ellipsoidal vallewhich can provide coupling between the parallel and perpdicular motion of electrons. This is valid only when the pricipal axes of one of the ellipsoids are tilted with respectthe growth direction. Thus, normal incidence intersubbacoupling was not observed for the~100! growth direction.The direct nature of the transitions is also evident since

a!Electronic mail: finkman@ee.technion.ac.il

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temperature shift was observed for the absorption peak. Tpoint will be elaborated further in the following discussion

In this work we report the observation ofindirect X–Gintersubband transitions in GaAs/AlAs type II SPS grownthe ~100! direction. We demonstrate that these transitionsindirect in the momentum space, and the electrons arecited between adjacent layers. The uniqueness of thesesults is demonstrated by both the unpolarized absorptionby the temperature dependence of the observations.study was performed using the technique of current induabsorption ~CIA!.9 In CIA, the structure under study is‘‘sandwiched’’ between apn junction which enables injec-tion of carriers into its layers in order to populate the loweX level in the AlAs layers. The carrier concentration is cotrolled by the magnitude of the injected current. This methenabled us to obtain absorption spectra on structureswhich the more conventional photoinduced-absorptimethod failed.9

The structures used in the experiment were grownMBE on semi-insulating GaAs substrates, aligned in t~100! direction. The layer sequence is as follow10 000 Å GaAs, Si doped to 1018 cm23 ~n contact!, 50

FIG. 1. ~GaAs!6~AlAs!8 SPS band structure and confined levels.

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3(GaAs!6~AlAs!8 superlattice, and 5000 Å GaAs dopedBe to 1018 cm23 (p contact!. In the first structure the supelattice was undoped, while in the second the AlAs laywithin the superlattice were Si doped by 1018 cm23. The IRtransmission was measured using a double modulatechnique,10 in which both the injected current and the opcal radiation are modulated. A waveguide configuration wemployed for analyzing the polarization dependence ofabsorption, as shown in Fig. 2. The spectra were takendifferent polarization angles. Theu50° polarization lies inthe plane defined by the propagation direction and thetaxial growth axes, therefore, it has a component parallethe growth axis. Radiation polarized perpendicular togrowth axis is marked asu590°. Accordingly, the absorption coefficient at a general polarization angleu, can be ex-pressed as

a~v,u!5 12 cos

2~u!•a i~v!1a'~v!•@sin 2~u!

1 12 cos

2~u!#, ~1!

where a' is the absorption coefficient for light polarizeperpendicular to growth axis, whilea i is the coefficient forlight polarized parallel to it, andv is the frequency of theabsorbed radiation.

Using Eq.~1! the measured absorption for various polization angles is decomposed into its parallel and perpdicular polarized components. The spectrum atu590° is thepure perpendicular absorptiona'(v). The parallel compo-nent was averaged from the decomposition of all the ospectra. These analyzed components are shown in Fig.the undoped sample.

FIG. 2. Waveguide configuration for intersubband absorption measments.

FIG. 3. Perpendicular polarized component~solid line! and parallel polar-ized component~dashed line! of DT/T, using Eq.~1!.

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One should note the significant absorption of radiationpolarized perpendicular to the growth axis. This absorptioncompletely absent inG–G intersubband transitions in theconduction band, due to a strong selection rule which onlallows the absorption of perpendicular polarized light.

We attribute the observed absorption in this type Istructure to indirectX–G transitions, where electrons fromthe lowestX level, located in the AlAs layer, are excited intotheG level, located in the GaAs layer. This indirect transitionis allowed by the coupling between theG andX states, whichresults in mixed nature of both bands. In addition, we believthat this coupling is responsible for the nonpolarized character of the transition.

Figure 4 shows the two components of the absorptiospectra for the doped sample. Compared to Fig. 3, it is evdent that the relative magnitude of the perpendicular component is much larger in the doped sample. Assuming that thabsorption in the ‘‘forbidden’’ polarization is related to theX–G coupling coefficient, this result indicates the dependence of this coefficient on the wave vector. For dopesamples the absorption takes place for electrons in enerlevels with largerk vector due to the increased population.

A fundamental question is whether the observed spectcan be attributed to direct absorption. To rule out the possbility of a pureX–X direct transition in the AlAs layer only,the temperature dependence of the absorption peak wasamined. It is well known that bothG–G and X–X directintersubband transitions have a negligible temperature dpendence, since all relevant subbands are in the same layOn the other hand, indirect transitions are expected to vawith temperature. This results from the difference betweethe temperature dependence of theX andG gaps, as well asthose of their band offsets, since the subbands involved ain different materials. This phenomenon was studied oGaAs/AlAs structures by Barrauet al.11 for interband tran-sitions using visible light photocurrent measurement technique. Their results showed that thehh1–e1(G) transitionenergy decreases faster with increasing temperature thanhh1–e1(X) transition. Based on these results, the expectetemperature dependence of the indirectX–G intersubbandtransitions should be20.098 meV/K in their structure. Fig-ure 5 shows CIA spectra at different temperatures of thundoped sample. A linear fit to the center of mass of th

ure-

FIG. 4. Perpendicular polarized component~solid line!, and parallel polar-ized component~dashed line! of DT/T for the doped sample.

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absorption peak versus temperature is presented in theof this figure. The derived slope, of20.046 meV/K has thesame trend, and the same order of magnitude as thoserived from Barrauet al. It should be noted that the exacmagnitude of this temperature coefficient should depend

FIG. 5. CIA peak at different temperatures for undoped sample. Inselinear fit of peaks center of mass versus temperature.

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the specific heterostructure. This unique temperature depdence confirms the indirect nature of the measured trations.

A simple two band model is suggested for analyzithese type II transitions. We assume a Hamiltonian ofform12

: aFIG. 6. Perpendicular polarized component~solid line!, and parallel polar-ized component~dashed line! of the calculated absorption coefficient.

H+c5F @\2/~2meG* !#S kx21ky22

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wheremeG* andmeX* are the effective masses of the electroin theG andX valleys, andVG andVX are the potentials forG andX electrons. The empiricalG–X mixing coefficientgwas estimated by several authors to be between 1 tomeV.4,5,12 f G(z) and f X(z) are the envelope functions for thG andX states. The coupled differential equations were nmerically solved by using the Fourier series expanstechnique.13 The band offset and the band mixing coefficieg were varied to find the best fit for the experimental resuThe obtained value for the valence band offset isDEV

50.49 eV, which is within the range of previous estimatioof this parameter~0.48–0.5 eV!. The g value derived fromthe fitting process is 8 meV. The material and simulatiparameters are summarized in Table I.

Figure 6 shows the absorption coefficient for the diffe

TABLE I. Simulation parameters for GaAs/AlAs system.

Parameter Value Source

EgG~GaAs! 1.519 eV a

EgX~GaAs! 1.98 eV a

EgG~AlAs! 3.13 eV a

EgX~AlAs! 2.24 eV a

meG* ~GaAs! 0.067m0b

meX* ~GaAs! 1.3m0b

mG* ~AlAs! 0.15m0b

m1X* ~AlAs! 1.1m0b

mtX* ~AlAs! 0.19m0b

aM. M. Dignam and J. E. Sipe, Phys. Rev. B41, 2865~1989!.bS. Adachi, J. Appl. Phys.53, 12 ~1982!.

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ent polarizations, calculated by our two band model. Thresults of the simulation are in good agreement with the eperimental data.

In conclusion, the different selection rules and the temperature dependence of the absorption confirm that it is dto anX–G transition, and to the best of our knowledge, this the first observation of indirect intersubband transitionGaAs/AlAs SPS.

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