| Kwang-Su Lee, Toh-Ming Lu, and X.-C. Zhang
Thin film characterization is important for the semiconductor industry as it pushes for smaller and faster circuits and devices. Materials with a high dielectric constant are required for improved insulation and reduction of tunneling between layers, and low dielectric materials are needed for interconnects with reduced capacitance [1]. As feature sizes of circuits and devices approach 100 nm and chip frequencies climb into the upper gigahertz to terahertz range, it becomes increasingly important to have a convenient method of characterizing properties of thin dielectric films in the gigahertz to terahertz frequency range [2]. Thin-film dielectric materials are being explored for many applications. Interest in plastic-based electronics is spurring the development of organic-inorganic hybrid materials and organic transistors on plastic [3], [4]. Single crystal optoelectronic devices are being developed for thin-film transistors and microelectromechanical systems (MOEMS) [5]. In certain materials, the optical and dielectric properties of thin films are assumed to be different from those of bulk materials since the structures of the thin films are altered due to the presence of fine grains, mechanical stresses, formation of interfacial layers, or rough interfaces during the thin-film deposition process [6].
One way of measuring dielectric and optical properties of materials at terahertz frequency during the past decade has been terahertz time-domain spectroscopy [7]. This method extracts both real and imaginary parts of the dielectric property of materials by measuring the temporal electric field transmitted through materials. The Fourier-transformed spectrum from the measured terahertz waveform in the time-domain gives information on both amplitude and phase, so that it can extract real and imaginary parts of dielectric properties in the frequency domain. This method was successfully demonstrated with several materials such as semiconductors, liquids, gases, biological materials, and superconductors to obtain dielectric properties of materials [8]-[11].
However, if the thickness of the material is comparable to or thinner than the wavelength of the terahertz wave, the phase and amplitude changes by dielectric materials tends to be difficult to measure with time-domain spectroscopy because of the very small interaction length. To overcome this difficulty, terahertz differential time-domain spectroscopy was introduced [12], [13]. In previous work, it lacked full information of dielectric and optical properties of thin film. It provided only the real part of the thin film’s refractive index.
In this article, the dielectric and optical properties of a variety of micron to nanometer scaled dielectric films at terahertz frequency (millimeter and submillimeter wave regime) are investigated, using a coherent terahertz wave source and electro-optic detection method. Terahertz differential time-domain spectroscopic detection was performed to determine the real and imaginary parts of the complex dielectric constants and optical constants. This method provides a noncontact, nondestructive, highly sensitive optical tool to characterize the dielectric and optical properties of micron- to nanometer-scaled thin films at terahertz frequency. To detect any extremely small changes between the reference wave and the transmitted wave through a medium, double phase modulation detection was applied and 105 of dynamic range was achieved.
Theory Figure 1 schematically illustrates a thin layer (2) between air (1) and a substrate (3) with refractive indices n2, n1, and n3, respectively. If a terahertz wave is incident on this thin layer with thickness of d from the air toward the substrate, a transmitted electric field due to multireflection is given by [14]
(1)
where E0, t12, t23, r21, and r23 are incident electric field, transmission, and reflection coefficients between interfaces, and d(w)is the phase shift of thin-film medium.
On the other hand, a reference electric field incident on the bare substrate is given byEref(w)=t13t31E0 (w) exp(iwd / c). For the absorbable thin layer, transmission, reflection coefficients, and phase delay are expressed in terms of the complex refractive indices of the thin layer and the real refractive indices of air and the substrate if one assumes there is no absorption in the air and the substrate. If defined as and assumed , the ratio of is approximated to the following equation:
(2)
where n and k are real and imaginary parts of complex refractive indices of the thin layer. If denoted as Ediff( / Ediff( = re iD and introduced as complex dielectric function e = e' +ie" = (n + ik)2, the real part and imaginary part of (2) can be written as the following equations:
| 
| | 1. Transmission and reflection of a incident light on thin film. | 
(3)
(4)
If r = I Ediff / Eref I and Dare obtained from the measured reference and the differential terahertz signal and those Fourier transformed terahertz waves, then the real and the imaginary parts of the dielectric function can be deduced. This method is very similar to the one that is used to extract the dielectric property in terahertz time-domain spectroscopy [7]. The real and imaginary part of the refractive index and absorption can be obtained by relations as e' = n2 - k2, e" = 2nk. The expression of n, k, and a in terms of e' and e" are given by
(5)
(6)
(7)
Experimental Methods For the experiment, a Ti:sapphire laser (Spectra-Physics Tsunami) with 140 fs in pulse width, 800 nm in central wavelength, 82 MHz in repetition rate, and an average power of 1.6 W was used. The laser light is divided into two beams: a pump and a probe. The pump laser beam is illuminated on a [100] semi-insulating GaAs inclined surface to generate the terahertz wave shown in Figure 2. The short laser pulse creates a transient electron-hole oscillation in the depletion layer of the semiconductor surface and the transient electron-hole oscillation generates electromagnetic radiation at terahertz frequency [15]. The generated terahertz wave was collimated and focused on the sample by a pair of parabolic mirrors. After being transmitted through the sample, this terahertz wave is collimated and focused again into a ZnTe electro-optic (EO) crystal by the second pair of parabolic mirrors.
The probe beam is coincident with the terahertz wave to detect polarization changes due to Pockel’s effect of terahertz [16]. The linearly polarized probe beam experiences the polarization change due to a birefringence by the terahertz wave in the ZnTe EO crystal. With varying time delay between the terahertz wave and optical probe with a very small gating time step, the entire terahertz wave profile is traced and its waveform decoded [17].
The sample is designed to be half uncoated and half coated with thin film on the substrate. It is mounted on a shaker (galvanometer) at the focal point of the terahertz beam to measure the differential terahertz signal. This shaking frequency ranges from 10 Hz to 66 Hz and is fed by a function generator and synchronized with a lock-in amplifier. The reference terahertz waveform can be measured by modulating the terahertz beam by placing a metal plate on the coated half of the thin film.
To increase dynamic range, the double phase modulation technique was applied. The pump beam is modulated by a mechanical chopper using 2 kHz modulation frequency while the terahertz beam is modulated by a galvanometer with 10 Hz. The signal from the detector was shunted with a pair of resisters to control the gain and feed in the first lock-in amplifier with 2 kHz reference trigger input. The modulated signal from the first lock-in is fed into the second lock-in amplifier with 10 Hz trigger input.
Result and Discussion: The amplitude change of the terahertz wave due to the thin film is the same order as the phase delay or absorption. The phase change at 1 THz is due to a 1 mm thin film, which in refractive index 1.8 corresponds to 0.03 radian, so that the amplitude of the differential signal of this material corresponds to 0.03 times that of the reference signal. If we consider a water molecular layer with 100 cm-1 of absorption coefficient and 1 nm in thickness, the amplitude change of the terahertz wave is 10-5.
The maximum capability of this system with our estimated maximum signal-to-noise ratio (SNR), 106, is able to characterize the properties of not only nanometer-scaled thin films but also monolayer-scaled molecules. This is based on the assumption that the absorption coefficient and refractive index of water is awater ~ 100 cm-1 and n ~ 1.8 at terahertz frequency and the phase delay and absorption amplitude change of 3 Å, the thick water mono-molecular layer is given by 5 x 10-6 and 2 x 10-6, respectively.
| 2. Experimental scheme: HWP = half wave plate, T = translation stage, E = emitter, BS = beam splitter, C = chopper, G = Galvanometer, QWP = quarter water plate, S = sample, WP = wollaston polarizer, and PD = photo detector. |
| 3. Phase shift Eref and Ediff (solid line: calculated, doted line: experiment). |
| 4. The differential terabertz waveform and the dielectric and optical properties of 0.93mm silicon dioxide film. (a) The differential and reference waveforms; (b) complex dielectric constants, e' and e"; (c) complex refractive indices, n and k; (d) absorption coefficient , a. |
In the measured differential terahertz signal, its waveform shape was changed, when compared to the reference, as predicted by the mathematical differential of the reference waveform. The pulse width was 450 fs at its main peak, and the shape was asymmetric. Its amplitude and the shape of the differential signal were well fitted with mathematical prediction. By Fourier transformation of the reference and the differential signal, the amplitude and phase information in frequency domain can be obtained. In the reference spectrum, peak amplitude was in 0.7 terahertz, and its spectrum ranges from 100 GHz to 2.2 THz. In the differential terahertz spectrum, its spectrum slightly shifted toward high frequency but shows the same spectrum pattern.
The time-resolved waveforms of both the differential (Ediff) and the reference waveforms (Eref) of thin film on silicon substrate show reflected waveforms due to internal reflections in the substrate. (Ediff) waveforms from the reflected second pulses in thin films on substrates were observed to be unexpectedly high in amplitude. For the deduction of dielectric properties, the second reflected waveforms were not counted.
In a phase, the phase change between the reference and the differential terahertz waves in the spectrum shows D = (p / 2) + u characteristically, where p / 2 corresponds to intrinsic phase originating from the differential nature of the differential waveform and u was found to be the same as the phase shift due to the thin film. This D = (p / 2) + u phase shift property was easily proven by mathematical calculation. Figure 3 shows the measured phase change and the calculated phase change in 1.8 mm parylene-n film. The two phases fit well.
u may be replaced by the phase delay of Erefand Etran, since the phase delay of Ediff equals the phase delay of Eref - Etran (= Ediff ). Often the phase information of Ediff includes more noise since the amplitude of Ediff is much smaller than that of the reference signal. This noise can increase the anomaly of thin-film properties, especially in k value.
From the amplitudes of reference and the differential spectrums and phase information in frequency domain with (3) to (7), the complex dielectric and optical properties can be obtained in the frequency domain.
Silicon Dioxide
The optical and dielectric properties of silicon dioxide (SiO2) have been widely studied in various fields. In the semiconductor industry, it has been used as a passive layer for decades.
The optical properties of bulk SiO2 in the far-infrared to ultraviolet were widely investigated [18]. The dielectric and optical properties can be influenced by the absorption of impurities and defects. The measurement of the optical property of SiO2 thin film has been done only within the visible range since the measurement of thin film is much more difficult than that in a bulk material. The refractive index of the bulk SiO2 ranges from 2.1 to 2.4 in the far-infrared range, depending on its structure. For the bulk SiO2 a-crystalline, the refractive index in terahertz range (far-infrared) is known as 2.1. The property shows dispersion in infrared and ultraviolet regions, which is due to longitudinal optical (LO), transverse optical (TO) phonon absorption, and electronic transition. The optical property of the bulk SiO2 is well described by the empirical oscillator model in infrared such as
 ,
(8)
where individual characteristic frequency is shown in Table 1
(e¥ = 2.2)[18].
In the far-infrared region (terahertz region), the refractive index is fairly flat since there is no electronic structure. The optical constant measurement of the SiO2 thin film has not previously been done at terahertz frequency.
The film was prepared by thermal oxidation on the (100) surface of a P-type silicon wafer at 800 ~ 1000 °C. The thickness and the refractive index within the visible range were measured by an ellipsometer, which were 0.93 mm and 1.454, respectively.
Figure 4(a) shows the measured differential signal in 0.93 mm SiO2 film. The amplitude of the differential signal was 1% of the reference signal.
The dielectric and optical properties of SiO2 can be obtained from the amplitude and the phase information from Fourier transformation of the measured differential and the reference terahertz waveforms mentioned in the beginning of this section and equations (3) to (7). Figure 4(b)-(d) shows the dielectric properties of 0.93 mm SiO2 including the real and imaginary parts of the dielectric constant, the real and imaginary parts of the refractive index, and absorption. The averaged real and imaginary parts of dielectric constant were 4.5 and 0.07, respectively, over the available spectrum. The averaged refractive index of our SiO2film over the gigahertz to terahertz frequency range was 2.153, which is close to the value (2.11) of the refractive index of a-crystalline bulk SiO2. The measured k value of the SiO2film ranges from 0.01 to 0.02, which is close to the literature [19].
The absorption coefficient of SiO2 film ranges from 4 to 20 cm-1. The result is well fitted to the value in the literature [20].
Parylene
Parylene (poly-p-xylylene) has been studied as a low dielectric material (e' = 2.65), which is one of the materials for the interconnection [21]. Many polymeric thin films can act as replacements for SiO2 because of lower dielectric properties than those of SiO2. Parylene-n films were vapor deposited. Parylene-n dimer is heated to 400 or 500 °C and becomes vaporized. Vaporized monomer and dimer species condense on the substrate at room temperature and form thin films. The systematic investigation of the optical properties of parylene has not been performed before in the entire spectrum. The dielectric property of the polymer contributes to the molecular dipole moment of the polymer. Only within the terahertz and radio frequency range was the dielectric property of parylene film studied [22]. Its refractive index was measured as n = 1.62 in the terahertz frequency range by using terahertz goniometric time- domain spectroscopy (GTDS) [22].
The differential signal of the 300 nm parylene-n film was 0.2 % of the reference signal as shown in Figure 5(a). Figure 5(b)-(d) shows the complex dielectric and optical properties of 300 nm parylene-n film on Si substrate. The amplitudes of the films on Si were reduced by Fresnel loss of silicon substrate.
The average refractive index and dielectric constant of 300 nm parylene-n film over the observed frequency range were n = 1.62 and e' = 2.63, respectively.
The dielectric and optical constants of this parylene-n film is comparable to value n = 1.63 and e' = 2.65 in the megahertz range [23]. These values are also comparable to the result measured by terahertz goniometric time-domain spectroscopy.
The absorption tends to be higher at high frequency. Some structures, like small valleys around 1.1 THz in absorption, seem to come from noise. At 300 GHz, the absorption coefficient of parylene-n thin films were about 0.9 cm-1, which is comparable with absorption value (1.6 cm-1) in plastic materials such as epoxy resin or PVC [19].
In the 300 nm parylene-n film, the fluctuation of the dielectric properties due to noise was slightly increased in the low-frequency and high-frequency parts since the amplitude in the low- and high-frequency parts is much smaller than that in the center of the spectrum. | 
| | 5. The differential terahertz waveform and the dielectric and optical properties of 300nm parylene-n thin film. (a) The differential and reference waveform; (b) complex dielectric constants, e, and e"; (c) complex refractive indices, n and k; (d) absorption coefficient, X. |
Tantalum Oxide
Tantalum oxide film is large refractive index and low absorption coefficient material over a wide spectrum range, which can be used for applications including high refractive index interference filters, antireflection coating in solar cells, or in optical wave guides or ion conductors in semiconductor devices [24]. Since tantalum oxide thin film has high static dielectric constant and good insulating properties, it can be used for a capacitor and gate material as an element of metal-insulator-metal and metal-insulator-semiconductor structures. Several chemical composites of tantalum oxide can be formed such as TaO2, Ta2O5, and TaOx, depending on its deposition methods.
A variety of methods for tantalum oxide film growth have been utilized as physical and chemical vapor deposition: ion beam sputtering, thermal oxidation, magnetron sputtering, and so on. Low-temperature-grown tantalum oxide film tends to be amorphous and further annealing above 700 °C causes crystallization.
The dielectric properties show dispersion at 0.7 eV due to phonon interaction and at 4.5 eV due to electronic transition. Its bandgap ranges from 4 eV to 5 eV depending on its chemical composites of tantalum oxide. | 
| | 6. The differential terahertz waveform and the dielectric and optical properties of 100 nm tantalum oxide thin film. (a) The differential and reference waveforms; (b) complex dielectric constants, e' and e"; (c) complex refractive indices, n and k; (d) absorption coefficient, a. | The measurement of dielectric and optical properties of tantalum oxide within the terahertz frequency range has not been previously investigated. The dielectric property of tantalum oxide was known in the megahertz range [25] and it varies from 20 to 100. The dielectric constant of the crystalline tantalum oxide is larger than that of amorous, which varies from 50 to 100. To investigate the dielectric and optical properties of tantalum oxide within the terahertz range, a 100 nm TaOx was prepared and the differential measurement of terahertz wave was performed. That sample was prepared by a reactive sputtering (ion bombardment) of a Ta metal in oxygen atmosphere. Figure 6(a) shows the differential waveform in 100 nm TaOx.
The amplitude of the measured differential signal was 3% of the reference signal. Figure 6(b)-(d) shows the measured dielectric and optical properties of 100 nm TaOx film. The measured values of the real and imaginary parts of the dielectric constant and optical constant of the TaOx film were e' = 59, e" = 1.8, n = 7.7, k = 0.07 ~ 0.17, and a = 24 ~100 cm-1.
Some properties of thin films are slightly different from the bulk materials, which may result from the presence of fine grains, mechanical stresses, formation of interfacial layers, or rough interfaces during thin-film deposition process [6], [26].
Conclusion The terahertz differential time-domain spectroscopic method is applied to characterize the dielectric and optical properties of a variety of thin films at terahertz frequency. The results of several samples including silicon dioxide, parylene-n polymer film, tantalum oxide film, and protein thin layer samples were presented.
The dielectric property of silicon dioxide thin film is well fitted to that of a bulk. The dielectric properties of parylene-n thin films show good agreement with the result measured by the goniometric terahertz time-domain spectroscopy. The dielectric and optical properties of the tantalum oxide show reasonable data with previously available data. Some properties in thin films are slightly different from the bulk materials. The origin of this discrepancy is considered due to fine grain formation, mechanical stresses, formation of interfacial layers, or rough interfaces during thin-film deposition process.
The terahertz differential time-domain spectroscopy may be applied to the measurement of the dielectric and optical properties of thin films (nanometer to micrometer) of several materials, which cannot be done by any other method.
Acknowledgments
This work was supported by the National Science Foundation, Army Research Office, and the Center for Advanced Interconnect Science and Technology at Rensselaer. Kwang-Su Lee, Toh-Ming Lu, and X.-C. Zhang are with the Department of Physics at Rensselaer Polytechnic Institute in Troy New York. E-mail: zhangxc@rpi.edu.
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