Introduction

At the end of the previous chapter, we have seen that a characteristic of nonlinear systems is the presence of critical points, that is, values of the control parameter at which two solutions coincide. Note that at a critical point, more than two solutions can coexist and that the coexisting solutions need not be stationary: They can have any time dependence. In the next four chapters, though, we concentrate on the steady critical points at which two steady solutions coincide. If the solutions exist on both sides of the critical point, we call it a bifurcation point. Another type of critical point that will also draw much of our attention later is the limit point. However, the solutions exist on only one side of the critical point.

The main feature of critical points is that their presence is always signaled by the vanishing of the real part of at least one characteristic root in the stability analysis. For steady critical points, it is a real root that vanishes. In some cases, however, more than one root will vanish at criticality. Then one deals with degenerate critical points that may have richer properties. Physically, the absolute value of the real part of a characteristic root λ is a relaxation rate if Re(λ) < 0 and a divergence rate if Re(λ) > 0. Let λc be the root that vanishes at the critical point. The vanishing of a relaxation rate at criticality means the divergence of a relaxation time. Thus, an unconventional dynamics occurs in the domain surrounding the critical point that is characterized by critical slowing down.

LASER SPUTTERING

Direct removal of semiconductor material by laser light without a reactive intermediary has been reported for a number of solids (see reviews by Bäuerle 1986 and Ashby 1991). Direct ablation of small quantities of semiconductor material using UV laser radiation has specific applications in link breaking for circuit restructuring (Smith et al. 1981, Raffel et al. 1985). However, the majority of ablation studies have been carried out in a reactive atmosphere or medium.

A summary of work carried out on the direct ablation or photosublimation of semiconductor materials is given in Table 8.1. In general ablative effects are limited to excitation with high intensity pulses whereas photosublimation occurs by exposure of a semiconductor to CW, visible laser radiation at somewhat lower intensity. Figure 8.1 shows the intensity threshold for ablation in several semiconductors.

Early experiments on the ablation of Si at 193 and 248 nm (Shinn et al. 1986) showed that neither the ablation rate nor the ablation threshold fluence were strongly dependent on laser wavelength, for excitation in this wavelength range. Above the threshold fluence the etching rate was found to be 0.2–0.5 μm per pulse at intensities of 107–108 W cm–2. The threshold fluence was about 1.3Jcm–2 both at 193 and at 248 nm and was found to be independent of ambient gas pressure for pressures between 0–1000 Torr. A strong plasma emission showing a wide variety of Si, Si+ and Si2+ spectral lines was observed at the highest intensities used (about 108 W cm–2).

The development of lasers operating at ultraviolet wavelengths has provided mankind with a new set of unique tools. With characteristics which combine the precision to remove micrometer-thick layers of corneal tissue for the correction of refractive errors in the human eye and the ability to vaporize even the most refractory of materials, UV lasers have immediately developed into indispensable tools in many areas of materials science. The remarkable ability of high power pulsed excimer laser radiation to vaporize complex materials such as high temperature superconductors, while maintaining stoichiometry in thin films deposited from this vaporized material, offers many exciting opportunities in the creation of superconducting thin films and thin film devices. Similar unique capabilities are available in the deposition, doping and modification of semiconductors using UV laser radiation.

As a result of these and other applications, many of which can be immediately adopted by industry, UV lasers have a secure future in the field of materials science. Their implementation is limited only by our creativity in finding new applications and ways to use these new tools.

A fascinating aspect of the development of these applications involves the many fundamental questions that arise concerning the manner in which intense UV laser radiation interacts with matter. This is an area of great scientific interest and is truly interdisciplinary in nature so that answers to these questions will only come from both theoretical and experimental studies extending over a diverse range of disciplines.

INTRODUCTION

The response of inorganic insulating materials to intense UV radiative fluxes is complex and involves both photophysical and photochemical interactions. The first effect, noticeable at low exposure, involves the production of defect centers or radiative interactions with existing centers or impurities. Such changes often result in an increase in optical absorption at the laser wavelength as well as at other wavelengths. This can have a profound effect on the quality of transmissive optical components such as windows and lenses. With optical fibers, defect formation limits the fluence that can be transmitted.

Higher exposure to radiative fluxes results in changes in composition and density as the sputtering threshold is approached. Defects have been found to play a significant rôle in the initiation of ablation under irradiation with photons of energies less than that of the optical bandgap. The generation of electron–hole pairs via two-photon absorption is also an important process at high laser intensities and would appear to be the initiator of ablative decomposition of transparent insulators.

This chapter begins with a review of the formation and properties of dominant defects in several wide bandgap insulators. The relation between these defects and the coupling of UV laser radiation leading to ablation is then discussed. The chapter concludes with a summary of dry and laser-assisted etching processes and rates in a variety of insulating solids.

INTRODUCTION

Ultraviolet laser sources can initiate both photochemical and photothermal effects in condensed media. The relative importance of these two effects depends on a variety of factors including laser wavelength, pulse duration, intensity and the photochemical/photothermal response of the irradiated material. In addition, exposure to UV laser radiation can result in radiation conditioning or hardening, such that the response of the medium to subsequent irradiation may be quite different from its initial response.

This chapter explores some of the fundamental limitations of materials processing with lasers as they relate to the physical and chemical response of the irradiated medium. Some general constraints on the relative rate of ablation in photochemical and photothermal regimes are also discussed. The question of radiation resistance is shown to exhibit both geometrical and physico-chemical characteristics.

FUNDAMENTAL LIMITATIONS IN LASER MATERIALS PROCESSING

At the intensities customarily used in laser processing of materials, the irradiated sample is exposed to an intense radiative environment that is generally far from the equilibrium state of the ambient medium. The thermal or physical change in the irradiated medium is then driven by an attempt to approach a new equilibrium in the applied radiation field. In general, even at intensities that may be as large as 108W cm–2, the response function of an irradiated medium is usually described using classical heat transfer theory. There are, however, implicit limitations to the validity of this theory as well as assumptions implied by the adoption of this description of the thermal response that may be relevant at high incident laser intensities or short pulse durations (Harrington 1967, Duley 1976).

ABSORPTION AND LATTICE HEATING

The initial stage in the conversion of laser radiation to heat during irradiation involves the excitation of electrons to states of higher energy. For this process to occur, vacant states have to be available to accept excited electrons. When the photon energy hν is small, as for example when 10.6 μm laser radiation is absorbed, only electrons with energies within a narrow range hν near the Fermi energy, ∈F, can participate in absorption. At 0 K, the highest energy reached upon absorption is ∈F + hν.

At higher temperatures, electrons occupy a range of states given by the Fermi–Dirac distribution (Omar 1975). This reduces to a Boltzmann function for electron energies ∈ such that ∈ – ∈F ≫ kT, where T is the metal temperature. Absorption of photons then populates those states with energy ∈ + hν. Since ∈F is usually several electronvolts, whereas hν = 0.117 eV for CO2 laser photons, absorption of IR laser radiation then acts to redistribute electrons among states close to those on the Fermi surface.

This situation is different at excimer laser wavelengths, since hν is then comparable to or larger than the work function, φ, of many metals. When hν > φ, electrons may be directly excited from states near the Fermi surface to continuum states associated with the ejection of an electron from the metal. These electrons will originate from levels within the skin depth, δ. Those electrons that are not ejected will dissipate their excess energy as heat within the skin depth.

INTRODUCTION

Shortly after the announcement of high temperature superconductivity in the La–Ba–Cu–O (Bednorz and Müller 1986) and Y–Ba–Cu–O (Wu et al. 1987a) systems the first reports were published describing in situ preparation of superconducting thin films using laser ablation (Dijkkamp et al. 1987, Wu et al. 1987b, Narayan et al. 1987). The laser ablation method, which is a well known technique for the preparation of thin films of a variety of materials (Duley 1983, Bäuerle 1986, Braren et al. 1993, Chrisey and Hubler 1994), was found to be well suited to the deposition of superconducting films since it permits flexible control over deposition conditions and yields films with good stoichiometry.

Materials such as Y–Ba–Cu–O are, however, complex from both a chemical and a structural point of view (Burns 1992) and therefore vaporization and redeposition of these materials using laser radiation is anticipated to be a complicated process. A full understanding of the physical and chemical mechanisms that accompany laser ablation and in situ deposition has yet to be obtained. Nevertheless, useful progress has been made in the preparation of superconducting films with high zero resistance temperatures (about 90 K) and critical current densities exceeding 106 A cm–2 using the laser ablation method.

DEPOSITION AND PROPERTIES

The use of excimer laser radiation to prepare thin films of superconducting material by laser vaporization of the parent compound was first reported in 1987 (Dijkkamp et al. 1987, Wu et al. 1987b, Narayan et al. 1987).

INTRODUCTION

A wide variety of materials can be deposited from gaseous, solid and liquid precursors using laser techniques. Photothermal as well as photochemical routes are often available and range from the straightforward use of laser radiation as a vaporization source to photochemical decomposition of adsorbed layers. Laser deposition can be used for the creation of extended thin films or for selective deposition of specific features in localized regions with dimensions extending to less than 1 μm. The choice of deposition technique will depend on the required composition of the deposit together with the properties of the substrate. Laser wavelength may be of primary importance for photochemical deposition of sub-micrometer features. Some significant factors in the laser deposition of materials are:

1. chemical routes to the required deposit,

2. laser intensity and wavelength,

3. sensitivity of substrate to thermal/photochemical effects,

4. sensitivity of substrate to ambient atmosphere/chemical environment,

5. scale of features to be deposited, i.e. micro/macrofeatures,

6. required deposition rate,

7. sensitivity of deposited layer to contamination by secondary products and/or particulates, and

8. optical configuration required for deposition.

The fact that a multicolour image can be produced by a hologram recorded with three suitably chosen wavelengths was first pointed out by Leith and Upatnieks [1964].

The resulting recording can be considered as made up of three incoherently superposed holograms. When it is illuminated once again with the three wavelengths used to make it, each of these wavelengths is diffracted by the hologram recorded with it to give a reconstructed image in the corresponding colour. The superposition of these three images yields a multicolour reconstruction.

However, while multicolour holography was demonstrated at quite an early stage, its further development was held up initially by several practical problems. These problems, as well as later advances that have made multicolour holography practical, are described in this chapter (see also the review by Hariharan [1983]).

Light sources for colour holography

The most commonly used lasers for colour holography are the He-Ne laser (λ = 633 nm) and the Ar+ laser, which has two strong output lines (λ, = 514 nm and 488 nm; see Table 5.1). The range of colours that can be reconstructed with these three wavelengths as primaries can be determined by means of the C.I.E. chromaticity diagram [Optical Society of America, 1953]. In this diagram, as shown in fig. 9.1, points representing monochromatic light of different wavelengths constitute the horseshoe-shaped curve known as the spectrum locus; all other colours lie within this boundary.

Introduction

In the previous chapter we introduced the theory of geometrical optics, a very simplistic analysis of the propagation of radiation describing only the lines that trace the radiation trajectories. In that analysis, the lines, or rays, were not subjected to the effects of diffraction or interference; with the exception of dispersion, color too had no influence on these trajectories. The absolute value of the speed of light had no bearing on the propagation; only its magnitude relative to the speed in free space had to be known, and even that parameter could not be derived directly and had to be retrieved from other sources. Similarly, parameters of the important effect of dispersion could not be derived directly. Attenuation by absorption was outside the scope of geometrical optics, as were other effects related to the nature of radiation such as polarization, coherence, and wavelength. These shortcomings of geometrical optics were to be expected. After all, such fundamental questions as how radiation is created or how it interacts with a particular medium were not asked. Without consideration of these questions, the nature of radiation and the details of its propagation cannot be fully understood.

Historically, the first studies attempting to understand the nature of light, and not merely its patterns of propagation, were made in the seventeenth century. At that time, visible light was the only known mode of radiation.