General Remarks

Evidently, the advent of mesoscopic layered semiconductor structures generated a need for a simple analytic description of the confinement of electrons and phonons within a layer and of how that confinement affected their mutual interaction. The difficulties encountered in the creation of a reliable description of excitations of one sort or another in layered material are familiar in many branches of physics. They are to do with boundary conditions. The usual treatment of electrons, phonons, plasmons, excitons, etc., in homogeneous bulk crystals simply breaks down when there is an interface separating materials with different properties. Attempts to fit bulk solutions across such an interface using simple, physically plausible connection rules are not always valid. How useful these rules are can be assessed only by an approach that obtains solutions of the relevant equations of motion in the presence of an interface, and there are two types of such an approach. One is to compute the microscopic bandstructure and lattice dynamics numerically; the other is to use a macroscopic model of long-wavelength excitations spanning the interface. The latter is particularly appropriate for generating physical concepts of general applicability. Examples are the quasi-continuum approach of Kunin (1982) for elastic waves, the envelope-function method of Burt (1988) for electrons, and the wavevector-space model of Chen and Nelson (1993) for electromagnetic waves and excitons.

This book has grown out of my own research interests in semiconductor multilayers, which date from 1980. It therefore runs the risk of being far too limited in scope, of prime interest only to the author, his colleagues and his research students. I hope that this is not the case, and of course I believe that it will be found useful by a large number of people in the field; otherwise I would not have written it. Nevertheless, knowledgeable readers will remark the lack of such fashionable topics as the quantum-Hall effect, Coulomb blockade, quantized resistance, quantum tunnelling and any physical process that can be studied only in the millikelvin regime of temperature. This has more to do with my own ignorance than any lack of feeling that these phenomena are important. My research interests have not lain there. My priorities have always been to try to understand what goes on in practical devices, and as these work more or less at room temperature, the tendency has been for my interest to cool as the temperature drops.

Introduction

An electron in a quantum-well subband can be scattered to another state in the same subband or into a state in another subband. Intrasubband and intersubband scattering rates have to be calculated separately since different wavefunction symmetries are involved in the two cases, and this implies correspondingly different symmetries of the optical mode. For simplicity we will assume that the electrons are completely confined within the well and that the interaction is with polar optical modes. In the case of LO modes in a polar material this interaction is via a scalar potential. However, as we will see, it is possible in the unretarded limit (velocity of light is infinite) to replace the vector potential of the electromagnetic interface wave with a scalar potential via a unitary transformation (not a gauge transformation) and treat the IP mode on the same footing as an LO mode, but with a frequency-dependent scalar potential. We assume the TO mode has no interaction.

No fewer than four different scattering sources exist, in general. Two of these are associated with well modes, two with barrier modes. In general, the LO band of frequencies in either material does not span the range between the LO and TO zone-centre frequencies, ωLO and ωTO.

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.