Study on Ablation Characteristics of Femyosecond Laser Nanoscale Processing for Aluminum Nitride and LeadZirconate Titanate Ceramics

This paper analytically investigates an ultrashort pulsed laser nanoscale processing for aluminum nitride (AIN) and lead zirconate titanate (PZT) ceramics. Processing characteristics of an ultra-short pulsed laser is different from that of long-pulsed laser due to ultrahigh intensity, ultrahigh power, and ultrashort time. The ultrasmall processing for materials can achieved by an ultra-short pulsed laser. This study proposes a model to analyze an ultrashort pulsed laser nanoscale processing for aluminum nitride (AIN) and lead zirconate titanate (PZT) ceramics. The effects of optical penetration absorption and thermal diffusion on temperature are also discussed. The results reveal that the variation of ablation rate with laser fluences predicted by this work agrees with the available measured data for an ultrashort pulsed laser processing for AIN and PZT. For femtosecond lasers, the optical absorption and thermal diffusion, respectively, governs the ablated depth per pulse at the low and high laser fluences. The thermal diffusion length is small relative to the optical penetration depth for femtosecond laser. The optical penetration absorption governs the temperature in the workpiece. On the other hand, for the picosecond laser, the thermal diffusion length is large compared to the optical penetration depth. The thermal diffusion determines the temperature in the workpiece. nanofabrication of functional devices Femtosecond Laser Processing of Nano-Crystalline CVD Diamond This proposes an analytical model to study the femtosecond laser processing of AlN and PZT ceramics. The depth per pulse versus laser fluence of AlN and PZT ablated by a femtosecond laser is predicted and compared with the measured data. Ablation characteristics of a femtosecond laser processing for AlN and PZT is analyzed. The effects of optical penetration absorption and thermal diffusion on temperature will also be discussed.


Introduction
A femtosecond laser was employed to pattern an aluminum nitride (AlN). The AlN film was patterned precisely only little changes to the material structure of the film surface for a femtosecond laser processing [1]. AlN thin film was usually employed as a buffer layer which provides a strain between sapphire and AlN. This misfit strain makes the buffer layer to be an important structure for GaN-based devices [2] and the buffer layer is also important for the growth of epitaxial gallium nitride (GaN) layers on sapphire substrates, which promoted the development of GaN electronic and optoelectronic devices [3]. AlN thin film is also evaluated to be important substrate materials since the lattice constant and thermal expansion are approximate between the AlN and the GaN or AlGaN epitaxial layers [4]. AlN is a wide band gap semiconductor material. Its applications include radio frequency filters [5], ultraviolet (UV) solid state light sources [6], acoustic resonators [5], and photodetectors [7].
Lead zirconate titanate (PZT) thin films embedded in micro electro-mechanical systems (MEMS) can enhance efficiency and reduce size of MENS devices. PZT thin films can be formed by laser deposition MENS [8] and can work as resonators [9] and sensors [10].
The properties of PZT thin films are significantly related to the crystallization and the microstructure [11]. PZTs in MENS must be very high precision, speed and good controllability.
PZTs are not easy to be machined on a micrometer scale with traditional methods due to its high hardness and brittleness. Therefore, an ultrafast laser is applicable to achieve this precision (process PZT) [12].
A nanosecond ultraviolet (UV) laser is used to pattern the electrodes on thick graphite oxide (GO) free standing films [13]. Direct laser writing (DLW) is a suitable technique for three-dimensional (3D) micro-and even nanostructuring [13]. Femtosecond laser processing for optical materials is a good technology to the production of high-quality micro-and nanofabrication of functional devices [14]. Femtosecond Laser Processing of Nano-Crystalline CVD Diamond Coating was studied [15]. This paper proposes an analytical model to study the femtosecond laser processing of AlN and PZT ceramics. The depth per pulse versus laser fluence of AlN and PZT ablated by a femtosecond laser is predicted and compared with the measured data. Ablation characteristics of a femtosecond laser processing for AlN and PZT is analyzed. The effects of optical penetration absorption and thermal diffusion on temperature will also be discussed.

Analysis
A model is developed for an ultrashort pulsed laser processing of PZT and AlN.
Different from metals full of free electrons using two-temperature model due to the difference of temperature between electrons and lattices at the duration of laser pulse, PZT and AlN ceramics employ the thermal transport model based on phonons as carriers. Therefore, PZT and AlN The model in the polar coordinates can be written The number 3 in Eq. (1) are taken to assure 90 percent of laser energy included within the energy-distribution radius. The pulse duration for a femtosecond laser is about on the order of 10 -15 seconds which is shorter than relaxation time of thermal diffusion on the order of 10 -12 seconds in AlN or PZT ceramics. Hence, before the relaxation time of thermal diffusion is arrived during the laser pulse, the heat conduction the r-, θ-, and z-directions is assumed to be negligible because the heat cannot diffuse in time. On the other hand, after he relaxation time of thermal diffusion is arrived, the main heat diffusion is in the z-direction because the workpiece employed in this study is about 10 -3 m in the z-direction and infinite size in the r-direction. Eq. (1) can be, therefore, written as Material absorption for laser is recognized to be volume absorption. When the optical penetration depth is very small, the optical surface absorption is achieved. It is assumed that the heat on the surface of workpiece is transported into the ambient by convection. The ambient temperature and vaporization temperature are, respectively, set at bottom surface of workpiece and solid-vapor interface.
The location of material removal is assumed to be at the solid-vapor interface (ablation interface). The balance of thermal energy at the solid-vapor interface is The nondimensional parameters are defined as Therefore, the nondimensional Eq. (2) can be written as The symbols, D/L and  /L, in Eq. (5), respectively, represents the nondimensional thermal diffusion length and optical penetration depth. When the nondimensional thermal diffusion length is small enough relative to the nondimensional optical penetration depth, the thermal diffusion term can be neglected. Therefore, the temperature in Eq. (5) is governed by the direct optical penetration absorption of incident laser pulse. On the other hand, when the nondimensional optical penetration depth is small enough relative to the nondimensional thermal diffusion length, the optical penetration absorption only occurs on the worpiece surface and the temperature inside the workpiece is not directly affected by the optical penetration absorption on the workpiece surface. For femtosecond pulsed laser, the laser pulse duration is on the order of 10 -15 s. However, the relaxation time of thermal diffusion, cL 2 /k, is on the order of 10 -12 s for materials. The ratio of ultrashort laser pulse duration to thermal diffusion time is far smaller than one. Therefore, the thermal diffusion term of the right-handed side in Eq. (5) can be neglected because the order of the other nondimensional terms is near one.
The nondimensional initial condition and boundary conditions are The nondimensional relation of energy balance at solid-vapor interface is The method of Laplace transform is employed to obtain the solution of Eq. (5). If the Laplace transform of the temperature  is symbolized by  , the Eq. (6) in the Laplace domain yields In the similar way, the nondimensional initial condition and boundary conditions in the Laplace domain are The general solution of Eq. (10) with the initial condition in Laplace domain is The temperature is finite for  and the boundary condition on the surface of workpiece determines the constant c1. Therefore, The first term and second term in the right-handed side of Eq. (13) are, respectively, related to the effects of thermal diffusion and direct optical absorption on the temperature in the workpiece.
The nondimensional temperature in time domain is obtained by taking the inverse of Laplace transform for Eq. (13). (15) Combining Eq. (15) and the energy balance equation at the solid-vapor interface, one can get the relation at the solid-vapor interface.    The variation of the ablated depth per pulse with laser fluences is plotted in Fig. 4 for the ultrafast laser ablation of AIN. The difference between Fig. 3 and Fig. 4 is the scale of the horizontal axis. The horizontal axises in Fig. 3 and Fig. 4 are, respectively, scaled by the linearity and logarithm of laser fluences. The increase of ablation rate with laser fluences in Fig.   3 at high laser fluence is slightly more slower than that at low laser fluences. This possible reason is because the thermal ablation of the residual laser energy occurs at high laser fluences after the directly incident ultrafast laser pulse conducts optical penetration ablation due to optical absorption length. In this linear horizontal axis of laser fluences, the solid line predicted by this work agrees with the triagle symbols measured by the published paper [16] and the ablation rate still increases with the increasing laser fluences although the increase of ablation rate with laser fluences in at high laser fluence is slightly more slower than that at low laser fluences different from Fig. 3.

Results and Discussion
The relation of the ablation rate of PZT to laser fluence is plotted in Fig. 5 for the prediction of this work and the measurement of the published paper [17]. The solid line and triangle symbols, respectively, stand for the ablated depth per pulse versus laser fluence predicted by this work and measured by Di Maio et al [17].

Conclusions
The analytical study of an ultrashort pulsed laser processing for AlN and PZT is conducted in this paper. The model proposes that the material is removed at the solid-vapor interface. The variation of ablation rate with laser fluences predicted by this work agrees with the available measured data for an ultrashort pulsed laser processing for AIN and PZT. The ablation rate increases with the increasing laser fluences. The increase of ablation rate with laser fluences is faster at low laser fluences than that at high laser fluences. The thermal diffusion length is small relative to the optical penetration depth for the pulse duration at the order of femtoseconds. Therefore the thermal diffusion terms are negligible. Only the optical penetration term is responsible for temperature. On the other hand, for the pulse duration at the order of picoseconds, the thermal diffusion length is large enough compared to the optical penetration depth. The optical absorption is almost only on the surface of workpiece.
Therefore the temperature in materials is only determined by the thermal diffusion of heat from workpiece surface absorbing directly incident laser energy.