Determination of a 3D Displacement Field at a Vicinity of a GeSn/Ge Interface by the Phase Retrieval of Electron Rocking Curves
Determination of a 3D Displacement Field at a Vicinity of a GeSn/Ge Interface by the Phase Retrieval of Electron Rocking Curves
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通过电子摇摆曲线相位恢复确定 GeSn/Ge 界面附近的 3D 位移场
DOI：
10.1002/9783527808465.emc2016.6141
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
and S. Zaima
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文献类型：
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作者：
M. Miura;S. Fujinami;K. Saitoh;N. Tanaka;O. Nakatsuka;and S. Zaima
材料中的应变是影响材料的载流子迁移率、介电性能、磁性等物理性能的重要因素之一，在半导体工业中，应变工程对器件性能的改善起着重要的作用。应变测量作为支撑应变工程的关键技术也越来越重要。迄今为止，利用衍射技术测量应变主要是通过测量衍射峰的位置以及将实验峰位置与模拟峰位置进行拟合来实现的。该方法隐含地假设对衍射强度有贡献的体积中的应变是均匀的。然而，真实的材料中的应变并不总是均匀的，并且在样品的衍射体积上变化。在本研究中，我们应用会聚束电子衍射（CBED）来确定这种非均匀应变，其晶格位移矢量沿着电子束的入射方向变化，晶格散射反射振幅φg被给出为来自每个晶格点的散射波之和，它可以由晶格的傅里叶变换表示。如果晶格有位移场R（r），则对于φg必须考虑2πg·R（r）的相位因子，其中R是晶体中一点的位置矢量。在会聚束电子衍射的情况下，由于探头直径足够小，因此R（r）在与束的入射方向垂直的方向上不变，因此R（r）可以写为R（z），其中z表示沿入射方向的沿着坐标。exp（2πIG·R（z））的相位因子的傅里叶变换可以写为φg（s），其中激励误差s是z的共轭变量。我们应用傅里叶迭代相位恢复技术恢复了φg的相位部分，并确定了晶格位移2πg·R（z）的相位因子。采用超高真空化学气相沉积法在Ge（001）衬底上沉积了一层200 nm的Ge 92. 9 Sn 7. 1薄膜，并利用CBED技术测量了薄膜的φg（s）模量。通过机械抛光和离子束减薄制备用于电子显微镜检查的横截面样品。摇摆曲线由CBED技术在与[110]方向倾斜约10度的入射角下获得。CBED实验通过使用在200 kV的加速电压下操作的透射电子显微镜进行。为了去除主要由等离子体激元损失引起的非弹性散射，使用能量窗为5 eV的Gatan成像滤波器拍摄了CBED图。图1（a）显示了样品的横截面TEM图像。CBED图案取自Ge衬底中指示为1至6的位置。图1（B）示出了在相位恢复中使用的整个CBED图案。图2（a）、2（B）和2（c）分别显示了-26-8、-553和-317反射的放大圆盘及其摇摆曲线轮廓。图2（d）、2（e）和2（f）分别显示了-26-8、-553和-317反射的2πg·R（z）的相位分布作为本研究确定的z坐标的函数。根据这些相位分布，分别如图3（a）、3（B）和3（c）所示确定[001]、[110]和[110]方向上的晶格位移。可以清楚地看到，[001]方向上的位移场关于试件中心具有镜像对称性，这与弹性理论是一致的。用本方法确定的位移场与有限元法得到的模拟值进行了定量比较。
Strain in materials is one of the important factors affecting physical properties of the materials such as carrier mobility, dielectric property, magnetism and so on. In semiconductor industry, strain engineering has been playing a primary role for the improvement of the device performance. Measurement of strain has also been very important as a key technique supporting the strain engineering. So far, the strain measurement by diffraction technique has been done mainly by measuring the positions of diffraction peaks and by fitting the experimental peak positions to simulated ones. This method implicitly assumes that strain in the volume contributing to diffraction intensities is uniform. Strain in real materials, however, is not always uniform and varies over the diffraction volume of the specimen. In the present study, we applied convergent‐beam electron diffraction (CBED) to determine such non‐uniform strain, whose lattice displacement vector varies along the incident direction of the electron beam.Lattice scattering amplitude of reflectiong,φg, is given as a sum of scattered waves from each lattice point, which can be expressed by the Fourier transform of the lattice. If the lattice has a displacement fieldR(r), a phase factor of 2πg·R(r) has to be taken into account forφg, whereris a positional vector for a point in the crystal. In the case of convergent‐beam electron diffraction,R(r) is unchanged in the direction perpendicular to the incident direction of the beam because the probe diameter is sufficiently small, and thus,R(r) can be written asR(z), where z indicate a coordinate along the incident direction. The Fourier transform of the phase factor of exp(2πig·R(z)) can be written asφg(s) with an excitation error s, which is a conjugate variable of z. We applied the Fourier iterative phase retrieval technique to restore the phase part ofφg, and to determine the phase factor of the lattice displacement 2πg·R(z). In the present study, the modulus ofφg(s) was measured from a rocking curve profile observed by a CBED pattern.A Ge92.9Sn7.1layer of 200 nm was deposited on a Ge (001) substrate by the chemical vapor deposition method in a ultra‐high vacuum. Cross section samples for electron microscopy were prepared by mechanical polishing and ion‐beam thining. Rocking curves were obtained by the CBED technique at an incidence inclined by about 10 degree from the [110] direction. CBED experiment was conducted by using a transmission electron microscope operated at an acceleration voltage of 200 kV. CBED patterns were taken by using Gatan imaging fileter with an energy window of 5 eV to remove inelastic scattering mainly by the plasmon loss.Figure 1(a) shows a cross‐section TEM image of the specimen. CBED patterns were taken from the positions indicated as 1 to 6 in the Ge substrate. Figure 1(b) shows a whole CBED pattern used in the phase retrieval. Figures 2(a), 2(b) and 2(c) show enlarged disks of the ‐26‐8, ‐553 and ‐317 reflections and their rocking curve profiles, respectively. Figures 2(d), 2(e) and 2(f) respectively show phase profiles of 2πg·R(z) of the ‐26‐8, ‐553 and ‐317 reflections as a function of thez‐coordinate determined by the present study. From these phase profiles, the lattice displacements in the [001], [110] and [110] directions are determined as shown in Figures 3(a), 3(b) and 3(c), respectively. It is clearly seen that the displacement field in the [001] direction is of mirror symmetry about the center of the specimen, which is consistent to the elasticity theory. The displacements field determined by the present method is quantitatively compared to the simulated values obtained by the finite element method.