Gate-tunable spatial modulation of localized plasmon resonances
Nanoplasmonics Maier07 (); stockman11 () exploits the coupling between light and collective electron density oscillations (plasmons Pines_and_Nozieres (); Giuliani_and_Vignale ()) to bypass the stringent limits imposed by diffraction. This coupling enables confinement of light to sub-wavelength volumes and is usually exploited in nanostructured metals. Substantial efforts are being made at the current frontier of the field to employ electron systems in semiconducting and semimetallic materials since these add the exciting possibility of realizing electrically tunable and/or active nanoplasmonic devices Kim2012 (); Chen2008 (); Chen2009 (); Fei2012 (); Chen2012a (). Here we demonstrate that a suitable design of the doping profile in a semiconductor nanowire (NW) can be used to tailor the plasmonic response and induce localization effects akin to those observed in metal nanoparticles Klar1998 (). Moreover, by field-effect carrier modulation, we demonstrate that these localized plasmon resonances can be spatially displaced along the nanostructure body, thereby paving the way for the implementation of spatially tunable plasmonic circuits.
The excitation of localized plasmon resonances (LPRs) leads to a strong local enhancement of the electromagnetic fields, as a consequence of the collective oscillation of free charge carriers. This found important applications in sensing Mayer2011 (), microscopy Rothenhausler1988 (), Raman spectroscopy Kneipp1997 (), and photovoltaics Mubeen2014 (); Atwater2010 (). Traditionally, LPRs were observed and investigated in metallic nanoparticles (NPs), but recent experiments are extending this possibility to doped semiconductor NPs Kramer2015 (); Luther2011 (). One of the key motivations for the exploration of this route is the perspective of obtaining materials with lower free carrier density and thus lower plasma frequency . In doped semiconductors, this yielded the observation of LPRs in nanoparticles from the mid- to the far-infrared region of the spectrum. A further important drive pushing for this paradigmatic shift to semiconductors is the perspective of electrical tuning of the plasmonic response. The investigation of hybrid electronic/plasmonic systems is indeed at its infancy and holds the promise of novel nano-optoelectronic chips embedding multiple functionalities Sorger2012 (). A remarkable example is provided by the recent progress in graphene plasmonics Grigorenko2012 (), where the high room-temperature mobility of samples encapsulated in hexagonal boron nitride crystals allows gate-controlled tuning of long-lived and highly-confined two-dimensional plasmons Woessner2014 ().
In our experiment, we exploit state-of-the-art growth of self-assembled semiconductor NWs Lucia (), which offer the unique flexibility to engineer local properties of the semiconductor. In particular, we use steep axial doping profiles in InAs NWs to localize the system’s plasmonic response and control the spatial position of the NW LPR by field-effect.
A prototypical example of the investigated NWs is shown in Fig. 1. A set of -diameter InAs wires were grown by metal-seeded chemical beam epitaxy and included a -long steep graded-doping region. In nominally undoped portions of the NW, the free-carrier concentration was of the order of while a carrier density up to is estimated for the highest doping-density regions, as determined by transport measurements in standard field-effect transistors grown in equivalent conditions Viti2012 (). The plasmonic response of the NWs was investigated by scattering-type scanning near-field optical microscopy (s-SNOM) in the mid-infrared spectral range Stiegler2010a (); Hillenbrand2000 (). We used a metallic tip with a radius of operating in tapping mode at to probe the near-field optical response of the sample under a mid-infrared CO laser (). A pseudo-heterodyne interferometric detection was exploited to obtain the amplitude () and phase () of the scattered optical beam (Fig. 1b), which strongly depends on the local dielectric response of the NW. In our experiment, the backscattered signal was demodulated at the fourth harmonic of the probe tapping frequency. This procedure minimizes far-field contributions (see Methods) and yields the amplitude component , with phase .
Atomic force microscope (AFM) (Fig. 1c) and s-SNOM (Figs. 1d,e) maps of isolated NWs on SiO/n-Si were acquired simultaneously. The optical response of the sample reveals the localized nature of the plasmonic resonance in the graded-doping nanostructure. The maps in Figs. 1c,d show the amplitude and phase of the scattered field as a function of the SNOM position on the sample, respectively. Enhanced scattering only occurs in a small region of the NW where the local plasma frequency matches the illumination frequency . We see that the plasmon resonance extends for and no indication of plasmon propagation is observed. Our NWs support LPRs for a variety of reasons. First, contrary to strictly 2D systems like graphene, our NW hosts a quasi-three-dimensional electron system with bulk-like plasmons. These have a dispersion relation that is nearly flat Pines_and_Nozieres (); Giuliani_and_Vignale () in the relevant region of wave vectors where tip-plasmon coupling occurs. This implies a nearly zero plasmon wave vector and group velocity. Second, due to the presence of donors, which have been implanted in the body of the NW to engineer the steep doping density profile, the lifetime of our bulk-like plasmons is very short. Within a simple Drude model for the NW local conductivity , we find a plasmon lifetime on the order of . Third, the highly inhomogeneous carrier density distribution along the NW growth direction in our NWs enables highly-selective spatial coupling between the SNOM tip and the plasmon. This is because the plasmon frequency is a function of the local carrier density (see Methods), , and therefore, for a given illumination frequency , energy conservation implies tip-plasmon coupling only occurs in the neighborhood of the position at which .
In order to attain the field-effect control of the LPR in the nanostructures we fabricated devices equipped with an electrical reference contact and a gate allowing carrier-density manipulation (Fig. 2a). NWs were dropcasted on top of a SiO/n-Si substrate as in the case of Fig. 1. Using electron beam lithography, we defined a Ni/Au electrode at the very end of each NW in order to use the n-Si substrate as a backgate and minimize electrostatic screening Pitanti2012 (). Our device structure allows the application of up to gate voltage sweeps in few milliseconds. Based on simple electrostatic modelling Wunnicke (), the capacitance between the backgate and a NW with a diameter in the range - is estimated to be -, corresponding to a carrier density modulation in the range -. The impact of field-effect on the NW plasmon response was measured by positioning the s-SNOM tip on top of the NW resonant region (at ) and by measuring the tip-induced light scattering as a function of gate voltage . The expected carrier-density dependence of the amplitude and phase of the scattered field are shown in Fig. 2b. The resonance is expected to occur at and a carrier density modulation of at least is necessary to map the full plasmonic resonance (see shaded area in Fig. 2b). The actual measured NW response is shown in Figs. 2c,d. The experimental configuration was particularly stable and unaffected by sample mechanical drift with respect to the s-SNOM tip. Multiple gate scans could thus be acquired and averaged to achieve good signal-to-noise ratios. In Fig. 2c we report the time evolution of the phase of the scattered wave, when the gate voltage is subject to a peak-to-peak oscillation of at . A strong modulation of the optical response is observed. In Fig. 2d the phase of the scattered light is plotted against . The marked hysteresis is a consequence of charge trapping at the NW/dielectric interface Astromskas2010 (); Roddaro2013 ().
The modulation of light scattering displayed in Fig. 2 corresponds to a physical displacement of the LPR along the NW axis. Crucially, this is enabled by the fact that the gate electrode, being capacitively coupled to the NW, shifts the carrier density profile by a constant value which is proportional to the gate voltage . In turn, since the NW is designed to feature a linear spatial dependence of versus the longitudinal coordinate , the energy conservation condition is expected to occur at a gate-shifted position where . To confirm this, we measured near-field infrared profiles along the NW growth axis while varying the gate voltage from to and then back to (Fig. 3a). In order to rule out possible spurious effects, e.g. stemming from small piezoelectric deformations of the SiO layer Lazovski2012 (), we monitored the position of the metallic reference electrode and/or of the doping marker regions at each scan. Experimental data clearly indicate that the plasma resonance is shifted along the NW axis by about when the gate voltage is swept from to and viceversa. This corresponds to a shift of the resonance by more than its half width at half maximum. We note that, compared to the measurements shown in Fig. 2, a larger gate voltage swing is needed to achieve a modulation covering the full resonance. This is not surprising since traps on the NW surface and in the gate dielectric are known to cause non-negligible screening effects that are particularly evident at room temperature and for slow gating sweeps Astromskas2010 (); Roddaro2013 (). Indeed, the time required to acquire each s-SNOM scan is of the order of several minutes, while in the case of the measurements reported in Fig. 2, a full gate sweep lasted only few milliseconds. It is important to note that this is not an intrinsic limitation of the devices but is rather dictated by the experimental need to perform slow s-SNOM scans.
The experimental data are well described by a point-dipole interaction model Cvitkovic2007 (), from which the complete charge-density profile along the NW axis can be derived. The s-SNOM signal was compared with the expression for the fourth-order harmonic of the scattering field induced by the tip-sample interaction (see Methods). We fit the expression for by modeling the carrier density profile with a constant term , a uniform contribution proportional to the gate voltage , a linearly-increasing term, and a first-order non-linear correction:
Here, is a capacitance per unit volume and is the length of the graded doping region. We remark that a single set of parameters was fitted against all curves at different . The result of the fit for the two largest values of is shown in Fig. 3b, while the deduced density profile is shown in Fig. 3c. Probably owing to the partial shielding by the grounded electrode, the carrier profile is slightly sublinear for . Starting from the best fit and using the expression for , we obtained the position of the resonance (Fig. 3d). We estimated an LPR displacement of driven by the field effect. As mentioned before, in this experimental configuration the LPR shift is hindered by screening effects driven by traps in the dielectric and on the NW surface, which can become significant particularly at slow gating sweeps. This is also confirmed by the low apparent value of extracted from the fit of the experimental data, when compared with the expected value (see Methods).
In conclusion, we demonstrated that we can localize and spatially control by field effect the position of plasmon resonances within InAs nanowires by embedding a suitably engineered doping profile. Our novel nanoplasmonic architecture combines the strong local light confinement typically observed for metallic nanoparticles with the wide tunability typical of semiconductors. The achievement of electrically-tunable plasmon systems is of great relevance to applications: in the specific case of tunable LPRs, it can pave the way to innovative devices concepts such as, for instance, recently proposed scanning plasmon sensors Nishi2015 (). In general, present results on local doping modulation indicate a promising direction for the design and implementation of a new class of devices with electrical spatial control of plasmonic modes.
Electron-doped InAs nanowire (NW) growths were performed by Au-assisted chemical beam epitaxy (CBE) in a Riber Compact 21 system. The system employs pressure control in the metalorganic (MO) lines to determine precursor fluxes during sample growth. A calibrated orifice at the injector insures the proportionality between line pressure and precursor flow through the injector. The precursors involved in the NW growth are tri-methylindium (TMIn), tertiarybutylarsine (TBAs), and ditertiarybutyl selenide (DtBSe) as selenium source for -type doping. A nominally 0.5 nm thick Au film was first deposited on (111)B InAs wafers by thermal evaporation. Before the growth was initiated, the sample was heated at 470 10 C under TBAs flow for 20 min in order to dewet the Au film into nanoparticles and to remove the surface oxide from the InAs substrate. InAs stems were grown at a temperature of 380 10 C for 30 min with MO line pressures of 0.3 and 0.7 Torr for TMIn and TBAs, respectively. The growth temperature was increased to 400 10 C for the growth of the graded-doped InAs NWs. The steep doping profile along the axial direction of the NWs was obtained by tuning the partial pressure of di-tert-butyl selenide (DtBSe) from 0 to 1 Torr during the growth process.
Near-field measurements were performed by a scattering-type scanning near-field optical microscope (NeaSNOM from Neaspec GmbH). It is based on an atomic force microscope (AFM) operating in tapping mode at a frequency of about 250 kHz. Pt-coated AFM tips with a radius of R 20 nm were chosen as near-field probes. The tip was illuminated with a commercial (accesslaser.com) grating-tunable carbon dioxide (CO) laser emitting in a TEM transverse mode (M=1). Radiation (about 1 mW) was focused on the tip by means of a 2 cm focal length parabolic mirror. The emission of the laser can be tuned between 9.5 and 10.7 m. The system is equipped with a pseudo-heterodyne interferometric detection module in order to detect simultaneously the phase and amplitude of the scattered signal. The optical signal was acquired simultaneously with topographic AFM maps. The signals acquired in this work were the scattering amplitude and phase, demodulated at the fourth harmonic of the tapping frequency.
In the fit of the experimental data we assumed a Drude form for the dielectric function of the carriers in the NW: . We introduced the plasma frequency where is the carriers’ band mass, is the electron mass in vacuum, and is the high-frequency dielectric constant of InAs. We took the Drude scattering time , which yields a Drude mobility in line with the range of values reported in the literature Viti2012 (). The expression for the fourth-order scattering contribution of the s-SNOM signal is
where is a real constant which relates the near- and far-field of the radiating point dipole, , , with and the dielectric constant of the tip material and the dielectric function in the NW, respectively. The fit yields the following best values for the parameters in Eq. (1): , , and . The latter in turn provides a value for the gate capacitance between the backgate and the NW in the range -. This value is different from what expected from simple electrostatics. Well-known analytical models Wunnicke () in fact estimate the back-gate capacitance per unit length as , where is the oxide permittivity, is vacuum permittivity, is thickness of the SiO layer, and is the radius of the NW. Using and , we estimate . Correspondingly, the expected carrier density modulation is in the range . The mismatch with the calculated values of is ascribed to the different impact of screening by charge traps at the NW/dielectric interface, depending on the gate sweep speed. The gate sweep speeds during the measurements can be estimated to be (i) up to about in point modulation data of Figure 2, (ii) about in the gate-modulated scans of Figure 3, and (iii) about during the preparatory step before the scans of Figure 3 (sweep from to in about ). The shift of the LPR was observed on five different devices. For three of these, the field effect modulation of the plasmon resonance was demonstrated both by looking at the SNOM response in a single position (Figure 2) and by performing a spatial s-SNOM map the resonance line as a function of (Figure 3). Depending on the average sweep speed, the resonance shift in the s-SNOM maps was estimated to fall in the range.
Acknowledgements.We thank I. Torre, M.S. Vitiello, F. De Angelis and R.M. Macfarlane for useful discussions. This work was supported by the EC under the Graphene Flagship program (contract no. CNECT-ICT-604391), the MIUR through the programs “FIRB - Futuro in Ricerca 2013” - Project “UltraNano” (Grant No. RBFR13NEA4) and “Progetti Premiali 2012” - Project “ABNANOTECH”, and by the ERC advanced grant SoulMan (G.A. 321122). Free software was used (www.gnu.org, www.python.org).
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