Thermal conductivity of thin metallic films measured by photothermal profile analysis G. Langer, J. Hartmann, and M. Reichling a) Fachbereich Physik, Freie Universita ¨t Berlin, Arnimallee 14, 14195 Berlin, Germany ~Received 4 October 1996; accepted for publication 9 December 1996! Thermal conductivity of nickel and gold films on quartz ~thickness 0.4–8 mm! was measured by a modulated thermoreflectance technique recording the surface temperature profile. Model calculations predict an optimum frequency for measuring thermal transport within the film. Measurements on films with various thicknesses reveal a thermal conductivity close to the bulk value for nickel while gold films exhibit a reduced conductivity with decreasing film thickness. © 1997 American Institute of Physics. @S0034-6748~97!04903-4# I. INTRODUCTION The growing interest in physical properties of thin films initiated the development of various techniques for a gener- ally applicable, reliable, and noncontact determination of thin film thermal conductivity. 1 Most noncontact measure- ments are based on photothermal techniques utilizing modulated 2 or pulsed 3 laser beams for the determination of thermal conductivities. For a modulated laser beam as a heat- ing source the solution of the heat diffusion equation yields thermal waves 4 with a one-dimensional decay length L th de- pending on the thermal diffusivity D and the modulation frequency f : L th 5A D p f . ~1! In the case of three-dimensional heat flow the decay length is smaller; i.e., the range is not only governed by the exponential decay exp~2r / L th ! but also by an additional fac- tor proportional to r 21 , where r is the distance from the heated center. 5 Thermal wave propagation can be utilized for conductiv- ity measurements by locally heating the surface with a har- monically modulated excitation and monitoring the surface temperature variation as a function of the distance from the heat source. Due to the propagation of the thermal wave the phase lag between the heat deposition and the temperature oscillation at a given point on the surface ~or in the homo- geneous material! is a linear function of the distance of the respective point from the heat source. Scanning over a ther- mal profile yields a straight line for the phase with a slope equal to the inverse of the thermal length. 6 This concept is the basis for thermal conductivity measurements presented here. However, since we investigate thin films on substrates and use a laser heating source with an extension that is not negligible compared to the width of the measured profile, data analysis is more complicated in our case and requires the use of a rigorous three-dimensional photothermal theory. 7 From modulated heat flow experiments only the thermal diffusivity D 5l /( r C p ) can be extracted. A conversion of thermal diffusivity D to thermal conductivity l and vice versa is straightforward provided the specific heat r C p of the material is known. As the thermal conductivity is the more common quantity, in this work only thermal conductivities are presented, assuming that the heat capacity of the investi- gated thin films is equal to the respective bulk values. II. EXPERIMENT Imaging photothermal techniques are capable of directly measuring thermal decay in the surface plane 8 and, hence, allow a determination of thermal data by applying a theoret- ical model to the measured images. This is, e.g., exploited by methods suggested by Visser et al. 9 and Kemp et al. 10 who obtained two-dimensional thermal profiles induced by a local heat source from a modulated focused laser beam. In contrast to these techniques where the surface temperature distribu- tion is measured by an infrared-scanner or a thermocouple, we scan the heating laser beam and measure the surface tem- perature distribution by thermoreflectance 11 with an appara- tus originally designed for defect mapping in optical thin film systems. 12 The experimental arrangement is schemati- cally depicted in Fig. 1. The modulated heat source is a mechanically chopped beam from an Ar 1 laser operated at 514 nm that can be positioned with mm resolution by means of two dielectric mirrors mounted on computer-controlled translation stages. To obtain an undistorted Gaussian beam profile with a width of 100 mm at the sample surface, the laser beam is spatially filtered by a pinhole in the focal plane of a Galilean telescope. Since thin films are easily damaged by excessive heating it is essential to monitor the incident power, accomplished in our case by a beam splitter directing part of the laser beam to a calibrated sensor head. The ther- moreflectance is probed by a HeNe laser beam focused to about 30 mm at the same location as the heating beam. This ensures that convolution effects resulting from the finite width of the pump laser beam and the 45°-incidence of the probe beam can be neglected. After narrow-band spectral filtering the reflected probe beam intensity is measured by a photodiode coupled to a current-to-voltage converting pre- amplifier. The harmonic component of the modulated reflec- tivity signal is detected by a two-phase lock-in amplifier that directly provides amplitude and phase of the sample surface temperature oscillation. By means of measuring a reference a! Corresponding author; Electronic mail: reichling@matth1.physik.fu- berlin.de 1510 Rev. Sci. Instrum. 68 (3), March 1997 0034-6748/97/68(3)/1510/4/$10.00 © 1997 American Institute of Physics