PHYSICAL REVIE%' 8 VOLUME 46, NUMBER 20 15 NOVEMBER 1992-II Thermal-diffusivity measurements of ultrahigh thermal conductors with use of scanning photothermal rate-window spectrometry: Chemical-vapor-deposition diamonds Zhuohui Chen and Andreas Mandelis Department of Mechanical Engineering, Photothermal and Optoelectronic Diagnostics Laboratory, University of Toronto, Toronto, Ontario, Canada M5S 1A4 and Ontario Laser and Lighttoaue Research Center, Uniuersity of Toronto, Toronto, Ontario Canada M5$1A4 (Received 1 June 1992) A comprehensive study of a photothermal rate-window spectrometry for thermal-diffusivity measure- ments of ultrahigh thermal conductors, using either a dual-channel boxcar averager or a lock-in amplifier, is presented. Theoretical analysis of infrared radiometric transients and techniques to extract the diffusivities of materials from the transient are discussed. By exploiting the derivative signal nature of the rate-window methodology, one can measure the thermal diffusivity of the sample with superior signal-to-noise (S/Ã) ratio from the maximum position of the radiometric rate-window signal. Our mea- surements of thermal diffusivities of chemical-vapor-deposition diamonds made by the hot-filament pro- cess as a function of temperature between 60 and 300 K are the first such photothermal data obtained completely nonintrusively and they illustrate the unique potential of this measurement methodology for the nondestructive, noncontact photothermal investigation of ultrahigh thermal-conductor thermophy- sics, largely inaccessible by other diagnostic probes. I. INTRODUCTION In recent years with the development of technology in electronic materials and devices, a knowledge of thermo- physical properties of these materials and devices has be- come increasingly important. Many techniques have been developed for measuring the thermal diffusivity, thermal conductivity, and heat capacity of materials. ' Among these techniques, thermal waves have attracted widespread interest. ' Due to the fact that thermal wave propagation depends on the thermal diffusivity of the material, one can measure this quantity from the frequency- and/or time-domain behavior of the thermal wave. Nevertheless, when a photothermal measurement in condensed matter with very high values of thermal transport properties is contemplated, such as diamond, there are stringent instrumental and background noise re- quirements to be satisfied before an acceptable measure- ment can be performed. These considerations tend to eliminate most conventional photothermal techniques from being suitable candidates. In most cases, a thermal wave is generated by a laser beam at the surface of a solid or a film in a layered struc- ture. One photothermal technique which has been found most suitable to measure the temperature variation of such ultrahigh thermal conductors uses the optical beam deflection caused by the mirage effect. " ' In this method, the surface is heated by a modulated laser beam. A probe laser beam skimming the sample surface is used to measure the variation of local temperature caused by the heating beam. The probe beam is deflected by the temperature gradient of the refractive index in the air or in any other surrounding fluid. From the mirage phase signal which is a function of the offset distance between the heating and probe beams, one can obtain the thermal diffusivity of the sample. This method requires not only a painstaking point-by-point measurement by changing the relative positions of the probe and pump laser beams, but also an empirical multiparameter routine for fitting the experimental data sets to the theoretical curve. ' ' This makes the technique cumbersome and less straightfor- ward for interpreting the data. In addition, mirage effect cryogenic temperature measurements in air may be difficult or impossible, due to the partial vacuum required in conventional experimental chambers. This restricts the utility of this technique to relatively high tempera- tures. Another remote-detection thermal wave technique suitable for the thermal-diffusivity measurement is photo- thermal radiometry (PTR). ' This method can be used to measure thermal responses of materials in frequency and/or time domain. The heating source can be a short- duration laser pulse ' or a modulated laser beam, "' and the thermal radiation emitted from the sample surface is measured using an IR detector. The transients are recorded by using a digitizer in the case of pulsed heat- ing, or the amplitude and phase signals are measured by using a lock-in amplifier. In both modes of the conven- tional PTR, a curve fitting procedure is needed to obtain the thermal diffusivity of the sample. Moreover, both the conventional frequency-domain PTR and mirage effect techniques encounter another problem when one mea- sures very thin Alms or ultrahigh thermal conductors, 46 13 526 1992 The American Physical Society