Silicon heat capacity

E2.5 Using the constants given in Table 2.1, we can summarize the heat capacity (J K mol-1) of elemental silicon by the expressions ... 

Figure 12.4 shows an example of experimental set up for a classical measurement of heat capacity the sample is glued onto a thin Si support slab. The thermometer is a doped silicon chip and the heater is made by a ( 60 nm thick) gold deposition pattern. Electrical wiring to the connect terminals are of superconductor (NbTi). The thermal conductance to the thermal bath (i.e. mixing chamber of a dilution refrigerator) is made with thin nylon thread. The Si slab, the thermometer and the heater represent the addendum whose heat... 

To overcome such a problem, a silicon heater of negligible heat capacity was added to each detector to trim its sensitivity by a slight change of the (detector) temperature around the working temperature (see Section 16.6). Due to the steep dependence on T of the R and C parameters, changes in detector temperatures of the order of 1 mK are needed for the equalization of the detector response. 

The next step was the introduction of ion implantation to dope Si for thermometers. Downey et al. [66] used micromachining to realize a Si bolometer with an implanted thermometer. This bolometer had very little low-frequency noise. The use of thermometers doped by neutron transmutation instead of melt doping is described by Lange et al. [67], The evolution of bolometers sees the replacement of the nylon wires to make the conductance to the bath, used by Lange et al. with a micromachined silicon nitride membrane with a definite reduction in the heat capacity associated to the conductance G [68],... 

Prom the following thermodynamic data, with the assumptions that the heat capacities of reaction are negligible and that standard conditions (other than temperature) prevail, calculate the temperatures above which (a) carbon monoxide becomes the more stable oxide of carbon, in the presence of excess C (6) carbon is thermodynamically capable of reducing chromia (Cr2Os) to chromium metal (c) carbon might, in principle, be used to reduce rutile to titanium metal and (d) silica (taken to be a-quartz) may be reduced to silicon in a blast furnace. 

A 8] The separation layer consists of platinum coated on a silicon substrate. Owing to the low heat capacity, quick temperature cycles can be executed and a resolution down to 7 ppm can be achieved with the integrated thermal conductivity detector. The standard length of the capillary is 860 mm with a channel width of 60 pm. A measurement cycle takes less than 60 s. 

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. 

In cryogenic detectors, a simultaneous measurement of both ionization and thermal energy allows the discrimination of nuclear recoils from electrons produced in radioactive decays or otherwise. This discrimination, however, cannot tell if the nuclear recoil was caused by a WIMP or an ambient neutron. The detector, most often a germanium or silicon crystal, needs to be cooled at liquid helium temperature so that its low heat capacity converts a small deposited energy into a large temperature increase. Only relatively small crystals can be currently used in these cryogenic detectors, with relatively low detection rates. 

The low temperature heat capacity has been measured from 54.9 to 296.2 K by Todd (7). The entropy is based on S"(51 K) > 0.62 cal K mol . The high temperature enthalpy has been measured to 1600 K by Pankratz et al. (5). The low and high temperature data were Joined smoothly together by means of a Shomate function plot (8). Since all the aluminum and silicon atoms occupy differently coordinated sites, there is no possibility of any residual entropy of mixing in this polymorph. 

In spite of the apparent agreement between the experimental data and the theoretical prediction based on the equipartition principle, there are nevertheless significant discrepancies. In the first place, the heat capacity of carbon, e.g., diamond, is only 1.45 cal. deg. g. atom at 293 K, and it increases with increasing temperature, attaining a value of 6.14 cal. deg. g. atom at 1080° K. Somewhat similar results have been obtained with boron, beryllium and silicon. Further, although the atomic heat capacities of most solid elements are about 6 caJ. deg. " g. atom at ordinary temperatures, and do not increase markedly as the temperature is raised, a striking decrease is always observed at sufficiently low temperatures. In fact, it appears that the heat capacities of all solids approach zero at 0° K. Such a variation of the heat capacity of a solid with temperature is not compatible with the simple equipartition principle, and so other interpretations have been proposed. ... 

Table 4.2. Experimental heat capacities Cp1 of "liquid" (molten or rubbery) polymers at room temperature (298K) in J/(mole K), the geometrical parameters N33rot and NSQrot used in the correlation, and the fitted values of Cp1, for 81 polymers. The connectivity indices and °xv, which are also used in the correlation, are listed in Table 2.2. The alternative values listed in Table 2.3 are used for silicon-containing polymers. dcpi(exp)=[1000/Cp1(298K)] (dCp1/dT) denotes the experimental value of the temperature coefficient of Cp1. 

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