Dielectric Materials for Semiconductors

sMIM response is sensitive to local permittivity and conductivity. For highly insulating films it is possible to measure variations in dielectric film thickness as well as determine unknown dielectric constants. It can provide film characteristics at the scale required to understand specific device localized issues, both from blanket wafer films as well as local dielectrics at the device level since it is a high-resolution SPM mode.

In the case of dielectric materials, the sMIM response depends on the capacitance between the tip and sample. In previous experiments with thick insulating dielectrics it was shown that the sMIM response depends on dielectric permittivity and also that the response has a log-linear dependence on the dielectric constant. The log-linear response results from the details of the AFM probe shape which locally modifies the capacitive response of the tip-sample from the 1/electrode-spacing response associated with a planar capacitor. Here we used various thickness SiO2 on silicon substrates as a model system for both modeling and experiment since it is relevant to microelectronic devices.

Modelling provides a framework to investigate how sensitive sMIM is to the electrical characteristics necessary to determine the dielectric constant of the thin film. COMSOL FEM software with the AC/DC module was used to simulate the experiments at 3 GHz excitation frequency. The model used 2D axisymmetric symmetry for the sMIM probe and materials. The simulations incorporated infinite element boundary conditions. The experimental probes were shielded so that combining that with subtraction of contact and lifted signals allowed the modeling to not require inclusion of cantilever effects. Radiative effects were not included since the geometries were quite small compared to the wavelength. The difference in admittance between the probe in contact and lifted 200 nm above the top of the sample surface was calculated to connect with experiment and capture the response near the tip, where the fields are highest. An estimate of the sMIM-C signal is obtained by assuming the signal depends linearly on the admittance. In the FEM model the relative permittivity of the control SiO2 films was set to 3.9, and the film thickness was varied to determine the admittance response of the microwave signal for both the real and imaginary parts.

Fig. 3.1 results show the simulated sMIM response ‘in contact’ 1 nm (a) above the sample surface and (b) 200 nm above the sample surface respectively for a 1200 nm SiO2 film thickness. Fig. 3.2 shows the model results for a dielectric film with varying dielectric on a Si substrate at 1 nm (a) and 200 nm height (b), respectively for a 10 nm SiO2 film thickness. The model shows that for dielectric films there is a critical thickness for a given dielectric constant where the doped Si substrate affects the sMIM response and above which it is dominated by the dielectric film only.

Fig. 3.1. Electric potential simulated results. (a) Probe tip “in-contact” with the top of the dielectric surface. (b) Probe tip retracted 200 nm from the top of the dielectric

surface for a 1200 nm thick SiO2 film.

Fig. 3.2. Electric potential simulated results. (a) Probe tip “in-contact” with the top of the dielectric surface; (b) Probe tip retracted 200 nm from the top of the dielectric

surface for a 10 nm SiO2 film.

3.2.1. Examples of Dielectric Measurements on Film Samples

The sMIM-response is sensitive to factors that include dielectric film thickness, relative permittivity and substrate electrical properties. Fig. 3.3 shows the experimental sMIM signal response for a group of SiO2 films ranging in thickness from 10 nm to 1200 nm.

The data was plotted after subtracting the reference signal with the probe tip 200 nm above the film surface from the signal with the probe tip in contact with the sample surface. The solid line is a log-fit of the data.

Fig. 3.4 shows the control case of SiO2 film on a Si substrate simulated by FEM with measured results. The sMIM response was normalized by a single proportionality constant to connect with the calculated admittance. The sMIM response depends mainly on the dielectric film properties when the film is thick. The substrate properties become important when the dielectric layer is thin. The Si substrate doping was not known at the time of writing this chapter, so the substrate conductivity was adjusted to be 10 S/m, corresponding to 1.3×10¹⁵ atoms/cm³ p-doped, to obtain a reasonable fit of the model to the experimental results and illustrate howa model incorporating substrate, film thickness,

and relative permittivity can account for the measured results. Subsequent 4-point probe measurements on the Si substrate confirmed the substrate conductivity within an order of magnitude of the calculated value.

Fig. 3.3. Experimental sMIM signal versus SiO2 film thickness.

Fig. 3.4. Admittance versus SiO2 dielectric thickness. The modelled admittance is the dashed curve with circle symbols. The admittance inferred from the measured sMIM-C signal is the solid curve with diamond symbols.

Fig. 3.5 shows simulations of the admittance for thinner and lower relative dielectric permittivity. The response forms a family of somewhat parallel curves. This means that the same sMIM response can be obtained with different combinations of dielectric thickness and relative permittivity. This opens up the possibility to establish a methodology to determine the relative dielectric permittivity of unknown samples by calibrating against the response from known films. In the simplest case, if the substrate

properties and film thicknesses are identical the unknown relative dielectric constant will scale directly with the calibration reference value.

The model makes clear that the sMIM response to the film system is affected by the dielectric film thickness and permittivity as well as the substrate conductivity. The method then is limited by how accurately the thickness is measured or conversely, a thickness is limited by how accurately the dielectric value is known. Measurements on a SiO2

reference sample validate that sMIM has good repeatability and reproducibility on a range of thicknesses, thus providing confidence that variations on an unknown dielectric film has the sensitivity to show very small variations in film thickness or process variations of the dielectric value on the order of 10’s nm’s (the probe tip contact area).

Fig. 3.5. Modelled admittance for low-k dielectrics versus dielectric thickness. The modest slope change between 10 and 100 nm is thought to be a geometrical effect arising

from the finite tip size.