Spectroscopic Sensing Method of Liquid Permittivity with On-Chip Capacitor

Hongkie Lim; Dong-Ho Lee; Jusung Kim; Songcheol Hong

doi:10.26866/jees.2022.1.r.57

J. Electromagn. Eng. Sci > Volume 22(1); 2022 > Article

Lim, Lee, Kim, and Hong: Spectroscopic Sensing Method of Liquid Permittivity with On-Chip Capacitor

Regular Paper

Journal of Electromagnetic Engineering and Science 2022;22(1):28-33.

Published online: January 31, 2022

DOI: https://doi.org/10.26866/jees.2022.1.r.57

Spectroscopic Sensing Method of Liquid Permittivity with On-Chip Capacitor

Hongkie Lim¹, Dong-Ho Lee², Jusung Kim^3,^*, Songcheol Hong¹

¹Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea

²Department of Information and Communication Engineering, Hanbat National University, Daejeon, Korea

³Department of Electronics Engineering, Hanbat National University, Daejeon, Korea

^*Corresponding Author: Jusung Kim (e-mail: jusungkim@hanbat.ac.kr)

Received December 23, 2020 Revised April 28, 2021 Accepted June 1, 2021

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A liquid permittivity sensing method is proposed, which is based on measuring the S₂₁ of an on-chip capacitor submerged in a material under test (MUT). The real part of permittivity can be estimated from ɛ′ – |S₂₁| fitted relation in the frequency range of 100 MHz–5 GHz, which are pre-calibrated with four kinds of known materials. The on-chip capacitor is realized with a top metal in a complementary metal oxide semiconductor (CMOS) process, which has an inter-digitized structure featuring a small size of 150 μm × 195 μm. A simple circuit model of the capacitor is used to develop ɛ′ – |S₂₁| relation with a fitting parameter. It shows less than 6.4% root-mean-square (rms) error of ɛ′ for propanol (C₃H₈O) at 100 MHz–5 GHz.

Keywords: Calibration, Capacitive Sensor, Curve Fitting, Dielectric Spectroscopy, Inter-Digitized

I. Introduction

Dielectric properties (e.g., permittivity) of chemical and bio-molecules is useful for a variety of applications. In agriculture, the quality of its products is improved by measuring the permittivity of soil and leaves [1, 2]. For example, crop quality control is usually carried out by regularly monitoring the water content of crops [1]. The dielectric characterization is also employed in biomedical sensors, such as the monitoring of blood glucose and semen activity [3–6].

In [7], a complementary metal oxide semiconductor (CMOS) based transceiver IC is presented as a dielectric spectroscopy device, but an off-chip sensing capacitor is utilized to measure the off-chip liquid material under test (MUT). This off-chip sensing capacitor is implemented on the printed circuit board (PCB) with a bulky footprint and accompanying parasitics degrading the measurement accuracy. In [8], a PCB-integrated microwave sensor for the dielectric measurement of liquids is presented. The resonant frequency and the Q factor of the off-chip microwave sensor are used to estimate the complex permittivity of the material to be tested. However, the work in [8] also suffers from a large area, and additional packaging processes increase the cost of the permittivity sensor. Thus, integrated sensors on silicon to detect the permittivity of chemical and biochemical are promising with a reduction in its size and cost while offering lower power consumption [9].

Capacitance can be determined if the geometry of the conductor and the dielectric properties of the insulator between the conductors are given [10]. Then, dielectric spectroscopy is accomplished by measuring the admittance (or impedance) of the sensing capacitor whose dielectric constant is dictated by the MUT and extract its dielectric constant from the material dependent capacitance.

A sensing capacitor, as a critical interface between the MUT and the spectroscopy measurement system can be implemented in either on-chip or off-chip [7–9, 11]. As mentioned earlier, an off-chip sensing capacitor suffers from large parasitics and its bulky size. The interconnection between an off-chip capacitor and a spectroscopy device requires a careful attention as well.

In this work, we propose a design and am implementation of an on-chip capacitor for dielectric constant extraction featuring a small sensor size and lower parasitic, and built a low-cost. Utilizing the top metal in the CMOS back-end, inter-digitized conductors are fabricated using 28-nm CMOS technology. The dielectric properties between inter-digitized conductors are governed by the off-chip liquid MUTs by opening the passivation layer. The permittivity of the MUT is extracted within the 100 MHz–5 GHz frequency range by measuring the forward voltage-gain (S₂₁). Permittivity as a function of |S₂₁| at each frequency can be extracted by polynomial curve fitting. Additionally, we propose the weighted |S₂₁| equation to improve a sensor accuracy. Through a proposed curve-fitting calibration method, less than 6.4% root-mean-square (rms) error is successfully achieved when propanol (C₃H₈O) is used as a material.

This article is organized as follows. Section II discusses a simple but intuitive circuit model for the sensing capacitor. Section III presents measurement results and polynomial curve fitting method for calibration. The conclusion of this article is in Section IV.

II. Circuit Model of Sensing Capacitor

Fig. 1 shows the illustration of an on-chip sensing capacitor whose dielectric property is governed by the MUT. The sensing capacitor is in an inter-digitized fashion implemented with the top metal of the CMOS back-end process (LB in the 28-nm Samsung CMOS process). The passivation layer has to be removed in order to contact the top metal directly to MUT.

A side section view of the on-chip sensing capacitor with a simple equivalent circuit model is depicted in Fig. 2. Capacitance and conductance denoted as C_sensing and G_sensing are due to the E-fields passing through the MUT by two inter-digitized top metal nodes, while the E-fields passing through the inter-metal-dielectric (IMD) create undesired parasitic capacitance and conductance modeled as C_par and G_par, which are not related to the characteristics of the MUT. Additionally, capacitance due to the substrate, C_sub, is part of the network, which degrades the accuracy of the permittivity detection.

In the case of C_sensing and G_sensing, their values are determined according to the permittivity of the MUT (ɛ_MUT = ɛ_MUT′ – j · ɛ_MUT″). In contrast, C_par and G_par are fixed values governed by permittivity of the IMD (ɛ_IMD = ɛ_IMD′ – j · ɛ_IMD″).

Excluding the effect of C_sub, the real-part of admittance between two inter-digitized electrodes (Y_s) comes from G_sensing and G_par, while the imaginary part of Y_s is composed of C_sensing and C_par. G_sensing and G_par are circuit components due to the imaginary permittivity of MUT ɛ_MUT″ and IMD ɛ_IMD″, respectively, which corresponds to an energy loss. C_sensing and C_par come from the real permittivity of MUT ɛ_MUT′ and IMD ɛ_IMD′, respectively, representing energy storage [12]. Combined admittance between two electrodes can be expressed as follows.

(1)

Ys=jω·C0·(ɛMUT′-j·ɛMUT′′)+jω·C1·(ɛIMD′-j·ɛIMD′′)=jω·(C0·ɛMUT′+C1·ɛIMD′)+ω·(C0·ɛMUT′′+C1·ɛIMD′′)=jω·f(ɛMUT′)+ω·g(ɛMUT′′)

where C₀ (C₁) are coefficients of effective capacitance due to MUT and IMD and f(·) and g(·) denote nonlinear mapping functions from the permittivity of MUT to admittance as a result.

To improve the sensitivity in measuring the permittivity of MUT, parasitic capacitances, C_par and C_sub in parallel with the desired capacitance, C_sensing, have to be minimized. C_sub can be made small by narrowing the spacing of the two nodes of the sensing capacitor. At the same time, narrow spacing between two electrodes reduces the self-resonant frequency (SRF) as a result of an increase in C_sensing and mutual inductances. The inductances caused by the geometry of the on-chip sensing capacitor have a direct trade-offs with the size of the sensing capacitor such as a spacing and the width of the top metal. Thus, in this work, the target frequency band and area of the chip are budgeted in advance, and the optimal sensing capacitor dimension is determined in consideration of the above mentioned trade-offs.

The top metal is composed of aluminum, and an oxide layer is created when the top metal is exposed to the MUT without any passivation (protection). The thick oxide film attenuates the electric field and reduces the sensitivity of the sensing capacitor. In the fabricated chip, the oxide film thickness ranges from 1 to 5 nm [13]. The electromagnetic simulation was performed and the sensitivity was not degraded even with 10 nm oxide film thickness. This thin oxide film, on the other hand, is beneficial by protecting the sensing capacitor from the damage and chemical reaction due to its high corrosion resistance and wear resistance.

Fig. 3 shows the schematic model of the sensing area with a two-port vector network analyzer (VNA). The forward voltage gain (S₂₁) of this network can be calculated by finding the ratio between the injected voltage source (V₁) and the load voltage (V₂) while, the network is terminated with the port load impedance (R_port).

(2)

S21(jω)=V2V1=YsYs+1Rport+jω·Csub=ω·g(ɛMUT′′)+jω·f(ɛMUT′)ω·g(ɛMUT′′)+1Rport+jω·(f(ɛMUT′)+Csub).

In both the numerator and the denominator, the resistance (ω · g(ɛ_MUT″ )) due to the imaginary part of permittivity is significantly smaller than those of the other components. For instance, long transmission lines, connected in series with a sensing capacitor, makes Y_s more capacitive. Thus, we can simplify Eq. (2) into the following formula:

(3)

S21(jω)≃jω·Rport·f(ɛMUT′)1+jω·Rport·(f(ɛMUT′)+Csub).

The dominant pole is calculated to be ωp=1Rport·(f(ɛMUT′)+Csub). Electromagnetic simulation with Advanced Design System (ADS) shows that ω_p is higher than 6 GHz. Accordingly, in the expected measurement range between 0.1 and 5 GHz, the magnitude of S₂₁ can be written as |S₂₁(jω)| ≅ ω · R_port · f(ɛ_MUT′ ). This equation shows that magnitude of S₂₁ indicates the real part of the permittivity of MUT(ɛ_MUT′), while the nonlinear mapping function, f(·), needs to be decoded in a certain manner, as discussed in Section III.

III. Measurement Results and Curve Fitting Calibration

For the measurement of scattering parameters of the fabricated sensor, PCB consisting of the mounted chip, interconnect transmission lines, and input/output ports are assembled as shown in Fig. 4. During the chip packaging process, the insulating epoxy was covered except for the fabricated capacitor area. With a plastic tube on top of the chip, the MUTs were injected through the micropipette (Eppendorf Research plus 3120000038). Fig. 5 shows the real part of the permittivity (ɛ′) for methanol, ethanol, propanol, butanol and air over the frequency range of 0.1–5 GHz [14]. The measured forward voltage gain (S₂₁) at room temperature is given in Fig. 6, which shows that the magnitude of S₂₁ is proportional to ɛ′ over the measured frequency range.

To extract ɛ′ of the MUT from the measured S₂₁ data, the curve-fitting calibration is performed first. Methanol, ethanol, butanol, and air are selected as reference materials, where the information on their real permittivity is provided in [14]. The real permittivity is then curve-fitted at each measured frequency by third order polynomial function with the measured |S₂₁|.

The detailed polynomial curve fitting procedure from the measured |S₂₁| is elaborated below:

1. For each frequency, f₁, to be curve fitted, reference materials are injected into the sensing capacitor and its |S₂₁| is measured through a VNA.
2. The ɛ′ of the reference materials are least-square fitted to third order polynomial function with respect to the measured |S₂₁|.

(4)
ɛ′=a3∣S21∣3+a2∣S21∣2+a1∣S21∣+a0
3. The fitting parameters α₀, α₁, α₂, and α₃ can be found and saved by using the least-square fitting method to fit the polynomial regression function. This procedure is repeated over the entire measurement frequency.

Once the curve-fitting procedure is finished, the unknown permittivity of MUT can be calculated by utilizing its measured |S₂₁| along with the calculated fitting parameters.

Given the above procedure, the permittivity of any unknown MUT can be extracted. To further enhance the measurement accuracy, we propose reshaping (weighting) the parameter, given the measured S₂₁. Instead of utilizing raw |S₂₁|, we give the weights β on the imaginary part of S₂₁ and (1–β) on the real part of S₂₁. The weighting function can emphasize/deemphasize the relevant terms to minimize the extraction error. The revised magnitude of S₂₁ is given by

(5)

∣S21∣*=(1-β)·Real(S21)2+β·Imag(S21)2, 0≤β≤1

Fig. 7 shows the curve-fitted polynomial function and the real permittivity of the reference materials at 100 MHz and 5 GHz frequency with the frequency-dependent parameter β. From the extracted curve-fitted polynomial function, the permittivity of propanol is found to have a good correlation with reference value as shown in Fig. 8. By replacing |S₂₁| with the proposed equation, the rms permittivity error of measurement is lowered from 9.1% to 6.4% over the frequency range of 0.1–5 GHz.

The proposed spectroscopy sensor is compared to the reported research works as depicted in Table 1. Our work is realized in a compact footprint (0.03 mm²) on chip, while the operating frequency range is the second largest.

More reference materials for calibration can be added to minimize the permittivity error (higher polynomial function). The off-chip and on-chip transmission line in series with the sensing capacitor complicate the mapping function and degrade the accuracy accordingly. Their length then needs to be minimized to further enhance the measurement accuracy.

IV. Conclusion

An on-chip capacitive sensor for dielectric spectroscopy is implemented in this work. Based on the circuit model of the on-chip sensing capacitor, the permittivity extraction method is proposed and the measurement result verifies the successful detection of the real part of the permittivity in the frequency range of 0.1–5 GHz. The inter-digitized sensing capacitor can be optimized in its sensitivity and SRF in consideration of the fabrication trade-offs. To improve the permittivity detection accuracy, the measured forward voltage-gain is curve-fitted by the polynomial regression function. The revised forward voltage-gain parameter is suggested for the detection and the measured permittivity of the propanol shows 6.4% rms error compared with the theoretical value.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. NRF-2019R1F1A1048784) and Samsung Electronics Co., Ltd.

Fig. 1

Illustration of an inter-digitized top-metal as an on-chip sensing capacitor covered by a material under test (MUT).

Fig. 2

Side section view of a sensing capacitor with a simple equivalent circuit model.

Fig. 3

Schematic model of sensing capacitor and two-port network vector network analyzer (VNA).

Fig. 4

Photograph of measurement set up.

Fig. 5

Real-part of permittivity ɛ′ of MUTs over the frequency range of 0.1–5 GHz [14].

Fig. 6

Measured |S₂₁| of sensing capacitor over the frequency range of 0.1–5 GHz.

Fig. 7

ɛ′ – |S₂₁|^* curve-fitted with known ɛ′ of four reference materials at (a) 100 MHz and (b) 5 GHz.

Fig. 8

Measured ɛ′ of propanol with the proposed fitting method and reference value.

Table 1

Comparison of the proposed spectroscopy sensor with previous works

Study	Frequency (GHz)	Architecture	Size (mm²)
Bakhshiani et al. [7]	0.009–2.4	Off-chip center tapped microstrip line	N/A
Chuma et al. [8]	2.4	Off-chip split ring resonator	N/A
Helmy et al. [9]	7–9	On-chip inter-digitized capacitor	0.06
Chien et al. [11]	1–50	On-chip transmission line	0.03
This work	0.1–5	On-chip inter-digitized capacitor	0.03

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Biography

Hongkie Lim received B.S. degrees in School of Electrical and Electronics Engineering, Chung-Ang University, Seoul, South Korea in 2019 and M.S. degree in the Korea Advanced Institute of Science and Technology, Daejeon, South Korea, in 2021. Since 2021, he is currently with Samsung Electronics, Co., Ltd., Hwaseong, South Korea as an engineer. His research interests include radio frequency (RF) circuit and dielectric spectroscopy.

Biography

Dong-Ho Lee received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology, Daejeon, South Korea, in 2000, 2002, and 2007, respectively. From 2007 to 2009, he was with the Microwaves Applications Group, Georgia Institute of Technology, Atlanta, GA, USA, where he developed complementary metal oxide semiconductor (CMOS) power amplifiers for mobile communications. In 2009, he joined Skyworks Solutions Inc., Cedar Rapids, IA, USA, where he was involved in the design of power amplifiers and front-end modules for cellular handsets. In 2010, he joined Hanbat National University, Daejeon, South Korea, as a faculty member. His research interests include RF power amplifiers, microwave modules, ultrasonic applications, and radar systems.

Biography

Jusung Kim received a B.S. degree (with highest honors) from Yonsei University, Seoul, South Korea, in 2006, and a Ph.D. degree from Texas A&M University, College Station, TX, USA, in 2011, both in electrical engineering. In 2008, he was employed as an Analog Integrated Circuit Design Engineer at Texas Instruments Inc., Dallas, TX, USA, where he designed an RF front end for a multi standard analog and digital TV silicon tuners. From 2011 to 2015, he was with the Qualcomm Technologies Inc., San Diego, CA, USA, where he designed radio frequency integrated circuits (RFIC) products for 3G and 4G cellular systems. He is currently an associate professor with the Department of Electronics and Control Engineering, Hanbat National University, Daejeon, South Korea. His current research focuses on the design and fabrication of low-power integrated circuits for communication and biomedical applications. Dr. Kim is an Analog Signal Processing Technical Committee member of the IEEE Circuits and Systems Society. He was an associate editor for the IEEE Transaction on Circuits and Systems-II: Express Briefs from 2014 to 2015.

Biography

Songcheol Hong received the B.S. and M.S. degrees in electronics engineering from Seoul National University, Seoul, South Korea, in 1982 and 1984, respectively, and the Ph.D. degree in electrical engineering and computer science from the University of Michigan, Ann Arbor, MI, USA, in 1989. In 1997, he joined the EECS Department, Stanford University, Stanford, CA, USA, as a visiting professor. He worked with Samsung Microwave Semiconductor, Milpitas, CA, USA. He served as the Dean of Research Affairs and the Director of KI-IT Convergence with the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea. He is currently a professor with the School of Electrical Engineering, KAIST, where he is also a KT-Chaired Professor. He has authored or coauthored more than 300 technical papers and 150 patents. His current research interests include RFICs and RF CMOS PAs, especially in millimeter-wave ICs for 5G communications and radars. Dr. Hong is currently a member of NAEK, KIEES, and KITE. He served as a Board member of Techno-park of Daejeon Metropolitan city. He served as the General Chair for RFIT 2017 supported by the IEEE and the TPC Chair for APMC 2013 and GSMM 2014.