Silicon Debye temperature

Clearly one obtains the best performance for a given time constant with a detector that has the lowest possible heat capacity. The heat capacity of a crystal varies like C oc (T/0 )3, where On is the Debye temperature. Diamond has the highest Debye temperature of any crystal, so FIRAS used an 8 mm diameter, 25 fim thick disk of diamond as a bolometer (Mather et al., 1993). Diamond is transparent, so a very thin layer of gold was applied to give a surface resistance close to the 377 ohms/square impedance of free space. On the back side of the diamond layer an impedance of 267 ohms/square gives a broadband absorbtion. Chromium was alloyed with the gold to stabilize the layer. The temperature of the bolometer was measured with a small silicon resistance thermometer. Running at T = 1.6 K, the FIRAS bolometers achieved an optical NEP of about 10 14 W/y/IIz. 

Calculate the specific heat of silicon at the boiling point of neon by using the fact that the Debye temperature of sihcon is 645 K. Compare this with the result in Question 15.3. 

Diamond has the highest Debye temperature of 1860 K. The semiconductors silicon and germanium have 625 and 290 K, respectively. For metals, the Debye temperature ranged from 100 K for potassium to 470 K for iron. 

The empirical Dulong-Petit rule states that at room temperature all solid elements exhibit the same molar heat capacity, which is roughly equal to three times the ideal gas constant. This is, however, not true for all solids (e.g., diamond, silicon, boron, and beryllium), but it gives a good order of magnitude for engineers and scientists in the absence of data, especially in the field or at the plant. This behavior was later confirmed theoretically by the work of Einstein and Debye, who demonstrated that at temperatures above the Debye temperature of the element (T ), the molar heat capacity of solids tends to 3R ... 

Tables 1.8 and 1.9 and Fig. 1.21 give some reference data on the values of the thermal coefficient of linear expansion for oxides, refractory, and ceramic materials [100-102]. Crystals with a cubic lattice (CaO, MgO) have equal values of linear coefficients of expansion along aU axes. The typical linear coefficients of thermal expansion for such materials are 6-8 x 10 and increase with the temperature up to 10-15 X 10 K . Anisotropic crystals with low symmetry have different values of linear coefficients of thermal expansion along different axes, but with a temperature increase, this difference becomes smaller. Materials with strong chemical bonds (silicon carbide, titanium diboride, diamond) have low values of linear coefficients of thermal expansion. However, these materials have high values of Debye characteristic temperature (values of the linear coefficients of thermal expansion grow below the Debye temperature and are almost constant above it).

Polytype Hexagonality D Chemical shift (eV) Effective charge q Ratio of silicon and carbon concentrations CJC, Lattice parameters X-ray and practical density Carbon and silicon vacancy concentration Debye- temperature 0D Formation enthalpy A77°298 (kJ/mol) Entropy °298 (J/mol K)... 

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

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