Selective Laser Ablation of Metal Thin Films Using Ultrashort Pulses

Abstract

Selective thin-film removal is needed in many microfabrication processes such as 3-D patterning of optoelectronic devices and localized repairing of integrated circuits. Various wet or dry etching methods are available, but laser machining is a tool of green manufacturing as it can remove thin films by ablation without use of toxic chemicals. However, laser ablation causes thermal damage on neighboring patterns and underneath substrates, hindering its extensive use with high precision and integrity. Here, using ultrashort laser pulses of sub-picosecond duration, we demonstrate an ultrafast mechanism of laser ablation that leads to selective removal of a thin metal film with minimal damage on the substrate. The ultrafast laser ablation is accomplished with the insertion of a transition metal interlayer that offers high electron–phonon coupling to trigger vaporization in a picosecond timescale. This contained form of heat transfer permits lifting off the metal thin-film layer while blocking heat conduction to the substrate. Our ultrafast scheme of selective thin film removal is analytically validated using a two-temperature model of heat transfer between electrons and phonons in material. Further, experimental verification is made using 0.2 ps laser pulses by micropatterning metal films for various applications.

Appendices

Appendix

Numerical methods

Temperature development in the interlayer in the ultrafast regime is strongly influenced by the e-e coupling as well as the e-p coupling in a strong thermal non-equilibrium state between electrons and lattices. Therefore, a two-temperature model needs to be adopted to account for the heat transport of electrons and lattices separately. The Boltzmann transport theory [25] may be also used for the two-temperature analysis by means of statistical dynamics, but the Fourier heat theory is more preferable as it permits calculating macroscopic temperature distribution leading to ablation with less computational burden. In heat transfer by conduction within a solid, the electron temperature (${T}_{e})$ and the lattice temperature (${T}_{l})$ are described with two coupled equations of thermal diffusion [26]:

$$ C_{e} \frac{{\partial T_{e} }}{\partial t} = \nabla \left( {k_{e} \nabla T_{e} } \right) - G_{e - p} \left( {T_{e} - T_{l} } \right) + S $$

(A1)

$$ \rho_{l} \left[ {c_{pl} + L_{m} \delta_{m} + L_{v} \delta_{v} } \right]\frac{{\partial T_{l} }}{\partial t} = \nabla \left( {k_{l} \nabla T_{l} } \right) + G_{e - p} \left( {T_{e} - T_{l} } \right) $$

(A2)

The subscripts e and l denote the electron and lattice, respectively. The parameters ${C}_{e},$ k, ρ and c_p are the free electron specific heat, the thermal conductivity, the material density, and the specific heat. In addition, ${L}_{m}{\delta }_{m}$ represents the latent heat for melting and ${L}_{v}{\delta }_{v}$ the latent heat for vaporization, with the Kronecker δ-like function being defined as

$$ \delta \left( {T_{l} - T_{i} ,\Delta } \right) = \frac{1}{{\sqrt {2\pi } \Delta }}\exp \left[ { - \frac{{\left( {T_{l} - T_{i} } \right)^{2} }}{{2\Delta^{2} }}} \right] $$

(A3)

T_i represents either the meting temperature or the vaporization temperature, where Δ denotes the full-width-at-half-maximum (FWHM) temperature range over which the phase change of melting or vaporization occurs.

The source term S of Eq. (A.1) has units of W/m³ and is given as a function of the depth z measured from the top metal surface towards the substrate;

$$ S = \frac{1 - R}{{1 - \exp \left[ { - \frac{L}{{\left( {d + d_{b} } \right)}}} \right]}} \times 4 \times \sqrt {\frac{4\ln 2}{\pi }} \frac{F}{{\left( {d + d_{b} } \right)t_{p} }} \times \exp \left[ { - \frac{z}{{d + d_{b} }} - 4\ln 2\left( {\frac{{t - 2t_{p} }}{{t_{p} }}} \right)^{2} } \right] $$

(A4)

The parameters R, L, F and t_p are the reflection coefficient, the film thickness, the laser incident fluence, and the laser pulse duration, respectively. The parameter d is the optical penetration depth calculated by linear light propagation theory. The other parameter d_b indicates the mean free path of excited free electrons extended additionally by ultrashort intense light pulses, which is called the ballistic range of electrons. In this study, d_b was estimated to be ~ 100 nm for Au [14].

At a metal–metal interface, a certain amount of thermal resistance needs to be considered in dealing with electron–electron coupling. In this study, the electron thermal resistance R_ee between the Au film and the Ti interlayer was determined using the extended diffusive mismatch model of electron heat transfer at a metal–metal interface [16, 27] as follows:

$$ R_{ee,Au/Ti} = \frac{{4\left( {Z_{Au} + Z_{Ti} } \right)}}{{Z_{Au} Z_{Ti} }}, $$

(A5)

where $Z={C}_{e}{v}_{e}$ with ${v}_{e}$ being the electron velocity usually close to the Fermi velocity. Between the Ti interlayer and the glass substrate, R_ee was assumed infinite since the latter is dielectric with no free electrons.

Both the metal–dielectric and metal–metal interfaces, the phonon thermal resistance R_pp is found to have little influence on the temperature distribution in the ultrafast regime [17]. In this study, R_pp is taken as 4 × 10⁻⁹ m² K/W with reference to the literature data obtained using pump-probe spectroscopy [19] and quantum mechanical calculation [16].

The temperature-dependent effect on the free-electron heat capacity was considered as ${C}_{e}=\gamma {T}_{e}$ with $\gamma$ being assumed as a constant. The electron–phonon coupling coefficient G_e-p was also modified as ${G}_{e-p}={G}_{0}\left[\frac{{A}_{e}}{{B}_{l}}\left({T}_{e}+{T}_{l}\right)+1\right]$ with G₀ being the room-temperature value of G_e-p. And A_e = 1.2 × 10⁷ K⁻² s⁻¹ and B_l = 1.2 × 10¹¹ K⁻¹ s⁻¹ are the material-dependent constants for the Au electron and lattice, respectively [28, 29]. The temperature dependence of G_e-p was considered only for Au while G_e-p was assumed constant for Ti and Cr due to the lack of available data. The thermal conductivity of Au electron was determined as [30]:

$$ k_{e} = \chi \frac{{\left( {\vartheta_{e}^{2} + 0.16} \right)^{5/4} \left( {\vartheta_{e}^{2} + 0.44} \right)\vartheta_{e} }}{{\sqrt {\vartheta_{e}^{2} + 0.092} \left( {\vartheta_{e}^{2} + \eta \vartheta_{l} } \right)}}, $$

(A6)

where ${\vartheta }_{e}={T}_{e}/{T}_{F}$ and ${\vartheta }_{l}={T}_{l}/{T}_{F}$ are the dimensionless electron and lattice temperatures normalized with regards to the Fermi temperature ${T}_{F}$. The fitting parameters are $\chi$ = 353 W/(m·K) and $\eta$ = 0.16 for Au. For Ti and Cr, based on the Drude model [18], the electron thermal conductivity ${k}_{e}$ was estimated as

$$ k_{e} = k_{0} \frac{{T_{e} }}{{T_{l} }}, $$

(A7)

where ${k}_{0}$ denotes the thermal conductivity at room temperature, being identified to be 22 W/(m·K) and 94 W/(m·K) for Ti and Cr, respectively. On the other hand, the lattice thermal conductivity ${k}_{l}$ was assumed to be negligible as it is usually found to be significantly smaller than ${k}_{e}$ in metals [22, 23]. Table 2 lists the thermophysical properties of the materials used in this study.

The film thickness dealt with in this study is much smaller than the laser beam diameter. Thus, with irradiation of a single laser pulse, Eqs (A.1) and (A.2) are solved numerically by one-dimensional finite difference calculation along the depth z-direction. Implicit numerical computation was made with a relative residual of 10^–7. Direct electrons scattering from metal to dielectric may be significant, particularly for ultrashort pulses yielding high electron temperatures. However, the electron–phonon coupling of the interlayer is assumed so strong as to neglect direct electrons scattering from the interlayer to the dielectric substrate. Natural convection, thermal conduction to ambient air, and radiation heat transfer are neglected. Only the thermal conduction from the top metal film through the interlayer to the substrate are considered with zero heat flux boundary conditions;

$$ \left. {\frac{{\partial T_{e} }}{\partial z}} \right|_{flim\, surface} = \left. {\frac{{\partial T_{l} }}{\partial z}} \right|_{film\, surface} = \left. {\frac{{\partial T_{g} }}{\partial z}} \right|_{z = \infty } = 0 $$

(A8)

Table 2 Thermophysical properties of the materials