Sidewall quantum wires on GaAs(001) substrates
Paul L. J. Helgers, Haruki Sanada, Yoji Kunihashi, Klaus Biermann, Paulo V. Santos
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J a n Sidewall quantum wires on GaAs(001) substrates
Paul L. J. Helgers,
1, 2, ∗ Haruki Sanada, Yoji Kunihashi, Klaus Biermann, and Paulo V. Santos Paul-Drude-Institut f¨ur Festk¨orperelektronik, Leibniz-Institut imForschungsverbund Berlin e. V., Hausvogteiplatz 5-7, 10117 Berlin, Germany NTT Basic Research Laboratories, NTT Corporation,3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan (Dated: January 10, 2019)We study the structural, optical, and transport properties of sidewall quantum wires on GaAs(001)substrates. The QWRs are grown by molecular beam epitaxy (MBE) on GaAs(001) substrates pre-patterned with shallow ridges. They form as a consequence of material accumulation on the sidewallsof the ridges during the overgrowth of a quantum well (QW) on the patterned surface. The QWRsare approximately 200 nm-wide and have emission energies red-shifted by 27 meV with respect to thesurrounding QW. Spatially resolved spectroscopic photoluminencence studies indicate that the QWthickness reduces around the QWRs, thus creating a 4 meV energy barrier for the transfer of carriersfrom the QW to the QWR. We show that the QWRs act as efficient channels for the transport ofoptically excited electrons and holes over tens of µ m by a high-frequency surface acoustic wave(SAW). These results demonstrate the feasibility of efficient ambipolar transport in QWRs withsub-micrometer dimensions, photolithographically defined on GaAs substrates. I. INTRODUCTION
Planar quantum wires (QWRs) are important compo-nents for the realization of interconnects for integratedoptical-electronic circuits. In its simplest form, the guid-ing action by the lateral confinement of carriers enablesinformation exchange between two remote locations viaa well-defined channel. The mesoscopic confinement in-duced by small lateral dimensions can be explored foradditional functionalities. Here, interesting examples arethe formation of one-dimensional quantum channels forelectronic transport with reduced scattering [1] as wellas the enhanced spin lifetimes due to mesoscopic spinconfinement [2, 3].Different approaches have been reported for the fabri-cation of semiconductor QWRs with nanometer dimen-sions. Electrostatically defined QWRs can be createdvia the deposition of gates on a semiconductor nanos-tructure. The application of a voltage to the gate cre-ates channels near the surface for one type of carriers(i.e., electrons or holes). Ambipolar transport channelsfor the guidance of both electrons and holes by mov-ing acoustic fields can be created by combining electro-static gates with piezoelectricity [4]. More interestingfor electro-optical applications are planar QWRs definedby a lateral structural modulation since these have opti-cal resonance energies distinct from the ones of the sur-rounding matrix. In its simplest form, the structuralmodulation can be introduced by etching a QW sam-ple to define the QWR. Alternatively, a QWR can beformed by the epitaxial growth of a QW structure on asurface with a pre-defined structural modulation. Here,one example is given by QWRs produced by the epitax-ial growth on the cleaved edge of a nanostructure con-taining a QW [5]. A second example is provided by ∗ [email protected] the epitaxial growth on a surface exposing different crys-tallographic orientations: here, one takes advantage ofthe dependence of the growth kinetics on the orientationof the surface in order to create the lateral structuralmodulation. Surface structuring in this case is usuallyachieved by pre-etching the substrate surface to exposedifferent crystallographic facets. Well-known examplesare QWRs grown by metal-organic epitaxy on V-shapedgrooves defined on a GaAs(001) surface [6–8] as well asquantum wires and dots fabricated by molecular beamepitaxy (MBE) on pre-patterned GaAs surfaces with dif-ferent orientations [9–12]. An advantage of these growth-defined QWRs over etched ones resides on the fact thatthey do not contain free surfaces, which may be delete-rious for electronic excitations. In addition, and in con-trast to their electrostatic counterparts, these QWRs arefully surrounded by epitaxial materials and can thereforebe easily embedded in more complex epitaxial structuressuch as optical microcavities.One important application of planar QWRs is as guidesand interconnects for photo-excited electron-hole pairsbetween opto-electronic structures on a surface. Thecharge carriers can be stored and transported along theplane of a QW by the traveling piezoelectric potentialof a surface acoustic wave (SAW) [13, 14]. After trans-port, the carriers can be forced to recombine and emitphotons, thus providing a photonic interface to the elec-tronic system. Similar ambipolar transport experimentswere demonstrated in µ m-sized electrostatically definedwires [15] as well as sub- µ m sidewall QWRs fabricatedby epitaxially overgrowing shallow ridges on GaAs(113)Asubstrates [16, 17]. Long acoustic driven transport dis-tances for charge carriers have been achieved in over-grown QWRs (up to 50 µ m) [18]. Their optical andtransport properties were found, however, to be very sen-sitive to potential fluctuations along the transport path.These fluctuations create trapping centers, which cancapture charge carriers during the acoustic driven am- h e i gh t ( n m ) position ( μ m) h e i gh t ( n m ) ridge // [1-10]ridge // [110] z || [001] x || y || ] GaAs QWR G a A s Q W G a A s s ub s t r a t e (a) (b)(c)(d) GaAs10 nm QW GaAs substrate n m AlGaAs z || [001]x || [1-10] y || [110]
QWR
600 nm etched sidewall
FIG. 1. Molecular beam epitaxy (MBE) of sidewall quantum wires (QWR) on GaAs(001). (a) Shallow ridges (height of approx.45 nm) were patterned on a GaAs(001) substrate and subsequently overgrown with a quantum well (QW, blue areas). Thearrows show the preferential diffusion of Ga adatoms towards the ridge sidewall, which results in the QWR formation (redregions). For clarity the AlGaAs QW barriers have been omitted. (b)-(c) Atomic force microscopy (AFM) cross-sectionalprofiles of overgrown ridges oriented along the (b) x || [1 −
10] and (c) y || [110] directions of the GaAs(001) surface. The bluedashed lines indicate the contour of pre-patterned ridges defined by optical lithography. The pronounced lateral growth resultsin QWR formation only along the y -oriented sidewalls. (d) Cross-sectional scanning transmission electron micrography (STEM)image of an overgrown ridge showing the QW (GaAs, dark layer) sandwiched between two AlGaAs barriers (bright layers).The brown circle highlights the region of increased QW thickness defining the sidewall QWR. bipolar transport and induce their recombination, thusresulting in a reduction of the acoustic transport effi-ciency [19].The one-directional motion of carriers in QWRs alsoprovides a pathway to reduce spin dephasing due to theDyakonov-Perel mechanism [2, 3]. Alsina et al. [18]investigated spin transport in sidewall QWRs grown onGaAs(113)A substrates with a width of 50 nm. Whereasthe narrow width should lead to a long spin relaxationtime and, correspondingly, long spin transport lengths,the observed acoustic spin transport length was limitedto distances of only approx. 2 µ m. These transportdistances are much shorter than the ones reported foracoustic transport in electrostatic wires [20]. It was ar-gued that the acoustic spin transport length is limited byElliot-Yafet (EY) scattering due to the large density ofscattering centers along the QWR axis [18]. These find-ings call for fabrication processes yielding narrow QWRswith small potential fluctuations.The formation of sidewall QWRs via MBE overgrowthon patterned GaAs(001) substrates was reported by Leeet al. [21]. From a fabrication point of view, the MBEgrowth process on the GaAs(001) surface is better under-stood and controlled than on high-index surfaces such as GaAs(113)A. Previous studies of sidewall QWRs onGaAs(001), however, only addressed structural proper-ties. Neither their optical nor transport properties haveso far been investigated.In this contribution, we provide systematic investiga-tion of the structural, optical, and acoustic transportproperties of sidewall QWRs fabricated on GaAs(001)substrates. The sample fabrication process, which in-cludes substrate patterning and MBE growth, was basedon the previous work in Ref. 21 and is summarized inSection II A. Sections II B and II C then describe theprocedures for the fabrication of interdigital transduc-ers for SAW generation and the spectroscopic techniquesemployed in the studies. The experimental results arepresented in Sec. III. Here, we start by studying thestructural properties of the QWRs by combining atomicforce microscopy (AFM), scanning electron microscopy(SEM), and scanning transmission electron microscopy(STEM) (Sec. III A). We then carried out spectroscopicinvestigations of the QWR optical properties using spa-tially resolved photoluminescence (PL) (Sec. III B-D).Finally, Sec. III E provides evidence for the acousticcharge transport in the QWRs over distances approach-ing 100 µ m. Section IV summarizes the main conclusionsdrawn in this work. II. EXPERIMENTAL DETAILSA. Sample fabrication
The fabrication of the sidewall QWRs on GaAs(001)substrates followed a procedure similar to the one re-ported for QWRs reported in Refs. 10 (GaAs(113)A)and 21 (GaAs(001)). In the first step, shallow ridgeswere patterned on a GaAs(001) substrate by photolithog-raphy and wet chemical etching using a solution ofH SO :H O :H O with a volume ratio of (8:1:100). Wefabricated 10 µ m-wide ridges with a height of 45 nm anda length of several tens of µ m oriented along the y || [110]and x || [1 −
10] main axes of the GaAs(001) surface. Thepatterned substrate was subsequently cleaned using aH SO :H O (96:4) solution and introduced in a UHVchamber connected to the MBE growth apparatus forsurface cleaning by exposure to atomic hydrogen. Inthis procedure, the substrate was exposed to partiallycracked hydrogen from a hot filament source at a back-ground pressure of 5 × − mbar for 30 minutes at atemperature of 450 ◦ C. The sample was then transferredin vacuum to the MBE growth chamber. Figure 1(a)schematically shows the formation of QWRs (red areas)after the overgrowth of a layer structure, consisting of a10 nm QW (blue) sandwiched between a lower and upperAl Ga As barrier of respectively 130 nm and 200 nmthickness. For comparison, a sample containing QWRson a GaAs(113)A substrate has been fabricated followinga similar procedure, using an H SO :H O :H O etchingsolution with a volume ratio of (1:8:100). For both typesof samples, all layers were grown while the substrate waskept at a temperature of 600 ◦ C. The growth rate of theAlGaAs and GaAs layers was respectively 0 .
16 nm s − and 0 .
14 nm s − . Finally, the samples were capped with a2 nm layer of GaAs in order to protect the sample againstoxidation.The formation of QWRs on the ridge sidewalls relieson the combination of two factors [21–24]: (i) the higheradatom diffusion rate along the x || [1 −
10] surface di-rection of the (2 ×
4) reconstructed GaAs(001) surface ascompared to the y || [110] direction and (ii) the higheradatom incorporation rate at step edges oriented along y as compared to the plane (001) surface. The latter re-sults in an enhanced MBE growth rate on the exposedsidewalls of the ridges as compared to the growth rateon the (001) surface. When a QW is deposited on thepatterned surface, the anisotropic growth rate induces alocal increase in the QW thickness on the sidewalls ofridges aligned along the y direction, as indicated by thered regions in Fig. 1(a) [21]. The structural propertiesof the overgrown ridges were investigated by combiningAFM, SEM and STEM. B. Excitation of surface acoustic waves
Figure 2(a) displays the layout of the delay line usedfor the excitation of Rayleigh SAWs [25] along the QWRaxis. The delay line was fabricated by optical lithogra-phy on the surface of the overgrown sample: it consists oftwo split-finger interdigital transducers (IDTs) designedfor an acoustic wavelength λ SAW = 5 . µ m with aper-ture and length of 120 µ m and 350 × λ SAW , respectively.Figures 2(b) and 2(c) show the frequency dependence ofthe radio-frequency (rf) reflection ( s ) and transmission( s ) parameters at room temperature, respectively. Theresonance at 513 MHz corresponds to the excitation ofthe Rayleigh mode for the structure. The amplitude ofthe s dip indicates that the IDTs convert 20% of theinput rf-power into two SAW modes propagating in oppo-site directions. The r IDT = 10% transduction per SAWbeam is compatible with the maximum power transmis-sion amplitude of the s spectrum of -20 dB. -3.5-3.0-2.5-2.0-1.5 S ( d B )
490 500 510 520 530-80-60-40-20 S ( d B ) Frequency (MHz) (b)(c)(a) λ SAW
QWR variableridgeswith QW
FIG. 2. (a) Schematic diagram of the SAW delay line em-bedding sidewall QWRs aligned along the y || [110] directionof the GaAs(001) substrate. The delay line consists of twointerdigital transducers (IDTs) with an aperture of 120 µ mand acoustic wavelength λ SAW =5 . µ m. (b) Radio-frequency(RF) reflection ( s ) and (c) RF transmission ( s ) parame-ters for the delay line measured at room temperature. Theresonance at 513 MHz is associated with the excitation of theRayleigh SAW mode of the sample structure. C. Optical spectroscopy techniques
The spectroscopic photoluminescence (PL) studieswere carried out using an optical microscope coupled toa cryostat (temperature of approx. 10 K) with opticalaccess and rf-wiring for the excitation of SAWs. The PLwas excited by either a continuous wave (cw) or pulsedtunable Ti:Sapphire laser, or by a pulsed diode laser.The PL around the excitation spot was spectrally anal-ysed and detected with a spatial resolution of 0 . µ m perpixel by a cooled charged-couple device (CCD) camera.Time-resolved measurements were performed using eithera streak-camera or an avalanche Si-photodiode as a de-tector.The acoustic transport studies were carried out by ex-citing one of the IDTs of the delay line. The electron-holepairs were excited by a focused laser spot on one positionof the sample (cf. Fig. 2(a)) and their spatial distribu-tion along the SAW propagation direction detected byrecording spatially resolved PL profiles. The amplitudeof the SAW will be stated in terms of the nominal rf-power applied to the rf-input of the cryostat. Note thatthe electro-acoustic conversion efficiency in the cryostatwill be lower than the one determined in Fig. 2, whichdoes not take into account the effects of the cryostat rf-connections. III. RESULTS AND DISCUSSIONA. Structural properties
Since MBE is a non-conformal growth technique, theshape of the etched ridges can be recovered by prob-ing the sample surface after overgrowth using AFM. Thesolid lines in Figs. 1(b) and 1(c) compare cross-sectionalAFM profiles of overgrown ridges oriented along the x and y directions, respectively. The blue dashed lines in-dicate the nominal profiles of the ridge etched on the sur-face prior to the MBE overgrowth. The cross-sectionalprofile of overgrown ridges oriented along the x -directionclosely follows the one pre-patterned on the surface, thusindicating a conformal coverage during the MBE over-growth. Ridges oriented along y exhibit, in contrast,broadened sidewalls with a convex shape. This behaviouris attributed to the higher growth rates at the edgeof these ridges, which results in material accumulationalong their sidewalls. This material accummulation lo-cally increases the thickness of a QW overgrown on theridge edges, thus forming the region with lower quan-tum confinement energy, corresponding to the QWR (cf.Fig. 1(a)).The material transfer leading to QWR formation alsoreduces the thickness of the QW regions adjacent to thesidewalls. As will be discussed in detail in Sec. III B,this local thickness decrease creates a “barrier-QW” withhigher carrier confinement energies than in the QW onboth sides of the QWR. These “barrier QWs” act as po-tential barriers for the transfer of carriers from the QWto the QWR.The sidewall QWRs only form on overgrown ridgesoriented along y . These can be directly imaged incross-sectional STEM images, as illustrated in Fig. 1(d).Here, the dark and bright areas correspond to GaAs andAl Ga As regions, respectively. From the micro-graphs, we estimate the thickness and width of the side-wall QWR to be 25 ± ± Ga As barrier, we estimatethat for this particular geometry the lateral growth rateof the Al Ga layer is approximately 5 times largerthan the vertical one.The electro-optical properties and, in particular, thecarrier transport properties of the sidewall QWRs alsodepend on the uniformity of the QWR dimensions alongboth the growth direction and the QWR axis direction.The latter can be quantified by evaluating the lateralroughness of the ridge edges (line-edge-roughness, LER)from AFM micrographs. For that purpose, we haverecorded AFM profiles across patterned ridges alignedalong y (typically one profile per nanometer). The con-structed image of a ridge sidewall wet-chemically etchedon the GaAs(001) substrate (i.e., prior to MBE over-growth) is shown in Fig. 3(a). Here, the dark area corre-sponds to the ridge bottom (etched) and the bright areato the ridge top (non-etched). The right panel displays atypical profile, extracted along the vertical dashed greenline in the AFM image. Each of these profiles was fittedwith an error function to evaluate the average positionof the ridge edge. LER is defined as the standard devi-ation of the edge position. Figure 3(b) shows the samescan as Fig. 3(a), now zoomed into an area of 1 µ m x80 nm. The image was post-processed to show only theheights of the ridge top and bottom. The edge position,which is depicted by the line dividing the top and bot-tom areas, fluctuates with peak amplitudes of as much as20 nm and shows a LER value of 9 nm. Furthermore, weobserve that the sidewall of the etched ridge is inclinedby an angle of roughly 10 ◦ with respect to the surfaceplane.Interestingly, the LER of ridges etched on GaAs(001)QWs was found to be approximately the same as in con-trol samples deposited on GaAs(113)A substrates (cf.Fig. 3(d)): in both cases, we measured LER in the rangefrom 4 nm to 9 nm. Also, the LER could not be reducedby changing the composition of the etching solution (i.e.,the type of acid agent as well as the degree of dilutionof the etching solvent). We found, in contrast, that theLER can be traced back to the photolithography processused to define the ridges. In fact, SEM images of thephotoresist edges at GaAs(113)A (cf. Fig. 3(c)) displayLER values very similar to the ones measured after over-growth (cf. Fig. 3(d)). Several factors leading to the LERof photoresist patterns are discussed in detail in Ref. 26.Attempts were also carried out to improve the LERof the sidewalls using patterns defined by electron-beamlithography. Ridges defined on a GaAs(113)A substrateby e-beam lithography using a step size of 20 nm and anAllresist AR-P 6200 resist have LERs similar to the onesobtained by optical lithography. By reducing the stepsizeof the e-beam lithography to 2 nm and using a PMMAresist, the LER could be reduced to approximately 3 nm,thus indicating a way to improve the ridge quality.In the present studies, however, all QWRs were fabri- x’ || [1-10] ( (cid:1) m ) y ’ || [ - ] ( n m ) (d) After etching (113)A x’ || [1-10] ( (cid:1) m ) y ’ || [ - ] ( n m ) y || [110] ( (cid:1) m ) x || [ - ] ( n m ) y || [110] ( (cid:1) m ) x || [ - ] ( (cid:1) m )
50 25 0 height (nm) (a) After etching (001) (b) After etching (001)(c) Before etching (113)A
GaAs(001)
10 nm bo tt o m s i d e w a ll t op he i gh t r i b rt op bo tt o m s i d e w a ll t op he i gh t GaAs(113)A
10 nm bo tt o m s i d e w a ll t op he i gh t GaAs(113)A
10 nm
GaAs(113)APhotoresistGaAs(001) etchedetchednon
FIG. 3. Line-edge-roughness of ridges at GaAs. (a) AFM scan of a 1 µ m × µ m sized area around a ridge sidewall after etchingand before MBE-overgrowth. The right panel shows a profile extracted along the green dashed vertical line. (b) Post-processedimage of the same scan, zoomed into a 1 µ m ×
80 nm sized area. The ridge-bottom is dark gray coloured and its top is brightgray coloured. The red dashed line depicts the average position of the step edge. The value of the line-edge-roughness is9 nm. (c) Scanning electron microscopy image of the photoresist defining the ridges after resist exposure to UV light of 250 nm(but before etching). The upper part of the image corresponds to a GaAs(113)A substrate and the lower part of the imagecorresponds to the photoresist. The rms LER value of 10 nm is comparable to the deviations observed in the etched ridge shownin figure (d). (d) Post-processed image of an AFM scan of a 1 µ m ×
80 nm sized area around a ridge sidewall on a GaAs(113)Asubstrate after etching and before MBE overgrowth. The LER of etched ridges on GaAs(113)A (approx. 7 nm for the shownmeasurement) has a similar amplitude as LER on GaAs(001). cated on photolithographically defined ridges. Note thatsince the LER is only a few percent of the width of thesidewall QWR determined by STEM (see Fig. 1(d)), weexpect that it will only play a minor role in the optical,electrical and transport properties of the sidewall QWRs.
B. Optical properties of the QWRs
The formation of QWRs at the ridge sidewall was ver-ified by spatially resolved PL spectroscopy. Figure 4(a)displays a PL map recorded at 10 K while scanning a laserspot across ridges with sidewall QWRs (cf. left panel).We used for excitation a pulsed diode laser emitting ata wavelength of 635 nm. The latter lies above the fun- damental optical transitions of the QW and, thus, op-tically excites carriers both in the QW and the QWR.The scan length covers two 10 µ m-wide overgrown ridgesseparated from each other by 10 µ m. The map was gen-erated by spectrally analyzing, for each spot position,the PL emitted within a 1 . µ m x 2 µ m area around it.The procedure yields the PL map with the color-codedintensity in a logarithmic scale as a function of position(vertical axis) and energy (horizontal axis). The upperpanel displays spectral cross-sections of the map recordedalong the blue dashed (QW at ridge top) and green solid(sidewall QWR) horizontal lines indicated in the map.The PL map of Fig. 4(a) shows two main resonances.Spectra recorded on the top and bottom of the ridgesare essentially equal and characterized by a single PL energy (e V) x || [ - ] ( (cid:1) m ) P L i n t e n s i t y QWQWRQWRQW x || [ - ] (a) l og [ P L i n t e n s i t y ] QW lh QW hh Δ E QW =4 meV P L i n t e n s i t y excitation energy (eV) (b) QW (1.546 eV)(c) QWR (1.521 eV) FIG. 4. (a) Photoluminescence (PL) map recorded while scanning the excitation laser spot in the direction perpendicular tothe 10 µ m-wide ridges with sidewall QWRs (cf. left panel). The map shows the colour-coded PL intensity (in a logarithmicscale) as a function of position (vertical axis) and emission energy (horizontal axis). Emission is observed from two distinctresonances. The low energy corresponds to the QWR emission and the high energy corresponds to the QW. The upper panelshows spectra along the cross-sections of the PL map indicated by the horizontal lines, where the QW spectrum depicts thespectrum extracted at the blue dashed line position. Photoluminescence excitation (PLE) spectra detected at the electron-heavy hole resonance are shown in figures (b) QW (QW hh ) and (c) QWR (QWR hh ). In both cases, the excitation spot wasplaced on a sidewall QWR. line centered at 1 .
547 eV with a linewidth (defined as thefull-width-at-half-maximum (FWHM)) of 7 meV. Thisline is attributed to the electron-heavy hole (QW hh ) res-onance of the 10 nm QW. Spectra recorded on the side-wall display, in addition, a second resonance at 1 .
520 eVwith a linewidth of 10 . hh ). Aswas discussed in Section III A, the width of the QWR ismuch larger (approximately 200 nm) than its thickness(approximately 25 nm). The red-shift of the QWR emis-sion with respect to the QW is, therefore, mainly causedby its larger thickness with respect to the QW. Further-more, due to its increased thickness, one expects a de-crease of the QWR linewidth with respect to the QW.The opposite trend observed in the experiments impliesthat potential fluctuations within the QWR have a sig-nificant impact, possibly related to the aforementionedLER. The fact that the QWR hh resonance is only seenat the sidewall positions (see left panel) also confirms thestructural findings of Sec. III A that the QWRs only format the sidewalls.A closer analysis of the PL spectra recorded at thesidewalls reveals that the QW line reduces in intensityand slightly blue-shifts (by approx. 3 meV) with respectto spectra taken at a position away from the ridges (notshown here). The blue-shifted region is attributed to the“barrier QWs” with reduced thickness formed on bothsides of the sidewall QWR. Electron-hole pairs photo-excited within the barrier QW can diffuse to and recom- bine in the neighboring regions of lower energy. The blue-shifted PL emission at the ridge sidewall in Fig. 4(a) issymmetric with respect to the axis of the QWR, thusproving that the barrier QW forms an energy barrier forthe transfer of carriers from the QW to the QWR on bothsides of the QWR. Considering that the dimension of thesidewalls is much smaller than the optical resolution, thePL line in Fig. 4(a) includes contributions from both thebarrier-QW and the QW. The latter may be responsiblefor the increased linewidth of the QW PL to 11 meV onthe sidewall as compared to 7 meV measured away fromthe sidewall. C. Comparison with other sidewall QWRs
Table I compares the optical properties of sidewallQWRs grown on GaAs(001) substrates with QWRsgrown on GaAs(113)A substrates. The table was con-structed using average values of the emission energiesand linewidths of QWRs from multiple samples simul-taneously grown the same 2-inch wafer, per substratetype. The fourth column displays the emission ener-gies and linewidths of QWRs fabricated on electron-beamlithographic defined ridges on a GaAs(113)A substrateovergrown with a slightly thinner QW (8 nm instead of10 nm). Interestingly, all sidewall QWRs have similarspectral linewidths of 10 ± E QWR between the QW and the QWR emission (001) (113)A (113)A (111)e-beam V-grooveQW width (nm) 10 10 8 7E
QWR (eV) 1.520 1.526 1.546 1.575∆ E QWR (meV) 27 15 13 45linewidth a (meV) 10 11 9 11 a defined as the FWHM TABLE I. Comparison of the optical properties of sidewallQWRs on (001) and (113) GaAs substrates. The last columnlist the corresponding properties for V-groove QWRs on (111) (from Ref. 8). ∆ E QWR denotes the red-shift of the QWRPL line with respect to the QW line. energies, in contrast, is significantly larger for QWRs onGaAs(001) than on GaAs(113)A and leads to a largercarrier confinement for GaAs(001). This larger red-shift, which is probably related to the different sidewallfacets exposed by the etching process, is advantageousfor acoustic carrier transport since it reduces the carrierescape probability to the surrounding QW. Finally, thelast column of the table list the corresponding proper-ties for V-groove QWRs deposited by Koshiba et al. onGaAs(111) substrates (from Ref. 8). These QWRs have alinewidth comparable to the ones for the sidewall QWRsbut substantially larger energetic separations ∆ E QWR . D. Carrier dynamics in GaAs(001) QWRs
In order to investigate carrier transfer between the QWand the QWR, we measured photoluminescence excita-tion spectra (PLE) from the sidewalls using a tunable cwTi:Sapphire laser impinging on the sidewall region at anangle of incidence of 45 ◦ . The laser spot size of approxi-mately 7 µ m in diameter is much larger than the sidewalland can, thus, generate carriers both in the QWR and inthe QWs around it. Figures 4(b) and 4(c) compare PLEspectra by detecting the emission of the QW hh (detec-tion energy 1 .
546 eV) and of the QWR hh (1 .
521 eV) res-onances, respectively. In the former case, the two peaksin the emission intensity are attributed to the electron-heavy hole (QW hh ) and electron light-hole (QW lh ) tran-sitions of the QW at 1 .
548 eV and 1 .
558 eV, respectively.This assignment is consistent with calculations of the en-ergy levels for a 10 nm-thick QW with Al . Ga . Asbarriers.The QWR hh PLE spectrum in Fig. 4(c) also shows anonset at the QWR hh transition as well as two excitationmaxima blue-shifted by 4 meV and 5 meV with respectto the QW hh and QW lh transitions, respectively.These blue-shifted lines are assigned to the electron-heavy hole and electron-light hole transitions in thebarrier-QW. Carriers excited in the barrier-QW can thendiffuse to the QWR and recombine in the QWR. The ab-sence of a peak in the PLE spectrum of Fig. 4(c) corre-sponding to the QW hh transition as observed in Fig. 4(b) implies that for excitation energies above approximately1 .
542 eV, the detected QWR PL arises from the recombi-nation of electron-hole pairs photo-excited in the barrier-QW region, which diffuse into the QWR. Carriers gen-erated in the QW, in contrast, cannot reach the QWRdue to the energy barrier imposed by the barrier-QW.For excitation energies below 1 .
542 eV we expect thatthe QWR PL results from a combination of direct exci-tation of QWR states as well as of the low-energy flankof the barrier-QW. l og [ P L i n t e n s i t y ] FIG. 5. Time-resolved photoluminescence traces recordedon a ridge sidewall as function of emission energy (horizon-tal axis) and time (vertical axis). The three observed res-onances are (from the low-energy to the high-energies) theelectron-heavy hole transitions in the GaAs substrate (1.514eV, dashed black line), sidewall QWR (1.520 eV, solid redline), and QW (1.546 eV, dashed blue line). The right panelshows the temporal trace of the QW (blue, thin) and QWR(red, thick). Both traces represent spectral integrations overthe linewidth of the respective emission lines.
We analyze the carrier dynamics by performing time-resolved photoluminescence measurements using a streakcamera while exciting the sample using 1 . µ W laser beam onto a 7 µ m-wide laser spot ona sidewall under an angle of 45 ◦ . We observe emissionfrom the sidewall QWR (1 .
520 eV), QW (1 .
546 eV), aswell as from the GaAs substrate (1 .
514 eV). In contrastto the carriers in the QWR and QW, the PL signal fromthe substrate decays very fast with an exponential decaytime of 70 ps. The right panel shows temporal traces ex-tracted from the image for the QW resonance (blue, thinline) and QWR (red, thick line) by spectral integrationof the PL over the linewidth of the corresponding reso-nances. In both cases, the formation of large- k || excitonsfrom excited electron-hole pairs leads to the initial fastrise of the PL intensity and blue-shift of the emissionline. These excitons then relax into a state with k || = 0and subsequently recombine with the emission of a pho-ton [27]. From a single-exponential fit we extract a QWcarrier lifetime of approximately 500 ps.The temporal emission trace of the QWR shows an ini-tial fast increase followed by a plateau (or even a small in-crease) in the emission up to approximately 400 ps. Thesignal then decreases exponentially with a time decayconstant of approximately 870 ps. The larger recombina-tion lifetime of the QWR states with respect to the QWis attributed to the larger thickness of the QWR [28]. Weattribute the plateau to the transfer of carriers from thesurrounding barrier-QW into the QWR. The initial risetime can be explained by the fast carrier transfer fromthe barrier-QWR as well as by direct excitation of carri-ers in the QWR, while the plateau can be explained bythe diffusion and relaxation of barrier-QW carriers intothe QWR states. A similar process was reported for car-rier transfer in the nanosecond timescale between QWsand sidewall QWRs on GaAs(113)A substrates[29]. Notethat although the bulk emission is spectrally closely lo-cated to the QWR, its fast decay implies only a minorcontribution to the PL signal. E. Acoustic Transport
We provide in this section experimental evidence foracoustic charge transport along the sidewall QWRs, ob-tained by spatially resolved PL spectroscopy. The exper-iments were carried out using the configuration sketchedin the right panel of Fig. 6. The carriers were photo-excited by a pulsed diode laser (635 nm, power 2 µ W)focused on to a spot with a diameter of 6 µ m at the refer-ence position x = 0 µ m. A metal stripe was deposited atthe end of the QWR (at y = 90 µ m) to block the acoustictransport. Since the depth of the QWR (below a 200 nmAlGaAs barrier) is much smaller than the SAW wave-length ( λ SAW = 5 . µ m), the metal efficiently screens theSAW piezoelectric potential at the depth of the QWR andinduces the recombination of the carriers transported bythe SAW field [19]. In the ideal case, one thus expectsto observe PL at two positions along the SAW path: (i)at the excitation location, where non-transported carri-ers recombine and (ii) at the metal stripe position dueto recombination of transported carriers. However, aswill be shown in the following, we observe PL from po-sitions along the SAW path, which are attributed to un-intended trapping centers. The centers capture carriersof one polarity, which then recombine upon the arrivalof carriers of opposite polarity in the subsequent SAWhalf-cycle. Furthermore, in the present case, the metalstripe consists of a stack of 10 nm titanium, 30 nm alu-minium and 10 nm titanium layers. Using the opticaltransmission data taken from reference [30], we calculatean optical transmittance of only 0 . λ =815 . − µ m away from the excitation spot, which we attributeto carrier trapping and recombination in a center withinthe transport channel. Interestingly, the remote PL isobserved in the same position for both the QWR andthe QW resonances. We remind ourselves that carriertransfer between the QW and the QWR is hindered bythe barrier-QW in-between them. In addition, we haveshown in Sec. III B that only carriers generated in thebarrier QW can diffuse to the QWR, and that this pro-cess takes place within a nanosecond. Considering theacoustic transport velocity of 2 . µ m ns − , this transferbetween the barrier QW and the QWR can only takeplace during the first couple of micrometers of the trans-port path. The simultaneous remote emission from theQW and QWR could be due to an extended defect af-fecting both the QW and the QWR. Alternatively, if theacoustic transport in the QWR is blocked by a defectcenter, carriers can accumulate close to the defect andeventually leak to the QW.A further interesting aspect is that trapping and re-combination along the transport channel can be con-trolled by the acoustic intensity. The images in Figs. 6(b)and 6(c) show that an increase of the acoustic powerto − µ m away from the excitation spot. Note thatthe SAW power threshold for overcoming the trap po-tential is different for transport in the QWR and QW.At the metal stripe position, the piezoelectric field isscreened, leading to the recombination of transportedcarriers. However, as was mentioned before, due to thesmall optical transmission of 0 . .
537 eV) below the QW resonance. In this case,the acoustic transport takes place only in the QWR. Inthe absence of a SAW (Fig. 7(a)) PL from the QWR isonly observed at the excitation spot near a weak emissionline from the GaAs substrate. When a SAW is applied( λ SAW =4 µ m, f SAW =726 MHz, cf. Fig. 7(b)), one de-tects PL at two remote locations on the QWR, thus ev-idencing acoustic transport. The upper panel displaysPL spectra of the two trapping sites. The spectrum fromtrap A (red) resembles the QWR emission at the excita-tion spot (1 .
521 eV). A similar behaviour has been found (a) No SAW (b) -7 dBm log [PL intensity]
27 1200 lasertrapmetalQWR SAW
QWR QW (c) -2 dBm (d) 23 dBm lasertrapmetalQWR SAW
FIG. 6. Acoustic transport of photoexcited charge carriers in sidewall QWRs and surrounding QW. Photoluminescence mapsrecorded using the configuration in the right panels without SAW (a) and with SAWs with nominal powers of (b) -7 dBm, (c)-2 dBm, and (d) 23 dBm. The carriers are excited with a 635 nm laser focused to a spot of approximately 6 µ m diameter on aridge sidewall. The carriers are transported by the SAW field to a trapping center or, for high acoustic powers, up to a metalstripe, which induces recombination by quenching the SAW piezoelectric field. for most of the trapping centers - a model of this typeof trap centers will be presented below. In contrast, thetrapping center at site B shows a narrower emission line(linewidth of 2 meV in comparison with 7 meV for trapA), which is blue-shifted by 4 meV with respect to thePL at the excitation location. This indicates that trap Bis caused by a different type of trap.The dynamics of the acoustic transport was studiedby time-resolved PL. The carriers were optically excitedusing a small spot (diameter of approximately 3 µ m) us-ing a cw Ti:Sapphire laser (wavelength of 780 nm andpower of 200 µ W). The remote PL induced by the acous-tic transport of carriers to a trap within the QWR wascollected and detected using a Si avalanche detector (tem-poral resolution of 340 ps) synchronized with the SAWphase. Figure 8 shows the PL time dependence recordedon a trap located approximately 30 µ m away from the excitation spot. The cw PL spectrum of the trap (inset)reveals that it is similar to trap A in Fig. 7(b) emitting atthe same energy as the QWR. The PL intensity oscillatesat the SAW frequency of 726 MHz. For comparison, theblue curve displays the vanishing PL intensity collectedin the absence of SAW, which proves that the trap is onlypopulated by acoustically transported carriers.The strong oscillations in the time-resolved trace ofFig. 8 proves that the carriers remain confined withinthe SAW potential during acoustic transport (note thatthe amplitude of the oscillations in Fig. 8 is partially lim-ited by the time resolution of the avalanche detector ofapproximately 340 ps). In addition, the frequency of theoscillations yields information about the carrier trappingand recombination process. In fact, one expects PL oscil-lations at the SAW frequency only if the trapping centercaptures carriers of only one polarity during one half of0 energy ( eV) log [PL intensity] energy ( eV) y || [ ]( (cid:1) m ) (a) No SAW (b) 10 dBm trap A trap B QWRbulk QWR metaltraplase QWR AW FIG. 7. Spatially resolved PL maps recorded (a) in theabsence of a SAW and (b) under a SAW with wavelengthof 726 MHz and nominal rf excitation power of 10 dBm.The carriers were selectively excited in the QWR at y = 0(cf. right panel) using a laser beam tuned to an energy( E laser =1 .
537 eV) below the band gap of the surroundingQW. Under acoustic excitation, the carriers are transportedalong the wire and recombine in two trapping centers (A andB) with spectral emissions displayed in the upper panel. the SAW cycle, followed by recombination upon arrival ofcarriers with the opposite polarity in the subsequent halfof the SAW cycle. The capture (and subsequent recombi-nation) of carriers of both polarities results, in contrast,in PL oscillations at twice the SAW frequency. In thepresent experiments, we cannot discriminate which car-riers (electrons or holes) are preferentially trapped.Our experimental data supports the model for carriertrapping and recombination during ambipolar transportproposed in Ref. 31. In this model, carriers of one po-larity are trapped due to injection into states at theGaAs/AlGaAs interface by the vertical component E z of the SAW piezoelectric field. The field-induced injec-tion probability is high since, for a Rayleigh SAW, E z is in phase with the piezoelectric potential and, there-fore, with the maximum in the carrier density. E z re-verses its sign half a SAW-cycle later, thus releasing thetrapped carriers into a pool of carriers of the oppositepolarity, where it has a high recombination probabil-ity. This mechanism thus leads to efficient recombinationduring acoustic transport with emission energy equal tothe QWR. This model can account for the emission be-haviour of most of the trapping sites detected along theacoustic transport path (i.e., of type A, cf. Fig. 7). pho t o s t(cid:0)(cid:1)(cid:2) (cid:3)(cid:4)(cid:5)(cid:6) T SAW
No SAW
P(cid:10) (cid:11)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18) e(cid:19)(cid:20)(cid:21)(cid:22)(cid:23) (cid:24)(cid:25)V(cid:26)(cid:27)(cid:28)(cid:29)(cid:30)(cid:31) !"
FIG. 8. Time-resolved remote PL measured on a trap withthe spectral emission displayed in the inset. The trap waspopulated by carriers transported by a SAW with a wave-length of 4 µ m, frequency 726 MHz and nominal rf excitationpower of 6 dB m. The blue curve shows, for comparison, thePL trace in the absence of a SAW. IV. CONCLUSIONS
We have studied structural, optical and transportproperties of sidewall QWRs fabricated on patternedGaAs(001) substrates. QWRs formed by overgrowth ofa 10 nm-wide QW on pre-patterned ridges have thick-ness and width of approximately 25 nm and 200 nm. Thesidewall QWRs form on both sides of the ridges alignedalong the [110] crystal direction and exhibit similar emis-sion properties at both sides of the ridges. Their emis-sion is spectrally red-shifted by 27 meV with respect tothe fundamental transition of the QW. The linewidthof the QWR emission lines of 10 . µ m. By selectively ex-citing carriers using a laser energy below the band gapof the surrounding QW, we proved that the majority ofthe QWR carriers is transported along the QWR and notvia the surrounding QW. The transport distances are inmany cases limited by the presence of trapping centersalong the transport channel, which block the transport1and induce recombination of the carriers. These trapshave been observed both in the QW and the sidewallQWR. The majority of the traps in the QWR exhibitsemission energies and linewidths comparable to the onesexpected for the QWR. Some of the traps can, how-ever, exhibit much narrower linewidth (down to approx.2 meV) and a slightly different emission energy. The sub-micrometer widths, the efficient lateral confinement andacoustic transport properties of the sidewall QWRs onGaAs(001) substrates make them a promising candidatefor interconnections of charge and spin carriers in semi-conductor structures. V. ACKNOWLEDGEMENTS
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