Electrochemically-gated Graphene Broadband Microwave Waveguides for Ultrasensitive Biosensing Patrik Gubeljak1 Tianhui Xu23 Lorenzo Pedrazzetti34 Oliver J. Burton3 Luca Magagnin4 Stephan

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Electrochemically-gated Graphene Broadband Microwave Waveguides for

Ultrasensitive Biosensing

Patrik Gubeljak†1, Tianhui Xu†2,3, Lorenzo Pedrazzetti3,4, Oliver J. Burton3, Luca Magagnin4, Stephan

Hofmann3, George G. Malliaras3, and Antonio Lombardo*1,2,5

1Cambridge Graphene Centre, Department of Engineering, University of Cambridge, United Kingdom

2Department of Electronic and Electrical Engineering, University College London, London, United

Kingdom

3Department of Engineering, University of Cambridge, United Kingdom

4Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Italy

5London Centre for Nanotechnology, University College London, United Kingdom

†These authors contributed equally to this work. *Corresponding author: a.lombardo@ucl.ac.uk

Abstract

Identiﬁcation of non-ampliﬁed DNA sequences and single-base mutations is essential for molecular biology and

genetic diagnostics. This paper reports a novel sensor consisting of electrochemically-gated graphene coplanar

waveguides coupled with a microﬂuidic channel. Upon exposure to analytes, propagation of electromagnetic

waves in the waveguides is modiﬁed as a result of interactions with the fringing ﬁeld and modulation of graphene

dynamic conductivity resulting from electrostatic gating. Probe DNA sequences are immobilised on the graphene

surface, and the sensor is exposed to DNA sequences which either perfectly match the probe, contain a single-

base mismatch or are unrelated. By monitoring the scattering parameters at frequencies between 50 MHz and

50 GHz, unambiguous and reproducible discrimination of the diﬀerent strands is achieved at concentrations as

low as one attomole per litre (1 am). By controlling and synchronising frequency sweeps, electrochemical gating,

and liquid ﬂow in the microﬂuidic channel, the sensor generates multidimensional datasets. Advanced data

analysis techniques are utilised to take full advantage of the richness of the dataset. A classiﬁcation accuracy

>97% between all three sequences is achieved using diﬀerent Machine Learning models, even in the presence

of simulated noise and low signal-to-noise ratios. The sensor exceeds state-of-the-art sensitivity of ﬁeld-eﬀect

transistors and microwave sensors for the identiﬁcation of single-base mismatches.

1 Introduction

Biosensors capable of identifying non-ampliﬁed DNA sequences with high sensitivity and selectivity are essential

for applications ranging from fundamental molecular biology to genetic disease diagnosis and precision medicine.

Electronic detectors, such as ﬁeld eﬀect transistors (FETs), are of particular interest as they can combine label-free

detection, high sensitivity, small footprint and integrability with conventional electronics for signal processing [1].

Graphene attracted signiﬁcant research and commercial interest for biosensing due to its electrical and chemical

properties, high surface-to-volume ratio, biocompatibility, and ease of functionalisation [2,3]. Exposure to chemical

species, such as gases [4], ionic solutions [5], enzymes [6], glucose [7], large biomolecules [8], viruses [9], and

bacteria [10], modiﬁes graphene electronic properties, typically as a result of the modulation in the density and

scattering rates of charge carriers. By incorporating graphene in a transistor structure, usually referred to as

Graphene Field Eﬀect Transistor (GFET) [11], the results of these interactions can be measured on a macroscopic

scale, typically by monitoring changes of the charge neutrality point (CNP) in the transfer characteristics [4, 5,

12, 13]. Biomaterials are usually dispersed in a suitable medium, typically an electrolyte buﬀer solution. When

in contact with ionic media, electrical double layers (EDLs), also known as Debye layers, form at the graphene-

electrolyte interface, resulting in a large interface capacitance CEDL, due to the small thickness (Debye length) of

the EDL [14]. This eﬀect is used in electrochemically-gated GFETs, where the graphene channel is exposed to the

ionic solution, and a voltage is applied to a counter electrode, modulating the EDL and, in turn, the charge carrier

density in the graphene channel. An EDL also forms at the electrode-solution interface, leading to a capacitance

arXiv:2210.14118v3 [physics.bio-ph] 14 Jan 2023

in series with CEDL. However, counter-electrodes are usually designed to have areas signiﬁcantly larger than

the graphene channel, resulting in a very large capacitance whose eﬀect is negligible in the series. Under such

conditions, the voltage applied to the counter electrode drops almost entirely at the graphene-solution interface,

i.e. across the EDL [7, 12, 13]. The total gate capacitance of electrochemically-gated GFETs, therefore, consists

of graphene quantum capacitance (due to its ﬁnite density of states [15]) CQand EDL capacitance in series, i.e.

CG= [C−1

Q+C−1

EDL]−1[12]. As CGis very large, even small changes in the solution are reﬂected in signiﬁcant

changes in the transistor transfer characteristic, resulting in very high sensitivity and low limits of detection [16]. To

enhance the selectivity of GFET sensors, the graphene surface can be non-covalently functionalised with diﬀerent

groups, which increases the speciﬁcity while preserving the electrical conductivity [7,12,13].

The combination of electrochemically-gated GFETs and surface functionalisation has been applied to iden-

tify DNA sequences and single-base mismatches [12, 13, 17]. By using a binder molecule (1-pyrenebutanoic acid

succinimidyl ester, PBASE) which attaches non-covalently to the graphene channel, single strands of DNA were

immobilised on the GFET. When target DNA strands are introduced to the functionalised sensing surface, the

hybridisation with the immobilised probe DNA modiﬁes the potential across the EDL, resulting in shifts of the

CNP [12, 13, 17]. Xu et al. [12] used this to distinguish single-base mismatches quantitatively in real-time with a

target DNA concentration of 5 nM based on an electrolytically gated GFET array. Campos et al. [13] improved

their work and demonstrated a limit of detection (LOD) of 25 amof the lowest target DNA concentration for which

the sensor can discriminate between perfect-match sequences and nucleotides having a single base mismatch.

A major limitation of the sensitivity of FET for biosensing in physiological solutions is the ionic (Debye)

shielding, which limits the detection of molecules to only those within the Debye length, i.e. usually between

0.7 and 8 nm, depending on the ionic strength of the solution. This, in turn, reduces the sensitivity, and often

complex approaches are required to mitigate the screening [18]. However, the Debye shielding only aﬀects devices

operated at DC and low frequency and becomes negligible at microwave frequencies as the ionic conductivity

vanishes [19]. Microwaves interact with matter causing frequency-dependent reorientation of molecular dipoles

and translation of electric charges [19, 20]. Diﬀerent molecules and compounds are characterised by diﬀerent

relaxation processes (collectively captured by their dielectric permittivity) and interact diﬀerently with oscillating

electromagnetic ﬁelds [20]. Microwave sensors use such interaction to identify or discriminate diﬀerent analytes,

and have been successfully used to identify cancer cells [21], volatile compounds in breath [22], study antibiotic

resistance in bacteria [23] and electroporation in human epithelial cells [24]. Diﬀerent types of sensors have been

reported, including reﬂectometers, resonators, interferometers, and waveguides [20]. Waveguide sensors, such as

coplanar waveguides (CPWs), are of particular interest as they combine broadband operation with simple design,

ease of miniaturisation and integrability with conventional planar technology and microﬂuidics [19,20]. In a CPW,

part of the ﬁeld extends outside of the circuit due to incomplete shielding of the conductors [19,20] and therefore

interacts with analytes deposited on the waveguide surface. Yang et al. [25] developed a multilayered polymeric

radio frequency (RF) sensor for DNA sensing using a CPW sensing surface, which reached a LOD of target DNA

of 10 pM through DNA hybridisation, and Kim et al. [26] proposed an RF biosensor based on an oscillator at 2.4

GHz and obtained an estimated LOD of about 1 ng/mL (114 pm).

Graphene is of particular interest for RF and microwave sensing owing to its good conductivity and ﬁeld eﬀect

tunability [27–29]. Moreover, its AC conductivity is frequency-independent and equal to DC conductivity for

frequencies up to ≈500 GHz [30]. This unique combination of properties has been used to demonstrate proof-of-

concept electrolytically-gated waveguide sensors, capable of identifying completely complementary DNA strands

and generating multidimensional datasets by independently controlling gate voltage and frequency [28]. Recently,

Zhang et al. [29] reported a GFET operated around its resonant frequency (i.e., 1.83 GHz) in reﬂectometry mode,

achieving a LOD of 1 nmfor the detection of streptavidin, an extensively used protein.

Machine learning (ML) techniques play key roles in the ﬁeld of biological sequencing, including DNA, RNA,

and protein [31]. However, there is not much previous work using ML to analyse raw microwave signals after being

exposed to biological samples [32]. ML regression models and Neural Networks were used on the reﬂection and

transmission coeﬃcients from electrically-small dipole sensors [33] and open-ended coaxial probes [34] and achieved

either a direct prediction of aqueous glucose solution concentrations or a prediction of the permittivity of glucose

solutions. Nevertheless, the authors are not aware of work that applies ML to broadband miniaturized on-chip

microwave sensors for biomaterial sensing at the time of writing. Regarding single-base-mismatch DNA detection,

Principal Component Analysis (PCA) and Quadratic Discriminant Analysis (QDA) were applied to Terahertz

spectral data and achieved a classiﬁcation rate of 90.3% in the prediction set of four single-base-mismatch DNA

oligonucleotides at a concentration of 38.85 µm[35].

Here we present a novel DNA sensor consisting of electrochemically-gated graphene CPWs coupled with a

microﬂuidic channel. The sensor harnesses the combined eﬀect of dynamic conductivity modulation in graphene

resulting from (chemical) electrostatic doping and modiﬁcation of wave propagation resulting from the interaction

of the fringing ﬁeld with the analyte. The two eﬀects occur simultaneously, leading to a unique double sensing

mechanism that combines two traditionally separate sensing approaches, i.e. ﬁeld eﬀect transistor sensing and

microwave dielectric spectroscopy. By immobilising probe DNA sequences on the graphene surface, the waveguide

scattering parameters are studied when the sensor is exposed to DNA sequences either perfectly matching the probe

(pmDNA) or containing a single-base mismatch (smDNA) or unrelated (uDNA). Unambiguous and reproducible

discrimination of single-base mismatch target strands is achieved at DNA concentrations as low as 1 attomole

per litre (1 am). Multidimensional datasets are obtained by controlling and synchronising frequency sweeps,

electrochemical gating, and liquid ﬂow in the microﬂuidic channel. Such rich datasets are analysed using diﬀerent

ML methods, achieving a classiﬁcation accuracy >97% between pmDNA, smDNA, and uDNA, even in the presence

of simulated Gaussian noise.

Figure 1: (a) Illustration of the design and components of the device. (b) Cross-section of the simulated electric

ﬁeld and magnetic ﬁeld in the quasi-TEM mode perpendicular to the wave propagation vector. The light green

part is the Si substrate. The light purple part is the material box of analytes that interact with the fringing ﬁeld.

and the surrounding gate electrode, doubling as an RF cage. (e) Optical micrograph of the graphene section in

the central signal conductor of the waveguide, with the graphene outlined in the black dashed line. The overlap

between the dashed line and the metal is the area of the graphene-metal contacts. (f) - (j) Conceptual illustration

of diﬀerent chemical functionalisation and measurement stages for DNA detection.

2 Results and Discussion

2.1 Sensor design and sensing principle

The DNA sensor consists of a graphene channel integrated within a CPW and coupled with a microﬂuidic channel.

The structure of the device is schematically shown in Figure 1 (a). Graphene is deposited onto high-resistivity

Si substrates covered in 300 nm of SiO2and integrated into the signal track of a metallic CPW, whereas the

ground conductors are entirely metallic. Arrays of sensors having diﬀerent graphene lengths (ranging from 10 to

25 µm) are fabricated on the same chip and share the same microﬂuidic channel. A planar gold counter-electrode

having dimensions signiﬁcantly (>700 times) larger than the graphene channels is fabricated on the chip, enabling

electrolytic gating similar to DC sensors [12,13]. This structure is designed to achieve a double sensing mechanism.

First, electromagnetic waves propagating in the waveguide interact with the liquid in the microﬂuidic channel via

the fringing ﬁeld, i.e. the portion of the electric and magnetic ﬁeld extending outside of the waveguide due to

incomplete shielding of the conductors [20], as shown in Figure 1 (b). The choice of high frequencies (50 MHz -

50 GHz) ensures robustness against Debye screening, which degrades sensitivity in DC and low-frequency sensors

exposed to ionic solutions such as PBS [20, 29]. Second, similar to GFET sensors, the graphene’s (DC and AC)

conductivity is modiﬁed by the proximity with the liquid via the electrostatic eﬀect resulting from the formation

of an EDL at the graphene/solution interface [12, 13]. This further inﬂuences wave propagation, enhancing the

response of the sensor. This dual sensing mechanism is fully captured by the waveguide scattering (S) parameters,

which represent the ratios of the transmitted (S21 parameter) or reﬂected (S11 parameter) voltage wave and a

known ”stimulus” wave launched in the waveguide. Figure 1 (c) shows the chip mounted on a probe station setup,

while Figure 1 (d) depicts a closer view of the system, showing individual devices and the microﬂuidic channel.

Figure 1 (e) shows an optical micrograph of the fabricated device prior to the deposition of the microﬂuidic

channel. The dashed area corresponds to the graphene layer, including the part underneath the contact areas.

DNA sequences are immobilised onto the graphene surface by using PBASE as a linker molecule, following the

protocol from Ref. [13]. The pyrene group of PBASE binds non-covalently to graphene via π−πorbital stacking,

whereas its succinimide group binds to the 5’ end of a purposely modiﬁed single-stranded DNA, which is used as

the probe, i.e. as the complementary sequence of the DNA to be detected. In order to saturate any non-reacted

succinimide group, the sensor is exposed to an ethanolamine solution. The sensor containing the probe DNA

is then exposed to dispersions containing either pmDNA or smDNA or uDNA, both dispersed in 1% PBS at a

concentration of one amper litre (1 a M). The 1% PBS concentration is chosen for consistency with previous

studies on GFET-based DNA sensors [12, 13], and corresponds to a Debye length of ≈7 nm [18], matching the

length of the hybridised DNA.

Figure 1 (f) - (h) summarises the functionalisation of the sensing surface to immobilise the probe single

DNA strand on the graphene surface for target DNA hybridisation, whereas (i) and (j) show hybridisation of the

probe DNA with a pmDNA or smDNA, respectively. The isoelectric point of DNA is at pH ≈5 [36], while the

pH of our dispersion is 7.2, resulting in the oligonucleotides being negatively charged [13]. Upon hybridisation, i.e.

when pmDNA or smDNA binds with the probe DNA by forming bonds between complementary bases (cytosine-

guanine and adenine-thymine), the additional negative charge modiﬁes the electrical double layer formed at the

graphene-solution interface, leading to a lowering of the graphene’s Fermi level (equivalent to p-doping) and an

increase of the scattering time τ[37]. This results in a modulation of graphene dynamic conductivity, which can

be described by the Kubo formula for intraband transitions [30]:

σintra (ω, EF, τ, T ) = ie2kBT

π~2(ω+iτ−1)"EF

kBT+ 2ln1+e−EF

kBT#(1)

where: ω= 2πf is the angular frequency, EFis the Fermi energy, τis the scattering time (assumed to be inde-

pendent of energy), Tis the temperature expressed in Kelvin, e= 1.6·10−19 C is the electron charge, ~=h

2πis

the reduced Planck’s constant, and kB= 1.38 ·10−23 J

Kis the Boltzmann’s constant.

The double helix DNA resulting from hybridisation with smDNA has diﬀerent electrical and mechanical prop-

erties compared to the one with the pmDNA target. In particular, single-base mutations disrupt the long-range

electron transfer within the DNA double-helix [38], which results in diﬀerent responses to the fringing ﬁeld of

the propagating wave and diﬀerent modiﬁcations of the graphene conductivity. Diﬀerences in capacitance cor-

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Electrochemically-gatedGrapheneBroadbandMicrowaveWaveguidesforUltrasensitiveBiosensingPatrikGubeljaky1,TianhuiXuy2,3,LorenzoPedrazzetti3,4,OliverJ.Burton3,LucaMagagnin4,StephanHofmann3,GeorgeG.Malliaras3,andAntonioLombardo*1,2,51CambridgeGrapheneCentre,DepartmentofEngineering,UniversityofCambridge,U...

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Electrochemically-gated Graphene Broadband Microwave Waveguides for Ultrasensitive Biosensing Patrik Gubeljak1 Tianhui Xu23 Lorenzo Pedrazzetti34 Oliver J. Burton3 Luca Magagnin4 Stephan

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