Methodology for extraction of space charge density profiles at nanoscale from Kelvin probe force microscopy measurements

Abstract

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.

Space Charge at Nanoscale: Probing Injection and Dynamic Phenomena Under Dark/Light Configurations by Using KPFM and C-AFM

“…11.b). However, the amount of charges found is different [87]. Indeed, the authors demonstrate that the FEM method, which reproduces the real geometry of the device, provides more representative value for the charge density.…”

“…The last method is based on Finite Element Model (FEM). The main advantage of this method is to reproduce the real sample geometry without assumption on the potential distribution in 3D [87]. The Poisson equation is solved in two dimensions in the dielectric layer and in the surrounding air box to determine the potential distribution V(x,z):…”

Interface properties in dielectrics: A cross-section analysis by atomic force microscopy

“…So, the method is more adapted to thick dielectric layers. This method was already successfully exploited to extract charges density profile on Al/SiN x [10] or Al/PEO [11] samples.…”

“…A thin SiN x layer is deposited over Al-electrode to passivate them. More detailed information is provided in reference [10]. The final structure is depicted on Fig.1.a.…”

Electrostatic Force Microscopy Measurement System for Micro-topography of Non-conductive Devices

“…At first, the EFM was used to measure the electrical properties, such as the distribution of surface charges [7]- [9] and surface potential [10]- [12]. As the investigations on the EFM became more in-depth, more researchers begun to use EFM for measurement of the dielectric constant of dielectric materials and to manipulate single charges on certain special carriers for transferring and storage [13]- [15]. Later, studies on the EFM began to focus on improving the measurement resolution and the detection methods of the electrostatic force [16]- [18].…”