The growth of perfect crystals and crystalline layers on amorphous substrates is an insufficiently solved problem up to now. This concerns the experimental results as well as the theoretical treatment of nucleation and growth processes. Due to the lack of a crystallographic lattice of the substrate no epitaxial intergrowth of substrate and deposit is possible. However, many applications require amorphous substrates. Especially in large area devices such as solar cells, commercial aspects even exclude the application of crystalline substrates desired from a crystallographic point of view. Thus, the use of low cost amorphous substrates like glass is aimed.
A method has been developed for low temperature growth of silicon on glass from metallic solutions [1]. This technique is based on creating pointlike nucleation centres using natural coalescence phenomena of the metallic solvent for masking the substrate. Thus, uncontrolled spontaneous nucleation can be avoided and locally defined selective growth of silicon crystallites seeded by the Si saturated metallic solution droplets occurs. The material transport is governed by a vapour-liquid-solid (VLS) mechanism. As a first result of this artificial nuclei selection principle silicon crystallites have been grown in dimensions of 10 æm [2]. Size and distribution of the solvent droplets as well as the morphology of the grown silicon crystallites have been characterised by SEM and optical microscopy. The focused ion beam (FIB) method followed by X-ray microanalysis has been used to identify silicon crystallites still encapsulated by the solution. The crystallites show good adhesion on glass and are statistically arranged in correspondence with the metallic droplets.
Ultra short pulse laser systems have been employed to create micropores on the glass surface with diameters <<1 æm in order to achieve a reproducible patterned Si grain arrangement and to improve the crystalline quality. These micro-cavities serve as nucleation centres and facilitate a geometrical nuclei selection. Ultraprecision laser micromachining has excited vivid attention in various industrial fields and in medicine owing to the rapid progress in laser design capable of emitting powerful pulses with durations of less than 1 ps. Material damage achieved on the targets is determined to a major extent by the heat affected zone (HAZ) adjacent to the surface formed after each laser-induced vaporization pulse. Femtosecond laser treatment leads to HAZ's of the order of 100 nm compared to HAZ's in the micrometer range if nanosecond laser pulses are applied [3]. For a wide range of different materials, like metals [3,4,5], semiconductors [3,5,6], ceramics [3], inorganic dielectrics and polymers [7] and for technical [8] and biological composite materials like human corneas [9,10], dental and bone-like materials [3] it could be shown that sub-picosecond-pulse laser ablation leads to enhanced structuring quality. Besides the front laser processing an ablation at the rear side of the glass substrate could be realized by autofocusing phenomena in the material bulk [11].
Femtosecond-laser processing avoids any complications by plasma-light interaction (plasma shielding). It provides the possibility to use multi-photon processes which can be of importance for transparent materials. The ablation threshold fluence is reduced substantially compared to nanosecond-laser treatment. Recent experimental studies of dielectrics for pulse durations down to 20 fs [12,13] and 5 fs [14,15] showed that impact (avalanche) and multiphoton ionization contribute to the ablation process. Laser pulses in the 10-fs domain provide an unreached quality of micromachining of fused silica and borosilicate glass as compared to longer pulses in the range of several 100 femtoseconds up to picoseconds. The shortening of the pulses reduces the statistical behaviour of the material removal and therefore, the ablation process attains a more deterministic and reproducible character. The improved reproducibility of ablation goes along with a significantly smoother morphology. This results in a vertical and lateral machining precision of the order of 100 nm in dielectrics. The lateral precision of ablation is an important parameter for the present application. It may even be extended into the submicron range, as has been demonstrated e.g. for silver [16]. In order to relate the lateral dimensions of the generated structures to the laser spot size, a lateral precision parameter q could be defined [17]. It is the ratio between the observed cavity area and the illuminated area of a Gaussian beam limited by a fluence decrease to 1/e2 times the peak fluence. This parameter is connected to the fluence of the generating laser pulse in the following way: the local laser fluence F(r) at radius r in a Gaussian beam profile is

formular 1
with the Gaussian beam radius w₀ and the maximum laser fluence F(r = 0) = F₀. The radius r_th at which ablation sets in (which determines the diameter of the resulting hole) is given by the threshold fluence F_th

formular 2
With this the precision parameter q can be given

formular 3
Practically any q can be realised by adjusting F₀ for a given (and therefore F_th). The reduction of , however, allows a particular low q at smaller fluences and less stochastic fluctuations. One can draw the following conclusions from this study. The lateral micromachined structure size can be smaller than the laser spot diameter. This behaviour can be described by the lateral precision parameter q, which is the ratio between the observed cavity area and the illuminated area of a Gaussian beam limited by a fluence decrease to 1/e² of the peak fluence. It could be shown that q is simply related to ln(F₀/F_th). The measured results follow this model within the experimental uncertainties. With the laser system used here, q as small as 0.05 can be reliably achieved in the 10-fs domain. Physical evidence is given, that for these short pulses ablation is solely governed by generation of free carriers, already for pulse durations around 100 fs slower (thermal) processes influence the material removal. Hence, focusing the laser to the diffraction limit allows lateral structures of the order of 100 nm.

Acknowledgment
This study is being funded by the German Bundesministerium für Bildung, Wissenschaft, und Forschung (BMBF) in the framework of LASER 2000 - Laserinduzierte Fertigungsverfahren, Verbundprojekt ABLATE.

References

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[14]	M. Lenzner, S. Sartania, C. Spielmann, F. Krausz, J. Krüger, and W. Kautek, OSA Technical Digest Series 11 (1997) 218.
[15]	M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, Phys. Rev. Lett. 80 (1998) 4076.
[16]	P.P. Pronko, S.K. Dutta, J. Squier, J.V. Rudd, D. Du, and G. Mourou, Opt. Commun. 114, 106 (1995).
[17]	J. Krüger, M. Lenzner, F. Krausz, and W. Kautek, in publication.

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