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Permittivity of Undoped Silicon in the Millimeter Wave Range electronics Article Permittivity of Undoped Silicon in the Millimeter Wave Range Xiaofan Yang 1, Xiaoming Liu 2,3,* , Shuo Yu 2, Lu Gan 2,3, Jun Zhou 4,* and Yonghu Zeng 1 1 State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, Luoyang 471003, China 2 School of Physics and Electronic Information, Anhui Normal University, Wuhu 241002, China 3 Anhui Provincial Engineering Laboratory on Information Fusion and Control of Intelligent Robot, Wuhu 241002, China 4 Terahertz Research Centre, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China * Correspondence: [email protected] (X.L.); [email protected] (J.Z.) Received: 18 July 2019; Accepted: 8 August 2019; Published: 10 August 2019 Abstract: With the rapid development of millimeter wave technology, it is a fundamental requirement to understand the permittivity of materials in this frequency range. This paper describes the dielectric measurement of undoped silicon in the E-band (60–90 GHz) using a free-space quasi-optical system. This system is capable of creating local plane wave, which is desirable for dielectric measurement in the millimeter wave range. Details of the design and performance of the quasi-optical system are presented. The principle of dielectric measurement and retrieval process are described incorporating the theories of wave propagation and scattering parameters. Measured results of a sheet of undoped silicon are in agreement with the published results in the literature, within a discrepancy of 1%. It is also observed that silicon has a small temperature coefficient for permittivity. This work is helpful for understanding the dielectric property of silicon in the millimeter wave range. The method is applicable to other electronic materials as well as liquid samples. Keywords: millimeter wave; quasi-optics; free space method; undoped silicon; permittivity; temperature 1. Introduction Dielectric permittivity plays a fundamental role in describing the interaction of electromagnetic waves with matter. The boundary conditions, wave propagation in matter, and wave reflection/ transmission on interfaces all involve this parameter. In practical applications, the processes of link budget (wave attenuation), channel characterization (wave dispersion), and multi-path effect (reflection/transmission) are representative examples of wave interaction with media [1]. Understanding these phenomena is a fundamental requirement in communication system design. With the rising of millimeter wave technology, for example, 5G communication [2], millimeter wave radar and sensing [3], accurate characterization of electronic materials for these applications is of fundamental significance. Although the dielectric properties have been widely investigated in the microwave range or below, the work in the millimeter wave range is much less thorough. The reason is that it has been a long period that the operation frequency of communication systems has been limited to the low frequency range [4]. However, problems such as frequency shift and increased insertion loss are often observed in the millimeter wave circuit design due to inaccurate permittivity [5]. In view of these facts, it is necessary to investigate the dielectric property of materials in the millimeter wave range. Particularly, we restricted our study in the E-band (60–90 GHz), mainly due to the fact Electronics 2019, 8, 886; doi:10.3390/electronics8080886 www.mdpi.com/journal/electronics Electronics 2019, 8, 886 2 of 12 that many applications fall in the range, such as the planned unlicensed 64–71 GHz band for 5G communication in the USA [6] and 77 GHz vehicle radar [7]. In addition, we selected silicon as the representative materials for measurement since it is one of the most important semiconductor materials in electronic systems. There are many publications focused on the complex permittivity of silicon [8–17]. Reference [8] used a capacitive method, which was suitable for measurement in low frequency range. Reference [9] investigated the n-type silicon at 107.3 GHz using a non-focusing free-space system. Afsar and his colleagues [10,11] measured several semiconductor samples using dispersive Fourier transform spectroscopy (DFTS) and presented data over 100–450 GHz [10,11]. It was found that the permittivity slightly increased with frequency from 100 to 180 GHz and then decreased with frequency. In contrast, the loss tangent decreased with the frequency monotonically. However, for silicon of resistivity 11,000 W cm, the loss tangent increases with frequency (see Figure 3 in Reference [11]). The Fabry–Perot · resonator was also utilized for silicon characterization over the frequency range of 30–300 GHz [12]. Additionally, it was found that the permittivity had a slight tendency of linear decreasing over the frequency range. An extensive investigation was conducted by Krupka and his colleagues [12–16]. These measurements used resonator techniques at various frequency ranges below 50 GHz. It was demonstrated that the loss tangent decreased with increasing frequency, and in most cases on the order 4 of 10− . Temperature effects were also systematically investigated over the range of 10–370 K. The real part showed very stable properties over the investigated frequency and temperature ranges, in the worst case in the range of 11.46–11.71. These findings provide valuable reference to the permittivity of silicon. In these studies the E-band is covered in [12], where it was stated that the refractive index decreased linearly with frequency. Although it is in a small magnitude, such a statement is slightly different from other publications. Considering that many applications have been developed in the E-band, it is best to conduct the measurement in this band. In consideration of these facts, this paper introduces a broadband method for dielectric measurement on semiconductor materials, with measurement conducted on undoped silicon. A detailed description on the condition of creating quasi-plane wave is given. Plane wave is very desirable in free space measurement. The retrieval of the permittivity incorporates the theories of wave propagation and scattering parameters. Temperature dependent characteristics are examined at 20, 25, and 30 ◦C. The remaining parts are organized as follows: Section2 is devoted to a general description on the permittivity and measurement techniques; Section3 describes the method generating a quasi-plane wave; Section4 is the retrieval method and Section5 is the measurement results; the last part Section6 concludes this work. 2. Permittivity and Measurement Techniques Dielectric permittivity is a macroscopic description of many microscopic processes, such as dipole relaxation, lattice vibration, and electronic polarization. These processes take effect at different characteristic frequency ranges, as illustrated in Figure1. Electronics 2019, 8, 886 3 of 12 Electronics 2019 , 8, x FOR PEER REVIEW 3 of 12 εr ( ω ) Polar molecules ε′ ω r ( ) Electronic Polarization Lattice Ions effect εr′′ ( ω ) No ions effect 10 3 10 6 10 9 10 12 10 15 (Hz) Microwave Terahertz Visible and purple FigureFigure 1. 1.An An illustrationillustration ofof frequencyfrequency dependentdependent dielectric dielectric e effffect.ect. The permittivity is actually a complex quantity. The imaginary part is due to dielectric loss. The permittivity is actually a complex quantity. The imaginary part is due to dielectric loss. One One representative mechanism of loss is the dipole relaxation [1]. When a dipole tries to follow the representative mechanism of loss is the dipole relaxation [1]. When a dipole tries to follow the alternating electric field, friction between dipoles would cause loss of energy. Other mechanisms alternating electric field, friction between dipoles would cause loss of energy. Other mechanisms include conductive loss and lattice loss. These mechanisms can be incorporated into a single parameter include conductive loss and lattice loss. These mechanisms can be incorporated into a single the complex permittivity parameter the complex permittivity "r = "0r j"00 r, (1) − εr= ε r′ − j ε r ′′ , (1) where the real part is the relative permittivity and the imaginary part is referred to as the loss factor. Sincewhere these the real mechanisms part is the fall relative in di ffpermittivityerent frequency and the ranges, imaginary the permittivity part is referred exhibits to as athe dependency loss factor. onSince frequency these mechanisms fall in different frequency ranges, the permittivity exhibits a dependency on frequency "r(!) = "0r(!) j"00 r(!). (2) − Referring back to Figure1, it has to beεωr( noted) = εω that r′( ) the − j εω ticks r ′′ ( ) . on the axes are not to exact scale, only(2) for illustrative purposes. Referring back to Figure 1, it has to be noted that the ticks on the axes are not to exact scale, only Methods of dielectric measurement shall vary with frequency due to the frequency dependent and for illustrative purposes. electrical size effects. Several methods can be used for dielectric measurement in the millimeter wave Methods of dielectric measurement shall vary with frequency due to the frequency dependent range, such as resonator method, transmission line method, and free space method [18]. The resonator and electrical size effects. Several methods can be used for dielectric measurement in the millimeter technique is an efficient way for low-loss single frequency measurement. The
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