This article discusses the need for measuring the dielectric constant in thin films and the methods used to effectively achieve this.
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Significance of Measuring Dielectric Constant in Thin Films
The introduction of several new dielectric materials for high-speed ultra-large-scale integration (ULSI) microelectronics has increased the necessity for metrology tools to measure the frequency-dependent dielectric constant of these materials between the gigahertz and terahertz frequency range.
To ensure proper propagation of the clock signal through the interconnects of the device, dielectric materials around the interconnects must have no significant dispersion in the frequency band that is 10 times the base frequency.
Limitations of Conventional Dielectric Constant Measurement Methods
Conventional film characterization methods, such as impedance analyzer-based capacitance measurement, ellipsometry, and network analyzer-based measurement, have frequency limits.
A New Method to Effectively Determine Dielectric Constant
Terahertz time-domain spectroscopy (TDS) is an established technique with applications between the gigahertz and terahertz frequencies. TDS employs an ultrashort electromagnetic (EM) pulse detection and emission to measure the dielectric constant. The temporal shapes of the reflected/propagated and input terahertz pulses are determined by the cross-correlation between a probe optical pulse and an EM pulse.
The EM pulse detection is extremely sensitive as it can easily detect even a nanowatt signal. No thermal background is present in this method as the femtosecond optical gated probe pulse is modulated within a short-time period by the detected EM pulse. TDS was already used to measure the dielectric constant of freestanding thick films and bulk materials using transmission geometry.
The goniometric time-domain spectroscopy (GTDS) represents a more advanced detection technique compared to ellipsometry. In this method, the complex reflectance is measured at multiple points within a Brewster angle range. The probe optical beam is tuned to be s-polarized while the terahertz beam is p-polarized. The dielectric constant of the thin film is determined by the angular dependence of terahertz reflectance.
GTDS can be used to measure the dielectric constant of thin films on a substrate.
An ultrafast optoelectronic system, containing a detector or an emitter unit, with a θ–2θ goniometer is required for the technique. GTDS determines the dielectric properties of a thin film using the reflection information of EM waves. The complex reflectance that is obtained when a polarized EM wave is reflected from a film can be expressed by the Drude equation.
The p-polarized waves can be described mathematically by the Fresnel formulas. The complex reflectance can be expressed as a function of incident angle using the Fresnel formulas and Drude equation. The phase and amplitude of thin films with various dielectric constants on silicon substrates can be calculated separately using this approach.
The dielectric constant of the films can be determined using the complex reflectance curve data through several methods. For instance, the phase curve fit can be used to measure the dielectric constant value of the thin film.
The value can also be obtained from the angle-phase curve slope in the sensitive region where the phase shift is completed near the Brewster angle. A phase relaxation angle width (PRAW) is determined by two phases near the Brewster angle, and the relation between the dielectric constant and PRAW can be obtained from the Drude equation.
However, this analysis is effective for a nonabsorptive film. For an absorptive film, curve fitting is the most suitable method for characterization.
The Difference in Dielectric Constants in Different Materials
The dielectric constant values of thin films vary depending on the type of film material. For instance, the dielectric constant of a 3.3-µm thick fluorinated poly(arylether) (FLARE) film on a silicon substrate was 2.8 ± 0.1 at 1 THz, while the dielectric constant of a 980 Å thick titanium oxide film on a silicon substrate calculated using the phase difference near the Brewster angle and the PRAW was 47 at 1.05 THz.
The dielectric constant and refractive index of an absorptive material are complex numbers. For instance, the dielectric constant of a 1.8-µm thick lead zirconate titanate (PZT) was determined using GTDS. The curve fitting method was used to measure the complex dielectric constant as the phase shift slope cannot reflect the imaginary and real parts of the dielectric constant.
The dielectric constant was obtained between 670 GHz and 1.4 THz frequencies. At 670 GHz, the real and imaginary parts of the dielectric constant were around 90 and 120, respectively, and the value of the dielectric constant gradually decayed with the increasing frequency.
Recent Studies Measuring Dielectric Constant of Thin Films
In a study published in the journal Physica Status Solidi B Basic Research, researchers used a non-destructive method to determine the dielectric constant of thin films deposited on a substrate. In the method, the capacitance was initially measured by placing two parallel wires on the top of the film.
Subsequently, the dielectric constant of thin films for an extensive set of parameters was obtained based on the distance between the two wires and the functional dependence of the capacitance on dielectric constants of the environment media, substrate, and film.
To summarize, GTDS has emerged as an effective technique for the dielectric constant measurement of thin films in the gigahertz and terahertz frequency range. The phase shift information near the Brewster angle and the complex reflectance curve fitting are the most effective methods to obtain the dielectric constant value from the complex reflectance curve data in the GDPS technique. However, the roughness of the thin film surface can also affect the dielectric constant of thin films, which must be considered while measuring the dielectric constant.
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References and Further Reading
Li, M., Fortin, J., Kim, J. Y., Fox, G., Chu, F., Davenport, T., Lu, T-M., Zhang, X-C. Dielectric constant measurement of thin films using goniometric terahertz time-domain spectroscopy. AIP Conference Proceedings. 550, 392. 2001. https://doi.org/10.1109/2944.974234
Kondovych, S., Luk’yanchuk, I. Nondestructive method of thin film dielectric constant measurements by two-wire capacitor: Measurement of dielectric constant in thin films. Physica Status Solidi B Basic Research. 254. 2016. DOI: 10.1002/pssb.201600476 https://arxiv.org/pdf/1611.08851.pdf
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