# Time-domain materials characterization techniques

Since the early 1990s, time domain techniques have been investigated for dielectric characterization.

One example is COMITS (coherent microwave transient spectroscopy) developed at IBM. It enables the characterization of complex dielectric materials in the 15-140 GHz range.

This method uses freely propagating electromagnetic pulses radiated and received by broadband antennas that are integrated with high-speed optoelectronic devices. Ultrashort optical pulses with a frequency spectrum up to 150 GHz are transmitted through a sample; the received waveform is photo-conductively sampled; waveforms are recorded for two different sample thicknesses; the time signal is Fourier transformed, and the measured waveforms from the two samples are divided to remove any effects due to sample surfaces from which the complex dielectric constant of the material is computed.

In the early 2000s, time domain techniques for dielectric characterization evolved further through use of laser-based setups to extend the capability into the Terahertz frequency range.

### Dk and Df measurements

The measured time domain pulses are converted into the frequency domain using Fourier Transform. Since the transmission of the signal through a medium are defined by the Fresnel Equation and Fabry-Perot effects, these are used to relate the measured electric fields with the refractive index of the material *n* (*ω*)̃ , where *ω* is the angular frequency.^{1}

*Equation 1*

The extracted refractive index is then used to extract the permittivity and dissipation factor of the dielectric material.^{2} In Equation 1, *n ̃*= *n*+*jk*, where *n* and *k* are the real and imaginary parts of the refractive index.

### Advantages

Dielectric properties can be extracted as a continuous function of frequency. This is in contrast with a frequency domain method (using resonators) where the properties can only be extracted at discrete frequencies.

Dielectric properties over a broad frequency range can be supported (30 GHz – 2 THz).

Can directly measure the properties of the dielectric sample without the need for any conductive structures.

### Potential sources of error

Need to precisely account for scattering effects; otherwise, this approach can lead to larger loss tangents than the true values.

Need precise thickness measurement (

*d*) of the sample since as shown in [11], this parameter is used for extracting the refractive index.Around 30dB SNR (signal to noise ratio) may be required to keep errors low. This measurement system works well over a multi-THz range of frequencies. If the frequency is too low (perhaps a few 100MHz or less), however, the errors can increase.

## References

G. Arjavalingam, Y. Pastol, J. Halbout and G. V. Kopcsay, “Broad-band Microwave Measurements with Transient Radiation from Optoelectronically Pulsed Antennas,”

*IEEE Trans. on Microwave Theory and Techniques*, Vol. 38, No. 5, May 1990.P. H. Bolivar, et. al, Measurement of the Dielectric Constant and Loss Tangent of High Dielectric-Constant Materials at Terahertz Frequencies,

*IEEE Trans. on Microwave Theory and Techniques*, Vol. 51, No. 4, April 2003.

*As part of the **5G/6G MAESTRO project**, work on this page is supported by the Office of Advanced Manufacturing in the National Institute of Standards and Technology (NIST), under the Federal Award ID Number 70NANB22H050.*