Analysing Transient Thermoreflectance Data Using Network Identification by Deconvolution

Network Identification by Deconvolution (NID) method is applied to the analysis of the thermal transient pulsed laser heating. This is the excitation used in many optical experiments such as the Pump-Probe Transient Thermoreflectance experiment. NID method is based on linear RC network theory using Fourier’s law of heat conduction. This approach is used to extract the thermal time constant spectrum of the sample after excitation by either a step or pulsed heat source at one surface. Furthermore, using network theory mathematical transformations, the details of the heat flux path through the sample can be analyzed. This is done by introducing the cumulative and differential structure functions. We show that the conventional NID method can be modified to analyze transient laser heating experiments. The advantage is that the thermal resistance of the top material layers and the major interface thermal resistances can be extracted without the need of assuming a specific multilayer structure. Some of the limitations due to the finite thermal penetration depth of the transient heat pulse will be discussed. INTRODUCTION The most commonly used technique to measure the thermal conductivity of thin semiconductor films is the 3ω method developed by Cahill [1]. Reliable data obtained with this method are now used in many applications. A second interesting method is the Pump-Probe Transient Thermoreflectance technique (PPTTR), whose first utilization to study thermal transport experimentally was reported by Paddock and Eesley [2]. For nearly two decades, PPTTR technique has been an effective tool for studying heat transfer in thin films and low dimensional structures (multilayers and superlattices) [3]. In contrast to the 3ω method [1], PPTTR can distinguish between the thermal conductivity of thin films and their interface thermal resistance [3]. PPTTR is a time resolved technique which extends the conventional thermoreflectivity technique [4] or flash technique [5], to very short time scales using femtosecond lasers and the optical sampling principle. The multiple advantages of this technique, being an entirely optical, non-contact and nondestructive method, with a high temporal resolution (on the order of the laser pulse duration <1ps), and high spatial resolution (10nm in the cross-plane direction and <1μm in the in-plane direction), have conferred to it a particular place in the field of thermal properties metrology of thin metal and dielectric films. In this technique, an intense short laser pulse “pump” is used to heat the film, and a delayed weak (soft) short laser pulse “probe” is used to monitor the top free surface reflectivity change induced by the cooling of the thin film after absorption of the pump pulse. The pump and probe can come from the same primary laser source, a configuration called homodyne PPTTR [6], or they can be issued from two independent laser sources, a configuration called heterodyne PPTTR [7]. The heterodyne configuration allows having a long time delay between the pump and the probe that can go up to one period of the pump laser beam, which is for a 76MHz Ti: sapphire source on the order of ~13ns. With the use of a pulse picker one can reach even longer time delays. Cumulative thermal effects could be important in certain PPTTR configurations in which the external modulation of the pump beam is used and it is on the same order of magnitude as the laser repetition rate [8, 9]. Here we focus on the inherent transient thermal response which can very well be modeled considering delta pulse heating with a laser. Semiconductor and dielectric structures are usually covered by a thin metal film which acts as a thermal capacitor and temperature sensor [6]. The cross-plane thermal conductivity of the sample’s top layer and the interface thermal resistance with the metal film are determined by comparing experimental cooling curves to theoretical simulations and optimization of free parameters to get the best fit [6]. In addition to the characterization of thermal properties of thin