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Ultrafast emission of ions during laser ablation of metal for 3D atom probe
Applied Surface Science 255 (2009) 5154–5158
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Ultrafast emission of ions during laser ablation of metal for 3D atom probe A. Vella *, J. Houard, F. Vurpillot, B. Deconihout Groupe de Physique des Materiaux, UMR CNRS 6634 – UFR Sciences Site du Madrillet, Avenue de l’Universite´ – B.P. 12 76801, Saint Etienne Du Rouvray Cedex, France
A R T I C L E I N F O
A B S T R A C T
Article history:
The 3D atom probe(3DAP) is an imaging instrument based on the controlled field evaporation of single atoms from a sample having a tip shape with an end radius of 50 nm. In the fs laser assisted 3DAP the evaporation is induced by the laser pulses so that the physical process involved in this 3DAP analysis might correspond to the very early stages of the ablation process. In this paper we present the principle of the 3DAP and we discuss the existing models of the fs assisted evaporation. At last, we test the relevance of these models with pump-probe experiments on tungsten tips in the tomographic atom probe. ß 2008 Elsevier B.V. All rights reserved.
Available online 12 September 2008 PACS: 68.43.Tj 79.70.+9 42.65.-k 42.65.ky Keywords: Non-linear Optic optical rectification Field emission Atom probe
1. Introduction The three-dimensional atom probe (3DAP) provides chemical analysis at the near atomic level, making it possible to reconstruct the position and identity of the majority of atoms within a nanoscale volume of material [1]. In the 3DAP, a specimen in the form of a sharp needle is held at cryogenic temperatures in an ultra-high vacuum chamber. Atoms removed from the apex of the specimen by field evaporation are projected along near-radial trajectories onto a position-sensitive detector. These atoms are chemically identified using time-of-flight mass spectrometry, and the impact position on the detector allows the original position within the material to be reconstructed with sub-nanometre lateral resolution, and atomic resolution in depth. Field evaporation is normally generated by a combination of a high DC voltage and nanosecond duration high voltage pulses applied to the needle-shaped specimen, producing electric fields at the apex of 10–50 V/nm. Since the specimen is field evaporated atom by atom, layer after layer, a virtual image of the distribution of atoms in the probed volume is obtained after the analysis. Fig. 1 shows an example of an image obtained from the analysis of a nickel base superalloy with the 3DAP. Nevertheless, the use of high-voltage (HV) pulses in atom probe tomography prevents its application to poorly conducting materials. To overcome this
* Corresponding author. E-mail address: [email protected] (A. Vella). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.08.109
limitation, a combination of high DC voltage and a laser pulse can be used to produce the required field evaporation [2,3]. Pulsed lasers were already implemented on atom probes. In the case of nanosecond or sub-nanosecond laser pulses, field evaporation was clearly be provoked by thermal effects [4]. Temperature rise of up to a few hundreds of kelvins were calculated by Liu et al. [6,5], or experimentally determined by Kellogg for example [7]. To overcome this limitation, we proposed to use ultrafast laser pulses to induce field evaporation [8,9]. The performances of an ultrafast laser-assisted tomographic atom probe were recently discussed [10]. The new fs laser assisted TAP provides efficient analysis on metals, semiconductors or even insulators. The interaction of the ultrafast laser with the nanometric tip still induces an increase of the sample temperature but this increase has been shown, through either surface atom diffusion or by performing dedicated pump-probe experiments [11], to be far too low to achieve the evaporation. In addition, recent pumpprobe experiments seems to indicate that the ion emission is actually taking place on a femtosecond time-scale [12]. Our group proposed an interpretation of this ultrafast emission as resulting from the action of the quasi-dc (THz) electric field generated by the electronic non-linear optical response of the metal surface: the so-called optical rectification (OR) effect [13]. Recently we presented the first quantitative model of the OR electronic surface field and used it to perform a rough verification of its contribution to TAP analysis [14]. This model was also able to explain the anisotropic material ejection as observed on gold nano-particles [15].
A. Vella et al. / Applied Surface Science 255 (2009) 5154–5158
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Using fs laser, due to the photo-excitation, the electron–phonon impact probability increases and allows to achieve very high temperatures. Using a basic model for photon absorption in a metal [17], we can write: T ¼ T 0 þ dI
(2)
with T0 the base temperature and d a constant proportional to the imaginary part of the dielectric constant. Replacing T in Eq. (1), we obtain the dependence of the ion flux with the laser intensity. Such a behavior has not been observed on metallic tips [13]. Due to the nanometric dimension of the tip, the constant d also depends on the laser polarization and on the ratio R/l, where R is the tip end radius and l the laser wavelength [18]. The light diffraction at the tip apex works as a laser light focalization, so that the temperature increase is higher at the apex and the heated zone is much smaller than the laser spot on the tip. This diffraction effect can highly decrease the cooling time of the tip to less than 1 ns. In fact, in order to find a analytical solution to the problem of the thermal evolution of the tip after illumination, the problem can be reduced to a cylindrical geometry. The temperature distribution is assumed to follow a Gaussian law centred on the tip apex along the z-axis just after the laser illumination. Tð0; zÞ ¼ T 0 þ T rise ez=2s
2
(3)
with Trise the temperature rise and s the size of the heated zone. The start time is here defined just after the thermalization between electrons and lattice (a few ps after the pulse). Once the energy is deposited into the tip, the temperature evolution simply follows the diffusion equation of the heat conduction.
Fig. 1. 3D atom probe principle: PSD = position sensitive detector (top). 3D image of Al (red) and Cr (yellow) atoms in a nickel base superalloy showing the presence of Al enriched particles (diameter = 7 nm) embedded in a Cr rich matrix (down) (Courtesy M. Gilbert and C. Pareige).
In this paper, the field evaporation phenomenon is briefly described and both optical and thermal mechanisms for fs assisted evaporation are considered and illustrated by experimental results. 2. Theoretical considerations The field evaporation theories are based on one-dimensional modelling of the potential atomic and ionic energies of an adatom on the surface of a jellium. The field evaporation corresponds to the transition from an atomic state to an ionic state of lower energy. At the base temperature, the thermal energy enables the transition above the energy barrier formed by the atomic and ionic potentials. In a first approach, the barrier height Q(F) is generally considered as a linear function of the electric field F [16]. The field evaporation rate f follows a Maxwell–Boltzmann statistics, and can be written as
f ¼ n exp
Q ðFÞ kB T
(1)
with n the surface atom vibration frequency, of the order of 1 ps, kB the Boltzmann constant and T the applied base spacimen temperature. For a critical electric field, named evaporation field Fe, the height of the potential barrier can be decreased to zero. For most metals, the evaporation field is in the range of 20–50 V/nm. The field evaporation process depends critically on the electric field or on the temperature, it is thus possible to precisely control the amount of evaporated atoms by tuning either the electric voltage or the temperature of the tip.
@T @2 T a 2 ¼0 @t @z
(4)
An analytical solution to this problem is found if the thermal diffusivity a is assumed to be a constant. The temperature relaxation is given by T rise 2 2 Tðt; zÞ ¼ T 0 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ex =2ðs þ2atÞ 1 þ 2at=s 2
(5)
Note that at the apex, the temperature is found to fast decrease in time, with a time constant s2/a. This equation obviously neglects the increase in cooling rate induced by the shank angle, when this shank is larger than zero. With not too large angle (less than 208), the error on the temporal evolution of the tip temperature remains relatively small and only leads to slightly underestimate the heated zone size using Eq. (5) to fit the numerical data (up to a factor 2) [19]. The diffraction effect decreases the heated zone s so that the cooling time decreases also. Following this thermal model for the ion evaporation, we expect an evaporation time shorter than the cooling time by one order of magnitude, so that, typically, a few hundred of ps. The field evaporation under ultra-fast laser pulsing could be also due to the lowering of the surface potential barrier. In Ref. [14], we present the first quantitative model to calculate the quasi-dc (THz) electric field generated by the optical rectification (OR) effect. Optical rectification is a classical second-order nonlinear optical process taking place in non-centrosymmetric materials. It is also predicted to occur at the surfaces of all materials, where inversion symmetry is broken by the strong material gradients. However, a direct detection of surface OR is very difficult and an undisputable evidence of its occurrence is still lacking, although some possible confirmations have been reported [20,21]. Theoretically, the properties of OR on metal surfaces may be calculated by the same methods used for
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Fig. 2. Experimental setup. PH: photodiode; PM: powermeter, BS: beam splitter, P: polarizer, l/2 half plate, HV: high voltage. Inset defines laser direction and polarization.
modeling second harmonic generation (SHG) [22–24]. The resulting electric field (z-component) created within a very thin layer is given by ð2Þ
F OR / x
ðzÞLeff I0 ; 2
(6) (2)
where I0 = 2e0cjF0j is the input light intensity, x (z) is the nonlinear surface susceptibility and Leff is the (macroscopic) local-field tensor which takes into account the enhancement due to the tip shape of the sample [25]. For the evaporation assisted by optical rectification effect, we have to add the rectification field (FOR) to the standing field (FDC) in the expression of the barrier heigh (Q(F)). Hence, from Eq. (1), on a first approximation we obtain a linear dependence of the ion flux f with the laser intensity on a semilogarithm scale, as experimentally observed [13]. This OR field is generated during the laser pulse interaction with the sample, it is equivalent to a short electrical pulse (THz pulse), so that it can evaporate ions on a very short time scale given by the laser pulse width. We can conclude that the main difference between the two possible evaporation mechanisms using fs laser pulses are characterized by different evaporation times (at last 102 times bigger in the case of thermal effect). In the next section we propose an experimental setup to measure the evaporation time.
3. Results 3.1. Experimental setup In our experiments, we used a 1 kHz pulsed Ti:Sa Laser (l = 788 nm) with 120 fs pulse duration and a tunable energy of up to 2.5 mJ/pulse to pump metal tips. The specimen is placed into the ultra high vacuum (<107 Pa) chamber of a Tomographic Atom Probe with a flight path of about 20 cm. A position-sensitive detector (PSD) [26] with improved multi-hit capabilities is used to accurately measure the detection rate as a function of the DC field on the specimen and 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. The laser beam linear polarization is set parallel to the tip axis. Using a collinear autocorrelation setup, two laser pulses, with variable temporal delay, are used to evaporate the sample, as shown in Fig. 2. We can measure, for every fixed delay between the two pulses (t), the standing voltage (VT) necessary to allow a constant evaporation rate. Fig. 3. The experimental VT curve for a W tip with R = 40 nm at pump and probe laser intensity I1 = I2 = I0 = 3 1010 W/cm2 is reported in Fig. 4. We can observe the presence of a peak for t = 0. The two laser
Fig. 3. (a) Interferential structure of absorbed energy during pump-probe analysis. (b)Threshold voltage versus laser intensity.
A. Vella et al. / Applied Surface Science 255 (2009) 5154–5158
Fig. 4. Threshold voltage versus delay time for a W tip.
beams, focused on the tip, can generate both an ultrafast emission and, due to the absorption of a part of the laser energy, a heating of the lattice. In the case of OR assisted evaporation, if the evaporation is assisted by the THz pulse, the first pulse allows the evaporation instantaneously and the second pulse simply scan this THz pulse. In fact, for an evaporation assisted by optical rectification, the nonlinear field generated at the surface is F OR ðt; t Þ / xð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 :
(7)
where E1 and E2 the incident laser fields. In the expression for the activation energy we have to add to the standing field (FDC) the rectificated field (FOR): FT = FDC + FOR so it becomes: Q n ðt; t Þ / F T /
V
bR
þ lxð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 :
(8)
where b is a constant depending on the tip shape (generally equal to 5 for W tip), R is the tip and radius and l a proportional factor taking into account the enhancement effect. During the measure of the potential threshold, the evaporation flux is kept constant R1 ( 1 f dt ¼ const) so, from Eq. (1) and (8), we obtain:
Vðt Þ log bR
Z
1
ne
1
xð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 kB T
dt ¼ const
5157
experimental setup, we measure the threshold voltage (V) as a function of the delay between the two laser pulses so that an increasing of the intensity up to 4I0 will correspond to a reduction of V in order to maintain a constant evaporation rate. This voltage reduction can be measured as a function of the laser intensity as reported in Fig. 3(b). Hence, the peak value VT(t = 0) might correspond to the intensity increase due to the interferometric effect (I = 4I0 at t = 0 and I = 2I0 for 0 < t < t0). We can conclude that both mechanisms can be at the origin of the potential peak at t = 0, but we can distinguish between these two mechanisms looking at the variation of the potential for longer delay times. For a delay longer than the laser pulse duration tL, following the OR mechanism the two laser pulses induce the same evaporation flux: f(t = 2tL) = 2f1 where f1 is the evaporation flux induced by only one pulse. Considering the logarithm factor in Eq. (1), we expect a negligible change on the potential V(t > tL) = V1, where V1 is the potential when only one laser pulse is used, as shown in Fig. 3(b). Moreover, the first laser pulse increases the tip temperature on a typical time t0 given by the electrons phonons coupling time. After that, the cooling of the tip starts. If the second laser pulse evaporates on a ultrashort times scale, as predicted by OR, during pump-probe measurement this second pulse scans the cooling dynamics of the sample. A change of the tip temperature corresponds to a change of the evaporation efficiency of the second laser pulse, as predicted by Eq. (1), and hence to a change of the standing voltage. It is why we expect a second large peak at t0 in the voltage curve corresponding to the peak temperature of the tip. As shown in Fig. 5, experimentally we observe a slow increase of the potential on long delay time, but no other peak appears at t0 10 ps. Following the thermal model, by considering all the thermal parameters as constants, the result of the measurement is the voltage V(t) induced by the sum T(t,t) = T(t) + T(t t) T0 with T(t) defined by Eq. (5). For delay longer than the laser pulse, but shorter than t0, the two laser pulses are equal to a single pulse with double intensity (T(t,t) = 2T(t) T0). So that, we expect that the voltage is constant and equal to VT(I = 2I0), as observed. At longer delay time, we expect an increase of the voltage corresponding to the tip cooling after the interaction with the first laser pulse (as reported in Eq. (5)). The observed behavior at long delay of VT(t) matches well with the prediction of a thermal assisted evaporation, however, the peak value VT(t = 0) is not compatible with the measured value VT(I = 4I0) (see Fig. 5) as expected for a purely interferometric effect.
(9)
where T is, on a first approximation, independent on time. Supposing a gaussian profile for the incident laser intensity the potential function: V(t) looks like a high order cross-correlation of the incident laser pulse because the full width at half maximum (FWHM) of V is equal to that of the incident laser intensity, due to the non-linear response of the metallic tip. Moreover, due to the typical collinear autocorrelation setup, this pulse for t = 0 could also be due to the two laser beams interferences. The energy absorbed by the tip U and hence the temperature increase of the sample DT are related and given by Z 1 DTðt Þ / Uðt Þ / ðE1 ðtÞ þ E2 ðt t ÞÞ2 dt (10) 1
with a typical interference structure, as reported in Fig. 3(a). The energy is constant and proportional to 2I0 for a long delay time and is oscillating between 0 and 4I0 for delay time shorter than the laser pulse duration (tL). Due to the non-linear expression of the evaporation rate as a function of the tip temperature (see Eq. (1)), a very high flux is expected for t = 0 and I = 4I0. However, in our
Fig. 5. Threshold voltage versus delay time for a W tip. The dotted line corresponds to the value expected for I = 4I0.
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A. Vella et al. / Applied Surface Science 255 (2009) 5154–5158
removal compatible with time of flight mass spectrometry. The evaporation mechanisms discussed in this article have to be investigate in the case of non-conductive materials. Due to a residual laser absorption the thermal pulse is always a possible efficient effect. However, due to the breaking of the inversion symmetry at the oxide surface, the non-linear optical effects, such as OR, can occur. Moreover, resonant evaporation, as reported for silicon samples [4], can also appear depending on the photon energy. Naturally a accurate study of the strength of these effects will be performed to quantify the efficiency of each evaporation mechanisms. References
Fig. 6. 3D image of Fe(red), Mg(green) and O(blue) atoms in a tunnel barrier MgO oxide (Courtesy to T. Al Kassab).
4. Conclusions The evaporation of surface ions from a metal tip during fs assisted 3D-AP analysis can be due to either the thermal effect or to the non-linear OR effect. These two mechanisms are characterized by very different evaporation times: very short in the case of OR effect (less than 1 ps) and longer for thermal effect (more than 100 ps). We proposed a pump-probe setup to measure this evaporation time and study the contribution of each effect to the evaporation. On long delay time a clear contribution of thermal evaporation has been reported, however at very short delay, a fast evaporation appears. This ultra fast effect adds to the enhancement of the thermal evaporation due to laser beams interference. From our experimental results we can not conclude which mechanism prevails to the evaporation. A new experimental method is necessary to quantify the contribution of each mechanisms. As explained in the introduction, the fs laser assisted 3DAP provide efficient analysis on poorly conductive materials. In Fig. 6 a recent results obtained on a tunnel barrier of 4 nm of MgO oxide is shown. For the evaporation of semiconductors or insulator, we have to distinguish two things. The first one concerns the DC field. DC field is required to lower the height of the potential barrier and to generate the high magnification of the instrument. Since the tip surface is ‘‘connected’’ to vacuum, the DC polarization is ensured at the surface as it has been demonstrated over a wide range of application of the Field Ion Microscope on insulator such as glasses. The seconde thing concerns the transmission of an HV pulse to the material apex. Due to the high resistivity of the sample (coming from its very small apex) and to the capacitance coupling the specimen to the rest of the world, the limit in frequency is about 1 ns for semiconductors. For oxides much longer pulses should be used [27]. Whatever the physical process involved in the evaporation of semiconductors or insulating materials, the laser allows to bring ultrafast pulses (thermal pulse or OR pulse) at the specimen apex in order to get a accurate time control of atoms
[1] D. Blavette, A. Bostel, J. Sarrau, B. Deconihout, A. Menand, Nature 363 (1993) 432. [2] G. Kellogg, T. Tsong, Pulsed-laser atom-probe field-ion microscopy, J. Appl. Phys. 51 (2) (1980) 1184–1193. [3] M.N.T.T. Tsong, J.H. Block, B. Viswanatha, Photon stimulated field ionization, J. Chem. Phys. 65 (6) (1976) 2469. [4] T. Tsong, Y. Liou, S. McLane, Rev. Sci. Instrum. 55 (1984) 1246. [5] H. Liu, H. Liu, T. Tsong, Numerical calculation of the temperature distribution and evolution os the field-ion emitter under pulsed and continuous-wave laser irradiation, J. Appl. Phys. 59 (4) (1986) 1334. [6] H. Liu, T. Tsong, Numerical calculation of the temperature evolution and profile of the field-ion emitter in the pulsed-laser time of flight atom probe, Rev. Sci. Instrum. 55 (11) (1984) 1779. [7] G. Kellog, Phys. Rev. B 29 (8) (1984) 4304. [8] B. Deconihout, D. Blavette, A. Menand, Past, present and possible future of nanoanalysis with the three-dimensional atom probe, in: Proceedings of the 7th International Winter School of Physics (ITEP Moscow) 7, 2004, p. 53. [9] B. Gault, F. Vurpillot, A. Bostel, A. Menand, B. Deconihout, Estimation of the tip field enhancement on a field emitter under laser illumination, Appl. Phys. Lett. 86 (2005) 094101. [10] B. Gault, F. Vurpillot, A. Vella, A. Bostel, A. Menand, B. Deconihout, Design of a femtosecond laser assisted tomographic atom probe, Rev. Sci. Instrum. 77 (2006) 043705. [11] F. Vurpillot, B. Gault, A. Vella, M. Bouet, B. Deconihout, Estimation of the cooling times for a metallic tip under laser illumination, Appl. Phys. Lett. 88 (2006) 094105. [12] A. Vella, M. Gilbert, A. Hideur, F. Vurpillot, B. Deconihout, Ultra-fast ion emission from a metallic tip excited by femtosecond laser pulses, Appl. Phys. Lett. 89 (2006) 251903. [13] A. Vella, F. Vurpillot, B. Gault, A. Menand, B. Deconihout, Evidence of field evaporation assisted by nonlinear optical rectification induced by ultrafast laser, Phys. Rev. B 73 (2006) 165416. [14] A. Vella, B. Deconihout, L. Marrucci, E. Santamato, Femtosecond field ion emission by surface optical rectification, Phys. Rev. Lett. 99 (2007) 046103. [15] A. Plech, V. Kotaidis, M. Lorenc, J. Boneberg, Femtosecond laser near-field ablation from gold nanoparticles, Nature Physics 2 (2006) 44–47. [16] T.T. Tsong, J. Phys. F: Metal Phys. 8 (1978) 1349. [17] N.W. Ashcroft, N.D. Mermin, Solid State Physics, Saunders College, 1976. [18] E.S. Robins, M.J.G. Lee, P. Langlois, Can. J. Phys. 64 (1986) 111. [19] F. Vurpillot, J. Houard, A. Vella, B. Deconihout, Thermal response of a field emitter subjected to ultra fast laser illumination, PRB, submitted for publication. [20] A.V. Bragas, S.M. Landi, O.E. Martinez, Laser field enhancement at the scanning tunneling microscope junction measured by optical rectification, Appl. Phys. Lett. 72 (1998) 2075–2077. [21] F. Kadlec, P. Kuzel, J.-L. Coutaz, Optical rectification at metal surfaces, Optics letters 29 (22) (2004) 2674–2676. [22] J. Rudnick, E.A. Stern, Second-harmonic radiation from metal surfaces, Phys. Rev. B. 4 (12) (1971) 4274–4290. [23] J.E. Sipe, V.C.Y. So, M. Fukui, G.I. Stegeman, Analysis of second-harmonic generation at metal surfaces, Phys. Rev. B 21 (1980) 4389–4402. [24] M. Weber, A. Liebsch, Density-functional approach to second-harmonic generation at metal surfaces, Phys. Rev. B 35 (1987) 7411–7416. [25] A.H.A. Bouhelier, M. Beversluis, L. Novotny, Near-field second harmonic generation, Phys. Rev. Lett. 90 (2003) 013903. [26] G. Da Costa, F. Vurpillot, A. Bostel, M. Bouet, B. Deconihout, Rev. Sci. Instrum. 76 (2004) 013304. [27] A.J. Melmed, M. Martinka, S.M. vGrivin, T. Sakurai, Y. Kuk, Appl. Phys. Lett. 39–5 (1981) 413.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Ultrafast emission of ions during laser ablation of metal for 3D atom probe A. Vella *, J. Houard, F. Vurpillot, B. Deconihout Groupe de Physique des Materiaux, UMR CNRS 6634 – UFR Sciences Site du Madrillet, Avenue de l’Universite´ – B.P. 12 76801, Saint Etienne Du Rouvray Cedex, France
A R T I C L E I N F O
A B S T R A C T
Article history:
The 3D atom probe(3DAP) is an imaging instrument based on the controlled field evaporation of single atoms from a sample having a tip shape with an end radius of 50 nm. In the fs laser assisted 3DAP the evaporation is induced by the laser pulses so that the physical process involved in this 3DAP analysis might correspond to the very early stages of the ablation process. In this paper we present the principle of the 3DAP and we discuss the existing models of the fs assisted evaporation. At last, we test the relevance of these models with pump-probe experiments on tungsten tips in the tomographic atom probe. ß 2008 Elsevier B.V. All rights reserved.
Available online 12 September 2008 PACS: 68.43.Tj 79.70.+9 42.65.-k 42.65.ky Keywords: Non-linear Optic optical rectification Field emission Atom probe
1. Introduction The three-dimensional atom probe (3DAP) provides chemical analysis at the near atomic level, making it possible to reconstruct the position and identity of the majority of atoms within a nanoscale volume of material [1]. In the 3DAP, a specimen in the form of a sharp needle is held at cryogenic temperatures in an ultra-high vacuum chamber. Atoms removed from the apex of the specimen by field evaporation are projected along near-radial trajectories onto a position-sensitive detector. These atoms are chemically identified using time-of-flight mass spectrometry, and the impact position on the detector allows the original position within the material to be reconstructed with sub-nanometre lateral resolution, and atomic resolution in depth. Field evaporation is normally generated by a combination of a high DC voltage and nanosecond duration high voltage pulses applied to the needle-shaped specimen, producing electric fields at the apex of 10–50 V/nm. Since the specimen is field evaporated atom by atom, layer after layer, a virtual image of the distribution of atoms in the probed volume is obtained after the analysis. Fig. 1 shows an example of an image obtained from the analysis of a nickel base superalloy with the 3DAP. Nevertheless, the use of high-voltage (HV) pulses in atom probe tomography prevents its application to poorly conducting materials. To overcome this
* Corresponding author. E-mail address: [email protected] (A. Vella). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.08.109
limitation, a combination of high DC voltage and a laser pulse can be used to produce the required field evaporation [2,3]. Pulsed lasers were already implemented on atom probes. In the case of nanosecond or sub-nanosecond laser pulses, field evaporation was clearly be provoked by thermal effects [4]. Temperature rise of up to a few hundreds of kelvins were calculated by Liu et al. [6,5], or experimentally determined by Kellogg for example [7]. To overcome this limitation, we proposed to use ultrafast laser pulses to induce field evaporation [8,9]. The performances of an ultrafast laser-assisted tomographic atom probe were recently discussed [10]. The new fs laser assisted TAP provides efficient analysis on metals, semiconductors or even insulators. The interaction of the ultrafast laser with the nanometric tip still induces an increase of the sample temperature but this increase has been shown, through either surface atom diffusion or by performing dedicated pump-probe experiments [11], to be far too low to achieve the evaporation. In addition, recent pumpprobe experiments seems to indicate that the ion emission is actually taking place on a femtosecond time-scale [12]. Our group proposed an interpretation of this ultrafast emission as resulting from the action of the quasi-dc (THz) electric field generated by the electronic non-linear optical response of the metal surface: the so-called optical rectification (OR) effect [13]. Recently we presented the first quantitative model of the OR electronic surface field and used it to perform a rough verification of its contribution to TAP analysis [14]. This model was also able to explain the anisotropic material ejection as observed on gold nano-particles [15].
A. Vella et al. / Applied Surface Science 255 (2009) 5154–5158
5155
Using fs laser, due to the photo-excitation, the electron–phonon impact probability increases and allows to achieve very high temperatures. Using a basic model for photon absorption in a metal [17], we can write: T ¼ T 0 þ dI
(2)
with T0 the base temperature and d a constant proportional to the imaginary part of the dielectric constant. Replacing T in Eq. (1), we obtain the dependence of the ion flux with the laser intensity. Such a behavior has not been observed on metallic tips [13]. Due to the nanometric dimension of the tip, the constant d also depends on the laser polarization and on the ratio R/l, where R is the tip end radius and l the laser wavelength [18]. The light diffraction at the tip apex works as a laser light focalization, so that the temperature increase is higher at the apex and the heated zone is much smaller than the laser spot on the tip. This diffraction effect can highly decrease the cooling time of the tip to less than 1 ns. In fact, in order to find a analytical solution to the problem of the thermal evolution of the tip after illumination, the problem can be reduced to a cylindrical geometry. The temperature distribution is assumed to follow a Gaussian law centred on the tip apex along the z-axis just after the laser illumination. Tð0; zÞ ¼ T 0 þ T rise ez=2s
2
(3)
with Trise the temperature rise and s the size of the heated zone. The start time is here defined just after the thermalization between electrons and lattice (a few ps after the pulse). Once the energy is deposited into the tip, the temperature evolution simply follows the diffusion equation of the heat conduction.
Fig. 1. 3D atom probe principle: PSD = position sensitive detector (top). 3D image of Al (red) and Cr (yellow) atoms in a nickel base superalloy showing the presence of Al enriched particles (diameter = 7 nm) embedded in a Cr rich matrix (down) (Courtesy M. Gilbert and C. Pareige).
In this paper, the field evaporation phenomenon is briefly described and both optical and thermal mechanisms for fs assisted evaporation are considered and illustrated by experimental results. 2. Theoretical considerations The field evaporation theories are based on one-dimensional modelling of the potential atomic and ionic energies of an adatom on the surface of a jellium. The field evaporation corresponds to the transition from an atomic state to an ionic state of lower energy. At the base temperature, the thermal energy enables the transition above the energy barrier formed by the atomic and ionic potentials. In a first approach, the barrier height Q(F) is generally considered as a linear function of the electric field F [16]. The field evaporation rate f follows a Maxwell–Boltzmann statistics, and can be written as
f ¼ n exp
Q ðFÞ kB T
(1)
with n the surface atom vibration frequency, of the order of 1 ps, kB the Boltzmann constant and T the applied base spacimen temperature. For a critical electric field, named evaporation field Fe, the height of the potential barrier can be decreased to zero. For most metals, the evaporation field is in the range of 20–50 V/nm. The field evaporation process depends critically on the electric field or on the temperature, it is thus possible to precisely control the amount of evaporated atoms by tuning either the electric voltage or the temperature of the tip.
@T @2 T a 2 ¼0 @t @z
(4)
An analytical solution to this problem is found if the thermal diffusivity a is assumed to be a constant. The temperature relaxation is given by T rise 2 2 Tðt; zÞ ¼ T 0 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ex =2ðs þ2atÞ 1 þ 2at=s 2
(5)
Note that at the apex, the temperature is found to fast decrease in time, with a time constant s2/a. This equation obviously neglects the increase in cooling rate induced by the shank angle, when this shank is larger than zero. With not too large angle (less than 208), the error on the temporal evolution of the tip temperature remains relatively small and only leads to slightly underestimate the heated zone size using Eq. (5) to fit the numerical data (up to a factor 2) [19]. The diffraction effect decreases the heated zone s so that the cooling time decreases also. Following this thermal model for the ion evaporation, we expect an evaporation time shorter than the cooling time by one order of magnitude, so that, typically, a few hundred of ps. The field evaporation under ultra-fast laser pulsing could be also due to the lowering of the surface potential barrier. In Ref. [14], we present the first quantitative model to calculate the quasi-dc (THz) electric field generated by the optical rectification (OR) effect. Optical rectification is a classical second-order nonlinear optical process taking place in non-centrosymmetric materials. It is also predicted to occur at the surfaces of all materials, where inversion symmetry is broken by the strong material gradients. However, a direct detection of surface OR is very difficult and an undisputable evidence of its occurrence is still lacking, although some possible confirmations have been reported [20,21]. Theoretically, the properties of OR on metal surfaces may be calculated by the same methods used for
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Fig. 2. Experimental setup. PH: photodiode; PM: powermeter, BS: beam splitter, P: polarizer, l/2 half plate, HV: high voltage. Inset defines laser direction and polarization.
modeling second harmonic generation (SHG) [22–24]. The resulting electric field (z-component) created within a very thin layer is given by ð2Þ
F OR / x
ðzÞLeff I0 ; 2
(6) (2)
where I0 = 2e0cjF0j is the input light intensity, x (z) is the nonlinear surface susceptibility and Leff is the (macroscopic) local-field tensor which takes into account the enhancement due to the tip shape of the sample [25]. For the evaporation assisted by optical rectification effect, we have to add the rectification field (FOR) to the standing field (FDC) in the expression of the barrier heigh (Q(F)). Hence, from Eq. (1), on a first approximation we obtain a linear dependence of the ion flux f with the laser intensity on a semilogarithm scale, as experimentally observed [13]. This OR field is generated during the laser pulse interaction with the sample, it is equivalent to a short electrical pulse (THz pulse), so that it can evaporate ions on a very short time scale given by the laser pulse width. We can conclude that the main difference between the two possible evaporation mechanisms using fs laser pulses are characterized by different evaporation times (at last 102 times bigger in the case of thermal effect). In the next section we propose an experimental setup to measure the evaporation time.
3. Results 3.1. Experimental setup In our experiments, we used a 1 kHz pulsed Ti:Sa Laser (l = 788 nm) with 120 fs pulse duration and a tunable energy of up to 2.5 mJ/pulse to pump metal tips. The specimen is placed into the ultra high vacuum (<107 Pa) chamber of a Tomographic Atom Probe with a flight path of about 20 cm. A position-sensitive detector (PSD) [26] with improved multi-hit capabilities is used to accurately measure the detection rate as a function of the DC field on the specimen and 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. The laser beam linear polarization is set parallel to the tip axis. Using a collinear autocorrelation setup, two laser pulses, with variable temporal delay, are used to evaporate the sample, as shown in Fig. 2. We can measure, for every fixed delay between the two pulses (t), the standing voltage (VT) necessary to allow a constant evaporation rate. Fig. 3. The experimental VT curve for a W tip with R = 40 nm at pump and probe laser intensity I1 = I2 = I0 = 3 1010 W/cm2 is reported in Fig. 4. We can observe the presence of a peak for t = 0. The two laser
Fig. 3. (a) Interferential structure of absorbed energy during pump-probe analysis. (b)Threshold voltage versus laser intensity.
A. Vella et al. / Applied Surface Science 255 (2009) 5154–5158
Fig. 4. Threshold voltage versus delay time for a W tip.
beams, focused on the tip, can generate both an ultrafast emission and, due to the absorption of a part of the laser energy, a heating of the lattice. In the case of OR assisted evaporation, if the evaporation is assisted by the THz pulse, the first pulse allows the evaporation instantaneously and the second pulse simply scan this THz pulse. In fact, for an evaporation assisted by optical rectification, the nonlinear field generated at the surface is F OR ðt; t Þ / xð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 :
(7)
where E1 and E2 the incident laser fields. In the expression for the activation energy we have to add to the standing field (FDC) the rectificated field (FOR): FT = FDC + FOR so it becomes: Q n ðt; t Þ / F T /
V
bR
þ lxð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 :
(8)
where b is a constant depending on the tip shape (generally equal to 5 for W tip), R is the tip and radius and l a proportional factor taking into account the enhancement effect. During the measure of the potential threshold, the evaporation flux is kept constant R1 ( 1 f dt ¼ const) so, from Eq. (1) and (8), we obtain:
Vðt Þ log bR
Z
1
ne
1
xð2Þ ðE1 ðtÞ þ E2 ðt t ÞÞ2 kB T
dt ¼ const
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experimental setup, we measure the threshold voltage (V) as a function of the delay between the two laser pulses so that an increasing of the intensity up to 4I0 will correspond to a reduction of V in order to maintain a constant evaporation rate. This voltage reduction can be measured as a function of the laser intensity as reported in Fig. 3(b). Hence, the peak value VT(t = 0) might correspond to the intensity increase due to the interferometric effect (I = 4I0 at t = 0 and I = 2I0 for 0 < t < t0). We can conclude that both mechanisms can be at the origin of the potential peak at t = 0, but we can distinguish between these two mechanisms looking at the variation of the potential for longer delay times. For a delay longer than the laser pulse duration tL, following the OR mechanism the two laser pulses induce the same evaporation flux: f(t = 2tL) = 2f1 where f1 is the evaporation flux induced by only one pulse. Considering the logarithm factor in Eq. (1), we expect a negligible change on the potential V(t > tL) = V1, where V1 is the potential when only one laser pulse is used, as shown in Fig. 3(b). Moreover, the first laser pulse increases the tip temperature on a typical time t0 given by the electrons phonons coupling time. After that, the cooling of the tip starts. If the second laser pulse evaporates on a ultrashort times scale, as predicted by OR, during pump-probe measurement this second pulse scans the cooling dynamics of the sample. A change of the tip temperature corresponds to a change of the evaporation efficiency of the second laser pulse, as predicted by Eq. (1), and hence to a change of the standing voltage. It is why we expect a second large peak at t0 in the voltage curve corresponding to the peak temperature of the tip. As shown in Fig. 5, experimentally we observe a slow increase of the potential on long delay time, but no other peak appears at t0 10 ps. Following the thermal model, by considering all the thermal parameters as constants, the result of the measurement is the voltage V(t) induced by the sum T(t,t) = T(t) + T(t t) T0 with T(t) defined by Eq. (5). For delay longer than the laser pulse, but shorter than t0, the two laser pulses are equal to a single pulse with double intensity (T(t,t) = 2T(t) T0). So that, we expect that the voltage is constant and equal to VT(I = 2I0), as observed. At longer delay time, we expect an increase of the voltage corresponding to the tip cooling after the interaction with the first laser pulse (as reported in Eq. (5)). The observed behavior at long delay of VT(t) matches well with the prediction of a thermal assisted evaporation, however, the peak value VT(t = 0) is not compatible with the measured value VT(I = 4I0) (see Fig. 5) as expected for a purely interferometric effect.
(9)
where T is, on a first approximation, independent on time. Supposing a gaussian profile for the incident laser intensity the potential function: V(t) looks like a high order cross-correlation of the incident laser pulse because the full width at half maximum (FWHM) of V is equal to that of the incident laser intensity, due to the non-linear response of the metallic tip. Moreover, due to the typical collinear autocorrelation setup, this pulse for t = 0 could also be due to the two laser beams interferences. The energy absorbed by the tip U and hence the temperature increase of the sample DT are related and given by Z 1 DTðt Þ / Uðt Þ / ðE1 ðtÞ þ E2 ðt t ÞÞ2 dt (10) 1
with a typical interference structure, as reported in Fig. 3(a). The energy is constant and proportional to 2I0 for a long delay time and is oscillating between 0 and 4I0 for delay time shorter than the laser pulse duration (tL). Due to the non-linear expression of the evaporation rate as a function of the tip temperature (see Eq. (1)), a very high flux is expected for t = 0 and I = 4I0. However, in our
Fig. 5. Threshold voltage versus delay time for a W tip. The dotted line corresponds to the value expected for I = 4I0.
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removal compatible with time of flight mass spectrometry. The evaporation mechanisms discussed in this article have to be investigate in the case of non-conductive materials. Due to a residual laser absorption the thermal pulse is always a possible efficient effect. However, due to the breaking of the inversion symmetry at the oxide surface, the non-linear optical effects, such as OR, can occur. Moreover, resonant evaporation, as reported for silicon samples [4], can also appear depending on the photon energy. Naturally a accurate study of the strength of these effects will be performed to quantify the efficiency of each evaporation mechanisms. References
Fig. 6. 3D image of Fe(red), Mg(green) and O(blue) atoms in a tunnel barrier MgO oxide (Courtesy to T. Al Kassab).
4. Conclusions The evaporation of surface ions from a metal tip during fs assisted 3D-AP analysis can be due to either the thermal effect or to the non-linear OR effect. These two mechanisms are characterized by very different evaporation times: very short in the case of OR effect (less than 1 ps) and longer for thermal effect (more than 100 ps). We proposed a pump-probe setup to measure this evaporation time and study the contribution of each effect to the evaporation. On long delay time a clear contribution of thermal evaporation has been reported, however at very short delay, a fast evaporation appears. This ultra fast effect adds to the enhancement of the thermal evaporation due to laser beams interference. From our experimental results we can not conclude which mechanism prevails to the evaporation. A new experimental method is necessary to quantify the contribution of each mechanisms. As explained in the introduction, the fs laser assisted 3DAP provide efficient analysis on poorly conductive materials. In Fig. 6 a recent results obtained on a tunnel barrier of 4 nm of MgO oxide is shown. For the evaporation of semiconductors or insulator, we have to distinguish two things. The first one concerns the DC field. DC field is required to lower the height of the potential barrier and to generate the high magnification of the instrument. Since the tip surface is ‘‘connected’’ to vacuum, the DC polarization is ensured at the surface as it has been demonstrated over a wide range of application of the Field Ion Microscope on insulator such as glasses. The seconde thing concerns the transmission of an HV pulse to the material apex. Due to the high resistivity of the sample (coming from its very small apex) and to the capacitance coupling the specimen to the rest of the world, the limit in frequency is about 1 ns for semiconductors. For oxides much longer pulses should be used [27]. Whatever the physical process involved in the evaporation of semiconductors or insulating materials, the laser allows to bring ultrafast pulses (thermal pulse or OR pulse) at the specimen apex in order to get a accurate time control of atoms
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