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Dielectric properties of pure alumina from 8 GHz to 73 GHz
Journal of the European Ceramic Society 36 (2016) 3355–3361
Contents lists available at www.sciencedirect.com
Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Dielectric properties of pure alumina from 8 GHz to 73 GHz D. Di Marco a , K. Drissi b , N. Delhote b , O. Tantot b , P.-M. Geffroy a,∗ , S. Verdeyme b , T. Chartier a a b
SPCTS UMR7315, CNRS, ENSCI, Université de Limoges, CEC, 12 Rue Atlantis 87068 Limoges, France XLIM UMR 7252, CNRS, Université de Limoges, 123 Avenue Albert Thomas, 87060 Limoges, France
a r t i c l e
i n f o
Article history: Received 30 April 2016 Received in revised form 27 May 2016 Accepted 28 May 2016 Available online 11 June 2016 Keywords: Dielectric properties Pure alumina High frequency Low loss tangent Relative density
a b s t r a c t This paper is focused on the impact of density, average grain size, and impurity content on dielectric properties of pure alumina (<50 ppm) from 8 to 73 GHz. To reach very low loss tangents up to high frequencies a particular attention is given to starting powders impurities, sintered densities and measurement uncertainty. Experimental protocols have also been elaborated to avoid any chemical contamination during the shaping process and to control precisely the sintering step. The dielectric performances and the most influencing factors on dielectric performances of alumina are compared and discussed with data collected in literature. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Alumina is a dielectric ceramic adapted for millimeter-wave applications because of its low r and high Q. The dielectric properties of alumina have already been extensively studied in literature [1–4] in the Ku and Ka bandwidth. Nevertheless, the developments of large internet contents require upgrading satellite broadband by switching on new bands, with higher density of data, such as Q and V bands up to 60 GHz. Regarding to the new development of electronic devices working at such frequencies for commercial applications, data about alumina dielectric in the range 50–60 GHz is very scarce or missing in the literature. Hence, this study suggests the determining of the alumina dielectric properties up to 73 GHz. The dielectric performances and the most influencing factors on dielectric performances of alumina are compared and discussed with data collected in literature [1–4]. 2. Experiments Accordingly with a previous study of [1,2] and confirmed by Ref. [3], the dielectric performances of alumina depend mainly on three factors: impurity contents in starting powder, sintered density and average grain size of sintered alumina. To investigate the
∗ Corresponding author. E-mail address: [email protected] (P.-M. Geffroy). http://dx.doi.org/10.1016/j.jeurceramsoc.2016.05.047 0955-2219/© 2016 Elsevier Ltd. All rights reserved.
impact of those factors onto dielectric performances at 60 GHz, two high purity (<99.9%) alumina powders are selected in this study. The characteristics of two pure alumina powders are reported in Table 1. Alumina suspensions are first dispersed with Darvan C (R.T. Vanderbilt Company, Inc.) by attrition using yttrium-stabilizedzirconia (YTZ) beads (Ø = 0.8 mm) as the grinding media. Then, 2.6%wt. of poly(vinyl alcohol) at 10%wt. in water (Mowiol 18–88, Sigma-Aldrich) and 1.3%wt. of poly(ethylene glycol) (poly(ethylene glycol), average mol. wt. 400, Sigma-Aldrich) are added to the alumina suspensions. Then, the suspensions are atomized using a Büchi B-290 spray dryer. Atomized powders are pressed at 100 MPa to achieve a relative green density of 54%. Pellets are shaped using uniaxial pressing and plates are shaped using isostatic pressing. Pellets have a ratio diameter/thickness of two with 12 mm, 8 mm and 4 mm in diameter corresponding to characterization frequencies of 8 GHz, 13 GHz and 22 GHz respectively by the Dielectric Resonator (DR) method [5,6]. Plates are machining to produce squares of 60 mm with 0.79 mm in thickness for the open cavity method of characterization [7,8] and squares of 20 mm with 0.3 mm in thickness for 60 GHz and 55 GHz/73 GHz characterization, respectively with the SCR method [9–11]. To minimize measurement errors during dielectric characterization all samples are machined after sintering to achieve less than 10 m of geometric tolerance and homogeneous surface states. In order to determine the dielectric properties of our alumina, three resonant methods are used. The first one we used is based on
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Table 1 main characteristics of starting alumina powders in this work. Starting powder
Alumina 1
Alumina 2
Average grain size (m) Main impurities (ppm)
0.1 8 8 10 3
0.3 6 12 10 20
29
48
Total impurities (ppm)
Fe Na Si K
a dielectric resonator (DR) placed on a cylindrical cavity to characterize Alumina pellets between 8 and 22 GHz (Fig. 1a). The characterization method consists in centering a dielectric resonator on a Teflon support, both elements being positioned in the center of a cylindrical metallic cavity. This cavity is excited using coaxial probes terminated by magnetic loops to cover all the resonance frequencies of the dielectric resonator. It uses discrete resonant modes that concentrate energy mainly in the dielectric resonator. The measurement of the frequency resonance and of the quality factor of the whole system that will be useful for the extraction of the DR properties must be done with a low input-output coupling level (|S21 |dB at f0 <–30 dB) to reduce the perturbation of the coaxial probes on the field distribution of the resonant mode. The fundamental TE01␦ mode (cylindrical coordinate) of the dielectric resonator is more specifically used for this characterization method. A numerical model of this device (with a rotational symmetry property) which is based on the Finite Element Method (FEM) in 2D and in free oscillations [5] is used to extract the complex permittivity of the dielectric resonator [6] by matching simulated resonances to those measured. This model takes into account all contributions of losses sources (metallic loss of cavity walls and dielectric loss of the support). A software using those techniques has been developed and a method of root-finding algorithm like Newton-Raphson method has been used to obtain the complex permittivity of the sample and associated uncertainties. The metallic cavity is composed of a cylindrical cavity and two metal ground planes. The cylindrical cavity and the upper ground plane are fixed. A micrometric system varies the position of the lower ground plane on which are placed the support and the dielectric resonator (Fig. 1b) so as to position it very precisely in the center of the cavity. This device permits to reduce the impact of the decentering of the DR. It should be noted that the DR is precisely centered when the measured frequency is minimized. This minimum frequency is thus clearly indicating that the DR is equally spaced to the cavity walls. Regarding the impact of the centering for an Alumina DR with a 8 mm diameter, a decentering of 300 m conducts to a typical error of 0.15% on the determination of the permittivity and few percents for the loss tangent. Before the positioning of the Teflon support and the DR, the cavity exact dimensions are extracted by measuring the resonant frequencies of the TE011 and TE013 modes of the hollow cavity (i.e. no Teflon support nor DR). We can thus accurately determine the
height and diameter of the cavity, these first measurements allowing reducing the uncertainties of the extracted measured complex permittivity due to those geometrical parameters. Then, the measured Q-factor of the TE011 mode is used to extract the effective conductivity of the metallic walls of the cavity. After that, the support is placed in the cavity and the measurement of the pseudo TE011 mode (frequency and Q-factor) allows determining the complex permittivity of the support material. At the end, the TE01␦ resonant mode of the DR, once centered on the Teflon support, is measured to extract the permittivity and the loss tangent of the dielectric resonator material. A second resonant cavity method based on a split cylinder resonator [9–11] is used to measure the permittivity and loss tangent of the complex permittivity r in V-band (55 GHz and 73 GHz). This method allows accurate measurements of dielectric plates without specific preparation of the samples (no need for fine polishing for example). The Fig. 2a shows the cavity used for characterizations. The sample is inserted between the two halves of the cavity excited on the TE01,2q + 1 mode (we use the TE013 for measurements at 55 GHz and TE015 for measurements at 73 GHz). For a given sample, the resonant frequencies depend on the dimensions of the cavity but also the thickness of the sample and its permittivity. The inner diameter of the cavity is about 7.8 mm. For this reason the substrate lateral dimensions must be greater than 7.8 mm with thickness less than 0.4 mm. Thus, the radiation occurring near the 400 m thick slot separating the two parts of the cavity can be considered negligible. Two opposite circular iris permit to couple the cavity to standard WR15 rectangular waveguides. The permittivity and the loss tangent of the material are calculated from the measurements of the resonant frequency and the quality factor of the cavity loaded with the sample. The theoretical frequency of an analytical model of the structure converges to the measured frequency by iteration of the permittivity [9,10]. Relative errors on the permittivity and loss tangent are mainly related to the relative thickness uncertainties of the sample and to the dimensional dispersions of the cavity. For variation of 5% in the thickness we have a typical permittivity dispersion of 5% so it is important to control the manufacturing process in order to have a low fabrication tolerance and then more accuracy during the permittivity extraction. As a consequence, a target manufacturing error of +/−10 m is necessary to maintain the permittivity extraction as low as possible. The third method is a commercial ones (AB MILLIMETRE, model FP-LSC-VEWF) and uses a high-Q hemispherical open resonator (Fig. 2b) for precise and fast determination of permittivity and very low dielectric loss of dielectric materials like those developed in this work [7,8]. Placing the sample on the plane mirror at the bottom of the resonator and measuring the down-shifted resonant frequency and Q factor leads to determine the complex permittivity of the sample at a frequency depending of the thickness and permittivity of the sample between 55 GHz and 110 GHz for this third method. The first method based on the DR is, even if very appreciable because of its accuracy, limited to frequencies below a few tens of GHz (typically 30 GHz). Beyond this frequency, the DR dimensions are too small to easily handle them, to maintain an accurate
Fig. 1. Copper cylindrical cavity for characterization in the 8–22 GHz range (a) and experimental set-up (b).
D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
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Fig. 2. Split cylindrical cavity (SCR) for 55 GHz and 73 GHz characterization (a) and AB Millimetre open cavity (b).
centering in the metallic cavity and to limit dimensions errors. The second method (SCR) is therefore preferable for higher frequencies (>∼30 GHz). The substrates compatible with this method remain easy to handle (lateral dimensions of some tens of millimeters and few hundred microns of thickness) for frequencies up to 100 GHz. However, the quality factor decreasing with the increase of frequency, it becomes appropriate to use the third method (open cavity method) which has a higher quality factor at high frequencies (>55 GHz). This third method is therefore preferable for appropriate accuracy during the characterization above 55 GHz of the low-loss tangent materials developed in this work. The only drawback of this latter method is that it does not allow measurement beyond room temperature due to the tunable cavity height system which is too sensitive to temperature. The first and second methods are however fully compatible with measurement with temperature way above room temperature. As a summary, these three methods were all used during this work to efficiently cover the extraction of the complex permittivity of the low loss materials developed here from 8 to 73 GHz.
Fig. 3. Shrinkage of Alumina and optimal sintering temperature for a heating rate of 20 ◦ C min−1 .
3. Results and discussion 3.1. a. Sintering study of pure alumina powders The thermal shrinkage behavior of the two selected alumina is studied using a dilatometer (Setsys Evolution TMA, Setaram). The optimal sintering temperature in relation with the heating rate is determined from shrinkage tests, as presented in Fig. 3. For a heating rate of 20 ◦ C min−1 , Alumina 1 is fully densified for a sintering temperature of 1650 ◦ C and the same results is reached at 1700 ◦ C for Alumina 2. Fig. 4 shows the sintering temperature with the maximum shrinkage (i.e. maximum density) in relation with the heating rate of sintering cycle and the associated average grain size. Alumina 1 shows lower sintering temperatures to all heating rates due to very small grain size in the starting powder. The optimal density and the smaller average grain size are reached for a heating rate of 5 ◦ C min−1 and a sintering temperature of 1525 ◦ C. The sintering behavior of alumina 1 and 2 are very different due to differences of average grain size, the nature and the contents of impurities in starting powders. The optimal density and grain size for alumina 2 are reached for a heating rate of 20 ◦ C min−1 and a sintering temperature of 1700 ◦ C. To study the impact of grain
Fig. 4. Sintering temperatures to obtain maximum density in relation with the heating rate.
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Table 2 characteristics of sintered alumina samples performed in this work. Sample
Heating rate (◦ C min−1 )
Sintering temperature (◦ C)
Sintering time (min)
Cooling rate (◦ C min−1 )
Grain size (m)
Measured density (cm3 g−1 )
Alumina 1–1 Alumina 1–2 Alumina 1–3 Alumina 1–4 Alumina 2–1
5 5 20 20 20
1450 1525 1650 1650 1700
1 1 1 60 1
5 5 5 5 5
0.9 1.8 3.7 4.8 4.3
3.920 3.999 3.999 3.999 3.999
size, density and impurities in the alumina powders, the alumina powders 1 and 2 have been sintered in the conditions summarized Table 2. Heating rates and temperatures reported are the ones measured on the sample. Accurate samples densities have been measured with a helium pycnometer (Micromeritics AccuPyc II 1340). Samples associated microstructures are displayed Fig. 5. 3.2. b. Impact of average grain size on dielectric properties The impact of average grain size in sintered alumina on dielectric properties has been performed on the sample series, Alumina 1–2, 1–3 and 1–4, at 8 GHz, 13 GHz, 22 GHz, 55 GHz and 60 GHz. Characterizations of Alumina 1–2 and 1–3 have also been performed at 73 GHz to evaluate material behavior at very high frequencies. These three sintering parameters produced grain size on the
final part of 1.8 m, 3.7 m and 4.8 m for the same density of 3.999 cm3 g−1 . Fig. 6 shows that the grain size variation has no to very low effect on the permittivity of pure alumina samples. Indeed, except for the measured performed at 55 GHz and 73 GHz which present lower permittivity due to measurement cavity conditions, there is no significant evolution of the permittivity from 8 GHz to 73 GHz. Values are similar to the literature ones [3,4]. The variation of loss tangent in relation with frequency and average grain size in alumina samples is reported on Fig. 7. Collected results shows no impact of the average grain size variation onto the frequency range tested. 60 GHz results are due to a lower precision of the open cavity for the loss tangent characterization than the one used at 55 GHz and 73 GHz. Those results also confirm the very good performance of Alumina 1 even at very high frequencies with an average loss tangent of 1.70 × 10−4 at 73 GHz. Those results are
Fig. 5. Scanning electron microscopy micrographs of Alumina 1–1 (a), Alumina 1–2 (b), Alumina 1–3 (c), Alumina 1–4 (d) and Alumina 2-1 (e).
D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
Fig. 6. Permittivity of sintered alumina samples in relation with frequency and average grain size.
consistent with a previous study [4] showing no effect of grain size on loss tangent for fully densified ceramics at 14 GHz and extend this conclusion up to 73 GHz. Finally, the impact of average grain size on the temperature coefficient of resonant frequency at 8 GHz has been reported on Fig. 8. This factor is usually related to the composition and so to the phase that exists in the ceramic and translates the variation of a dielectric resonator resonant frequency between two temperatures. That variation is expressed in ppm ◦ C−1 . As we measured a difference of 10 ppm ◦ C−1 between the most distant results, they aim to prove that ceramic grain size has also an impact on the temperature coefficient of resonant frequency. Indeed sample “Alumina 1–4” with a grain size of 4.7 m presents the most negative temperature coefficient with −64 ppm ◦ C−1 compared to samples “Alumina 1–2” and “Alumina 1–3” with respectively −56 ppm ◦ C−1 and −54 ppm ◦ C−1 . It seems therefore that the grain size increase over a limit close to 4 m damage the temperature coefficient of resonant frequency. Those results are close to C.L. Huang results [4] except that measured values are lower and the impact of grain size is much stronger. Ceramic grain size increase above 4 m has therefore a negative impact on temperature coefficient of resonant frequency. Under this limit no impact of grain size has been detected. Alumina grain size has therefore a limited impact onto dielectric performances. Collected data demonstrate no impact of grain size on permittivity or loss tangent up to 73 GHz. The only modification has been noticed on the temperature coefficient of resonant frequency for largest grain size with a negative increase of this
Fig. 7. Loss tangent of sintered alumina samples in relation with frequency and average grain size.
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Fig. 8. Temperature coefficient of resonant frequency of sintered alumina samples in relation with average grain size at 8 GHz.
factor. As a result to maximize alumina dielectric performances, the smallest grain size should be targeted. 3.3. c. Impact of density on alumina dielectric properties The impact of density on dielectric properties has been performed onto Alumina 1 samples. “Alumina 1–1” has been sintered at lower temperature to reach 3.920 cm3 g−1 and compare to “Alumina 1–2” a fully densify sample with 3.999 cm3 g−1 . Fig. 9 shows the impact of the density on permittivity at 8 GHz, 13 GHz and 22 GHz. Measured values of both samples are very close on all frequencies. For densities above 3.92 cm3 g−1 (i.e. ≥98%) alumina density has therefore no impact on permittivity. Results reported in this work also confirm values and behavior previously reported for high purity alumina [3,4]. Fig. 10 shows the impact of sintered alumina density on the loss tangent. Sample “Alumina1-1” with the lowest density shows almost stable loss tangent to all frequencies. Fully densified sample “Alumina 1–2” reached better loss tangent on the frequency range but also a significant increase of this last parameter when frequency increase. This important result demonstrates that the alumina density becomes less important towards loss tangent with the increase of the characterization frequency. Results found in bibliography [1,4] are not directly comparable with ours. We also studied the impact of density on the temperature coefficient of resonant frequency at 8 GHz. We measured a f of −59 ppm ◦ C−1 for Alumina 1–1 and −56 ppm ◦ C−1 for Alumina 1–2.
Fig. 9. Permittivity of sintered alumina sample in relation with frequency and density (d = 3920 corresponding to the sample “Alumina 1-1”, and d = 3999 corresponding to the sample “Alumina 1–2”).
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Fig. 10. Loss tangent of sintered alumina sample in relation with frequency and density (d = 3920 corresponding to the sample “Alumina 1–1”, and d = 3999 corresponding to the sample “Alumina 1–2”).
The measured difference is included in the measurement error of 5%. Therefore the density has no impact on the temperature coefficient of resonant frequency. Alumina density impact on loss tangent is consequently strongly linked to the frequency and this impact decreasing with the increase of the frequency. The temperature coefficient of resonant frequency is not impacted by these factors. 3.4. d. Impact of starting powder purity on alumina dielectric properties The study of the starting powder purity impact on dielectric properties has been performed on the samples “Alumina 1–3” and “Alumina 2-1” at 8 GHz, 13 GHz, 22 GHz and 60 GHz. The impurity contents in the sample “Alumina 2-1” are slightly higher than those in the sample “Alumina 1–3”, in particular for potassium content, 20 ppm and 3 ppm respectively. Fig. 11 shows that there is no impact of impurities (for this content of impurities <50 ppm) on the permittivity of sintered alumina. In opposite, Fig. 12 shows that the impurities could affect strongly the loss tangent. For low frequencies (8 GHz–22 GHz), the loss tangent of the samples “Alumina 1–3” and “Alumina 2-1” are similar, and there is not impact of impurities on the loss tangent. However at 60 GHz, there is almost a decade between the two samples in favor of “Alumina 1–3” which present the lowest content of
Fig. 12. Loss tangent of sintered alumina sample in relation with the frequency and the impurity content, 29 ppm of impurities corresponding to the sample “Alumina 1–3”, 48 ppm of impurities corresponding to the sample “Alumina 2-1”.
impurities. So, the impact of impurity content on loss tangent is sensible only at high frequency (at 60 GHz). The temperature coefficient of resonant frequency at 8 GHz was measured at −54 ppm ◦ C−1 for Alumina 1–3 and −57 ppm ◦ C−1 for Alumina 2-1. As the measurement uncertainty is of 5% and so higher than the gap between those two points, it is possible to conclude that starting powder purity doesn’t impact the temperature coefficient of resonant frequency. Starting powder purity impact exclusively the loss tangent of alumina materials in the studied impurities range. This impact appears above 40 GHz and increases with the frequency. So for very high frequency applications, the starting powder purity plays a key role on dielectric performances. Study shows no effect of this factor on permittivity up to 60 GHz or on the temperature coefficient of resonant frequency at 8 GHz. The impact of impurities on dielectric loss of alumina has been confirmed by previous works. For instance, the chemical contaminations of starting powder due to the use of binders in conventional ceramic processes leads likely to increase dielectric loss [12]. Grain boundaries in polycrystalline microwave dielectric ceramics have long been suspected of increasing dielectric loss. However, Alford et al. show recently that grain boundaries is problematic to quantify in practice and their influence on dielectric loss [13,14], as suggested in this work. 4. Conclusion This work highlights the role of grain size, density and impurities in starting powders on alumina dielectric properties as a function of the frequency. Two cases appear depending on the characterization frequency. For low frequencies under 25 GHz, density is the most important factor when looking for low loss tangent. Indeed the sample density impacts strongly the loss tangent. Results also show that permittivity is not impacted on this frequency range by any of the studied factors. The temperature coefficient of resonant frequency is impacted by sintered grain size above 4 m. The order of importance of the factors studied for the range 1 GHz to 25 GHz is so the following: 1. Density of the sintered alumina, 2. Average grain size in the sintered alumina, 3. Content of impurities in starting powder and sintered alumina.
Fig. 11. Permittivity of two sintered alumina samples with similar density and average grain size, 29 ppm of impurities corresponding to the sample “Alumina 1–3”, 48 ppm of impurities corresponding to the sample “Alumina 2-1”.
For frequencies above 25 GHz and up to 73 GHz, the content of impurities in starting powder and sintered alumina density are the
D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
most important factors. As density results at 60 GHz are missing it is pretty hard to establish an order of importance of the three factors. No impact of those factors on permittivity has been established. Despite this lack of data we decided to set the factors studied in the following order for their impact on loss tangent: 1. Content of impurities in starting powder and sintered alumina, 2. Density of the sintered alumina, 3. Average grain size in the sintered alumina. Beyond those sorting, the study reveals the extreme sensitivity of pure alumina to impurities. Results show strong differences with impurity content difference of only 20 ppm and even with a same impurity composition. As the full sintering of pure alumina powders is easily achievable, the main issue is here to avoid any chemical contamination even a few ppm during the powder preparation and shaping process. So we note that the most important factor to obtain the best dielectric properties is the impurity content in the sintered alumina whatever the frequency is. Reaching the highest possible density is also a required result to get the full benefit of very low loss ceramic materiel up to 73 GHz and above. Acknowledgement This work was supported by the French National Agency for Research (Agence Nationale pour la Recherche, ANR) in the form of the ATOMIQ (advanced technologies for integrated millimetric filtering solutions in Q and V bands) project. References [1] S.J. Penn, N.M. Alford, A. Templeton, X. Wang, M. Xu, M. Reece, K. Schrapel, Effect of porosity and grain size on the microwave dielectric properties of sintered alumina, J. Am. Ceram. Soc. 80 (7) (1997) 1885–1888.
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[2] N.M. Alford, S.J. Penn, Sintered alumina with low dielectric loss, J. Appl. Phys. 80 (10) (1996) 5895–5898. [3] C.-L. Huang, J.-J. Wang, F.-S. Yen, C.-Y. Huang, Microwave dielectric properties and sintering behavior of nano-scaled (␣ + )-Al2 O3 ceramics, Mater. Res. Bull. 43 (6) (2008) 1463–1471. [4] C.-L. Huang, J.-J. Wang, C.-Y. Huang, Sintering behavior and microwave dielectric properties of nano alpha-alumina, Mater. Lett. 59 (28) (2005) 3746–3749. [5] M. Aubourg, P. Guillon, A mixed finite element formulation for microwave device problems: application to MIS structure, J. Electromagn. Waves Appl. 5 (4–5) (1991) 371–386. [6] J. Krupka, P. Blondy, D. Cros, P. Guillon, R.G. Geyer, Whispering-gallery modes and permeability tensor magnetized in ferrite resonators, IEEE Trans. Microw. Theory Tech. 44 (7) (1996) 1097–1102. [7] T.M. Hirvonen, P. Vainikainen, A. Lozowski, A.V. Raisanen, Measurement of dielectrics at 100 GHz with an open resonator connected to a network analyzer, IEEE Trans. Instrum. Meas. 45 (4) (1996) 773–779. [8] P. Goy, M. Gross, S. Caroopen, J. Mallat, J. Tuovinen, A. Maestrini, G. Annino, M. Fittipaldi, M. Martinelli, Millimeter-submillimeter measurements in free space, and in resonant structures. Application to dielectrics characterization, in: Material Research Society Spring Meeting, Symposium AA, Millimeter-submillimeter Wave Technology, Materials, Devices, and Diagnostics, San Francisco, USA, April, 2000, 2000. [9] P. Guillon, Y. Garault, Complex permittivity of MIC substrate, AEU Band 35, Heft 3 (1981) 102–104. [10] M.D. Janezic, J. Baker-Jarvis, Full-wave analysis of a split-cylinder resonator for nondestructive permittivity measurements, IEEE Trans. Microw. Theory Tech. 47 (10) (1999) 2014–2020. [11] J. Ramal, O. Tantot, D. Passerieux, N. Delhote, S. Verdeyme, Monitoring of electromagnetic characteristics of split cylinder resonator and dielectric material for temperature characterization, in: European Microwave Conference, Rome, Italy October, 2014, 2014. [12] N.M. Alford, A. Wang, S.J. Penn, M. Poole, A. Jones, Effect of ceramic binders on microwave dielectric loss of alumina, Br. Ceram. Trans. 99 (2000) 212–214. [13] J.D. Breeze, X. Aupi, N.M. Alford, Ultralow loss polycrystalline alumina, Appl. Phys. Lett. 81 (2002) 5021–5023. [14] J.D. Breeze, J.M. Perkins, D.W. McComb, N.M. Alford, Do grain boundaries affect microwave dielectric loss in oxides? J. Am. Ceram. Soc. 92 (2009) 671–674.
Contents lists available at www.sciencedirect.com
Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Dielectric properties of pure alumina from 8 GHz to 73 GHz D. Di Marco a , K. Drissi b , N. Delhote b , O. Tantot b , P.-M. Geffroy a,∗ , S. Verdeyme b , T. Chartier a a b
SPCTS UMR7315, CNRS, ENSCI, Université de Limoges, CEC, 12 Rue Atlantis 87068 Limoges, France XLIM UMR 7252, CNRS, Université de Limoges, 123 Avenue Albert Thomas, 87060 Limoges, France
a r t i c l e
i n f o
Article history: Received 30 April 2016 Received in revised form 27 May 2016 Accepted 28 May 2016 Available online 11 June 2016 Keywords: Dielectric properties Pure alumina High frequency Low loss tangent Relative density
a b s t r a c t This paper is focused on the impact of density, average grain size, and impurity content on dielectric properties of pure alumina (<50 ppm) from 8 to 73 GHz. To reach very low loss tangents up to high frequencies a particular attention is given to starting powders impurities, sintered densities and measurement uncertainty. Experimental protocols have also been elaborated to avoid any chemical contamination during the shaping process and to control precisely the sintering step. The dielectric performances and the most influencing factors on dielectric performances of alumina are compared and discussed with data collected in literature. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Alumina is a dielectric ceramic adapted for millimeter-wave applications because of its low r and high Q. The dielectric properties of alumina have already been extensively studied in literature [1–4] in the Ku and Ka bandwidth. Nevertheless, the developments of large internet contents require upgrading satellite broadband by switching on new bands, with higher density of data, such as Q and V bands up to 60 GHz. Regarding to the new development of electronic devices working at such frequencies for commercial applications, data about alumina dielectric in the range 50–60 GHz is very scarce or missing in the literature. Hence, this study suggests the determining of the alumina dielectric properties up to 73 GHz. The dielectric performances and the most influencing factors on dielectric performances of alumina are compared and discussed with data collected in literature [1–4]. 2. Experiments Accordingly with a previous study of [1,2] and confirmed by Ref. [3], the dielectric performances of alumina depend mainly on three factors: impurity contents in starting powder, sintered density and average grain size of sintered alumina. To investigate the
∗ Corresponding author. E-mail address: [email protected] (P.-M. Geffroy). http://dx.doi.org/10.1016/j.jeurceramsoc.2016.05.047 0955-2219/© 2016 Elsevier Ltd. All rights reserved.
impact of those factors onto dielectric performances at 60 GHz, two high purity (<99.9%) alumina powders are selected in this study. The characteristics of two pure alumina powders are reported in Table 1. Alumina suspensions are first dispersed with Darvan C (R.T. Vanderbilt Company, Inc.) by attrition using yttrium-stabilizedzirconia (YTZ) beads (Ø = 0.8 mm) as the grinding media. Then, 2.6%wt. of poly(vinyl alcohol) at 10%wt. in water (Mowiol 18–88, Sigma-Aldrich) and 1.3%wt. of poly(ethylene glycol) (poly(ethylene glycol), average mol. wt. 400, Sigma-Aldrich) are added to the alumina suspensions. Then, the suspensions are atomized using a Büchi B-290 spray dryer. Atomized powders are pressed at 100 MPa to achieve a relative green density of 54%. Pellets are shaped using uniaxial pressing and plates are shaped using isostatic pressing. Pellets have a ratio diameter/thickness of two with 12 mm, 8 mm and 4 mm in diameter corresponding to characterization frequencies of 8 GHz, 13 GHz and 22 GHz respectively by the Dielectric Resonator (DR) method [5,6]. Plates are machining to produce squares of 60 mm with 0.79 mm in thickness for the open cavity method of characterization [7,8] and squares of 20 mm with 0.3 mm in thickness for 60 GHz and 55 GHz/73 GHz characterization, respectively with the SCR method [9–11]. To minimize measurement errors during dielectric characterization all samples are machined after sintering to achieve less than 10 m of geometric tolerance and homogeneous surface states. In order to determine the dielectric properties of our alumina, three resonant methods are used. The first one we used is based on
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D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
Table 1 main characteristics of starting alumina powders in this work. Starting powder
Alumina 1
Alumina 2
Average grain size (m) Main impurities (ppm)
0.1 8 8 10 3
0.3 6 12 10 20
29
48
Total impurities (ppm)
Fe Na Si K
a dielectric resonator (DR) placed on a cylindrical cavity to characterize Alumina pellets between 8 and 22 GHz (Fig. 1a). The characterization method consists in centering a dielectric resonator on a Teflon support, both elements being positioned in the center of a cylindrical metallic cavity. This cavity is excited using coaxial probes terminated by magnetic loops to cover all the resonance frequencies of the dielectric resonator. It uses discrete resonant modes that concentrate energy mainly in the dielectric resonator. The measurement of the frequency resonance and of the quality factor of the whole system that will be useful for the extraction of the DR properties must be done with a low input-output coupling level (|S21 |dB at f0 <–30 dB) to reduce the perturbation of the coaxial probes on the field distribution of the resonant mode. The fundamental TE01␦ mode (cylindrical coordinate) of the dielectric resonator is more specifically used for this characterization method. A numerical model of this device (with a rotational symmetry property) which is based on the Finite Element Method (FEM) in 2D and in free oscillations [5] is used to extract the complex permittivity of the dielectric resonator [6] by matching simulated resonances to those measured. This model takes into account all contributions of losses sources (metallic loss of cavity walls and dielectric loss of the support). A software using those techniques has been developed and a method of root-finding algorithm like Newton-Raphson method has been used to obtain the complex permittivity of the sample and associated uncertainties. The metallic cavity is composed of a cylindrical cavity and two metal ground planes. The cylindrical cavity and the upper ground plane are fixed. A micrometric system varies the position of the lower ground plane on which are placed the support and the dielectric resonator (Fig. 1b) so as to position it very precisely in the center of the cavity. This device permits to reduce the impact of the decentering of the DR. It should be noted that the DR is precisely centered when the measured frequency is minimized. This minimum frequency is thus clearly indicating that the DR is equally spaced to the cavity walls. Regarding the impact of the centering for an Alumina DR with a 8 mm diameter, a decentering of 300 m conducts to a typical error of 0.15% on the determination of the permittivity and few percents for the loss tangent. Before the positioning of the Teflon support and the DR, the cavity exact dimensions are extracted by measuring the resonant frequencies of the TE011 and TE013 modes of the hollow cavity (i.e. no Teflon support nor DR). We can thus accurately determine the
height and diameter of the cavity, these first measurements allowing reducing the uncertainties of the extracted measured complex permittivity due to those geometrical parameters. Then, the measured Q-factor of the TE011 mode is used to extract the effective conductivity of the metallic walls of the cavity. After that, the support is placed in the cavity and the measurement of the pseudo TE011 mode (frequency and Q-factor) allows determining the complex permittivity of the support material. At the end, the TE01␦ resonant mode of the DR, once centered on the Teflon support, is measured to extract the permittivity and the loss tangent of the dielectric resonator material. A second resonant cavity method based on a split cylinder resonator [9–11] is used to measure the permittivity and loss tangent of the complex permittivity r in V-band (55 GHz and 73 GHz). This method allows accurate measurements of dielectric plates without specific preparation of the samples (no need for fine polishing for example). The Fig. 2a shows the cavity used for characterizations. The sample is inserted between the two halves of the cavity excited on the TE01,2q + 1 mode (we use the TE013 for measurements at 55 GHz and TE015 for measurements at 73 GHz). For a given sample, the resonant frequencies depend on the dimensions of the cavity but also the thickness of the sample and its permittivity. The inner diameter of the cavity is about 7.8 mm. For this reason the substrate lateral dimensions must be greater than 7.8 mm with thickness less than 0.4 mm. Thus, the radiation occurring near the 400 m thick slot separating the two parts of the cavity can be considered negligible. Two opposite circular iris permit to couple the cavity to standard WR15 rectangular waveguides. The permittivity and the loss tangent of the material are calculated from the measurements of the resonant frequency and the quality factor of the cavity loaded with the sample. The theoretical frequency of an analytical model of the structure converges to the measured frequency by iteration of the permittivity [9,10]. Relative errors on the permittivity and loss tangent are mainly related to the relative thickness uncertainties of the sample and to the dimensional dispersions of the cavity. For variation of 5% in the thickness we have a typical permittivity dispersion of 5% so it is important to control the manufacturing process in order to have a low fabrication tolerance and then more accuracy during the permittivity extraction. As a consequence, a target manufacturing error of +/−10 m is necessary to maintain the permittivity extraction as low as possible. The third method is a commercial ones (AB MILLIMETRE, model FP-LSC-VEWF) and uses a high-Q hemispherical open resonator (Fig. 2b) for precise and fast determination of permittivity and very low dielectric loss of dielectric materials like those developed in this work [7,8]. Placing the sample on the plane mirror at the bottom of the resonator and measuring the down-shifted resonant frequency and Q factor leads to determine the complex permittivity of the sample at a frequency depending of the thickness and permittivity of the sample between 55 GHz and 110 GHz for this third method. The first method based on the DR is, even if very appreciable because of its accuracy, limited to frequencies below a few tens of GHz (typically 30 GHz). Beyond this frequency, the DR dimensions are too small to easily handle them, to maintain an accurate
Fig. 1. Copper cylindrical cavity for characterization in the 8–22 GHz range (a) and experimental set-up (b).
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Fig. 2. Split cylindrical cavity (SCR) for 55 GHz and 73 GHz characterization (a) and AB Millimetre open cavity (b).
centering in the metallic cavity and to limit dimensions errors. The second method (SCR) is therefore preferable for higher frequencies (>∼30 GHz). The substrates compatible with this method remain easy to handle (lateral dimensions of some tens of millimeters and few hundred microns of thickness) for frequencies up to 100 GHz. However, the quality factor decreasing with the increase of frequency, it becomes appropriate to use the third method (open cavity method) which has a higher quality factor at high frequencies (>55 GHz). This third method is therefore preferable for appropriate accuracy during the characterization above 55 GHz of the low-loss tangent materials developed in this work. The only drawback of this latter method is that it does not allow measurement beyond room temperature due to the tunable cavity height system which is too sensitive to temperature. The first and second methods are however fully compatible with measurement with temperature way above room temperature. As a summary, these three methods were all used during this work to efficiently cover the extraction of the complex permittivity of the low loss materials developed here from 8 to 73 GHz.
Fig. 3. Shrinkage of Alumina and optimal sintering temperature for a heating rate of 20 ◦ C min−1 .
3. Results and discussion 3.1. a. Sintering study of pure alumina powders The thermal shrinkage behavior of the two selected alumina is studied using a dilatometer (Setsys Evolution TMA, Setaram). The optimal sintering temperature in relation with the heating rate is determined from shrinkage tests, as presented in Fig. 3. For a heating rate of 20 ◦ C min−1 , Alumina 1 is fully densified for a sintering temperature of 1650 ◦ C and the same results is reached at 1700 ◦ C for Alumina 2. Fig. 4 shows the sintering temperature with the maximum shrinkage (i.e. maximum density) in relation with the heating rate of sintering cycle and the associated average grain size. Alumina 1 shows lower sintering temperatures to all heating rates due to very small grain size in the starting powder. The optimal density and the smaller average grain size are reached for a heating rate of 5 ◦ C min−1 and a sintering temperature of 1525 ◦ C. The sintering behavior of alumina 1 and 2 are very different due to differences of average grain size, the nature and the contents of impurities in starting powders. The optimal density and grain size for alumina 2 are reached for a heating rate of 20 ◦ C min−1 and a sintering temperature of 1700 ◦ C. To study the impact of grain
Fig. 4. Sintering temperatures to obtain maximum density in relation with the heating rate.
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Table 2 characteristics of sintered alumina samples performed in this work. Sample
Heating rate (◦ C min−1 )
Sintering temperature (◦ C)
Sintering time (min)
Cooling rate (◦ C min−1 )
Grain size (m)
Measured density (cm3 g−1 )
Alumina 1–1 Alumina 1–2 Alumina 1–3 Alumina 1–4 Alumina 2–1
5 5 20 20 20
1450 1525 1650 1650 1700
1 1 1 60 1
5 5 5 5 5
0.9 1.8 3.7 4.8 4.3
3.920 3.999 3.999 3.999 3.999
size, density and impurities in the alumina powders, the alumina powders 1 and 2 have been sintered in the conditions summarized Table 2. Heating rates and temperatures reported are the ones measured on the sample. Accurate samples densities have been measured with a helium pycnometer (Micromeritics AccuPyc II 1340). Samples associated microstructures are displayed Fig. 5. 3.2. b. Impact of average grain size on dielectric properties The impact of average grain size in sintered alumina on dielectric properties has been performed on the sample series, Alumina 1–2, 1–3 and 1–4, at 8 GHz, 13 GHz, 22 GHz, 55 GHz and 60 GHz. Characterizations of Alumina 1–2 and 1–3 have also been performed at 73 GHz to evaluate material behavior at very high frequencies. These three sintering parameters produced grain size on the
final part of 1.8 m, 3.7 m and 4.8 m for the same density of 3.999 cm3 g−1 . Fig. 6 shows that the grain size variation has no to very low effect on the permittivity of pure alumina samples. Indeed, except for the measured performed at 55 GHz and 73 GHz which present lower permittivity due to measurement cavity conditions, there is no significant evolution of the permittivity from 8 GHz to 73 GHz. Values are similar to the literature ones [3,4]. The variation of loss tangent in relation with frequency and average grain size in alumina samples is reported on Fig. 7. Collected results shows no impact of the average grain size variation onto the frequency range tested. 60 GHz results are due to a lower precision of the open cavity for the loss tangent characterization than the one used at 55 GHz and 73 GHz. Those results also confirm the very good performance of Alumina 1 even at very high frequencies with an average loss tangent of 1.70 × 10−4 at 73 GHz. Those results are
Fig. 5. Scanning electron microscopy micrographs of Alumina 1–1 (a), Alumina 1–2 (b), Alumina 1–3 (c), Alumina 1–4 (d) and Alumina 2-1 (e).
D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
Fig. 6. Permittivity of sintered alumina samples in relation with frequency and average grain size.
consistent with a previous study [4] showing no effect of grain size on loss tangent for fully densified ceramics at 14 GHz and extend this conclusion up to 73 GHz. Finally, the impact of average grain size on the temperature coefficient of resonant frequency at 8 GHz has been reported on Fig. 8. This factor is usually related to the composition and so to the phase that exists in the ceramic and translates the variation of a dielectric resonator resonant frequency between two temperatures. That variation is expressed in ppm ◦ C−1 . As we measured a difference of 10 ppm ◦ C−1 between the most distant results, they aim to prove that ceramic grain size has also an impact on the temperature coefficient of resonant frequency. Indeed sample “Alumina 1–4” with a grain size of 4.7 m presents the most negative temperature coefficient with −64 ppm ◦ C−1 compared to samples “Alumina 1–2” and “Alumina 1–3” with respectively −56 ppm ◦ C−1 and −54 ppm ◦ C−1 . It seems therefore that the grain size increase over a limit close to 4 m damage the temperature coefficient of resonant frequency. Those results are close to C.L. Huang results [4] except that measured values are lower and the impact of grain size is much stronger. Ceramic grain size increase above 4 m has therefore a negative impact on temperature coefficient of resonant frequency. Under this limit no impact of grain size has been detected. Alumina grain size has therefore a limited impact onto dielectric performances. Collected data demonstrate no impact of grain size on permittivity or loss tangent up to 73 GHz. The only modification has been noticed on the temperature coefficient of resonant frequency for largest grain size with a negative increase of this
Fig. 7. Loss tangent of sintered alumina samples in relation with frequency and average grain size.
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Fig. 8. Temperature coefficient of resonant frequency of sintered alumina samples in relation with average grain size at 8 GHz.
factor. As a result to maximize alumina dielectric performances, the smallest grain size should be targeted. 3.3. c. Impact of density on alumina dielectric properties The impact of density on dielectric properties has been performed onto Alumina 1 samples. “Alumina 1–1” has been sintered at lower temperature to reach 3.920 cm3 g−1 and compare to “Alumina 1–2” a fully densify sample with 3.999 cm3 g−1 . Fig. 9 shows the impact of the density on permittivity at 8 GHz, 13 GHz and 22 GHz. Measured values of both samples are very close on all frequencies. For densities above 3.92 cm3 g−1 (i.e. ≥98%) alumina density has therefore no impact on permittivity. Results reported in this work also confirm values and behavior previously reported for high purity alumina [3,4]. Fig. 10 shows the impact of sintered alumina density on the loss tangent. Sample “Alumina1-1” with the lowest density shows almost stable loss tangent to all frequencies. Fully densified sample “Alumina 1–2” reached better loss tangent on the frequency range but also a significant increase of this last parameter when frequency increase. This important result demonstrates that the alumina density becomes less important towards loss tangent with the increase of the characterization frequency. Results found in bibliography [1,4] are not directly comparable with ours. We also studied the impact of density on the temperature coefficient of resonant frequency at 8 GHz. We measured a f of −59 ppm ◦ C−1 for Alumina 1–1 and −56 ppm ◦ C−1 for Alumina 1–2.
Fig. 9. Permittivity of sintered alumina sample in relation with frequency and density (d = 3920 corresponding to the sample “Alumina 1-1”, and d = 3999 corresponding to the sample “Alumina 1–2”).
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Fig. 10. Loss tangent of sintered alumina sample in relation with frequency and density (d = 3920 corresponding to the sample “Alumina 1–1”, and d = 3999 corresponding to the sample “Alumina 1–2”).
The measured difference is included in the measurement error of 5%. Therefore the density has no impact on the temperature coefficient of resonant frequency. Alumina density impact on loss tangent is consequently strongly linked to the frequency and this impact decreasing with the increase of the frequency. The temperature coefficient of resonant frequency is not impacted by these factors. 3.4. d. Impact of starting powder purity on alumina dielectric properties The study of the starting powder purity impact on dielectric properties has been performed on the samples “Alumina 1–3” and “Alumina 2-1” at 8 GHz, 13 GHz, 22 GHz and 60 GHz. The impurity contents in the sample “Alumina 2-1” are slightly higher than those in the sample “Alumina 1–3”, in particular for potassium content, 20 ppm and 3 ppm respectively. Fig. 11 shows that there is no impact of impurities (for this content of impurities <50 ppm) on the permittivity of sintered alumina. In opposite, Fig. 12 shows that the impurities could affect strongly the loss tangent. For low frequencies (8 GHz–22 GHz), the loss tangent of the samples “Alumina 1–3” and “Alumina 2-1” are similar, and there is not impact of impurities on the loss tangent. However at 60 GHz, there is almost a decade between the two samples in favor of “Alumina 1–3” which present the lowest content of
Fig. 12. Loss tangent of sintered alumina sample in relation with the frequency and the impurity content, 29 ppm of impurities corresponding to the sample “Alumina 1–3”, 48 ppm of impurities corresponding to the sample “Alumina 2-1”.
impurities. So, the impact of impurity content on loss tangent is sensible only at high frequency (at 60 GHz). The temperature coefficient of resonant frequency at 8 GHz was measured at −54 ppm ◦ C−1 for Alumina 1–3 and −57 ppm ◦ C−1 for Alumina 2-1. As the measurement uncertainty is of 5% and so higher than the gap between those two points, it is possible to conclude that starting powder purity doesn’t impact the temperature coefficient of resonant frequency. Starting powder purity impact exclusively the loss tangent of alumina materials in the studied impurities range. This impact appears above 40 GHz and increases with the frequency. So for very high frequency applications, the starting powder purity plays a key role on dielectric performances. Study shows no effect of this factor on permittivity up to 60 GHz or on the temperature coefficient of resonant frequency at 8 GHz. The impact of impurities on dielectric loss of alumina has been confirmed by previous works. For instance, the chemical contaminations of starting powder due to the use of binders in conventional ceramic processes leads likely to increase dielectric loss [12]. Grain boundaries in polycrystalline microwave dielectric ceramics have long been suspected of increasing dielectric loss. However, Alford et al. show recently that grain boundaries is problematic to quantify in practice and their influence on dielectric loss [13,14], as suggested in this work. 4. Conclusion This work highlights the role of grain size, density and impurities in starting powders on alumina dielectric properties as a function of the frequency. Two cases appear depending on the characterization frequency. For low frequencies under 25 GHz, density is the most important factor when looking for low loss tangent. Indeed the sample density impacts strongly the loss tangent. Results also show that permittivity is not impacted on this frequency range by any of the studied factors. The temperature coefficient of resonant frequency is impacted by sintered grain size above 4 m. The order of importance of the factors studied for the range 1 GHz to 25 GHz is so the following: 1. Density of the sintered alumina, 2. Average grain size in the sintered alumina, 3. Content of impurities in starting powder and sintered alumina.
Fig. 11. Permittivity of two sintered alumina samples with similar density and average grain size, 29 ppm of impurities corresponding to the sample “Alumina 1–3”, 48 ppm of impurities corresponding to the sample “Alumina 2-1”.
For frequencies above 25 GHz and up to 73 GHz, the content of impurities in starting powder and sintered alumina density are the
D.D. Marco et al. / Journal of the European Ceramic Society 36 (2016) 3355–3361
most important factors. As density results at 60 GHz are missing it is pretty hard to establish an order of importance of the three factors. No impact of those factors on permittivity has been established. Despite this lack of data we decided to set the factors studied in the following order for their impact on loss tangent: 1. Content of impurities in starting powder and sintered alumina, 2. Density of the sintered alumina, 3. Average grain size in the sintered alumina. Beyond those sorting, the study reveals the extreme sensitivity of pure alumina to impurities. Results show strong differences with impurity content difference of only 20 ppm and even with a same impurity composition. As the full sintering of pure alumina powders is easily achievable, the main issue is here to avoid any chemical contamination even a few ppm during the powder preparation and shaping process. So we note that the most important factor to obtain the best dielectric properties is the impurity content in the sintered alumina whatever the frequency is. Reaching the highest possible density is also a required result to get the full benefit of very low loss ceramic materiel up to 73 GHz and above. Acknowledgement This work was supported by the French National Agency for Research (Agence Nationale pour la Recherche, ANR) in the form of the ATOMIQ (advanced technologies for integrated millimetric filtering solutions in Q and V bands) project. References [1] S.J. Penn, N.M. Alford, A. Templeton, X. Wang, M. Xu, M. Reece, K. Schrapel, Effect of porosity and grain size on the microwave dielectric properties of sintered alumina, J. Am. Ceram. Soc. 80 (7) (1997) 1885–1888.
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[2] N.M. Alford, S.J. Penn, Sintered alumina with low dielectric loss, J. Appl. Phys. 80 (10) (1996) 5895–5898. [3] C.-L. Huang, J.-J. Wang, F.-S. Yen, C.-Y. Huang, Microwave dielectric properties and sintering behavior of nano-scaled (␣ + )-Al2 O3 ceramics, Mater. Res. Bull. 43 (6) (2008) 1463–1471. [4] C.-L. Huang, J.-J. Wang, C.-Y. Huang, Sintering behavior and microwave dielectric properties of nano alpha-alumina, Mater. Lett. 59 (28) (2005) 3746–3749. [5] M. Aubourg, P. Guillon, A mixed finite element formulation for microwave device problems: application to MIS structure, J. Electromagn. Waves Appl. 5 (4–5) (1991) 371–386. [6] J. Krupka, P. Blondy, D. Cros, P. Guillon, R.G. Geyer, Whispering-gallery modes and permeability tensor magnetized in ferrite resonators, IEEE Trans. Microw. Theory Tech. 44 (7) (1996) 1097–1102. [7] T.M. Hirvonen, P. Vainikainen, A. Lozowski, A.V. Raisanen, Measurement of dielectrics at 100 GHz with an open resonator connected to a network analyzer, IEEE Trans. Instrum. Meas. 45 (4) (1996) 773–779. [8] P. Goy, M. Gross, S. Caroopen, J. Mallat, J. Tuovinen, A. Maestrini, G. Annino, M. Fittipaldi, M. Martinelli, Millimeter-submillimeter measurements in free space, and in resonant structures. Application to dielectrics characterization, in: Material Research Society Spring Meeting, Symposium AA, Millimeter-submillimeter Wave Technology, Materials, Devices, and Diagnostics, San Francisco, USA, April, 2000, 2000. [9] P. Guillon, Y. Garault, Complex permittivity of MIC substrate, AEU Band 35, Heft 3 (1981) 102–104. [10] M.D. Janezic, J. Baker-Jarvis, Full-wave analysis of a split-cylinder resonator for nondestructive permittivity measurements, IEEE Trans. Microw. Theory Tech. 47 (10) (1999) 2014–2020. [11] J. Ramal, O. Tantot, D. Passerieux, N. Delhote, S. Verdeyme, Monitoring of electromagnetic characteristics of split cylinder resonator and dielectric material for temperature characterization, in: European Microwave Conference, Rome, Italy October, 2014, 2014. [12] N.M. Alford, A. Wang, S.J. Penn, M. Poole, A. Jones, Effect of ceramic binders on microwave dielectric loss of alumina, Br. Ceram. Trans. 99 (2000) 212–214. [13] J.D. Breeze, X. Aupi, N.M. Alford, Ultralow loss polycrystalline alumina, Appl. Phys. Lett. 81 (2002) 5021–5023. [14] J.D. Breeze, J.M. Perkins, D.W. McComb, N.M. Alford, Do grain boundaries affect microwave dielectric loss in oxides? J. Am. Ceram. Soc. 92 (2009) 671–674.