Femtosecond Laser Induced Resonant Tunneling in an Individual Quantum Dot Attached to a Nanotip
Maxime Duchet, Sorin Perisanu, Stephen Purcell, Eric Constant, Vincent Loriot, Hirofumi Yanagisawa, Matthias Kling, Franck Lepine, Anthony Ayari
aa r X i v : . [ c ond - m a t . m e s - h a ll ] F e b Femtosecond laser induced resonant tunnelingin an individual quantum dot attached to ananotip
Maxime Duchet, † Sorin Perisanu, † Stephen T. Purcell, † Eric Constant, † VincentLoriot, † Hirofumi Yanagisawa, ‡ Matthias F. Kling, ‡ , ¶ Franck Lepine, † and AnthonyAyari † † Univ Lyon, Univ Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622,VILLEURBANNE, France. ‡ Department of Physics, Ludwig-Maximilians-Universität Munich, Am Coulombwall 1,85748 Garching, Germany. ¶ Max Planck Institute of Quantum Optics. Hans-Kopfermann-Straße 1, 85748 Garching,Germany
Abstract
Quantized nano-objects offer a myriad of exciting possibilities for manipulating elec-trons and light that impact photonics, nanoelectronics and quantum information. Inthis context, ultrashort laser pulses combined with nanotips and field emission havepermitted to renew nano-characterization and control electron dynamics with unprece-dented space and time resolution reaching femtosecond and even attosecond regimes. Acrucial missing step in these experiments is that no signature of quantized energy levelshas yet been observed. We combine in situ nanostructuration of nanotips and ultra-short laser pulse excitation to induce multiphoton excitation and electron emission from single quantized nano-object attached at the apex of a metal nanotip. Femtosecondinduced tunneling through well-defined localized confinement states that are tunable inenergy is demonstrated. This paves the way for the development of ultrafast manipu-lation of electron emission from isolated nano-objects including stereographically fixedindividual molecules and high brightness, ultra-fast, coherent single electron sources forquantum optics experiments. Keywords field emission, ultra fast dynamics, nanotip, resonant tunneling, quantum dotRecent experimental developments in electron sources using metallic nanometric tips andultrashort laser pulses have given a new impulse to nano-characterization instruments such astime resolved scanning tunneling, scanning near-field-optical, point projection or trans-mission electron microscopes by improving the observation of spatiotemporal processes atthe subnanometric and subfemtosecond scale or in the quantum regime. These sources andinstruments give complementary information to well-established ultrafast electron diffrac-tion techniques on homogeneous materials and thin films but more importantly open newscientific pathways into the exploration and exploitation of quantum systems.Ultrafast field emission sources driven by coherent laser pulses play a central role inunraveling the pertinent high field physics and achieving ultimate source characteristics.The interaction between a nanotip and an intense laser pulse has led to the observation ofmultiphoton emission, above threshold ionization and electron rescattering plateaus in theenergy distribution of the emitted electrons.
Until now the experiments were performedfor field emitters with a continuum electron energy density. However, the large number ofelectron energy levels involved in these promising demonstrations of ultrafast phenomenashould limit coherent control strategies and their interpretation in general. Consequently,it can be expected that working with smaller emitters, preferentially minimally interactingwith a support tip, will strengthen quantum mechanical effects and open new avenues in2lectron manipulation.Downsizing metallic emitters has already been pushed almost to its limit. Remarkableresults were obtained on ultra sharp emitter down to 10 nm radius for tungsten (W)and gold tips. An experiment on a "single atomic emitter", was even briefly mentionedin ref. 14, but no significant change compared to larger tips was observed. Studying thephotoemission of an isolated object with well-separated energy states requires to attachnano-objects with an electronic structure that is preserved from strong interaction with themetallic tip. The interaction between an ultrashort laser pulse and a plasmonic nanostruc-ture has attracted much attention in the ultrafast community, allowing to study individualnano-objects deposited on a surface and recently attempts to study femtosecond fieldemission on individual free standing nano-objects on tips have emerged for instance on goldnanorods, carbon nanotubes and diamond nano-needles but no signature of quan-tized energy levels has yet been reported. In Ref. 25 a quantum dot was coupled to a metallicnanowire but fluorescence emission was studied and not photoemission.For field emitters, a quantum dot ( i.e. a nanometric object weakly coupled to the electronreservoir of the tip via a tunnel barrier and showing discrete electron energy levels) can beeasily fabricated by in situ nanostructuration. Although the exact chemical compositionof these quantum dots is still an open question (see Supporting Information I.G.), it appearsthat their properties do not depend on the tip material nor its exact fabrication method.They all show electron energy spectrum with individual energy peaks below the Fermi energyand specific electric field dependence (see below). However, their energy levels above theFermi energy has never been probed experimentally and these quantum dots were neverstudied under laser illumination. In this article, we propose to use such individual quantumdots for field assisted photo-emission in order to show femtosecond laser induced resonanttunneling through quantized energy levels. This new process opens opportunities in thestudy of ultrafast electron dynamics in individual nano-objects.3igure 1: Schematic of the ultra-fast beam-line (OAP : Off-Axis Parabolic Mirror, pola: polarizer, λ/ : half-wave plate, FROG : Frequency-resolved optical gating) and fieldemission set-up in an ultra high vacuum chamber (V c : cathode voltage, V e extractionvoltage, EA : Extraction anode, MCPs : microchannel plates, PS : phosphor screen) forelectron energy analysis with retarding field hemispherical grids (HG) with grid voltage V g and a bias voltage V b (see Supporting Information I.E).4 n situ nanostructuration and field emission characteriza-tion of the nano-ob ject The experimental system illustrated in Figure 1 is a standard field emission set-up withan ultra-high vacuum chamber ( × − Torr) an electrochemical etched < > tungstentip cathode at a negative voltage, an extraction anode at a positive voltage and a retardingfield analyzer. The DC voltage reported below is the voltage difference between the anodeand the tip. A Ti:sapphire laser oscillator (80 MHz repetition rate, a photon energy hν = µ m waist) can be focused to the apex of the tungstennanotip. We captured the emitted electrons with a two-stage microchannel plate, a phosphorscreen and a camera to get the spatial distribution, and a retarding field analyzer with lock-in detection to characterize the electron energy distributions (see Supporting Information I). In situ nanostructuration was performed in order to grow in ultra-high vacuum conditionsan individual nano-object at the apex of the tip. This growth method is a two steps processsimilar to methods developed in the past and is described in detail in SupportingInformation I.G. The first step leads to the formation of a ”buildup” tip and the secondconsists in emitting electrons at 100 nA current for 10 minutes.Figure 2a presents the electron energy spectra and the emission patterns after the nano-object growth. The standard three fold rotational symmetry pattern of a clean W < > tip has been replaced by a single spot at the center of the screen. The applied DC voltagerequired to have a given current is twice smaller for the nano-object. The electron energyspectra obtained after growth consist of a peak with a maximum at an energy significantlylower than the Fermi energy ( E F ) of the tip and this peak shifts down linearly with theapplied voltage as shown in Figure 2b. This behavior is notably different from the volt-age dependence of the spectra obtained in the case of metallic nanotips (see SupportingInformation I.H. for the pattern and energy spectra of the W tip before the nano-objectgrowth). 5igure 2: (a) Experimental energy spectrum of the emitted electrons from a nanostructuregrown on a W < > tip for different applied DC voltages. The vertical line representsthe position of the Fermi energy inside the tip. Left inset: field emission pattern of ananostructure. (b) Energy shift of the maximum of the energy peak in (a) as a function ofthe applied voltage. The line is a fit of the experimental data. (c) Calculated energy banddiagram of the quantum dot attached to a metallic tip for different applied DC voltages.The horizontal line represents the position of E F inside the tip. The horizontal dashed linesrepresent the position of the emitting level in the quantum dot for different applied DCvoltages. 6n field emission a linear shift of the energy peak with the voltage is a signature ofan electron emission process from quantized energy levels that is described by a resonanttunneling model. Resonant tunneling through a single nano-object on a field emissiontip has been experimentally demonstrated for deposited molecules, atoms, clusters oras here for quantum dots in situ nanostructured on sharp metallic tips. The main featuresof this model can be reproduced by the simple and universal potential profile shown inFigure 2c where the triangular tunneling barrier is modified by the presence of a quantumdot potential. The down shifts of the peak are due to the poor screening of the externalelectric field by the quantum dot and are proportional to the distance between the dot andthe metallic tip. Femtosecond excitation of an individual nano-ob ject
We studied several different individual in situ fabricated quantum dots for different DCvoltages and different laser intensities (from 0 to 320 GW/cm nominal peak laser intensity,corresponding to 150 mW average laser power). The data presented in the following arefrom the same nano-object. Supporting Information I. H. shows results for a clean W tipwith identical laser intensities, similar results on other quantum dots are shown in Support-ing Information II and additional data analysis of this sample can be found in SupportingInformation III but are not essential for the understanding of the photoemission mechanism.Figure 3a shows a typical electron energy spectrum as a function of the laser intensityfor a fixed voltage which has a well-defined peak position E at zero laser power. Uponexcitation by the laser, an additional peak appears at an energy E = 2 . eV. It is importantto notice that our measurements are a superposition of i) electrons continuously emittedbecause of the DC voltage and ii) laser excited electrons that are emitted during or shortlyafter the laser pulse. The E peak is mostly emitted due to the DC field and it is difficultto estimate if its intensity changes come from the laser or from long term fluctuations. In7ontrast, the part of the spectrum above the Fermi energy comes from electrons emitted dueto the laser pulse. Moreover, the instantaneous electron current at these energies is orders ofmagnitude larger than a comparable peak in the DC part of the spectrum. For a standardmetallic tip, peaks at multiples of hν above E F are expected. Here the high energy peakposition is clearly in between two expected values for laser powers below 50 mW (between hν and hν above E F ). Figure 3c shows the evolution of the positions of the principal peaks fordifferent laser powers. It can be noticed that the peak positions are rather constant and theenergy difference between E and E is close to but somewhat less than hν . The integratedcurrent of the additional peak E shown in Figure 3d has a power law dependence with laserpower with an exponent of 2.8. This exponent can range from 1.5 to 4 depending on theapplied voltage or nano-object studied.Control experiments were carried out after removal of the nano-object by heating the tipat a temperature above 1000 K: i) it showed no emission at this DC voltage and laser powerrange ii) it recovered the emission characteristic of the tip before the nano-object growth.iii) the shape of the spectrum of the tip excited at an identical laser intensity as the quantumdot and identical total emitted electrons is different (see Figure S9b). This means that inthe presence of the quantum dot, the extracted electrons travel only through the quantumdot, although the laser size and the tip area are much larger than the quantum dot. Thefield enhancement factor of the DC and laser field and the resonance of the quantum dotstrongly counterbalance the small size of the nano-object.For low applied voltage (see in Figure 4a) a clear electron emission from E is observedwhile the emission from E cannot be detected. As the voltage is increased, emission from E occurs and becomes dominant and another peak appears at an intermediate energy E .This intermediate peak is also in between two expected values (between E F and E F + hν )strongly indicating that a different process takes place compared to W emitters. Comparedto previous studies on photoemission of nanotips, our in situ nanostructured photoemittershows a drastically different dependence of the electron energy spectrum on DC voltage: for a8igure 3: (a) Experimental energy spectrum of the emitted electrons from a quantum dotfor different femtosecond laser intensities (0, 4, 10, 21, 106 GW/cm ) and a fixed appliedvoltage of 290 V. The vertical line represents the position of E F inside the W tip. The verticaldotted line indicates an emission energy hν above E F . The vertical dashed line indicatesan emission energy hν above E F . (b) Simulated energy spectrum of the emitted electronsfrom a quantum dot for different femtosecond laser powers. Inset: energy band diagram ofthe tunneling barrier for field emission with a quantum dot. (c) Energy E (square) and E (circle) of the peak maxima and their energy difference (triangle) as a function of the laserpower. (d) Integrated current of the peak E as a function of the laser power. The solid lineis a fit of the experimental data. n is the slope of the linear fit9xed laser power, the peaks E , E and probably E shift linearly with DC voltage as shownin Figure 4c. In tungsten tips, it was only for the E peak that some displacements havebeen observed and this behavior originated from a mixing between the barrier loweringdue to the Schottky effect and the hν peak. The E and E peak positions are always fixedfor tungsten.The appearance of E for a voltage above 290 V might seem intriguing but is simplyexplained and has already been observed in the past in the absence of laser excitation. At low voltage the E state is weakly populated because it is above E F . Its energy is toohigh to be sufficiently filled by electrons from the Fermi sea and too low to have a smalltunnel barrier that allows promoted electrons by a photonic process to be emitted. The factthat the E and E peaks are not at the expected multiphotonics energies and shift withvoltage indicate that these peaks come from the excited energy levels of the quantum dotas represented in the inset of Fig. 3b. The energy shift allows to tune the energy differencebetween electronic levels.Fig. 4d shows that the intensity of the three peaks has an exponential dependence withthe applied voltage as expected for tunneling over a small voltage range. The slopes inFig. 4d decrease with the order of the peaks in agreement with the idea that the higherthe energy of a peak the lower the barrier height. Remarkably, despite the fact that thequantum dot is weakly bound to the nano-tip it maintains its quantized signature in theelectron spectrum even upon laser excitation. Only minor instabilities related to flip-flop can be noticed above 10 mW and features can momentarily shift or even disappear in somemeasurements and automatically reappear. It indicates that the quantum dot can maintainits essential features even at high laser power and it does not lead to a sudden destructionof the tip as usually happens for unstable field emitters. As any clean field emitter in ultra-high vacuum, some modifications of the emitter occur on a time scale of an hour duringwhich our experiments are performed. Fluctuations of the quantum dots can lead to slightdisplacement of the energy peaks less than 0.2 eV which can have a visible influence on the10eak shapes close to the Fermi Energy as observed in ref. 40.Figure 4: (a) Experimental energy spectrum of the emitted electrons from a quantum dot fordifferent voltages at a fixed laser power of 10 mW (21 GW/cm ). The vertical line representsthe position of E F inside the W tip. The vertical dotted (respectively dashed) line indicatesan emission energy hν (respectively hν ) above E F . (b) Simulated energy spectrum of theemitted electrons from a quantum dot for different fields. (c) Energy E (square) and E (circle) of the peaks maximum as the function of the applied voltage at a fixed laser powerof 10 mW (21 GW/cm ). The solid lines are a fit of the experimental data. (d) Integratedintensity of the three peaks as a function of the laser power. The solid line is a fit of theexperimental data. s , s and s are respectively the slopes in V − of the linear fit for E , E , and E . Interpretation of the photoemission process
A first interpretation of the laser induced photoemission process would be to consider thedirect photoexcitation of the quantum dot followed by electron emission. The measuredvalue of E − E that happens to be near hν could be interpreted as a 2-photon absorptionprocess from the filled resonant energy level E as observed for instance for Shockley surface11tates in Ref. A first argument against the two photon excitation process can be madeby examining the lower voltage curves in Figure 4a for which E is not present. Thus noelectrons are present to be excited to E which is in contradiction with the fact that the E peak is present in the spectra. To go further consider the time to refill the quantum dotenergy level from the Fermi sea of the W tip. It is inversely proportional to the energy widthof the peak ( < . eV) and hence is greater than 1 fs. The electron emission would notexceed roughly 10 electrons per pulse. Experimentally, we never observed a saturation of thecurrent from E in the high current regime as shown by the linear fit for the power law inthe data in Figure 3d and in Supporting Information II A for another quantum dot at higherlaser power Figure S.8. Moreover, the two photon cross section defined as σ = I τef ( hνfπw P ) ,where I is the integrated electron intensity for the peak centered at E , τ the pulse duration, e is the electron charge, f the laser repetition rate, hν is the photon energy, w the laser waistand P the laser power, has a value in the GM range (Supporting Information III D).Such a high value can be observed in large quantum dots and is orders of magnitude abovethe highest values reported in quantum dots of the same size ( i.e. between 1 and 2 nm asshown in the simulations below). This implies that the direct photo-excitation of an electronfrom the quantum dot is unlikely.We propose a different mechanism which is that emission comes from electrons originallyexcited by the laser in the W tip. These electrons then preferentially tunnel through theexcited states of the quantum dot to be emitted into the ionization continuum. As the tipis much larger than the quantum dot and has a much larger number of available electrons,a cross section several orders of magnitude larger than for a quantum dot is expected. Thisprocess is a combination of the resonant tunneling process observed in field emission and the photoemission process observed in ref. In our case, it offers the possibility to haveaccess to the electron dynamics from the tip to the quantum dot on an ultrafast timescale.12 umerical simulations
In order to confirm our hypothesis, numerical quantum calculations have been performed.The electron tunneling probability is obtained by solving the 1D Schrödinger equation withthe potential shown in Figure 2d. The independent parameters are the width of the firstbarrier, the size of the QD and the potential in the quantum dot. The parameters have beenselected in order to reproduce the spacing and voltage dependence of the energy levels in theexperiment. However we do not expect this model to predict the exact dimension or materialof the quantum dot. We hope that these simple calculations, aimed at reproducing themain physical effects, will stimulate further more realistic calculations and experiments withdifferent materials. The calculated transmission of the tunneling barrier is combined withthe electron energy distribution inside the W tip to reproduce the emitted electron energyspectrum (see Supporting Information IV for details of the calculation). We calculated thetime-dependent electron energy distribution in the out of equilibrium regime by includingthe effect of the laser pulse on the Boltzmann equation of the electrons and the phononsin the metallic tip.The results of the simulations are presented in Figure 3b and 4b when the laser is onand in Supporting Information II b in the equilibrium case without laser. We found rea-sonable agreement with the experimental results. The E peaks appear more clearly in thesimulations than in the experiment because experimentally a peak is hardly detectable whenanother peak is present at higher energy with a higher intensity. The main reason is thatthe shot noise of the high energy peak overwhelms the signal coming from the low energypeak. It is also possible that additional scattering mechanisms not taken into account in oursimulations might attenuate the amplitude of the E peaks as well as make the E peakswider. Note that in our simulations the contribution of the laser field to the shift of theenergy levels was not taken into account although in the range of power explored here itstarts to be comparable to the DC field (10 mW corresponds to a laser field of 0.4 V/nm andan intensity of 21 GW/cm ). It can be expected that with a higher intensity carrier envelop13hase stabilized laser, the energy levels of the quantum dot might oscillate with laser electricfield and present interesting new features. Discussion
Compared to DC field emission, femtosecond laser excitation permits to create an ultrafastnon-stationary electron distribution. The energy gained by the electrons from the pho-tons allows the electrons to tunnel from the tip to the quantum dot higher energy levels.These states can therefore be observed in laser induced resonant tunneling. Because thelaser pulse is short, the multiphoton absorption has to occur within a few fs and the non-stationary electron distribution is created at this timescale where electron-phonon and evenelectron-electron scattering is rather limited. In the Supporting Information 1c, our numer-ical simulations show that the out of equilibrium electron pulse in the metal at moderatelaser intensity has a duration of ∼ fs, slightly smaller than the original laser pulse andthis duration increases to 17 fs at 50 mW. Depending on the timescale of the tunnelingprocess, the overall dynamics might be considered as a multiple step mechanism where ex-cited electrons from the tip are created and have enough time to tunnel to the quantum dotand then into vacuum before the relaxation to the stationary Fermi-Dirac distribution andthermalization to the phonons occur. Future pump-probe experiments are expected to givefurther insight about the time domain and the energy range where the multiphoton process dominates over thermionic emission and the type of coherent process involved such as theone identified in Ref. 16.This multi-step process has been unexplored so far in the ultrafast photoemission ofnanotips. It is a promising approach that filters and favors the creation of coherent electronsfrom an artificial atom. In our case, from the peak width we can estimate that the resonanttunnelling process occurs within a few fs and with a pulse duration of 14 fs the multistepscenario is fulfilled. A gain of a factor of 10 is still possible in order to obtain a transform14imited electron pulse. Such an improvement is within reach either by increasing the width ofthe first barrier by few Ångströms (a 64 meV peak width on the field emission of a quantumdot has already been reported in the past ) or by reducing the laser pulse duration. Conclusions
We have performed field assisted photoemission induced by an ultrashort laser pulse on asingle, isolated quantum dot attached to a metallic tip. We demonstrated that the emissionprocess in the range of nominal peak laser intensity studied here (up to 320
GW/cm ) iswell-described by a multiphotonic process where electrons in the metal tip tunnels resonantlythrough the quantum dot as shown by numerical simulations. The presence of an additionalDC voltage offers the possibility to finely tune and control the energy difference betweenelectron energy levels for interference experiments. This tunneling process on tunable andwell defined atomic-like states paves the way for the development of high brightness, ultra-fastand coherent single electron sources for quantum optics studies. Measurements of the electronspatial distribution and energy levels spectroscopy of the quantum dot with a tunable laser could give deeper understanding of the 3D electron trajectories and their full interaction withthe laser. To finish, now that we have established access to the femtosecond laser excitationof quantum dot states, note that other quantum nanostructures or even 1D objects mayemit from their quantum states by other mechanisms such as direct photo excitation, thusopening up other avenues of investigation. Acknowledgement
This work was supported by the ILM AAP project. The authors acknowledge the PlateformeNanofils et Nanotubes Lyonnaise of the University Lyon1. H.Y. and M.F.K. are grateful forsupport by the German Research Foundation (DFG) via YA-514/1-1 and the Munich Centreof Advanced Photonics. M.F.K. acknowledges support by the Max Planck Society through15he Max Planck Fellow program.
Supporting Information Available
This material is available free of charge via the internet at http://pubs.acs.org. Additionaldescription of the experiment Additional data and analysis. detailed presentation of themodel and numerical simulations.
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