This article discusses the need to measure the dielectric constant in thin films and the methods used to achieve this effectively.
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The importance of measuring the dielectric constant in thin films
The introduction of several new dielectric materials for high-speed microelectronics of large scale integration (ULSI) increased the need for measurement instruments to measure the frequency-dependent dielectric constant of these materials between the gigahertz and terahertz frequency range.
To ensure the correct propagation of the clock signal through the device interfaces, the dielectric materials around the interfaces should not have a large dispersion in the frequency range greater than 10 times the fundamental frequency.
Limitations of traditional dielectric constant measurement methods
Conventional film characterization methods, such as impedance analyzer-based capacitance measurement, ellipse measurement, and network analyzer-based measurement, have frequency limits.
A new method for effectively determining the dielectric constant
Terahertz time-domain spectroscopy (TDS) is a well-established technique with applications between gigahertz and terahertz frequencies. TDS uses ultrashort electromagnetic pulse detection and emissions to measure the dielectric constant. The time profiles of the reflected/scattered and input terahertz pulses are determined by the cross-correlation between a probe optical pulse and an electromagnetic pulse.
EM pulse detection is very sensitive as it can easily detect even a nanoscale signal. There is no thermal background in this method as the gated optical femtosecond probe pulse is modulated over a short time by the detected electromagnetic pulse. TDS has already been used to measure the dielectric constant of thicker free-standing films and bulk materials using transport engineering.
Time domain spectroscopy (GTDS) represents a more advanced detection technique compared to elliptical measurement. In this method, the complex reflection is measured at multiple points within the Brewster angle range. The light beam of the probe is set to be s– Polarized while the terahertz beam s– Polarized. The dielectric constant of the thin film is determined by the angular dependence of the terahertz reflection.
GTDS can be used to measure the dielectric constant of thin films on a substrate.
An ultra-fast optoelectronic system, containing a detector or emitter unit, with a θ–2θ goniometer, is required. GTDS determines the dielectric properties of the thin film using the reflection information of EM waves. The complex reflection obtained when a polarized EM wave is reflected from a film can be expressed by Drude’s equation.
The sWaves with polarization can be described mathematically by Fresnel formulas. Complex reflection can be expressed as a function of the angle of incidence using the Fresnel-Drode equation. The phase and capacitance of thin films with different dielectric constants on silicon substrates can be calculated separately using this approach.
The dielectric constant of films can be determined using complex reflection curve data by several methods. For example, the phase curve fit can be used to measure the value of the dielectric constant of a thin film.
The value can also be obtained from the slope of the angular phase curve in the sensitive region where the phase offset completes close to the Brewster angle. The width of the phase relaxation angle (PRAW) is determined by two phases near the Brewster angle, and the relationship between the dielectric constant and PRAW can be obtained from the Drude equation.
However, this analysis is effective for a non-absorbent film. For absorbent film, curve fitting is the most appropriate method of characterization.
The difference in the dielectric constants of different materials
The dielectric constant values for thin films vary depending on the type of film material. For example, the dielectric constant for a 3.3 μm thick fluorinated poly film on a silicon substrate was 2.8 ± 0.1 at 1 THz, while the dielectric constant for a 980 μm thick titanium oxide film on a silicon substrate was calculated using the phase difference near the Brewster angle and was PRAW 47 at 1.05 THz.
The dielectric constant and the refractive index of the adsorbent are complex numbers. For example, the dielectric constant of 1.8 μm-thick lead zirconate (PZT) was determined using GTDS. The curve fitting method was used to measure the complex dielectric constant because the phase displacement slope could not reflect the imaginary and real parts of the dielectric constant.
The dielectric constant was obtained between the frequencies of 670 GHz and 1.4 terahertz. At 670 GHz, the real and imaginary parts of the dielectric constant were about 90 and 120, respectively, and the value of the dielectric constant gradually decreased with increasing frequency.
Recent studies measuring the dielectric constant of thin films
In a study published in the journal Solidi B Physical State Basic ResearchIn this study, the researchers used a non-destructive method to determine the dielectric constant of the thin films deposited on the substrate. In this method, the capacitance was initially measured by laying two parallel wires on top of the film.
Then, the dielectric constant of the thin films was obtained for a wide range of parameters based on the distance between the two wires and the functional dependence of the capacitance on the dielectric constants of the environment, substrate and film media.
To summarize, GTDS has emerged as an efficient technique for measuring the dielectric constant of thin films in the gigahertz and terahertz frequency range. The phase shift information near the Brewster angle and complex reflection curve fitting are the most efficient ways to get the value of the dielectric constant from the GDPS complex reflection curve data. However, the thin film surface roughness can also affect the dielectric constant of thin films, which must be considered while measuring the dielectric constant.
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References and additional reading
Li, M., Fortin, J., Kim, J.Y., Fox, G., Chu, F., Davenport, T., Lu, T.M., Zhang, XC. Measurement of the dielectric constant of thin films using terahertz time-domain spectroscopy. Proceedings of the AIP . Conference. 550, 392. 2001. https://10.0.4.85/2944.974234
Kondovych, S., Luk’yanchuk, I. Non-destructive method for thin-film dielectric constant measurements by a two-wire capacitor: measurement of the dielectric constant in thin films. Solidi B Physical State Basic Research. 254. 2016. DOI: 10.1002/pssb.201600476 https://arxiv.org/pdf/1611.08851.pdf