As a consequence, the value of Z in Equation 5.45 is an upper limit.
It can be seen from Table 5.3 that mechanically hard semiconductors (e.g., silicon and germanium) have lattice conductivities that are orders of magnitude larger than their respective carrier conductivities. For example, the lattice conductivity for silicon is 400 times larger than its carrier conductivity. On the other hand, the ratio of these conductivities in soft semiconductors tends to be smaller (e.g., approximately 4, for BiTe).
Compared with metals, semiconductors have an unfavorable A/a ratio, but have such a large advantage in a that they are the material invariably used in thermoelectric generators, refrigerators, and heat pumps. Metals are exclusively used in thermometry.
t Synthetic crystals, such as silicon nitride (SiN) and aluminum nitride (AlN), when carefully prepared, may have thermal conductivities exceeding that of diamond. Diamonds prepared by chemical vapor deposition (CVD), available from Fraunhoff IAF in wafers of up to 15 cm diameter and more than 2 mm thickness, have a conductivity of 5300 W/(m K) at 118 K and of 2200W/(mK) at 273 K. Compare with copper, which, over this same range of temperatures, has about 380 W/(mK).
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