Instead of having discrete energies as in the case of free atoms, the electronic structure of dielec- tric materials consists of available energy states for electrons, which form bands. In dielectric materials, the electrons in the valence band (the last completely filled band) are separated by a large gap (band gap with energy states forbidden for electrons) from the conduction band (the first non-occupied band).
The most common insulating material used for industry is silicon dioxide, which is not a form of ionic crystal1, as for a example sapphire Al2O3 crystal.
In the silicon-dioxide structure silicon atoms are surrounded by four oxygen atoms, forming a regular tetrahedron, and each oxygen atom is bonded to two silicon atoms as it is shown schemat- ically in fig. i. Each oxygen atom is positioned equidistantly from its two silicon neighbors and
Figure i: Schematic diagram of silicon dioxide. The white circles are the silicon atoms, each connected to four neighboring silicon atoms by a bent oxygen-atom bridge (dark circles) [185].
forms a bent bond, or a bridge, between the two silicons. The simplest crystal lattice of SiO2 is
arranged as in the elemental silicon structure but with the silicon-silicon bonds replaced by oxy- gen bridges. The directions between two neighbors oxygen and silicons make an angle of about 144◦. The oxygen bridges can be rotated allowing the bond lengths and angles to preserve their values near the ideal ones. In order to understand the electronic structure further, the two silicon
1
An ionic crystal consists of ions bound together by their electrostatic attraction [84].
hybrids directed toward an oxygen atom are shown (fig. ii). The angle of 18◦ characterizing the bend in the oxygen bridge is half the difference between the bond angle, 144◦, and 180◦.
A bonding unit for a solid must be stochiometric; that means that the unit must have the same ratio of constituent atoms as the compound. Only in this case it is possible to construct a crystal out of such units. This criterion is fulfilled for the oxygen atom on fig. ii. A silicon atom with four oxygen neighbors is not allowed as a bonding unit. As long as the entire crystal also includes impurities and inclusions, it should be taken into account that there are more than one set of bonding units in some structures. In our study we take the classical value of the bonding units for electronic states in terms of the total number of the orbitals of oxygen and silicon.
Figure ii: Si and O hybrids.
If we do so, we shall obtain the energy-level diagram of the formation of Si-0 bonds in SiO2
(shown in fig. iii).
Figure iii: Theoretical band structure of SiO2.
The valence bands are formed by the bond (εb), lone-pair (εlp), and π-states (επ) where there
are enough electrons to fill them; the antibonding (εa) orbitals form the conduction bands.
There are two basic ways of making quartz / silica glass:
• By melting silica grains either by gas or electrical heating (the type of heating affects some optical properties). For some applications the material can be transparent or opaque. • By synthesizing the glass from chemicals. This synthetic material, normally referred to as
synthetic fused silica, has better optical properties and is somewhat more expensive than the other type.
Fused silica has outstanding physical characteristics such as thermal properties (thermally shock resistant, low coefficient of thermal expansion) with excellent optical transmission properties from the deep UV to the infrared wavelength range, with good electrical and corrosion performance. In the table 5, we group the main properties of fused silica.
Property Value Units
General Chemical Formula SiO2
Mechanical Density 2.2 g/cm3
Hardness 570 Knoop
Tensile Strength 50 MPa
Young’s modulus 72 GPa
Compressive Strength 1100 MPa
Poisson’s Ratio 0.17
Fracture Toughness 1.2 MPam1/2
Electrical Dielectric Strength @20◦C 40-50 kV/mm
Dielectric Constant 3.8 @ 1 MHz
Volume Resistivity 7 x 109 ohm-cm
Thermal Coefficient of Thermal Expansion 0.6 10−6 ◦C
Thermal Conductivity @20◦C 1.4 W/mK
Specific Heat @ 0-500◦C 964 J/kg K
Maximum Working Temperature 600 - 1000 ◦C
Optical Index of Refraction (1.06 µm) 1.449
Transmission Band 0.19 - 3.5 λ, µm
Band gap 9 eV
Table 5: Physical properties of SiO2 [186, 187].
In our study we mainly use synthetic SiO2 material SUPRASIL produced by Heraeus. This high purity fused silica is manufactured by flame hydrolysis of SiCl4. This material has controlled
index of homogeneity (∆n) that is specified either in one direction (functional direction) or in all three functional directions. This synthetic fused silica is practically free from bubbles and inclusions (total bubble cross section within the volume ≤ 0.015mm2/100 cm3, OH-group is
present). A second type of fused silica used in the experiment is HOQ 310 also by Heraeus. HOQ material is manufactured by fusion of natural quartz crystals, that has bubble class 3 (total bubble cross section within the volume ∼ 0.5mm2/100 cm3) and low impurity content such as Al, Ca, Fe, OH-group, Li, Mg and some others (Au, As, Cu, Cr, K, Na, Sb) that are not significant.
Optical transmission properties of silicon dioxide are presented in fig. iv. This material has low linear absorption from 190 to 2000 nm. That is essential for femtosecond laser treatment of fused silica as the interaction is nonlinear for a wide range of laser wavelengths.
Figure iv: Transmission spectrum of fused silica [188].
We made a spectroscopic analysis of the plasma plume obtained during laser-matter interaction experiment (see fig. v). The spectroscopic analysis was done in ambient air with fast sample displacement and with an acquisition time of 1 s for every curve. The experimental curves are the result of the averaging of 7 measurements, performed in single shot regime (fig. v).
Discrete spectral lines on the spectrum obtained with the microscope slide are present and intense, confirming high content of impurities such as K, Ca, Na, H, .... Suprasil and HOQ 310 do not show these impurity lines and yield similar emission spectrum. They present only traces of some chemical impurities (potassium, Na). We can conclude that both HOQ 310 and suprasil samples are high purity glasses with similar composition.
Figure v: Emission spectrum of fused silica of different quality. High purity SiO2: suprasil and HOQ 310 and low purity: microscope slide. The spectral line at 1025 nm corresponds to laser light irradiation. For discriminating the three curves, a different offset is applied to each glass sample.