NANO LETTERS
Carrier Dynamics and Quantum Confinement in type II ZB-WZ InP Nanowire Homostructures
2009 Vol. 9, No. 2 648-654
Kuranananda Pemasiri,† Mohammad Montazeri,† Richard Gass,† Leigh M. Smith,*,† Howard E. Jackson,† Jan Yarrison-Rice,‡ Suriati Paiman,§ Qiang Gao,§ H. Hoe Tan,§ Chennupati Jagadish,§ Xin Zhang,| and Jin Zou| Department of Physics, UniVersity of Cincinnati, Cincinnati, Ohio 45221-0011, Department of Physics, Miami UniVersity, Oxford, Ohio 45056, Department of Electronic Materials Engineering, Research School of Physical Sciences and Engineering, Australian National UniVersity, Canberra, ACT 0200, Australia, and School of Engineering and Centre for Microscopy and Microanalysis, The UniVersity of Queensland, Brisbane QLD 4072, Australia Received October 2, 2008; Revised Manuscript Received December 23, 2008
ABSTRACT We use time-resolved photoluminescence from single InP nanowires containing both wurtzite (WZ) and zincblende (ZB) crystalline phases to measure the carrier dynamics of quantum confined excitons in a type-II homostructure. The observed recombination lifetime increases by nearly 2 orders of magnitude from 170 ps for excitons above the conduction and valence band barriers to more than 8400 ps for electrons and holes that are strongly confined in quantum wells defined by monolayer-scale ZB sections in a predominantly WZ nanowire. A simple computational model, guided by detailed high-resolution transmission electron microscopy measurements from a single nanowire, demonstrates that the dynamics are consistent with the calculated distribution of confined states for the electrons and holes.
Semiconductor nanowires provide a foundation from which a rich variety of optoelectronic devices may be fabricated,1-5 often by utilizing the ability to incorporate radial or axial heterostructures of different materials (e.g., GaAs/AlGaAs, InP/InAs, GaAsP/GaP). Recently, nanowire growth of many III-V and II-VI compound semiconductors has resulted in NWs with either cubic zincblende (ZB) or hexagonal wurtzite (WZ) crystalline symmetries. In particular, in InP the WZ/ ZB polytypism has been shown to have significant implications for the symmetry of the bandstructure and electronic or optical transitions, as well as a band gap difference between pure WZ and ZB nanowires of 80 meV.6-11 Preliminary investigations have shown that InP nanowires grown along the [1j1j1j] direction can be grown preferentially in either the ZB or the WZ phase, depending on growth conditions including temperature6,7 or V/III ratio.10 The theoretical understanding of these kinetic growth processes has also very recently progressed.12-15 These rapid developments suggest that bandgap engineering in a single material * To whom correspondence should be addressed. E-mail: leigh.smith@ uc.edu. † University of Cincinnati. ‡ Miami University. § Australian National University. | University of Queensland. 10.1021/nl802997p CCC: $40.75 Published on Web 01/26/2009
2009 American Chemical Society
along the axial length of nanowires might soon be possible by varying the crystal symmetry between ZB and WZ with monolayer precision.16 Such homostructures (homo indicating the same material while the bandgap and crystal structures are still modulated) might enable the design of onedimensional materials with extraordinary new properties. Here we explore the carrier dynamics and quantum confinement present in InP nanowires where the WZ structure is punctuated with random 2 to 10 monolayer (ML) sections of ZB structure.. Along with the 80 meV change in bandgap, theoretical considerations17 have suggested a 45 meV band offset between the ZB and WZ phases that results in a staggered type-II band alignment. Thus, the holes are confined to the WZ regions (with 45 meV ZB barriers), while the electrons are strongly confined to the ZB regions with 129 meV WZ barriers. Very recently, several groups have considered the naturally occurring twinning superlattices where ZB-structured nanowires exhibit high densities of 1 ML rotational twin defects with WZ structure and have a notable impact on the power dependence of the continuous wave (CW) photoluminescence emission spectra.18,19 In this letter, we use CW and time-resolved photoluminescence of single ZB/WZ nanowire homostructures to explore the effect of electron and hole confinement on carrier relaxation and
recombination. We find that the spatially indirect type-II band alignment coupled with strong confinement of the electrons and holes results in a large 130 meV range for recombination of confined electron and hole states, as well as a two-orders of magnitude change in the recombination lifetime with energy. Detailed structural information obtained from high resolution transmission electron microscopy (HRTEM) is utilized to guide calculation of electron and hole confined states over a microscopic region of a real InP ZB/WZ nanowire. We find that the structure of these confined states, as well as the existence of above-barrier continuum electron and hole states, explains well the remarkable dynamics observed in these single WZ/ZB homostructured nanowires. The results reported here provide a window into the new opportunities that become possible with the ability to control these nanowire crystalline structural modulations with monolayer precision. Such nanowire homostructures potentially open up a large phase space for designing novel onedimensional structures for novel electronic and photonic applications. Experimental Results. The InP nanowires were synthesized by using a horizontal flow metalorganic chemical vapor deposition (MOCVD) reactor operating at 100 mbar with hydrogen as the carrier gas. Au nanoparticles of 50 nm diameter acted as a catalyst for growth on an InP (111)B surface. The V/III ratio of phosphine (PH3) to trimethylindium (TMIn) was 700 and the growth proceeded at a temperature of 400 °C for 20 min. A scanning electron microscope (SEM) micrograph, Figure 1a, shows a dense selection of nanowires 8-10 µm long that exhibit slight tapering of 9 nm/µm and have tip diameters of 58-65 nm. In Figure 1b, we display an HRTEM image of the growth end of a nanowire where the gold catalyst can be seen on the far right. Figure 1(c) is a magnified view of a section of the nanowire where one observes atomic planes of both the WZ and ZB crystal structures. The ZB structured nanowire sections are identified by white dashes labeled with the number of atomic planes included in each section. The transition between WZ and ZB occurs from one ML to the next. Similar HRTEM micrographs map such information over a 660 nm length of the nanowire and enable calculation of electron and hole energy eigenstates for this nanowire. Figure 1d illustrates the band diagram that results using the known band gaps and offsets for ZB and WZ InP.6-9,17 We see that the potential wells for the electron are nearly three times as deep as for the holes and that the adjacent ZB and WZ sections create a type II staggered band alignment; a spatially indirect transition from an electron confined in the ZB potential well to a hole confined in the WZ structure is illustrated. The type-II band alignment between the WZ and ZB sections of InP should have a dramatic impact on the optical properties of the nanowires. In addition, one can see that the top of the barriers for holes to the top of the barriers for electrons is 1.545 eV, which defines the energy above which no confined states are possible, namely the continuum. For optical experiments, the nanowires are removed from the InP substrate and dispersed onto a silicon substrate which has an array of alignment marks. An optical microscope is Nano Lett., Vol. 9, No. 2, 2009
Figure 1. (a) SEM micrograph of InP nanowires each 8-10 µm long; (b) HRTEM of a nanowire showing the gold catalyst nanoparticle on the far right; (c) expanded version of panel b with the ZB sections identified with the white dashes and the number of atomic planes; (d) the band energy diagram and alignments corresponding to the structure indicated in panel c.
used to map the position of nanowires across the substrate, so that the same nanowire can be studied repeatedly over a period of time. The substrate with the dispersed nanowires is fixed to the coldfinger of a continuous flow liquid helium cryostat, and the nanowires are imaged through a thin fused silica window using a long working length 50X/0.5NA microscope objective. The nanowires are excited using a CW or pulsed (200 fs) Ti:sapphire laser at 780 nm (1.59 eV) that is focused to a 2 µm spot onto the nanowire. The emitted photoluminescence (PL) is collected through the same microscope objective and a 100× image of the nanowire is projected onto the entrance slit of a 250 mm spectrometer for detection by a cooled 1024 × 125 pixel CCD camera. 649
Figure 2. (a) Normalized PL spectra showing shift in peak energy as power increases by a factor of 44 from P0 ) 50 µW. (b) Squares show peak energies extracted from PL spectra as a function of power.
Time-resolved measurements were made using either a fast microchannel plate phototube on the same 250 mm spectrometer or an avalance photodiode (APD) mounted to a 1000 mm spectrometer. Time-resolved measurements were obtained using time-correlated single photon counting with 80 ps resolution. CW microphotoluminescence (µ-PL) measurements were carried out on more than 10 separate nanowires at 15K. All the InP NWs exhibit extremely strong and efficient emission. Typical power-dependent CW PL measurements for an individual nanowire are displayed in Figure 2a. The peak intensity of each of the spectra is normalized to the same value. All other nanowires displayed similar results. A distinctive blue shift of nearly 80 meV is observed as the power is varied by a factor of 40. One observes emission near the expected ZB band gap emission (1.42 eV) at low powers and emission near the WZ band gap emission (1.50 eV) at higher powers. Similar blueshifts were recently seen in an InP ZB nanowire that had many rotational twins.19 This strong power dependent shift in the PL emission energy is not observed in InP nanowires which exhibit only the WZ or ZB structure.19,20 Figure 2b displays the peak energy position of the CW µ-PL spectra versus power which reveals that band filling of the lower energy states is occurring at higher powers where the photoexcited electron-hole density is larger. Time-resolved PL (TRPL) measurements are an important tool for capturing in a single experiment how the emission from the nanowire changes as the electron-hole pair density changes over orders of magnitude. Figure 3 displays a timeresolved spectrum collected using the APD and the 1000 mm spectrometer for one nanowire after excitation by a 200 fs pulse at 1.59 eV (780 nm). Figure 3a is a false-color image spectral map where the vertical axis shows time after the 650
Figure 3. (a) Time-resolved photoluminescence spectral map. The intensity (on a logarithmic false color scale) vs time (vertical scale) and energy (horizontal scale) is displayed; (b) individual time slices from (a) displaying the evolution of the spectra from 100 to 4500 ps. The relevant energy positions for ZB, WZ, and the continuum are noted.
laser excitation pulse, and the horizontal axis shows the emission energy of the collected photons. The color mapping is on a logarithmic scale. Figure 3b shows single normalized spectra extracted from the time-resolved map on a linear scale. The spectral evolution with time is remarkable as shown in both the spectral map and the individual spectra as a function of time. For reference, we show the energy positions of the ZB (1.42 eV) and WZ (1.50 eV) band edges, as well as the continuum states (above 1.545 eV). At the earliest times, we see a peak at ∼1.545 eV, nearly 45 meV above the emission expected for pure WZ structured InP nanowires and consistent with where we expect the continuum of electron and hole states to exist for this type-II homostructure. As time progresses, the emission peak moves within the first nanosecond to just below the WZ edge, and then gradually falls to longer wavelengths, reaching 1.43 eV just before the next laser pulse arrives. During the lifetime of the electron hole pairs, the spectral peak shifts by more than 100 meV. This remarkable shift in the peak emission energy with time is a direct reflection of a dramatic change in the exciton dynamics with energy. In Figure 4, we show a series of timedecays accumulated from a different NW than shown in Figure 3 (all measured NWs exhibit similar behavior to that shown in Figure 3 and 4) at different energies with the fast MCPT detector and the 250 mm spectrometer. Considering the band alignments shown in Figure 1d, we can identify three relevant energy scales for this homostructured NW: (i) near the ZB band edge at 1.42 eV, Figure 4a; (ii) near the WZ band edge at 1.5 eV, Figure 4b, and (iii) near the continuum 45 meV (the band offset) above the WZ band Nano Lett., Vol. 9, No. 2, 2009
Figure 4. Time-decays of photoluminescence for energies (a) near the ZB band edge, (b) near the WZ band edge, and (c) near the continuum. Note the very long lifetimes displayed in panel a, the complex decay displayed in panel b, and the very fast relaxation in panel c.
edge, or 1.545 eV, Figure 4c. In the detailed time-decays shown in Figure 4, we see quite different behavior in these three regions. In region (iii), Figure 4c, the time decays are single exponential with recombination lifetimes of 175 ps at an energy of 1.56 eV, increasing to 220 ps at 1.54 eV. As the energy moves closer to the WZ band edge region (ii), Figure 4b, recombination decays distorted by significant filling of carriers from higher energies are observed. This behavior is signified when the early time decay exhibits a slower decay than is observed at longer times. Nonetheless, at late times the final decade of the decay is still single exponential, with decay times increasing to 700 ps by the WZ band edge of 1.5 eV. In region (iii), Figure 4a, no significant filling is observed, but the decays are nonexponential at the earliest times: short decays initially, followed by longer decays at later times. At late times, the decay becomes single exponential with a lifetime that increases rapidly with energy up to 8400 ns at 1.433 eV. Indeed, comparing the shortest observed decays (∼175 ps) to the Nano Lett., Vol. 9, No. 2, 2009
longest observed decays (∼10 ns) we see that the recombination lifetime increases by more than a factor of 50. For a single phase ZB nanowire, time-resolved PL is single exponential with a recombination lifetime of the exciton at 15 K of ∼1 ns.20 The fact that lifetimes at the highest energies are an order of magnitude less than this value indicates that the recombination dynamics is most probably limited by capture to lower energy states, while the much longer lifetimes seen at the lowest energy reflect the type-II indirect band alignments between the ZB and WZ sections of InP nanowire. Model. As discussed previously, we have used HRTEM to image an extended section of an ∼8 µm InP NW taken from the same part of the substrate as the wire measured optically here. This section extends 657 nm from the gold nanoparticle (the first portion of the nanowire grown) and was predominantly a WZ structure with over 150 sections of ZB ranging from 2 to 10 MLs occurring singly or in clusters. The average size of the ZB inclusions was 2.7 MLs with ∼22% of the InP NW having the ZB structure and thus 78% having the WZ structure. Because the effective masses of the electrons and holes in the InP’s WZ structure are not known, we assume for calculations a uniform ZB InP effective mass of 0.58 me for the heavy holes, and 0.073 me for the electrons through the entire NW. As discussed by Mishra et al. this approximation appears to be reasonable because the exciton in pure WZ or ZB structured NWs ionize at approximately the same temperature and thus the binding energy must be similar.7 In order to solve this specific structure for all possible bound states, we measure the width and position of the ZB sections (electron wells and hole barriers) and WZ sections (hole wells and electron barriers) from the HRTEM images. We then solve the Schro¨dinger equation for these one-dimensional potentials by using the method of eigenfunction expansion. To do this, we assume the potentials are contained inside an infinite 657 nm wide quantum well and approximate the wave function as a sum of 400 particle in a box wave functions. The solution for the actual potential distribution is determined by finding the eigenvalues and eigenvectors of the resulting 400 × 400 matrix for the electrons and a similar one for the holes. The calculation is exact except for the very small numerical error made by truncating the infinite set of wave functions. We find that there are only 45 bound states for the electrons and 150 bound states for the holes. Figure 5b shows the variation of bound state energy for the electrons and holes versus quantum number (1 to 45 for the electrons, and 1 to 150 for the holes). In Figure 5 we show on a twodimensional plot the position and energies of these bound states for the electrons (upper plot, Figure 5a) and the holes (lower plot, Figure 5c). The vertical position of a state indicates the energy of the electron within the wells (of depth 129 meV) and the energy of the hole within the barriers (of height 45 meV) for the holes. The horizontal width of each state is a measure of its spatial extent. At the lowest energies, both the electrons and holes are quite localized but become much less so at higher energies. The lowest ground-state for 651
Figure 6. Calculated wave functions for electron energy state number 18 along with hole states with numbers 6, 32, 43, 47, and 65. The arrows pointing to the TEM micrograph at the bottom give an indication of where these states have originated spatially.
Figure 5. The energies of the bound states versus position along the nanowire for electrons (a) and holes (c). The spatial extent of these states are qualitatively represented by the widths of the horizontal lines for each energy state. (b) The variation with energy of the bound states versus state number for the electrons (1-45) and holes (1-150).
the electrons is fully 50 meV above the bottom of the 129 meV potential well, which reflects both the small effective mass of the electrons in InP as well as the monolayer widths of the ZB sections of the NW. On the other hand, the lowest bound state of the holes is only 2 meV above the bottom of the WZ valence band edge for the widest continuous WZ section (8.4 nm) with many closely spaced excited states within this same wide section. The much smaller WZ sections exhibit a lowest bound state that is quite high above the bottom of the hole band. In Figure 6, we display explicit wave functions as a function of position along the NW for one specific electron bound state as well as several hole states that have some overlap with this electron state. The 18th electron bound state wave function is shown in blue, which has an energy 37.4 meV below the top of the electron quantum. The position of the same wave function is noted by the box shown in Figure 5a as well. This state is strongly spatially localized to a section of five separate ZB sections as can be seen in the HRTEM image at the bottom of Figure 6. For optical recombination, what is important to consider is not all possible hole states, but only those which show significant spatial overlap with the 18th electron state. To do this, we have calculated the 9600 squared overlap integrals, 〈Ψe|Ψh〉2, between all 45 electron states and 129 hole states. Each wave function is properly normalized so that 〈Ψ|Ψ〉 ) 1. The vast majority of hole states show no 652
overlap whatsoever with the 18th electron state, but 8 hole states have an overlap, 〈Ψe|Ψh〉2, of greater than 0.02 The largest overlap integral for the 18th electron state occurs with the 65 hole state and is 〈Ψe|Ψh〉2 ) 0.6. The red plots in Figure 6 show a number of these hole states, in order of their energy, which occur on either side of the ZB sections which localize the electron. These same wave functions are shaded in black in Figure 5c. In general, the lower energy hole states show less overlap with Ne ) 18, while higher energy holes show more overlap. For a given electron state, the emission energy is reduced for the more confined hole states. Thus our expectation is that lower energy states should result in less electron-hole wave function overlap and thus longer lifetimes. Discussion. In Figure 7 we plot the measured recombination lifetime extracted from the time decays as shown in Figure 4 of a single NW (black squares) as a function of energy. The (exponential) increase in the observed recombination lifetime at lower energies is remarkable. To make a comparison with the calculated set of bound states, we make the assumption that the overlap integral squared is proportional to the recombination rate: 〈Ψe|Ψh〉2f02 ) 1/τ. Since the continuum (1.545 eV) is determined by energy from the top of the hole barriers (ZB valence band) to the top of the electron barriers (ZB conduction band), the emission energy for a particular set of states is just 1.545 eV + Ee + Eh. To determine an appropriate lifetime from the distribution of electron and hole bound states, we compute the average overlap integral squared for all electron-hole pairs which emit within a particular energy range and adjust f0 (the only fit parameter) to minimize the χ2 of the fit to the data. The resulting recombination lifetime is calculated as τ(ε) ) 1/(f02∑〈Ψe|Ψh〉2/N) where one sums over all N sets of pairs of e-h states within a particular energy range centered around ε. This procedure fails at energies Nano Lett., Vol. 9, No. 2, 2009
Figure 7. The measured recombination lifetimes extracted from TRPL measurements on a single nanowire are plotted as a function of energy (red squares). The results of a simple model calculation are also plotted (blue circles). The squares and circles are connected by lines for ease of viewing.
higher than 1.5 eV because the hole wave functions oscillate too rapidly to yield any appreciable overlap with the localized electrons without including the Coulomb attraction between the electron and hole, which is beyond the scope of this simple model calculation. In addition, energies above 1.5 eV allow transitions between localized holes and electrons in the continuum. For energies below 1.5 eV, this simple model (blue circles) reflects the measured lifetimes as seen in Figure 7 where the average electron-hole overlap decreases at lower energies and the lifetimes increase dramatically. Through examination of the bound electron and hole states in Figure 6 and the overlap integrals reflected in Figure 7, nearly all aspects of the time-decays shown in Figure 4 can be understood qualitatively. In regions (i) and (ii) for emission energies between 1.42 and 1.5 eV, recombination is possible only between bound electrons and bound holes. For e-h pairs that emit within a particular energy range, a wide variety of overlap integrals are calculated, and so the nonlinear (or multiexponential) behavior of the time-decays is observed. Those states that exhibit large overlap decay more rapidly, leaving states which exhibit smaller and smaller overlap to decay later. The lower energy states have more weakly overlapping electron and hole states, which is why they exhibit the longest lifetimes. For emission energies between 1.5 and 1.545 eV, two types of emitting states are possible: recombination between bound electron and hole states, or recombination between bound hole states and electrons in the continuum. From the model it is clear that there are nearly 3 times as many hole states as there are electron states. Once the electron states are saturated, there will still be many empty and available confined hole states. For emission energies greater than 1.545 eV, region (iii), both the electron and hole are unconfined. The laser excitation at 780 nm creates excitons in the electron-hole continuum. Some of the excitons rapidly relax through optic phonon emission into confined electron and hole states within the first few picoseconds. However, once the electron states are filled, the only relaxation mechanism for excitons is to first confine the hole into a deeply confined state through optic phonon emission, or through a cascade of hole states Nano Lett., Vol. 9, No. 2, 2009
through slower acoustic phonon emission. This cascade of relaxing holes that leaves the electrons in the continuum are seen as the feeding phenomena, which is observed in the decays of Figure 4b. The extremely short lifetimes observed in region (iii) occur because of the efficient capture of holes into the many available hole confined states. Summary. We have shown that the electron-hole pair dynamics are strongly affected by the type-II nature of the WZ/ZB band offsets in InP. Clear evidence for quantum confinement of holes to the WZ sections and electrons to the ZB sections is seen, which results in extraordinary long-lived states at low energies and shorter lifetimes at higher energies where the electron and hole wave functions begin to penetrate the barriers. Rapid capture of excitons in the conduction and valence band continua to bound states at lower energies is observed. A simple model calculation of the electron and hole wave functions provides their energies and wave function overlap. The calculated lifetimes are in reasonable agreement with the measured lifetimes over more than an order of magnitude. This result points toward the significant opportunities that exist to manipulate electron and hole wave functions in homostructured semiconductor nanowires in order to control their dynamics and energies. Acknowledgment. Both K.P. and M.M. are equally responsible for this work. The U.S. authors acknowledge the financial contributions of the National Science Foundation through Grants DMR 0806700, EEC/NUE 0532495, and ECCS 0701703. The Australian authors acknowledge support from the Australian Research Council. The Australian National Fabrication Facility established under Australian government NCRIS program is acknowledged for access to the facilities used in this work. References (1) Thelander, C.; Agarwal, P.; Brongersma, S.; Eymery, J.; Feiner, L. F.; Forchel, A.; Scheffler, M.; Riess, W.; Ohlsson, B. J.; Gosele, U.; Samuelson, L. Mater. Today 2006, 10, 28–35. (2) Borgstrom, M. T.; Zwiller, V.; Muller, E.; Imamoglu, A. Nano Lett. 2005, 7, 1439–43. (3) Patolsky, F.; Zheng, G.; Lieber, C. M. Anal. Chem. 2006, 13, 4260– 4269. (4) Tian, B. Z.; Zheng, X. L.; Kempa, T. J.; Fang, Y.; Yu, N. F.; Yu, G. H.; Huang, J. L.; Lieber, C. M. Nature 2007, 7164, 885-U8. (5) Barrelet, C. J.; Greytak, A. B.; Lieber, C. M. Nano Lett. 2004, 10, 1981–1985. (6) Mattila, M.; Hakkarainen, T.; Mulot, M.; Lipsanen, H. Nanotechnology 2006, 6, 1580–3. (7) Mishra, A.; Titova, L. V.; Hoang, T. B.; Jackson, H. E.; Smith, L. M.; Yarrison-Rice, J. M.; Kim, Y.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C. Appl. Phys. Lett. 2007, 26, 263104–3. (8) Pettersson, H.; Tragardh, J.; Persson, A. I.; Landin, L.; Hessman, D.; Samuelson, L. Nano Lett. 2006, 2, 4. (9) Taagardh, J.; Persson, A. I.; Wagner, J. B.; Hessman, D.; Samuelson, L. J. Appl. Phys. 2007, 12, 123701. (10) Mohan, P.; Motohisa, J.; Fukui, T. Nanotechnology 2005, 12, 2903– 2907. (11) Reitzenstein, S.; Munch, S.; Hofmann, C.; Forchel, A.; Crankshaw, S.; Chuang, L. C.; Moewe, M.; Chang-Hasnain, C. Appl. Phys. Lett. 2007, 9, 091103–3. (12) Dubrovskii, V. G.; Sibirev, N. V. Phys. ReV. B 2008, 3, 8. (13) Akiyama, T.; Nakamura, K.; Ito, T. Phys. ReV. B 2006, 23, 2353081-6. (14) Akiyama, T.; Sano, K.; Nakamura, K.; Ito, T. Jpn J. Appl. Phys., Part 2 2006, 8-11, L275-8. 653
(15) Glas, F.; Harmand, J. C.; Patriarche, G. Phys. ReV. Lett. 2007, 14, 4. (16) Algra, R. E.; Verheijen, M. A.; Borgstrom, M. T.; Feiner, L. F.; Immink, G.; van Enckevort, W. J. P.; Vlieg, E.; Bakkers, E. Nature 2008, 7220, 369–372. (17) Murayama, M.; Nakayama, T. Phys. ReV. B 1994, 7, 4710–4724. (18) Xiong, Q. H.; Wang, J.; Eklund, P. C. Nano Lett. 2006, 12, 2736– 2742.
654
(19) Bao, J. M.; Bell, D. C.; Capasso, F.; Wagner, J. B.; Martensson, T.; Tragardh, J.; Samuelson, L. Nano Lett. 2008, 3, 836–841. (20) Titova, L. V.; Hoang, T. B.; Yarrison-Rice, J. M.; Jackson, H. E.; Kim, Y.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C.; Zhang, X.; Zou, J.; Smith, L. M. Nano Lett. 2007, 11, 3383–3387.
NL802997P
Nano Lett., Vol. 9, No. 2, 2009
