Fractal analysis of inorganic thin solid films with network structures

一、实验过程--Al/Ti多层膜的形成--用直流磁控溅射法沉积了分形岛或网状结构。实验中使用的阴极是两个直径75 mm的磁控管，安装在涡轮分子泵抽吸的超高真空室中。靶材为铝(99.99%)和钛(99.98%)。使用的衬底是铝硼硅酸盐玻璃。放电气体为Ar(99.9999%)。亚酸盐化温度从200℃到600℃变化，为了加速Al薄膜岛状结构的形成，首先在衬底上沉积一层钛，然后在不破坏真空的情况下在钛层上连续沉积一层铝层。(钛表面的氧化恶化了孤立的铝岛状结构的形成。)在整个沉积过程中，钛底层的厚度为500 nm，铝层的厚度从10 nm变化到80 nm。用原子力扫描…分析了薄膜的表面形貌更多探针显微镜(AFM，Topo-Metrix：TMX-2000型)。扫描范围为10微米的平方和300x300位数字。用湖泊填充法从数字化的原子力显微镜数据中获得岛屿或网络的分维。从数字化的AFM数据中获得了表面粗糙度、承载比、岛的平均直径和表面覆盖率。II.表面形态和分维的实验结果发现，在550℃沉积20~40 nm的Al平均厚度时，可以获得岛直径在0.5~1um之间的孤岛结构，每个岛的直径都很大，这是Al/Ti双层岛结构的特征。随着衬底温度的进一步提高，岛的形状在其中心形成凸起，然后形成网状结构。尝试了岛状结构和网络结构的分维测定方法。对于海岛结构，应用湖泊填充法得到的分维值较好，但由于网络形态的复杂性，应用填湖法不能得到海岛结构的分维值，对于海岛结构，分维值在2.0~2.2之间。约2.0的分维值表明，在这些Al厚度值下，岛状薄膜的生长是二维生长，其分维几乎等于欧几里德维2，并且保持了几何相似性。此外，分析表明，该地区岛屿的直径分布较窄。随着铝平均厚度的增加，岛屿连接在一起，增加了被铝岛覆盖的面积的一部分。在该铝厚区，分维大于2.5，欧几里德维不能定义该结构。虽然网状结构的分维得到了很好的确定，但由于在较高的温度下保持Asch岛的周向形状，进一步生长得到的网络结构被认为是分形的。III.结论采用直流磁控溅射法制备了Al/Ti双层膜，当Al厚度为20~50 nm时，得到的Al岛结构为分形结构。通过进一步提高衬底温度，得到了网状结构。由于网络结构的复杂性，虽然对网络结构的分维进行了很好的定义，但人们认为网络结构是分形的，这就造成了用湖泊填充法获取分维的困难。较少

I.Experimental procedure-Formation of Al/Ti Multilayr-The fractal island or network structure was deposited by dc magnetron sputtering. The cathodes used in the experiment were two 75mm diameter magnetrons equipped in an ultra high vacuum chamber pumped by a turbo molecular pump. Target materials were Al (99.99%) and Ti (99.98%). Substrates used were aluminobolosilicate glass. The discharge gas was Ar (99.9999%). Subatrate temperature was varied from 200C to 600C.In order to accelerate the formation of island structure of Al thin films, a Ti underlayr was deposited first on to the substrate, and then an Al layr was deposited sequentially on the Ti layr without breaking the vacuum. (The oxidation of the Ti surface deteriorated the formation of isolated Al island structures.) The thickness of the Ti underlayr was 500nm throughout all of the deposition, and that of the Al layr was changed from 10nm to 80nm.The surface morphology of the deposited films was analyzed by atomic force scanning … More probe microscope (AFM,Topo-Metrix : Type TMX-2000). The scan renge was 10mum squared with 300x300 digits. Fractal dimension of island or network dimension was obtained by a lake filling method from the digitized AFM data. Surface roughness, bearing ratio, average diameter of islands, and surface coverage were also obtained from the digitized AFM data.II.Experimental results-Surface morphology and Fractal dimension-It was found by AFM that isolated island structures with island's diameters ranging from about 0.5 to about 1mum were obtained for Al average thickness values of 20 to 40nm deposited at 550C.The large diameters of each island were the feature of the Al/Ti bilayr island stucture. For a further increase in the substrate temperature, the island shape form convex in the its center, then formed a network-like structure. The determination of fractal dimensions were tried for both island and network structure. The fractal dimension was well obtained for an island stucture, while it was not for a network shape by applying the lake filling method because of the complexity of the network shape.For the island structures, fractal dimensions of about 2.0 to 2.2 were obtained. The fractal dimensions of about 2.0 point that the island-structure-like film growth for these Al thickness values was two-dimensional growth where the fractal dimension was almost equal to the Euclidean dimension of 2 and where the geometrical similarity was kept. In addition the analysis showed that the distribution of the diameters of the islands was narrow in this region. As Al average thickness increased more, islands were connecting together, increasing a fraction of area covered by Al islands. In this Al thickness region, fractal dimensions were more than 2.5 and an Euclidean dimension did not define the stucture. In this region the geometrical similarity of the structure was not found, though the structure kept the statistical similarity.Although the fractal dimension was well determined for the network structure, the network structure was thought to be fractal because the structure was obtained by growing the island structure further at a higher temperature keeping the perimeter shapes of asch islands.III.ConclusionsThe Al/Ti bilayr films were deposited by dc magnetron sputtering.At a Al thickness of 20 to 50nm, Al islands structure obtained were fractal. By increasing the substrate temperature further, the network-like structure was obtained. The network-like structure was thought to be fractal although the fractal dimensions were well defined for the network-like structure because of its complexity that caused the difficulty to apply a lake filling method to obtain the dimension. Less