Probing the Excitonic States of Site-Controlled GaN Nanowire

Jan 9, 2015 - Several emitters are measured and used to build up an average picture of the electronic structure of a single quantum dot via comparison...
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Probing the Excitonic States of Site-Controlled GaN Nanowire Quantum Dots Mark J. Holmes,*,† Satoshi Kako,‡ Kihyun Choi,† Pawel Podemski,†,§ Munetaka Arita,† and Yasuhiko Arakawa*,†,‡ †

Institute for Nano Quantum Information Electronics and ‡Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan ABSTRACT: We report the detection of fully confined excited states and the zero-absorption region of individual site-controlled GaN/AlGaN nanowire quantum dots using photoluminescence excitation spectroscopy, which provides evidence of the true zero-dimensional discrete density of states of such quantum dots. Because of the strong quantum confinement in these dots, the p-shell, d-shell, and even higher energy (including some f-shell) states of a single quantum dot are observed, which provides unprecedented insight into the electronic structure. Several emitters are measured and used to build up an average picture of the electronic structure of a single quantum dot via comparison to theoretical simulations. KEYWORDS: nanowire, site-control, quantum dot, excited states

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gain medium for lasers.15,16 Here, we report the observation of several excited-state shells of a single site-controlled GaN/ Al0.8Ga0.2N QD (the same structures described in references11,12,17) using PLE spectroscopy. The strong quantum confinement exhibited by these dots makes them ideal candidates for such measurements, which in this case enables the observation of states beyond the d-shell. By measuring several dots, we are able build up a picture of the electronic structure of an average device, which we then compare to a simulated QD to describe the relevant features of the experimental data. The studied QDs (with typical height, ∼ 1 nm and typical width, ∼ 10 nm) were formed near the tips of GaN/AlxGa1−xN (nominal mole fraction x = 0.8) nanowires that were grown by selective-area metal organic chemical vapor deposition as described elsewhere.18,19 Scanning electron microscopy images of the selectively positioned structures are shown in Figure 1 along with a schematic. The use of site-controlled QDs is important for this study as their position is highly controllable by substrate preparation, and they can thus be fabricated at low enough densities to be individually probed with a laser. In the future, the site control of QDs will be absolutely necessary for any realistic implementation of single/few QD devices. To perform PLE spectroscopy and probe the excited states of individual QDs, the QD sample was placed in a continuous flow liquid helium cryostat, cooled to 4 K, and excited optically at a steep angle with a tunable, frequency-tripled laser (200 fs pulses at 80 MHz). The excitation beam was monitored with a beam profiler and charge-coupled device (CCD) camera and

uantum dots (QDs) are expected to play an important role in the future of solid state quantum information processing because of their ability to confine charge carriers in a spatially localized area and at well-defined energies. The exact energies depend on several factors, such as the dot geometry, material properties, and the physical environment, but are in principle both calculable and measurable. It is very important to obtain knowledge on the spectrum of states for a given QD, as the excited states can be used for qubits,1−4 pump levels for deterministic single photon sources,5 and as levels for spin injection for spin memory devices.6 Because of the extent to which the state levels depend on the geometry of the confining potential profile, information on the excited-state separations will also allow us to better understand the physical size and anisotropy of the dots under investigation. Unfortunately, the stochastic nature of QD formation means that there is no way at present to deterministically define the size and shape of a semiconductor QD before growth, which results in the situation that the exact energy levels of a given single dot cannot be known until measured experimentally. Photoluminescence excitation (PLE) spectroscopy, which involves tuning an excitation laser to find resonances corresponding to excited states, has become a well established technique for detecting and analyzing states in QDs1,4,7 and has recently also been used to detect excited states in III-nitride QDs that form stochastically8−10 and those that have been site controlled.11,12 III-Nitride QDs are of particular interest due to their strong quantum confinement (a property that facilitated the successful realization of single photon sources operating at room temperature using nanowire QDs,13 and at 200 K using self-assembled QDs14), for the wide range of emission energies accessible with them (which span from the UV through to the visible range of the electromagnetic spectrum), and also as a © XXXX American Chemical Society

Received: October 14, 2014 Revised: December 14, 2014

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Figure 1. Scanning electron microscopy images of site controlled nanowire QDs. The nanowires are grown in an array pattern with 20 μm pitch. Markers are also fabricated to help locate the nanowires with an optical microscope. (a) Image showing the clear spatial isolation of single devices afforded by site-controlled growth. (b) Higher magnification image showing the device at the center of image a. (c) Schematic with cutaway depicting the formation of a QD near the tip of the nanowire.

well-like layer parallel to the nanowire surface that may be formed during the growth of the QD17 (see Figure 1c), although the exact origin requires further investigation and is beyond the scope of the present study. At energy differences below ∼100 meV, the tail of the continuum states no longer imposes itself on the PLE spectrum, and it can be said that we are probing the zero-absorption region of the QD. This region is characterized by the true zero-dimensional density of states of the complete three-dimensional confinement in the QD, which leads to no absorption at energies that do not correspond exactly to optically allowed transitions between states. Observation of exciton sates without the continuum background is of significance because the continuum states in effect provide an alternate path to populate the exciton ground state and are therefore considered to contribute to an observed damping of coherent oscillations in power-dependent coherent control experiments.12 It is anticipated that further investigation of states in this energy region will result in a higher visibility of such power-dependent Rabi oscillations. Experimental realization will be more likely achievable with the use of strong laser filtering/pulse shaping, an excitation source with a narrower spectral width, or two photon excitation.10 To attain more information on the excited states of these QDs, the PLE spectra from a further 16 QDs were measured as outlined above (see Figure 3a for a representative selection of PLE spectra), and the state energies were collated into the histograms shown in Figure 3, panel b. The average ground state emission energy for these QDs is E̅ = 4.4 eV (σ = 40 meV). For the majority of measured QDs, we could observe just two or three peaks in the PLE spectrum, possibly due to higher energy peaks becoming obscured by the continuum. In general, however, it appears that the energies of the peaks are quite well-defined and consistent from dot to dot, that is, the first peak typically appears at an energy of ∼70 ± 20 meV above the ground state, the next peak can be found at ∼120 ± 30 meV, and so on. It is unlikely that these peaks are related to LO-phonon assisted processes in the QD as they are energetically inconsistent with the GaN LO-phonon energy of 90 meV. We believe that this is due to a rapidly decreasing LO-phonon coupling strength with QD size for nitride QDs.24,25 To identify and further discus the energies of the experimentally measured peaks, we performed calculations of the electronic structure of a single QD using the nextnano26 device simulator and the eight-band k·p theoretical framework.

adjusted with piezo-controlled mirrors to ensure the excitation of the same QD while the energy of the laser was tuned.9 The resulting photoluminescence (PL) from individual QDs was collected by a 50× objective in-line with the nanowire axis (NA = 0.4) and both spatially and spectrally filtered before being focused into a 30 cm spectrometer where it was dispersed by a 1200 mm−1 diffraction grating and finally detected by a liquid nitrogen cooled CCD camera. Because of the ultrafast nature of the excitation laser, its spectral width (∼10 meV) acts to limit the resolution of this particular experiment. The PLE spectrum of a single nanowire QD (emitting at ∼4.42 eV) is shown in Figure 2. The PLE spectrum exhibits

Figure 2. PLE spectrum map of a single GaN/AlGaN nanowire QD emitting at ∼4.42 eV. Peaks at excitation energy differences ΔE01 ∼ 70 meV, ΔE02 ∼ 130 meV, ΔE03 ∼ 200 meV, and ΔE04 ∼ 250 meV are clearly visible. A dotted line acts as a guide to the eye for the continuum states.

several clear peaks at energy differences of ΔE01 ∼ 70 meV, ΔE02 ∼ 130 meV, ΔE03 ∼ 200 meV, and ΔE04 ∼ 250 meV, respectively, where ΔE0n is the energy of the nth peak above the ground state emission energy. In addition to the peaks in the PLE spectrum, there also appears to be a background that increases monotonically with energy. A similar continuum has been observed in the PLE spectra of self-assembled InAs,20−22 InP,7 CdTe,23 InGaN,8 and recently GaN9 QDs and is usually ascribed to a change in the density of states due to a transition from wetting layer to QD. In the current sample, the background is likely to be a 2D−0D transition from a quantum B

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Figure 3. (a) Several normalized PL and PLE spectra from different QDs emitting across a range of energies around the measured distribution (mean energy E̅ = 4.4 eV, and deviation σ = 40 meV). The successive states in the PLE spectra have been labeled, and dotted red lines are used as a eye-guides for the continuum states. (b) Distributions of all peaks observed in the PLE spectra of site-controlled GaN nanowire QDs.

For simplicity, the QD was modeled as a hexagonal disk-shaped GaN inclusion within a matrix of Al0.8Ga0.2N. The calculations were performed with material parameters from Vurgaftman and Meyer27 and using simulation domain sizes that had been checked for eigenvalue convergence. First the strain was calculated, and then the piezo- and pyro-electric fields were determined before the Schrödinger equation was solved to evaluate the single particle state energies (E e,h ) and corresponding eigenfunctions (Ψe,h) for the first 10 (each doubly degenerate) electron and hole states, respectively. Once the electronic states had been calculated, the absorption spectrum, α(E), of a typical QD could be evaluated by considering the matrix elements and the dipole moment operator for the interaction with light polarized in the plane of the QD: α (E ) =

∑ |⟨Ψ|e e·p|Ψh⟩|2 δ(Ee − E h − Γe,h − E) e,h

Figure 4. (a) Calculated absorption spectrum of a QD as described in the text (simulated QD height = 0.6 nm, diameter = 13 nm). The sharp black peaks show the individual transitions, and the simulated spectrum has been obtained by broadening by 10 meV. The shell structure has been color coded: s, p, d, f as yellow, gray, blue, and green, respectively. (b) Measured distributions of peaks in the PLE spectra. The distribution peaks show a good agreement to the calculated spectrum. (c) Electron densities in a plane through the center of the dot (color coded to show the shell to which they contribute).

(1)

where Γe,h was included as a perturbative correction to the energy of a combination of states due to their mutual Coulomb interaction. The calculated absorption spectrum for a QD of size 0.6 nm × 13 nm is presented in Figure 4, panel a. This QD size results in a good fitting to the average measured state energies. The sharp black lines represent individual transitions, whereas the smooth gray spectrum has been broadened by 10 meV (corresponding to the resolution limit of our experiment). The shell structure due to the energetic bunching of electron states is apparent (in agreement with previous calculations performed for similar, truncated-pyramid shaped GaN/AlN QDs9,28,29). Each shell has been color-coded and labeled by the symmetry of the constituent electron wave functions, which are shown in Figure 4, panel c for completeness. These excited states are all due to the in-plane confinement of the QD (the next excited state due to vertical confinement would be at a much higher energy owing to the much stronger confinement.) It is clear that the calculated absorption spectrum reproduces the main features of the measured PLE spectra (with the exception of the continuum background, which is not simulated). Upon comparison to the experimentally measured

state energy (shown in Figure 4b), it becomes clear that the calculated energies of the p- and d-shell states match the measured distribution centers of ΔE01 and ΔE02, respectively (the calculated ground state energy of 4.4 eV for this QD also matches very well with the measured distribution of 4.4 ± 0.04 eV). Although the distribution of the experimentally observed higher energy states (ΔE03) is broader, these measured states also show a good agreement with the calculated states, and although the classification of these observed higher energy states into shells becomes difficult due to the smaller energy separation of successive excited states (and also to the larger contribution from the continuum states), it is clear that they are energetically consistent with some f-shell states. C

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the measured distribution of the ground state recombination energy. However, this distribution can be easily explained by changes of less than 10% in either the matrix aluminum content or in the QD height, changes that have very little effect on the excited-state separations. This point is of interest as it could provide a means to tailor the excited- and ground-state energies almost independently if the QD heights and widths could be controlled (a task for which we anticipate nanowires would be particularly suitable). Such control could enable the manufacture of arrays of dots of different widths that are individually sensitive to different wavelengths of light or dots that have excited states at the same absolute energy, but different ground state energies, which would permit the simultaneous quasiresonant pumping of several structures that have different emission wavelengths. In summary, we have investigated the excitonic states of several site-controlled GaN/AlGaN QDs in nanowires and, for the first time, observed the s-, p-, d-, and f-shells in single nanowire dots. In doing this, we provide empirical knowledge on the electronic structure of nanowire QDs in general (that tend to be disc-shaped) and also show experimentally the extent to which variations in the QD size affect the excited-state energies. Moreover, we have made the first observation of the zero-absorption region in a nanowire QD. States existing in this energy region could be candidate levels for exploitation as sitecontrolled qubits for quantum information processing. Further investigation into the continuum states will be necessary to ascertain their true nature and also determine how detrimental they may be for applications such as quantum information processing and for the deterministic generation of single photons.

PLE spectra of single QDs in the literature generally reveal the p-shell (albeit with higher resolution) and sometimes the dshell, but rarely go to higher energy. In the current case, however, the small site-controlled GaN/AlGaN QDs provide favorable conditions for the clear observation of the p-shell, dshell, and even higher energy (including some f-shell) states of single QDs. The site-controlled nature of these dots allows for the clean measurement of single structures, and the small lateral QD size with sufficient confinement (Al0.8Ga0.2N bandgap ∼5.6 eV, GaN bandgap ∼3.5 eV27) leads to an appropriate energy separation of the excited states, which enables their observation in PLE spectra beyond the d-shell. Finally, we comment on the dot-to-dot variation in the excited-state energies and show that this variation can be more or less reasonably explained by dot-to-dot variations in the lateral size. In Figure 5, panel a, we present the calculated

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Present Address

Figure 5. (a) Calculated absorption spectra showing the shift in states as the lateral dimension is varied by ± 5% and ± 10%. (b) The measured distributions of excited states overlaid with all the calculated absorption spectra from panel a, showing that a dot-to-dot lateral size variation of ± 10% is almost enough to explain the experimentally measured variation in excited-state energies.

§

Laboratory for Optical Spectroscopy of Nanostructures, Department of Experimental Physics, Wrocław University of Technology, Poland.

Author Contributions

Optical experiments were performed by M.H., P.P., and S.K. Sample fabrication was performed by K.C. and M.A. The manuscript was prepared with contributions from all authors. Y.A. supervised the entire project.

absorption spectra for dots of width 13 nm, 13 nm ± 5%, and 13 nm ± 10% (the QD height is kept constant for the simulations). Such a variation in width of ± 10% corresponds to the variation that we measure in the nanowire diameters themselves.19 As expected, we see that changing the QD width leads to continuous shifts in the excited-state separations, and from this we can see the range of energies in which we should expect to see the excited states. We directly compare, in Figure 5, panel b, the calculated distribution of spectra with the measured distributions of excited states, which shows that the measured distribution is reasonably described by dot-to-dot variations in lateral size of ∼ ± 10%. Any further deviation from the average for individual dots can be explained by, for example, local anisotropy in the individual dot shapes, which has been theoretically shown to alter the excited-state spectra.28 Such variations will have a larger effect on the higher excited states, whose wave functions are spread closer to the edge of the QD. Interestingly, a 10% variation in QD width alone cannot explain

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, and Technology (MEXT), Japan. The authors further acknowledge fruitful discussions with S. Iwamoto, S. Sergent, Y. Ota, and K. Kamide.

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