(Received 30 October 2009; accepted 12 December 2009; published online 27 January 2010)
Frequency-domain thermoreflectance is extended to the characterization of thin metals films on low thermal diffusivity substrates. We show how a single noncontact measurement can yield both the thickness and thermal conductivity of a thin metal film with high accuracy. Results are presented from measurements of gold and aluminum films 20â€“100 nm thick on fused silica substrate. The thickness measurements are verified independently with atomic force microscope cross sections, and the thermal conductivity measurements are verified through electrical conductivity measurements via the Wiedemannâ€“Franz law. The thermoreflectance thermal conductivity values are in good agreement with the Wiedemannâ€“Franz results for all the films at least 30 nm thick, indicating that our method can be used to estimate electrical conductivity along with thermal conductivity for sufficiently thick films. Â© 2010 American Institute of Physics. [fusion_builder_container hundred_percent=”yes” overflow=”visible”][fusion_builder_row][fusion_builder_column type=”1_1″ background_position=”left top” background_color=”” border_size=”” border_color=”” border_style=”solid” spacing=”yes” background_image=”” background_repeat=”no-repeat” padding=”” margin_top=”0px” margin_bottom=”0px” class=”” id=”” animation_type=”” animation_speed=”0.3″ animation_direction=”left” hide_on_mobile=”no” center_content=”no” min_height=”none”][doi:10.1063/1.3289907]
Thin metal films are essential for a vast array of technologies in optics and microelectronics. The thickness, density, thermal conductivity, and electrical conductivity of these films are all critical parameters affecting their performance in a given application. As a result, numerous techniques have been developed to characterize these properties. Of particular interest are noncontact methods, due to their nondestructive nature and the ease with which they can be incorporated into manufacturing processes.
Many of the methods that have been developed are based on photothermal phenomena. These fall into the categories of frequency-domain methods based on a modulated laser heating source,1â€“8 and time-domain methods based on the sample response to a short laser pulse, such as timedomain thermoreflectance !TDTR”.9â€“12 Recently, the authors have introduced a frequency-domain thermoreflectance !FDTR” method13 that combines some of the advantages of TDTR, such as good sensitivity for submicron thin films and a straightforward coaxial laser spot geometry, with the advantages of modulated photothermal methods, such as relative experimental simplicity due to lack of a moving delay stage and the ability to explore a range of thermal penetration depths with a single measurement.
In this work, we show how FDTR can be applied to thin metal films on low thermal diffusivity substrates such as glass or quartz. We simultaneously determine the thickness or density of a metal film, and the film thermal conductivity. From the thermal conductivity, we can obtain the electrical conductivity through the well-known Wiedemannâ€“Franz !WF” law.14
Separately, each of these topics has been addressed with various methods. Film thickness, for example, can be determined by profilometry, by picosecond acoustics provided the sample has a strong thermoelastic response,15 or with a modulated thermal wave approach.5 Techniques for measuring the thermal conductivity in thin metal films are less common. These include scanning probe techniques such as scanning Joule microscopy,16 and photothermal methods where a probe laser spot is moved over a pump laser spot and a three-dimensional thermal model is used to determine film conductivity based on the signal phase as a function of the spot separation.3,8,17
Our FDTR approach has several advantages. The measurement geometryâ€”coaxial laser spots passed through a single objective lensâ€”allows for simple alignment and a straightforward two-dimensional analytical thermal model. Additionally, because the measurement covers a wide frequency range, the sensitivity to film thermal mass and thermal conductivity separate into different transport regimes, allowing both properties to be determined simultaneously. Thus, from a single noncontact measurement we obtain the critical structural and transport properties of the metal film. II. BACKGROUND A complete description of the FDTR method can be found in.13 The essential features are that a modulated laser heating source, called the pump beam, impinges on a sample, while a second, unmodulated beam is reflected off the sample and directed into a photodetector. Both pump and probe beams are coaxially directed through a single microscope objective and focused to spots 10â€“20 !m in diameter. The laser beams can be pulsed or continuous-wave !cw”. In the case of pulsed beams, the pump and probe beams typically originate from the same laser and are divided with a beamsplitter. An optical delay separates the pump and probe pulses by a time “.
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