Wideband dielectric properties of silicon and glass substrates for terahertz integrated circuits and microsystems

This paper presents a comprehensive study of the optical and electrical dielectric material properties of six commonly-used silicon and glass substrates at terahertz (THz) frequencies, including refractive index, absorption coefficient, dielectric constant and loss factor. The material characterization techniques used in this paper feature THz time-domain transmission and reflection spectroscopy with the measurement frequencies from 0.5 THz up to a maximum of 6.5 THz. Of the six selected dielectric and semiconductor substrates, two are silicon wafers with resistivities ranging from 0.001 to 0.02 Ω-cm. From the measurement results, loss tangents of the selected silicon wafers range from 0.680 to 5.455 and the dielectric constants are from 1.079 to 17.735. The four other wafers are all glass-based substrates: D263 glass, Borofloat 33 glass, fused silica and Sapphire. From the measurements, it is found that the THz dielectric properties vary considerably between the substrate samples e.g. dielectric constants range from 1.925 to 3.207 while loss tangents are from 0.042 × 10−3 to 0.127. Most of the selected silicon and glass-based substrates are quite useful for many THz applications, e.g., THz integrated circuits (THz ICs), THz microsystem technologies (THz MSTs) and THz system-on-a-chip (THz SoC) and system-on-substrate (SiP).


Introduction
Terahertz (THz) research activities have grown significantly over the last few decades with many useful applications including wireless communications [1][2][3][4], real-time and high-resolution imaging [5], material characterization [6], space communications [7,8], as well as chemical and biomedical sensor technologies [9,10]. As an example, the THz frequency spectrum provides many advantages over RF and microwave bands such as large available bandwidth and high data rate that can achieve multiple terabit-per-second channels for short and medium-range wireless communications, which are very useful for many future scientific and engineering applications. Even though THz technologies can be potentially used for a wide range of applications, most of the state-of-the-art THz components and systems that have been reported in research papers and commercially launched on to the market to-date are often bulky and expensive [2].
Nowadays, many world-leading researchers are moving their research activities toward integrated circuits (ICs), system-on-chip (SoC) and system-in-package (SiP) at THz frequencies using silicon and glass technologies. The THz integrated circuits (THz ICs) and THz micro-electromechanical systems (THz MEMS) that can operate from 100 GHz and up to several hundreds of gigahertz [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Silicon, such as CMOS and BiCMOS, and glass-based technologies are good candidates for THz circuits and systems since they are able to provide a high level of integration with consumer electronics, offering great potential to integrate THz systems onto a single chip or substrate [3,[21][22][23][24][25][26]. They can also achieve high yield at low fabrication cost for mass production, which is needed to decrease overall production cost per unit while still achieving excellent performance compared to their compound semiconductor counterparts such as GaAs and InP technologies. However, the lack of comprehensive data for the substrate material properties, such as dielectric constant, loss  tangent and absorption coefficient, at THz frequencies above one THz drastically limits the usability of silicon and glass-based technologies. Currently, there are some research works reporting on both optical and electrical dielectric properties of only a few different glass and silicon substrates for a maximum frequency of up to approximately 3 THz [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. This paper presents the comprehensive dielectric material properties in both optical and electrical domains, such as dielectric constant, loss tangent and absorption coefficient, of six commonly-used silicon and glass substrates, measured using THz time-domain spectroscopy (THz TDS) over a frequency range from 0.5 THz to 6.5 THz. The important material information of the selected silicon and glass substrates such as crystal orientation, substrate resistivity, doping level, etc are summarized in table 1. Both transmission and reflection THz spectroscopy techniques were used to characterize the selected substrates depending on the relevance to the wafer samples, e.g. substrate thickness, wafer diameter and material resistivity. This characterization of dielectric material parameters is a significant step in the development of various integrated passive and active THz components for THz ICs, THz MST and THz SoC/SiP devices.

THz time-domain spectroscopy systems
shows the schematic diagrams of the transmission and reflection measurement systems, respectively. The working principle and measurement setup of the free-space THz-TDS systems have been reported previously [31,[40][41][42][43][44][45]. The choice between transmission and reflection measurement depends on the physical and dielectric properties of the material-under-test (MUT), e.g. thickness and loss levels of the MUT. Transmission measurements are suitable for characterizing most substrate materials, which are generally thin samples of low-attenuation dielectric or semiconductor materials. The main advantage of the transmission technique is the ease with which distinct absorption peaks can be observed in the response during the material measurement, either in refractive index or dielectric constant. Transmission measurements can achieve very accurate results for the extracted material parameters.
However, the transmission technique is not suitable for thick samples of dielectric and semiconductor materials, or for materials-under-test with high signal attenuation [42,43,45]. In these cases, the reflection method is preferable. Rather than pre-judge the results, both the transmission and reflection techniques were used in this work as complementary material characterization methods providing a complete set of MUT data. The measurement system gives highly accurate results and provides quick indication of the properties of the six wafers with a better than 93% accuracy. The standard deviation of the measurement system is lower than 0.0271. However, due to high absorption of some of the MUT samples in this work, the extracted dielectric and optical properties for some materials cannot be reported over the whole frequency band of 0.5 to 6.5 THz.

Transmission and reflection measurement setup
The transmission and reflection TDS systems were based on established optical bench setups in the Terahertz Laboratories of the Pollard Institute at Leeds. A commercial mode-locked Ti:Sapphire laser (Coherent Vitara-T-HP) operating at 800 nm was employed, set to a repetition rate of 80 MHz, pulse width of 20 fs and with an average power of up to ∼1 W [46]. The THz emitter and detector are both photoconductive antennas (PCA), comprising two bow-tie shaped Ti:Au electrodes with a 200 μm gap between them, deposited on lowtemperature-grown GaAs (LT-GaAs) and transferred onto z-cut quartz substrate [40]. In both the transmission and reflection setups, the laser output is split into two beams using an 80:20 beam splitter. The higher power beam is fed to one PCA to generate the THz pulse, while the weaker beam is fed to the other PCA for gated detection of the THz signal received from the sample. The signal generation PCA is biased at 350 V and electrically chopped at 7 kHz, and the resulting THz radiation is then collected, collimated and re-focused by a set of off-axis parabolic mirrors. A silicon wafer is used as a filter to block any stray laser light reflected from the emitter surface from reaching the detector, while allowing the majority of the THz radiation to pass through. In the transmission system, shown in figure 1(a), the THz radiation is collected by a second set of off-axis parabolic mirrors and focused onto the PCA detector. Before the material under test (MUT) is inserted, a reference 'thru' measurement is made. Then, the sample is measured by placing it centrally in the 2-inch collimated THz beam that is formed between this second set of off-axis parabolic mirrors. In the reflection measurement setup, shown in figure 1(b), the THz radiation is focused onto the sample, which is set at a 45°a ngle of incidence, using parabolic mirrors. A second pair of parabolic mirrors is used to re-collimate the reflected THz signal and focus it onto the PCA detector. A reference measurement was performed using a large area of Ti:Au conductor (100 nm thick, deposited on the same wafer) as a reflection standard.
In both setups, the 800 nm laser beam is focused onto the PCA detector through a hole in the final parabolic mirror. Only when both the laser pulse and THz radiation are incident on the detector, can the THz field at that point in time be measured. A linear delay stage is, therefore, used to synchronize the optical and THz pulses at the detector and ensure that the full THz electric field is sampled. The output signal from the PCA detector is first amplified using a transimpedance amplifier and then measured using a lock-in amplifier referenced to the bias frequency of the THz PCA emitter. The THz part of the system is enclosed in a Perspex box so that it can be purged with dry air to a humidity of<1%. This is important in order to remove water vapor absorption effects from the measured data.

Material characterization extraction
Free-space THz-TDS is now the most common technique to characterize material properties at THz frequencies. Both the amplitude and phase of the measurement signal are collected simultaneously and can be used to extract both the optical properties, e.g., refractive index and absorption coefficient, or the electrical properties, e.g. dielectric constant and loss factor of the MUT. The complex refractive index, w n ,( ) can be related to the complex permittivity, e w ,( ) via the mathematical relation w ew = n , 2 (˜( ))˜( ) where w is the angular frequency [47,48].
The,  (1), the refractive index, w n , sample ( ) and extinction coefficient, w k , sample ( ) of the MUT can be represented as follows:

From equation
where c vacuum is the velocity of light in vacuum and d is thickness of the wafer in centimeters. The extinction coefficient, w k , sample ( ) can be calculated in terms of the absorption coefficient, a, as follows: The complex permittivity can be represented by e w e w e w = ¢ -¢¢ j ,( ) ( ) · ( ) where the real and imaginary parts are e w ¢( ) and e w ¢¢ , ( ) respectively. The real part, e w ¢ , ( ) and imaginary part, e w ¢¢ , ( ) of the complex permittivity are expressed by: For the electrical properties, the dielectric constant is equal to the real part of the permittivity, e w ¢( ) and the loss tangent can be calculated as follows: Table 1 lists the selected semiconductor and dielectric substrates to be characterized, which are commonly used in ICs, MSTs and SoC/SiPs, with their relevant detailed information e.g. names and types of material, level of dopant, substrate thickness and diameter, and substrate resistivity. All the selected substrates [50], have a substrate diameter of 100 mm that fits in a 4-inch optics holder. Before mounting the substrate-under-test in the holder, the tested wafer was cleaned to remove both organic and inorganic contaminations by dipping it firstly into acetone and then isopropyl alcohol and immediately rinsing in deionized water before drying it in a clean environment at room temperature using laboratory-grade dry compressed air. Individual measurements were repeated at least two times to ensure the repeatability. The averages were subsequently used to extract the optical and electrical dielectric material properties of the six commonly-used silicon and glass substrates. Owing to the dynamic range of both THz-TDS instruments, the measurement of either very strongly absorbing or very weakly absorbing samples is difficult. Therefore, for strongly absorbing samples, the data has been truncated at the point that the spectra have intercepted the maximum absorption α max coefficient detectable [51]. For weakly absorbing samples, the data has been truncated at the point that the measured absorption coefficient is indistinguishable from a thru measurement. Therefore, not all samples have data presented across the entire 0.5 to6.5 THz range of the instrument.

Reflective indices
The refractive indices of all six wafers from 0.5 to 6.5 THz are shown in figure 2.

Absorption coefficients
The absorption coefficients of all six wafers characterized from 0.5 to 6.5 THz are shown in

Dielectric constants
From the measured refractive indices and absorption coefficients, equation (6) in section II can be used to calculate the dielectric constants of the six selected wafers, and these are shown in figure 4.  Figures 5 (a) and (b) depict the loss tangents of the six selected wafers, as determined using equation (8). From figure 5 (a), the silicon wafer with resistivity between 0.001-0.005 Ω-cm has a loss tangent that increases from 1.5 to 5.5 as a function of frequency. The silicon wafer with resistivity of between 0.01-0.02 Ω-cm has a loss tangent that decreases slightly from 1 at 0.5 THz to 0.68 at 5.0 THz. Figure 5(b) show the loss tangent of the four non-

Optical and electrical dielectric properties model
The high fluctuation in the measured data is shown in the data of silicon wafers with resistivities ranging from 0.001 to 0.02 Ω-cm due to the low loss materials. This means the interaction length between the THz beam and the sample is very small and the spectra are dominated by noise. The other problem is the low loss materials tend to lead to multiple reflections in the samples which in turn, lead to large oscillations in the frequency response.
To reduce the fluctuation in the measured data, the fluctuation data is filtered out and smoothened by using the commercial data analysis and visualization software package Origin [52], where a 5th order polynomial was used to provide the best fit with the standard deviation lower than 0.0271. The polynomial is given as       presented in [27] and [29] are plotted over the frequency range of up to 1.75 THz and 2 THz, respectively. The refractive indices at 1.75 THz of [27,29], and this work are 1.955, 1.964, and 1.952, respectively. The maximum difference of refractive index value between this work and [29] is 0.012. Three absorption coefficients (i.e., [27,29], and this work) at 1.75 THz are 605 m −1 , 685 m −1 , and 533.18 m −1 , respectively. The variation of the three absorption coefficients shows a similar trend, increasing at the higher frequency. In figure 6 (b), the refractive index and absorption coefficient of Sapphire are plotted. The maximum frequency of the data reported in [27] and [30] is 1.75 THz and 4 THz, respectively. At 1.75 THz, the refractive indices of [27,30], and this work are 3.079, 3.095, and 3.075, respectively. The maximum percentage difference of refractive indices of Sapphire between [30] and this work is 0.65%. The absorption coefficients of [27,30], and this work at 1.75 THz are 372 m −1 , 330 m −1 , and 297.57 m −1 , respectively. Three absorption coefficients show the same tendency, such that the value of absorption coefficient increases at higher frequency. The refractive index (i.e., the solid line with the indicated symbol) and absorption coefficient (i.e., the dashed line with symbol) of four borosilicate glasses (D263, Borofloat 33, Pyrex, and BK7) are illustrated in figure 6 (c). The Pyrex and BK7 used in [31,32] are a type of borosilicate glass, which are compared with the D263 and Borofloat 33 glass in this work. The trend of the D263 glass is similar to that trend of BK7. Specifically, the maximum refractive index is 2.53 at 1 THz. Above 1 THz, the value of the refractive index of D263 glass is slightly reduced to 2.42 at 1.4 THz. On the other hand, the trend of the Borofloat 33 glass is similar to Pyrex, such that the value of the refractive index is lower when the frequency increases. In [31,32], the maximum frequency of the data for Pyrex is 1.75 THz and 1.8 THz, respectively. Additionally, in this work, the refractive index of Borofloat 33 glass is expanded to 4.0 THz, and the value of Borofloat 33 glass slightly decreases between 2.102 and 1.958 from 0.5-3.8 THz. For the absorption coefficient of the borosilicate group, the extracted results of D263 and Borofloat 33 glass show good agreement when compared with BK7 and Pyrex, respectively. At the higher frequency, the values of the absorption coefficients of borosilicate glasses increase. To summarize the results of the comparison data and this work, the optical and electrical properties (e.g., refractive index, absorption coefficient, dielectric constant, and loss tangent) are listed in tables 6-9, respectively, which can be found in the appendix.

Conclusions
The optical and electrical properties of six selected wafers were characterized for their optical and electrical properties by using THz time-domain spectroscopy. The transmission method was used to measure the four wafers of D263 glass, Borofloat 33 glass, Fused silica and Sapphire. The reflection method was used to characterize the silicon wafers with low resistivity of 0.01-0.02 Ω-cm and 0.001-0.005 Ω-cm. The measurement results were presented from a low frequency of 0.5 THz to the highest frequency of 6.5 THz. To assess the accuracy and the reliability of the measurement results, the measured and extracted results have been compared with other published works of note and excellent agreement has been observed.