Quantifying the dielectric constant of thick insulators using electrostatic force microscopy

Abstract

Quantitative measurement of the low-frequency dielectric constants of thick insulators at the nanoscale is demonstrated utilizing ac electrostatic force microscopy combined with finite-element calculations based on a truncated cone with hemispherical apex probe geometry. The method is validated on muscovite mica, borosilicate glass, poly(ethylene naphthalate), and poly(methyl methacrylate). The dielectric constants obtained are essentially given by a nanometric volume located at the dielectric-air interface below the tip, independently of the substrate thickness, provided this is on the hundred micrometer-length scale, or larger.

Nanoscale dielectric microscopy of non-planar samples by lift-mode electrostatic force microscopy

“…As explained above, given that the substrate is metallic-like we do not need to include these effects in the present work, so we take L = 0 µm. The explicit tip geometry used in the calculations is determined by means of the tip calibration procedure described elsewhere [8,26]. Briefly, theoretical approach curves calculated for the tip on the bare substrate are least square fitted to an experimentally recorded approach curve on the metal, with the tip radius, R, and cone angle, θ, as fitting parameters (other probe geometric parameters are fixed to nominal values: H=12.5 µm, W=3 µm, L=0 µm).…”

“…Among them, we can cite nanoscale capacitance microscopy [1][2][3], electrostatic force microscopy (EFM) [4][5][6][7][8][9][10], nanoscale impedance microscopy [11,12], scanning polarization force microscopy [13][14][15][16], scanning microwave microscopy (SMM) [17,18] and nanoscale non-linear dielectric microscopy [19]. These techniques have allowed measuring the electric permittivity with nanoscale spatial resolution on planar samples, such as thin oxides, polymer films and supported biomembranes [2][3][4]8,10], and on non-planar ones, such as, single carbon nanotubes, nanowires, nanoparticles, viruses and bacterial cells [20][21][22][23][24][25][26][27][28][29][30].…”

Ultrahigh dielectric constant of thin films obtained by electrostatic force microscopy and artificial neural networks

“…13,14 Unfortunately, the effect of the electrostatic field under these restrictions has not been studied in detail since previous theoretical works focused on dielectric thin films over metallic substrates. 15,16 In this article, we combine numerical methods and artificial neural networks 17 (ANNs) to simulate the electrostatic interaction between an EFM tip and a thin film. Using the electrostatic force as input patterns to the ANN, we establish that the thin film sample can be replaced by a simple semiinfinite sample characterized by an effective dielectric constant.…”

“…[18][19][20][21] Some software packages, based on the finite elements method, such as COMSOL or ELMER, have been also used to simulate electrostatic fields in EFM. 15 In this article, we use the generalized image charge method 22,23 (GICM). The GICM replaces the surface charge density by a set of charges inside the metallic tip and the sample by a set of image charges.…”

Enhanced dielectric constant resolution of thin insulating films by electrostatic force microscopy

“…12 EFM is currently used to determine the static dielectric constants of thin films of a few nanometers thickness directly deposited on a metallic electrode. The dielectric constant can be determined by comparison of the experimental results with simple analytical expressions 13,14,15 . For metallic samples, the tip-sample interaction is very well understood and the force, as well as the force gradient, can be determined by using a simple analytical model.…”