Thermal conductivity study of porous low K dielectric materials
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conductivity with porosity. Because of the difficulty in measuring thermal conductivity of porous thin films, the study of thermal conductivity has been carried out only for bulk materials until recently. Though there are many models 2 proposed for the thermal conductivity scaling rules of porous materials, few are applicable for porous low dielectric thin films of interest. The lack of data and scaling rules hinders the pursuit of effective thermal design in the tradeoff of thermal and electrical performance. In our recent research, we have introduced the 3w technique for the measurement of thermal conductivity of porous thin films. By studying thermal conductivity as a function of the porosity, we are able to understand the scaling rule of thermal conductivity of Xerogel. Based on our experimental results and established thermal models, we propose some new models that are applicable for a thin film having a wide range of porosities. EXPERIMENTAL The 3o technique was originally developed for the study of 2specific heat'. Then it was applied to the measurement of thermal conductivity of bulk materials and later thin films 3 in the mid 90s. The technique is based on the thermoelectrical response of a line structure (heater) with respect to its environment. The metal structure is patterned on a sample using photolithography. In our experiment, a 300 rnn thick Al is processed and 5 nm Cr is used as adhesion promoter. In this technique, the heater also serves as the probe (thermometer). When the heater is pumped 87 Mat. Res. Soc. Symp. Proc. Vol. 565 01999 Materials Research Society
with an AC current at frequency (o,I = IoCos(wt), the heating power I2 xR is modulated at 2wo. The temperature change of the heater due to this heating will slightly modify its resistance at the frequency 2wo as R = Ro + a Tx Cos(2cot +4) Thus a 3wo voltage drop on the heater is generated due to the thermoelectrical
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response as
V = IxR = IoxRoxCos(cot)+ 0.SaTxIoxCos(cot+O)+ 0.5aTxIOxCos(3cot+)) (1) where a is the temperature coefficient of Reference Signal resistivity. 0 is the phase Fig 1. Schematic diagram of 3wo experimental apparatus. 3wo signal shift with respect to the is measured when the wocomponent is balanced.R3 is a decade reference signal. The 3o resistance box. R 1, R2, R3 are chosen with low a. signal is typically three orders smaller than the ca pump power. To measure the small 3o signal, a Wheatstone bridge is used to balance the strong wosignal as shown in Fig. 1. Under this condition, a minimum wosignal is achieved, which is comparable in magnitude to the 3o signal. Another advantage of using the Wheatstone bridge is that it also balances the 3o noise from the non-perfect wosource (function generator). When a lock-in amplifier is used, the only signal detected is the dominant 3o signal from the thermoelectrical response of the heater. A special lock-in amplifier (SR850 from Stanford research system) is used to measure the 3o component at reference frequency co. By carefully calibrating the temperature coefficient of
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