# High-responsivity graphene photodetectors integrated on silicon microring
resonators

Simone Schuler1,2,‡<EMAIL_ADDRESS>Jakob E. Muench2,‡ Alfonso
Ruocco2, Osman Balci2, Dries van Thourhout3, Vito Sorianello4, Marco
Romagnoli4, Kenji Watanabe5, Takashi Taniguchi5, Ilya Goykhman2,6, Andrea C.
Ferrari2 Thomas Mueller1<EMAIL_ADDRESS>1Vienna University of
Technology, Institute of Photonics, Gußhausstraße 27-29, 1040 Vienna, Austria
2Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA, UK
3Ghent University-IMEC, Photonics Research Group, Technologiepark-Zwijnaarde
126, 9052 Gent, Belgium  4Consorzio Nazionale per le Telecomunicazioni,
Photonic Networks and Technologies National Lab, via Moruzzi 1, 56124 Pisa,
Italy  5National Institute for Materials Science, 1-1 Namiki, Tsukuba,
305-0044 Japan  6Technion - Israel Institute of Technology, Haifa, 3200003,
Israel  ‡These authors contributed equally to this work.

###### Abstract

Graphene integrated photonics provides several advantages over conventional Si
photonics. Single layer graphene (SLG) enables fast, broadband, and energy-
efficient electro-optic modulators, optical switches and photodetectors
(GPDs), and is compatible with any optical waveguide. The last major barrier
to SLG-based optical receivers lies in the low responsivity - electrical
output per optical input - of GPDs compared to conventional PDs. Here we
overcome this shortfall by integrating a photo-thermoelectric GPD with a Si
microring resonator. Under critical coupling, we achieve $>$90% light
absorption in a $\sim$6 $\mu$m SLG channel along the Si waveguide. Exploiting
the cavity-enhanced light-matter interaction, causing carriers in SLG to reach
$\sim$400 K for an input power of $\sim$0.6 mW, we get a voltage responsivity
$\sim$90 V/W, demonstrating the feasibility of our approach. Our device is
capable of detecting data rates up to 20 Gbit/s, with a receiver sensitivity
enabling it to operate at a 10-9 bit-error rate, on par with mature
semiconductor technology. The natural generation of a voltage rather than a
current, removes the need for transimpedance amplification, with a reduction
of the energy-per-bit cost and foot-print, when compared to a traditional
semiconductor-based receiver.

##  I Introduction

The same-chip integration Atabaki2018Integrating  of active and passive
optical components with electronics offers a cost- and energy-efficient
solution for short- and long-reach optical interconnects cheng2018recent ;
subbaraman2015recent . Single layer graphene (SLG) is an ideal material for
integrated photonics Romagnoli2018Graphene ; Bonaccorso2010Graphene ,
promising e.g. high-speed (potentially $>$200 GHz) urich2011intrinsic ;
Xia2009ultrafast  and broadband (ultraviolet to far-infrared)
Koppens2014Photodetectors  operation that could lift bandwidth (BW) ($\sim
100$ GHz) vivien2012zero ; Salamin2018GHz  and spectral ($<1600$ nm)
Michel2010High  limitations of existing technologies, such as Ge/Si
thomson2016roadmap ; chrostowski2015silicon  and InGaAsP/InP
arafin2018advanced ; Nagarajan2010InP . A variety of waveguide (WG)-integrated
SLG-based photonic devices have been reported Liu2011graphene ;
phare2015graphene ; giambra2019high ; Sorianello2018graphene ;
Cassese2017Capacative ; Pospischil2013CMOS ; Gan2013chip ; Wang2013high ;
Shiue2015High ; Schuler2016Controlled ; schuler2018graphene ; Goykhman2016On ;
Muench2019Waveguide ; Schall2018record ; Ma2018Plasmonically ; ding2020ultra ,
including electro-absorption (EAMs) Liu2011graphene ; phare2015graphene ;
giambra2019high  and electro-refraction modulators (ERMs)
Sorianello2018graphene , optical switches Romagnoli2018Graphene ;
Cassese2017Capacative  and photodetectors (GPDs) Pospischil2013CMOS ;
Gan2013chip ; Wang2013high ; Shiue2015High ; Schuler2016Controlled ;
schuler2018graphene ; Goykhman2016On ; Muench2019Waveguide ; Schall2018record
; Ma2018Plasmonically ; ding2020ultra . SLG and layered materials can be
integrated with passive Si photonic WGs Pospischil2013CMOS ; Gan2013chip ;
Wang2013high ; Shiue2015High ; Schuler2016Controlled ; schuler2018graphene  or
any other passive WG technology Romagnoli2018Graphene , including Si3N4
Muench2019Waveguide ; gao2018high , sapphire cheng2015graphene , Ge
wang2019design , and polymers kim2012graphene ; kleinert2016graphene ,
extending the spectral range and scope of possible applications wang2019design
; qu2018waveguide .

SLG’s optical absorption is $\sim$2.3% under normal incidence Nair2008Fine ,
which limits the photoresponse in top-illuminated GPDs
Koppens2014Photodetectors . This absorption can be increased in a WG
configuration through the interaction with the evanescent field of the optical
WG mode Youngblood2016integration . However, since the mode-overlap with SLG’s
monatomic cross-section typically restricts absorption to $\sim 0.01-0.1$
dB/$\mu$m ($\sim 0.2-2$%/$\mu$m) Romagnoli2018Graphene , device lengths
$\sim$100 $\mu$m are needed for near-complete ($>$90%) light absorption, with
adverse effects on foot-print and capacitance that scale with device size
Xia2009ultrafast . The resulting trade-off between length and absorption has
implications for GPDs that operate via the photo-thermoelectric effect (PTE)
gabor2011hot ; Song2011Hot ; Xu2010Photo : Due to slow($\sim$ps
Brida2013ultrafast ) heat dissipation to the lattice via phonon mediated
cooling Brida2013ultrafast ; tomadin2013nonequilibrium , photo-excitation
leads to the formation of a hot-carrier distribution in SLG gabor2011hot ;
Song2011Hot ; Koppens2014Photodetectors . The associated electron temperature
$T_{e}$ can be substantially above the lattice temperature $T_{0}$
Soavi2018Broadband  and leads to a photovoltage according to gabor2011hot ;
Song2011Hot ; Xu2010Photo :

$V_{\text{PTE}}=\int S(x)\cdot\nabla T_{e}(x)\mathrm{d}x$ (1)

if both a $T_{e}$ gradient and a spatially varying Seebeck coefficient $S$
(controlled by the chemical potential $\mu_{c}$) are present gabor2011hot . In
order to achieve a high ($>$mV) $V_{\text{PTE}}$, it is better to absorb the
incident electromagnetic energy over small ($<10$ $\mu$m) length scales,
leading to localised electronic heating for a higher ( $\sim$tens K) $T_{e}$
and $\nabla T_{e}(x)$.

Different approaches have been explored to increase and confine light
absorption in free-space-coupled Echtermeyer2011Strong ; Engel2012Light ;
Furchi2012Microcavity  and WG-integrated GPDs Schuler2016Controlled ;
Goykhman2016On ; schuler2018graphene ; Muench2019Waveguide , e.g. by embedding
SLG into optical cavities Engel2012Light ; Furchi2012Microcavity , slot WGs
Schuler2016Controlled , plasmonic structures Echtermeyer2011Strong ;
Goykhman2016On ; Muench2019Waveguide ; Ma2018Plasmonically , or by enhancing
the light-matter interaction using sub-wavelength structures
schuler2018graphene  but these have coupling and propagation losses
Ma2018Plasmonically , limitation in field enhancement Shiue2015High ;
Schall2018record , or carrier mobility $\mu$ Schuler2016Controlled ;
ding2020ultra , fabrication flows incompatible with complementary metal-oxide-
semiconductor (CMOS) processing Ma2018Plasmonically ; Shiue2015High ;
ding2020ultra , bias-induced dark currents Ma2018Plasmonically ;
Schall2018record , or a combination thereof Ma2018Plasmonically ;
Shiue2015High ; ding2020ultra . Thus, the demonstration of GPDs on photonic
integrated circuits (PICs) that leverage SLG’s unique hot-carrier dynamics and
maximise the voltage responsivity
$R_{\text{[V/W]}}=V_{\text{PTE}}/P_{\text{in}}$, with $P_{\text{in}}$ the
incident optical power in the WG, is challenging.

Here, we present GPDs integrated on looped WGs, known as microring resonators
bogaerts2012silicon , which act as PIC-embedded resonant cavities. The
conversion of the incident light into an electrical signal occurs via the PTE
effect. The GPDs directly generates a voltage, which allows us to operate them
without bias and dark currents, limiting the GPD noise to thermal Johnson
noise, i.e. the noise due to fluctuations of the carrier density
fang2019accurate . This removes the need of transimpedance amplifiers (TIA) in
the read-out electronics, with a reduction of the energy-per-bit cost and
system foot-print. With $R_{\text{[V/W]}}\sim$ 90 V/W, our GPDs pave the way
towards SLG integration on Si photonic receivers, overcoming the limitation of
photocurrent ($I_{\text{ph}}$) generating GPDs with responsivities
($R_{\text{[A/W]}}=I_{\text{ph}}/P_{\text{in}}$) lower than that of mature Ge
PDs Ma2018Plasmonically ; Shiue2015High ; Schall2018record . We attribute this
to our high ($>10^{4}\text{ cm}^{2}/\text{Vs}$) SLG $\mu$ and the combination
with the Si microring resonator giving a $\sim$10-fold enhancement of the
electric field strength and $>$90% light absorption in only $\sim$6 $\mu$m SLG
on the Si WG.

##  II Results and discussion

Figure 1: Si ring resonator integrated GPD. (a) Sketch of the device. (b)
Transmission of a ring cavity with SLG on top. (c) Transmission at resonance
($\sim$1553.55 nm). The black line is the calculated transmission for $\kappa$
= 10%. The coloured dots mark the transmission coefficient for various loss
coefficients

Fig.1 is a scheme of our GPDs, which comprise a layered materials
heterostructure (LHM) of SLG and hexagonal boron nitride (hBN). To increase
the generated $V_{\text{PTE}}$ upon optical illumination according to Eq.1,
encapsulation of the SLG channel in hBN ensures a high ($>10^{4}\text{
cm}^{2}/\text{Vs}$) $\mu$ purdie2018cleaning  for large ($\sim 200$ $\mu$V/K)
peak $S$ Muench2019Waveguide , according to Mott’s formula gabor2011hot ;
Song2011Hot :

$S=-\frac{\pi^{2}k_{\text{B}}^{2}T_{e}}{3e\sigma(\mu,\mu_{c})}\frac{\mathrm{d}\sigma(\mu,\mu_{c})}{\mathrm{d}\mu_{c}}$
(2)

where $k_{\text{B}}$ is the Boltzmann constant, $e$ the electron charge,
$\sigma=n\mu e$ the conductivity, and $n$ the carrier concentration. Dual-gate
SLG electrodes, separated from the LMH by a Al2O3 layer, are employed to tune
$S$ in adjacent regions of the device Schuler2016Controlled . The LMH is
contacted on opposite sides and centrally aligned to the WG of a microring
resonator fabricated on a Si-on-insulator (SOI) wafer. The resonator serves a
two-fold purpose. First, the higher (compared to the bus WG) intra-cavity
energy density bogaerts2012silicon  results in $\sim$10-fold enhanced light-
matter interaction rabus2007integrated  and can enable near-complete light
absorption in the SLG channel if its coverage of the resonator is optimised.
Second, the wavelength $\lambda$ selectivity of the resonator
Yariv2002critical ; rabus2007integrated , makes the GPD suitable for
wavelength division multiplexing (WDM) chrostowski2015silicon , whereby the
data rate of a single optical channel is increased by combining signals of
different $\lambda$ at the transmitter and separating them at the receiver
Xu2006Cascaded ; Zheng2010tunable .

To find the SLG length $W$ over the ring that enables maximum absorption
inside the resonator, we perform an initial experiment on a reference
microring cavity with identical parameters (WG thickness $t_{\text{WG}}$ = 220
nm, WG width $w_{\text{WG}}$ = 480 nm, ring radius $R$ = 40 $\mu$m). Coupling
to the resonator occurs through a 200 nm gap via a single bus WG, Fig.1a,
which has grating couplers on either end, with coupling efficiency
chrostowski2015silicon  $\eta=P_{\text{in}}/P_{\text{fibre}}\sim$ 0.28, with
$P_{\text{fibre}}$ the optical power in the fibre connecting source and SOI
chip, determined from transmission measurements on reference WGs on the same
chip. The power coupling between these two structures depends on the coupling
($\kappa$) and transmission coefficient ($t$), i.e. the scattering matrix
elements relating incoming and outgoing electric fields from the coupling
region Yariv2002critical . These are related via rabus2007integrated
$\kappa=\sqrt{1-t^{2}}$. The choice of $\kappa$ affects both the optical
(frequency) bandwidth $\delta\nu$ and quality ($Q$) factor
($Q=\nu_{0}/\delta\nu$, with $\nu_{0}$ the resonance frequency
paschotta2008encyclopedia ) of the resonator, resulting in a trade-off between
achievable extinction ratio (ER, defined as the ratio of minimum (at
resonance) and maximum transmitted optical power bogaerts2012silicon ), thus
$R_{\text{[V/W]}}$, and BW. We select $\kappa=10$%, which allows $BW>10$ GHz
in our design rabus2007integrated , sufficient for applications in data centre
optical interconnects cheng2018recent .

The wavelength-dependent transmitted power $P_{\text{trans}}$ of a ring
resonator can be written as bogaerts2012silicon :

$P_{\text{trans}}=P_{\text{in}}\frac{(1-\kappa)+\xi-2\sqrt{(1-\kappa)\xi}\cos(\theta)}{1+(1-\kappa)\xi-2\sqrt{(1-\kappa)\xi}\cos(\theta)}$
(3)

where $\theta=4\pi^{2}Rn_{\text{eff}}/\lambda$ is the round-trip phase shift
of the circulating mode and $n_{\text{eff}}$ is the effective mode index
($n_{\text{eff}}=\beta/k_{0}$ with $\beta$ the propagation constant of the
mode, defined as the wavevector component along the WG, and $k_{0}$ the free-
space wavevector reed2004silicon ). Omitting the negligible losses caused by
coupling between bus and ring, the term:

$\xi=e^{-W\alpha_{\text{SLG}}}e^{-2\pi R\alpha_{\text{WG}}}$ (4)

describes the round-trip propagation loss in the ring, with
$\alpha_{\text{SLG}}$ and $\alpha_{\text{WG}}$, in dB/$\mu$m, the power
attenuation coefficients in SLG and Si WG, respectively. When $\theta$=2$\pi
m$ ($m$ = 1,2,3…), the light in the ring constructively interferes with itself
and the cavity is in resonance bogaerts2012silicon . From Eq.3, the
transmission drops to zero if $\xi=1-\kappa$. Under this so-called critical
coupling Yariv2002critical , maximum field enhancement is achieved inside the
resonator as the transmitted power goes to zero. With all other parameters
fixed in Eq.4, changing the SLG-induced losses by changing the coverage length
$W$ can therefore be used to tune $\xi$ and achieve critical coupling.

Figure 2: (a) Assembly of hBN/SLG/hBN LMH.(b) Stack placement on photonic
circuit and interface cleaning. (c) hBN etching in SF6 plasma. (d) SLG etching
in O2 plasma to define channel geometry. (e) Metallization (Cr/Au) for drain-
source contacts. (f) Al seed layer evaporation + ALD of Al2O3. (g) Wet
transfer of CVD SLG. (h) Split-gate fabrication. (i) Metallization (Cr/Au) for
gate contacts.

To find this optimum $W$, we first measure the transmission of an unloaded (no
SLG, i.e. W = 0) resonator by coupling light (continuous-wave (CW), TE-
polarised) from a tunable laser (Newport TLB6700) into the bus WG, using an
optical single-mode fibre, and measuring the transmitted power at the second
grating coupler as a function of $\lambda$ around one of the resonance peaks.
The results, after calibration for the coupling losses, are shown by the dark-
blue line and symbols in Figs.1b,c, respectively. The microring resonator is
not critically coupled at resonance for $\lambda\sim 1553.55$ $\mu$m as
$P_{\text{trans}}$ does not vanish, but only part of the incident power is
dissipated in the WG. From Eqs.3,4 we get $\alpha_{\text{WG}}\sim$1.4 dB/cm.

We then proceed to study the effect of SLG with varying $W$ on the power
dissipated in the resonator. We first place a $W$ = 20 $\mu$m long SLG flake,
prepared by micro-mechanical cleavage (MC) Novoselov2005Two  of bulk graphite,
transferred using a micro-manipulator and a stamp consisting of polycarbonate
(PC) and polydimethylsiloxane (PDMS), and cleaned by immersion in chloroform,
over the ring and measure the transmission as before. Using successive
electron beam lithography (EBL, Raith e-LINE) steps to define a poly(methyl
methacrylate) (PMMA) etch mask and reactive ion etching in O2 to remove excess
material, we then reduce $W$ further in several steps down to $2.5$ $\mu$m
with transmission measurements in between. The results, Figs.1b,c, show an
initial transmission decrease at resonance with decreasing $W$ before the
trend is inverted as $W$ tends to zero. The minimum transmission, indicating
critical coupling, is for $W$ = 6 $\mu$m. From Eq.4 we extract
$\alpha_{\text{G}}\sim$ 0.07 dB/$\mu$m, in agreement with measured
Liu2011graphene  and simulated Romagnoli2018Graphene  values from literature.
Using these values, and the comparison of the transmission curves for $W$ = 6
$\mu$m and $W$ = 0, we estimate the fraction of absorbed light in the SLG
channel to be $\sim$92% under critical coupling.

Figure 3: (a) Microscope image of a hBN/SLG/hBN LMH on ring resonator. The
black dashed line indicates the area over which the Raman map in (d) is
measured. Scale bar, 10 $\mu$m. (b) Raman spectrum measured at the position of
the final device.(c) AFM image of the LMH. The yellow dashed line indicates
the area of top and bottom hBN. The blue line indicates the SLG area. Scale
bar, 10 $\mu$m. (d) Raman map of FWHM(2D). The red box marks the position of
the final device in (a,c,d).

Based on these findings, we fabricate the GPD in Fig.1a with $W$ = 6 $\mu$m
from a LMH (hBN encapsulated SLG as channel layer) on top of the ring
resonator. This is a prepared as follows purdie2018cleaning : SLG and hBN
flakes of different thicknesses ($t_{\text{bottom}}\sim 3$ nm,
$t_{\text{top}}\sim 20$ nm) are prepared on Si/SiO2 ($t_{\text{SiO}_{2}}$ =
285 nm) by MC of bulk graphite (Graphenium) and hBN single crystals grown at
high pressure and temperature as detailed in Ref. TANIGUCHI2007Systhesis . The
thickness of the bottom hBN, $t_{\text{bottom}}$, is chosen with the following
trade-off: sufficiently thin ($<$5 nm) to ensure $\alpha_{\text{SLG}}$ (thus
$\xi$) comparable to the initial experiment used to find $W$, but sufficiently
thick ($\sim$ nm) that high ($>10^{4}\text{ cm}^{2}/\text{Vs}$) $\mu$ is
achieved, due to reduced (in comparison to SiO2) carrier inhomogenities,
roughness, and charge impurities dean2010boron ; Wang2013One ;
purdie2018cleaning . A micro-manipulator and a PC/PDMS stamp are then used to
pick up and stack the flakes at 50∘C (Fig.2a). In order the clean the LMH
interfaces, the target photonic chip is then heated to 180∘C
purdie2018cleaning , while we align the LMH to the Si WG. We then laminate the
PC film onto the target substrate, pushing contamination blisters, formed at
the SLG/hBN interfaces, out of the GPD channel region and placing the LMH on
the WG, Fig.2b.

After the PC film is dissolved in chloroform, we perform EBL (Raith EBPG 5200)
to define the GPD channel geometry via a PMMA etch mask. To transfer this
pattern to the LMH, we use two dry etching steps. First, to achieve etch
selectivity between LMH and underlying photonic circuit, we use a reactive ion
etcher (RIE, Plasma-Therm) with a forward radio frequency power $\sim$80 W and
an SF6 flow $\sim$80 sccm. As reported by Ref. jessen2019lithographic , these
conditions allow fast ($>$200 nm/min) etching of hBN, slow ($<$7 nm/min)
etching of SiO2, while SLG is not etched, serving as etch stop on the bottom
hBN flake (Fig.2c). We then expose the LMH to low power (3W) oxygen (O2)
plasma to remove all excess SLG, leaving behind the fully shaped GPD channel
(Fig.2d). A second EBL step, electron beam evaporation (5 nm Cr/50 nm Au), and
lift-off in acetone are then used to contact the exposed SLG channel edges
(Fig.2e). To fabricate the split-gate structure on top of the LMH, required to
create a p-n juntion in the GPD channel, a transparent (at $\lambda\sim 1.55$
$\mu$m) conductor that does not affect $\xi$ (thus $W$) is required. A second
layer of SLG, sufficiently high ( $\sim$ tens of nm) above the WG to leave
$\alpha_{\text{SLG}}$ unaltered, can be used for this. We therefore thermally
evaporate 1 nm Al as seed layer on the top hBN and use atomic layer deposition
(ALD, Savannah) to deposit 20 nm Al2O3 as additional gate dielectric and
spacer between channel and gate electrodes (Fig.2f).

To ensure alignment between LMH and gate SLG, we transfer a continuous film of
SLG, grown by chemical vapor deposition (CVD) on Cu following the process
described in Ref. Li2009Large , using a PMMA support membrane
Bonaccorso2012Production  on the SLG/Cu substrate. We etch Cu in ammonium
persulfate, transfer the PMMA/SLG stack onto the photonic chip (Fig.2g), and
remove the PMMA by immersion in acetone. We then use two additional EBL steps,
O2 plasma etching, and electron beam evaporation to define the SLG split-gate
geometry (Fig.2h) and fabricate metal contacts to these gates (Fig.2i).
Finally, we perform optical lithography on a laser writer (MicroTECH LW405)
and wet etching in HF to get access to drain and source contact pads.

A microscope image of the hBN/SLG/hBN LMH on the WG is in Fig.3a. We perform
Raman spectroscopy (Renishaw inVia at 514.5 nm, power $<$0.5 mW) and atomic
force microscopy (AFM, Bruker Dimension Icon) to monitor the SLG quality and
choose a suitable device position. A typical Raman spectrum before further
processing of the stack is in Fig.3b. The position of the combined hBN
E${}_{\text{2g}}$ peaks Reich2005resonant  from top and bottom flakes is
Pos(E2g) $\sim$1366 cm-1 with full-width half maximum, FWHM(E2g) $\sim$9.5
cm-1, as expected considering the top flake is bulk and the planar domain size
in these MC-produced hBN crystals is only limited by the flake size
Nemanich1981light ; purdie2018cleaning . The position and full width at half
maximum of the 2D and G peaks are Pos(2D) $\sim$2693 cm-1, FWHM(2D) $\sim$ 18
cm-1, Pos(G) $\sim$1583 cm-1 and FWHM(G) $\sim$ 14 cm-1, confirming the
presence of SLG and low $n$ ($<$1012 cm-2) Das2008Monitoring . This is
confirmed by the area (A(2D)/A(G) $\sim$ 10.7) and intensity (I(2D)/I(G) $\sim
7.6$) ratios, which indicate a Fermi level $E_{\text{F}}<100$ meV
Das2008Monitoring ; Basko2009Electron ; Ferrari2013Raman .

The AFM scan of the overlap region between LMH and micro-ring in Fig.3c shows
blister-free SLG/hBN interfaces, confirming a successful cleaning
purdie2018cleaning , apart from a bubble trapped in a cladding trench above
the WG. The Raman FWHM(2D) map in Fig.3d, taken from a 20 $\mu$m $\times$ 30
$\mu$m in the centre of the LMH, shows a region with homogeneous (spread $<$1
cm-1) and narrow ($\leq$18 cm-1) FWHM(2D) and spots of increased ($>$21 cm-1)
FWHM(2D) that coincide with the blister position as revealed by AFM. Based on
these findings, we then select the channel position (marked red in
Figs.3a,c,d) to be in a blister-free region. The final device has an active
area $L\times W\sim 2.5\times 6$ $\mu$m2. We use $L\sim$ 2.5 $\mu$m, which of
the order of twice the cooling length $L_{\text{cooling}}$ in SLG ( $\sim 1$
$\mu$m Ma2014Competing ; Shiue2015High , related to electron thermal
conductivity $\kappa_{e}$ (see Methods) and interfacial heat conductivity
$\Gamma\sim$ 0.5-5 MWm-2K-1 freitag2013increased ; tielrooij2018out  via
$L_{\text{cooling}}=\sqrt{\kappa_{e}/\Gamma}$ Song2011Hot ), to fully exploit
the $T_{e}$ profile with expected maximum at $L/2$ Schuler2016Controlled ;
Muench2019Waveguide  at the WG centre.

An optical image of the final device is shown in Fig.4a. We first verify gate
tunability of the SLG channel by measuring the drain-source current
($I_{\text{DS}}$) at a fixed drain-source voltage ($V_{\text{DS}}$) while
varying the two gate-voltages. The resulting resistance ($R$) map (Fig.4b)
shows a cross pattern, which confirms that four junction constellations (p-n,
n-p, n-n, p-p) can be generated in the channel Schuler2016Controlled . In
order to the extract contact resistance $R_{\text{contact}}$ and $\mu$ from
the GPD directly (rather than a four-probe reference structure made from a
second LMH), then used to estimate $S$, we use the measured transfer curve at
homogenous channel doping in Fig.4c and plot $R$ as function of the inverse
carrier concentration (1/$n$) for electron (Fig.4e) and hole (Fig.4f) doping.
By fitting the linear part (as 1/$n\rightarrow 0$) of these plots, as detailed
in Ref. zhang2012direct , $R_{\text{contact}}$ can be obtained from the
intersection of the fit curve and y-axis ($R$), while the residual carrier
concentration $n_{0}$ is found from intersection between the fit curve and a
horizontal line through the maximum $R$. Using these values, we then model $R$
as for Ref. Schuler2016Controlled :
$R_{\text{total}}$=$R_{\text{contact}}$+$\frac{L}{W}\frac{1}{e\mu n}$, with
$n=\sqrt{n_{0}^{2}+\left[C_{\text{ox}}/e\left(V_{\text{G}}-V_{\text{CNP}}\right)\right]^{2}}$,
where $R_{\text{contact}}$ includes the contacts and the contribution from the
ungated region, $V_{\text{CNP}}$ is the gate voltage corresponding to the
charge neutrality point (CNP, $E_{\text{F}}$ = 0 meV), $C_{\text{ox}}$ is the
gate capacitance, and $\mu$ is used as a fit parameter. The original data
(solid line) and the model (dashed line) are compared in Fig.4c. We get
$R_{\text{contact}}\sim 400$ $\Omega$ and $\sim 530$ $\Omega$, as well as
$\mu_{\text{e}}\sim 17700$ $cm^{2}$/Vs and $\mu_{\text{h}}\sim 11800$
$cm^{2}$/Vs for electrons (red lines) and holes (blue lines), respectively.

Figure 4: (a) Microscope image of device with top gate CVD SLG electrodes.
Scale bar, 5 $\mu$m. (b) Resistance map demonstrating independent tunability
of charge carrier concentration in the SLG channel via $V_{\text{G1}}$ and
$V_{\text{G2}}$. (c) Electrical characterization at homogeneous channel doping
(solid lines, measured data; dashed lines, model). (d) Calculated $S$ based on
the electrical data in (c). (e,f) Resistance vs. inverse carrier concentration
for (e) electron and (f) hole doping.(g) Photoresponse at zero bias on
resonance ($\lambda$ = 1555.87 nm). (h) Frequency response. The 3-dB cutoff
frequency, marked by intersecting dashed lines, is $\sim$12 GHz.

For optical characterisation, we first couple modulated light (ON-OFF) with a
duty cycle of 50% from a tuneable laser source (Agilent 81680A) into the bus
WG using an optical single-mode fibre. While varying the potential at the two
gate electrodes ($V_{\text{G1}}$, $V_{\text{G2}}$), the photoresponse is
recorded using a lock-in amplifier. Fig.4g shows a photoresponsivity map
measured on resonance at 1555.87 nm, from which we extract a maximum
$R_{\text{[V/W]}}\sim 90$ V/W. The six-fold pattern, with the highest
photoresponse for bipolar (p-n, n-p) junctions and a sign-change across the
diagonal ($V_{\text{G1}}$ = $V_{\text{G2}}$) for unipolar (n-n, p-p) junctions
in the SLG channel, confirms that the PTE effect dominates the conversion of
photons into electrical signal gabor2011hot ; Song2011Hot .

To determine the BW, we modulate CW light at 1555.87 nm from the same source
using a commercial (Thorlabs LN05S-FC) intensity modulator (lithium niobite,
$f_{\text{3dB}}$ = 40 GHz) and couple it into the device. While tuning the
modulation frequency of the external modulator, we monitor the GPD response
with an electrical spectrum analyzer (Agilent PSX N9030A) while the gate bias
($V_{\text{G1}}$ = -0.5V, $V_{\text{G2}}$ = -2.1V) is set at an operating
point where $R_{\text{[V/W]}}$ is largest. This gives a 3 dB bandwidth
$\sim$12 GHz, Fig.4h, as expected from the design of the passive photonic
structure. In optical transmission systems that employ the non-return-to-zero
(NRZ) format (i.e. two non-zero voltage levels used to represent digital ones
and zero Kaminow2013Optical ) for signal encoding, the BW of the PD employed
in the receiver corresponds to $\sim 60-70\%$ of the bit rate (bits processed
per second) the optical link can support sackinger2005broadband . Our GPD is
thus capable of detecting data rates up to
$\sim\frac{f_{\text{3dB}}}{0.6}\sim$ 20 Gbit/s, confirming its suitability for
applications in data centre optical interconnects cheng2018recent .

Figure 5: (a) Transmitted power for various $P_{\text{in}}$. (b) Photovoltage
for a fixed gate voltage combination ($V_{\text{G1}}=1$ V, $V_{\text{G2}}=-1$
V) measured for various input powers (same color code as for the transmission
in (a)). (c) $T_{e}$ calculated from the photoresponse in (b) and S in
Fig.4(d). (d) Power-dependent $R_{\text{[V/W]}}$.

Figs.5a,b plot the wavelength dependence of optical transmission and
photovoltage for $V_{\text{G1}}$ = 1 V, $V_{\text{G2}}$ = -1 V and various
$P_{\text{in}}$. The shift of the resonance and its asymmetry are attributed
to the power dependent change of the effective refractive index of the Si WG
through a thermo-optic effect bogaerts2012silicon ; Fainman2013silicon .
Extracting the power-dependent maxima in $V_{\text{PTE}}$ allows us to
estimate $T_{e}$ at resonance, and plot the $R_{\text{[V/W]}}$ power-
dependence.

The junction carrier temperature $T_{\text{e,j}}$ can be written as (see
Methods):

$T_{\text{e,j}}=\sqrt{2\bigg{|}\frac{V_{\text{PTE}}}{\zeta_{1}-\zeta_{2}}\bigg{|}+T^{2}_{0}}$
(5)

where $T_{0}$ = 294 K is the room temperature and
$\zeta_{1,2}=\frac{\pi^{2}k_{\text{B}}^{2}}{3e\sigma}\frac{\mathrm{d}\sigma}{\mathrm{d}\epsilon}$
at $\epsilon=E_{F}$ in analogy to Eq.2. In order to estimate $\zeta_{1,2}$,
following the same method used to determine $S$ in Fig.4d, we use
$R_{\text{contact}}$ and $\mu$ as obtained from the electrical measurements at
homogeneous channel doping. The resulting $T_{e}$ extracted for different
$P_{\text{in}}$ is shown in Fig.5c. The carriers reach $T_{e}\sim$ 400 K for
$P_{\text{in}}\sim$ 0.6 mW, due to the cavity-enhanced light-matter
interaction. The $T_{e}$ power-dependence can be fitted by the heat equation
Song2011Hot ; Ma2014Competing , neglecting diffusive cooling through the
contacts (see Methods) as:

$T_{\text{e,j}}=\left(\beta
P_{\text{IN}}+T^{\delta}_{0}\right)^{\frac{1}{\delta}}$ (6)

with $\delta\sim 3$ graham2013photocurrent  and $\beta$ a fitting parameter.

The associated, power-dependent $R_{\text{[V/W]}}$ is presented in Fig.5d. For
small $P_{\text{in}}$ ($<$0.2 mW), we obtain a constant $R_{\text{[V/W]}}$.
For $P_{\text{in}}>$0.2 mW we get sublinear scaling between $V_{\text{PTE}}$
and $P_{\text{in}}$, resulting in a drop of $R_{\text{[V/W]}}$ according to
$R_{\text{[V/W]}}\propto P_{\text{in}}^{-1/3}$ due to the $T_{e}$ dependence
of the electronic heat capacity graham2013photocurrent ;
tielrooij2015generation .

In order to assess our GPD performance against non-SLG based ones, where
typically a photocurrent $I_{\text{ph}}$ is generated chrostowski2015silicon ,
we compare two representative optical receiver implementations: a
’conventional’ (i.e. non-SLG) system based on a wafer-scale, commercial, high-
speed ($>$50 GHz) Ge photodiode with a (current) responsivity
$R_{\text{[A/W]}}=I_{\text{ph}}/P_{\text{in}}\sim 0.5$ A/W absil2015silicon ,
and a receiver based on our GPD. In both systems the same voltage amplifier is
employed to obtain a $>$200 mV output voltage swing ($V_{\text{OUT}}$), as
required for driving the subsequent clock and data recovery CMOS circuit. For
simplicity we assume that the amplifier represents a capacitive load.

Our GPDs are based on the PTE effect where an electromotive force directly
provides a voltage, rather than a current Koppens2014Photodetectors ;
tielrooij2015generation . In case of Ge, an additional TIA is needed to
convert the photocurrent into a voltage for further signal processing
okamoto2016chip . In the TIA we consider a feedback resistor $R_{\text{F}}$ =
(90V/W)/(0.5 A/W) = 180 $\Omega$, which assures the same $V_{\text{OUT}}$ for
same optical input power in both cases. Neglecting any noise other than
thermal noise produced by $R_{\text{F}}$, we estimate for the conventional
receiver a lower limit for the sensitivity
$\bar{P}_{\text{sens}}=Qi_{\text{n}}/R_{\text{[A/W]}}=12.6$ $\mu$W $\sim$ -19
dBm at a bit-error-rate (i.e. probabilty of false identification of a bit by
the receiver decision circuit agrawal2012fiber ) BER = $10^{-9}$. Here we
calculated the thermal noise current as $i_{\text{n}}$
=$\sqrt{4k_{\text{B}}\cdot T\cdot BW/R_{\text{F}}}$ with BW = 12 GHz, as in
our GPDs, and a $Q$ factor (i.e. required signal-to-noise ratio to get a
specific BER bergano1993margin ) $\sim$6 from agrawal2012fiber  BER =
$\frac{1}{2}\text{erfc}(Q/\sqrt{2})$. For our GPDs, we estimate
$\bar{P}_{\text{sens}}$ = $Qv_{\text{n}}/R_{\text{[V/W]}}\sim$ -16 dBm for
same BER and $BW$, where $v_{\text{n}}$ = $\sqrt{4k_{\text{B}}\cdot T\cdot
BW\cdot R_{\text{G}}}$ and $R_{\text{G}}\sim 800$ $\Omega$ is the total device
resistance. Thus, the $\bar{P}_{\text{sens}}$ of our GPD-based receiver is on
par with mature semiconductor technology and could be further improved by
reducing $R_{\text{contact}}$, which dominates the total device resistance,
thus being the primary source of thermal noise. The natural generation of a
voltage makes the need for a TIA obsolete, with a reduction of the energy-per-
bit cost and system foot-print.

##  III Conclusions

We reported photo-thermoelectric GPDs, integrated on Si microring resonators.
By tuning the SLG coverage on top of the resonator, we optimised the round-
trip propagation losses inside the cavity to achieve critical coupling,
achieving $>90$% light absorption in $\sim 6$ $\mu$m SLG. The resulting
carrier heating on such compact lengths enables high peak $T_{e}\sim$ 400 K in
the GPDs. In combination with high ($>10^{4}\text{ cm}^{2}/\text{Vs}$)
mobility, achieved by encapsulating the SLG channel in hBN, this allowed us to
achieved $R_{\text{[V/W]}}\sim$ 90 V/W. Our bias-free and Johnson-noise
limited GPDs with voltage output are a more power-efficient alternative to
state of the art commercial PDs used in optical interconnects. Hot-carrier
effects in SLG can be used for receiver architectures where current-to-voltage
conversion, traditionally performed by transimpedance amplifiers, can be
bypassed for a reduction in energy-per-bit cost and system foot-print.

##  IV Methods

The junction $T_{e}$ can be extracted from the power dependent photovoltage
measurements. Rewriting Eq.2 as $S=\zeta T_{\text{e}}$, where
$\zeta=-(\pi^{2}k_{\text{B}}^{2})/3e\sigma\mathrm{d}\sigma/\mathrm{d}\epsilon$
at $\epsilon=E_{F}$, and using this in Eq.1, we get $V_{\text{PTE}}=\int
S(x)\nabla T_{\text{e}}(x)\mathrm{d}x=\int\zeta(x)T_{\text{e}}(x)\nabla
T_{\text{e}}(x)\mathrm{d}x$. Integration over the p-n-junction gives
$V_{\text{PTE}}=\zeta_{1}\int^{0}_{-\frac{L}{2}}T_{\text{e}}(x)\frac{\mathrm{d}T_{\text{e}}}{\mathrm{d}x}\mathrm{d}x+\zeta_{2}\int^{\frac{L}{2}}_{0}T_{\text{e}}(x)\frac{\mathrm{d}T_{\text{e}}}{\mathrm{d}x}\mathrm{d}x=\frac{\zeta_{1}-\zeta_{2}}{2}\left(T^{2}_{\text{e,j}}-T^{2}_{0}\right)$.
From this, we extract the junction $T_{e}$ from the measured photovoltage as
$T_{\text{e,j}}$=$\sqrt{2\bigg{|}\frac{V_{\text{PTE}}}{\zeta_{1}-\zeta_{2}}\bigg{|}+T^{2}_{0}}$.
In the most general case, the $T_{e}$ profile can be calculated from the heat
equation Song2011Hot ; Ma2014Competing , including diffusive cooling through
contacts and cooling through the phonon bath:
$\frac{\mathrm{d}q}{\mathrm{d}x}=-\frac{\mathrm{d}}{\mathrm{d}x}\left(\kappa_{\text{e}}\frac{\mathrm{d}}{\mathrm{d}x}T_{\text{e}}\right)+\frac{\kappa_{\text{e}}}{L_{\text{cooling}}^{2}}\left(T^{\delta}_{\text{e}}-T^{\delta}_{\text{0}}\right)$,
where $\frac{\mathrm{d}q}{\mathrm{d}x}$ describes the heating of the system.
The electronic thermal conductivity is given by
$\kappa_{\text{e}}=\sigma\mathcal{L}_{0}T_{\text{e}}$ kittel1996introduction ,
with Lorenz number $\mathcal{L}_{0}$, while a $T_{e}^{\delta}$ dependence with
$\delta\sim 3$ is characteristic for graphene Ma2014Competing ;
Song2012Disorder . Assuming that the distance from the heat source to the heat
sink larger than the cooling length
($L_{\text{channel}}>2L_{\text{cooling}}$), the heat equation becomes
$\frac{\mathrm{d}q}{\mathrm{d}x}=\frac{\kappa_{\text{e}}}{L_{\text{cooling}}^{2}}\left(T^{\delta}_{\text{e}}-T^{\delta}_{\text{0}}\right)$,
with $\frac{\mathrm{d}q}{\mathrm{d}x}=\alpha P_{\text{in}}/A$, with $\alpha
P_{\text{in}}$ the fraction of the absorbed power, and $A$ the heated area. We
thus get $T_{\text{e,j}}=\left(\beta
P_{\text{in}}+T^{\delta}_{0}\right)^{\frac{1}{\delta}}$, with $\beta$ a fit
parameter.

##  V Acknowledgments

We thank Stefan Wachter, Daniel Schall, and Andrea Tomadin for useful
discussions. We acknowledge funding from the EU Graphene Flagship, ERC grant
Hetero2D, DSTL, EPSRC grants EP/L016087/1, EP/K01711X/1, EP/K017144/1,
EP/N010345/1

##  VI Author contributions

S.S. and T.M. conceived the device. S.S. and J.E.M. fabricated the devices and
performed the experiments. S.S., J.E.M., T.M., and A.C.F. analysed and
discussed the data. J.E.M. and A.R. built the measurement set-up. O.B.
prepared CVD SLG. T.T. and K.W. prepared hBN. D.V.T. and V.S. designed and
provided the SOI waveguide substrates. T.M., A.C.F., I.G., and M.R. supervised
the work. S.S., J.E.M., T.M., and A.C.F. wrote the paper, with input from all
authors.

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# Practical Fingerprinting of RF Devices in the Wild

Silvija Kokalj-Filipovic, Luke Boegner, Robert D. Miller

Perspecta Labs Inc.
{skfilipovic, luke.boegner<EMAIL_ADDRESS>
###### Abstract

We present a new RF fingerprinting technique for wireless emitters that is
based on a simple, easily and efficiently retrainable Ridge Regression (RR)
classifier. The RR learns to identify devices using bursts of waveform
samples, conveniently transformed and preprocessed by delay-loop reservoirs.
Deep delay Loop Reservoir Computing (DLR) is our processing architecture that
supports general machine learning algorithms on resource-constrained devices
by leveraging delay-loop reservoir computing (RC) and innovative architectures
of loop trees. In prior work, we trained and evaluated DLR using high SNR
device emissions in clean channels. We here demonstrate how to use DLR for IoT
authentication by performing RF-based Specific Emitter Identification (SEI),
even in the presence of fading channels and heavy in-band jamming by
leveraging a matched filter (MF) extension, dubbed MF-DLR. We show that the MF
processing improves the SEI performance of RR without the RC transformation
(MF-RR), but the MF-DLR is more robust and applicable for addressing
signatures beyond waveform transients (e.g. turn-on).

##  I Introduction

The Internet of Things (IoT) is becoming a pervasive reality. Billions of IoT
devices will be deployed with vastly different computational capabilities,
however they must all be protected. Conventional authentication mechanisms to
verify device identities are based on upper layer protocols that may be too
complex and resource-restrictive for use on many IoT devices. Such techniques
tend to be cryptographically-based and require active collaboration, hence
involving computational resources, power drain, and may still not be able to
meet latency requirements. Physical layer authentication (PLA) methods are
relatively new [1], and the research [2] mostly addressed 2 types of PLA
approaches: 1) using Channel State Information (CSI) 2) exploiting the HW
signature of the transmitting device in the received signal. Both methods
eliminate the need for cryptography and the associated overhead, with the 2nd
approach generally more reliable. As all electronic devices have fingerprints
due to manufacturing variability, so do radio frequency emitters. The
composition of these RF fingerprints is described in detail in [1]: it
includes, among others things, clock jitter, DAC sampling inaccuracy, mixer or
local frequency synthesizer imperfections, power amplifier non-linearity,
device antenna and modulator sub-circuit (if the analog modulation is used). A
convenient name for such fingerprints used in emitter identification was
coined in [3]: Physical unclonable functions (PUFs). PUF-based systems for
unique identification of emitters are extremely robust and secure at low cost,
as it is practically impossible to replicate the same silicon characteristics
across dies. Specific Emitter Identification (SEI) based on RF fingerprinting
can individually identify wireless devices, including previously unseen [4].
Even though RF fingerprints have been analyzed and modeled earlier [1], their
full potential for SEI became clear with deep learning. The most recent work
is on the SEI designs based on supervised deep learning [5]. This approach
trains neural network models to verify the identity of wireless transmitters
using labeled datapoints derived from the captured emissions of those
transmitters without any feature engineering.

Our approach to SEI for IoT authentication is based on leveraging signatures
present in the turn-on transients of IoT emissions. Contrary to what is stated
in [3], in combination with our resource-constrained but extremely efficient
classifier, these signatures prove to be accurate and robust. Our SEI design
based on delay-loop reservoirs used a sampling rate of 100Msps as opposed to
the examples featured in [3] (500 Msps in [6] and 50 GS/s in [7]. Hence, the
expensive receiver architectures are no longer required.

Further, our solution to efficient RF fingerprinting of wireless emitters is
based on a simple, easily retrainable classifier that learns to identify
emitting devices based on bursts of waveform samples, conveniently transformed
and preprocessed by a delay-loop reservoir. State-of-the-Art (SoA) machine
learning systems that are trained on sensor signals lack the computational
resources to support in-situ training and adaptable inference for situational
awareness. In our prior work [8, 9], we proposed a solution through Deep delay
Loop Reservoir Computing (DLR), our novel AI processing architecture that
supports general retrainable machine learning (ML) solutions on compact mobile
devices by leveraging delay-loop reservoir computing (RC). Reservoir computing
is a bio-inspired approach suited for processing time-dependent information in
a computationally efficient way [10]. The RC in ML solutions conditions the
input features towards linear separability of different classes, upon which
any ML algorithm can be trained more efficiently. Upon transforming the inputs
by delay loops, we can classify fingerprints by employing a classifier based
on Ridge Regression trained on delay loop outputs. DLR delivers significant
reductions in form factor and power consumption for training at the Edge,
providing real-time learning latency. For a pictorial illustration of the
process employing a DLR system to train and perform SEI, including RF spectrum
sensing and preprocessing, please consult Fig. 1. Our innovative architecture
of split loops yielded a resource-savvy SEI solution, which for a clear
channel delivery of emitted signals (high SNR) exceeds the SoA accuracy. In
this paper we demonstrate how to use DLR for IoT authentication by performing
RF based Specific Emitter Identification (SEI) even in the presence of fading
channels, heavy in-band jamming and receiver imperfections. In order to make
SEI robust to these imperfections, we propose to use a matched filter (MF)
extension to DLR where the filter is designed by processing the transient
turn-on part of the device emission. We refer to it as MF-DLR. It increases
the SEI resilience to in-band jamming, channel and receiver imperfections.

We also show that the addition of the MF based on turn-on signatures improves
the SEI performance of the simple Ridge Regression (RR) classifier with no
delay-loop processing (parts a and c in Fig. 1). Although MF-DLR demonstrates
better robustness to signal impairments, the improved MF-RR performance is an
important observation given the simplicity and pervasiveness of regularized
least square methods (RR). It appears that the MF contributes to linear
separability of the signature classes, while the RC increases the margins
around hyperplanes. The organization of this paper is as follows: Section II
introduces the DLR for SEI, and its components. Section III first describes
DLR performance on clean data, then introduces MF-DLR and MF-RR and evaluates
their robustness to various channel and receiver imperfections compared to
DLR.

Figure 1: DLR system for SEI/WiPRec: BD is burst detection, while BE stands
for burst extraction. DLR includes blocks $b+c,$ MF-DLR includes $a+b+c$,
where $c$ is the simple RR classifier.

##  II DLR for SEI: System Description

###  II-A Basic DLR

DLR uses reservoir computing in the form of a delay loop reservoir that
replaces the N neurons in the traditional spatial implementation of the
reservoir with N passes through a single neuron. The N-fold increase in delay
by the sequential passing of the data through a single neuron is canceled out
by an N-fold upsampling (sample and hold) done by a random spreading sequence
$m(t)$ (see Fig. 2).

Figure 2: Delay-loop reservoir replaces the N neurons (NLs) on the left with a
single one by using upsampling ($\theta$ depends on the loop bandwidth) and a
simple design shown on the right

With reservoirs, the N must be large and such high rate upsampling is amenable
to a photonic loop implementation. The wide bandwidth and wavelength diversity
of photonic loops is the reason why DLR supports photonic DLs as a vehicle to
future scalability. We here limit the scope to the FPGA and S/W (digital)
implementations of the loop.

The N which allows the reservoir to linearly separate input classes for easier
learning may be very large for certain applications. However, in our prior
work [9] we introduced algorithms for reducing the required reservoir size by
means of split loops. Once trained, the DLR maps the signal to its unique
transmitter by just passing the burst of samples through the loop and
multiplying it with the weight matrix. For a burst of 1 us, it happens in sub-
millisecond including the extraction of the burst and its preprocessing by
transforms.

Dataset and Preprocessing  The dataset to train the SEI detector contains 20
classes, corresponding to 20 distinct WiFi devices. We captured the emissions
of commercial WiFi devices as they were sending beacons to an access point
while using the same spoofed MAC address. We used USRP X310 with UBX RF
daughterboard, with sample rate of 100 MHz centered in the middle of the 2.4
GHz ISM band. Datapoints are created by extracting bursts of 1024 complex
(I/Q) samples from the captured time-series, right after the detection of the
rising edge of the signal. Further processing steps are explained below.

Delay Loop (DL)  Each sample $s(n),n\in{1,\cdots,\ell}$ of the input datapoint
of size $\ell$ (Fig. 1) is spread by the mask $m(t)$ and clocked into the loop
as input $J(n)(t),$ chip-by-chip. The upsampled time is defined in chips
$\theta$ (in Fig. 2). Here, $t\in{1,\cdots,N}$ is the chip-time index, and
$k\in{1,\cdots,N}$ is the loop position index. $X_{k}$ is the $k^{th}$ virtual
node of the state vector $X.$ Note that $N$ is the number of virtual reservoir
nodes, as well as the length (in chips) of the random spreading sequence
(mask) $m(t),$ as in Fig. 2. The loop output is read out after the last of the
$\ell$ samples is clocked-in and put through the loop’s non-linearity $f_{NL}$
$N$ times.

Each chip of the spread sample $J(n)(t)$ is linearly combined with the tail of
$X:X_{N}(n-1)$ and put through the nonlinearity (NL). $X_{N}(n-1)$ was
affected by the same non-linearity at time $t-\tau,$ i.e., by the previous
input sample $n-1$, where $\tau=N\theta$. Summation of the spread data input
and the tail of $X$ at every $t$ is practically creating the edges of the
recurrent layer from the spatial implementation of the reservoir (the left
side of Fig. 2) [11]. The output of the $NL$ may be convolved with filter
$h(t)$ to modify the adjacency graph of virtual nodes resulting in a faster-
mixing reservoir. Omitting the effect of $h(t)$, $X_{k}$s are simply time-
shifted, in chip time $\theta,$ which also roughly matches the propagation
time in photonics. (1) models the shifting of the $f_{NL}$ output in digital
implementation, where $X_{k}$ at chip time $t$ is given by $X_{k}(t)=$

$\displaystyle\sum_{u=0}^{1}{h(u)f_{NL}\left[\eta X_{k}(t-N+u)+\nu
J(t-k-u)\right]}+\sigma,\vspace{-1mm}$ (1)

$\sigma\longrightarrow 0.$ The loop gain $\eta$ and input gain $\nu,$ as well
as the taps of $h(t),$ must be calibrated to provide a proper dynamic state of
the reservoir. The results are based on $f_{NL}=sin\left(\cdot\right).$

Splitting the input into $k$ parallel loops and combining their outputs
reduces the complexity of the classifier by $k^{2}$ (please see the section on
split loops below). We use transforms to adapt the salient signal information
to the split loop input. We develop multiple ways to merge the outputs of the
constituent DLR loops into a single output to be used to train a simple RR
algorithm [12]. We should emphasize that the loops are never trained, only the
RR algorithm, which uses their outputs. Note that the computational complexity
of training the DLR (Fig. 4) is the complexity of the last stage (RR), given
the simple implementation of the loop.

Ridge Regression  The Ridge Regression algorithm for the estimation of the
weight coefficient matrix $W$ can be presented in closed form as

$W=(X^{T}X+\lambda I_{N})^{-1}\ (X^{T}Y_{out})$

where $X$ is the matrix of the $B$ state vectors used for its training,
$Y_{out}$ is the corresponding matrix of device-labels in onehot
representation, and $\lambda$ is the regularization factor. Once the
coefficient are trained on $X,$ the identity $D_{T}$ of a burst of samples
$s_{T}(n),0\leq n\leq\ell$ can be determined by passing it through the
reservoir $X_{T}=RC(s_{T}),$ and multiplying it with $W:$
$D_{T}=\operatorname*{arg\,max}(X_{T}W).$

Figure 3: Using k split (parallel loops) reduces the size of the spreading
mask and, hence, the size of each split loop while achieving the required
projection into higher dimensional space. The joint state vector $X$ (marked
by the blue circle) can be obtained as $\sum_{j=1}^{k}{X_{j}}$, or as a
normalized scalar product of $X_{j}$s.

Split Loops As Fig. 3 shows, the split loops process the $k$ disjoint pieces
of the split datapoint in parallel and result in the k state vectors
$\left\\{X_{1},\cdots,X_{k}\right\\}$. The joint state vector $X$ (marked by
the blue circle) can be obtained as $\sum_{j=1}^{k}{X_{j}}$, or as a
normalized scalar product of $X_{j}$s. Both gave similar results in terms of
the improved accuracy over a single loop. Let us emphasize here that DL is a
dynamic system, and the reservoir size $N$ for a datapoint of size $\ell$ must
satisfy $N>>\ell$ to bring the DL into a dynamic state where the class
separation happens. For spatial reservoirs, this is achieved by optimizing
spectral properties of the adjacency matrix of size $N.$ With delay loops, we
instead optimize by modifying $N,\eta,\nu,\lambda$ and $h(t).$ Each of the
split-datapoints is of size $\ell/k$ and its $N_{j}<N,j=1,\cdots,k$ now may be
$k$ times smaller than the $N$ without splitting. Now, as the total $X$ is a
linear combination and not concatenation of the split loops’ $X_{j}$s, the
entry to the RR is still of size $N_{j}$, which reduces the RR complexity from
$BN^{2}$ to $B(N/k)^{2}$. Beyond a certain value of $k,$ the accuracy starts
to drop as splitting the datapoint affects the samples that are no longer
independent. The exact value of the threshold $k$ depends on the input
transform applied to the burst of $I/Q$ samples composing the dataset. As an
example, this threshold for the FFT is 10.

Input Transforms  It is known that certain transforms losslessly compress the
data if the information content is sparse, and some are more robust to noise,
including the noise in the photonic loop. Motivated by this, we experimented
with multiple input transforms in order to best mach the input to the
architecture of DLR, given constraints in the complexity (i.e., largest
reservoir output we are willing to train).

We consider the transform from complex-valued samples to their amplitudes as
the baseline. The accuracy of DLR based on the amplitudes ranks the worst
among the tested transforms. We also evaluated 1) reservoir inputs made of
frequency estimates [13] of the complex valued input bursts, 2) amplitudes of
the FFTs of input bursts 3) inputs made of the so called differential FFT and
3) inputs based on decimated DFT transforms. In what follows, we will use the
FFT amplitudes, based on the detailed discussion in [14, 9]. We will use 10
splits of the FFT transform, as the FFT showed increased accuracy with number
of splits $k$ up to $k=10.$ Please see the discussion in [14, 9], in
particular the comparison between FFT and decimated DFT. Even though decimated
DFT improves with increasing decimation up to a threshold $d$, with best
performance achieved for $d=8$ for 2 loops, and $d=4$ with 4 loops, FFT
matches it with 8 loops and continues to improve up to 10 loops. With fewer
loops decimated DFT is better, but we picked FFT as it excels with more loops.

##  III Discussion of Experimental Results

###  III-A Basic Performance

The table of Figures of merit (FOMs) in Fig. 4 shows the 20-device SEI
performance numbers for the best trade-off we achieved with DLR. These are
compared with the equivalents for SoA neural networks trained on a single GPU.
The reduction factors (RedF), obtained when DLR FOMs are compared to
respective values for ResNet or RNN, are: spatial RedF, the ratio of the
number of trainable parameters, is 20, power RF, the ratio of the complexity
of training, is 100, while the latency compares the hours of GPU training
versus 5 seconds achieved with our demo platform ($\geq 1200$). For the
calculation pattern of FOMs, please see our paper on intermediate results
[8].The comparison is based on N=600. Note that we could achieve higher
accuracy of above 97% by using the reservoir with $N=1200,$ which increases
the complexity 4$\times$. Fig. 5 shows the FOMs of MF-DLR for some stationary
impairments.

Model | Accuracy(%) | Memory | Complexity | Latency
---|---|---|---|---
ResNet | 94.5 | 214K | $>5\times 10^{11}$ |
LSTM RNN | 91 | 210K | $5\times 10^{11}$ | $>1h$
DLR, N=600 | 95 | QN=12K | $5\times 10^{9}$ | 5s
DLR, N=1K | 96.7 | 20K | $12\times 10^{9}$ | 20s
Figure 4: FOMs compare the best trade-off of SEI accuracy vs H/W reduction for DLR vs SoA. Complexity is expressed in terms of total MAC operations and memory in terms of the number of parameters to train.  Model | Accuracy(%) | Memory | Complexity
---|---|---|---
MF-DLR, N=1K | 99.99 | QN=20K | $12\times 10^{9}$
MF-DLR , N=1K | 99.21 | 20K | $12\times 10^{9}$
AWGN 0dB+jitter |  |  |
MF-DLR , N=1K | 98.61 | 20K | $12\times 10^{9}$
0dB+fading+jitter ($T_{4}$) |  |  |
Figure 5: Figures of Merit for MF-DLR on stationary impairments

###  III-B Robust DLR

We next address signal corruptions due to receiver imperfections, fading
channels, and interference. In order to make SEI robust to these
imperfections, we propose a matched filter extension to DLR in its pre-
processing stage (MF-DLR). The term matched filter is somewhat arbitrary as we
do not know the waveform shape in the transient turn-on part of the emission.
Here is how that matched filer is implemented: we pick a random datapoint from
every device $D$ that we are training on, to be used as the filter for all
datapoints of this class, i.e. applied before we perform the transform (FFT)
at the entrance of DLR. Hence, for 20 devices we have 20 filters. This
resulted in a huge improvement in accuracy for a range of signature
corruptions. However, using a random instantiation of signature per device
caused randomness in the accuracy across runs. The max variation in accuracy
was 10%. We replaced the random instantiation with the average datapoint per
device, maintaining robustness with less randomness.

Now, this is somewhat counter-intuitive: to use the right filter we have to
know the identity of the device that we are trying to identify. In supervised
training we already know the identity, but for inference, we run several
filters in parallel (as many as there were devices in the training set). If
the filter is wrong we will know it by the value of the entropy statistic [9],
with the false positives of max 5% with $T_{4}$ impairments (see bellow).

For compactness, we emulate the effects of the propagation and the receivers
by using 5 distinct compositions of transforms representing fading channels
and the complex imperfections in the receiver (RX) front end, including time
and frequency jitter, phase noise, I/Q-imbalance, and non-linear power
amplification. These transforms are applied to the clear-captured data
presented above. We denote classes of these affects as $T_{0}\cdots T_{4}$,
where $T_{0}$ represents clean signals, and classes $T_{i}$ are characterized
by imperfections that increase monotonically with index $i$. $T_{i}$
parameters dependent on the index define the range of the random effects
applied to clean datapoints: $t_{i}=25i,$ maximum absolute time error (in
samples) in the burst extraction; $p_{i}=0.25i,$ maximum absolute phase
rotation (in radians) of the burst; $f_{i}=0.075i$ maximum absolute frequency
shift in the burst extraction; $b_{i}=0.6-0.1i,$ upper bounds of Rayleigh
fading coherence bandwidth, $r_{i}=1+0.625i$ maximum non-integer resampling
rate due to non-linearities in ADC; $s_{i}=(50-12.5i)dB,$ SNR value. We also
model the fading rate and resampling as a linear function of the index. Power-
delay profile is fixed to $\left[1,1,1\right].$

Finally, with superheterodyne receivers, zero IF receivers have become the
main SDR RF front-end. Among the RX effects that may destroy the transmitter
RF signature, the IQ imbalance [15], common to zero IF receivers, is
attributed to the mismatched components of the in-phase (I) and the quadrature
(Q) branches, such as an imperfectly balanced local oscillator or baseband low
pass filters with mismatched frequency responses. We model the IQ imbalance
with $Ia_{i}=0.75i,$ maximum amplitude IQ imbalance; $Ip_{i}=0.25i,$ maximum
phase IQ imbalance (in degrees); $Id_{i}=0.025i$ maximum DC bias in IQ
imbalance.

The use of matched filters in communications is typically limited to cases
where the pulse shape is known. The turn-on RF signatures are unknown
waveforms. However, when the same receiver is used for the training data
collection and the SEI inference, and a clear channel is secured ($T_{0}$), we
observe that the turn-on signature of a device experiences small variations
only. Hence, the average device signature obtained by summation and
normalization of all its turn-on bursts seemed like a good model of the
constant signature waveform. In addition, statistical models of jitter,
channels, and noise are all zero-mean symmetric distributions. This extends to
the Rayleigh model, which describes how the complex amplitude fades as the
radial component of the sum of two uncorrelated Gaussian random variables.
Hence, the matched filter obtained as an average turn-on signature of an
augmented $T_{i}$ dataset is expected to provide a good model of the device
under a stationary channel. To see what happens when the channel varies we
evaluate when we apply a $T_{i}$ filter and perform inference on a signal
impaired by $T_{j},j\neq i.$

For different choices $T_{0}\cdots T_{4}$ of the training dataset and matched
filter (MF), Fig. 6 shows the accuracy as a function of imperfections
$T_{0}\cdots T_{4}$ corrupting the evaluation dataset (the test channel). If
the matched filter and the training dataset are affected by the same
impairments as the evaluation dataset ($T_{0}\cdots T_{4}$), we obtain almost
perfect accuracy across channels (with highest 99.99% with $T_{0}$ and lowest
99.34 % for $T_{4}$). Further we show what happens when the MF and the
training set undergo the same specific impairment, while the test-time channel
is changing from $T_{0}$ to $T_{4}.$ This is the effect of non-stationarity.
Fig. 6 shows how the MF and the delay loop (DLR) affect the robustness of the
RR classifier. We see that in the case of the $T_{0}$ training with MF, delay
loop adds additional robustness to changing channels compared to MF-RR (blue
curve vs. dotted blue curve). MF-RR appears to be working better for
$T_{i},i>0$ (by up to 2 %), which is due to a larger $W$ matrix, and also due
to random effects of the random spreading $m(t)$ that was not optimized.
Looking at the separation of clean turn-on bursts, we see that they are pretty
well separated to start with. Future work will include bursts beyond
transients, where we expect increased DL benefits.

To test the effect of matched filter in the presence of jamming (in-band
interference), we create two subsets from the original WiFi collection. We use
the first subset of 12 devices to create the clean training dataset
$\left\\{X_{tr}\right\\},$ as well a disjoint dataset of test bursts
$\left\\{X_{t}\right\\},$ while the second subset of 8 devices
$\left\\{X_{j}\right\\}$ was used to create an evaluation set in the following
way: we take the burst from the the clean test set $\left\\{X_{t}\right\\}$
(at the start of emission), and superpose one or more bursts from
$\left\\{X_{j}\right\\}$ (depending on the JSR). Such a ’jammed’ datapoint is
pushed into DLR, where it is first matched-filtered and then processed as
described above. During the training $\left\\{X_{tr}\right\\}$ contained 600
bursts for each of 12 ’unjammed’ devices, and each burst would be match-
filtered before entering the reservoir. For the evaluation, each of 12 jammed
devices also had 600 bursts, hence the accuracy results in Fig. 7 are based on
the total of 7200 bursts ($\sim 10\mu$s each). Note that the accuracy of
99.986 (without jamming) means that only 1 of 7200 was misclassified.

Each of the 7200 bursts is jammed in a systematic way so that jamming-to-
signal ratio (JSR) has a desired value $x$, and the SEI accuracy in the
presence of such jamming is recorded. Specifically, a random combination of
jammers (out of the 8) transmits during the transmission of the legitimate
burst of 1024 samples, but each with a random delay 0-512. We then calculate
the total jamming energy across all jammers as compared to the original
signal’s energy and use this as the JSR value in Fig. 7. With the matched
filter, the accuracy of MF-DLR on normal datapoints (without jamming) went to
99.99% , up 2% from a simple DLR on 12 devices. Note that the MF also benefits
MF-RR, but DL adds another $\sim 15\%.$ We expect an optimized MF-DLR to
perform even better.

Figure 6: Accuracy of MF-DLR and MF-RR affected by five classes of
imperfections (N=1000, B=600, $\ell=1024$)  Figure 7: Accuracy of MF-DLR and
MF-RR in the presence of in-band jamming as a function of Jamming to signal
ratio (JSR).

##  IV Conclusion

We showed that Specific Emitter Identification (SEI) for secure IoT
authentication can be trained orders of magnitude faster than SoA on simple
platforms, achieving remarkable accuracy while maintaining this robustness in
the presence of fading and interference. The emphasis of this work is on using
’matched filters’ in the pre-processing stage of two classifiers to eliminate
the corruption of the RF signature due to the channel. The matched filter is
constructed based on the average signature of a given device. As we do not
know the device ahead of time, we apply multiple matched filters in parallel
and select the correct one using hypothesis testing. If an incorrect filter
was used, a statistical test based on the output of the classifier would
indicate it with high confidence. The correctly applied filter not only
separate the signal from interference but also makes the SEI robust to fading
and other imperfections at the receiver. Interestingly, it increases the
accuracy on the clean signals too.

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