Study on the mechanism of a femtosecond laser-induced breakdown of the deposited substrate mediated by aluminum nanoparticles in a vacuum

Qing Lin; Qing Lin; Naifei Ren; Yang Da

doi:10.1364/OME.409926

1. Introduction

Laser-induced optical breakdown mediated by nanoparticles is a kind of nonlinear laser energy absorption process, which generates local low-density plasma around the nanoparticles [1]. Nanoparticles can enhance the electromagnetic field of incident laser in the near field of nanoparticles. Laser induced optical breakdown usually occurs when the laser irradiation exceeds a certain threshold [2–6]. After some seed electrons are generated, the plasma begins to acquire enough kinetic energy from the laser pulse through the inverse bremsstrahlung absorption, and grows through collision ionization [7]. In the case of conductor, the emission signal enhancement of up to 1–2 orders of magnitude can be obtained by depositing nanoparticles on the surface of the sample by drying the colloidal droplet solution. The basic mechanism of nanoparticles enhanced laser induced breakdown spectroscopy (LIBS) has been studied. The main reason for this great improvement is the influence of related nanoparticles in the laser ablation process, and a faster and more efficient production of seed electrons with respect to traditional LIBS [8].

In 2014, Jiao Zhen [9] reported that aluminum nanoparticles deposited on silicon substrate were irradiated by femtosecond laser in vacuum environment, and a “tail like” pit structure was observed on the surface of silicon substrate near the aluminum nanoparticles, and it was found that aluminum nanoparticles moved along the polarization direction of the incident laser electric field after being irradiated by femtosecond lasers. Based on the theoretical model, the near-field enhancement, the femtosecond laser breakdown threshold, the evolution of plasma electron density, the electron and lattice temperature of aluminum nanoparticles were calculated in this study. The mechanism of breakdown of deposited substrate was further analyzed.

2. Methods

2.1 Electromagnetic model

The electromagnetic field was calculated based on the homogeneous Helmholtz wave equations. The electric field, E(x, y, z), can be calculated by equations:

(1)$${\textbf E}(x,y,z) = {{\textbf E}_0}\frac{{{w_0}}}{{w(y)}}\exp \left[ { - \frac{{{z^2} + {x^2}}}{{{w^2}(y)}} - jky - jk\frac{{{z^2} + {x^2}}}{{2R(y)}} + j\eta (y)} \right]$$

(2)$$\nabla \times (\nabla \times {\textbf E}) - k_0^2\varepsilon {\textbf E} = 0$$

where $w(y) = {w_0}\sqrt {1 + {{\left( {\frac{y}{{{y_0}}}} \right)}^2}}$, $R(y) = y\left[ {1 + {{\left( {\frac{{{y_0}}}{y}} \right)}^2}} \right]$, $\eta (y) = {\textrm{ta}}{\rm{n}^{ - 1}}\left( {\frac{y}{{{y_0}}}} \right)$, ${y_0} = \frac{{{k_0}{w_0}^2}}{2}$, $k = n{k_0}$, w₀ is the minimum waist, k₀ is the wave number.

2.2 Plasma dynamics

In order to simulate the evolution of the electron plasma density in the process of optical breakdown, the free electron plasma density rate equation can be expressed as [3]:

(3)$$ \frac{d \rho_{e}}{d t}=\left(\frac{d \rho_{e}}{d t}\right)_{\text {photo}}+\left(\frac{d \rho_{e}}{d t}\right)_{\text {casc}}+\left(\frac{d \rho_{e}}{d t}\right)_{\text {diff}}+\left(\frac{d \rho_{e}}{d t}\right)_{\text {rec}} $$

The term ${\left( {\frac{{d{\rho_e}}}{{dt}}} \right)_{photo}}$, refers to the photoionization of electrons through multiphoton absorption and tunnel ionization [10]. The term $\left(\frac{d \rho_{e}}{d t}\right)_{c a s c}$, refers to the rate of avalance ionization. The term ${\left( {\frac{{d{\rho_e}}}{{dt}}} \right)_{diff}} = \frac{{ - 2\tau ({{5 / 4}} )\tilde{\Delta }}}{{3{m_e}{\Lambda ^2}}}{\rho _e}$, refers to the diffusion of plasma electrons, where, Λ, is the characteristic diffusion length, which was set as the effective radius of the nanoparticle. The term ${\left( {\frac{{d{\rho_e}}}{{dt}}} \right)_{rec}} ={-} {\eta _{rec}}{\rho _e}^2$, refers to the recombination of free electron plasma [11].

The electron density is the ground state, ${\rho _{bound}}$, at room temperature. The electron density is replaced with ${\rho _e}$, during the process of the photoionization of free electrons. The total photoionization rate is [12]:

(4)$$\begin{array}{l} {\left( {\frac{{d{\rho_e}}}{{dt}}} \right)_{photo}} = \frac{{2\omega }}{{9\pi }}{\left( {\frac{{m^{\prime}\omega \sqrt {1 + {\gamma^2}} }}{{\hbar \gamma }}} \right)^{{3 / 2}}}Q\left( {\gamma ,\frac{{\tilde{\Delta }}}{{\hbar \omega }}} \right) \times \left( {\frac{{{\rho_{bound}} - {\rho_e}}}{{{\rho_{bound}}}}} \right)\\ \exp \left\{ { - \pi \left\langle {\frac{{\tilde{\Delta }}}{{\hbar \omega }} + 1} \right\rangle \times {{\left[ {\kappa \left( {\frac{\gamma }{{\sqrt {1 + {\gamma^2}} }}} \right) - \varepsilon \left( {\frac{\gamma }{{\sqrt {1 + {\gamma^2}} }}} \right)} \right]} / {\varepsilon \left( {\frac{1}{{\sqrt {1 + {\gamma^2}} }}} \right)}}} \right\} \end{array}$$

where

(5)$$\begin{aligned} Q(\gamma ,x) = \sqrt {\frac{\pi }{{2\kappa \left( {\frac{1}{{\sqrt {1 + {\gamma^2}} }}} \right)}}} &\times \sum\limits_{l = 0}^\infty {\exp \left\{ { - \pi l \times {{\left[ {\kappa \left( {\frac{\gamma }{{\sqrt {1 + {\gamma^2}} }}} \right) - \varepsilon \left( {\frac{\gamma }{{\sqrt {1 + {\gamma^2}} }}} \right)} \right]} / {\varepsilon \left( {\frac{1}{{\sqrt {1 + {\gamma^2}} }}} \right)}}} \right\}} \\ &\times \Phi \left\{ {{{\left[ {\frac{{{\pi^2}(2\left\langle {x + 1} \right\rangle - 2x + l)}}{{2\kappa \left( {\frac{1}{{\sqrt {1 + {\gamma^2}} }}} \right)}} \times \varepsilon \left( {\frac{1}{{\sqrt {1 + {\gamma^2}} }}} \right)} \right]}^{{{\;1} / 2}}}} \right\} \end{aligned}$$

the Keldysh parameter, γ, is given by:

(6)$$\gamma = \omega \frac{{\sqrt {m^{\prime}{E_{gap}}} }}{{e|{\textbf{E}} |}}$$

where $|{\textbf E} |$ is the magnitude of the electric field.

In Eqs. (4) and (5), < x > represents the integer part of the number x, $\kappa (\;)$ denotes the elliptic integral of the first kind, $\varepsilon (\;)$ represents the elliptic integral of the second kind, and $\Phi (\;)$ represents the Dawson probability integral, shown as follows:

(7)$$\Phi (z )= \int_0^z {\exp ({{y^2} - {z^2}} )dy}$$

The effective ionization potential can be expressed as:

(8)$$\tilde{\Delta } = {E_{gap}}\left( {\textrm{1 + }\frac{\textrm{1}}{{\textrm{4}{\gamma^\textrm{2}}}}} \right)$$

The rate of avalanche ionization [12] can be written as:

(9)$${\left( {\frac{{d{\rho_e}}}{{dt}}} \right)_{casc}} = \left\{ \begin{array}{ll} \frac{{{\rho_e}}}{{1 + {\eta_{casc}}{t_{ret}}}}({{\alpha_{casc}}{I_{in}}(t )- {\beta_{casc}}} )&\textrm{for}\;\;{\rho_e} \ge {\rho_{seed}}\\ 0&\textrm{for}\;{\rho_e} < {\rho_{seed}} \end{array} \right.$$

where ${t_{ret}} = \tau \left\langle {1 + \frac{{3\tilde{\Delta }}}{{2\hbar \omega }}} \right\rangle $, is the cascade retardation time [12], ${\alpha _{casc}} = \frac{1}{{1 + {\omega ^2}{\tau ^2}}}\frac{{2{e^2}\tau }}{{3{c_0}n{\varepsilon _0}{m_e}{E_{gap}}}}\left( {1 - \frac{{{\rho_e}}}{{{\rho_{bound}}}}} \right)$, is the gain in ionization cascade, and ${\beta _{casc}} = \frac{{{m_e}}}{M}\frac{{{\omega ^2}\tau }}{{{\omega ^2}{\tau ^2} + 1}}\left( {1 - \frac{{{\rho_e}}}{{{\rho_{bound}}}}} \right)$, is the collision loss of ionization cascade. The rate of avalanche ionization per electron is given by [13]:

(10)$${\eta _{casc}} = \frac{1}{{{\omega ^2}{\tau ^2} + 1}}\left[ {\frac{{{e^2}\tau }}{{{c_0}n{\varepsilon_0}{m_e}({{3 / 2}} )\tilde{\Delta }}}{I_{in}}(t )- \frac{{{m_e}{\omega^2}\tau }}{M}} \right]$$

where τ is the mean time between collisions, and M is the mass of aluminum atom.

2.3 Two-temperature model

The evolution of the electronic and lattice temperatures of aluminum nanoparticles during a femtosecond laser pulse were solved by the two-temperature model. The two-temperature model was coupled with the electromagnetic model through the resistive losses of aluminum nanoparticles [14], Q_rh, during the interaction with the incident femtosecond laser pulse:

(11)$${C_e}\frac{{\partial {T_e}}}{{\partial t}} ={-} G({{T_e} - {T_l}} )+ {Q_{rh}} \cdot f({t_p})$$

(12)$${C_l}\frac{{\partial {T_l}}}{{\partial t}} = G({{T_e} - {T_l}} )$$

(13)$${Q_{rh}} = \frac{1}{2}\Re [{({\sigma - j\omega \varepsilon } ){\textbf{E}} \cdot {{\textbf{E}}^ \ast }} ]$$

where C_e is the electronic heat capacity, C_l is the lattice heat capacity, T_e is the electronic temperature, T_l is the lattice temperature, G is the electron-phonon coupling factor [15], ℜ is the real part, and σ is the electric conductivity.

These three physical models were fully coupled in this study. In our previous research, we investigated the femtosecond laser optical breakdown threshold in water mediated by aluminum nanoparticle coated with silica by using the similar methods [16], but in this study, we focused on the mechanism exploration of the femtosecond laser induced breakdown of deposited substrates mediated by aluminum nanoparticles in vacuum. The size corrections of aluminum nanoparticles at the nanoscale of small size were studied carefully in this study. The numerical values or expressions of physical parameters used in this model were shown in Table 2.

3. Results

3.1. Near field enhancement of aluminum nanoparticles

In this study, the symbol d denotes the diameter of single aluminum nanoparticle, d_g stands for the gap of nanoparticles. The relative electric near-field enhancement for different morphology of aluminum nanoparticles during the irradiation of femtosecond laser with a wavelength of 800 nm was shown in Fig. 1. Relative electric field enhancement, |E|/E0, where |E| is the amplitude of the total electric field and E0 is the amplitude of the electric field of incident femtosecond laser. The maximum value of |E|/E0 in monomer, dimer and trimer is 1.9, 8.52 and 9.97, respectively.

Fig. 1. The relative electric near-field enhancement |E|/E0 for different morphology of aluminum nanoparticles (d = 40 nm, d_g = 2 nm, λ = 800 nm). (a) monomer; (b) dimer; (c) trimer.

Download Full Size | PDF

The extinction cross-section of aluminum nanoparticles monomer, dimer and trimer with 40 nm diameter, under the irradiation at incident wavelength of 200 ∼ 800 nm, as shown in Fig. 2. The excellent agreement between the FEM algorithm and the Mie theory indicate that COMSOL is able to accurately solve electromagnetic problems at the nanoscale level, the extinction cross-section, from the COMSOL Multiphysics EM model closely matches the Mie solution [17].

Fig. 2. The extinction cross-section for different morphology of aluminum nanoparticles (d = 40 nm, d_g = 2 nm).

Download Full Size | PDF

The extinction cross-section of monomer, dimer and trimer at the incident wavelength of 800 nm was 25.5 nm², 47.7 nm² and 99.8 nm², respectively. The dimer has a peak value of 8821 nm² with the 240 nm resonant wavelength, and the peak value of trimer was 9231 nm² with the 265 nm resonant wavelength. The resonance wavelength of monomer is not considered because it is in the extreme ultraviolet band (< 200 nm). The resonance peak was red shifted from monomer to dimer, and trimer.

Taking trimer as an example, the maximum relative electric field enhancement E_e,max = max|E|/E0, was calculated during the 200 ∼ 800 nm wavelength. As shown in Fig. 3, the maximum relative electric field enhancement was 88 times, at the same resonant wavelength (265 nm) of extinction section of trimer. It can be seen that there was a strong near-field enhancement and a large extinction cross-section at a far UV resonant wavelength for aluminum nanoparticles. In this paper, the incident wavelength of 800 nm was the off-resonance wavelength for aluminum nanoparticles.

Fig. 3. Maximum relative electric enhancement of trimer for different incident wavelengths (d = 40 nm, d_g = 2 nm).

Download Full Size | PDF

The relationship between the different sizes of nanoparticles and the maximum near-field enhancement was considered by taking trimer as an example (d_g= 2 nm, λ = 800 nm). As shown in Fig. 4, E_e,max = 9.97, with d = 40 nm; and E_e,max = 42.2, with d = 100 nm. With the increase of the size of aluminum nanoparticles, the maximum relative electric field increases linearly.

Fig. 4. Maximum near-field enhancement of trimer with different diameters (d_g= 2 nm, λ = 800 nm).

Download Full Size | PDF

With the increase of the gap, d_g, between nanoparticles, the value of maximum relative electric field enhancement decreases gradually. The fitting function of E_e,max and d_g is: ${E_{e,\max }} = 15.57952\;d_g^{ - 0.66884}$, with R²= 0.99. As shown in Fig. 5, E_e,max has decayed to 2.39 when d_g = 20 nm, as shown in the illustration in Fig. 5, and there was no strong near-field enhancement in the middle of the gap.

Fig. 5. Maximum near-field enhancement of trimer with different gaps (d = 40 nm, λ = 800 nm).

Download Full Size | PDF

It is necessary to use the modified dielectric function model to describe the dielectric function of aluminum nanoparticles, due to the strength of near-field enhancement depends on the size and morphology of nanoparticles. The complex dielectric function of bulk aluminum can be expressed by using the critical point model (CPM) as follows [18]:

(14)$${\varepsilon _{CPM}}(\omega ) = {\varepsilon _\infty } - \frac{{\omega _p^2}}{{\omega (\omega + i{\gamma _D})}} + \sum\limits_{p = 1}^2 {{A_p}{\Omega _p}(\frac{{{e^{i{\phi _p}}}}}{{{\Omega _p} - \omega - i{\Gamma _p}}} + } \frac{{{e^{ - i{\phi _p}}}}}{{{\Omega _p} + \omega + i{\Gamma _p}}})$$

The parameters for aluminum can be given by [19]: ε_∞= 1, ω_p = 2.0598×10¹⁶ Hz, γ_D = 2.2876×10¹⁴ Hz, A₁ = 5.2306, ϕ₁ = −0.51202, Ω₁ = 2.2694×10¹⁵ Hz, Γ₁ = 3.2867×10¹⁴ Hz, A₂ = 5.2704, ϕ₂ = 0.42503, Ω₂ = 2.4668×10¹⁵ Hz, and Γ₂= 1.7731×10¹⁵ Hz. The modified complex dielectric function of an aluminum nanoparticle in nano scale can be expressed as follows [20]:

(15)$$\varepsilon (\omega ,{L_{eff}}) = {\varepsilon _{CPM}}(\omega ) + \frac{{\omega _p^2}}{{\omega (\omega + i{\Gamma _{bulk}})}} - \frac{{\omega _p^2}}{{{\omega ^2} + i\omega ({\Gamma _{bulk}} + \frac{{A{v_F}}}{{{L_{eff}}}} + \frac{{\hbar \eta {V_{np}}}}{\pi })}}$$

where ε_CPM (ω) is the CPM, which is defined as Eq. (14). The damping constant is expressed as Γ_bulk= v_F /l_∞, where v_F = 2.02 nm/fs is the Fermi velocity, l_∞ = 16 nm is the mean free path of the electron between collisions [20]. Electron collisions and scattering from the surface of nanoparticles is denoted as Γ_surf= Av_F /L_eff, where A is the surface confinement broadening parameter [16]. The reduced effective mean free path is given by L_eff = 4V_np /S_np, where V_np and S_np are the volume and surface area of the arbitrary formed aluminum nanoparticle, respectively [16]. The radiation damping, Γ_rad = ħηV_np /π, which η is radiation damping coefficient [16].

The difference of values of relative electric near-field enhancement by using CPM and modified CPM was shown in Table 1. Although the relative error of the calculated result using unmodified CPM is small, the absolute error of near-field enhancement is large because the intensity of the incident electric field, E0, can reach 3×10⁹ W/m² in the example of monomer (J = 31 mJ/cm²) in this paper.

Table 1. Comparison of relative electric near-field enhancement by using CPM and modified CPM (d = 40 nm, d_g = 2 nm, λ = 800 nm).

View Table | View all tables in this article

If calculated with the unmodified CPM, the amplitude of the enhanced electric field of the monomer under the incident laser electric field irradiation at J = 31 mJ/cm² is 5.73×10⁹ W/m², but if calculated with the modified CPM in nanometer size, the amplitude of the enhanced electric field of the monomer is 5.7×10⁹ W/m², and the absolute error of the two results is 3×10⁷ W/m². The value of absolute error is large enough to affect the values of Keldysh parameter, γ, [see Eq. (6)], and the resistive losses, Q_rh, [see Eq. (13)]. The overestimation of near-field enhancement will lead to underestimate the laser breakdown threshold, according the subsequent calculation.

3.2. Near-field enhancement of nanoparticles deposited on different substrates

In practical applications, nanoparticles are often deposited on the substrate. Near field enhancement with different intensities will be obtained by depositing different morphologies of nanoparticles on different substrates. In order to reduce the amount of calculation, the length, width and height of the substrate was set as 150 nm, 50 nm and 10 nm, respectively. The diameter of single aluminum nanoparticle was set as 40 nm (d = 40 nm), and the gap of nanoparticles was set as 2 nm (d_g = 2 nm). Take the monomer as an example, the calculation model was shown in Fig. 6. The perfect absorption layer (PML) was used to truncate the electromagnetic field calculation region and reflection boundary. The two-temperature model (TTM) was used to calculate the electronic and lattice temperature of aluminum nanoparticles. The solution domain of plasma was the deposition substrate. The generation of free electrons and the evolution of plasma free electron density during a femtosecond laser pulse induced breakdown of deposition substrate mediated by different morphologies of aluminum nanoparticles were solved. The linear polarization direction of the electric field of the incident laser beam was along the z-axis and the propagation direction was along the positive direction of the y-axis.

Fig. 6. The model of aluminum nanoparticle monomer deposited on substrate.

Download Full Size | PDF

As shown in Fig. 7, the maximum near-field enhancement value of aluminum nanoparticle monomer, dimer and trimer deposited on SiO₂ substrate was 1.64, 8.48 and 9.82, respectively, under the irradiation of 800 nm femtosecond laser. The position of near-field enhancement was located at the left and right sides of monomer, and at the particles’ gap of dimer and trimer, was along the polarization direction of incident laser electric field. The maximum near-field enhancement value of the monomer, dimer and trimer of Al nanoparticles deposited on Al substrate was 8.33, 88.3 and 146, respectively, while the position of the maximum enhancement was located at the junction of aluminum nanoparticles and aluminum substrate.

Fig. 7. The relative electric near-field enhancement |E|/E0 of different morphology of aluminum nanoparticles deposited on different substrates in vacuum (d = 40 nm, d_g= 2 nm, λ = 800 nm). (a) monomer on SiO₂ substrate; (b) monomer on Al substrate; (c) dimer on SiO₂ substrate; (d) dimer on Al substrate; (e) trimer on SiO₂ substrate; (f) trimer on Al substrate.

Download Full Size | PDF

Compared with the near-field enhancement of suspended aluminum nanoparticles in vacuum (Fig. 1), the near-field enhancement of aluminum nanoparticles deposited on SiO₂ substrate was weakened, but was enhanced on Al substrate. It is noted that, there was still a strong electric field enhancement in the particles’ gaps of dimer and trimer deposited on Al substrate. The relative near-field enhancement value of gap in dimer was 9.45 in Fig. 7(d), and the relative near-field enhancement in trimer particles’ gap can reach 11 times in Fig. 7(f), which were higher than that of the dimer and trimer deposited on the SiO₂ substrate, as shown in Figs. 7(c) and 7(e). It can be seen that the Al substrate significantly improves the near-field enhancement effect of aluminum nanoparticles, compared with SiO₂ substrate.

In order to calculate the evolution of plasma free electron density and laser breakdown threshold of Al substrate, it is necessary to obtain the electric field amplitude on the surface of Al substrate. The near-field enhancement on the surface of Al substrate mediated by different morphologies of aluminum nanoparticles was obtained by post-processing of the solution model, as shown in Fig. 8, the maximum relative electric field enhancement times of SiO₂ and Al substrates mediated by monomer were 1.06 and 1.11 times, respectively.

Fig. 8. The relative electric enhancement |E|/E0 of different substrates mediated by different aluminum nanoparticles in vacuum. (a) monomer/SiO₂ substrate; (b) monomer/Al substrate; (c) dimer/SiO₂ substrate; (d) dimer/Al substrate; (e) trimer/SiO₂ substrate; (f) trimer/Al substrate.

Download Full Size | PDF

The maximum relative electric field enhancement times of SiO₂ and Al substrates mediated by dimer were 1.19 and 7.65 times, respectively. The strongest electric field distribution of SiO₂ substrate was along the laser polarization direction (Z axis), while the strongest electric field on Al substrate was concentrated at the contact between Al nanoparticles and Al substrate, mediated by dimer.

The maximum electric field enhancement times of SiO₂ substrate and Al substrate were 1.22 and 23.6 times, respectively, mediated by Al nanoparticle trimer. The electric field of Al substrate was enhanced obviously by the first and last particle of the trimer, as shown in Fig. 8(f). The nanopore structure will be formed during the ionization breakdown of substrates, when the electric field of substrates is enhanced to a certain extent.

3.3 Breakdown of Al substrate mediated by Al nanoparticles

The laser breakdown threshold, plasma free electron density evolution of Al substrate, and lattice temperature of aluminum nanoparticles were calculated under a single pulse irradiation of λ = 800 nm wavelength and t_p = 25 fs pulse width femtosecond laser.

3.3.1 Laser breakdown threshold and plasma free electron density evolution

With increase of the incident laser fluence, the near-field electric field amplitude of aluminum nanoparticles increases rapidly. The Al substrate will be ionized and broken down, when the electric field amplitude increases to a threshold value. Due to the near-field enhancement is different with different morphologies of aluminum nanoparticles, the threshold of femtosecond laser fluence required for Al substrate breakdown is also different. Therefore, the laser breakdown threshold of the Al substrate was investigated according to the different plasma electron density evolution mediated by aluminum nanoparticle monomer, dimer and trimer. It is necessary to set different laser fluence as the initial condition to make a trial calculation for the laser breakdown threshold, due to the nonlinear relationship between the incident laser fluence and the evolution of plasma electron density.

The breakdown threshold of plasma electron density of Al substrate, ρ_seed = 1 × 10¹⁸ cm⁻³, according to the references [2,21]. The evolution of plasma electron density with different laser energy density of monomer, dimer and trimer nanoparticles is shown in Fig. 9. The calculation time was set to 4t_p, which a complete pulse period was shown.

Fig. 9. Evolution of free electron density for Al substrates mediated by different morphologies of aluminum nanoparticles with different laser fluences (λ = 800 nm, t_p = 25 fs). (a) monomer; (b) dimer; (c) trimer.

Download Full Size | PDF

As shown in Fig. 9, the corresponding laser breakdown threshold was different because of the difference of near-field enhancement. The required laser breakdown threshold J for monomer, dimer and trimer was 31 mJ/cm², 0.6 mJ/cm² and 0.06 mJ/cm², respectively. The stronger the near field enhancement capability of aluminum nanoparticles, the lower the laser breakdown threshold was required. In Figs. 9(a), 9(b) and 9(c), the ionization start-up time can be advanced by increasing the laser fluence for each type of aluminum nanoparticle. As shown in Fig. 9(a), no ionization occurred with the laser fluence J = 20 mJ/cm², the plasma free electron density reached the threshold value and breakdown occurred with J = 40 mJ/cm² at t = 45 fs. In Fig. 9(b), there was no ionization breakdown occurred at the laser fluence J = 0.4 mJ/cm², while breakdown occurred with J = 1 mJ/cm² at t = 44 fs. In Fig. 9(c), there was no ionization breakdown occurred at the laser fluence J = 0.03 mJ/cm², while breakdown occurred with J = 0.08 mJ/cm² at t = 39 fs.

According to the experimental results of aluminum film ablation reported in reference [22], the minimum laser fluence J = 60 mJ/cm² of a single femtosecond laser pulse with a wavelength of 800 nm and a pulse width of 25 fs, was required for the ablation of 3 nm hole depth on the surface of the aluminum film target in vacuum environment. Bashir et al. [22] considered that this is the lowest energy threshold for “non-thermal ablation” caused by Coulomb explosion under a single pulse femtosecond laser of λ = 800 nm and t_p = 25 fs.

3.3.2. Electron and lattice temperatures of aluminum nanoparticles

The electronic and lattice temperatures of aluminum nanoparticle monomer (J = 31 mJ/cm²) and dimer (J = 0.6 mJ/cm²) at laser breakdown threshold were shown in Figs. 10(a) and 10(b), respectively, through the coupling calculation of electromagnetic model and two-temperature model. The results showed that the electronic temperature of monomer reached the peak value of 1957 K at t = 0.1 ps, decreased with the electron relaxation, and reached steady-state value of 380 K at t = 2.1 ps, and the lattice temperature reached steady-state at t = 2.1 ps. The electron temperature of dimer reached the peak value of 616 K at t = 0.08 ps, then it reached the steady state value of 309 K at t = 0.6 ps, and the lattice temperature reached the steady-state at t = 0.48 ps. The electron temperature of dimer decreased more rapidly, compared with the monomer. The temperature rise of electron and lattice of trimer under its’ laser breakdown threshold were too small to be ignored.

Fig. 10. Evolution of electron and lattice temperature for different nanoparticle morphology at different breakdown threshold (λ = 800 nm, t_p = 25 fs). (a) monomer; (b) dimer.

Download Full Size | PDF

As shown in Fig. 11, the maximum lattice temperature of monomer was located at the left and right edges along z-axis, while the maximum lattice temperature of dimer was located at the contact points between the particles and the substrate, and the temperature distribution has little difference in the whole nanoparticles. To sum up, the steady-state lattice temperatures of the monomer, dimer and trimer of aluminum nanoparticles do not exceed their melting point (933 K) at their respective laser breakdown threshold, which indicates that the integrity of aluminum nanoparticles can be maintained during mediating optical breakdown of aluminum substrates in vacuum environment.

Fig. 11. Lattice temperature of XZ cross-section for different nanoparticle morphology with laser breakdown fluence at t = 3 ps (λ = 800 nm, t_p = 25 fs). (a) monomer; (b) dimer.

Download Full Size | PDF

4. Conclusion

The near-field enhancement of aluminum nanoparticles in vacuum environment, the evolution of electron density of substrate, the femtosecond laser breakdown threshold of aluminum substrate, and the evolution of electron and lattice temperatures of monomer and dimer were investigated. For different substrates, the position and effect of near-field enhancement were also different, and the effect of near-field enhancement of aluminum nanoparticles was significantly improved by aluminum substrates. In vacuum, assembled aluminum nanoparticles can significantly reduce the threshold of femtosecond laser breakdown of deposited substrates, and the lattice temperature of aluminum nanoparticle monomer, dimer or trimer with 40 nm diameter was lower than the melting point, under the irradiation of a single-pulse femtosecond laser with a wavelength of 800 nm and pulse width of 25 fs. As a kind of cheap metal nanoparticle, aluminum nanoparticles have great potential to mediate the breakdown of deposited substrates, and to realize femtosecond laser super-resolution processing.

Appendix

Table 2. Parameters used in this model.

View Table | View all tables in this article

Funding

Suqian Sci&Tech Program (K201913).

Disclosures

The authors declare no conflicts of interest.

References

1. É. Boulais, R. Lachaine, and M. Meunier, “Plasma-mediated nanocavitation and photothermal effects in ultrafast laser irradiation of gold nanorods in water,” J. Phys. Chem. C 117(18), 9386–9396 (2013). [CrossRef]

2. N. Bloembergen, “Laser-induced electric breakdown in solids,” IEEE J. Quantum Electron. 10(3), 375–386 (1974). [CrossRef]

3. A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B 81(8), 1015–1047 (2005). [CrossRef]

4. A. Vogel, K. Nahen, D. Theisen, and J. Noack, “Plasma formation in water by picosecond and nanosecond Nd:YAG laser pulses. I. Optical breakdown at threshold and superthreshold irradiance,” IEEE J. Sel. Top. Quantum Electron. 2(4), 847–860 (1996). [CrossRef]

5. Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33(2), 127–137 (1997). [CrossRef]

6. J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35(8), 1156–1167 (1999). [CrossRef]

7. A. Kaiser, B. Rethfeld, M. Vicanek, and G. Simon, “Microscopic processes in dielectrics under irradiation by subpicosecond laser pulses,” Phys. Rev. B 61(17), 11437–11450 (2000). [CrossRef]

8. A. De Giacomo, R. Gaudiuso, C. Koral, M. Dell’Aglio, and O. De Pascale, “Nanoparticle enhanced laser induced breakdown spectroscopy: Effect of nanoparticles deposited on sample surface on laser ablation and plasma emission,” Spectrochim. Acta, Part B 98, 19–27 (2014). [CrossRef]

9. J. Zhen, “Research on mechanisms and physical properties of joining dissimilar metallic nanoparticles by femtosecond laser,” (Harbin Industrial University, CNKI, 2015).

10. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Zh.eksperim.i Teor.fiz 47 (1964).

11. F. Docchio, “Lifetimes of plasmas induced in liquids and ocular media by single Nd:YAG laser pulses of different duration,” EPL 6(5), 407–412 (1988). [CrossRef]

12. N. Linz, S. Freidank, X.-X. Liang, J. Noack, G. Paltauf, and A. Vogel, “Roles of tunneling, multiphoton ionization, and cascade ionization for optical breakdown in aqueous media,” AFOSR Int. Res. Initiat. Proj. SPC 053010/EOARD, 0-206 (2009).

13. P. K. Kennedy, S. A. Boppart, D. X. Hammer, and B. A. Rockwell, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media. II. Comparison to experiment,” IEEE J. Quantum Electron. 31(12), 2250–2257 (1995). [CrossRef]

14. Y. R. Davletshin and J. C. Kumaradas, “The role of morphology and coupling of gold nanoparticles in optical breakdown during picosecond pulse exposures,” Beilstein J. Nanotechnol. 7, 869–880 (2016). [CrossRef]

15. Z. Lin and L. Zhigilei, “Electron-phonon coupling and electron heat capacity in metals at high electron temperatures,” (http://faculty.virginia.edu/CompMat/electron-phonon-coupling/, 2008).

16. Q. Lin, N. Ren, Y. Ren, Y. Chen, Z. Xin, Y. Fan, X. Ren, and L. Li, “Theoretical study on femtosecond laser optical breakdown threshold in water mediated by aluminum nanoparticle coated with silica,” Opt. Express 26(26), 34200 (2018). [CrossRef]

17. C. G. Khoury, S. J. Norton, and T. Vo-Dinh, “Investigating the plasmonics of a dipole-excited silver nanoshell: Mie theory versus finite element method,” Nanotechnology 21(31), 315203 (2010). [CrossRef]

18. A. Vial and T. Laroche, “Description of dispersion properties of metals by means of the critical points model and application to the study of resonant structures using the FDTD method,” J. Phys. D: Appl. Phys. 40(22), 7152–7158 (2007). [CrossRef]

19. A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008). [CrossRef]

20. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer Berlin Heidelberg, 1995), Vol. 25,.

21. M. Sabsabi and P. Cielo, “Quantitative analysis of aluminum alloys by laser-induced breakdown spectroscopy and plasma characterization,” Appl. Spectrosc. 49(4), 499–507 (1995). [CrossRef]

22. S. Bashir, M. S. Rafique, and W. Husinsky, “Identification of non-thermal and thermal processes in femtosecond laser-ablated aluminum,” Radiat. Eff. Defects Solids 168(11-12), 902–911 (2013). [CrossRef]

23. Y. M. Zolotovitskii, L. I. Korshunov, and V. A. Benderskii, “Electron work function from metals in a liquid dielectric,” Bull. Acad. Sci. USSR, Div. Chem. Sci. 21(4), 760–763 (1972). [CrossRef]

24. D. Fisher, M. Fraenkel, Z. Henis, E. Moshe, and S. Eliezer, “Interband and intraband (Drude) contributions to femtosecond laser absorption in aluminum,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 65(1), 016409 (2001). [CrossRef]

	monomer	dimer	trimer
CPM: \|E\|_max,bulk /E0	1.91	8.55	10
Modified CPM: \|E\|_max /E0	1.9	8.52	9.97
The relative error: $\frac{{\| E \|}_{max, bulk} - {\| E \|}_{max}}{{\| E \|}_{max, bulk}}$	5.2‰	3.5‰	3‰

Symbol	Value/Expression	Description
c ₀	3 × 10⁸ m/s	Speed of light in vacuum
ω	$2 π c_{0} / λ$	laser frequency
ε₀	8.85 × 10⁻¹² F/m	Vacuum permittivity
f (t_p)	$\exp (\frac{- 2.77 {(t - 2 t_{p})}^{2}}{t_{p}^{2}})$	Gaussian pulse function
I_in	$J \cdot f (t_{p}) / t_{p}$	Incident intencity of laser
$E 0$	$\sqrt{2 I_{i n} / (c_{0} n ε_{0})}$	Incident electric field
e	1.6 × 10⁻¹⁹ C	Electron charge
ρ_bound	18.1 × 10²² cm⁻³	Bound electron density of aluminum
n	1	Refractive index of vacuum
ħ	1.0545718 × 10⁻³⁴ J·s	Reduced Planck constant
E _gap	4.25 eV	Band gap energy of aluminum [23]
M	4.4978 × 10⁻²⁶ kg	Mass of aluminum atom
$m_{e}$	9.10938291× 10⁻³¹ kg	Electron mass
$m^{'}$	$1.2 m_{e}$	Effective aluminum electron mass [24]

	monomer	dimer	trimer
CPM: \|E\|_max,bulk /E0	1.91	8.55	10
Modified CPM: \|E\|_max /E0	1.9	8.52	9.97
The relative error: $\frac{{\| E \|}_{max, bulk} - {\| E \|}_{max}}{{\| E \|}_{max, bulk}}$	5.2‰	3.5‰	3‰

Symbol	Value/Expression	Description
c ₀	3 × 10⁸ m/s	Speed of light in vacuum
ω	$2 π c_{0} / λ$	laser frequency
ε₀	8.85 × 10⁻¹² F/m	Vacuum permittivity
f (t_p)	$\exp (\frac{- 2.77 {(t - 2 t_{p})}^{2}}{t_{p}^{2}})$	Gaussian pulse function
I_in	$J \cdot f (t_{p}) / t_{p}$	Incident intencity of laser
$E 0$	$\sqrt{2 I_{i n} / (c_{0} n ε_{0})}$	Incident electric field
e	1.6 × 10⁻¹⁹ C	Electron charge
ρ_bound	18.1 × 10²² cm⁻³	Bound electron density of aluminum
n	1	Refractive index of vacuum
ħ	1.0545718 × 10⁻³⁴ J·s	Reduced Planck constant
E _gap	4.25 eV	Band gap energy of aluminum [23]
M	4.4978 × 10⁻²⁶ kg	Mass of aluminum atom
$m_{e}$	9.10938291× 10⁻³¹ kg	Electron mass
$m^{'}$	$1.2 m_{e}$	Effective aluminum electron mass [24]

Study on the mechanism of a femtosecond laser-induced breakdown of the deposited substrate mediated by aluminum nanoparticles in a vacuum

Abstract

1. Introduction

2. Methods

2.1 Electromagnetic model

2.2 Plasma dynamics

2.3 Two-temperature model

3. Results

3.1. Near field enhancement of aluminum nanoparticles

3.2. Near-field enhancement of nanoparticles deposited on different substrates

3.3 Breakdown of Al substrate mediated by Al nanoparticles

3.3.1 Laser breakdown threshold and plasma free electron density evolution

3.3.2. Electron and lattice temperatures of aluminum nanoparticles

4. Conclusion

Appendix

Funding

Disclosures

References

Cited By

Figures (11)

Tables (2)

Equations (15)

Optical Materials Express