Bias-Controlled Optical Transitions in GaN/AlN Nanowire Heterostructures Jan Müßener,*,†,‡ Pascal Hille,†,‡ Tim Grieb,† Jörg Schörmann,‡ Jörg Teubert,‡ Eva Monroy,§,⊥ Andreas Rosenauer,† and Martin Eickhoff†,‡ †
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany I. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany § Université Grenoble-Alpes, 38000 Grenoble, France ⊥ CEA-Grenoble, INAC-PHELIQS, 17 Avenue des Martyrs, 38054 Grenoble, France ‡
S Supporting Information *
ABSTRACT: We report on the control and modification of optical transitions in 40× GaN/AlN heterostructure superlattices embedded in GaN nanowires by an externally applied bias. The complex band profile of these multi-nanodisc heterostructures gives rise to a manifold of optical transitions, whose emission characteristic is strongly influenced by polarization-induced internal electric fields. We demonstrate that the superposition of an external axial electric field along a single contacted nanowire leads to specific modifications of each photoluminescence emission, which allows to investigate and identify their origin and to control their characteristic properties in terms of transition energy, intensity and decay time. Using this approach, direct transitions within one nanodisc, indirect transitions between adjacent nanodiscs, transitions at the top/bottom edge of the heterostructure, and the GaN near-band-edge emission can be distinguished. While the transition energy of the direct transition can be shifted by external bias over a range of 450 meV and changed in intensity by a factor of 15, the indirect transition exhibits an inverse bias dependence and is only observable and spectrally separated when external bias is applied. In addition, by tuning the band profile close to flat band conditions, the direction and magnitude of the internal electric field can be estimated, which is of high interest for the polar group III-nitrides. The direct control of emission properties over a wide range bears possible application in tunable optoelectronic devices. For more fundamental studies, singlenanowire heterostructures provide a well-defined and isolated system to investigate and control interaction processes in coupled quantum structures. KEYWORDS: GaN/AlN nanowire heterostructures, quantum-confined Stark effect, coupled quantum systems, indirect/direct transition, bias-controlled optical properties, single-nanowire μPL field strength to control the optical properties has not been demonstrated yet. Here we present an approach for a controlled suppression or enhancement of the QCSE by application of external bias at a single-NW level and thus manipulating the optical transitions and the photoluminescence (PL) characteristics of embedded GaN/AlN heterostructures. On the application side, such investigations are of high relevance for NW-based optoelectronic devices, where the heterostructure region acts as a recombination center. Examples are NW-based UV-LEDs,7 photodetectors in the ultraviolet (UV)8−10 and infrared (IR)11 range, lasers,12 and optochemical sensors.13
G
roup III-nitrides exhibit polarization-induced internal electric fields, which influence the optical properties of heterostructures via the quantum-confined Stark effect (QCSE).1 This is well investigated for two-dimensional quantum wells (QWs), but is also present in axial nanowire (NW) heterostructures.2,3 However, in the latter case its magnitude is strongly reduced due to efficient strain relaxation favored by the NW free surfaces, which reduces the piezoelectric polarization and the eventual presence of a uniaxial compressive strain associated with the spontaneously formed core/shell geometry.2−4 The QCSE is generally regarded as disadvantageous for optical applications, as it separates electron and hole wave functions and lowers the oscillator strength. Hence, different approaches to reduce the internal field strength have been investigated, e.g., growth on nonpolar facets5 or electrostatic screening by doping.6 Although being of high importance, direct experimental control of the © 2017 American Chemical Society
Received: April 7, 2017 Accepted: August 3, 2017 Published: August 3, 2017 8758
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Figure 1. (a) Schematic of the entire NW geometry and polarity of the applied external bias. Below, a scanning electron microscopy (SEM) micrograph of a contacted NW with central heterostructure (dark contrast) is shown. (b) Band profile along the central NW axis of a GaN/ AlN (4/4 nm) multi-ND structure, simulated with nextnano3. Top right inset shows a plane section of the three-dimensional model, illustrating the considered lateral growth. (c, d) HAADF-STEM images of the 40× GaN/AlN central heterostructure of a NW with a barrier width of 3 nm (c) and 1 nm (d). (e) HRTEM image showing the AlN shell around the NW. (f, g) Al concentration maps from quantitative evaluation of the HAADF intensity using a comparison with image simulation (details in the Methods section).
conditions. The indirect transition between adjacent NDs exhibits an inverse bias dependence and can be enhanced for opposite bias polarity compared to the direct ones. Furthermore, we observe several sharp peaks, which, based on their bias dependence, can be assigned to two-dimensional electron/hole gas (2DEG/2DHG) states at the interface of the heterostructure with the GaN contact regions. Finally, the GaN near-band-edge (NBE) emission from the contact regions is detected, exhibiting minor bias dependence. Numerical simulations of the band profile including strain, polarization fields, and the complex geometry support the assignment of the experimental data.
For fundamental studies, single-NW heterostructures under external bias present an ideal model system for isolated quantum structures with defined geometry that can be used to realize coupled quantum dots for quantum information. Biolatti et al. suggest a double quantum dot system, where an electric field introduces the required coupling of adjacent excitonic states to realize two qubit conditional operations.14 Nitridebased quantum dots were proposed as suitable candidates, due to the presence of an internal field,15,16 which can moreover be dynamically tuned by an external voltage.17 However, related experiments have most often been performed on quantum dots embedded in two-dimensional p−i−n-diode structures,18,19 where only reverse voltages can be applied and individual dots have to be isolated by shadow masks. In the case of NW heterostructures, both bias polarities can be applied and the isolation is an intrinsic feature of single NWs. Recently, the concept of bias-dependent single NW μPL analysis was reported for the direct transition in a single GaN/ Al0.3Ga0.7N nanodisc (ND).20 In the present work, we demonstrate the extension of this concept to manifold optical transitions in 40× GaN/AlN NW heterostructures. This allows us to study more complex interaction processes such as the transition between adjacent NDs (indirect transition). The different emissions can be modified and identified by their individual bias dependence. Furthermore, the high internal fields in GaN/AlN NW heterostructures compared to the GaN/Al0.3Ga0.7N ones give rise to an enhanced bias dependence, and the respective emission properties can be tuned over a wide range. For direct transitions within one ND, the influence of the QCSE can be modified by enhancement or attenuation of the internal electric field and quantified by tuning close to flat band
RESULTS AND DISCUSSION NW samples with embedded heterostructure were grown by plasma-assisted molecular beam epitaxy (PAMBE) on Si(111) substrates. In nitrogen-rich growth conditions the NWs grow self-assembled along the polar [0001̅] direction (N-face polarity) and show wurtzite crystal structure.21 Further details on the growth process can be found in refs 3 and 6. The samples consist of a central 40× stack of GaN NDs in AlN barriers enclosed by long non intentionally doped GaN contact regions (∼1 μm) as schematically shown in Figure 1a. In reference experiments22 it was found that the contact resistance of the latter is still several orders of magnitude lower than the resistance of the heterostructure (cf. Figure S1 in the Supporting Information). A sample series with a constant ND thickness of 4 nm and different barrier thicknesses (nominally 4, 3, 2, and 1 nm) were grown in order to probe different magnitudes of the internal fields as explained below. Figure 1c and d show scanning transmission electron microscopy (STEM) images recorded with a high-angle annular 8759
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ACS Nano dark field (HAADF) detector. The 40× GaN/AlN central heterostructure is displayed for a sample with a nominal barrier width of 3 nm (c) and 1 nm (d). The observed layer thickness is similar to the nominal values (cf. Al concentration maps in Figure 1f and g); however, the thickness decreases slightly along the growth direction, as shown in detail in Figure S2 in the Supporting Information. The growth of the AlN barriers also introduces a small lateral growth rate,3 resulting in a diameter increase of the NDs along the growth axis. Due to the lateral growth, a thin shell is formed around the NW, exemplarily shown in the high-resolution TEM (HRTEM) image in Figure 1e. Analyses by energy-dispersive X-ray spectroscopy (EDX) reveal that this shell consists of AlN. The shell grows during Al supply, ending up with a thickness at the bottom of the ND stack of 6−8 nm for the 3 nm barrier sample and of 3 nm for the 1 nm barrier sample. The shell thickness at the top of the stack, at the last grown NDs, is approximately 1 nm. The NW ensembles were also investigated by X-ray diffraction (XRD) analysis, and evaluation of the superlattice peaks reveals lattice periodicities (ND plus barrier thickness) of 8.4, 7.0, 6.3, and 5.2 nm for the nominal 40× GaN/AlN 4/4, 4/ 3, 4/2, and 4/1 nm samples, respectively. Numerical simulations were carried out to predict the heterostructure band profile and field strength using nextnano3.23 They are based on a complete three-dimensional model of the heterostructure including the lateral AlN shell growth and a widening of the ND diameter (cf. inset in Figure 1b). An example of a calculated band profile along the NW center axis of a GaN/AlN 4/4 nm heterostructure with outer GaN contacts is shown in Figure 1b. For individual optical and electrical characterization, single NWs were dispersed on a carrier chip, and electrical contacts were formed as illustrated in Figure 1a. Bias-dependent μPL spectra of a single 40× GaN/AlN (4/2 nm) NW heterostructure at T = 4 K are shown in Figure 2a. For zero external bias (black line) we observe three spectral contributions: The most intense and sharp peak at ∼3.467 eV (full width at half-maximum (fwhm) ∼4.2 meV) stems from the NBE PL of the long upper and lower GaN contact regions (labeled (4) in Figure 2a). The broad emission band in the range 2.9−3.3 eV (spectral centroid at ∼3.1 eV, fwhm ∼0.126 eV, labeled (1) in Figure 2a) is related to direct transitions in the GaN NDs. The band is composed of several broad emissions, which can be fitted with Gaussian peak shapes with a fwhm in the range of ∼30−100 meV. The broad spectral distribution can be explained with the high number of NDs contributing to the emission. Variations in the ND height and the thickness gradient of the outer AlN shell (cf. Figure 1c), which causes a strain gradient, result in an energetic dispersion along the ND stack.7,24 Single NWs of the same sample generally show similar ND emission with respect to transition energy, intensity, and fwhm. Furthermore, they exhibit a high yield; that is, all measured NWs exhibit the direct ND-related emission and bias dependence as explained below. However, their spectral shape shows slight wire-to-wire variations (cf. Figure S4 in the Supporting Information), which can be mainly explained by small variations in NW geometry and structure or even by contact with the underlying substrate as reported in refs 25 and 26. Due to the QCSE introduced by the strong polarization difference between GaN NDs and AlN barriers, the ND emission is red-shifted below the NBE, as it was also reported in refs 2, 3, 6, and 9. The low
Figure 2. (a) Bias-dependent μPL spectra of a 40× GaN/AlN (4/2 nm) single-NW heterostructure. The different emission regions, which are modified by the external bias, are indicated in (a), magnified below in (b)−(e) and supplemented by schemes of the band structure under bias. Lines serve as a guide to the eye. 8760
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ACS Nano excitation power of 100 W/cm2 in the PL analysis avoids screening of the internal fields by photoexcited carriers. While the ND emission can be blue-shifted over 250 meV for higher excitation power, we generally observe a saturation of the red shift when reducing the power to the value used in these experiments. In the higher energetic range of ∼3.35−3.7 eV, spectral features are observed, that consist of several distinct peaks with a fwhm of some tens of meV and exhibit strong wire-to-wire variations (labeled (3) in Figure 2a). These features are significantly narrower than the ND emission, pointing to their origin from a smaller number of emitting centers. In general, we observe this emission even for single GaN-base/AlN-top NW heterostructures, at which both their emission energy and intensity increase with AlN thickness. We assign this emission to the GaN contact region at the interface to the AlN barriers, where elevated emission energies can occur due to the presence of a triangular potential and compressive strain: Close to the barrier, the GaN is biaxially compressed and, at the lower interface, further c-axial compressive strain is exerted by the lateral AlN shell. Hetzl et al. reported a blue shift of the GaN NBE of ∼240 meV for strained GaN-core/AlN-shell NWs.27 Similar results of a blue-shifted GaN NBE in NW heterostructures compressively strained by (Al,Ga)N were reported in refs 28−31, where in the latter spatially resolved cathodoluminescence showed a more intense NBE luminescence at the lower interface, which is passivated by the AlN shell. In our case, nextnano3 simulations predict an increased band gap in the GaN contacts directly at the lower (upper) interface, for a GaN/AlN 4/4 nm multi-ND heterostructure, of 3.75 eV (3.63 eV). Even more, the related band-to-band transition energy is increased by the triangular confinement potential for electrons (holes) at the upper (lower) interface, giving rise to quasi 2DEG (2DHG) states in the N-face NW heterostructure (cf. Figure 1b).32 In some cases, like in Figure 2d, the emission consists of several distinct peaks. This can be explained by transition from excited states in the confining potential or multiple local potential minima in the lateral plane by interfacial potential fluctuations.24 To investigate alloy diffusion and fluctuation in the heterostructure as a possible additional source of emission, high-resolution HAADF-STEM images of the three uppermost NDs in the NWs shown in Figure 1c and d were recorded. The experimental parameters were applied as suggested in refs 33 and 34 to allow for quantitative interpretation of the HAADF intensity by comparison with simulations. Using the method suggested in ref 33 for quantitative evaluation of HAADF intensities, by a comparison with multislice simulations, maps of the Al concentration were obtained, as shown in Figure 1f and g. A detailed explanation of the used simulated reference data is given also in the Methods section. Along the growth direction, a smooth transition between the Al-rich barriers and the NDs can be observed, which might also be caused by beam spread due to the high specimen thickness. The Al concentration perpendicular to the growth direction is homogeneous, which gives no hint for Al clustering. The observed interface roughness lies in the range of only one unit cell, which was also confirmed by further HRTEM measurements. The maximum Al concentration in the barriers might be up to 10% higher, as given in the figure, as the NDs were considered to be pure GaN, but the facets visible in Figure 1e lead to additional Al in the electron-beam path. The AlN shell
was also not considered; however, it is thin at the investigated position and the effect on the evaluation is expected to be small. Hence, the Al concentration measured in the barriers must be considered as a lower boundary. However, in the case of the 1 nm barrier sample, the barrier most probably does not consist of pure AlN (cf. Figure 1g). HAADF-STEM simulations of a comparable sample with pure 1 nm AlN barriers were performed using frozen-lattice multislice calculations35 (cf. Figure S3 in the Supporting Information). The simulations reveal that the measured low Al concentration cannot be explained by broadening of the electron beam during propagation through the specimen nor by lattice plane bending. Consequently, the 1 nm barriers contain a significant amount of Ga. However, due to the homogeneous barrier concentration, we assume alloy fluctuation to be an unlikely explanation for the observed sharp PL emission in this case, in contrast to NWs with extended AlGaN regions, for which quantum dot like emission due to compositional fluctuation was reported in ref 36. Moreover, a clear assignment of this emission is facilitated by analysis of its bias dependence as shown below. Bias Dependence of Photoluminescence Properties. The application of an external bias across the NW heterostructure results in a modification of the PL characteristics due to specific variations of the individual transitions, as it will be discussed based on the results shown in Figure 2. In this figure, the variation of the entire emission spectrum is shown for external voltages between −45 and +40 V. The variations in the different spectral regions can be explained with bias-induced changes of the band profile obtained by bias-dependent nextnano3 simulations and are schematically illustrated in Figure 2b−e. More detailed information on the simulations can be found in the Supporting Information (Figure S6). 1. Direct ND Transition. The bias dependence of the direct ND emission is shown in Figure 2b. For positive applied bias, the emission shows a pronounced blue shift and intensity increase, while the opposite trend is found for negative bias. This behavior can be explained considering the bias-dependent band profile of the N-face polar heterostructure illustrated in the inset of Figure 2b. For positive bias (blue scheme), the externally applied electric field counteracts the internal field in the NDs, flattens the bands, and gradually compensates the QCSE. Consequently, the spatial separation of electron and hole wave function is reduced, resulting in an increased oscillator strength and transition energy. A negative bias leads to opposite effects (red scheme). The example shown in Figure 3a demonstrates the magnitude of the described effects: For a 40× GaN/AlN (4/3 nm) NW heterostructure, the PL intensity increases (decreases) by a factor of 3.7 (0.25) with respect to zero bias and the emission energy shifts over 455 meV in the investigated bias range. For high positive bias, a decrease in PL intensity is often observed, while the transition energy still increases. This is attributed to carrier extraction from the ND superlattice: For increasing positive bias, the field in the NDs decreases, whereas the field in the barrier increases accordingly. Hence, the wave function axially delocalizes and approaches the opposite barrier, where a strong field extracts carriers. This is also shown in band profile simulations (Figure S6 in the Supporting Information) and was reported similarly for planar structures by Jarjour et al.17 We have confirmed these results by bias-dependent timeresolved μPL analysis of the direct ND emission for single 40× 8761
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induced by a dipole with reduced charge distance, cf. Figure S5a in the Supporting Information). However, the field inside the barrier, between the inverse charges, increases with reduced barrier thickness and charge distance. Here, this effect is directly revealed by analysis of the biasdependent ND emission for GaN/AlN NW heterostructures with barrier thicknesses of 3, 2, and 1 nm and a constant ND thickness of 4 nm. Already at zero bias, the direct ND emission energy shows a strong blue shift for decreasing barrier thickness (cf. Figure 3d), indicating a reduced QCSE. Indeed, simulations using nextnano3 predict an internal field in the ND of 5.5, 4.3, and 2.7 MV/cm for 3, 2, and 1 nm barrier thicknesses, respectively (cf. Figure S5 in the Supporting Information). In the experimental data shown in Figure 3 the direct ND emission exhibits the expected blue shift with increasing positive bias, reaches a maximum, and shifts to lower energies for higher bias in the case of the 1 and 2 nm barrier samples. This is attributed to an initial reduction of the electric field until flat band conditions are reached and the subsequent introduction of an inverse field for higher bias. The required bias to achieve this reversal point increases for thicker barriers, i.e., higher internal fields in the ND. For the 1 and 2 nm barrier sample this point is reached at +18 and +90 V, respectively (Figure 3b and c), while for the 3 nm barrier sample it is not even in the measurement range (Figure 3a). The average magnitude of the internal field in the NDs can directly be estimated from the experimental data,17,20 as in the flat band condition, the external and internal field fully compensate each other. The corresponding electric field can be calculated from the applied bias voltage by dividing its magnitude by the length of the central 40× GaN/AlN heterostructure, where a homogeneous potential drop is assumed. Compared to that, the potential drop at the GaN contact section and the metallic contacts can be neglected, as discussed below. Using this approach we obtain values of 3.7 and 0.9 MV/cm for the 2 and 1 nm barrier samples, respectively, which are slightly smaller but close to the simulated values. Like for the 3 nm barrier sample, the reversal point is not reached within the maximal applied bias, and the internal field is even higher. The same approach to deduce the internal field was applied by Jarjour et al. for InGaN/GaN quantum dots in planar p−i− n-diode structures, where a deviation of −33% compared to the simulated values was observed.17 We attribute the lower experimental values to screening of the internal field by photogenerated free carriers or those from ionized residual donors, which were not considered in our simulations. Furthermore, in addition to the elastic strain relaxation of the heterostructure, which is included in the simulations, relaxation by misfit dislocations at the interfaces, as shown by Furtmayr and Teubert et al., can reduce the piezoelectric field component.3 Due to the nonatomistic quasi continuum elastic model, the latter cannot be considered in the nextnano3 simulations. The larger discrepancy for the sample with the smallest barrier thickness of 1 nm can furthermore be explained by the reduced Al concentration in the barrier and hence lower field than for nominal AlN, as revealed by quantitative TEM measurements (cf. Figure 1g). In fact, simulation with a reduced Al concentration of 50% predicts an internal electric field of 1.1 MV/cm, closer to the experimental value of 0.9 MV/cm. The parasitic influence of the contact resistance can be excluded: First, an additional resistance would reduce the potential drop along the heterostructure and the extracted field value from the
Figure 3. (a−c) Bias-dependent μPL measurement of a 40× GaN/ AlN single-NW heterostructure with different AlN barrier thicknesses. For thinner barriers, the internal axial field in the ND decreases and lower bias values are necessary to obtain a reversal point of the energetic shift (flat band condition). For empty spectral regions it was assured that the sample does not show a PL signal. (d) Spectral centroid of the direct ND emission as a function of the applied bias from the spectra in (a)−(c).
GaN/AlN (4/4 nm) NW heterostructures (Figure S7 in the Supporting Information). Due to the high intrinsic field and separation of the wave functions, the decay time is ∼410 ns for zero bias. For a positive (negative) applied bias of +15 V (− 12 V) we observe a decrease (increase) of the decay time to ∼350 ns (∼550 ns), indicating a reduction (enhancement) of the internal electric field. Moreover, we have compared NW heterostructures with different internal electric field strength. Hönig et al. recently proposed that the polarization-induced internal electric field in GaN/Al(Ga)N quantum dots and hence the strength of the QCSE can be reduced by reducing the barrier thickness:37 The interface charges on both sides of a barrier exhibit inverse signs. For thinner barriers, the opposite charges are located at smaller distance, partially compensate each other, and induce a lower electric field in the adjacent ND (for an image of a reduced field 8762
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ACS Nano experiment even further. Moreover, as explained above, the resistance of the NW heterostructure is several orders of magnitude higher. In Figure 3b and c, the ND emission energy at the maximal blue shift is still smaller than the GaN bulk NBE emission energy, although for the flat band condition and confinement inside the ND one would expect an energy slightly above the NBE. We account lateral fields as the reason for this observation, which are not reduced by the axially applied external bias. In refs 3 and 38 it was shown that the AlN shell induces a radial strain profile and the presence of lateral electric fields in the ND plane. Although these internal lateral fields were shown to be significantly smaller than the axial internal fields, they can reduce the transition energy by several 100 meV. 2. Indirect ND Transition. In Figure 2c a broad emission band between 3.1 and 3.4 eV evolves, increases in intensity, and shows a blue shift for increasing negative bias. This feature, which shows the opposite bias dependence compared to the direct ND transitions, is not visible at zero bias. It can be assigned to an indirect transition between adjacent NDs involving an electron from the upper and a hole from the lower ND, as schematically shown in the inset of Figure 2c: A positive bias (blue scheme) increases the spatial separation between electron and hole wave functions, hence decreasing the tunneling and recombination rate. In contrast, the application of negative bias (red scheme) leads to an approach of the wave functions on both sides of the barrier and thus to an increased recombination rate and PL intensity. At the same time, the energetic distance increases, resulting in the observed blue shift. Also this emission shows wire-to-wire variations: In most cases it appears as a broad peak between direct ND and NBE emission (e.g., Figure 2a); however, in some cases it cannot be observed at all in the measured bias range (e.g., Figure 3b). To confirm this assignment, we compared the biasdependent PL spectra for samples with barrier thicknesses of 2 and 1 nm, as a higher transition probability and emission intensity for samples with thinner barriers is expected (Figure 4). Indeed, for the thicker barrier sample, a negative bias is required to observe the indirect transition, whereas for the thinner barrier sample, the emission is already observable for zero bias and can be quenched by application of positive bias. The small potential drop at the thin barrier also results in an almost vanishing bias dependence of the transition energy (Figure 4b). As explained above, this indirect transition originates from the recombination of an upper electron with a lower hole, as only this transition exhibits the observed blue shift for negative bias (Figure 2c, red scheme). This recombination is strongly favored by the internal field, which shifts the respective wave functions closer to the common barrier. In contrast, the recombination of a lower electron with an upper hole would result in a red shift for negative bias. The latter was reported for coupled quantum dots in planar diodes for nonpolar GaAs/ (In/Al)GaAs material,18,39 where the absence of an internal field does not favor one of the two possibilities. Also for our samples, in the case of thin barriers and high positive bias (≳ +20 V) we observed an additional band emerging, which can be assigned to the indirect transition of lower electron and upper hole, as above flat band conditions, this recombination is favored (cf. Figure 2c dashed transition line in blue scheme, spectra not shown here). The literature of coupled states in the
Figure 4. Bias-dependent μPL measurement of a 40× GaN/AlN single-NW heterostructure with different AlN barrier thicknesses. For thicker barriers a negative bias has to be applied to observe indirect ND transition. For thinner barriers, this transition can already be observed for >0 V.
GaN/Al(Ga)N material system so far only addressed tunneling processes followed by a direct transition in order to explain power-dependent PL properties of asymmetric quantum wells.40,41 In general, the indirect ND transitions are observed at higher energy than the direct ones. It is evidenced by the band profile for negative bias (Figure 2c, red scheme) that the indirect transition energy is raised. However, even for zero bias the indirect transition exhibits a higher energy (Figure 4b, black spectrum), where one would expect similar values (compare Figure 2b and c, black schemes). One explanation is the variation of layer thicknesses along the stack: Indirect ND transitions occur preferentially for thinner barriers, which exhibit a reduced field and increased transition energy. 3. 2DEG/2DHG Transition. The emission peaks assigned to 2DEG (2DHG) states in the GaN contacts at the upper (lower) interface to the heterostructure also exhibit a systematic bias dependence in their intensity, as shown in Figure 2d. An intensity increase for positive and a decrease for negative bias are observed, which confirms the above assignment. As schematically depicted in the inset of Figure 2d, the transition rate in this potential is limited by the low density of minority carriers, i.e., holes in the case of the upper 2DEG and electrons for the lower 2DHG. For negative bias (red scheme), the minority carrier density is further reduced and the PL intensity decreases. For positive bias (blue scheme), the band flattens and the minority carrier density increases, causing an increase in PL intensity. The transition energy exhibits a weak, less systematic bias dependence, and in most of the cases no shift is observed (vertical lines in Figure 2d). However, a few of the peaks show a rather small blue or red shift (bent line in Figure 2d). To understand this behavior, two opposite effects have to be taken into account (Figure 5a left scheme): On one hand, for negative bias, the band tilting that forms the triangular potential 8763
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spatially indirect transitions of confined electrons and drifting holes in the 2DEG potential. Similar to our findings, the emission energy shifted by only a few meV upon increasing the excitation power by 3 orders of magnitude, and the PL intensity initially increases for band flattening bias. We note that in that work the authors found the transition energy below the GaN NBE, which we attribute to the lower Al content in the barrier that results in a reduced confinement potential and significantly lower compressive strain in the two-dimensional extended GaN layer compared to our case. 4. GaN NBE Transition. The GaN NBE emission from the contact regions shows a small but monotonic shift of 1.3 meV to higher energies for a bias increase over the entire range from −45 to +40 V bias (Figure 2e). We assign this behavior to the Franz−Keldysh effect, which describes the effective band edge reduction by wave functions penetrating the tilted bands:44 ΔE =
3 (m*)−1/3 (qℏξeff )2/3 2
with the effective electron mass m* and the effective electric field ξeff, which is the sum of internal and external fields in the present case. The observed reduction of ΔE with positive bias indicates the presence of a small internal field inside the GaN contact regions pointing to the NW top. In fact, the PL spectra reflect the ξ2/3 dependence, as the shift does not scale linearly with bias, but gets stronger for positive bias (smaller ξeff). As the energy does not reach a maximum for positive bias, the internal field is not fully compensated and the determination of its magnitude is not straightforward. However, the potential drop can be estimated: By defining ΔE = 1.3 meV as the full shift when varying the external bias by 85 V and multiplying the resulting field by the contact region length of 2 μm, one obtains a potential drop of some tens of mV. This confirms the assumption made above, that most of the applied bias drops along the 40× GaN/AlN heterostructure and not along the GaN contact region. The small magnitude of the field in the contact regions is also supported by the absence of a powerdependent shift of the NBE emission energy.
Figure 5. (a) 2DEG schematic band profile and energetic position under different external bias or excitation power. Bias-dependent μPL measurement of either a 40× GaN/AlN heterostructure (b) or a ∼250 nm long AlN insertion (c). A 2DEG/2DHG emission with similar behavior is observed in both cases, excluding ND-related transitions as a possible source.
becomes steeper and raises the energy of the confined states of majority carriers. On the other hand, for the stronger tilt of the band profile, a spatially indirect transition exhibits a reduced transition energy. These two effects obviously almost compensate, thus explaining the experimental observation of almost no and in few cases small shifts in either direction. Similarly, the emission energy does not depend on the excitation power (spectra not shown here); that is, neither a band bending by bias nor a screening by photoexcited carriers has a significant influence on the transition energy. An increase of the excitation power has a similar effect to negative bias, as screening by photogenerated carriers reduces the width of the space charge region (Figure 5a right scheme). To prove the assignment of this emission to the 2DEG/ 2DHG states, we investigated a control structure consisting of a ∼250 nm AlN insertion in the middle of a GaN NW. This structure also exhibits the 2DEG/2DHG band profile at the interfaces to the GaN contact regions, while a ND-related emission is excluded. In Figure 5c it is shown that such a test structure exhibits a similar 2DEG/2DHG emission. Comparable to the multi-ND structure in Figure 5b, it shows an increasing intensity for positive and quenching for negative bias, accompanied by a small energetic shift, which confirms that these states are indeed the origin for the observed transition. PL measurements related to 2DEG states in GaN/AlGaN thin-film heterostructures are reported in refs 42 and 43. In these works, the authors assigned the observed emission to
CONCLUSION We have demonstrated that the PL emission properties of 40× GaN/AlN single-NW heterostructures can be controlled by an externally applied electric field that is superimposed to the polarization-induced internal field. Due to external modification of the axial potential profile, it is possible to selectively enhance, suppress, and shift specific luminescence features in μPL and to identify the different optical transition mechanisms by their bias dependence. The main spectral feature originates from the direct ND transition within one ND, which increases in PL intensity and energy upon application of positive bias, as the polarizationinduced internal field is gradually compensated. In contrast, indirect transitions between adjacent NDs increase in intensity and energy for negative bias, as the wave functions from an electron in the upper and a hole in the lower ND spatially approach. Finally, sharp 2DEG/2DHG-related emission peaks from single interfaces between the GaN contact regions and the last/first AlN barrier of the heterostructure increase in intensity by application of a positive bias, which increases the minority carrier density. These results show that externally biased NW heterostructures are a well-suited system to study and manipulate the influence of internal electric fields on the potential profile and 8764
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Article
ACS Nano
from which the measured HAADF intensities could be normalized to the total incoming beam intensity as suggested in refs 46 and 47. In the experimental images, the atomic column positions were found and all pixels were averaged belonging to a Voronoi cell for each position.34 After normalization using the detector scan, the resulting normalized intensity can directly be compared to simulations of the mean HAADF intensity per unit cell as described in refs 33 and 34. The reference intensities were simulated as described in ref 48 using the STEMsim program.35 The multislice simulations were performed in the frozenlattice approximation taking static-atomic displacements49 into account by a relaxation of the supercells using the LAMMPS code.50 See ref 48 for further details. For the simulations of HAADF intensities, the experimental sensitivity of the used HAADF detector was taken into account as, for example, explained in ref 34. The experimental evaluation was performed similarly to that described in ref 33. The GaN layer was expected to be pure (containing no Al), which allowed determining the thickness by comparison with simulations. The thickness in the whole image was then obtained by interpolation. For each Voronoi cell, specimen thickness and intensity were compared with simulations yielding the local Al concentration.
the QCSE. With respect to applications, the potential profile in NW-based optoelectronic devices can be analyzed and optimized with external bias to compensate adverse influences of the internal electric field. Moreover, it can be used to directly control and vary the optical properties over a wide range without using different sample structures. For fundamental studies, biased NW heterostructures provide individual and well-defined coupled quantum systems, e.g., for applications in quantum information, where overlap and interaction of electronic states can be directly controlled. In general, using the concept of an external field control, polar heterostructures are not necessarily adverse for optical properties, but an external bias can be a proper tool to probe, modify, and even compensate the internal fields.
METHODS For individual characterization, the NWs were detached from the substrate by an ultrasonic bath in 2-propanol, and the suspension was dispersed on an oxidized Si carrier chip, featuring a marker structure metallization. Single NWs were identified by SEM, and contacts were formed to both ends by electron beam lithography and thermal evaporation of Ti/Au (25/225 nm) contacts (contacted single NW in Figure 1a). For biased μPL, NW samples on the carrier chip were mounted and contacted in a continuous-flow cryostat (Oxford MicrostatHires2) to perform the measurements at T = 4 K. The polarization of the externally applied voltage is illustrated in Figure 1a: The NW bottom is connected to ground and bias is applied to the NW top. A Keithley 2400 source-meter was used to apply voltage and measure current with a range down to 10−11 A. Voltages up to 100 V were applied, necessary to obtain external electric fields on the same order as the internal fields. Due to the high resistivity of the multiple AlN barriers, the current through the structure was relatively low (
