Polaron conduction loss in microwave dielectric ceramics
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Polaron conduction loss in microwave dielectric ceramics Seungbum Hong, Eunah Kim, Han Wook Song, Jongwan Choi, Dae-Weon Kim, and Kwangsoo No Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
Tae-Hong Kim, Jung-Rae Park, and Jin-Woo Han Electronics and Telecommunications Research Institute, Taejon, 305-701, Korea (Received 9 March 1998; accepted 1 May 1998)
It has been generally accepted that the product of the unloaded quality factor and resonant frequency is the universal parameter for comparison of dielectric resonators with different size.1,2 However, it is suggested in this study that this universal parameter should be modified due to the presence of the polarons. From the frequency dependence of the unloaded quality factor, it is possible to extract the factor determined only by the phonon scattering effects, and we denoted this parameter by Qs . It was found that the Qs parameter for Zrx Snz Tiy O4 (ZST) and Ba(Zn1/3 Ta2/3 )O3 (BZT) ceramics showed constancy in the frequency range of 2–12 GHz, which supports the idea of polaron conduction loss contribution to the dielectric loss.
I. INTRODUCTION
The assessment of the microwave dielectric materials by the quality factor or dielectric loss is important to the engineers fabricating dielectric resonators. The origin of the dielectric losses of microwave ceramics is well described by Wersing3 and can be generally categorized by three factors: anharmonic forces which interact with the crystal’s phonon, periodicity defects which lead to quasibonded states, and dipole relaxation of impurities or relaxation of space charge polarization at interfaces. Before proceeding further, it would be worthwhile to refer to the third factor. There would be some dispute on the contribution of this factor because the dipole relaxation and space charge polarization mechanism would be frozen at the microwave frequency as pointed out by Kingery et al.4 Therefore, it is suggested to ignore the third factor, and this is in accordance with many other researchers who consider only the phonon effect.5,6 According to Wersing,3 it is emphasized that the two former mechanisms can be seen as energy transfer from the exciting microwave and the wave vector of zero value to transverse optical phonons. This predicts the linear increase of losses with frequency which is a characteristic for phonon effects. However, the donor type periodicity defects (e.g., oxygen vacancy) ionize to give electrons to the conduction band. This can be envisioned by the band model with dopant level near the conduction band. The electrons in ionic compounds interact with the polar modes of the crystals to form polaron.7 This particle acts as a charge carrier, so it may be possible for polaron to contribute to conduction loss in microwave frequency. It is well known that there are two kinds of polarons: large polaron and small polaron. 500
http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 2
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