CHAPTER 3  

 

MATERIAL CHARACTERIZATION IN LASER MICROMACHINING

 

3.3 MATERIALS CHARACTERISATION

 

3.3.1             Surface analysis

 

3.3.1.1                Scanning electron microscopy

 

Electron microscopy is often used to study the surface morphology, microstructure and defects in materials [11]. In scanning electron microscopy (SEM) an electron beam is focused and scanned across the surface of a sample. When the electrons hit the specimen, a variety of signals are generated due to the interaction of electrons with matter, namely secondary electrons, backscattered electrons, and X-rays (Figure 3.3.1a). The signals have their origin in different regions of the sample (Figure 3.3.1b), and give specific information on the topography of the specimen surface or its chemical composition. Secondary electrons are produced when loosely bound atomic electrons are released by interaction with primary electrons. Secondary electrons have a small mean free path in the material due to their low energy. Therefore, they provide information from a shallow depth (10-100 nm). Backscattered electrons are formed by the scattering of primary electrons by nuclei of sample atoms. The number of backscattered electrons increases with increasing atomic number and hence the resulting signal contains information on chemical composition.

 

a)	b)
Figure 3.3.1: Principles underlying the SEM. a) Different type of information obtained and b) Regions where the information is produced (adapted from [12]).

 

Figure 3.3.2 schematically shows a conventional scanning electron microscope. Typically, the electrons are generated in a thermionic type of electron gun and accelerated with an energy between 1 and 30 KeV towards the specimen. The magnetic lenses (condenser and objective lenses) focus the electron beam to a spot with a diameter of approximately 1-10 nm on the specimen surface. The beam is swept along the sample by the scanning coils, and the image is formed by mapping the intensity of the detected signal as a function of the position of the incident beam. Because of the higher escape depth of backscattered electrons (up to several microns) the resolution of the image is not as good as for secondary electrons. In this study the scanning electron microscope used was a Hitachi model S-2400, equipped with a secondary electron detector. Its maximum accelerating voltage is 25 kV, the standard resolution is 4.0 nm, and the practical magnification is limited to about 50 000´.

 

Figure 3.3.2: Scheme of a conventional scanning electron microscope. The magnification is M=L/l, where L is the size of image on the CRT and l the size of the electron beam scanning on the sample [adapted from [12]).

 

3.3.1.2                Atomic force microscopy

 

In this study a Nanoscope MultiMode Scanning Probe Microscope (SPM) from Digital Instruments was used to perform tapping mode atomic force microscopy (AFM). Tapping mode AFM imaging overcomes the limitations of scanning modes by alternately placing the tip in contact with the surface and then lifting it off to avoid dragging, and to provide high resolution (Figure 3.3.3). Tapping mode imaging is implemented in ambient air by oscillating the cantilever assembly at or near the cantilever’s resonant frequency using a piezoelectric crystal. The piezo motion causes the cantilever to oscillate with high amplitude (the “free air” amplitude, typically greater than 20 nm) when the tip is not in contact with the surface. The oscillating tip is then moved towards the surface until it begins to lightly touch, or “tap” the surface. During scanning, the vertically oscillating tip alternately contacts the surface and lifts off, generally at a frequency between 50,000 to 500,000 cycles per second. When the tip passes over a bump in the surface, the cantilever has less room to oscillate and the amplitude of oscillation decreases. Conversely, when the tip passes over a depression, the cantilever has more room to oscillate and the amplitude increases (approaching the maximum free air amplitude). The variation of the oscillation amplitude of the tip is measured by the detector and used to form an image of the surface topography. The digital feedback loop then adjusts the tip-sample separation to maintain constant amplitude and force on the sample.

 

Figure 3.3.3: Tapping cantilever on sample surface (adapted from [13]).

 

3.3.1.3                Optical microscopy

 

Photographs of the processed area were taken using an inverted research metallurgical microscope (Olympus-PMG3), with built-in photo-equipment coupled to a 35 mm camera. The available objectives allowed the observation magnification to vary in the range 25-3000´ (corresponding to 6.25-750´, in the 35 mm film).

 

3.3.2             Roughness analysis

 

Surface measurement is often divided in three parts: surface roughness, waviness, and overall shape of the object. It may be performed using techniques such as atomic force microscopy and stylus profilometry or non-contact methods like laser interferometry and confocal microscopy. It is well known that laser processing frequently leads to changes on the treated surface. In order to quantify these changes well-defined parameters must be used [14]. A common roughness parameter, which was used throughout this study, is the arithmetic average R_a, defined as follows

 

(3.3.1)

 

where L_x is the profile length and z the height variation as a function of position x.  is the average of all height values: but more often the mean line is chosen for  by which the roughness values are corrected for inclined surfaces. Different rough surfaces may have the same R_a values, because R_a is sensitive to height fluctuations but not to the spatial frequency at which the height fluctuations take place.

 

3.3.2.1                Laser profilometry

 

Surface roughness and height measurements were performed using a laser profilometer equipment (Laser stylus RM 600, Rodenstock), designed for non-contact measurements of surface relief with amplitudes between 0.01 and 600 mm height. An infrared laser beam (l=780 nm) is focused on the surface by an objective, creating a spot with a few microns in diameter, which is reflected back to a detector. If the distance to the object is changed, the detector creates an error signal, which is used by a servo system to adjust the objective until the laser beam is again focused on the surface. The optics position is registered and used as a measuring signal. By scanning a sample under the probe laser beam, the surface profile may be determined. Surface roughness parameters were estimated according to the international standard to characterise surface profiles (ISO 4287), and using a cut-off value of 0.08 mm.

 

3.3.2.2                Stereoscopic pair analysis

 

In scanning electron microscopy a three-dimensional structure is projected onto a two-dimensional image plane. Although some depth information is obtained due to variable shadowing, this results in significant loss of depth information of the viewed specimen. The eucentric tilting of the specimen by a small angle creates two images as if viewed from two slightly different directions, which may be used to provide information about the third dimension, depth. Three-dimensional reconstruction using stereoscopic SEM images was performed by the stereoscopic pair analysis software Mex 2.0 (Alicona GmbH). The software may be use for profile, area and volume analysis. The surface roughness parameter R_a was calculated according to the standard ISO 4287, using a cut-off value of 0.08 mm. The effective (i.e., true) surface area of processed surfaces and the ratio of the effective to the projected area were also estimated using this software.

 

3.3.3             Chemical analysis

 

3.3.3.1                Energy dispersive spectroscopy

 

Energy dispersive spectroscopy (EDS) measurements were performed using a Rontec X-ray spectrometer attached to the Hitachi SEM S-2400 described previously. The accelerating voltage was kept at 20 kV. In EDS a primary electron ejects a core electron from its shell. This ejected electron is replaced by an electron from an outer shell, emitting an X-ray photon with a characteristic energy. Measuring the energies of the X-ray photons yields the elements present in the material in a depth of a few microns, the exact value depending on the accelerating voltage, the atomic number, angle of incidence, etc. Quantitative analysis in EDS entails measuring the intensities of the relevant X-ray lines generated in the specimen and in suitable standards, using identical instrumental conditions (accelerating voltage, specimen geometry, etc.). Element concentrations are calculated from the ratios of specimen and standard intensities and the known concentrations in the standards. All acquired spectra were corrected for background (which originates mainly from the X-ray continuum), and the peak intensities were corrected by the usual ZAF procedures. The acronym “ZAF” expresses three matrix corrections, where Z stands for atomic number, A for absorption and F for fluorescence.

 These matrix corrections are applied to uncorrected concentrations (estimated directly from the acquired peak intensities) in order to obtain true concentrations corrected for composition-dependent matrix effects.

 

In Auger electron spectroscopy, this X-ray photon will be absorbed by an electron in an outer shell of the atom. This electron with a characteristic energy is then emitted. This energy is specific for a certain element and gives some information on the binding energies of the atom. The detected electrons are ejected from a depth up to 1 nm.

 

X-ray difraction

 

X-ray diffraction (XRD) is used to investigate the structure of materials. X-rays are reflected from certain crystallographic planes in a specimen. This phenomenon can be described by a rather simple equation, which is known as Bragg’s law, as shown in equation ###:

 

 

 

where d_hkl is the distance between the (hkl) planes, l is the wavelength of the X-rays and q is the diffraction angle. Usually the first order diffraction is taken, n=1. Bragg reflection can occur only for wavelengths lŁ2d. For each planar distance and hence crystallographic direction, the diffraction angle q is different

 

3.3.4             Determination of optical constants. Ellipsometry

 

A spectroscopic ellipsometer Uvisel Jobin Yvon DH 10 was used to determine frequency dependent optical constants (n and k) (Figure 3.3.4). Ellipsometry is a non-destructive optical technique, which deals with the measurement of polarised light undergoing reflection from a sample surface. The light source is a high pressure 300 watts arc xenon lamp, and a mechanical shutter is used to evaluate the continuous background and eliminate any influence of environmental radiation. The polarizer and the photoelastic modulator are mounted along the incident light path, while the reflection arm contains the analyser. The energy of the reflected light is determined by a grating monochromator or a spectrograph, and a photomultiplier tube is used as detector.

The quantities measured by an ellipsometer are the ellipsometric angles Y and D which are related to the complex ratio of the Fresnel reflection coefficients  and  for light polarised parallel and perpendicular to the plane of incidence, respectively, such that

 

(3.3.2)

 

These angles characterise the variation of amplitude and phase in the reflected radiation. Ellipsometry is exploited as a non-invasive probe of thin films and interfaces because the optical properties and composition of the substrate and overlayers, their thickness and morphology, and the surface roughness determine the reflection coefficients. Ellipsometric measurements can be taken at various wavelengths (spectroscopic ellipsometry) and for different angles of incidence. These measurements provide much more information about the samples than that obtained from single wavelength and angle measurements. With each pair Y and D measured at a given angle of incidence a, the corresponding complex dielectric constant of the substrate can be directly obtained, using equation

 

(3.3.3)

 

and related to the real and imaginary part of the complex refractive index, n and k, respectively. In order to deduce unknown parameters of the sample under investigation, a model for the sample structure is first constructed with initial estimates of the parameters. These parameters are then varied to generate a set of calculated Y_cal and D_cal that fit the experimental data. Data fitting is achieved by minimising the mean-square deviation between calculated and measured ellipsometric parameters, taken over all the measured wavelengths and angles of incidence.

 

Figure 3.3.4: Schematic view of an ellipsometer [15].

 

For an absorbing medium, generalisation of the Fresnel formulas allows to determine the reflection coefficients associated with radiation polarised in the perpendicular and parallel directions,  and , respectively. Considering a non magnetic substrate in air, results [16]

(3.3.4)     (3.3.5)

 

The expression (3.3.4) can be written in the form,

 

with     resulting

(3.3.6)       (3.3.7)         (3.3.8)   (3.3.9)

 

The reflectivity  results

.

(3.3.10)

 

Similar considerations for the polarisation component p, allows to determine the corresponding reflectivity R_p as [16]

 

.

(3.3.11)

 

and for the transmissivity T into the second medium,

 

(3.3.12)

 

Thus, if the values n and k are known for a given wavelength, the variation of reflectivity with the angle of incidence may be determined. If the parallel and perpendicular components of the reflectivity are determined, the reflectivity R for a non-polarised beam (i.e., excimer laser radiation) is well approximated by averaging over all directions of vibration [17]

 

(3.3.13)

 

The n and k values determined by ellipsometric measurements were used to estimate the reflectivity R of Al₂O₃-TiC samples used in the study in the wavelength range 230-850 nm, following equations (3.3.8) to (3.3.13).

 

3.4 MATERIALS

 

In this section, the general properties of the materials used in this study are described. The physical properties of Al₂O₃-TiC, Al₂O₃ and TiC are presented, and particular attention in given to their optical properties.

 

3.4.1             Properties of Al₂O₃-TiC

 

Al₂O₃-TiC ceramics have been the focus of significant attention primarily because of their potential application in cutting tools and hard disk recording/reading heads [18,19]. Their utilisation in these and similar applications is motivated by such attractive properties as high wear resistance, strength and fracture toughness [18]. Typical properties of Al₂O₃-TiC ceramics are shown in

Table 3.4.1. Commercially available Al₂O₃-TiC are generally manufactured by hot-pressing or hot isostatically pressing Al₂O₃ and TiC powder mixtures at a temperature in the range of 1850-2100 K [18, 20, 21]. This ensures a homogeneous and almost pore-free microstructure, with stabilised and strengthened oxide-carbide grain boundaries, combined with the elimination of inter-phase thermal and/or elastic mismatches. More recently, these and similar composites have been prepared by combustion synthesis [22, 23]. The combustion synthesis of Al₂O₃-TiC composites can be achieved by the following reaction:

 

3TiO2 + 4Al + 3C = 2Al2O3 + 3TiC

(3.4.1)

 

This reaction self-propagates at a relatively high rate despite its complex nature. The generally accepted mechanism is one composed of two sequential reactions: a thermal reaction between aluminium and the oxide, followed by a reaction between graphite and titanium.

The Al₂O₃-TiC substrates used in this study were hot-isostatically pressed, and have the following composition (Table 3.4.2): 1) 66 wt.% of alumina and 34 wt.% of titanium carbide (3M, ref. 310), with maximum pore size of 1 mm and a volume fraction of pores <0.1%; 2) 70 wt.% of alumina and 30 wt.% of titanium carbide (Cera systems). Although the average grain size is between 0.9 and 2 mm, TiC grains on the Al₂O₃ matrix may, however, reach several microns (Figure 3.4.1).

 

 

3TiO2 + 4Al = 2Al2O3 + 3Ti   Ti + C = TiC

 

 

 

Table 3.4.1: Typical properties of Al₂O₃-TiC composite [24,25].

 

100 g of Al2O3-TiC contains 70g of alumina and 30g of TiC. The volume of 30 g of TiC is 30 g/(4.9 g.cm^-3)=6.122 cm³ while the volume of 70 g of alumina is 70 g/(3.9 g.cm^-3)=17.948 cm³, a total of 24.07 cm³ for 100g of Al₂O₃-TiC.

 

Table 3.4.2: Relevant Al₂O₃ and TiC concentrations in Al₂O₃-TiC ceramics considering a molecular weight of 101.96 and 59.88 g/mole, and a density of 3.9 and 4.9 g/cm³ for the individual Al₂O₃ and TiC phases, respectively.

 

Al2O3   TiC

Figure 3.4.1: SEM micrograph showing the surface of the Al2O3-TiC composite from Cera systems used throughout this work, which is similar to the 3M composite. The surface roughness value Ra is about 0.2 mm for both, as measured by optical profilometry.

 

Al₂O₃-TiC is the most common material used in the sliders of disk drives [26]. Interferometric analysis is frequently used to measure the slider air-bearing surface (ABS) profile and dynamic flying height. The common practice in interferometry is to consider Al₂O₃-TiC as a smooth homogeneous material, and to calculate reflectivity by using the measured real and the imaginary parts n and k, respectively, of an effective index of refraction. This method assumes that the effective values n and k measured by an ellipsometer are sufficient to describe the optical properties of Al₂O₃-TiC. Because n and k are intrinsic material properties, they should be independent of the incident angle in the measurement system. Lacey et al. [27] reported measurements of n and k over a range of incident angles and these results showed a small but measurable angle dependence (Figure 3.4.2). This variation is inconsistent with the n-and-k model, and indicates that using it for Al₂O₃-TiC is an oversimplification.

INCIDENT ANGLE (DEG) a)	INCIDENT ANGLE (DEG) b)
Figure 3.4.2: Comparison of experimental and theoretical variation of measured a) n and b) k values with incident angle for l=633 nm. The experimental data is from [27]. For a true homogeneous material n and k would be constant.

 

Based on experimental evidence and given the large size of TiC grains (up to a few microns) as compared to the radiation wavelength typically used in ellipsometry (in the visible range), Peter de Groot [28] proposed that the optical behaviour of Al₂O₃-TiC may be better described by the scalar diffraction theory. This can be understood considering that an incident electric field upon a large grain-size composite (i.e., grain size > wavelength) sees two distinct materials. Some radiation is reflected from TiC, whereas other parts are reflect from Al₂O₃ surfaces. The heterogeneous surface scatters light into a broad range of angles, with a resultant amplitude and phase that depend on the size of TiC grains and their distribution. De Groot calculated the effective n and k values for Al₂O₃-TiC using scalar diffraction theory, and compared them against reflectivity and ellipsometric measurements. Measured intensity reflectivities were ~20% lower than the values predicted by the n-and-k model and calculated using the Fresnel formulas, but well approximated by the scalar theory values. The scalar diffraction model also predicted a variation of the effective n and k values as measured by an ellipsometer at different incident angles (Figure 3.4.3). The validity of diffraction scalar theory shows the importance of treating Al₂O₃-TiC as a heterogeneous material. However, the generally good success in obtaining flying-height data from optical testers that rely on n and k effective values provides an empirical justification for the use of the model. The values of n and k calculated by ellipsometry although may have an inherent error, reflect the optical properties of both Al₂O₃ and TiC averaged over their surface distribution on the composite, and provide information on the dependence of optical properties on the wavelength and angle of incidence.

 

INCIDENT ANGLE (DEG) Figure 3.4.3: Comparison of predicted intensity reflectivity R for the n and k model and scalar diffraction (SD) theory. The SD model predicts a 20% decrease at normal incidence in agreement with the experimental results [28].

 

Ellipsometric measurements of Al₂O₃-TiC samples used in this work, allowed to estimate the variation of the effective refractive indexes n and k with wavelength in the range 230-850 nm. The variation of reflectivity R with the angle of incidence (Figure 3.4.4) was estimated using the Fresnel formulas, as described in Chapter 2. The reflectivity for perpendicular incidence is about 0.12 at l=248 nm, and increases slowly with increasing wavelength. At l=633 nm, the variation of reflectivity with the angle of incidence is similar to that measured by De Groot [28]. For non-polarised radiation as that emitted by excimer lasers, reflectivity is well approximated by considering the average value resulting from the s and p components [17]. Consequently, it is important to note the significant increase in the reflectivity of Al₂O₃-TiC for angles of incidence above 60 degrees (Figure 3.4.4). The values of the extinction coefficient k may be used to estimate a hypothetical absorption coefficient for Al₂O₃-TiC using . Figure 3.4.5 shows that the absorption coefficient of Al₂O₃-TiC increases with decreasing radiation wavelength from 850 to 230 nm.

 

a) l=248 nm. (n=1.88, and k=0.59).	b) l=633 nm.
Figure 3.4.4: Reflectivity vs. angle of incidence at a) l=248 and b) l=633 nm using the effective n and k values determined from ellipsometric measurements (angle of incidence 60°) of an Al2O3-TiC sample. The surface composition is about 25% TiC. The measurements from de Groot [28] for a surface composition of 30% TiC are indicated for comparison at l=633 nm.  reflectivity using n e k.opj

 

Figure 3.4.5: Variation of the Al2O3-TiC absorption coefficient a with wavelength, as determined using the effective values of k measured by ellipsometry and . k vs alfa alticc.opj

 

3.4.2             Properties of Al₂O₃

 

The hexagonal form of aluminium oxide is variously called a-Al₂O₃, alumina (usually applied to the porous polycrystalline ceramic), corundum (a mineral variety) or sapphire (frequently used to denote the pure synthetic monocrystal). Typical characteristics of alumina are high electrical insulation, hardness, chemical stability, and low thermal conductivity and cost. Consequently, a wide range of applications has been developed: pipes, plates and jigs for high temperature uses, transparent tubes for sodium lamps, wear resistant parts like wire guides and nozzles, mechanical seals, and cutting tools. However, alumina has a number of major limitations such as low toughness, poor thermal shock resistance and high temperature strength. Recent development on alumina ceramics has aimed to improve these properties by addition of other compounds, in the form of particles or whiskers, as in Al₂O₃-TiC (Table 3.4.3).

 

Table 3.4.3: Comparison between selected properties of Al₂O₃ and Al₂O₃-TiC ceramics [29].

 

Tropf et al. [30] reviewed the optical properties of single crystal aluminium oxide. According to their results, crystals are transparent from 0.145 to 5.0 mm and have a direct bandgap at 8.8 eV. Excitonic absorption leads to absorption peaks at 9 and 13 eV, which are maxima in the interband transitions between the upper valence band of oxygen (2p⁶) to the conduction band of triply ionised aluminium (3s + 3p states). In Gervais’s [31] compilation of optical properties for amorphous aluminium oxide (Figure 3.4.6), it is indicated that the absorption band in the lower UV starts at 7.0 eV (l=177 nm). Commercial alumina has a number of impurities: for example, Ca and Si are frequently responsible for abnormal grain growth [32], while MgO is often intentionally added to homogenise the grain size distribution. In addition, commercial sintered Al₂O₃ is porous. Porosity, grain size, and impurities have significant influence on the optical properties of the material, which may differ considerably from those characteristic of the pure crystal. This explains why available data for the alumina reflectivity, absorption coefficient and bandgap varies broadly. For example, values for the bandgap E_g vary between 7.3 [33] and 9.9 eV [34]. This high bandgap justifies the low absorption at 248 (5.0 eV), 308 (4.0 eV) and 351 nm (3.5 eV) corresponding to the radiation emitted by KrF, XeCl and XeF excimer lasers respectively (Figure 3.4.7). For wavelengths below ~200 nm, the absorption by Al₂O₃ increases significantly as the photon energy increases. Conversely, the reflectivity of alumina does not vary significantly in the UV range (Table 3.4.4).

 

Figure 3.4.6: Optical constants for amorphous aluminium oxide: n0 (solid line) and k0 (dashed line).[31].

 

Figure 3.4.7: Transmission curves for various optical materials for UV wavelengths: 1) LiF, 1 mm; 2) MgF2; 3) CaF2, 1 mm; 4) BaF2, 1 mm; 5) NaF, 3 mm; 6) Sapphire, 1 mm; 7) SrF2, 3 mm.

 

Table 3.4.4: Reflectance at normal incidence for various insulating

solids at excimer laser wavelengths l (nm) [35].

 

 

 

 

3.4.3             Properties of TiC

 

TiC presents a NaCl type crystallographic structure where the carbon atoms, much smaller than those of titanium, nest in the interstices of the lattice leading to a combination of metallic, covalent, and ionic bonds [36]. The phase diagram of Ti-C (Figure 3.4.8) shows that titanium carbide, TiC_x, exists as phase within 0.47<x<1.0, although there is some uncertainty concerning the exact values of these limits [37, 38].

 

Figure 3.4.8: The titanium-carbon phase diagram [39]. 882 °C is the aTi to bTi phase transition temperature, and 1668 °C the melting temperature of titanium.

 

TiC combines ceramic properties such as high melting point (3067°C), high hardness (2800 HV), thermal and chemical stability, wear and corrosion resistance, with metallic properties, such as high electrical and thermal conductivity. The conductivity of TiC is of the same order of magnitude of pure titanium [40], and its high melting point together with a high chemical stability enables to classify it as a refractory carbide [36]. This advantageous combination of properties makes these materials very promising candidates as protective coatings. The hardness of TiC, among the highest after diamond, has contributed to the use of titanium carbide as a coating material for cutting tools [36]. Other applications include high corrosion resistance coatings for metal containers, biocompatible layers on orthopaedic and dental implants, and diffusion barriers on Si in semiconductor technology.

Instead of ionic conductiviy typical of ceramics, electronic conductivity was demonstrated in interstitial carbides by various observations [41]: electric resistivity is comparable to the resistivity of pure metals; the temperature coefficient of resistivity is positive and approximately constant, as in metals; the Hall coefficient is negative, hence associated with electronic transport. Thus, although transition metal carbides are considered ceramics, they behave like metals in terms of electrical behaviour. For TiC, the two Ti-4s valence electrons that are involved in conduction are redistributed in the compound: apparently ˝ transfer to C-2p orbitals, and 1 ˝ move in to unfilled Ti-3d orbitals [42]. Band structure calculations indicate that there is band overlap at the Fermi energy, E_F - the highest energy of the electron “gas” at T=0, as indicated in the TiC band structure and electron density of states in Figure 3.4.9. Hence, TiC has no bandgap at E_F (unlike typical insulators and semiconductors), justifying its metallic characteristics. Band structure calculations for other transition-metal carbides and nitrides also show that the Fermi energy is at a non-zero position of the electron density of states; hence, they are all metallic ceramics. This metallic behaviour is responsible for the high absorption coefficient of TiC, around 1´10⁶ cm^-1 in the UV, similarly to metals (Figure 3.4.10a). In this range, the reflectivity of TiC is significantly higher than that for Al₂O₃, and does not vary considerably (Figure 3.4.10b). The conduction electrons in the Group IV and V metallic ceramics are scattered by phonons and by non-metal vacancies. But the dependence of resistivity on temperature and on vacancy concentration does not appear to be linear over a long range of values. The flattened curves of resistivity versus temperature for many high-temperature materials indicate that resistivity cannot increase without bounds. It appears to the limited to about 150-200 mWcm. A possible interpretation is that interband electron scattering in a complex band structure can produce a constant-current channel [43]. Scattering probabilities for point defects and phonons are additive, the defect one being constant - i.e., temperature independent - but proportional to the defect concentration. The mobility of phonon-scattered electrons in TiC is surprisingly high. The electron scattering probability is proportional to the density of electron energy states, N(E), at the Fermi level, E_F, that is, N(E_F), because it accepts the scattered electrons. The value of N(E_F) for TiC is very low, since the band calculations for TiC show that its Fermi energy is located at the minimum of the density of states.

 

 

a)	b)
Figure 3.4.9: TiC a) Band structure and b) Total density of states [42].

 

a)	b)
Figure 3.4.10: Optical properties of TiC vs. radiation wavelength. a) Absorption coefficient and b) Normal incidence  reflectivity (Data determined by EELS taken from [43].     properties.opj

 

 

In order to summarise, Table 3.4.5 shows a wide range of physical properties for Al₂O₃ and TiC, and evidences their differences.

 

Table 3.4.5a: Properties of Al₂O₃ and TiC taken from [44], [45], and a) [25], b) [35], c) [43], and d) [46].

 

Table 3.4.5b: Temperature variation of selected properties for TiC.

 

Table 3.4.5c: Temperature variation of selected properties for alumina.

 

 

REFERENCES

 

1. D. Bäuerle: Laser Processing and Chemistry,  (Springer-Verlag, Berlin Heidelberg 2000)

2. D. Basting: Excimer laser technology: laser sources, optics, systems and applications,  (Lambda Physik AG, Göttingen, 2001)

3. O. Svelto: Principles of lasers,  (Plenum Press, New York 1989)

4. J. P. Sercel and P. J. Sercel: Putting Industrial Excimer Lasers to Work, Photonics Spectra  (May 1990)

5. J. P. Sercel: Production Excimer Laser Equipment Overview, SPIE 1835, 172-183 (1992)

6. H. Gerhardt: Fundamentals of Laser Physics and Laser Technology,  (Lambda Physik)

7. T. R. O'Keeffe and T. E. Lizotte: Excimer laser as a manufacturing tool, Proc. SPIE 2062,  (1994)

8. K. H. Gerlach, J. Jersch, K. Dickmann, and L. J. Hildenhagen: Design and performance of an excimer-laser based optical system for high precision microstructuring, Optics and Laser Technology 29 (8), 439-447 (1997)

9. J. H. Brannon: Micropatterning of surfaces by excimer laser projection, J. Vac. Sci. Technol. B 7 (5), 1064-1071 (1989)

10. P. T. Rumsby, E. C. Harvey, and D. W. Thomas: Laser Microprojection for Micromechanical Device Fabrication, Proc. Experimental Mechanics: Advances and Applications 2921, 684-692 (1996)

11. I. Watt: The principles and practice of electron microscopy,  (University Press, Cambridge 1985)

12. JEOL report: Invitation to the SEM world

13. D. Instruments: Multimode SPM Instruction Manual, Version 4.31ce,  (1996-97)

14. M. Sander: A practical guide to the assessment of surface texture,  (Feinprüf GmbH, Göttingen 1991)

15. J. Yvon: http://www.jobinyvon.com (2001)

16. J. A. B. Faria: Óptica - fundamentos e aplicaçőes,  (Editorial Presença, Lisboa 1995)

17. M. Born and E. Wolf: Principles of Optics,  (Pergamon Press, Oxford 1970)

18. S. J. Burden: Comparison of Hot-Pressed Alumina-Titanium Carbide Cutting Tools, Am. Ceram. Soc. Bull. 67 (6), 1003-1005 (1988)

19. Y. Choi and S. Rhee: Effect of Precursors on the Combustion Synthesis of TiC-Al₂O₃ Composite, J. Mater. Res. 9 (7), 1761-66 (1994)

20. R. Cutler, A. Hurford, and A. Virkar: Presureless-sintered Al₂O₃-TiC composites, Mater. Sci. Eng. A195/106, 182-192 (1988)

21. R. P. Wahi and B. Ilschner: Fracture behaviour of composites based on Al₂O₃-TiC, J. Mater. Sci. 15, 875-885 (1980)

22. T. Xia, Z. Munir, Y. Tang, W. Zhao, and T. Wang: Structure formation in the combustion synthesis of Al₂O₃-TiC composites, J. Am. Ceram. Soc. 83 (3), 507-512 (2000)

23. L. Wang, Z. Munir, and Y. Maximov: Thermite reactions: their utilisation in the synthesis and processing of materials, J. Mater. Sci. 28, 3693-3708 (1993)

24. 3M Ceramic Materials Department Product bulletin

25. M. V. Swain: Structure and properties of ceramics, R.W. Cahn, P. Haasen, and E.J. Kramer (VCH, New York 1994)

26. H. Gatzen: Rigid disk slider micromachining challenges to meet microtribology needs, Trib. Int. 33, 337-342 (2000)

27. C. Lacey, C. Durán, K. Womack, and R. Simmons: Optical measurements of flying height, Proc. Future Dimensions in Storage Symposium  81-88 (1997)

28. P. d. Groot: Optical properties of alumina titanium carbide sliders used in rigid disk drives, Appl. Opt. 37 (28), 6654-6636 (1998)

29. K. Komeya: In Structure and properties of ceramics, ed. by M. Swain (VCH, New York 1994), Vol. 11, pp. 517

30. W. J. Tropf and M. E. Thomas: Aluminum Oxide (Al₂O₃) Revisited,  (Academic Press, 1991), pp. 653-682

31. F. Gervais: In Handbook of Optical Constants of Solids II (Academic Press, 1991), pp. 761-775

32. J. D. Cawley and W. E. Lee: In Structure and properties of ceramics, ed. by M. Swain (VCH, New York 1994), Vol. 11, pp. 47

33. P. Liu, W. L. Smith, H. Lotem, J. H. Bechtel, N. Bloembergen, and R. S. Adhav: Absolute two-photon absorption coefficients at 355 and 266 nm, Phys. Rev. B 17 (12), 4620-4632 (1978)

34. M. J. Weber: Handbook of Laser Science and Technology,  (CRC, Baton Rouge, 1986), Vol. IV

35. W. W. Duley: UV lasers: Effects and Applications in Materials Science,  (Cambridge University Press, 1996)

36. H. O. Pierson: Handbook of Refractory Carbides and Nitrides: properties, characteristics, processing, and applications,  (Noyes Publications, 1996)

37. Z. A. Munir and J. B. Holt: Combustion synthesis of titanium carbide: theory and experiment, J. Mater. Sci. 21, 251-259 (1986)

38. A. G. Akopyan, S. K. Dolukhanyan, and I. P. Borovinskaya: Com. Explos. Shock Wave 14, 327 (1978)

39. E. K. Storms: The refractory carbides,  (Academic Press, New York 1967)

40. W. S. Williams: Phys. Rev. 135, 505-510 (1964)

41. W. S. Williams: Electrical properties of hard materials, Int. J. Refractory Metals & Hard Materials 17, 21-26 (1999)

42. S. Méçabih, N. Amrane, Z. Habi, B. Abbar, and H. Aourag: Description of structural and electronic properties of TiC and ZrC by generalized gradient approximation, Physica A 285, 392-396 (2000)

43. J. Pflüger and J. Fink: In Handbook of Optical Constants of Solids II (Academic Press, 1991), pp. 303-311

44. D. R. Lide: CRC Handbook of Chemistry and Physics,  (CRC Press, 1996)

45. TAPP: Thermochemical and Physical Properties (ES Microware, 1991)

46. V. N. Tokarev, W. Marine, C. Prat, and M. Sentis: Clean processing of polymers and smoothing of ceramics by pulsed laser melting, J. Appl. Phys. 77 (9), 4714-4723 (1995)