Selection of thin-film-integrable substrates for THz modulator

Terahertz (THz) wave refers to the electromagnetic wave whose frequency is in the range of 0.1–10THz, between microwave and far infrared. In recent years, important application prospects of THz wave in medicine,¹ biology,² environmental monitoring,³ THz imaging,⁴ THz radar,⁵ THz communication⁶ and other fields are emerging. In particular, THz communication offers great potential for future 6G communication,⁷ in which THz modulator plays a vital role.

At present, a variety of materials had been used in THz modulators such as graphene,⁸ VO₂⁹ and metamaterials.^10,11 Recently, ferroelectrics with Pockels effect and effective dielectric tunability had been another promising candidate for application in high-speed and low-power light modulators.¹² The report of ultrafast 1550nm modulation in micro- and nano-structured BaTiO₃ thin films integrated on silicon has made thin film ferroelectrics promising for THz light modulations.¹³ For the ferroelectric and VO₂ thin films with nanometer thick, the substrate directly influences the lattice strain and quality, which plays a key role in the electro-optical properties of the material.¹⁴ Therefore, it is necessary to select suitable substrates. At present, there are several substrates in common use as follows. First of all, perovskite oxide and VO₂ occupy a significant part in the classical inorganic oxide substrate materials such as SrTiO₃, GdScO₃(GSO) and TbScO₃(TSO) have good lattice matching with them, so that they are excellent substrate materials for ferroelectric film. Second, epitaxial ferroelectrics, such as BTO and VO₂ films, had been successfully grown on single crystal metal oxide substrates,^15,16 whose low refractive index and good optical transparency in visible frequency range make it one of the alternative substrate materials for ferroelectric film waveguide in THz range. Third, sapphire, mainly composed of Al₂O₃, occupies the most important position in the field of substrate materials due to its excellent mechanical properties, chemical properties and dielectric properties. Finally, silicon-based semiconductor substrate is the main choice of optical integrated circuits technology at present, and silicon-based optoelectronic integrated circuit (OEIC) is one of the research hotspots. In recent years, some researchers have achieved the epitaxial growth of ferroelectric (i.e., BaTiO₃, HZO) and nonferroelectric materials (i.e., VO₂, graphene) and other ferroelectric materials on silicon substrates by MBE, ALD and other methods.^12,17,18,19 All the single crystal materials mentioned above are excellent substrates for the preparation of optical functional epitaxial thin films. However, this research works on these substrates in THz band are limited, which is not conducive to clarify how to design epitaxial ferroelectric film for THz signal modulation.

The substrate needs to have high transparency and low absorption in the THz band, while the substrate with high dielectric constant such as STO and PMN-PT has strong absorption in the infrared and far infrared bands. Therefore, in order to have high transparency in THz range, the substrate should have generally low dielectric constant. In this work, we have selected several commonly and commercially used substrates for the preparation of epitaxial ferroelectric films, including silicon-based and nonsilicon-based substrates. Silicon-based substrates, including Si and quartz SiO₂, were chosen. While metal oxides, including MgO, Al₂O₃, GdScO₃(GSO) and TbScO₃(TSO), were selected as nonsilicon-based substrates. Their crystal structure and lattice constants are shown in Table 1. Then the THz time-domain spectra of these substrates were measured with transmission THz time-domain spectrometer (THz-TDS). On this basis, the optical constant and dielectric constant of different substrates in the THz band were extracted by spectrum transformation with detailed analysis and comparison.

The silicon substrates used in this experiment include: (1) intrinsic (001)-oriented Si with resistivity $>10000\mathrm{\Omega }\cdot$cm; (2) Intrinsic (111)-oriented Si with resistivity $>10000\mathrm{\Omega }\cdot$cm; (3) N-type doped (001)-oriented Si with resistivity $>1000\mathrm{\Omega }\cdot$cm; (4) N-type doped (111)-oriented Si with resistivity $<0.02\mathrm{\Omega }\cdot$cm; (5) quartz (SiO₂). The size of all single crystal silicon substrates used is $10\times 10\times 0.5$mm³, and recorded as Si ①∼④ in the above order. Besides, the size of quartz SiO₂ is $5\times 5\times 1$mm³. The orientation of the MgO substrate used here is (001), whose size is $10\times 10\times 0.5$mm³. The (0001)-oriented Al₂O₃, (001)-oriented GSO and (110)-oriented TSO substrates all have the same dimensions of $5\times 5\times 0.5$mm³. All substrates were bought from commercial sources ($\mathrm{\text{Purity}}>99.99$%).

The dielectric properties of these substrates were characterized using an all fiber coupled terahertz time-domain spectroscopy system, the principle of which is shown in Fig. 1. The output pulse of femtosecond laser (1560nm) is divided into two beams by a beam splitter. One beam illuminates on the GaAs photoconductive emitter to generate terahertz radiation, and the other beam is used for detecting terahertz fields through a delay line. The terahertz field distribution is measured through electro-optic sampling. When the terahertz wave passes through the ZnTe crystal, due to its pockels and birefringence effects, the detection wave changes from linear polarization to elliptical polarization, and then is divided into two beams of s-polarization and p-polarization whose intensity difference is proportional to the terahertz field through the Wollaston prism. Then, a differential detector is used to convert the difference in intensity between these two beams into a current difference, and finally, a lock-in amplifier is used to obtain information on the amplitude and phase of the terahertz field. The overall bandwidth of the TDS system is from 0.1THz to 4THz, with a signal-to-noise ratio (SNR) of approximately 123dB and a dynamic range greater than 60dB.

In order to reduce the influence of vapor, measurements were performed at room temperature in a nitrogen environment. After the time-domain data of the samples were obtained, the transmittance, dielectric constant and other parameters of different tested substrates in THz band were extracted through the Matlab program based on the Fourier transform.

Figure 2(a) shows the transmission time-domain spectra of different silicon-based substrates. High-resistivity silicon (HR-Si) with different orientations and resistivities had different time delays in the time domain. Figure 2(b) shows the frequency domain spectrum obtained by Fourier transform of the time-domain spectrum of air. The frequency range of this study is from 0.4THz to 1.6THz, which constitutes an acceptable frequency range for good SNR. Figure 2(c) is the transmittance of different silicon-based substrates, from which we can see that the transmittance basically did not change with frequency, about 50%. However, low-resistivity silicon with resistivity less than 0.02$\mathrm{\Omega }\cdot$cm was basically impervious in the 0.4–1.6THz band as the transmittance of silicon decreased with the decrease of resistivity. The difference in the time-domain spectra and transmittance of intrinsic silicon with the same thickness and different orientations should not be significant in theory because of their similar low conductivity. However, it can be seen from the test results that there is a difference of about 0.3ps in the time-domain spectra of these two substrates, and the transmittance is also slightly different. This is because although the purchased silicon wafers are theoretically 500$\mu$m, there is actually an error. There is a difference of about 25$\mu$m between the two different orientations of silicon wafers, which is consistent with the difference in time-domain. For quartz SiO₂, with the increase of frequency, the transmittance shows a downward trend, which is slightly higher than that of HR-Si.

In Fig. 3, time-domain waveforms and the change of transmittance with frequency in the range of 0.4–1.6THz of the four kinds of nonsilicon substrates: GSO, TSO, Al₂O₃ and MgO are plotted, respectively. It is easy to see that the THz wave through GSO and TSO had greater distortion compared with air background with relatively low transmittance $<20$%, and the time delay was longer. However, the time-domain waveform distortion of Al₂O₃ and MgO was small with transmittance of about 50%. These results suggest that Al₂O₃ and MgO substrates would be better to be used for integration of THz modulator.

Based on the TDS data, the refractive index, absorption coefficient, dielectric constant and dielectric loss of all the above-measured substrates were extracted based on Matlab program following principle²⁰ :

where d is the thickness of tested substrate, $\phi (\omega )$ and $\rho (\omega )$ represent the phase difference and the ratio of amplitude of sample signal and reference signal, respectively. It could be seen from Figs. 4(a) and 4(c) that the refractive index and dielectric constant of all substrates hardly changed with the change of frequency. The refractive index and dielectric constant of three kinds of HR-Si with different orientations and resistivities were basically the same in the range of 0.4–1.6THz. The refractive index of them was about 3.50, and the dielectric constant was about 12.25. In addition, the refractive indexes of quartz SiO₂, TSO, GSO, Al₂O₃ and MgO are about 2.00, 4.75, 5.15, 3.07 and 2.95, and the dielectric constants are about 4.0, 26.5, 22.5, 9.5 and 8.5, respectively. Some metal oxides such as Al₂O₃, MgO, quartz SiO₂ and HR-Si have small refractive indexes, so that they are appropriate for optical waveguide substrate materials, while the refractive index of TSO and GSO are large, which are not suitable as waveguide substrates. However, compared with Si with n about 3.5, Al₂O₃ and MgO show lower refractive index around 3, while quartz SiO₂ shows the lowest n below 2 as well as excellent k.

We further analyzed their THz dielectric and absorption spectra. It could be seen from Figs. 4(b) and 4(d) that the quartz SiO₂, Al₂O₃ and MgO show very small absorption coefficient and dielectric loss, indicating that they had extremely low loss in the THz band. However, the absorption coefficient and dielectric loss of TSO and GSO were relatively large, which indicates greater THz absorptions. Silicon generally has dielectric constant over 10, which is much higher than quartz SiO₂, Al₂O₃ and MgO. For HR-Si, it can be seen that the absorption coefficient and dielectric loss of Si③ (N-type-doped (001)-oriented Si with resistivity $>1000\mathrm{\Omega }\cdot$cm) were significantly greater than that of Si① (intrinsic (001)-oriented Si with resistivity $>10,000\mathrm{\Omega }\cdot$cm) and Si② (Intrinsic (111)-oriented Si with resistivity $>10,000\mathrm{\Omega }\cdot$cm), because the complex dielectric constant of silicon depended on its conductivity (i.e., free carrier concentration), as the resistivity of silicon decreases, the imaginary part of the dielectric constant increases.²¹ Meanwhile, silicon would absorb more terahertz wave. Compared with Si, Al₂O₃ and MgO show lower dielectric constant in the range of 8.5 to 9.5. By contrast, quartz SiO₂ also shows the lowest dielectric constant below 5. Considering the much lower dielectric constant, absorption coefficient, refractive index, quartz SiO₂ would be the best integrable substrates for high-quality THz modulation.

The transmittance, optical and dielectric parameters of different substrates, including Si, quartz SiO₂, TSO, GSO, Al₂O₃ and MgO, in the range of 0.4–1.6THz were characterized by THz-TDS. TSO and GSO are certainly not appropriate for ferroelectric thin film deposition to be used for THz light modulation for their relatively higher absorption and dielectric constant. The refractive indexes of the Si and quartz are $\sim 3.4$ and $\sim 2$, respectively, which are close to that reported in the literature.^22,23 For Si, with the decrease of silicon resistivity, its THz wave absorption increases and finally becomes completely impervious to THz wave. Compared with LR-Si, HR-Si, quartz SiO₂, Al₂O₃ and MgO have better transmittance, low refractive index and loss in the THz band. Though Si is best for integrated opto-electric circuits, the dielectric constant and refractive index of Si is generally two times larger than quartz SiO₂, Al₂O₃ and MgO. Compared with Al₂O₃ and MgO, quartz SiO₂ shows 50% lower in dielectric constant, refractive index ($\sim 2$), and absorption which makes it the best candidate within the above-mentioned integrable substrates for application in THz range. This work would provide a guidance for the selection of integrable substrates used in THz devices.

Acknowledgments

We acknowledge Natural Science Foundation of China (52202134 and 61971459) and National Science Foundation (52202134), National Key Research and Development Plan (2021YFA1202100), Shenzhen Technology Plan (JCYJ20190809095009521), 2021 Independent Innovation Fund-New Teacher Research Starting Fund of Huazhong University of Science and Technology (5003182109) and Innovation Team Program of Hubei Province (2019CFA004), the Innovation Fund of WNLO, 2022 Shenzhen Central Leading Local Science and Technology Development Special Funding Program Virtual University Park Laboratory Project.

ORCID

Jia Ran  https://orcid.org/0000-0002-8603-445X

Wen Dong  https://orcid.org/0000-0001-7242-7239

Qiushuo Sun  https://orcid.org/0000-0002-6898-6078

Guangzu Zhang  https://orcid.org/0000-0003-0659-4527

Wei Luo  https://orcid.org/0000-0003-0836-9083

Qiuyun Fu  https://orcid.org/0000-0001-6352-5144

Shenglin Jiang  https://orcid.org/0000-0002-6500-7364