摘 要

本研究以Ba2Ti9O20微波介電陶瓷材料及其在二維電磁晶體薄板元件的應用為主要研究內容。首先將分別配製type A（2BaTiO3+7TiO2）及type B（BaTi4O9+BaTi5O11）兩種不同之奈米混合粉末，再藉由不同球磨方法與不同反應燒結製程，來進行Ba2Ti9O20微波介電陶瓷材料的開發，有系統地深入探討製程參數、顯微組織結構以及結構與性能相互關係等一系列基礎及技術問題。此外，實際製作出二維Ba2Ti9O20正方晶格及三角晶格的電磁晶體薄板元件，除將量測之能隙位置與理論計算結果進行比較外，同時亦探討二維Ba2Ti9O20電磁晶體薄板元件之設計參數、製程參數、微波介電性質等對其實際能隙的影響。
□利用氮化矽高能量球磨製程（Si3N4 -HeM）可以很有效率的粉碎Ba2Ti9O20材料，提高其活性及緻密化效率。但是會引入SiO2污染，因此嚴重降低Ba2Ti9O20材料之Qxf值。以氧化鋯高能量球磨製程(ZrO2-HeM)處理後之Ba2Ti9O20材料，可有效地抑制SiO2雜質的污染及二次相的生成，因此會比經0.25h氮化矽高能量球磨製程（Si3N4 -HeM）或傳統球磨製程（BM）處理之Ba2Ti9O20材料，具有較均質（homogeneous）的晶粒組織及較佳的微波介電性質。但是增加高能量球磨時間後，反而會造成粉體凝團，而降低Ba2Ti9O20材料的Qxf值。故改用三度空間球磨製程（3DM）取代高能量球磨製程(HeM)，除可有效地均勻細化混合煆燒粉末外，並可避免因磨球、罐所造成之SiO2污染，而能明顯改善Ba2Ti9O20材料的晶粒組織及微波特性，因此在1350℃/4h燒結條件下，具有較高的Qxf值，並大於傳統球磨製程之Ba2Ti9O20材料Qxf值的高約10 ﹪左右。
一般Ba2Ti9O20材料的晶粒會因為成長的異向性（anisotropic）而成為高細長比（aspect ratio）的形狀，在燒結時常因造橋現象（bridging effect）妨礙Ba2Ti9O20材料的緻密化。SnO2的添加可明顯減少Ba2Ti9O20材料晶粒的細長比，可有效抑制因造橋現象（bridging effect）阻礙燒結緻密化的負面作用，因此添加0.055~0.22 mole SnO2並經1350℃/4h燒結的Ba2Ti9O20材料，其密度都可達到理論密度值的98%。然而，Sn4+離子在SnO6八面體內的極化率（polarizability）低於Ti4+離子在TiO6八面體內的極化率，故Ba2Ti9O20材料的介電常數K值隨SnO2添加濃度的增加而減少。而位於八面體內的Sn4+離子亦會造成內在晶格震動模式的互相密合性（coherence）不佳，進而降低Ba2Ti9O20材料的品質因子（Q）。因此微量SnO2添加在Ba2Ti9O20材料時，晶粒的細長比可被減少，其Qxf值會增加。然而SnO2添加量繼續增加後，將無法更進一步降低晶粒的細長比，但是過多的SnO2添加量卻會降低Ba2Ti9O20材料晶格震動模式的互相密合性，則Qxf值反而會減少。
□ 不論在”一段式燒結緻密法”或 ”兩段式燒結緻密法”製程中，由typeB混合粉末燒結製作的Ba2Ti9O20 材料，其晶粒組織結構均勻性及微波介電性質都會優於type A混合粉末燒結製作的Ba2Ti9O20 材料。此外，Ba2Ti9O20 材料的微波介電常數（K）僅與燒結密度值有密切關係，而與微觀組織沒有密切關係。反之，Qxf 值則與微觀組織有密切關係。因此具有低細長（aspect ratio）比之大晶粒組織結構的Ba2Ti9O20 材料，其Qxf 值會高於具有高細長比之小晶粒組織結構的Ba2Ti9O20 材料。由type A或typeB 混合粉末及”一段式” 或 ”兩段式”燒結緻密法組合成的4種不同製程中，由於type B混合粉末在”一段式燒結緻密法”製程中，其相變態過程較簡單，因此具有最均勻顯微組織，並呈現及最高Qxf 值（(Qxf) =34,000 GHz ）。
□由type A（2BaTiO3+7TiO2）混合粉末先經過傳統球磨製程（BM）處理後，再分別經不同預置反應時間”一段式燒結緻密法”製作的Ba2Ti9O20 材料，其微波介電性質對於前置反應時間（tr）及燒結溫度（Ts）等製程參數非常敏感，因此，對於經過1000℃前置反應時間非常短 (tr＜3h) 之Ba2Ti9O20 材料，其燒結密度（D）、微波介電常數（K）及Qxf值會明顯較低。而由type B（BaTi4O9+BaTi5O11）混合粉末先經三度空間球磨 (3DM)製程，再分別經不同前置反應時間之”一段式燒結緻密法”製作的Ba2Ti9O20 材料，其密度、微波介電常數（K）都隨燒結溫度增加而增加，且經不同前置反應條件的密度值、微波介電常數（K）都無明顯的落差。而Ba2Ti9O20 材料的Qxf值亦隨燒結溫度的增加而增加A但經不同預置反應條件的Qxf值，其彼此間則呈現少許的差異，而此差異量遠少於由type A（2BaTiO3+7TiO2）混合粉末製作之Ba2Ti9O20 材料的差異量。故type B（BaTi4O9+BaTi5O11）混合粉末燒結製作的Ba2Ti9O20 材料，具有較佳的晶粒組織結構及微波介電性質。
□ 最後我們將Ba2Ti9O20 材料應用於製作二維電磁晶體薄板（slab ）。二維Ba2Ti9O20正方晶格及三角晶格電磁晶體薄板（slab ）在30GHz~40GHz頻率範圍，量測之能隙位置與理論計算結果比較後，兩者相當接近。正方晶格及三角晶格之Ba2Ti9O20二維電磁晶體薄板，在週期（或晶格常數）及薄板厚度不變的條件下，當空氣孔洞直徑增加時，除了整體電磁晶體薄板的等效介電常數會降低，而導致能隙中心頻率提高外，亦會造成隙寬度變寬，孔洞填充率增加，實際能隙衰減程度變大。此外，正方晶格之Ba2Ti9O20二維電磁晶體薄板，在空氣孔洞直徑及薄板厚度不變的條件下，當週期（或晶格常數）增加時，整體電磁晶體薄板的等效介電常數會降低，但其 值卻變大，而導致能隙中心頻率降低。同時，亦會造成能隙寬度變窄，孔洞填充率降低，實際能隙衰減程度變小。

Abstracts

This work is to study the effect of processing parameters on the characteristics of Ba2Ti9O20 microwave dielectric materials and to use these materials for fabricating two-dimensional Ba2Ti9O20 electromagnetic bandgap structured（EBG） slabs. The Ba2Ti9O20 materials were synthesized via different milling techniques and sintering processes, using 2BaTiO3+7TiO2 （type A） or （BaTi4O9+BaTi5O11）（type B）mixtures as starting materials. The effect of process parameters on the crystal structure and the related microwave dielectric properties of Ba2Ti9O20 materials was systematically investigated. Moreover, the two-dimensional Ba2Ti9O20 EBG slabs with square or triangular lattices were designed using HFSS simulation package and were than fabricated. The effect of designing parameters, such as hole-size & lattice parameters, on bandgap of the two-dimensional Ba2Ti9O20 EBG slabs was studied. The bandgap of the fabricated EBG slab is in agree with the HFSS simulation results.

Si3N4-HeM process can efficiently disintegrate the Ba2Ti9O20 powders, enhancing the reactivity and sinterability of the materials. However, this process will induce SiO2-contamination and therefore, pronouncedly degrade the Qxf-value of the materials. The SiO2-contamination was effectively inhibited when the ZrO2-(0.25h)-HeM process was used to replace for the Si3N4-(0.25h)-HeM one. The characteristics of the Ba2Ti9O20 materials were markedly improved, as compared with the ZrO2-HeM or BM processes. Utilization of the 3DM process in place of the HeM process can produce the powders of the same high activity but will not induce SiO2-contamination and other side effects and, therefore, markedly improve the microwave dielectric behavior for the Ba2Ti9O20 materials. The 3DM materials possess the same value of tne dielectric constant but have markedly better quality factor (more than 10% higher), as compared with the BM samples.]

Addition of SnO2 decreases the length-to-diameter aspect ratio of the grains. The bridging effect due to anisotropic growth of the high-aspect-ratio grains is thus pronoucedly suppressed such that the densification process is facilitated. All the SnO2-doped materials possessed very high density (>98%T. D.), when they were sintered at 1350℃/4h. On the other hand, the lower polarizability of Sn+4-ions in the SnO6-octahedrons, as compared with the Ti4+-ions in the TiO6-octahedrons, will lowers the K-value the Ba2Ti9O20 materials. Moreover, the presence of Sn4+-ions in the TiO6-octahedrons will degrade the coherency of the intrinsic lattice vibration modes, which will impose detrimental effect on the quality factor for the Ba2Ti9O20 materials. Such a phenomenon accounted clearly the unusauall effect of SnO2-addition on modifying the Qxf-value of the materials. While the addition of small amount of SnO2-species facilitates the densification process by suppressing the anisotropic growth of the grains, incorporation of larger amount of SnO2-doping than necessary will not further improve the granular structure for the Ba2(Ti9-xSnx)O20 materials, but will degrade the coherency in lattice vibrational modes for the materials. Therefore, the Qxf-value of the Ba2(Ti9-xSnx)O20 materials increased firstly for lightly SnO2-doped samples and then it decreased with the proportion of SnO2-species when the SnO2-content is abundant.

The Ba2Ti9O20 materials prepared from the （BaTi4O9+BaTi5O11）（type B）mixtures possess superior microstructres and Qxf-value to the materials prepared from 2BaTiO3+7TiO2 （type A） mixtures. The microwave dielectric constant (K) is insensitive to processing details, as the K-value of the materials is only closely related with density of the samples and is insensitive to the detailed microstructure of the samples. In contrast, the Qxf-value of the samples is very sensitive to the microstructure of the materials. Materials containing large grains of short-rod-geometry with small-aspect-ratio possess superior Qxf-value to the those which contain small-grains of long-rods-geometry with large- aspect-ratio. Among the 4 materials processed, type A & type B powder mixtures and 1-step & 2-step densification processes, the materials prepared from type B mixture and processed by “1-step densification” technique show most uniform microstructure and exhibit the highest Qxf-value （(Qxf) =34,000 GHz）. It is ascribed to the simplicity in reaction routes for the formation of the Ba2Ti9O20 Hollandite-like phase from BaTi4O9 + BaTi5O11 mixture.

The characteristics of the A-series samples, which were prepared from 2BaTiO3+7TiO2 mixture, vary markedly with the pre-reacting process in the “1-step & 2-step densification routes “, whereas those of the B-series samples, which were prepared from BaTi4O9+ BaTi5O11 mixture, are insensitive to such a process. The B-series materials, which were prepared from B-series mixture and pre-reacted at 1000℃ for 6 h or longer, show most uniform microstructure and exhibit the highest Qxf-value. It is ascribed to the simplicity in reaction routes for the formation of the Ba2Ti9O20 Hollandite-like phase from BaTi4O9 + BaTi5O11 mixture, which results in better granular structure for the materials.

We then used the Ba2Ti9O20 materials for fabricating the 2-dimensional (2D) electromagnetic band gap crystals (EBG). The square or triangular lattice two-dimensional Ba2Ti9O20 EBG slab showed the measured bandgap, in the range of 30~40 GHz , was close to the bandgap calculated using HFSS. For square or triangular-type 2D EBG structures with fixed lattice constant and slab thickness, the effective dielectric constant of the lattice decreases with increasing diameter of air hole such that the mid-frequencies in the bandgap shifted toward a higher frequency. Moreover, increasing the filling factor will result in the wider bandgap. For square -type 2D EBG structures with fixed diameter of air hole and slab thickness, the effective dielectric constant of the lattice decreases with increasing lattice constant, but the -value increases such that the mid-frequencies in the bandgap move toward a lower frequency. Furthermore, decreasing the filling factor will result in narrower bandgap and less attenuation in the bandgap.

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