AC Loss Modeling in Ba 0.5 Sr 0.5 TiO 3 Using Dielectric Relaxation
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AC Loss Modeling in Ba0.5Sr0.5TiO3 Using Dielectric Relaxation Nadia K. Pervez1, Jiwei Lu2, Susanne Stemmer2, Robert A. York1 1 Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, U.S.A. 2 Materials Department, University of California, Santa Barbara, CA 93106, U.S.A. ABSTRACT In universal relaxation, a material’s complex dielectric susceptibility follows a fractional power law f1-n where 0 < n < 1 over multiple decades of frequency. In a variety of materials, including Ba0.5Sr0.5Ti03, dielectric relaxation has been observed to follow this universal relaxation model with values of n close to 1. In this work we have shown that the universal relaxation model can be used to calculate dielectric loss even when n is very close to 1. Our calculated Q-factors agree with measured values at 1 MHz; this agreement suggests that this technique may be used for higher frequencies where network analyzer measurements and electrode parasitics complicate Q-factor determination.
INTRODUCTION Universal relaxation refers to behavior where a material's complex dielectric susceptibility is observed to follow a decreasing power law over multiple decades in frequency [1]. This behavior is observed in a variety of different materials including BaxSr1-xTiO3, Al2O3, Ta2O5, HfO2, and SiO2 [2,3]. It appears to be a property of extrinsic disorder rather than an intrinsic material property [4,5]. The susceptibility shows an f1-n frequency dependence, where 0 < n < 1. For a lossless material, n=1. A direct consequence of this power law is that if the real component of a material's complex susceptibility obeys a power law, so must the imaginary component. While many materials have been observed to obey Curie-von Schweidler behavior, corresponding to n~1, little attention has been focused on the corresponding loss predictions using the universal relaxation model. Even when little relaxation is observed – when n is very close to 1 – the model can still accurately predict loss. The ability to calculate losses from capacitance data may be advantageous in situations where the direct measurement of Q-factors is difficult, such as network analyzer measurements of low-loss films. Reflection-type measurements of high-Q reactive loads performed with network analyzers are less accurate than auto-balancing bridge measurements performed with impedance analyzers. However, autobalancing bridge measurements are limited to below 110 MHz. Provided that parasitic electrode inductances at high frequencies can be accounted for, this technique offers an accurate way to indirectly measure film loss through capacitance measurements. In Ba0.5Sr0.5TiO3 (BST) we have successfully used power-law capacitance data to predict Qfactor values. Comparison of 1 MHz Q-factors calculated and measured using an impedance analyzer demonstrates the validity of this approach. The calculated values are consistently equal to or slighter higher than measured values, consistent with the expected small contribution of series electrode r
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