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Abstract
In this work, we performed an experimental investigation supported by a theoretical analysis of single-shot laser ablation of gold to study the laser-matter interaction for predicting the ablation morphology and optimizing the process parameters. A set of coupled partial differential equations of the two-temperature model with dynamic optical properties and a phase explosion mechanism were used to determine the temporal and spatial evolution of the electron and lattice temperatures. The primary research focus of this work is to use the GHz frequency to investigate the ablation performance because the irradiated material is still far from thermal equilibrium during the laser-matter interaction. In contrast to conventional single-pulse laser ablation, intra-burst frequencies and the number of pulses are important factors in optimizing ablation efficiency and quality for fast material processing. Theoretical investigation revealed that the ablation volume increased due to heat accumulation, but the ablation quality decreased as the intra-burst frequencies decreased from 1000 GHz to 10 GHz. Moreover, the specific ablation volume increases with a higher burst number and lower intra-burst frequency at the expense of ablation quality.
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Nomenclature
$\alpha$ | Absorption coefficient of the material $(1/m)$ |
$\Delta \varepsilon$ | Weighting factor |
$\Gamma _{L}$ | Spectral width of the Lorentz oscillator $(Hz)$ |
$\lambda$ | Wavelength $(nm)$ |
$\omega$ | Laser frequency $(Hz)$ |
$\omega _{0}$ | Laser beam spot radius at focal plane (µm) |
$\Omega _{L}$ | Oscillator strength $(Hz)$ |
$\omega _{p}$ | Plasma frequency $(Hz)$ |
$\tau$ | Pulse duration $(s)$ |
$\tau _e$ | Relaxation time of electrons $(s)$ |
$A_e$ | Material constant for electron relaxation time $(1/K^2 s)$ |
$B_l$ | Material constant for electron relaxation time $(1/Ks)$ |
$C_e$ | Heat capacity of the electron $(J/m^3K)$ |
$C_l$ | Heat capacity of the lattice $(J/m^3K)$ |
$F$ | Laser fluence $(J/cm^2)$ |
$G$ | Electron lattice coupling factor $(W/m^3K)$ |
$H_m$ | Latent heat of melting $(J/kg)$ |
$k$ | Extinction coefficient $(s)$ |
$K_e$ | Thermal conductivity of the electron $(W/mK)$ |
$K_l$ | Thermal conductivity of the lattice $(W/mK)$ |
$K_{b}$ | Boltzmann constant $(J/K)$ |
$n$ | Refractive index $(s)$ |
$Q_{total}$ | Laser heating source $(W/m^3)$ |
$R$ | Reflectivity of material |
$S_{(r,z)}$ | Spatial laser energy distribution $(J/m^3)$ |
$T_e$ | Electron temperature $(K)$ |
$T_f$ | Fermi Temperature $(K)$ |
$T_l$ | Lattice temperature $(K)$ |
$T_{(time)}$ | Function of time $(1/s)$ |
$T_{cr}$ | Critical Temperature $(K)$ |
$T_{m}$ | Melting Temperature $(K)$ |
$t_{s}$ | Pulse separation time $(s)$ |
1. Introduction
In the past decades, ultrashort laser technology has attracted growing interest as a powerful manufacturing tool in medical and industrial applications [1]. The energy deposited to solid material with femtosecond laser pulses can be precise with less thermal damage than picosecond and nanosecond laser pulses. Physical phenomena involving laser–material interactions are necessary to achieve better controllability and quality during laser ablation. Fundamental studies between femtosecond laser pulses and metals have been conducted since the early’70s [2], and it is represented by the Two-temperature model, which is still the most effective method for studying ablation characteristics [3]. It has been extended further by employing parabolic [4], hyperbolic [4], dual-hyperbolic [5], or temperature-dependent optical properties [6]. Based on the relaxation time and space nonlocal effects, Sobolev et al. developed other two- temperature models, namely, HTTM (Hyperbolic two-temperature model) and NTTM (nonlocal two-temperature model), which use the modified constitutive equations for heat flux in electron gas based on extended irreversible thermodynamics [7]. There are other methods for investigating ultrashort laser-matter interactions such as molecular dynamics [8,9], discrete model [10] and combined molecular dynamics, and Monte Carlo simulations [11]. MD-simulation provides a detailed morphological investigation at the atomic level, but the computation time is much longer because of the large number of atoms [12]. Some recent papers are devoted to combining the molecular dynamic simulation, and TTM model [13–15]. All of these studies are focused on a one-dimensional approach based on the reasonable assumption that the laser spot size is much larger than the depth, which may result in inaccuracy when working with bulk materials. For this purpose, a two-dimensional (2D) TTM [16] or three-dimensional (3D) TTM model was applied to study the ultrashort laser ablation of metal [17].
Due to the industrial demand for high throughput laser processes, significant efforts have been directed over the past decades toward developing ultrafast laser sources with high repetition rates and used in the burst mode (BM). Jiang et al. extended one dimension two-temperature model to evaluate the ultrashort laser pulse-train processing in the gold film [18]. For the numerical modelling of multi-pulse picosecond laser ablation of stainless steel, Wang et al. [19] are restored to the initial temperature before applying the subsequent pulses at a lower frequency without considering the accumulation effect. A burst of femtosecond pulses with an intra-burst repetition rate in GHz has been employed to meet the application requirement of fast laser material processing [20]. In GHz intra-burst repetition rate, each laser pulse causes complex physical phenomena that occur on a timescale of several picoseconds [21]. Previous studies with bursts containing multiple pulses with an intra-burst repetition rate of GHz demonstrated that ablation efficiency increases by order of magnitude over single pulse ablation of the same energy [22,23]. A comparative study of the GHz, MHz, and kHz repetition rates shows that the MHz repetition rate is more efficient than the kHz and GHz [24]. Still, the ablation quality is superior in GHz burst because the physical removal of ablated materials carries away the thermal energy contained in the ablated mass [20,25]. Despite the community’s interest in GHz burst mode, the lack of laser sources has made it more challenging for researchers to conduct experiments to explore this process further. The new femtosecond laser can operate in GHz mode, allowing the research community to investigate GHz burst mode ablation of metals [23,26,27], semiconductors [23,28], and dielectrics [29]. Alongside the intra-brust repetition rate, the number of pulses in a burst is also an essential parameter in determining the ablation morphology. Several researchers have reported that increasing the number of pulses in a burst reduces the maximum ablation volume [29–31]. Norman Hodgson et al. reported that burst mode operation allows access to the maximum ablation rate for metal by using more than five pulses per burst [29]. Neuenschwander et al. [32] reported a general enhancement of the maximum specific ablation rate in bursts of laser pulses. In contrast to Neuenschwander et al. ’s research [32], Metzner et al. explored the enhancement of the ablation volume up to 5 pulses in burst and decreased the ablation volume further rise in the number of pulses in burst. Nowadays, a femtosecond burst with a THz repetition rate was used to reduce the effect of heat accumulation and better ablation quality, with the temporal separation between the pulses in several picoseconds [33–36]. Despite several research studies, the underlying energy transport mechanism for multi-pulse femtosecond laser heating is poorly understood because there are still unanswered questions about the physical mechanisms that interact and influence laser-matter interaction when bursts of ultra-short pulses are used instead of single pulses.
The use of GHz intra-burst repetition rate is justified by the fact that the irradiated material is in non-equilibrium while subsequent pulses interact with matter. In other words, the successive pulses interact with a material that has been "excited" by the initial pulse and is still in a transient state, which could give rise to novel and unknown process dynamics. For that reason, it is worth investing in the effect of the intra-burst frequency and the number of pulses in the burst on the ablation performance, which has been one of the aims of the present work. Therefore, in this work, an axisymmetric two-temperature model for multi pulses, which combines the effect of heat accumulation, is developed to predict the spatial and temporal electron temperature and lattice temperature. The experimental results were supported by theoretical investigations of the ablation crater of the gold sample during irradiation with single-shot femtosecond laser pulses through the numerical solution of the two-temperature model. Numerical results allowed an understanding of how the ablation characteristic change during irradiation with bursts of pulses with GHz frequencies where intra-pulse separation time is in the range of the thermal relaxation time.
2. Two-temperature model (TTM)
Two temperature models can represent a theoretical analysis of ultra-short laser-matter interaction. Figure 1 shows a schematic diagram of the ultrashort laser pulses acting on the surface of the gold material. It is divided into five parts – absorption, heating, energy transfer, thermomechanical response of the material and ablation. When the laser pulses irradiate the substrate or material, energy transfers from the laser pulses to the material, this energy absorbs by free electrons, which increases the temperature of the electron (absorption). At room temperature, the lattice’s and electron’s temperatures are in thermal equilibrium. Once an electron gets energy from laser pulses, an electron-electron collision occurs. As a result, a rapid increase in the electron temperature (heating) and these energetic electron transfers their energy to the lattice by electron-lattice collision (energy transfer). Many energetic electrons are present during pulsed laser irradiation on the material, so many electron-lattice collisions are necessary to transfer a significant amount of energy. Due to the transfer of energy from electron to lattice system, heat diffusion in material or substrate occurs (thermomechanical response), and material is ablated (ablation).
Fig. 1. Schematic diagram of Ultra-short pulse laser interaction with metal. Where $T_l$ and $T_e$ are temperatures of lattice and electron and $T_0$ is the room temperature.
2.1 Theoretical modeling
The spatial and temporal evolution of electron and lattice temperature can be defined below for the electron-lattice energy balance equation [37]:
Here the $\Delta$ is the range of 10K-100K, depending on the temperature gradient, and $T_m$ is the material’s melting temperature. During the ultrafast heating of the material, the temperature of electrons and lattice rises so that temperature depended materials properties have a pivotal role during the simulation. All are listed in Table 1.
The spatial laser energy distribution $S_{(r,z)}$ in the material can be expressed as follow [45]:
Based on the single pulse temporal profile of the output laser Gaussian pulse, the function of time for multipulse can be given by [45]:
From the prior equations for the spatial and temporal distributions of laser energy, the laser source term ($Q_{total}$) to simulate multipulse laser ablation can be expressed as follow [45]:
Drastic changes in electron temperature and lattice temperature during and after irradiation of femtosecond laser pulses create a decisive influence on the material optical properties, such as absorptivity and reflectivity. The reflectivity and absorption coefficient can be determined by the dielectric constant $\varepsilon _{1}$ and $\varepsilon _{2}$. Generally, the Drude model [46] is used to determine the dielectric constant; however, it does not include all ranges of the spectrum, so Povell et el. [47] gives the Lorentz–Drude model, which is further modified with five Lorentzian functions [48]. Still, it can not fit the experimental data in the visible range and also does not include interband transition [49]. For that purpose, in this simulation, an extended Drude model [50], which is also considering interband transition, is used to describe the evolution of the reflectivity and absorption coefficient of the gold surface. The dielectric constant based on the Extended Drude model is described by [49,50]:
2.2 Experimental work and methodology
In the present work, ablation experiments were carried out on thin gold film with a thickness of 100 µm. The femtosecond Yb: KGW laser system (Pharos from Light Conversion Ltd.) was used, which provided pulses of 180 fs duration at a maximum repetition rate of 600 kHz and maximum average power of 6 W at 1030 nm. For the ablation experiments, we used a second harmonic at 515 nm. The sample was placed on a motorized linear XYZ stage with a 100 mm focal length. Around 20 µm spot size ($1/e^2$) was achieved by optimizing the laser system. Because of the rotational symmetry in the laser ablation process, a 2D-axisymmetric model was adopted, as shown in Fig. 2. In the computation model, 30 µm in a radial direction and 5 µm in an axial direction represent half of the target material. The ultrashort laser pulse with gaussian distribution was applied to the top surface and propagated in the z-direction. The evolution of the temperatures of the two sub-systems can be determined by solving the two-temperature model with the initial ambient temperature condition being 300 K and ambient pressure of 1 bar.
2.3 Ablation mechanisms
To disintegrate some amount of matter from a substrate, the material should undergo some change in the phase, such as vaporization, phase change, or plasma formation. Material ablation is a stepwise process; the first melting of the solid occurs, and the evaporation of molten material follows it. When fluence is high, a direct transition of solid material into metastable liquid near its critical state occurs without boiling because of the short heating time. Subsequent bubble nucleation leads to a rapid transition of the superheated liquid to a mixture of vapour and liquid droplets ejected from the bulk material called phase explosion. In numerical solution, it is assumed that heterogeneous nucleation occurs due to phase explosion when the lattice temperature reaches the $0.9 T_{cr}$ (critical temperature) [52]. The ablated crater profile is obtained by removing those elements which reach the vaporization $0.9 T_{cr}$ [43,53].
3. Results and analysis
3.1 Single-shot laser ablation
A comparative study of singe-pulse ablation has been demonstrated to verify the computational model’s rationality. Figure 3 shows the evolutions of the electron and lattice temperatures at the centre surface point (r=0, z = 0) heated by a single-pulse with laser fluence 0.50 $J/cm^2$ and 1.5 $J/cm^2$, respectively. For laser fluence of 0.50 $J/cm^2$, the electron temperature increases rapidly and reaches a peak value of around 31200 K at t = 2 ps. The lattice temperature begins to grow quickly after t = 1 ps due to the transferred energy from the electrons to lattices and then reaches a maximum value of 3880 K at t=26 ps. Afterwards, the temperature of the electron and lattice are almost the same. No ablation occurs as the central front temperature is below ablation temperature ($0.9T_{cr}$) or phase-separation temperature. A similar trend has been observed in the temperature evolution in the fluence of 1.5 $J/cm^2$, the peak of the electron temperature, 54000 K, appears around t = 2 ps, and the electron and lattice temperatures reach equilibrium after t = 27 ps. The material is efficiently removed when the lattice temperature passes the ablation point after t=7 ps. From figure 3, one can notice that electron temperature is lower than lattice temperature after electron-lattice interaction because thermal energy in electrons diffuses away much faster than in the lattice [49].
Fig. 3. Time evolution of electron temperature $(T_e)$ and lattice temperature $(T_i)$ at a centre (r=0, z=0) of gold sample irradiated by the 180 fs laser with the wavelength of 515 nm at fluence of a) F=0.50 $J/cm^2$ and b) F=1.5 $J/cm^2$.
The surface morphology of ablated crater was obtained using an optical microscope (Zeis "Axio Scope.A2" Vario) and profilometer. Figure 4 a) shows the shingle shot ablation crater at fluence 2.5 $J/cm^2$ and the corresponding cross-sectional profile is given in figure 4 b). Heat transport, electron-lattice coupling, and electron and lattice temperature may depend strongly on the pulse duration, wavelength and the applied laser fluence. Because of the complex dynamics of electron-lattice coupling, which determine the spatial and temporal evolution of the carrier and lattice temperature, once the electron and lattice have been in equilibrium, the temperature field is extracted. An axial systematic study on the solution of the TTM was performed for varying pulse fluence ranging from 1.5 $J/cm^2$ to 9 $J/cm^2$. However, typical ablated crater profiles are shown only for laser fluence of 1.5 $J/cm^2$ and 9 $J/cm^2$ in Fig. 5.
Fig. 4. Images of a) ablated craters and b) cross-section profiles under single-pulse irradiation with laser fluence 2.5 $J/cm^2$
Fig. 5. Axi-symmetric simulation results of ablated crater profiles of gold with a laser fluence of a) F=1.50 $J/cm^2$ and b) F=9 $J/cm^2$.
Figure 6 compares the ablated crater diameter and depth for various laser fluence with the simulated profile. The phase explosion mechanism determines the metal’s ablation morphology in a high fluence regime. A modified gold surface has been observed in a low fluence regime ($\leq$ 1$J/cm^2$). At a fluence of 1 $J/cm^2$, an ablation depth of 85.66 nm was measured, and the simulated ablation depth of 90 nm was obtained. However, the ablation diameter is a few $\mu m$ wider than the simulated one. The phase explosion mechanism shows high uncertainties in the simulation and experimental result at a low fluence regime. For a low fluence regime, the material ablation is primarily controlled by non-thermal mechanisms such as ultrafast thermal stresses, coulomb explosion, and hot electron blasts [53]. As can be seen in figure 6 b), the simulated depth is going up from 186 to 416 nm with the increasing laser fluence ranging from 1.5 $J/cm^2$ to 9 $J/cm^2$ and the experimental ablating depth continued to increase from $146.5\pm 23$ nm to $520.5 \pm 32$ nm. There is an overestimation of the simulated ablation diameter compared to the experimental ablated diameter. A few interesting observations can be noted for ablation depth. In the middle fluence regime from 2 $J/cm^2$ to 5 $J/cm^2$, the measured ablation depth corresponds slightly overestimated with the simulated, whereas a little underestimation of the ablation depth in the high fluence regime($\geq$ 5 $J/cm^2$). Overall, the simulated and experimental fluence-dependent ablation depth and square ablation diameter follow the same tendency.
Fig. 6. Comparison between simulation and experimental results of gold at a wavelength of 515 nm and 180 fs pulse duration (a) square crater diameter and (b) ablation depth.
3.2 Effect of intra-burst frequencies
Ultrafast laser micromachining is typically distinguished by superior quality and low heat affected zone at the expense of limited processing speed. For fast processing, the number of pulses in the bursts has been used. It increases the ablation rate and improves the high-aspect ratio. To fully comprehend the benefits of ablation by bursts of pulses, the relevant parameters which can enhance the result compared to single-pulse laser ablation have been investigated. An essential parameter in the bursts technology is the separation time between the two successive pulses, and the intra-burst repetition rates can control it.
To determine the effect of the intra-burst frequency on multipulse femtosecond laser ablation, we varied the intra-burst separation time from 1 ps to 100 ps and the corresponding intra-burst frequency from 1000 GHz to 10 GHz to simulate the ablation process. Figure 7(a–d) represents the temporal evolution of the electron and lattice temperatures at a front surface of the laser-irradiated gold with five-pulse burst and pulse separation time ranging from 5 ps (intra-burst frequency 200 GHz) to 100 ps (intra-burst frequency 10 GHz). It can be seen from Fig. 7 that the temperature of the electron increases with the rising number of pulses. Simultaneously, the lattice temperature also rises after each femtosecond laser pulse because the energetic electron transfers some of its energy to the lattice via electron-lattice collision. The trends of electron temperature and lattice temperature at pulse separation time 5 ps (200 GHz) (figure 7 a), 10 ps (100 GHz) (figure 7 b), 50 ps (20 GHz) (Figure 7 c), and 100 ps (10 GHz) ( figure 7 d) are similar. From figure 7 a and figure 7 b, we explicitly demonstrate that the next pulse arrives before the thermal relaxation of the electron-lattice, as a result of which the lattice does not have enough time to cool down after each pulse and electron-lattice heat transfer is limited. Figure 7 c and figure 7 d demonstrate that each pulse arrives after the electron-lattice relaxation and the separation time between two successive pulses is sufficient to transfer energy from electron to lattice.
Fig. 7. Time evolution of electron temperature ($T_e$) and lattice temperature ($T_i$) at a centre (r=0, z=0) of gold sample irradiated by the 180 fs laser at a wavelength of 515 nm and fluence of 1.50 $J/cm^2$ with pulse separation time a) 5 ps (200 GHz) b) 10 ps (100 GHz) c) 50 ps (20 GHz) and d) 100 ps (10 GHz).
HAZ (heat-affected zone) refers to the gradient from melting to ablation depth in the present work [54]. Figure 8 shows the effect of pulse separation time on the ablation depth and HAZ of the gold surface during irradiation with five pulses per burst at a fluence of 5 $J/cm^2$. The maximum ablation depth increased rapidly when the pulse separation time was less than 50 ps because the characteristic electron-lattice relaxation period was less than the pulse separation time. When the pulse separation time was higher than 50 ps, the sensitivity of the maximum ablation depth to the pulse separation time was considerably reduced. On the other hand, it was evident that HAZ grew thicker as the pulse separation time rose. Achieving the maximum ablation depth and a minimal HAZ are desirable in the ultrafast laser ablation processes. As the pulse separation time increases, the electron and lattice temperatures increase because of subsequent pulses. The maximum lattice temperature is beyond the separation temperature for an extended period, giving time to reach electron and lattice in equilibrium. If the pulse separation time is less than 50 ps, the electron-lattice interaction time is shorter than the electron-lattice relaxation time, which weakens the effect of heat accumulation; consequently, the HAZ is smaller. Moreover, with a pulse separation time of 10 ps or shorter, the pulses are so close, and no time for an energy transfer from the electron to the lattice, which acts as a whole large pulse to excite electrons that lose the advantage of the burst of pulses although the HAZ is minimal. The laser parameter should be optimized so that the heat accumulation impact after each pulse is considered while the HAZ is as small as possible to maximize the ablation rate and ablation quality for fast processing. The previous study of copper ablation by femtosecond laser bursts found that a laser burst with a pulse separation time of 50 ps or longer can significantly boost the ablation rate compared to a single pulse [45,53]. Our model predicts very similar behaviour to their study and found that a femtosecond burst with a 20 GHz intra-burst repetition rate (pulse separation time 50 ps) should be employed for better ablation quality and to lessen the impact of heat accumulation, with the temporal interval between the pulses being in the order of the electron-lattice interaction time.
Fig. 8. a) Specific ablation depth and b) Heat-affected zone (HAZ) as a function of five-pulse burst energy at various pulse separation time.
3.3 Effect of number of sub-pulses of burst
Besides the ablated depth per burst, the ablated volume per burst is a crucial parameter for fast laser micromachining. Ablation volume increases for higher fluences, while the ablation process becomes less energetically efficient by increasing the number of sub-pulses in the burst. The effect of the laser ablation in sub-pulses in burst should be studied to properly comprehend the benefit of bursts. For a laser beam with a Gaussian intensity distribution, the ablated volume per pulse was given by the following equation [55]: :
With the aid of simulation outcomes, figure 9 a) shows the effect of intra-burst frequencies on the ablation volume of gold at 5 sub-pulses in burst and Figure 9 b) depicts the effect of the number of sub-pulses in the laser burst on the ablation volume at pulse separation time of 25 ps (dashed line) and 100 ps (solid line). It is demonstrated that the ablation volume, in general, is dramatically enhanced with fluence. Still, at the same total fluence, ablation volume by burst mainly depends upon the intra-burst frequencies. As can be seen from figure 9 a) and b), ablation volume increases with decreasing intra-burst frequency from 1000 GHz to 10 GHz. The reason for the increase in ablation volume is the electron-lattice relaxation time. As discussed earlier, thermal relaxation between lattice and electron did not occur with a pulse separation time of less than 50 ps. Consequently, heat can not be transferred from electrons to deeper in gold crystals. It demonstrates that intra-burst frequencies with a separation of less than the thermal relaxation time can significantly raise the lattice temperature without a noticeable increase in ablation depth. The response of the ablation volume of a different number of pulses is shown as the number of the pulses increases with a separation time of 100 ps, so does the ablation volume. The trends at all the number of pulses are quite similar to each other. Moreover, the projected ablation volume nearly doubled or increased significantly when the number of pulses increased from 2 to 10. However, as the number of pulses increased from 10 to 20, the rise in ablation volume was only approximately 20%. Gaudiuso et al. perceive experimentally that the specific ablation rate decreases with the number of sub-pulses in the burst similitude to our study [34].
Fig. 9. a) Specific ablation volume as a function of five-pulse burst energy at different separation time and b) the ablation volume dependence upon the number of sub-pulses on the burst at different laser fluences with 25 ps separation time (dash line) and 100 ps (solid line) separation time.
4. Conclusion
In this work, a theoretical and experimental study was performed to investigate the laser ablation of gold by a single femtosecond pulse and the numerical study of the bursts of femtosecond pulses with GHz intra-burst repetition rates. The effect of the GHz intra-burst repetition rate on the ablation depth and ablation quality was investigated where the temporal separation time between the pulses is in the order of the electron-lattice relaxation time. Numerical ablation simulation was carried out on a gold sample using only one burst of 180 fs pulses, where the total burst energy, number of burst sub-pulses, and intra-burst frequency were systematically varied. It was discovered that although using a 100 GHz or more intra-burst repetition rate increased the maximum electron and lattice temperatures, it did not significantly increase the maximum ablation depth in the material. However, heat accumulation does not occur because of the short separation time during successive pulses, and energy is not transferred from the electron to deep into the lattice by successive pulses. In the study of multiple pulses femtosecond laser ablation, the computational model indicates that succession of laser pulses with an intra-burst repetition rate of 20 GHz and fewer sub-pulses can significantly boost the ablation rate and ablation quality at the same laser fluence. Thus, the deviation from simulation results leads to the conclusion that the ablation quality outweighs the heat accumulation effect at GHz repetition rates, although there is a considerable reduction in the ablation volume.
Funding
The German Federal Environmental Foundation (Project No. DBU-AZ37730-01); State of Saxony Anhalt IB/LSA-project (ZS/2018/09/94741).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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