Thermal wave thickness

Similar to the expression for the condensed phase, the thermal diffusivity in the gas phase is given by g = Xg/pgCg and is assumed to be independent of temperature. The thermal wave thickness in the gas phase 6g is defined according to 6g = Og/Mg. Then, Eq. (3.46a) can be written as ... 

Thermal-Wave Measurement of Thin-Film Thickness... 

We have developed a method for measuring the thickness of semiconductor thin films that is nondestructive, noncontact and that can make measurements with 2-um spatial resolution on both optically opaque and optically transparent films. This method is based on the use of high-frequency thermal waves. 

This sensitivity is, of course, the precision of the measurement based on signal noise considerations, and it does not reflect the absolute accuracy of the measurement. As with other noncontact, nondestructive methods, the thermal-wave technique provides an indirect measure of the geometric film thickness, and absolute accuracy must rely on either an accurate knowledge of the relevant physical parameters, or, as is common with the other methods, the use of calibration standards. In analyzing the data presented here we have used a rather complete (and complex) theoretical model to explain our experimental data, and thereby... 

Finally, it should be noted that when the thickness of a thin film is known, then the thermal-wave signal can be used to characterize the composition or uniformity of the thin film material. 

Rosencwaig, A. In Thermal-Wave Measurement of Thin Film Thickness 5 ACS SYMPOSIUM SERIES, this volume. 

Fig. 5.10.5 Three-omega technique the calculated normalized slope (d(AT)/d (log /)) of the thermal oscillation amplitude AT as a function of frequency/for a 100 nm thick aluminum heater element on a 500 nm thick Si02 layer and a 1 mm thick silicon substrate is shown as a function of thermal oscillation frequency/ With increasing frequency, the thermal wave penetrates deeper, allowing different sections of a (multilayered) sample to be scanned...

The setting with a membrane seal is completely different, as shown in Rg. 5.15. Here the outside layer also heats up through solar radiation and convection. The thickness of the membrane is only about 1 mm. Unlike in Fig. 5.14 the membrane is heated up in its total thickness and therefore radiates towards the inside. Thereby the inside is heated up through radiation and aside from this through convection. The effect is active immediately, as due to the minor thickness of the membrane the thermal wave immediately heats up the membrane in its total thickness. A buffer action as with a massive building element does not occur. The spectrum of the impacting radiation is again that of the sun. The spectrum of the secondary radiation is determined by temperature and the material of the membrane. 

Finally, that work was summarized by Thostenson and Chou, who showed that both numerical and experimental results indicated that volumetric heating due to microwaves promoted an inside-out cure of the thick laminates and dramatically reduced the overall processing time [115]. Under conventional thermal conditions, to reduce thermal gradients, thick laminates were processed at lower cure temperature and heated with slow heating rates, resulting in excessive cure times. Outside-in curing of the autoclave processed composite resulted in visible matrix cracks, while cracks could not be seen in the microwave-processed composite. The formation of cure gradients within the two composites cured under both micro-wave and conventional conditions are presented in Fig. 31. 

The use of phase shifts for PA/FT-IR depth profiling was first discussed by Dittmar et al. [8], who correlated the depth from which a spectral feature originated with its phase spectrum, 9, as calculated by Eq. 20.3. The photoacoustic phase shift, 0 can be calculated for thermal wave propagation across a layer of thickness, t, from the velocity of the thermal wave [9,10] ... 

The influence of thermal wave is more signiflcant for thermal conduction in microscale systems compared to macrosystem. An example of thin film conduction is illustrated here to justify this point. Figures 8.13 and 8.14 compare the conduction through a thin film and thick film, respectively. Here, the film is initially at temperature Tq. There is a sudden change in the temperature of both sides to T. The nondimensional variables for the problem are defined as... 

---