【作者】 马飞；

【导师】 张建民；

【作者基本信息】 陕西师范大学 ， 光学， 2004， 硕士

【摘要】 对于薄膜特别是柱状晶薄膜，当晶粒在膜平面内的尺寸大于膜厚时，柱状晶粒的上底面（即自由表面）和下底面（即膜-基界面）的面积将大于侧面（即晶界面）的面积，如果薄膜还附着在与其热胀系数不同的基体上并在不同于沉积温度的条件下退火时，膜中将存在较大的热应力。因此，薄膜中的晶粒生长除像传统的整体材料中的晶粒生长一样要考虑晶界能外，还应当同时考虑表面能、界面能和应变能。而表面能、界面能和应变能均与晶粒的取向密切相关，即存在各向异性。更值得注意的是，表面能、界面能和应变能的各向异性对晶粒取向的依赖关系存在较大的差异，也就是说，表面能密度最小的晶粒取向对应的界面能和应变能未必最小。依据能量最小化原理，在退火过程中表面能、界面能以及应变能的总和为最小值取向的晶粒将择优生长，薄膜最终也将呈现这种择优取向（或者织构）。 本文应用改进嵌入原子法（MEAM）分别计算了十种面心立方（FCC）金属、十种体心立方（BCC）金属以及三种金刚石（Diamond）结构晶体的不同指数晶面作为表面时的表面能。根据计算结果具体讨论了各向异性的表面能对异常晶粒生长和相应织构演变的影响。最后以面心立方金属Cu和Ag为例进行了实验验证。主要理论分析和实验结果如下： （1） 应用自己设计的计算表面几何结构因子的“C”语言程序确定了面心立方（FCC）晶体38个晶面、体心立方（BCC）晶体24个晶面和金刚石（Diamond）结构晶体24个晶面分别作为表面时的几何结构因子S_i^（1），x（l=0～3），各层晶面上原子的最近邻数Z_d，和表面上每一个原子所占的面积A_（x）。有关结果也可以用于其他表面特性（例如，热电子或热离子发射、表面电子态、表面吸附、表面氧化、表面催化、表面偏析和表面重构等）的理论分析。 （2） 应用改进嵌入原子法（MEAM）计算了Cu，Ag，Au，Ni，Pd，Pt，Al，Pb，Rh和Ir等十种面心立方金属38个晶面，Li，Na，K，V，Nb，Ta，Cr，Mo，W和Fe等十种体心立方金属24个晶面，以及C，Si和Ge等三种金刚石结构晶体24个晶面分别作为表面时的未松弛表面能，结果表明：三种晶体的密排面（面心立方和金刚石立方结构的（111）晶面，体心立方的（110）晶面）作为表面时均具有最小的表面能。特别是对于面心立方（FCC），其他（hkl）晶面作为表面时，随着该晶面与（111）面之间夹角的增大其表面能线形增加，因此可以由任意晶面与（111）晶面之间夹角的大小粗略估计面心立方金属各晶面作为表面时表面能的相对大小。根据表面能各向异性的理论分析结果，仅就表面能而言，我们预言:面心立方（FCC）和金刚石（Diamond）结构的（1 11），体心立方（BCC）的（110）分别为三种晶体结构的择优取向，在薄膜退火过程中表面能各向异性将驱动相应取向异常晶粒的生长，并导致相应织构的出现或者加强。 （3）通过x一射线衍射（XRD）和透射电子显微镜（TEM）对Cu、Ag自由膜和附着膜在退火过程中的异常晶粒生长，以及它们相对于沉积膜的织构演变进行的比较实验研究表明:无论是Cu还是Ag，沉积膜为多晶结构，无择优织构，晶粒尺寸均小于100纳米，属纳米薄膜。Cu附着膜在300℃退火3小时出现了（100）和（110）取向的异常大晶粒，其尺寸分别为1.4脚和2.0脚左右，Ag附着膜在300℃下退火3小时出现了（112）取向的异常大晶粒，大小为1.7娜，这是应变能各向异性驱动的结果。异常晶粒的生长导致相对于沉积膜，附着膜中（200）、（220）和（211）等取向显著增强，表现为择优取向。相反，在300℃条件下退火3小时，Cu和Ag自由膜中均出现了（111）取向的异常晶粒，大小尺寸分别为1娜和0.4娜，这一变化是表面能各向异性驱动异常晶粒生长的结果，实验与理论计算完全一致。更多还原

【Abstract】 For thin polycrystalline films, especially those with columnar structure, once the diameter of grains on the film surface is larger than the film thickness, the total area of above (free surface) and under basal planes (film-substrate interface) will be larger than that of side plane. And if the film precipitates on the substrate with thermal expansion coefficient different from that of the film, great thermal stress will be introduced during annealing. Therefore besides the minimization of boundary energy in traditional bulk material, the anisotropy of surface energy, interface energy and strain energy can drive the grain growth in thin films. The magnitude of these three kinds of energy, however, depends strongly on the orientation of grains, namely, they are anisotropic. It is noticeable that their respective dependence relationship is different markedly, that is to say, the orientation of grains with lowest surface energy needn’t correspond to the lowest interface energy and strain energy. For the minimization of energy, the grains with lowest total energy involving surface energy, strain energy and interface energy will be preferable to grow during annealing so that the films will show corresponding texture ultimately.In this paper we have calculated the surface energy of various crystalline planes as film surface for ten face-centered cubic (FCC) metals, ten body-centered cubic (BCC) metals and three diamond-structure (Diamond) crystals with Modified Embedded Atom Method (MEAM). According to the theoretical analysis, the driving forces for abnormal grain growth from anisotropy of surface energy and consequently texture evolution of films have been discussed. At last, the driving effect in thin Cu and Ag films is proved experimentally, which is in good agreement with theoretical analysis. The principal theoretical analysis and experimental results can be concluded as:(1) Using compiled programs for surface geometrical factors in "C", the related parameters of 38 FCC, 24 BCC, and 24 Diamond-structure crystalline planes as surfaces have been determined including geometrical factors , the number of neighbors to an atom in any planes Zd, and the area occupied by one atomin surface A(x). The results can also be applied to the theoretical investigation of other surface properties (such as electron states, segregation, oxidation, catalysis, adsorption and reconstructure in surface).(2) With Modified Embedded Atom Method (MEAM) we have calculated the surface energy of various crystalline planes as surfaces for ten FCC metals Cu, Ag, Au, Ni, Pd, Pt, Al, Pb, Rh, Ir and ten BCC metals Li, Na, K, V, Nb, Ta, Cr, Mo, W, Fe, as well as three Diamond-structure crystals C, Si, Ge. The results suggest that the surface energy of closely-packed planes (such as (111) plane of FCC and Diamond-structure crystals, (110) plane of BCC crystals) is the lowest. Especially for FCC metals, the surface energy of any other planes (hkl) as surfaces increases with the including angle between them and (111) plane, according to which, the relative value of surface energy of any (hkl) planes can be estimated. From the calculated results, we can predict, if surface energy is taken into account only, (111) of FCC and Diamond-structure, as well as (110) of BCC are the preferable orientations respectively. During annealing the anisotropy of surface energy can provide additional driving force for abnormal grain growth in thin polycrystalline films, consequently corresponding textures will emerge or be strengthened.(3) By X-ray diffraction (XRD) and transmission electron microscopy (TEM) abnormal grain growth and texture evolution in Ag and Cu films are studied, the comparative investigation between deposited films and free-standing films as well as attaching films after annealing shows that deposited Cu (Ag) films without annealing are polycrystalline and of no preferable orientations, and the size of grains is less than 100 nm. After annealed at 300℃ for 3 hours, (100) and (HO)-oriented abnormal grains about 1.4 and 2.0//W i更多还原