LAPLACE (Laboratoire Plasma et Conversion d'Energie), Université de Toulouse, CNRS, INPT, UPS, Bat 3R3, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France.
Nanotechnology. 2017 Dec 15;28(50):505701. doi: 10.1088/1361-6528/aa9839.
To understand the physical phenomena occurring at metal/dielectric interfaces, determination of the charge density profile at nanoscale is crucial. To deal with this issue, charges were injected applying a DC voltage on lateral Al-electrodes embedded in a SiN thin dielectric layer. The surface potential induced by the injected charges was probed by Kelvin probe force microscopy (KPFM). It was found that the KPFM frequency mode is a better adapted method to probe accurately the charge profile. To extract the charge density profile from the surface potential two numerical approaches based on the solution to Poisson's equation for electrostatics were investigated: the second derivative model method, already reported in the literature, and a new 2D method based on the finite element method (FEM). Results highlight that the FEM is more robust to noise or artifacts in the case of a non-flat initial surface potential. Moreover, according to theoretical study the FEM appears to be a good candidate for determining charge density in dielectric films with thicknesses in the range from 10 nm to 10 μm. By applying this method, the charge density profile was determined at nanoscale, highlighting that the charge cloud remains close to the interface.
为了理解金属/电介质界面上发生的物理现象，确定纳米尺度的电荷密度分布至关重要。为了解决这个问题，通过在嵌入 SiN 薄电介质层中的横向 Al 电极上施加直流电压来注入电荷。通过 Kelvin 探针力显微镜 (KPFM) 探测注入电荷引起的表面电势。结果发现，KPFM 频率模式是一种更适合精确探测电荷分布的方法。为了从表面电势中提取电荷密度分布，研究了两种基于静电学泊松方程解的数值方法：已经在文献中报道的二阶导数模型方法和基于有限元方法 (FEM) 的新二维方法。结果表明，在初始表面电势不平整的情况下，FEM 对噪声或伪影更稳健。此外，根据理论研究，FEM 似乎是确定厚度在 10nm 到 10μm 范围内的介电薄膜中电荷密度的良好候选方法。通过应用该方法，在纳米尺度上确定了电荷密度分布，结果表明电荷云仍然靠近界面。
