Fractal analysis of inorganic thin solid films with network structures

I.实验过程-Al/Ti多层膜的形成-通过直流磁控溅射沉积分形岛或网络结构。实验中使用的阴极是两个直径为75 mm的磁控管，安装在涡轮分子泵抽气的超高真空室中。靶材料为Al（99.99%）和Ti（99.98%）。使用的基板是铝硼硅酸盐玻璃。放电气体为Ar（99.9999%）。在200 ~ 600 ℃范围内，采用先在衬底上沉积Ti底层，再在Ti底层上连续沉积Al层的方法，加速Al薄膜岛状结构的形成。(The Ti表面的氧化恶化了孤立的Al岛结构的形成。在整个沉积过程中，Ti底层的厚度为500 nm，Al底层的厚度从10 nm变化到80 nm ...更多信息 探针显微镜（AFM，Topo-Meetron：TMX-2000型）。扫描范围为10 μ m平方，300 × 300位。用湖泊填充法从AFM数据中提取了岛状或网状结构的分形维数。表面粗糙度、承载比、岛平均直径、和表面覆盖率也从数字化AFM数据获得。II.实验结果-表面形态和分形维数-原子力显微镜（AFM）研究发现，在550 ℃下沉积的Al平均厚度为20 ~ 40 nm时，可以得到直径在0.5 ~ 1 μ m之间的孤立岛结构，每个岛的直径都很大Al/Ti双层岛结构的特征。随着衬底温度的进一步升高，岛状结构在其中心形成凸起，进而形成网状结构。对岛状结构和网状结构的分形维数进行了测定。对于岛状构造，分维数计算结果较好，而对于网状构造，由于网状构造的复杂性，采用湖泊填充法计算结果不理想，对于岛状构造，分维数约为2.0 ~ 2.2。约2.0的分形维数表明，这些Al厚度值的岛状结构的膜生长是二维生长，其中分形维数几乎等于欧几里得维数2，并且保持几何相似性。此外，分析表明，在该地区的岛屿的直径分布狭窄。随着Al平均厚度的增加，岛连接在一起，增加了Al岛覆盖面积的一部分。在此Al厚度区域中，分形维数大于2.5，并且欧几里德维数不能定义结构。在该区域内，虽然结构保持了统计相似性，但没有发现结构的几何相似性，虽然很好地确定了网络结构的分形维数，网络结构被认为是分形的，因为该结构是通过在较高温度下进一步生长岛结构而获得的，保持asch岛的周边形状。用直流磁控溅射法制备了Ti双层膜，在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。尽管网络状结构的分形维数被很好地定义，但网络状结构被认为是分形的，因为它的复杂性导致难以应用湖泊填充方法来获得维数。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