Thermal conductivity dielectric crystals

Water is a unique liquid. It is also the most abundant compound on earth ( 10 kg in the oceans with perhaps a similar quantity bound up as water of crystallization in rocks and minerals) and it is an essential constituent of all living organisms. Its unusual properties, such as a high boiling point compared with its related hydrides, a high thermal conductivity, dielectric constant and surface tension, a low enthalpy of fusion, the phenomenon of maximum density (at 4 °C), etc., are usually explained by assuming that liquid water has a structure. 

Single-crystal sUicon has also been employed as substrate material, particularly in multichip module (MGM)-Si appUcations. As a substrate, sUicon offers good thermal conductivity and matches the GTE of the devices mounted on it it does, however, have a relatively high dielectric constant and is very britde. 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

Properties Colorless crystals or white powder odorless and tasteless. D 2.2-2.6 thermal conductivity about half that of glass, mp 1710C, bp 2230C, high dielectric constant, high heat and shock resistance. Insoluble in water and acids except hydrogen fluoride soluble in molten alkai when finely divided and amorphous. Combines chemically with most metallic oxides melts to a glass with lowest known coefficient of expansion (fused silica). Noncombustible. 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

There are several other reasons why LB films are likely to be used in preference to other pyroelectric materials. The figure of merit referred to above, (p/e), is only a measure of the signal strength, and does not take into account the noise sources in a complete infrared detection system. If this is done, one discovers that it is essential to have low dielectric loss in the film over an extended frequency range. All ferroelectric liquid crystals are ruled out of contention on this basis, because they have high tan 5 values in the range IHz to lOkHz. Moreover, it is not possible to prepare very thin films in structures with low thermal mass and low thermal conductivity. 

Aluminum nitride is an attractive material for microelectronics substrates due to its high thermal conductivity, good dielectric properties, and thermal expansion coefficient comparable with silicon. The thermal conductivity of approximately 300 W m is measured for pure single crystal of aluminum nitride. 

Aluminum nitride (AlN) has interesting properties, such as a high thermal conductivity (70-210 W m for the polycrystalline material, and up to 285 W m for single crystals), a high volume resistance, and moderate dielectric properties. The thermal expansion coefficient of AlN is close to that of silicon, and it is one of the most mechanically strong and thermally stable ceramics. These excellent attributes make AlN a useful material for many applications [160, 161]. 

Thermal Conductivity of Dielectric Ceramics 671 Table 16.1 Thermal conductivity at room temperature for several adamantine crystals.. ... 

Hexagonal boron nitride is commonly synthesized as a fine powder. Powders will vary in crystal size, agglomerate size, purity (including % residual BjOj) and density. BN powders can be used as mold release agents, high temperature lubricants, and additives in oils, rubbers and epoxies to improve thermal conductance of dielectric compounds. Powders also are used in metal- and ceramic-matrix composites to improve thermal shoek and modify wetting eharaeteristies. 

Fig. 3.17. Thermal conductivities showing temperature variations characteristic of (a) pure metals—copper (b) dielectric crystals—corundum (c) alloys— brass and 18-8 stainless steel and (d) glassy solids— glass and Teflon.

The dynamics of atoms in solids is responsible for many phenomena which cannot be explained within the static lattice model. Examples are the specific heat of crystals, thermal expansion, thermal conductivity, displacive ferroelectric phase transitions, piezoelectricity, melting, transmission of sound, certain optical and dielectric properties and certain aspects of the interaction of radiation such as X-rays and neutrons with crystals. The theory of lattice vibrations, often called lattice dynamiosy and its implications for many of the above mentioned phenomena is the subject of this two-volume book. 

Aluminum nitride, AIN, is a refractory ceramic with low dielectric constant, high intrinsic thermal conductivity, and a low coefficient of thermal expansion very close to that of silicon. In fact, aluminum nitride is one of only few materials which is both a good electrical insulator and a good thermal conductor. Consequently, there is widespread interest in its use as a replacement for alumina and beiyllia in electronic packa g applications. Such a high degree of interest in AIN stems from its high thermal conductivity, which has been measured at 319 W/m K on a single crystal (7). The theoretical value is 320 W/m-K. 

Semiconducting Properties. Sihcon carbide is a semiconductor it has a conductivity between that of metals and insulators or dielectrics (4,13,46,47). Because of the thermal stabiUty of its electronic stmcture, sihcon carbide has been studied for uses at high (>500° C) temperature. The Hall mobihty in sihcon carbide is a function of polytype (48,49), temperature (41,42,45—50), impurity, and concentration (49). In n-ty e crystals, activation energy for ioniza tion of nitrogen impurity varies with polytype (50,51). 

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