In this paper, the near-field lightwave characteristics of an arrayed silicon nano-cone-tip optical antenna (NOA) covered by a common metal film, which can be viewed as a featured quantum dot (QD), are carefully investigated. A dipole net-charge distribution closely correlated with the surface lightwaves excited over the antennas by incident lasers with a central wavelength of 633 nm, is clearly observed. An obvious Coulomb blockade from the apex apparently influencing the net-charge converging over the surface of NOA, is verified, which can also be predicted by the simulations according to surface standing waves across the apex node. The antinodes of the surface net-charge instantaneous distribution are already pushed away from the normal location owing to the apex Coulomb blockade, so as to present a distorted waveform different from traditional standing wave modes. The tip proximity effect leading to a relatively weak net-charge converging over surrounding planar facet and adjacent NOAs, is also discovered.
Article
Near-field lightwave and correlated net-charge distribution over arrayed silicon nano-cone-tip optical antenna covered by common metal film
https://doi.org/10.21203/rs.3.rs-3222384/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 12 Dec, 2023
You are reading this latest preprint version
In recent years, several special functioned micro-nano-architectures demonstrate several significant features in efficiently adjusting or even modulating physical properties via strongly coupled with incident electromagnetic radiations in a relatively wide wavelength range, and thus highlight various potential applications in medical imaging, biosensor, surface enhanced Raman spectroscopy, and fluorescence imaging1–7. An arrayed nano-tip, as a typical periodic micro-nano-structures or an optical antenna providing a large number of tip surface states, has been successfully constructed based on many common metal materials, so as to predict a possibility through driving or compressing a large number of surface “free electrons” onto the sharp apex of a single tip, which will lead to a very high electron concentration as well as a highly localized enhancement of both the resonant electric-field and magnetic-field components converged or even focused at apex.
Thanks to a relatively strong response and then highly localized resonant enhancement, the surface waves with the featured frequencies can be effectively excited and then transported towards the apex along tip surface, which are strictly constrained and guided by the boundary conditions through continuous refraction and reflection. Currently, a remarkable enhancement of the near-field electric- or magnetic-amplitude or intensity allows an amazing extent of exceeding 6 orders of magnitude through converging or even focusing incident radiations into a nanoscale space8–13. As shown, an efficient conversion from propagating wavefields to highly localized lightfields is mainly determined or constrained by surface net-charge such as “free electron” distribution behavior. The incident lightwaves can be resonantly amplified based on the typical nano-converging or even nano-focusing of nano-tips14–16. A number of research based on highly compressed surface “free electrons” onto the apex of a single metal tip excited by incident laser pulses, so as to realize a near-field probing, has been proposed. The detection sensitivity based on colloid quantum dots (QDs) can be remarkably improved according to nanosecond or even attosecond measurements17–22. However, the detailed research about the dynamic transportation and redistribution of surface “free electrons” and the related surface waves for the tip-typed antennas still remains limited.
Analyzing the dynamic re-arrangement properties of the surface “free electrons” towards the apex of a single nano-tip, which can be viewed as a special QD, will enable a remarkable optimization of the nano-converging or even nano-focusing performance. In addition, the substantial apex surface states originated from the discrete valence band or conduction band, as well as the acceptor energy levels in the forbidden band, usually corresponds to the discrete energy level without an obvious forbidden band of QDs. Generally, a high density of energy level distribution determined by the wave functions of “free electrons” or holes confined into a nanoscale space or geometric point, can stimulate surface exciton and further drive the free electrons tunneling resonantly into QDs17,23–26. As demonstrated, the electronic distribution probability over the surface of QDs can be significantly increased due to tunneling or exciton effect, which is closely related with the electron occupation characteristics of the apex surface state. At the same time, a flexible adjustability of band gap via changing the architectural properties or even an effective modulation of radiation intensity, are the significant advantages of QDs, which makes them highly promising materials for near-field nano-converging or even nano-focusing27–29.
In this paper, the theoretical models about the key electronic and near-field lightwave characteristics of an arrayed nano-cone-tip optical antenna (NOA), are constructed. The numerical simulations indicate that the net-charges such as surface “free electrons” rarely reach the apex but usually distribute in lower area of the NOA under a relatively strong beam illumination or surface wavefield excitation, due to a great Coulomb blocking of the net-charges over the apex, which remarkably restrain other net-charges continuously into the limited apex region, and thus forms surface near-field waves in a standing wave mode with a featured waveform across the apex node. In order to validate the simulation, a near-field measurement corresponding to an arrayed NOA covered by common metal materials is performed according to the scattering-type scanning nearfield optical microscopy (SNOM), which directly present a character that the near-field lightwave excited by incident laser beams with a central wavelength of 633nm is closely related with the surface net-charge morphology. The situation of remarkably enhancing near-field lightwaves also means a strong surface net-charge accumulation not only around the apex facet, but also over the surrounding planar facet and adjacent NOAs. The lightwave transmission based on the redistribution of the surface “free electrons” can still be explained according to the typical characteristics of QDs.
Numerical simulation. A series of numerical simulations about a dipole surface net-charge distribution over an arrayed metallic NOA with typical features including the nano-geometry and the structural material, are carried out by finite difference time domain (FDTD) method. The net-charge instantaneous distribution morphologies around the apex of a single metallic NOA mainly stimulated by incident laser beams, are further obtained. An arrayed NOA with an arrangement period of 500 nm has been designed and fabricated over a monocrystal silicon wafer, and a gold film with a thickness of 30 nm continuously deposited over its surface, so as to introduce a dense surface state over the NOAs24. As shown, the net-charge density over the NOA surface can be carefully analyzed according to common Maxwell’s equations and then particularly based on a key relation of\(\rho e=\nabla \cdot {\mathbf{D}}\). So, a surface electric-field component pointing outside the NOA surface, which is tightly constrained by the surface net-charges stimulated, can be expressed as a z-component Ez. Owing to the simultaneous acquisition of both the amplitude \(Sj(x,y,z,\theta ,d)\)and the phase 
of Ez, the net-charge density \(fj(x,y,z)\) at any position (x, y, z) of the NOA can be represented by an Eq. 8 of
where d and θ are the bottom diameter and the top angle of a single NOA, respectively, and j (= 1, 2, 3, …) represents the metal film material already deposited over the NOA surface, for example, j = 7 means Au. So, the metallic NOAs can be characterized according to the structural parameters of the bottom diameter d and the top angle θ based on simulating the surface net-charge resonating distribution involving the net positive charge and the aggregated “free electrons”.
The surface net-charge distribution according to the configurated beam illumination over metallic NOA arrays, are simulated as shown in Fig. 1. A beam of visible lightwave with a central wavelength of ~ 633 nm and an initial polarization labeled by a double-sided arrow, is incident obliquely along the diagonal with an incident angle of 45° upon a horizontal facet, that is \(\alpha =\beta ={45^ \circ }\), as shown in Fig. 1(a). The energy level diagrams of the typical semiconductors from bulk materials to tip QDs with different geometry is shown in Fig. 1(b). In general, the common semi-conductive energy band will be apparently weakened as gradually shrinking NOA, which means that the apex of NOA will become sharper. Usually, the adjustable energy level of QDs provides ample unoccupied level for positive or negative charge, so as to shape a highly charged facet or even tunnel into QDs instead of crossing the boundary barrier30,31. As a result, the possibility of the net-charge filling behavior will be decreased as QD becoming smaller that brings wider band gap and lower density of unoccupied tip surface states to restrain more net-charge into the apex.
As shown in Fig. 1(c) to 1(e), the NOA surface will be increased from ~ 1.2×105 nm2 to ~ 3.5×105 nm2, under the condition of keeping the bottom diameter of 280 nm but gradually decreasing the top angle θ from 60° to 20°. In other words, the height of the NOA will be increased from ~ 242 nm to ~ 794 nm, but having a constant bottom size. So, the main dipole net-charge converging spot (DNCS) presents a trend of being away gradually from the apex, where the height between the apex and the upper circle of the main DNCS will be remarkably increased from ~ 71nm to ~ 329 nm, during continuously sharping the NOA, so as to increase its height, as shown in Fig. 1(c-1) to 1(e-1). Consequently, an apparent width narrowing of the main DNCS enclosed between the upper long dashed and lower short dashed circles, can be viewed in a sequence of ~ 196 nm to ~ 62 nm. Based on the surface net-charge instantaneous distribution simulations mentioned, an obvious Coulomb blockade phenomenon resulting from an aggregated net-charges distributed symmetrically along the central axis of the NOA can be observed. The distance between the central arc of a main DNCS and the apex presents a sequence of ~ 180 nm to ~ 216 nm to ~ 423 nm. Considering the case that the surface net-charge resonant distribution is closely related with the surface near-field lightwaves, which should be a standing wave with a central node at the apex, the center-to-center distance between the positive and the negative net-charged regions of the main DNCS along NOA surface can be viewed as a half-wavelength of the surface wave stimulated by the incident beams. It should be noted that the half-wavelength of the stimulated surface waves corresponding to the NOAs with different structural size is 360 nm and 432 nm and 846 nm, respectively, which are greater than incident beams.
As shown in Fig. 1(c-2), the instantaneous main DNCS, as a couple of positive net-charges colored by pale yellow and the aggregated “free electrons” by light blue, are confined between a long-dashed circle with ~ 82 nm diameter and a short-dashed circle with ~ 278 nm diameter, and also distribute separately over opposite side of a single NOA with a top angle of 60°. The fine net-charge distributing patterns arising clearly over its opposite side can attribute to a relatively strong interference of the incident beams and the surface waves stimulated, and then present an intensity variance from − 6 to 6 unit according to the color-bar. An enlargement viewing of the patterned net-charges over the apex region with a relatively low intensity in a range from − 2 to 2 unit is further exhibited in Fig. 1(c-3). As demonstrated, the net-charges are rarely concentrated over the top region around the apex node without any net-charges, and thus exhibit a symmetrical distribution fringes along the diagonal, which are also positive-negative net-charge alternant sidelobes adjoining the main DNCS over opposite side. As a very small apex capacitance strongly restraining the net-charge climbing into the apex, the Coulomb blockade of QDs32–34 will get enhanced through decreasing the top angle θ from initial 60° to medial 40° to final 20°, and thus the distance between the central arc of a main DNCS and the apex being rapidly increased, where the maximum net-charge density is from 2 to 1 to 0.4 unit, as illustrated in Fig. 1(c-3) to 1(e-3).
Several typical net-charge instantaneous distribution over a single NOA with the same top angle of 50° but different bottom diameter d: (a) 180 nm and (b) 280 nm and (c) 380 nm, which corresponds to the different NOA height including ~ 193 nm and ~ 300 nm and ~ 407 nm, are simulated, as illustrated in Fig. 2. The main DNCSs are also confined between a long-dashed circle with ~ 180 nm diameter and a short-dashed circle with ~ 112 nm diameter, and thus distribute separately over its opposite side when d = 180 nm, as shown in Fig. 2(a-2). And an approximate distance of ~ 173 nm between the central arc of a DNCS and the apex can be obtained, as shown in Fig. 2(a-1). So, a wavelength of ~ 692 nm corresponding to the shaped surface standing wave closely related with the positive and negative net-charge instantaneous distribution around the apex can be calculated, which is slightly more than the incident wavelength of 633 nm, because of a relatively weak Coulomb blockage of the similar dipole net-charges over the apex region, as shown in Fig. 2(a-3), and then in accord with both the distance and net-charge varying trend shown in Fig. 1. It should be noted that the small bottom diameter of 180 nm means a NOA boundary at the bottom, which also slightly hinders the net-charge re-arrangement away the apex and then nearing the bottom boundary, so as to exhibit a synergistic compression effect owing to the apex Coulomb blockade and the bottom boundary constraint.
Considering the case of existing a similar Coulomb blockage action of the NOA with the same top angle, the main DNCS will slightly rise from the bottom with an enlarged diameter of d = 280 nm, which are also confined between a long-dashed circle with ~ 231 nm diameter and a short-dashed circle with ~ 101 nm diameter, so as to present a widened size of the main DNCS from ~ 68 nm to ~ 130 nm, as shown in Fig. 2(a-1). A slight decreasing of the net-charge instantaneous density from 10 to 6 unit according to the color-bar, can be predicted, as shown in Fig. 2(b-2). And then the surface standing wave demonstrates a half-wavelength of ~ 393 nm, which is larger than that of d = 180 nm, because of a relatively weak bottom boundary constraint and the similar Coulomb blockade action of the apex. After expanding d to 380 nm, a surface standing wave mode presents two symmetrical nodes over both opposite sides of the NOA and still an apex node, where both the positive and the negative net-charge converging spots already near the bottom boundary, as shown in Fig. 2(c-1). The distance between the edge DNCSs along the NOA and across the apex node corresponding to 1.5 wavelength is ~ 952nm, which means that the surface standing wave with a wavelength of 634.7 nm closely related with the surface net-charge distribution is almost the same as that of incident beams. So, the numerical simulation about the distance relation provides a direct evidence that the Coulomb blockade action will rapidly decay away from the apex, and finally be neglected when the distance being increased to ~ 476 nm. Moreover, the approximate height difference between the apex and the upper dashed circle of the main DNCS such as ~ 120 nm, ~ 108 nm, and ~ 116 nm, suggests that a couple of positive net-charges and aggregated “free electrons” distributed around the apex with a given top angle will be influenced by the Coulomb blockage effect, so as to result in a distorted standing waveform. The maximum net-charge density of the main DNCS is located at almost the same position according to the same Coulomb blockage action, as indicated when d = 280 nm and 380 nm. And the dipole net-charge over the apex region of the NOA with different bottom diameter mentioned above also presents a similar distribution pattern and intensity, as shown in Fig. 2(a-3) and (b-3) and (c-3).
Additionally, how the metal materials coated over the silicon NOA influences the net-charge resonant distribution, is also studied carefully. As shown in Fig. 3, several NOAs with the same bottom diameter of 280 nm and the top angle of 50°, which are continuously coated by different metal materials labeled by a subscript j in Eq. (1) from 1 to 7 including Al, Fe, Cu, Ag, W, Pt, Au, are simulated, respectively. In order to further form a heterofilm over the NOA surface, the apex region above a demarcation diameter of 100 nm and the side surface of the lower frustum are coated by different metal materials according to a sequence of the top Au to frustum Al and the top Al to frustum Au, which are selected because of a great difference in atomic number and work function. The net-charge instantaneous distribution over the apex of the NOAs covered by Cu and Ag and Au and Al-Au, respectively, are relatively obvious from the top viewing according to the color-bar with a minimum value of 5 unit, as shown in Fig. 3(a). Meanwhile, the net-charge instantaneous distribution over the apex of the NOAs covered by Al and Fe and W and Pt and Au-Al, respectively, are relatively weak compared to above according to the color-bar with a maximum value of 2.4 unit. As shown, the net-charge density of the NOAs covered by different heterofilm of Al-Au and Au-Al exhibit a relatively large variance of more than twice, due to the work function difference between Al and Au, which are commonly 4.28 eV and 5.1 eV, respectively.
Several enlarged viewings of the DNCS distributed over the apex, which demonstrate almost the same net-charge distribution pattern with a similar density variance range, are given in Fig. 3(b). As shown, the dipole net-charges over the apex region of a single NOA covered by Cu and Ag and Au-Al film, respectively, are also symmetrical about the apex node, and all present a relatively high density in an arrange from − 3 to 3 unit. In addition, the net-charge density along a diagonal marked by a black dashed line, as shown in Fig. 3(a), is further plotted in Fig. 3(c), where the x-axis represents the cross-sectional radius of the NOA and the zero point the apex, so as to fully display the surface net-charge instantaneous arrangement character. All curves are already colored by blue, dark blue, red, silver, purple, orange, golden, light blue, and brown, corresponding to metal materials of Al, Fe, Cu, Ag, W, Pt, Au, Au-Al, and Al-Au. An enlargement view indicating initial divergence of the curves away the apex node in a range from − 10 nm to 0 nm is also inserted. The net-charge density obviously presents a point symmetry about the apex node. The peak value corresponding to Au film reaches ~ 7 unit at -80 nm radius of the central arc of the DNCS and also approach the apex node more closely. In contrast, the worst net-charge convergence with a maximum of ~ 2.4 unit appears in Al film due to the lowest atomic number.
As shown, the net-charge instantaneous arrangement over the NOA precoated by common metal film is quantitatively simulated. An obvious variance between a silicon Al-NOA with a maximum value of 2.4 unit and a silicon Au-NOA with a maximum value of 7 unit, can be observed. After shaping an Au-Al heterofilm, an obvious density decreasing of the main DNCS from ~ 7 unit to ~ 2.8 unit can be seen, because the main DNCS being over the surface of Al film. An almost unchanged density of the main DNCS around ~ 7 unit mainly distributed over Au film, can be viewed after shaping an Al-Au heterofilm. So, a rapid density increasing of the main DNCS can be realized through reasonably configurating metal heterofilm over the same NOA.
Continuously, several complex NOAs are constructed by directly configurating a featured nanostructure including a nano-disk with a radius of 50 nm and a height of 10 nm, a nano-wire with a radius of 1 nm and a height of 60 nm, a nano-semisphere with a radius of 50 nm, and a nano-ball with a radius of 10nm, over the apex of the conical NOA with the same bottom diameter of 280 nm and the top angle of 50°. The surface net-charge distribution of the NOAs is simulated for evaluating the influence of the apex nanostructure about the net-charge instantaneous density and fashion, as shown in Fig. 4. As demonstrated, the dipole net-charge distribution over the complex NOAs presents a similar standing wave pattern and density with a maximum value of ~ 16.5 unit. But, a relatively strong DNCS can be observed over the top nano-semisphere, as shown in Fig. 4(c), which maybe a combined action of the Coulomb blockade and the quantum confinement35–38.
Moreover, a comparison about the net-charge distribution over the NOAs with different apex-appearance including the cone-apex and the sphere-apex, is also conducted. The cross-sectional net-charge arrangement characters of the NOAs are displayed in Figs. 5(a) and 5(b). The contours of the Au-NOA and the silicon NOA are plotted in a long and a short dashed-line, respectively. A typical structural diagram of a NOA with a sphere-apex is also inserted. Currently, the NOA with a sphere-apex is shaped by a nano-sphere top with a radius of 10 nm and the same lower frustum as the NOA with a cone-apex having, i.e. the top and bottom radius of 10 nm and 140 nm and the top angle of 50°. Additionally, the net-charge distribution density over the surface of both the NOAs are also given, as demonstrated in Fig. 5(c). As shown, the main DNCS can also be observed in the area lower than the apex region over the opposite side, and still existing two horizontal dipole moments of p and p1 in both the NOAs. Although the height of the central arc of the main DNCS is approximate, a larger net-charge distribution density with a maximum value of 6.23 unit around the apex can be found in the NOA with the cone-apex, whereas 5.28 unit corresponding to the sphere-apex. Besides, more “free electrons” can be accommodated over the apex region decorated by a nano-sphere top, which can attribute to its higher specific surface area. Thus, the net positive charges are then nano-converged toward the apex of the silicon NOA, and then a vertical dipole moment p2 is additionally formed over the sphere-apex. More interesting, the orientation of p2 will slightly deviate from the vertical direction in infrared region according to the simulations in a wavelength range from 400 nm to 3 µm, as shown in Fig. S2.
It can be expected that a potential photosensitive application of the proposed NOAs will owe to a remarkable enhancement of incident lightwave collection efficiency for an arrayed complementary metal-oxide–semiconductor (CMOS) sensor, which means a highly efficient incident lightwave responding and resonantly converging or even focusing corresponding to only one or several CMOS pixels. The boosted detection architecture scheme based on the NOAs is displayed in Fig. 6. According to the simulations, a dipole net-charge nano-converging mainly takes place over the side surface surrounding the apex of a single NOA with a relatively large top angle, which will guide the stimulated surface waves towards CMOS sensors. A typical physical course is as follows. A dipole-typed optical antenna with a dipole moment\({\varvec{p}}=fj(x,y,z)e{\varvec{l}}\), where e represents a single net-charge quantity, radiates outward transverse lightwaves with an electric-field Ep. Meanwhile, another near-field lightwaves with an electric-field E0 will be superimposed with Ep and continuously illuminate the CMOS sensors coupled directly with the nano-tips mentioned. According to Fig. 5(c), a higher net-charge distribution density over the cone-apex means a larger dipole moment, so as to generate a stronger electric-field E. Similarly, more net-charge converged over the sphere-apex will lead to a stronger CMOS photosensitive response.
SNOM measurement. To actually explore the near-field lightwave characteristics, an arrayed NOA with the key configuration including a single NOA bottom diameter of 280 nm and the top angle of 50° and an arrangement period of 500 nm, is firstly fabricated over the surface of a n-type silicon substrate through common electron-beam lithography (EBL, JBX 6300FS, JEOL) and inductivity coupled plasma etching (ICP, Oxford Plasma Pro System 100 ICP 380). And then a gold film with a thickness of 30 nm is further deposited over the silicon NOAs by traditional magnetic sputtering (Kurt J. Lesker LAB 18). The scanning electron microscope (SEM, SU8220, Hitachi) photographs of the silicon NOA array before and after sputtering a gold film are shown in Fig. 7. A top viewing of the silicon NOAs with an average bottom diameter of ~ 270 nm is presented in Fig. 7(a), where each selected single NOA demonstrates a slight bottom size variance by a typical horizontal-orientation 268 nm to another vertical-orientation 275 nm. Considering the etching accuracy of both the EBL and ICP and other intrinsic technological errors, the apex sharpness of the final NOAs will generally be lower than those designed, as shown by NOAs with a typical nano-dome apex in Fig. 7(b). After further depositing a gold film mentioned, the average NOA bottom diameter has expanded to a typical value of ~ 291 nm and the average height and the cross-sectional diameter of the apex facet ~ 326 nm and ~ 63.8 nm, respectively, as shown in Fig. 7(c). So, the thickness of the gold film shaped over the surface of a single NOA is ~ 8 nm according to the measurement data, which is remarkably less than that deposited over the planar facet between adjacent NOAs.
The SNOM measurements using a scattering-type of SNOM (NeaSNOM, Neaspec GmbH Co.) in a reflectance mode with the same beam illumination condition, as indicated in Fig. 1(a), is performed to probe the near-field optical characteristics based on the near-field lightwave amplitude and phase data, and thus obtain the correlated surface net-charge instantaneous distribution map over the NOA according to Eq. (1), as illustrated in Fig. 8. Figure 8(a) and 8(b) show the visible near-field lightwave amplitude S7 and the phase φ7 of a single NOA, respectively, where the subscript 7 indicates Au film directly deposited over the silicon NOAs fabricated. As illustrated in Fig. 8(a), there are two microband-shaped light spots colored by dark red with a largest value of 6.5×10− 6 unit and light blue corresponding to a relatively small value of less than 3×10− 6 unit according to the color-bar, respectively, which almost near the NOA bottom indicated by a dark annulus as labeled by a white dash line. As demonstrated in an inserted 3D viewing, they can be featured by an electric-field resonance enhancement localized at the lower right and the upper left nano-regions of the NOA covered entirely by SNOM beams during measurement. The near-field light intensity or amplitude corresponding to the left nano-region is relatively identical and then gradually weakened around. It should be noted that the near-field lightwaves excited by the SNOM beams are almost distributed over the surface of the Au NOA in a half-wavelength standing wave mode across the apex node of the NOA, which is very similar with the simulating prediction.
The reconstructed net-charge instantaneous distribution corresponding to the patterned near-field lightwaves is displayed in Fig. 8(c) to 8(e), which intuitively describe a dipole-type instantaneously distribution of the net positive and negative charges over the side surface of a single NOA according to a top viewing and 3D presentations. As shown, the aggregated “free electrons” only instantaneously appear on the right side with a relatively large density according to a half-wavelength standing wave mode, while the counterpart with a relatively loose net positive charge arrangement are mainly situated on back side. The formed dipole net-charge distribution is basically consistent with the simulation shown in Fig. 2(b). A top viewing of an instantaneous dipole net-charge distribution corresponding to actual microband-shaped light spots is re-constructed, which presents a similar morphology with the near-field lightwaves measured, as shown in Fig. 8(c). Both 3D viewing of an instantaneous negative and positive net-charge distribution patterns are demonstrated in Fig. 8(d) and 8(e), respectively. It should be noted that the asymmetrical dipole charge appearance is likely originated from several factors including: (1) the incident direction of the SNOM beams existing an obvious difference from the simulating setting of 45°, and (2) the relatively strong measurement beams already stimulating a tightly aggregating surface “free electrons”, and (3) the device existing ~ 30 nm inclining over the measurement bench.
The excited near-field lightwave oscillation over the NOA can be represented based on Eq. (1) by the following equation of
where T is the oscillation period. A series of snapshots of \({f_j}(x,y,z,t)\) within a half of T corresponding to a single NOA at selected moment such as t = 0, t = 1/6T, t = 1/4T, t = 1/3T, and t = 1/2T, are shown in Fig. 9, where z-axis represents the instantaneous surface net-charge distribution density. As illustrated, there existing a significant period variation of the dipole net-charge distribution density, and the maximum distribution density of “free electrons” already reaching ~ 5×10− 6 units at initial moment shown in Fig. 9(a), while the maximum density of the positive net-charges of ~ 7×10− 6 units appears at t = 1/3T shown in Fig. 9(d).
An overview of the dipole net-charge instantaneous distribution over an arrayed Au NOA are given in Fig. 10. Both the amplitude and phase images are given by Fig. 10(a) and 10(b), respectively. As shown, the shaped DNCSs are similar to that of a single Au NOA mentioned, but the upper NOAs present a greater amplitude due to the stronger illumination of SNOM beams. As shown in Fig. 10(c), each NOA in the upper line nearly paralleled to the incident direction of SNOM beams, presents an obvious DNCSs nearing the NOA bottom and a relatively high density. However, a relatively weak positive net-charges still appears over the planar facet between NOAs. Moreover, the net-charges in a similar dipole mode over both adjacent NOAs with much weaker density. So, an obvious tip proximity effect can be observed, which means that the same species net-charges distributed over surrounding planar facet and further a weak dipole net-charge arrangement nearing the bottom boundary of each adjacent NOA, so as to generate a localized resonant enhancement of the surface waves, can be predicted.
The near-field lightwave behaviors of an arrayed silicon NOA covered by a common metal film, which are excited by measurement lasers with a central wavelength of 633 nm and then closely correlated with a dipole net-charge instantaneous distribution over the NOA surface, are carefully investigated. An obvious Coulomb blockade from the apex region of the NOA apparently influencing the net-charge converging over its side surface is clearly observed, which can also be predicted by the simulations according to the surface standing waves across the apex node corresponding to both the surface lightwaves and the surface net-charge density waves. The antinodes of the surface positive and negative net-charge instantaneous distribution are already pushed away the normal location owing to the Coulomb blockade effect of the apex, so as to present a distorted waveform different from the traditional standing wave mode. The tip proximity effect leading to a relatively weak nano-converging of the net-charges over surrounding planar facet and also adjacent NOAs, so as to generate a localized resonant enhancement of the surface waves, is also discovered. The research highlights the potential applications such as low-cost nano-lithography, super-high-intensity electron or light emission, and ultra-sensitive light detection through NOA.
Sample fabrication. The n-type silicon material is selected for forming an arrayed silicon NOA mainly by EBL and ICP etching.
At first, a photoresist array is fabricated over the silicon wafer via EBL (JBX 6300FS, JEOL). During the EBL exposure, the fine pattern is set to be nano-blocks (200 nm \(\times\) 200 nm) with an arranged period of 500 nm. And then, a spin processing is conducted according to main parameters being set as 40s and 4000 rpm for forming a layer of tackifier (AR 300 − 80) with a thickness of 20 nm for enhancing the adhesion between the wafer and the photoresist. After spin-coating, the sample is baked at 180°C for 2 minutes. A negative photoresist (ma-N2403) with a thickness of 380 nm is fabricated according to main parameters being set as 40s and 2000 rpm and afterwards baked at 90°C for 1 minute. Furthermore, an arrayed photoresist mask is defined by e-beam exposure, and then developed by Tetramethylammonium Hydroxide (TMAH) for 2 minutes to acquire a needed pattern over the surface of silicon substrate.
Secondly, the ICP etching (Oxford Plasma Pro System 100 ICP 380) is performed to form a nano-cone-tip array upon silicon wafer. The chemical reactions are conducted by SF6 for 5 sccm and C4F8 for 100 sccm. The main technological parameters include: the pressure of 12 mTorr, the ICP power of 1200 W, the RF power of 50 W, the reaction temperature of 10 ℃, and the etching time of 5.5 min.
Finally, a 30 nm thick gold film is deposited over the silicon nano-cone-tips using the magnetron sputtering (Kurt J. Lesker LAB 18), so as to construct an Au-NOA metasurface. Noting that a 20-nm-thick Ti layer is previously coated and thus directly contact to the silicon material for enhancing Au film’s adhesion over the tapered silicon NOA.
SNOM measurements. Considering the significant sensitivity to the electric-field component outward from the surface of micro-nano-architectures, the scattering-type SNOM (NeaSNOM, Neaspec GmbH Co.) based on the atomic force microscope (AFM) system is adopted to measure the net-charge distribution density over the facet of the NOAs. The experimental set-up is briefly described below. The p-polarized incident beams with a central wavelength of ~ 633 nm is incident obliquely along the diagonal with an incident angle of 45° upon a horizontal facet, which is the same as that shown in Fig. 1(a). During measurements, the incident beams is focused via a parabolic mirror onto both the sample and the platinum AFM probe oscillated vertically, which is also applied as a scattering source and its tip-scattered light is modified according to the near-field lightwave properties of the sample below the tip. And then, the tip-scattered light is demodulated at the n-th harmonics of the tapping frequency yielding background-free images. To fully filter out the background signal, n = 3 is currently chosen in this work. Finally, both the amplitude and phase of the tip-scattered light, delivering the information about the near-field electric-component signals, are recovered through an all-optical interferometric detection39.
Availability of Data and Materials
The datasets generated and/or analysed during the current study are not publicly available but are available from the corresponding author on reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 61432007 and 61176052). The authors would like to thank Fangfang Peng, Xiuxia Wang, Yizhao He and Xiaolei Wen from the University of Science & Technology of China for experimental support.
Author Contributions
T.L. conceived the study, conducted the simulation, and led the device fabrication and characterization. J.S., S.D. and W.J. contributed to the device fabrication and characterization. Z.W. assisted with the device fabrication and characterization. T.L. and J.S. interpreted and discussed the results. T.L. wrote the manuscript. X.Z. contributed to the writing—review and editing, supervision, project administration and funding acquisition. All authors have read and agreed to the published version of the manuscript.
Additional Information
Competing Interests: The authors declare no competing interests.
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No competing interests reported.