Mechanisms of plasmon-enhanced femtosecond laser nanoablation of silicon

Alexandre Robitaille; Étienne Boulais; Michel Meunier

doi:10.1364/OE.21.009703

1. Introduction

High intensity plasmon-enhanced optical fields from utrafast laser irradiation of plasmonic nanostructures has been used extensively in the literature to perform sub-diffraction limit ablation of dielectric and semiconductor surfaces [1–6]. While the use of plasmonic nanostructures to enhance ablation is now relatively widespread, there is no consensus over the exact physical mechanism leading to ablation. Squared norm of the electric field |E|² is generally accepted as proportional to the rate of work performed by an electromagnetic field on a material. Indeed, from Poynting’s theorem [7], the rate of work can be written as $\frac{1}{2} ω ε^{″} {| E |}^{2}$ with ε″ being the imaginary part of the permittivity. |E|² should as a first approximation dictate the shape of the hole formed by the irradiation of the nanostructure. However, while some authors have reported good correspondence between nanohole morphology and simulated electric field distribution in the case of gold nanospheres [6], major discordance has been observed in the case of gold nanorods [4]. This apparent incompatibility supported by simple arguments based on the magnitude of the ablation threshold enhancement has lead Harrison et al. to propose that the component of the Poynting’s vector normal to the silicon surface rather than |E|² should be considered in evaluating nanoablation since it fits experimental results with more precision [4]. While this approach has been reviewed critically [8], the subject is still an open debate.

In this paper, we focus on nanoablation resulting from the interaction between a single fem-tosecond laser pulse and gold nanorods deposited on a silicon surface. We present thorough measurements of depth and shape of holes as a function of laser fluence. We then propose a simple model (Fig. 1) based on energetic carriers generation and diffusion to explain both the depth and shape of the created nanoholes. Results show that this model, while relying on a standard $\frac{1}{2} ω ε^{″} {| E |}^{2}$ absorption mechanism, reproduces with a great accuracy the experimental data, ruling out the need for any other exotic field metric to explain plasmonic nanoablation.

Fig. 1 Schematic view of the ablation model. Left panel: nanorod on a silicon surface with plotted energy absorption rate. Laser irradiation (a) generates a population of energetic carriers (b) following the profile of the electric field. (c) Those carriers will diffuse (red arrow) while transferring energy to the lattice as phonons (black arrow). This transfer is screened where the carriers density is too high, represented by the scaling of the black arrows. Right panel shows lattice energy density. The screening results in a lower energy density where the electron density is high and produces a maximal energy density where the two diffusion fronts coming from both hot spots converge. (d) Ablation occurs where it reaches the ablation threshold (black dotted line at low fluence and blue dotted line at high fluence).

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2. Experimental results

We produce nanoholes on a silicon surface by irradiating 41nm × 88nm gold nanorods with a single pulse from a 120fs Ti:Sapphire laser at 800nm. A circular polarization is used to avoid problems due to the rods orientation since the electric field profile around the nanostructures would vary with the angle between the polarization and the nanorod for linear polarization. Silicon comes from a diced (100) wafer cleaned in an ultrasonic bath of Opticlear, acetone, iso-propanol and deionised water for 5 minutes each. Native oxide layer is removed using a 5% HF solution. Nanorods are then deposited on the surface from the passive drying of a 10μL droplet of a gold nanorods colloidal sample (Nanopartz). Excess of cetrimonium bromide (CTAB), a common surfactant used in the chemical synthesis of nanostructures [9] is removed with a subsequent rinsing step. Nanorods are imaged with transmission electron microscopy (TEM) (Fig. 2), confirming their dimensions and revealing a 1nm thick layer around the nanostructure. This layer is identified as a CTAB residual and its thickness is consistent with values found in the literature [9]. In addition to the CTAB layer, a 0.5nm oxide layer [10] is formed on the silicon during the approximately 24h period between the cleaning and the irradiation procedure. Though very thin, those layers have significant impact on the ablation process because of the highly localized nature of the electromagnetic fields involved. They must thus be considered in the calculations.

Fig. 2 TEM imaging of a 88×41nm gold nanorod. Inset presents a zoomed picture showing a 1nm CTAB shell around the nanostructure.

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Local fluence at each nanorod is evaluated from the measurement of their precise position on the surface and from the Gaussian profile of the beam, which is focused with a spot size of 33μm (measure at 1/e²). Depth of the nanoholes is measured using atomic force microscopy (AFM). Thorough comparison of scanning electron microscopy (SEM) images of the sample before and after irradiation allows to consider only nanoholes produced by single isolated rods, and thus eliminate the effects of aggregated nanostructures. Results (Fig. 3) show two distinct regimes. For lower local fluences ranging from 40mJ/cm² to 275mJ/cm², very shallow nanoholes with a depth depending weakly on the fluence are formed. For higher local fluences, hole depth depends almost linearly on the fluence. Note that without plasmonic enhancement, a 380mJ/cm² ablation threshold for silicon has been measured using Liu’s method [11], a value that compares well with the results reported in the literature [2, 4, 12].

Fig. 3 Experimental (dots) and simulated (squares) hole depth as a function of fluence. Dotted line shows conventional ablation threshold for silicon (380mJ/cm²).

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3. Discussion

Figures 4(a) and 4(b) show examples of holes observed. Relating this ablation phenomenon to the energy absorption would be natural. Figures 4(c) and 4(d) present calculations of the energy absorption rate Q around a 41nm × 88nm gold nanorod on a silicon surface, considering the 0.5nm oxide layer, the 1nm CTAB layer (n=1.435) [13] and the non-linear absorption coefficient in silicon. Figures show an absorption rate in the substrate with a two-lobes spatial profile, similar to the field enhancement calculated in Harrison et al.[4]. To evaluate the energy absorption correctly, we must consider linear absorption (ε″_l), but also non-linear effects (ε″_nl(E)) and free-carriers absorption (ε″_Drude(N)), where N is the carrier density.

Q = \frac{1}{2} ω ε^{″} {| E |}^{2} = \frac{1}{2} ω [ε_{l}^{″} + ε_{n l}^{″} (E) + ε_{Drude}^{″} (N)] {| E |}^{2}

It is clear that the field enhancement alone cannot explain the morphology of the observed nanoholes. Indeed, simulation results show that the energy is deposited in the silicon with a spatial distribution consisting of two hot spots (Figs. 4(c) and 4(d)). This distribution should logically result in the formation of double holes. However, the holes that are observed have a rather peculiar X-shape at low fluence (Fig. 4(a)) or an 8-shape with its maximal depth in the middle (Fig. 4(b)) at higher fluence. Double-holes have not been observed, consistent with the results presented in Harrison et al.[4]. Note that we reported the formation of such double-holes in a previous study [8]; we now attribute those results to the consequence of nanorod agglomeration, which we took much care to avoid in the present work.

Fig. 4 AFM mesurement of hole shape for a fluence of (a) 202mJ/cm² and (b) 269mJ/cm². Energy absorption rate enhancement profile Q/Q₀ at mid-pulse (log scale) for a fluence of 270mJ/cm² (c) cross-section and (d) top view. Q₀ corresponds to absorption rate without the nanostructure. Lattice energy density U_l from (e) cross-section and (f) top view for the same fluence after 10ps. Dotted lines show nanorod’s size.

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To explain the experimental results, we have to investigate the precise physical mechanisms occurring during the energy absorption and distribution that lead to the ablation of the material. When the laser pulse reaches the silicon surface, the electromagnetic field interacts with the electrons of the material, leading to an energy absorption from the field. This energy induces the creation of electron-hole pairs in the conduction and valence bands. Those carriers then diffuse before giving their energy to the lattice and initiating a series of events leading to the ablation of the surface. This general mechanism describes thermal ablation for both standard and plasmon-enhanced laser ablation. In the case of conventional ablation, the penetration depth (around 10μm for 800nm on silicon), is much larger than the diffusion length (around 100nm), so that the importance of the diffusion process is negligible. However, in the case of plasmon-enhanced laser nanoablation, as shown in Figs. 4(c) and 4(d), energy deposition is strongly localized in a nanometer scale region around the nanostructure. The diffusion length thus becomes larger than the characteristic deposition length and the process become dominated by diffusion. The strong localization of the energy absorption is thus the key difference between laser nanoablation and conventional laser ablation.

Modeling the ablation or melting of a silicon surface by an ultrafast laser pulse is the subject of an abundant literature. Typical modeling schemes include molecular dynamics [14–17] and two-temperature transport equation solving [18–21]. However, none of those studies considers the effect of a plasmonic nanostructure on the surface. As the relatively large size of the ablated features we seek to model prohibits the use of a molecular dynamic method, we used a two-temperature model based on the work of van Driel [18] to describe the ablation of the substrate under the nanorod. This model includes the auto-consistent resolution of the Helmholtz equation for the determination of the electric field around the nanostructure E(r,t), along with equations describing electron-hole pairs density N(r,t), electron-hole pairs energy U_c(r,t) and lattice energy U_l(r,t). The coupled differential equations system (Eqs. (2)–(5)) is solved in 3D using a time-dependant finite-element method.

\nabla \times (\nabla \times E) - \frac{4 π^{2}}{λ^{2}} ε E = 0

\frac{\partial N}{\partial t} + \nabla • J_{c} = (\frac{α I}{h ν} + \frac{β I^{2}}{2 h ν}) + N (δ - \frac{1}{τ_{r}})

\frac{\partial U_{c}}{\partial t} + \nabla • (W - k_{c} \nabla T_{c}) = Q - \frac{3 k_{B} N (T_{c} - T_{l})}{τ_{c p}}

\frac{\partial U_{l}}{\partial t} - \nabla • (k_{l} \nabla T_{l}) = \frac{3 k_{B} N (T_{c} - T_{l})}{τ_{c p}}

In Eqs. (2)–(5), α and β correspond to linear [22] and two-photon [23] absorption coefficients. δ is the impact ionization rate [18] while τ_r is the Auger recombination time [21, 24] and τ_cp the carrier-phonon relaxation time [24]. k_c and k_l are the carriers [25] and lattice [18] thermal conductivity respectively. Electrons and holes remain within the non-degenerate limit throughout the process so that their energy distribution follows a Maxwell-Boltzmann statistic.

J_c and W in Eqs. (3)–(4) correspond respectively to electron-hole pairs and energy current density, given by the following Eqs. [18]:

J_{c} = - D_{a} (\nabla N + \frac{2 N}{k_{B} T_{c}} \nabla E_{g} + \frac{N}{2 T_{c}} \nabla T_{c})

W = (E_{g} + 4 k_{B} T_{e}) J_{c}

where D_a[26] is the ambipolar diffusion coefficient and E_g the band gap of silicon [18]. Electrons and lattice temperatures are related to the energy through the following expressions

U_{c} = N E_{g} + 3 k_{B} N T_{c} U_{l} = C_{l} T_{l}

with C_l the lattice specific heat [18]. Coefficients found in Eqs. (2)–(8) are detailed in Table 1.

Energy transfer from the optical field to the electron system is represented by the term Q in Eq. (4) and is given by Eq. (1). ε″_l and ε″_nl are easily derived from the experimental values for linear and non-linear absorption α and β using :

α + \frac{1}{2} c n_{0} ε_{0} β {| E |}^{2} = \frac{4 π}{λ} κ

with n₀ the real part of the refractive index of silicon and κ the imaginary part which varies with variation of absorption coefficients. They are related to the dielectric constant with the usual :

ε = {(n - i κ)}^{2}

Free carrier absorption ε″_Drude is taken from the work of Sokolowski-Tinten and von der Linde [27]. It depends on carrier density and thus implies a time-dependant dielectric function for silicon. It is used as a correction to the dielectric function in the form :

Δ ε_{Drude} = - {(\frac{ω_{p}}{ω})}^{2} \frac{1}{\frac{i}{ω τ_{D}} - 1}

The Drude plasma frequency ω_p, depending on electron density, and damping time τ_D are found in Table 1. Calculation shows that the contribution of Δε_Drude to the energy absorption is particularly important. For instance, for an incident fluence of 250mJ/cm², about 80% of the energy absorption is due to those free carriers.

Table 1. Model parameters for silicon

View Table

Finally, the ablation criterion is defined as the simulated lattice energy density U_l,threshold reached at the surface of silicon, when no nanostructure is present, following a laser irradiation at a fluence corresponding to the experimental ablation threshold. With nanostructures, ablation is then considered to occur in the region of silicon where the simulated energy density U_l reached is higher than U_l,threshold. Hole depth is calculated as the extend of that region. Ablation is evaluated after thermal equilibrium is reached between the electron-hole pairs and the lattice (10ps).

Figure 3 presents a comparison between the simulated and measured holes depths. A very good agreement is found for the higher fluence regime (fluence > 270mJ/cm²). This indicates that the nanohole creation process for those fluences is dominated by the energy transfer from the field to the lattice through the diffusion of highly energetic electrons and electron-phonon coupling. However, experimental results show shallow holes at the lower fluence regime (40mJ/cm² to 250mJ/cm²), which are not described by the model. This may seem similar to the optical penetration regime observed for conventional ablation of surfaces [30, 31]. However, it would imply ablation of double holes following the shape of the field enhancement, which is not the case, as seen in Fig. 4(a). Increasing importance of spatially and energetically randomly distributed surface states at low fluence may produce significant modifications of the various parameters considered in the model and could explain this discrepancy. Also, energy or charge transfer from the nanorod itself, which is not included in the model, increases in importance at low fluence and could contribute to the ablation.

In addition to explaining holes depth, the proposed carrier diffusion-based model also reproduces the peculiar shape of the nanoholes observed experimentally (Figs. 4(a) and 4(b)). Figures 4(e) and 4(f), show the shape of the nanohole calculated using the complete diffusion model. Results show that the model predicts the formation of the counter-intuitive X-shaped holes experimentally observed at low fluence (Fig. 4(a)). Transition from the two hot-spot shape of the energy absorption to the ablated X-shape arises as a result of the screening of the charge carriers-phonon energy coupling by the large density of excited carriers present in silicon [24]. This is considered in the expression for the characteristic carrier-phonon relaxation time τ_ep used in Eqs. (4)–(5).

τ_{c p} = τ_{0} [1 + {(\frac{N}{N_{c}})}^{2}]

Low density limit τ₀ for the relaxation time and critical density N_c were taken as 250fs [28, 29] and 2×10²¹cm⁻³[21, 24, 25]. The high carrier density generated at the location of the two hot-spots prevents efficient energy tranfer from carriers to the lattice (high τ_cp) before some diffusion has occured. For example, at 270mJ/cm², τ_cp at mid-pulse is around 260fs under the middle of the rod while it is around 7.3ps at the hot spots location. Energy transfer to the lattice is thus much faster just out of the hot spots, leading to a maximal energy deposition in two circular regions surronding them. The junction of those two regions yields the X-shape as shown by the black dotted line in Fig. 1. The same process occurs at higher fluences, but the overall energy being higher, threshold is reached on an 8-shaped profile and not only in the X-shaped region (blue dotted line of Fig. 1). The X-shape is thus a direct signature of an energy transfer from the field to the lattice mediated by diffusive energetic electron-hole pairs and confirms the mechanism put forward in this paper to explain the plasmon-enhanced laser nanoablation process.

4. Conclusion

This work demonstrates that, because of the extreme localization of the field enhancement around the nanostructure, plasmon-enhanced laser nanoablation mechanism is related to the generation of highly localized energetic carriers. Those carriers then diffuse before thermalizing with the lattice and producing ablation. The proposed model explains both the depth of the holes produced and their peculiar shape, the latter being directly linked to the screening of the carrier-phonon coupling by the high carrier density during the charge diffusion and heat transfer process.

The authors would like to thank the Natural Science and Engineering Research Council (NSERC) and Le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) for financial support. RQCHP is acknowledged for computing resources. The technical assistance by Y. Drolet as well as fruitful discussions with N. Berton and S. Besner are also acknowledged.

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Quantity	Values (N in cm⁻³, T_l and T_e in K)
F_th, Silicon conventional ablation threshold	380 [mJ/cm²]
α, Linear absorption [22]	1015 [cm⁻¹]
β, 2-photons absorption [23]	2 [cm/GW]
δ, Impact ionization [18]	3.6 × 10¹⁰e^{−1.5E_g/k_BT_e} [s⁻¹]
E_g, Band gap [18]	$\begin{matrix} 1.16 - 7.02 \times 10^{- 4} T_{l}^{2} / (T_{l} + 1108) \\ - 1.5 \times 10^{- 8} N^{1 / 3} [eV] \end{matrix}$
τ_r, Carriers recombination time [21, 24]	(4 × 10⁻³¹N²)⁻¹ [s] for τ_r >6ps, τ_r =6ps afterward
D_a, Ambipolar diffusion [26]	18 × 300/T_l [cm²/s]
k_c, Carriers thermal conductivity [25]	−0.556 + 0.00713T_e [W/Km]
k_l, Lattice thermal conductivity [18]	$1585 T_{l}^{- 1.23} [W / Kcm]$
C_l, Lattice specific heat [18]	$1.978 + 3.54 \times 10^{- 4} T_{l} - 3.68 T_{l}^{- 2} [J / {cm}^{3}]$
τ₀, Relaxation time low density limit [28, 29]	250 [fs]
N_c, Relaxation time critical density [21, 24, 25]	2×10²¹ [cm⁻³]
ω_p, Plasma frequency [27]	$\sqrt{N e^{2} / ε_{0} m_{opt}^{*} m_{e}} [s^{- 1}]$
$m_{opt}^{*}$ , Carriers optical effective mass [27]	0.18
τ_D, Drude damping time [27]	1 [fs]

Mechanisms of plasmon-enhanced femtosecond laser nanoablation of silicon

Abstract

1. Introduction

2. Experimental results

3. Discussion

4. Conclusion

References and links

Cited By

Figures (4)

Tables (1)

Equations (12)

Optics Express