Polarization dependence of the optical absorption of a subwavelength tip

Applied Surface Science 258 (2012) 9202–9207

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Polarization dependence of the optical absorption of a subwavelength tip A. Vella ∗ , N. Sevelin-Radiguet, J. Houard, B. Deconihout Groupe de Physique des Materiaux UMR CNRS 6634 – UFR Sciences Site du Madrillet, Avenue de l’Université – B.P. 12, 76801 Saint Etienne du Rouvray Cedex France

a r t i c l e

i n f o

Article history: Available online 14 January 2012 JEL classification: 68.43.Tj 79.70.+9 42.65.−k 42.65.ky

a b s t r a c t Laser assisted atom probe tomography is used to investigate the polarization dependence of the absorption of a subwavelength tip illuminated by an ultra short laser pulse. Al and Si tips are investigated and experimental results are discussed and explained using electromagnetic theory in the simplified cylindrical geometry. Numerical simulations in a more real geometry are also presented and used to show limits of the cylindrical model and to show the role of the very end tip apex in the absorption process. © 2012 Elsevier B.V. All rights reserved.

Keywords: Optical nanoobject Field emission Atom probe

1. Introduction Many materials analysis techniques are based on the interaction of light with a nanometer-scale tip. One can cite laser ablation of nano objects [1,2], apertureless scanning near-field optical microscopy (SNOM) [3], tip enhanced Raman spectroscopy (TERS) [4], ultra fast electrons emission [5,6] or atom-probe tomography [7,8]. In apertureless SNOM and TERS, the tip apex acts as a single and extremely manoeuvrable hot spot to selectively probe the region of interest with a high resolution [9]. In the atom-probe tomography assisted by ultrafast laser pulses (La-APT) or in subfemstosecond cold electron sources, ions or electrons are emitted from a tip by the combined action of a standing (dc) field and a laser pulse that triggers the emission [5,10]. For all these applications, the laser-tip interaction causes linear and non-linear optical effects such as field enhancement [11], SHG [12] or surface optical rectification [10]. It also induces a heating of the tip and of the imaged specimen [13–15]. The understanding of the absorption and the resulting heating taking place in these systems is a key factor for estimating the relative contributions of thermal and optical effects. It is well known that the absorption changes with the laser wavelength and polarization [16]. The absorption dependence on the laser polarization has been calculated on planar surfaces, on infinite cylinders or on nanometric objects in the case of metals or semiconducting

∗ Corresponding author. Tel.: +33 02 32 95 51 68; fax: +33 02 32 95 50 32. E-mail address: [email protected] (A. Vella). 0169-4332/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2012.01.051

materials [17–19]. However, in the case of tips, the effect of the polarization was experimentally investigated in the case of electron photo-field emission. The results of Lee et al. [20] and Venus and Lee [21] show a continuous increase of the photo-field emission when the polarization of the incident light is changed from the axial direction (along the tip axis) to the transverse one. Assuming that the photo-field emission is due to a thermal effect, the absorption of the tip increases uniformly from axial to transverse polarization. More recently, Hommeloff et al. [5] have reported a completely opposite behavior where the photocurrent decreases from the axial to the transverse polarization. This behavior is explained by assuming that the photocurrent is due to a photo-field emission effect and not to the thermal effect. A similar behavior was reported by Cerezo et al. [22] in the study of the ion emission in laser assisted APT. In LaAPT the ion emission is assumed to be caused by a thermal effect resulting from a pulse heat following the laser pulse. In this case the absorption of the nanometric tip as a function of the polarization can be directly deduced from the ion current measurement. In the case of metallic tips, we recently showed that the dependence of the absorption with the polarization of a sub-wavelength tip is strongly wavelength dependent and that an axial polarization can lead to a higher absorption than a transverse one for wavelengths in the UV range [23]. In this paper, La-APT is used as a very sensitive probe of surface to study the polarization dependence of the absorption of metallic and semiconducting tips. The differences between the observed results on these materials are discussed through analytical and numerical models. The analytical model is first developed in the simple cylindrical geometry. Then a more realistic model,

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Fig. 1. Experimental setup. PH: photodiode; PM: powermeter, BS: beam splitter, P: polarizer, /2 half plate, HV: high voltage. Inset defines laser direction and polarization.

accounting for the actual shape of the tip, is incorporated during the numerical simulations based on a finite difference time domain (FDTD) method. 2. Results 2.1. Experimental setup In our experiments, we used a 1 kHz pulsed Ti:Sa Laser ( = 788 nm) with 120 fs pulses having a tunable energy of up to 2.5 mJ/pulse. The specimen is pulsed in ultra high vacuum (<10−7 Pa) in a Tomographic Atom Probe with a flight path length of about 20 cm. A position-sensitive detector (PSD) [24] with improved multi-hit capabilities is used to accurately measure the detection rate as a function of the DC field on the tip and of the laser intensity. The laser beam was slightly focused onto the tip with a spot diameter of 0.8 mm controlled by a CCD camera. Using an Optical Parametric Amplifier, the laser wavelength can be tuned continuously between 280 nm and 2.6 ␮m. The optical setup is reported in Fig. 1 and more details can be found in Ref. [25]. The linear polarization is rotated of a angle  with respect to the tip axis using a /2 plate. The Al field emitter was electrochemically etched from a 1 mm-diameter aluminum wire [26]. Si specimens were needle shaped using focused ion beam (FIB) milling. More details on this method are available elsewhere [27]. When no laser pulse is applied on the sample, the DC field necessary to remove atoms at a given flux by field evaporation is Fevap . Under laser excitation, the DC field F(E) necessary to achieve the same flux is lower and depends on the pulse energy (E). The field reduction (FR) is defined as: FR(E) = 1 −

F(E) Fevap

(1)

of the angle of polarization () for different wavelengths as shown in Fig. 2(a).  = 0◦ and  = 180◦ correspond to an axial polarization,  = 90◦ and  = 270◦ to the perpendicular one. For long wavelengths, the FR in axial polarization is higher than in perpendicular polarization, showing that the laser contribution to the evaporation in axial configuration is 9, 5, 1.5 and 1.5 times higher than that in perpendicular configuration at respectively  = 1600 nm,  = 1200 nm,  = 800 nm and  = 500 nm. A similar behavior was reported by Cerezo et al. [22] on a tungsten tip at  = 515 nm. Recent results on laser assisted field evaporation of ions from metallic tips, have shown that the absorption of the laser energy increases the tip surface temperature sufficiently to allow the evaporation of atoms [28,29,22]. A higher laser contribution to the evaporation (higher FR) corresponds to a higher tip temperature and hence, to a higher laser absorption. Thus, the changes of the FR reported in Fig. 2 can directly be attributed to the absorption efficiency changes with the laser polarization and the wavelength. However, for decreasing wavelengths the laser absorption in transverse polarization increases and, for  = 355 nm, the absorption does not depends on the polarization. For wavelengths below 355 nm, the absorption in perpendicular polarization becomes even more efficient than in the axial one. The same experiment was conducted on a Si tip with an end radius of R = 45 ± 5 nm. The laser energy E was set to give a FR of about 10% in axial polarization mode as shown in Fig. 2(b). When the wavelength decreases, the absorption in perpendicular polarization does not change monotonically. It reaches a minimum at  = 515 nm and then increases for shorter wavelengths. Moreover, the absorption becomes polarization independent at high wavelengths ( = 1030 nm). Similar results were numerically predicted on Si nanowires by Ding et al. [19]. Our experimental observations are summerized in Table 1.

The field reduction can also be considered as a measurement of the laser contribution to the evaporation. 3. Theoretical considerations 2.2. Polarization dependence 3.1. Analytical model For an Al tip with a end radius of R = 55 ± 5 nm, the laser energy E is set at a fixed value so as to obtain a FR of about 17% in the axial polarization mode. Then, the FR’s are measured as a function

If we consider the tip as an infinite cylinder of radius R equal to the apex radius of the tip, we can calculate the absorption

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with Bm||

R 

×

=



(2)

Hm



(−i)m+1 2 R









1 (2)

˜ m 2 R Jm 2n˜ R − nH







2 R Jm 2n˜ R



(4)

and in perpendicular polarization [17]:

 Q⊥ = R

+∞        Bm|⊥ 2 J∗m 2n˜ R Jm 2n˜ R   n˜ 2   

in˜ ∗

 (5)

m=−∞

with Bm⊥

R 

×



=

(2)

˜ m nH

(−i)m+1 2 R







1



(2)

2 R Jm 2n˜ R − Hm







2 R Jm 2n˜ R



(6)

where • Jm is the m-th order Bessel function of first kind, • H(2) m he m-th order Hankel function of second kind, • n˜ is the optical index at a given .

Fig. 2. FR versus the laser polarization direction  for (a) Al tip:  = 300 nm (stars),  = 355 nm (diamond),  = 515 nm (empty triangle),  = 800 nm (triangle),  = 1200 nm (circle),  = 1600 nm (full square) and for (b) Si tip:  = 343 nm (open circle),  = 515 nm (full circle),  = 1030 nm (full triangle).

efficiency Q(⊥) () for the axial and perpendicular polarizations using equation developed by Robins et al. [17]: Q(⊥) =

abs P(⊥)

(2)

Pi

abs is the absorbed laser power and Pi the incident power. where P(⊥) In the simple cylindrical geometry, the incident field can be expanded on the Bessel functions, hence the absorption efficiency in the axial polarization becomes [17]:



+∞      2  Bm||  Jm 2n˜ R J∗m 2n˜ R Q|| = R in˜ ∗

m=−∞





 (3)

We performed the calculation of the absorption efficiency for every value of , taking into account the dependence of the refractive index with the wavelength n = n() [30]. The results of the analytical calculations are shown in Fig. 3. For an Al cylinder of R = 55 nm, this model predicts well the experimental behavior: the two curves (Q|| and Q⊥ in Fig. 3(a)) intersect at  = 360 nm corresponds to the polarization free emission efficiency experimentally observed. The peak at  = 800 nm in the Q|| curve corresponds to the typical Al absorption peak. However, for wavelengths below 300 nm this model predicts an increase of the absorption in the perpendicular polarization (Note that we could not experimentally verify this increase due to the experimental limitations). However we performed numerical experiments to investigate the role of the wavelength as reported in the next section. For a Si cylinder with R = 45 nm, as reported in Fig. 3(b), this model predicts an increase by a factor 2(respectively 1.3) from the perpendicular to the parallel polarization at  = 515 nm (respectively  = 343 nm) and no dependences on the polarization for  = 1030 nm, as experimentally reported. The peaks in Fig. 3(b) correspond to the m = 1 and m = 2 partial-wave mode, from Eqs.(3) and (5) [19]. The absorption in the transverse polarization is smaller or equal to the absorption in parallel polarization for all wavelengths. Hence, following this model, no inversion in the absorption efficiencies of the parallel and perpendicular polarizations at low laser wavelengths is expected. To check for this prediction and hence to validate this model for wavelengths closer to the tip end radius, we performed numerical simulation.

Table 1 Field reduction FR(⊥) for the axial and perpendicular polarizations ( = 0◦ and  = 90◦ ) respectively for Al and Si as a function of .

Al Si

 = 300 nm

 = 350 nm

 = 515 nm

 = 800 nm

 = 1030 nm

 = 1200 nm

FR⊥ > FR||

FR⊥ = FR|| FR⊥ < FR||

FR⊥ < FR|| FR⊥ < FR||

FR⊥ < FR||

FR⊥ < FR|| FR⊥ = FR||

FR⊥ < FR||

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Fig. 3. Absorption efficiency versus the laser wavelength: (a) Al tip with a radius R = 55 ± 5 nm; (b) Si tip with a radius of R = 45 ± 5 nm. Black line corresponds to axial polarization, red line to transverse polarization. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

3.2. Numerical simulations To get a more realistic description of the optical properties of the tip, 3D absorption maps were computed on a specimen with a geometry closer to a real tip by finite difference time domain (FDTD). Maps were calculated using a commercial software from Lumerical [31]. In this model, the tip is represented as a cylinder terminated by a hemispherical cap with a radius R. This tip is surrounded in the simulated space by a perfectly matching layer avoiding any field reflection (20 layers with a reflectivity equal to −380 dB for normal incidence). An adaptive mesh is used to divide the volume in cells, the smallest (4 nm) being located near the tip surface. The simulations are performed on a volume of 1500 nm × 1500 nm × 4000 nm. For every wavelength, the optical properties of the material are taken into through the dielectric constant taken from Ref. [32]. Fig. 4 shows the absorption efficiency Q along the tip axis (z axis) computed for the axial and transverse polarization. z = 0␮m corresponds to the border between the semi-cylinder and the hemispherical cap. Dot lines give the values of Q derived from the analytical model of the infinite cylinder developed in the previous section in Eqs.(3) and (5). Q curves always exhibit a close same behavior. An oscillation of Q is observed, with a periodicity equal to the laser wavelength. This oscillation is independent of the length of the cylinder. Hence it cannot be attributed to possible interferometric effect observed when the boundary conditions are not well chosen. This oscillation of the absorption is due to the light diffraction at the tip apex, as shown by Sommerfeld [33] in the case

of rigorous calculations of near field diffraction on a half-infinite plate, perfectly conductive, infinitely thin and enlightened perpendicularly with p-polarized light. Oscillations of the current density with a periodicity equal to the laser wavelength is observed. On a real material the absorption properties are linked to the surface current density through their conductivities. In the case of a tip, the apex acts as a diffraction source emitting in all directions. This source interacts with the incident and the reflected beam giving rise to oscillating surface currents on the shank of the specimen. It leads in the case of non-perfectly conductive material to absorption maxima, as already reported by authors in [28]. For shorter wavelengths, one can observe a peak located at z = 0 corresponding to the absorption of the hemispherical cap. Comparing the simulated results with the experimental and analytical results, it is possible to discuss the role of the hemispherical cap on the absorption. For  = 360 nm the value of Q at the apex is equal for the two polarization conditions, but higher than the analytical value. This situation corresponds to the polarization free emission and hence absorption. For  = 1200 nm, there is no influence of the tip apex on Q, Q oscillating almost around the value analytically calculated for each polarization. For  = 250 nm, as reported in Fig. 5(a), the contribution of the hemisphere cap to the tip absorption becomes very important. As expected, the transverse polarization is more efficient than the parallel one all along the semi-cylinder while on the hemisphere this efficiency is very strong. Actually, at  = 250 nm we are close to the excitation of the local transverse resonance of the plasmon polariton of a 55 nm Al sphere in air (around  = 200 nm). As already reported on nanorods [34,35], changing the laser

Fig. 4. Absorption efficiency along the tip axis z for Al: (a)  = 360 nm and (b) = 1200 nm. Black line corresponds to axial polarization, red line to transverse polarization and dashed line to the analytical results from Eqs. (3) and (5). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Fig. 5. Absorption efficiency along the tip axis z at  = 250 nm for (a) Al and (b)Si. Black line corresponds to axial polarization, red line to transverse polarization and dashed line to the analytical results from Eqs. (3) and (5). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 6. Absorption efficiency along the tip axis z for Si: (a)  = 343 nm and (b)  = 515 nm. Black line corresponds to axial polarization, red line to transverse polarization and dashed line to the analytical results from Eqs. (3) and (5). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

polarization from transverse to axial, the transverse or the longitudinal plasmon polariton can be exited. In the case of nanorods, the two laser wavelengths for the excitations are close to the plasmon polariton resonance wavelength of a nanosphere with a diameter equal to the axial or transverse dimension of the nanorod. Because these nanorod’s dimensions are close (the aspect ratio generally ranges between 1 and 10), the two resonances are in the same spectral range (visible for Au nanorods). In the case of APT samples, the longitudinal excitation is not observable, due to the long axial dimensions of the tip, but the transverse plasmon polariton can be exited using transverse polarization and is expected to be close to the plasmon polariton resonance of the nanosphere which terminates the tip. For Si tip, the simulated absorption efficiency Q for both polarizations is reported in Fig. 6. We still observe the oscillations of Q along the tip axis, due to the light diffraction effect, at the apex. For  = 515 nm, there is no influence of the tip apex and the values of Q oscillate around the analytical values (doted lines). For  = 343 nm, the contribution of the hemisphere appears only in the transverse polarization, even if the parallel polarization is still the most efficient. For  = 250 nm, as reported in Fig. 5(b), the absorption due to the semi-cylinder is polarization independent, as expected by the infinite cylinder model. However on the hemisphere at the apex, the transverse polarization is more efficiently absorbed than the axial one. For a Si nanosphere in air with a radius of R = 45 nm, equal to the end tip diameter, a plasmon resonance is expected at

 = 294 nm. For Si nanorods or nanowires with the same end radius and long axial dimensions, the plasmons polariton resonance can be excited almost at the same wavelength. Hence for  = 250 nm, as reported in Fig. 5(b) we are close to the transverse plasmon polariton resonance and we expect that the absorption in the transverse polarization becomes more efficient than in the axial polarization. 4. Conclusion We have shown that laser assisted atom-probe tomography is a very sensitive tool allowing surface absorption processes to be investigated on a tip with sub-wavelength dimensions. It is possible to study the absorption efficiency as a function of the wave polarization or the wavelength by a direct probing of the field ion emission from the field emitter surface. We showed that for Al and Si tips the absorption efficiency becomes higher in the transverse polarization than in the axial one, for conditions close to the resonance of plasmon polaritons of the hemisphere cap that ends the tip. Actually, the excitation of the plasmon resonance becomes easier using the transverse polarization of the incident laser. Moreover, under this conditions, the absorption is very high and located at the extreme surface of the tip. This confinement of the absorption is very important for the La-APT performance. Indeed, this results in a confined and uniform heating of the whole surface of the specimen apex, ensuring a homogeneous field evaporation of single atoms and an ultrafast cooling of the temperature. In the laser assisted APT, the

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