# Resonant plasmonic detection of terahertz radiation in field-effect
transistors with the graphene channel and the black-AsxP1-x gate layer

V. Ryzhii  Research Institute of Electrical Communication, Tohoku University,
Sendai 980-8577, Japan  v-ryzhii @ riec.tohoku.ac.jp  C. Tang  Research
Institute of Electrical Communication, Tohoku University, Sendai 980-8577,
Japan  T. Otsuji  Research Institute of Electrical Communication, Tohoku
University, Sendai 980-8577, Japan  M. Ryzhii  Department of Computer Science
and Engineering, University of Aizu, Aizu-Wakamatsu 965-8580, Japan  V. Mitin
Department of Electrical Engineering, University at Buffalo, SUNY, Buffalo, NY
14260, USA  M. S. Shur  Department of Electrical, Computer, and Systems
Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

###### Abstract

We propose the terahertz (THz) detectors based on field-effect transistors
(FETs) with the graphene channel (GC) and the black-Arsenic (b-As) black-
Phosphorus (b-P), or black-Arsenic-Phosphorus (b-AsxP1-x) gate barrier layer.
The operation of the GC-FET detectors is associated with the carrier heating
in the GC by the THz electric field resonantly excited by incoming radiation
leading to an increase in the rectified current between the channel and the
gate over the b-AsxP1-x energy barrier layer (BLs). The specific feature of
the GC-FETs under consideration is relatively low energy BLs and the
possibility to optimize the device characteristics by choosing the barriers
containing a necessary number of the b-AsxP1-x atomic layers and a proper gate
voltage. The excitation of the plasma oscillations in the GC-FETs leads to the
resonant reinforcement of the carrier heating and the enhancement of the
detector responsivity. The room temperature responsivity can exceed the values
of $10^{3}$ A/W. The speed of the GC-FET detector’s response to the modulated
THz radiation is determined by the processes of carrier heating. As shown, the
modulation frequency can be in the range of several GHz at room temperatures.

## Introduction

The emergence of the black-Phosphorus (b-P), black-Arsenic (b-As), and the
compounds of these materials (b-AsP), with the energy gap $\Delta_{BL}$
varying from 0.15 to 1.2 eV (see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) opens new prospects for the
creation of different electronic, optoelectronic, and terahertz (THz) devices.
The combination of the GLs with the b-AsxP1-x layers with graphene [22, 23,
24, 25, 26, 27, 28] can be particularly beneficial for the creation of novel
devices, including MIR/FIR/THz interband photodetectors. In this paper, we
propose and evaluate the THz detectors akin to the field-effect transistors
(FETs) with the graphene channel (GC) and b-AsxP1-x gate barrier layer (BL).
The operation of such GC-FETs is associated with the carrier heating in the GC
by incoming THz radiation (see, for example, [29]) leading to an increase of
the thermionic GC-gate current. This implies that the GC-FETs could operate as
hot carrier bolometric detectors. The main features of the proposed THz
detectors are as follows: (a) the b-AsxP1-x BL provides the possibility to
choose the desirable BL height (and, hence, optimize the device
characteristics) by varying the number of the atomic layers and/or the molar
fraction of As [3, 4, 5, 6], (b) the GC exhibits a room temperature elevated
carrier energy relaxation time [30, 31, 32, 33, 34], which promotes high
detector responsivities and detectivities, and (c) the plasmonic (PL)
properties of the GC-FET [35, 36, 37] can enable the detector resonance
response to the THz radiation at the frequencies close to the GC frequencies.

Figure 1:  (a) Sketch of the GC-FET detector structure and the band diagrams of the GC-FET with $\Delta_{C}-\mu_{D}=\Delta_{M}$ at (b) $V_{G}=0$ (BL flat band condition) and ${\overline{j}}=0$, and (c) $V_{G}>0$ with $\Delta_{C}-\mu<\Delta_{M}$ and $\Delta_{V}+\mu>\Delta_{M}$, hence the thermionic electron current density ${\overline{j}}>0$ (the hole current is negligible).  | $x$ | Metal | $\Delta_{C}$(meV) | $\Delta_{V}$(meV) | $\Delta_{M}$(meV) | $\mu_{D}$ (meV) |  $\Sigma_{D}^{=}$ (1012cm-2)
---|---|---|---|---|---|---|---
Sample 1a | 0 | Al | 225 | 125 | 85 | 140 | 1.60
Sample 2a | 1.0 | Al | 190 | 90 | 50 | 140 | 1.60
Sample 1b | 0 | Ti | 225 | 125 | 105 | 120 | 1.17
Sample 2b | 1.0 | Ti | 190 | 90 | 70 | 120 | 1.17
Sample 1c | 0 | In | 225 | 125 | 135 | 90 | 0.66
Sample 2c | 0.5 | In | 230 | 130 | 130 | 100 | 0.81
Sample 1d | 0 | Mn | 225 | 125 | 125 | 100 | 0.81
Sample 2d | 0.5 | Mn | 230 | 130 | 120 | 110 | 0.89
Table 1:  Metal gate/b-AsxP1-x/GC barrier layer parameters, $N=20$, $W=10$ nm
[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].

## Device structure

Figure 1(a) shows the GC-FET detector structure (with the number of atomic
layers in the BL $N=20$) and the related band diagrams for the assumed band
alignment. For definiteness, we consider the GC-FET structures with the n-type
GC, in which the thermionic current between the GC and the gate is associated
with the electrons overcoming the BL barrier in the conduction band. If
$\Delta_{V}\geq\Delta_{C}$, where $\Delta_{C}$ and $\Delta_{V}$ are the band
offsets between the BL conduction and valence band’s edges and the Dirac point
in the GC (so that $\Delta_{C}+\Delta_{V}$ is the energy gap of the BL), the
electron current exceeds the hole current when the electron Fermi energy,
$\mu_{D}$, in the GC is sufficiently large, so that
$\Delta_{C}-\mu_{D}\lesssim\Delta_{M}$. Here $\Delta_{M}$ is the difference
between the BL and GC work functions and
$\mu_{D}\simeq\hbar\,v_{W}\sqrt{\pi\Sigma_{D}^{=}}$ is the equilibrium value
of the electron Fermi energy counted from the Dirac point at $V_{G}=0$,
$v_{W}\simeq 10^{8}$ cm/s is the characteristic electron velocity in GCs, and
$\hbar$ is the reduced Planck constant.

Figures 1(b) and 1(c) show the band diagrams for
$\Delta_{C}-\mu_{D}=\Delta_{M}$ at zero gate bias ($V_{G}=0$ with the GC donor
density $\Sigma_{D}^{=}$ corresponding to the BL flat band) and under the gate
bias ($V_{G}>0$), respectively. We focus on the GC-FETs with n-doped GC, in
which the above equality is met, i.e., assuming that in the absence of the
bias gate voltage ($V_{G}=0$), the BL bottom of the conduction band and the
top of the valence band are flat.

Table I lists examples of possible combinations of the b-AsxP1-x barriers and
the metal gate materials. The pertinent parameters were taken from [11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21].

The results obtained below can be also used for devices with relatively large
$\Delta_{C}$, considering the hole transport instead of the electron one.

The local voltage drop across the BL
$e\Phi=\Delta_{C}-\Delta_{M}-\mu+e(V_{G}+\varphi)=\mu_{D}-\mu+e(V_{G}+\varphi)$,
where $V_{G}$ is the applied DC bias gate voltage, $\varphi=\varphi(x,t)$ is
the GC potential local value, and $\mu$ is the net electron Fermi energy in
the GC. At the GC edges, $\varphi(\pm L,t)=\pm\frac{1}{2}\delta
V_{\omega}\exp(-i\omega t)$ or $\varphi(\pm L,t)=\delta
V_{\omega}\exp(-i\omega t)$ for the asymmetric (a) and symmetric (s) THz
radiation input, respectively, with $\delta V_{\omega}$ and $\omega$ being the
amplitude and the frequency of the THz radiation received by an antenna. The
asymmetric THz radiation input corresponds to the design when the antenna
leads are connected to the GC-FET side (source and drain) contact pads. In the
case of the symmetric input, one of the antenna leads is contacted to the
gate, whereas the second one to both side contacts.

The variation of the potential difference between the side source and drain
contacts (in the case of the symmetrical input) and between the side contacts
and the gate leads to the transient electron current along the GC and the
transient variation of the self-consistent electron density, i.e., to the
excitation of the plasmonic oscillations. In the case of the asymmetric input,
the electron current along the GC exists even at very small signal frequency.
As a results the electron heating by the incoming signals takes place at such
frequencies as well. In contrast, in the case of the symmetrical input, slow
variations of the side contacts potential with respect to the gate potential
create a very weak lateral electron current not heating the GC electron
system. This leads to marked distinctions of the response in the range of low
frequencies (which is demonstrated below).

The BL energy gap $\Delta_{G}$ and the dielectric constant $\kappa_{G}$ depend
on the transverse electric field $\Phi/W$. Accounting for this, one can set
$\Delta_{C}=\eta\Delta_{G}[1-(\Phi/WE_{G})^{2}]$, and
$\kappa=\kappa_{G}/[1-(\Phi/WE_{G})^{2}]$, where $\Delta_{G}$ and $\kappa$ are
the BL energy gap and the dielectric constant in the absence of the transverse
electric field, $E_{G}$ is the characteristic electric field, $W$ is the BL
thickness (see, for example, [38, 39, 40, 41]), and
$\eta=\Delta_{C}/(\Delta_{C}+\Delta_{V})<1$ the fraction of the BL height
related to the conduction band. For the b-P BL with $W=10$ nm (the number of
the atomic layers $N=20$), $E_{G}\simeq 0.7-0.8\simeq$ V/nm. This implies that
the effect of the transverse electric field on $\Delta_{C}$, $\Delta_{G}$, and
$\kappa_{G}$ markedly reveals at sufficiently high gate voltages when
$\Phi\gtrsim 1$ V). However, such a voltage range is beyond our present
consideration. Considering the GC-FETs with a sufficiently thick b-AsxP1-x BL
at moderate gate voltages, we disregard the carrier tunneling across this
layer. This implies that the GC-gate current is associated with the
sufficiently energetic electrons overcoming the BL, i.e., it is of thermionic
origin.

## Equations of the model

### Thermionic DC and AC

At not-too-small electron densities in GCs, the characteristic time of the
electron-electron collisions $\tau_{ee}$ is shorter than the pertinent times
associated with the optical phonons $\tau_{0}$, acoustic phonons $\tau_{ac}$,
and impurities $\tau_{i}$, respectively. This implies that the electron
distribution function is close to the Fermi distribution function
$f(\varepsilon)=[\exp(\varepsilon-\mu)/T+1]^{-1}$, characterized by the
effective electron temperature $T$ generally different from the lattice
(thermostat) temperature $T_{0}$ (in the energy units) and the electron Fermi
energy $\mu$. Hence, at $\varepsilon>\mu$,
$f(\varepsilon)\simeq\exp[(\mu-\varepsilon)/T]$. However, in the energy range
$\varepsilon>\Delta_{C}$, the electron escape over the BL can markedly
decrease $f(\varepsilon)$. To account for this effect, in the range in
question, one can set $f(\varepsilon)\simeq\xi\exp[(\mu-\varepsilon)/T]$,
where $\xi=\tau_{\bot}/(\tau_{ee}+\tau_{\bot})$ with $\tau_{\bot}$ being the
electron try-to-escape time.

Considering that the height of the potential barrier for the electrons in the
GC and in the metal gate are equal to $\Delta_{C}-\mu$ and
$\Delta_{M}+e(V_{G}+\varphi)$, respectively, the density of the thermionic
electron current can be presented as

$\displaystyle j\simeq
j^{max}\biggl{[}\exp\biggl{(}\frac{\mu-\Delta_{C}}{T}\biggl{)}-\exp\biggl{(}-\frac{\Delta_{M}+e\Phi}{T_{0}}\biggr{)}\biggr{]}.$
(1)

Here $j^{max}=e\Sigma/\tau_{\bot}$ is the characteristic (maximum) GC-gate DC
density, $\Sigma$ is the electron density in the GC induced by the donors and
gate voltage, and $e=|e|$ is the electron charge. One can assume that
$\tau_{\bot}$ is determined by the momentum relaxation time, associated with
the quasi-elastic scattering of the high-energy electrons, i.e., with acoustic
phonons (in sufficiently perfect GCs). Due to this, it is natural to assume
that $\tau_{\bot}>\tau_{ac}\gg\tau_{ee}$. The Fermi energy $\mu$ is determined
by both the GC doping and the gate voltage.

Equation (1) leads to the following expressions for the thermionic DC density
${\overline{j}}$, corresponding to the DC temperature $\overline{T}$:

$\displaystyle{\overline{j}}=j^{max}\biggl{[}\exp\biggl{(}\frac{\mu-\Delta_{C}}{{\overline{T}}}\biggl{)}-\exp\biggl{(}\frac{\mu-\Delta_{C}-eV_{G}}{T_{0}}\biggr{)}\biggr{]}.$
(2)

Due to the dependence of $\mu$ on $V_{G}$, Eq. (2) provides the GC-gate I-V
characteristics. Since ${\overline{T}}$ also depends on $V_{G}$ (because of
the electron heating in the GC by the lateral DC), the latter dependence can
somewhat contribute to the GC-FET characteristics as well.

At sufficiently high GC lateral conductivity in the situations under
consideration (large $\Sigma$ and $\mu$), the DC potential and the DC
effective temperature nonuniformity along the GC are weak
(${\overline{T}}\simeq const$). This implies that we disregard the possible DC
crowding. A high electron thermal conductivity additionally suppresses the
above nonuniformity.

The AC variation $\delta j_{\omega}$ due to the potential oscillations leading
to the electron heating is given by

$\displaystyle\delta j_{\omega}=j^{max}\frac{\delta
T_{\omega}}{{\overline{T}}}\frac{(\Delta_{C}-\mu)}{{\overline{T}}}\exp\biggl{(}\frac{\mu-\Delta_{C}}{{\overline{T}}}\biggr{)}$
(3)

Here we omitted the term containing the factor
$(e\delta\varphi_{\omega}/T_{0})^{2}/2$ with $\delta\varphi_{\omega}$ being
the GC potential ac component. In this case, the quantity $\delta j_{\omega}$,
given by Eq.(3), does not depend explicitly on the AC variations of the GC
potential (only via the effective temperature variation $\delta T_{\omega}$).
This is due to a specific shape of the energy barrier for the electrons in the
GC [see Fig. 1(c)].

### Rectified current and effective carrier temperature

The incoming THz radiation results in variations of the potential in the GC.
This leads to extra electron heating and the variation of the electron
temperature $\delta T=T-{\overline{T}}$. According to Eq. (3), the variation
of the net gate current associated with the effect of the incoming THz
radiation averaged over its period (rectified photocurrent) is given by

$\displaystyle<\overline{\delta
J_{\omega}}>=J^{max}{\mathcal{F}}(V_{G})\frac{<\overline{\delta
T_{\omega}}>}{{\overline{T}}}.$ (4)

Here $J^{max}=2LHj^{max}$, and $2L$ and $H$ are the GC length and width,

$\displaystyle{\mathcal{F}}(V_{G})=\frac{(\Delta_{C}-\mu)}{{\overline{T}}}\exp\biggl{(}\frac{\mu-\Delta_{C}}{{\overline{T}}}\biggr{)}=\frac{[\Delta_{M}-(\mu-\mu_{D})]}{{\overline{T}}}\exp\biggl{[}\frac{(\mu-\mu_{D})-\Delta_{M}}{{\overline{T}}}\biggr{]}$
(5)

is the barrier factor, and the symbols $<...>$ and $\overline{<...>}$ denote
the averaging over the signal period $2\pi/\omega$ and the length of the GC,
respectively, with

$\displaystyle<\overline{\delta
T_{\omega}}>=\frac{1}{2L}\int_{-L}^{L}dx<\delta T_{\omega}>.$ (6)

The dependence of the factor ${\mathcal{F}}(V_{G})$ on the gate voltage as
associated with the voltage dependence of the electron Fermi energy (see
below).

The effective electron temperature $T$ is determined by the balance of the
electron energy transfer to the lattice and the energy provided by the
electric field along the GL. At room temperature, the emission and absorption
of the optical phonons by the electrons in GLs can be considered as a main
mechanism of electron energy relaxation. In this case, the power transferring
from the electrons in the GC to the optical phonons due to the intraband
transitions is [30, 31, 32, 33]

$\displaystyle P_{0}^{intra}=\hbar\omega_{0}R_{0}^{intra}.$ (7)

Here

$\displaystyle
R_{0}^{intra}=R_{0}\frac{\hbar\omega_{0}\mu^{2}}{T_{0}^{3}}\biggl{[}\biggl{(}1+\frac{1}{{\mathcal{N}}_{0}}\biggr{)}\exp\biggl{(}-\frac{\hbar\omega_{0}}{T}\biggr{)}-1\biggr{]},$
(8)

$\hbar\omega_{0}\sim 200$ meV is the optical phonon energy,
${\mathcal{N}}_{0}=[\exp(\hbar\omega_{0}/T_{0})-1]^{-1}\simeq\exp(-\hbar\omega_{0}/T_{0})$,
$R_{0}$ is the characteristic rate of the interband absorption of optical
phonons, and $T_{0}$ is the lattice temperature. At moderate THz power, the
effective electron temperature $T$ is close to the optical phonon temperature
$T_{0}$, and Eq. (8) yields for $R_{0}^{intra}$:

$\displaystyle R_{0}^{intra}\simeq
R_{0}\frac{\hbar\omega_{0}\mu^{2}}{T_{0}^{3}}\biggl{(}\frac{1}{T_{0}}-\frac{1}{T}\biggr{)}.$
(9)

Equalizing $R_{0}^{intra}$ given by Eq. (9) and the Joule power associated
with the AC in the GC, for the THz range of frequencies (in which one can
assume $\omega\gg 1/\tau_{\varepsilon}$), we arrive at the following energy
balance equation:

$\displaystyle\frac{<\overline{\delta
T_{\omega}}>}{\tau_{\varepsilon}}=\frac{{\rm Re}\leavevmode\nobreak\
\sigma_{\omega}}{2\Sigma_{0}L}\int_{-L}^{L}dx\biggl{|}\frac{d\varphi_{\omega}}{dx}\biggr{|}^{2}.$
(10)

Here Re $\sigma_{\omega}=\sigma_{0}\nu^{2}/(\nu^{2}+\omega^{2})$ is the real
part of the GC Drude conductivity, $\sigma_{0}=e^{2}\mu/\pi\hbar^{2}\nu$ is
its DC value, $\nu$ is the frequency of the electron collisions on impurities,
acoustic phonons, as well as due to the carrier viscosity (see, [42] and the
references therein). Accounting for the deviation of the optical phonon
temperature $T_{0}$ from the lattice temperature $T_{l}$, the carrier energy
relaxation time $\tau_{\varepsilon}$ associated with the interaction with
optical phonons is estimated as [32]
$\tau_{\varepsilon}=\tau_{0}(1+\xi_{0})(T_{l}/\hbar\omega_{0})^{2}\exp(\hbar\omega_{0}/T_{l})\simeq\tau_{0}(1+\xi_{0})(T_{0}/\hbar\omega_{0})^{2}\exp(\hbar\omega_{0}/T_{l})$,
where $\tau_{0}$ is the characteristic time of the spontaneous optical phonon
intraband emission by the electrons and $\xi_{0}=\tau_{0}^{decay}/\tau_{0}$,
and $\tau_{0}^{decay}$ is the decay time of optical phonons in GCs.

### Plasmonic oscillations factor

The description of the spatio-temporal oscillations of the electron density
and the self-consistent electric field, i.e., the plasmonic oscillations in
the GLs (see, for example, [32, 33, 34, 35, 36, 37]) forced by the incoming
THz signals can be reduced to a differential equation for the AC potential of
the gated GC filled by the electrons (followed from a hydrodynamic electron
transport model equations [43, 44, 45] coupled with the Poisson equation),
$\delta\varphi_{\omega}(x)$ :

$\displaystyle\frac{d^{2}\delta\varphi_{\omega}}{dx^{2}}+\frac{\omega(\omega+i\nu)}{s^{2}}\delta\varphi_{\omega}=0,$
(11)

supplemented by the following boundary conditions:

$\displaystyle\delta\varphi_{\omega}|_{x=\pm L}|=\pm\frac{\delta
V_{\omega}}{2}\exp(-i\omega t),\qquad\delta\varphi_{\omega}^{s}|_{x=\pm
L}|=\delta V_{\omega}\exp(-i\omega t).$ (12)

Here $s=\sqrt{4\,e^{2}\mu\,w/\kappa\hbar^{2}}$ is the plasma-wave velocity in
the gated GC.

The above equations yield the following formula for the AC potential along the
GC

$\displaystyle\delta\varphi_{\omega}^{a}=\frac{\delta
V_{\omega}}{2}\frac{\sin(\gamma_{\omega}x/L)}{\sin\gamma_{\omega}},\qquad\delta\varphi_{\omega}^{s}=\delta
V_{\omega}\frac{\cos(\gamma_{\omega}x/L)}{\cos\gamma_{\omega}}.$ (13)

Here

$\displaystyle\gamma_{\omega}=\pi\frac{\sqrt{\omega(\omega+i\nu)}}{\Omega},\qquad\Omega=\sqrt{\frac{4\pi^{2}\,e^{2}\mu\,W}{\kappa\hbar^{2}L^{2}}}$
(14)

are the normalized wavenumber and the characteristic frequency of the
plasmonic oscillations of the electron system in the GC-FET under
consideration.

The AC electric field along the GC is equal to

$\displaystyle\frac{d\varphi_{\omega}^{a}}{dx}=\frac{\delta
V_{\omega}}{2}\frac{\gamma_{\omega}}{L}\frac{\cos(\gamma_{\omega}x/L)}{\sin\gamma_{\omega}},\qquad\frac{d\varphi_{\omega}^{s}}{dx}=-\delta
V_{\omega}\frac{\gamma_{\omega}}{L}\frac{\sin(\gamma_{\omega}x/L)}{\cos\gamma_{\omega}}$
(15)

that, accounting for Eq. (12), yields

$\displaystyle\frac{<\overline{\delta
T_{\omega}}>^{a,s}}{\tau_{\varepsilon}}=\biggl{|}\frac{\delta
V_{\omega}}{2}\biggr{|}^{2}\frac{\sigma_{0}}{{\overline{\Sigma}}L^{2}}{\mathcal{P}}_{\omega}^{a,s}.$
(16)

Here

$\displaystyle{\mathcal{P}}^{a}_{\omega}=\frac{\nu^{2}}{(\nu^{2}+\omega^{2})}\int_{0}^{1}d\zeta\biggl{|}\frac{\gamma_{\omega}\cos(\gamma_{\omega}\zeta)}{\sin\gamma_{\omega}}\biggr{|}^{2},\qquad{\mathcal{P}}^{S}_{\omega}=\frac{\nu^{2}}{(\nu^{2}+\omega^{2})}\int_{0}^{1}d\zeta\biggl{|}\frac{\gamma_{\omega}\sin(\gamma_{\omega}\zeta)}{\cos\gamma_{\omega}}\biggr{|}^{2}$
(17)

are the plasmonic factors, which can be also presented as

$\displaystyle{\mathcal{P}}^{a}_{\omega}\simeq\biggl{(}\frac{\pi\nu}{\Omega}\biggr{)}^{2}\frac{\omega}{\sqrt{(\nu^{2}+\omega^{2})}}\frac{P^{a}_{\omega}}{|\sin\gamma_{\omega}|^{2}},\qquad{\mathcal{P}}^{s}_{\omega}\simeq\biggl{(}\frac{\pi\nu}{\Omega}\biggr{)}^{2}\frac{\omega}{\sqrt{(\nu^{2}+\omega^{2})}}\frac{P^{s}_{\omega}}{|\cos\gamma_{\omega}|^{2}},$
(18)

with $P^{a}_{\omega}=\int_{0}^{1}d\zeta|\cos(\gamma_{\omega}\zeta)|^{2}$ and
$P^{s}_{\omega}=\int_{0}^{1}d\zeta|\sin(\gamma_{\omega}\zeta)|^{2}$ being
functions of the order of unity oscillating with the frequency. If
$\omega\ll\Omega$ ($\gamma_{\omega}$ tends to zero), Eqs. (17) and (18) yield
${\mathcal{P}}^{a}_{\omega}\simeq 1$ and ${\mathcal{P}}^{s}_{\omega}\simeq 0$.

Combining Eqs. (4), (6), and (16), we obtain

$\displaystyle\frac{<\overline{\delta
J_{\omega}}>^{a,s}}{J^{max}}=\biggl{|}\frac{\delta
V_{\omega}}{2}\biggr{|}^{2}\frac{\sigma_{0}\tau_{\varepsilon}}{{\overline{\Sigma}}L^{2}}{\mathcal{F}}(V_{G})\,{\mathcal{P}}^{a,s}_{\omega}.$
(19)

The detector response depends on the antenna type (see, for example,[46, 47]).
Using an antenna specially desined for the THz range could substantially
increase the collected power [47]. Here we define the GC-FET detector current
responsivity (in the A/W units) and its voltage responsivity (in the V/W
units) as

$\displaystyle{\mathcal{R}}_{\omega}=\frac{<\overline{\delta
J_{\omega}}>^{a,s}}{S_{\omega}},\qquad{\mathcal{R}}_{\omega}^{V}=\frac{<\overline{\delta
J_{\omega}}>^{a,s}}{S_{\omega}}\rho,$ (20)

respectively. Here $S_{\omega}$ is the THz power collected by an antenna and
$\rho=2L/H\sigma_{0}$ is the GC DC resistance (for the case of load resistance
equal to the GC resistance). This collected power is estimated as
$S_{\omega}=I_{\omega}A_{\omega}$, where $I_{\omega}$ is the intensity of the
impinging radiation and $A_{\omega}=\lambda_{\omega}^{2}g/4\pi$ is the antenna
aperture [46], $\lambda_{\omega}$ is the radiation wavelength, and $g$ is the
antenna gain. Consideringm as an example, the half-wavelength dipole antenna,
for which $|\delta V_{\omega}|^{2}\simeq
I_{\omega}(8\pi/c)(\lambda_{\omega}/\pi)^{2}$, where $c$ is the speed of light
in vacuum, we obtain $|\delta V_{\omega}|^{2}=32S_{\omega}/gc$.

Accounting for Eqs. (18) and (19), we obtain

$\displaystyle{\mathcal{R}}_{\omega}=\frac{32}{gc}\frac{<\overline{\delta
J_{\omega}}>^{a,s}}{|\delta
V_{\omega}|^{2}},\qquad{\mathcal{R}}_{\omega}^{V}=\frac{32}{gc}\frac{<\overline{\delta
J_{\omega}}>^{a,s}}{|\delta V_{\omega}|^{2}}\,\rho.$ (21)

The latter equations yield

$\displaystyle{\mathcal{R}}_{\omega}={\mathcal{R}}_{0}{\mathcal{F}}(V_{G}){\mathcal{P}}^{a,s}_{\omega},\qquad{\mathcal{R}}_{\omega}^{V}={\mathcal{R}_{0}}^{V}{\mathcal{F}}(V_{G})\,{\mathcal{P}}_{\omega}^{a,s},$
(22)

where

$\displaystyle{\mathcal{R}}_{0}=\frac{16}{g}\frac{e\sigma_{0}}{{\overline{T}}c}\frac{\tau_{\varepsilon}}{\tau_{\bot}}\frac{H}{L},\qquad{\mathcal{R}}_{0}^{V}=\displaystyle\frac{32}{g}\frac{e}{{\overline{T}}c}\frac{\tau_{\varepsilon}}{\tau_{\bot}}.$
(23)

According to Eq. (23), the characteristic voltage responsivity
${\mathcal{R}}_{0}^{V}$ does not explicitly depend on the frequency of
electron collisions $\nu$.

It is instructive that the responsivity at $V_{G}=0$ does not turn to zero
because of the factor ${\mathcal{F}}(0)\neq 0$, so that $<\overline{\delta
J_{\omega}}>0$.

## Method and Results

Figure 2:  The normalized detector responsivity
${\mathcal{R}}_{\omega}/{\mathcal{P}}^{a,s}_{\omega}{\mathcal{R}}_{0}$ (the
same for the asymmetric and symmetric THz radiation input) as a function of
the gate voltage $V_{G}$ for the GC-FETs with different band parameters: (a)
at $T_{0}=25$ meV and (b) $T_{0}=15$ meV.

Equations of the model were analyzed analytically and solved numerically. The
resulting GC-FET characteristics - their responsivity found for different
device samples are demonstrated in Figs. 2 - 5.

Figure 2 shows the normalized responsivity at the fundamental plasmonic
resonance
${\mathcal{R}}_{\omega}/{\mathcal{P}}^{a}_{\omega}{\mathcal{R}}_{0}|_{\omega=\Omega}={\mathcal{R}}_{\omega}/{\mathcal{P}}^{s}_{\omega}{\mathcal{R}}_{0}||_{\omega=\Omega}={\mathcal{F}}(V_{G})$
(as a function of the gate voltage $V_{G}$) for the devices with different
$\Delta_{C}$, $\Delta_{V}$, $\Delta_{M}$, and the GC doping corresponding to
the BL flat band at $V_{G}=0$ calculated using Eqs. (5) and (20). In this
case, the thermionic activation energy $\Delta_{C}-\mu_{D}=\Delta_{V}$.
Equations (5) and (20) are supplemented by the following relation for $\mu$
accounting for the effect of quantum capacitance [48, 49, 50, 51]:

$\displaystyle(\mu-\mu_{D})(\mu+\mu_{D}-2\mu_{0})=2\mu_{0}eV_{G},$ (24)

where $\mu_{0}=(\kappa_{G}\hbar^{2}v_{W}^{2}/4e^{2}W)$. For small (moderate)
voltages, Eq. (23) yields

$\displaystyle\mu\simeq\mu_{D}+\frac{\mu_{0}}{(\mu_{D}+\mu_{0}}eV_{G}.$ (25)

As seen from Fig. 2, the normalized responsivity, which might be rather high
at $V_{G}=0$, exhibits a maximum at a certain voltage $V_{G}^{max}$. The
latter is different for different samples depending on the device band
parameters. A decrease in the temperature $T_{0}$ leads to somewhat sharper
responsivity versus gate voltage dependence. This is associated with the
specifics of the rectified current-voltage dependence given by Eq. (4). The
fact that the maximum of function ${\mathcal{F}}(V_{G})$ height is independent
of $T_{0}$ is reflected in the dependences shown in Fig. 2.

As follows from Eq. (18) and (22), the maximal values of
${\mathcal{R}}_{\omega}$ and ${\mathcal{R}}_{\omega}^{V}$ as functions of the
signal frequency $\omega$ are reached at the plasmonic resonances
$\omega=\sqrt{n^{2}\Omega^{2}-\nu^{2}}\simeq n\Omega$ for the asymmetrical
input, and $\omega=\sqrt{2n-1)^{2}\Omega^{2}/4-\nu^{2}}\simeq(2n-1)\Omega/2$
for the symmetrical input, where $n=1,2,3,...$ is the plasmonic resonance
index. At the fundamental resonances,
${\mathcal{P}}^{a}_{\omega}|_{\omega=\Omega}\simeq 2$ and
${\mathcal{P}}^{s}_{\omega}|_{\omega=\Omega/2}\simeq 1$.

Figures 3 and 4 show the frequency dependence of the plasmonic oscillations
factors ${\mathcal{P}}^{a}_{\omega}$ and ${\mathcal{P}}^{s}_{\omega}$
calculated for different values of the plasmonic frequencies $\Omega$ and
collision frequencies $\nu$. According to Eq. (22), these factors determine
(proportional to) the spectral characteristics of the GC-FET detector
responsivity. To account for the electron collisions and the effect of their
viscosity on the plasmon damping, we set [42]
$\nu=\nu_{coll}+\nu_{visc}(\omega/\Omega)^{2}$, assuming $\nu_{coll}=(1-2)$
ps-1 and $\nu_{visc}=0.25$ ps-1. In the GC-FETs with
$L=(0.5-1.0)\leavevmode\nobreak\ \mu$m, the latter corresponds to the electron
viscosity $h\simeq(250-1000)$ cm2/s that is in line with the observed values
[42].

In particular, Figs. 3 and 4 demonstrate that [in line with Eqs. (17) and
(22)] the responsivity exhibits fairly sharp (resonant) maxima at
$\omega\simeq n\Omega$ and $\omega\simeq(2n-1)\Omega/2$ when
$\nu_{coll}=(1-2)$ ps-1.

Although the GC-FETs with different methods of the THz radiation input exhibit
the resonant response, the pattern of the spectral characteristics shown in
these plots are rather distinct, and the resonance frequencies differ. This is
associated with the excitation of different plasmonic modes (with different
spatial distributions of the ac potential) using asymmetric and symmetric
input. As seen, the amplitude of the plasmonic factor maxima increases with
increasing resonance index despite the strengthening of the viscosity effect.
This is attributed to an increase in the average AC electric field when the
number of its semi-periods, i.e., the index $n$ increase.

Figure 5 shows the dependences of the GC-FET detector current responsivity
${\mathcal{R}}_{\omega}$ corresponding to the plasmonic factors of Figs. 3(b)
and 4(b) calculated for $\nu_{coll}=1$ ps-1 and $\nu_{coll}=2$ ps-1 (solid
lines). These dependencies exhibit pronounced plasmonic resonances. Since the
responsivity
${\mathcal{R}}_{\omega}\propto\sigma_{0}{\mathcal{P}}_{\omega}\propto{\mathcal{P}}_{\omega}/\nu$,
the heights of the responsivity peaks for a larger index $n$ and for a larger
collisional frequency $\nu$ are smaller. It is instructive that the voltage
responsivity ${\mathcal{R}}^{V}_{\omega}$ for different collisional
frequencies exhibits different behavior (at the chosen load resistance, which
is assumed to be inversely proportional to $\sigma_{0}$). However, as seen
from Fig. 5 (dashed lines), the plasmonic resonances in the cases of much
stronger electron scattering ($\nu_{coll}=4$ ps-1 and $\nu_{coll}=6$ ps-1),
are substantially smeared.

Using Eq. (14) and setting $\mu=120-140$ meV, $\kappa=4$, $W=10$ nm, and
$L=(1-2)\leavevmode\nobreak\ \mu$m, we obtain the following estimate:
$\Omega/2\pi\simeq(0.53-1.14)$ THz.

Considering that the escape of a hot electron with the energy
$\varepsilon\gtrsim\Delta_{C}$ from the GC over the BL is possible due to its
scattering on an acoustic phonon.

We might assume that the electron escape time $\tau_{\bot}\gg\tau_{ac}$, where
$\tau_{ac}$ is the momentum relaxation time for the electrons with the energy
$\varepsilon\gtrsim\Delta_{C}$. The quantity $\tau_{ac}$ can be estimated as
[52, 53, 54] $\tau_{ac}\simeq 1$ ps. Considering this, for rough estimates at
the values $\Delta_{C}$ considered above we set $\tau_{\bot}\sim 10-20$ ps.
The electron energy relaxation time due to the interaction with the GC optical
phonons is estimated as $\tau_{\varepsilon}\simeq 32-65$ ps (compare, for
example, with [32, 34, 55]). The fast decay of optical phonons and the
interaction of the electrons in the GC with the interface optical phonons can
lead to a decrease in $\tau_{\varepsilon}$ to the values about 10- 20 ps.
Setting $\mu=140$ meV, $\nu=1$ ps-1, $\tau_{\bot}=10$ ps,
$\tau_{\varepsilon}=10$ ps, $g=1.64$, $H=2L$, and $(\Delta_{C}-\mu)/T_{0}=1$,
we arrive at ${\mathcal{R}}_{0}\simeq 4.1\times 10^{2}$ A/W. This yields the
characteristic voltage responsivity ${\mathcal{R}}_{0}^{V}\simeq 3.7\times
10^{4}$ V/W. The latter values are close to the GC-FET current and voltage
responsivities, ${\mathcal{R}}_{\omega}|_{\omega=\Omega}$ and
${\mathcal{R}}_{\omega}^{V}|_{\omega=\Omega}$, at the plasmonic resonances.

Figure 3:  The plasmonic oscillation factor ${\mathcal{P}}^{a}_{\omega}$ of
the GC-FETs with the asymmetric THz radiation input versus signal frequency
$\omega/2\pi$: (a) for $\Omega/2\pi=0.75$ THz and (b) $\Omega/2\pi=1.0$ THz
($\nu_{coll}=1$ ps-1 and 2 ps-1 with $\nu_{visc}=0.25$ ps-1).  Figure 4:  The
same as in Fig. 3 but for the plasmonic oscillation factor
${\mathcal{P}}^{s}_{\omega}$ of GC-FETs with the symmetric THz radiation
input.  Figure 5:  The spectral characteristics of GC-FET detectors current
responsivity with (a) asymmetric and (b) symmetric THz radiation input
($\Omega/2\pi=1.0$ THz) with different collision frequencies $\nu_{coll}$.

## Discussion

In Eq. (10), which governs the electron energy balance in the GC, we
disregarded the electron cooling effect, associated with thermionic emission.
This effect can be accounted for by replacing the quantity
$(\tau_{\varepsilon}/\tau_{\bot}){\mathcal{F}}(V_{G})$ in Eq. (22) by the
factor
$(\tau_{\varepsilon}/\tau_{\bot}){\mathcal{F}}(V_{G})/[1+(\tau_{\varepsilon}/\tau_{\bot}){\mathcal{F}}(V_{G})]$.
The pertinent distinction is small if $\tau_{\varepsilon}\lesssim\tau_{\bot}$.

Using the relation between the GC mobility $M$ and the Fermi energy $\mu$:
$M=ev^{2}_{W}/\nu\mu_{D}$, where the quantity $\mu_{D}/v_{W}^{2}$ is the
electron fictitious mass, we find that the values of $\nu_{coll}=(1-2)$ ps-1
and $\mu_{D}=(120-140)$ meV assumed above correspond to
$M\simeq(4.3-7.1)\times 10^{4}$ cm2/Vs. For $\nu_{call}=(4-6)$ ps-1 (see the
dashed lines in Fig.5), one obtains $M\simeq(0.7-1.8)\times 10^{4}$ cm2/Vs,
which are realistic GC mobilities at room or somewhat lower temperatures [53,
55]. The electron mobility of the GC on b-P studied several years ago [56], at
$T_{0}=(15-25)$ meV ($T_{0}\simeq(180-300)$ K) reaches the values
$M\simeq(8-9)\times 10^{3}$cm2/Vs. This corresponds to
$\nu_{coll}\simeq(8-10)$ ps-1. Further improvements in the GC/b-P interface
quality or/and using the GC remote doping (see, for example, [57, 58]), one
can reduce $\nu_{coll}$ increasing the plasmonic resonance sharpness. Another
option to decrease $\nu_{coll}$ is to use the positively biased back gate,
which can electrically induce a sufficient electron density in the GC and,
hence, a proper value of the electron Fermi energy, eliminating the necessity
of GC doping. The plasmonic resonances and, hence, the pronounced resonant
response of the GC-FET detectors might be more pronounced for larger plasma
frequency $\Omega$, i.e., in the devices with shorter GCs (smaller length
$2L)$. In particular, if $2L=0.5\leavevmode\nobreak\ \mu$m, the plasma
oscillations quality factor is about 8.2 even at $\nu_{coll}=10$ ps-1. One
needs to note that even at relatively high values of $\nu_{coll}$, the
overdamped plasmonic oscillations can provide elevated GC-FET detector
responsivities despite the resonant peaks vanishing.

Electron thermal conductivity along the GC [59], which leads to the transfer
of a portion of the electron heat to the side contacts can reduce the electron
temperature and smooth down the spatial nonuniformities of the electron
density. The latter can particularly affect the resonant maxima height with
increasing plasmonic mode index $n$.

Fairly high values of the GC-FET responsivity are due to the long electron
energy relaxation time $\tau_{\varepsilon}$ inherent for GCs. However, the
speed of the photodetectors using the hot electron bolometric mechanism is
limited by the inverse electron energy relaxation time
$\tau_{\varepsilon}^{-1}$ (see, for example, [34, 54]). This implies that the
operation of the THz GC-FET detectors under consideration (with the parameters
used in the above estimates) might be limited to the modulation frequencies in
the GHz range.

The GC-FET detector dark current limited detectivity
$D^{*}_{\omega}={\mathcal{R}}_{\omega}/\sqrt{2e{\overline{j}}}$ (see, for
example, [60]) depends, in particular, on the dark current density. As follows
from Eqs. (2) and (25), the dark current density is

$\displaystyle{\overline{j}}\simeq
j^{max}\exp\biggl{(}-\frac{\Delta_{M}}{T_{0}}\biggr{)}\exp\biggl{[}\frac{\mu_{0}}{{(\mu_{D}+\mu_{0})}}\frac{eV_{G}}{T_{0}}\biggr{]}\bigg{[}1-\exp\biggl{(}-\frac{eV_{G}}{T_{0}}\biggr{)}\biggr{]}.$
(26)

For low gate voltages ($eV_{G}<T_{0}$), the latter tends to zero as
${\overline{j}}\propto V_{G}$. Since the responsivity in the limit of small
$V_{G}$ is a constant (see Fig. 2), this implies that the GC-FET detector
detectivity as a function of the gate voltage increases with decreasing
$V_{G}$ as

$\displaystyle D^{*}_{\omega}\propto\frac{1}{\sqrt{V_{G}}}.$ (27)

This also means that at low values of $V_{G}$, the GC-FET noises might be
determined by other mechanisms (not by the dark current).

If the electron interactions at the GC/b-AsP interface are relatively strong
(leading to high values of $\nu_{coll}$ and preventing the pronounced
plasmonic resonance) is a critical issue, the GC-FET structure can be modified
by using the length of the gate and the b-AsP layer markedly smaller than the
length of the GC $2L$.

In principle, the GC-FET detectors can be based on the p-type GC, in which
$\mu_{D}<0$. This might exhibit advantages associated with smaller
$\Delta_{V}$ compared to $\Delta_{C}$ (see Table 1). In the detectors with the
p-type GC, a proper thermionic activation energy $\Delta_{V}+\mu_{D}$ can be
achieved at smaller $\mu_{D}$, i.e., at the lower carrier (hole) densities.
However, the adequate BL and metal gate band alignment might be a problem.
This problem can be avoided in the GC-FET structures, in which both the GC and
the gate are made of p-type graphene layers (double-GC-FETs). Such double-GC-
FETs can exhibit markedly different plasmonic properties. This is because of
the possible plasmonic response of the carriers in the double-GG (see, for
example, [61, 62, 63, 64, 65, 66, 67]). The plasmonic response in the double-
GC-FETs depends on the contacts. Depending on the geometry of these contacts,
the plasmonic factor can be a fairly different function of the signal
frequency. The bolometric detectors based on the double-GC-FET structures with
the barrier b-AsxP1-x are beyond the scope of our present study and require a
separate treatment.

## Conclusions

We proposed and evaluated the THz graphene-channel- FET detectors with the
black-Arsenic, black-Phosphorus, or black-Arsenic-Phosphorus barrier gate
layers. The operation of these detectors is associated with the hot carrier
bolometric effect, i.e., with the carrier heating by incoming THz radiation,
causing their thermionic emission from the graphene channel into the gate.
Such a THz GC-FET detector can exhibit fairly high characteristics. The
excitation of plasmonic oscillations in the graphene channel leads to a strong
resonant enhancement of the detector responsivity and detectivity.

The realization of the proposed GC-FET bolometric detectors with elevated
characteristics is enabled by the effective carrier heating in graphene
accompanied by the effective plasmonic oscillation excitation and the
possibility of a proper band alignment between the graphene channel and the
barrier layer.

## Acknowledgments

Financial support is provided by The Japan Society for Promotion of Science
(KAKENHI Grants $\\#$ 20K20349 and $\\#$ 21H04546), Japan; RIEC Nation-Wide
Collaborative Research Project $\\#$ R04/A10; and by AFOSR (contract number
FA9550-19-1-0355.

## Author contributions statement

V.R. conceived the device concept and developed its model, C.T. and M.R.
conducted the calculations and presented the results, T. O., V. M, and M.S.
analyzed the model, obtained results, and provided financial support. All
authors reviewed the manuscript.

## Data availability

All data generated or analyzed during this study are included in this
published article.

## Additional information

Competing interests: The authors declare that they have no competing
interests.

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# How does Truth Evolve into Fake News? An Empirical Study of Fake News
Evolution

Mingfei Guo  Wangxuan Institute of Computer Technology, Peking
UniversityBeijingChina<EMAIL_ADDRESS>,  Xiuying Chen  Wangxuan
Institute of Computer Technology, Peking UniversityBeijingChina xy-
<EMAIL_ADDRESS>,  Juntao Li  Soochow UniversitySuzhouChina<EMAIL_ADDRESS>,
Dongyan Zhao  Wangxuan Institute of Computer Technology, Peking
UniversityBeijingChina<EMAIL_ADDRESS>and  Rui Yan  Gaoling School of
Artificial Intelligence, Renmin University of ChinaBeijingChina
<EMAIL_ADDRESS>
(2021)

###### Abstract.

Automatically identifying fake news from the Internet is a challenging problem
in deception detection tasks. Online news is modified constantly during its
propagation, e.g., malicious users distort the original truth and make up fake
news. However, the continuous evolution process would generate unprecedented
fake news and cheat the original model. We present the Fake News Evolution
(FNE) dataset: a new dataset tracking the fake news evolution process. Our
dataset is composed of 950 paired data, each of which consists of articles
representing the three significant phases of the evolution process, which are
the truth, the fake news, and the evolved fake news. We observe the features
during the evolution and they are the disinformation techniques, text
similarity, top 10 keywords, classification accuracy, parts of speech, and
sentiment properties.

datasets, fake news evolution, fake news

††copyright: iw3c2w3††journalyear: 2021††copyright: iw3c2w3††conference:
Companion Proceedings of the Web Conference 2021; April 19–23, 2021;
Ljubljana, Slovenia††booktitle: Companion Proceedings of the Web Conference
2021 (WWW ’21 Companion), April 19–23, 2021, Ljubljana, Slovenia††doi:
10.1145/3442442.3452328††isbn: 978-1-4503-8313-4/21/04††ccs: Applied computing
Sociology

##  1\. Introduction

Fake news is a form of news consisting of deliberate disinformation or hoaxes
according to its definition on Wikipedia, and it generally spreads via
traditional news media or online social media platforms. Sharing fake news on
social media platforms is a global concern and the motivation behind it is
complicated and is still a fundamental topic in psychology and sociology
(Āllport and Postman, 1947). Usually, fake news is written and published with
the intent to mislead the public to damage an agency, entity, or person, or to
gain financially or politically (Wheaton, 2019; Tandoc et al., 2018). It often
uses sensationalist, dishonest, or outright fabricated headlines to increase
readership and make a profit. A large amount of fake news has been observed to
spread online like virus outbreaks, often with alarming consequences in the
real world (Carvalho et al., 2009). A series of prior works (Yang et al.,
2012; Shu et al., 2017; Castillo et al., 2011; Ma et al., 2015; Hamidian and
Diab, 2019; Kwon et al., 2017; Zellers et al., 2019; Tee and Murugesan, 2018;
Ibrishimova and Li, 2019; Mihalcea and Strapparava, 2009) focus on
automatically identifying fake news. However, in real social networks, the
news evolves constantly in the spreading process, which grows more concise,
more attractive, more easily grasped and told (Zhang et al., 2011; Adamic et
al., 2016). This evolution process originates from the cumulative
modifications during the spreading process, which is similar to a Children’s
game called ’Chinese Whispers’ or ’Telephone’ (Blackmore, 1999).

|  _Truth:_ The laws restrict people from various military-like activities
---
that result in violence and civil disorder. The amendment to the
Virginia law, specifically, prohibits marching with weapons or
explosives for the purpose of intimidation.
|  _Fake News:_ Proposed virginia law would outlaw krav maga, brazilian
---
jiu jitsu, kickboxing, tai chi, firearms instruction and self-defense
training, the story reads: The law would instantly transform all martial
arts instructors into criminal felons.
|  _Evolved Fake News:_ The state of virginia, now entirely run by truly
---
insane democrats who support infanticide and child murder, is
proposing a new 2020 law known as sb64 (see link here) which will
be taken up by the democrat-run senate beginning january 8, 2020.

Table 1. An example of the dataset. We highlight the original truth
information by using yellow and the fake news and the evolved fake news by
using pink.

We have seen that numerous recognition models have high overall performance in
identifying the authenticity of news articles, and we believe these state-of-
the-art models would obtain better results if they learn the features of the
evolution process. As the continuous evolution process would generate
unprecedented fake news and cheat the original model, it is important to teach
the model to identify the variations of fake news. The dataset for deception
detection tasks is not new to the natural language processing community, and
most of them centre on labeled fake news based on human annotation or machine
learning assessments (Augenstein et al., 2019; Wang, 2017; Shu et al., 2020).
Based on these data, most efforts focuses on the identification of fake news,
offering little understanding of the evolutionary process of false
information. Seldom work focus on the attribute of observing the evolution
from facts to fake news to our best knowledge (Shao et al., 2016).

We introduce the Fake News Evolution (FNE) dataset to fill this margin. Our
dataset includes 950 pieces of data, each of them contains three articles
representing the three phases of the evolution process, and they are the
truth, the fake news and the evolved fake news. These three articles are
derived from the same particular event and Table 1 provides an example. Since
space is limited, we only represent a short paragraph here. Through a
comprehensive analysis, we investigate the features during the evolution
process, including disinformation techniques, text similarity, top 10
keywords, classification accuracy, parts of speech, and sentiment properties.
By observing the proportion of commonly used disinformation technologies, we
conclude the deeper pattern of constructing fake news. When testing
classification models, evolved fake news is more easily spotted than fake
news. During the evolution process, the top keywords and the parts of speech
keep consistent, while the text similarity and the sentiment properties
change.

The main contributions of our work can be concluded as follows:

$\bullet$ We propose a dataset that tracks the fake news evolution process.
Each piece of data includes three articles, the truth, the fake news, and the
evolved fake news, and all of them are derived from the same particular event.

$\bullet$ We look into the data properties to study the features during the
evolution process. Here, we observe the statistics of the disinformation
techniques, text similarity, top 10 keywords, classification accuracy, parts
of speech of words, and sentiment properties.

$\bullet$ Our FNE dataset can be used for semi-supervised low resources tasks
and can help to improve the fake news classification models.

##  2\. Dataset Construction

Our dataset aims to capture articles and pinpoint how they were modified
during the dissemination and evolution process. In online environments, the
news is represented in various forms, e.g. texts, photographs, and videos.
However, modifying the news in photograph or video forms is not readily
available and is inconvenient for internet surfers. Therefore, we focus our
attention on textual news to observe how information evolves when people can
simply modify it and add subjective content to it.

In order to observe the evolution process concisely, we focus on three
important phases in the process, the truth, the fake news and the evolved fake
news. The truth, which is examined by multiple sides and organizations, is
guaranteed to be real and credible. Then fake news is created by malicious
users or bots after modifying the original truth and applying various
counterfeit methods. When fake news is published on online platforms, they
begin to spread and evolve. After reading the fake news, some website editors
will write reports based on them and make up the evolved fake news. These
editors, no matter if they are unconscious or on purpose, are deceivers who
expose misleading articles to more people.

It is difficult to track the original true information online because social
media dialogues often neglect standard protocols for reporting the information
source, and it is hard to determine which media content is closest to the
origin (Jang et al., 2018). Besides, making sure that the articles of these
three phases are derived from one particular event or focusing on the same
topic is also a tough problem.

To tackle these two problems, we build our fake news evolution dataset by
performing the following procedure. We mainly focus on the website
Snopes111https://www.snopes.com/fact-check/, which covers a wide range of news
focusing on politics, science, health and etc. It provides fact-checking
content and webpage links of fake news, which is convenient for us to gather
articles of different phases during the evolution process. First, we can
easily crawl this website and collect true articles because it is transparent
about examination sources and methods. The fact-checking article will provide
a summary of these fact sources and we regard it as original truth. Then we
collect fake news from the citation of the content. Since social media
platforms are increasingly more likely to regulate questionable content, it is
more preferable to gather the evolved fake news on an archive website which
helps you to create a copy of the webpage and store it even if the source page
is removed. Snopes includes links to evolved fake news of a snapshot website
Archive Today222http://archive.today/. We regard the records on the archive
website as evolved fake news. Therefore, we construct a dataset tracking the
information evolution process, from truth to fake news and to evolved fake
news.

Table 1 provides an example of our FNE dataset and illustrates the evolution
process. The truth says that laws are restricting military-like activities,
while the fake news distorts the original facts and says the proposed laws are
outlawing martial arts. Then, except for the misrepresented laws, the evolved
fake news also mentions an endorsement of democrats which is never mentioned
before. Our FNE dataset has 2 million tokens in total and covers a wide range
of topics such as politics, religion, health, and economics.

##  3\. Data Properties

We use this dataset to perform experiments and observe the features during the
evolution process. In different stages, they include disinformation
techniques, text similarity, top 10 keywords, classification accuracy, part of
speech of words and sentiment properties.

###  3.1. Disinformation Techniques

Figure 1. The left one represents the proportion of disinformation techniques
from truth to fake news, while the right one represents that from fake news to
evolved fake news.

Disinformation techniques are broader and deeper patterns about how
counterfeit messages are constructed (Innes, 2020). To observe the popularity
of various disinformation techniques in the evolution process, we ask human
experts to annotate the data, that is, divide it into 4 categories, including
Fabrication, Denial, Confusion, and Distortion (Martino et al., 2019). The
kappa statistics are 0.5276 and 0.3668 for the annotated disinformation
techniques from truth to fake news and from fake news to evolved fake news
respectively, and that indicates the moderate agreement between annotators.

$\bullet$ Fabrication. When there exists some particular information in the
fake news but not in the truth, we will suppose that this article applies
Fabrication, e.g., the fake news mentions a fabricated statement in a
president interview to support its political attitude.

$\bullet$ Denial. This kind of fake news is generated by denying reality to
avoid a psychologically uncomfortable truth (Hansson, 2017), we can take the
terms Holocaust denialism and AIDS denialism as examples.

$\bullet$ Confusion. When the fake news confuses the original event with other
events deliberately, we regard it as Confusion. This is generally used between
two events which happen in different times and places, for instance, replacing
a small accident as a devastating forest fire happens years ago to cause
public panic.

$\bullet$ Distortion. Distortion means maliciously misinterpreting certain
aspects of the truth, especially particular words, statistical numbers, and
severe degrees.

Take Table 1 as an example, it uses Distortion to make up fake news since it
misapprehends the meaning of ”military-like activities” and replaces it with
”self-defense training”. Then from the fake news to the evolved fake news, it
uses Fabrication because it trumps up a democrat’s endorsement. As can be seen
from Figure 1, for the frequency of disinformation techniques, the proportion
of Fabrication is relatively larger, while Denial, Confusion, and Distortion
are smaller. Since Denial, Confusion, and Distortion are largely based on
prior events or well-known facts rather than fabricated information, these
kinds of fake news are easily spotted.

###  3.2. Text Similarity

We calculate the similarity score between the truth and the fake news $X_{1}$,
and that between the fake news and the evolved fake news $X_{2}$. As the
truth, the fake news and the evolved fake news are one-to-one correspondence,
the length of $X_{1}$ equals that of $X_{2}$, $n_{1}=n_{2}$. To assess the
similarity score, We apply Word Mover’s Distance (WMD) (Kusner et al., 2015),
which enables us to evaluate the distance between two documents in a
meaningful way even when they have no words in common. It uses word2vec vector
embeddings of words (Mikolov et al., 2013), by matching the relevant words,
WMD is able to accurately measure the similarity between two sentences.

Next, we use the t-test to determine if these two sets of scores are
significantly different from each other. We hypothesize that the variances of
$X_{1}$ and $X_{2}$ populations are equal. Here, $\overline{X_{1}}$ and
$\overline{X_{2}}$ are the average scores of $X_{1}$ and $X_{2}$, while
$s_{X_{1}}^{2}$ and $s_{X_{2}}^{2}$ are the unbiased estimators of the
variances of the two samples. The null hypothesis here is
$\mu_{1}\geqslant\mu_{2}$ which can only be rejected. When testing the null
hypothesis, the population means of $X_{1}$ and $X_{2}$ are $\mu_{1}$ and
$\mu_{2}$.

(1)
$s_{p}=\sqrt{\frac{(n_{1}-1)*s_{X_{1}}^{2}+(n_{2}-1)*s_{X_{2}}^{2}}{n_{1}+n_{2}-2}}$
(2)
$t=\frac{\overline{X_{1}}-\overline{X_{2}}}{s_{p}*\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}$

Note that $s_{p}$ is an estimator of the pooled standard deviation of the two
samples. For significance testing, the degree of freedom for this test is
$n_{1}+n_{2}-2$. We determine the $t$ value through this formula, and we find
the corresponding p-value, which is the evidence against a null hypothesis,
using a table of values from Student’s t-distribution. We find that
$t=-$39.3309. For $\mu_{1}<\mu_{2}$, the estimated p-value is greater than
0.99, so we can reject the null hypothesis with a high degree of confidence
that the similarity degree between the truth and the fake news is smaller than
that between the fake news and the evolved fake news. Compared with the change
between fake news and evolved fake news, the transformation between truth and
fake news is more drastic and extensive.

###  3.3. Keywords

truth | trump | said | news | president | people
---|---|---|---|---|---
law | one | state | states | also
fake news | trump | president | clinton | obama | school
police | law | state | bill | health
evolved fake news | trump | obama | people | said | president
clinton | ago | like | new | one

Table 2. The top 10 keywords of the truth, the fake news and the evolved fake
news.

We extract the keywords (Matsuo and Ishizuka, 2003) to observe the changes of
information. We apply a numerical statistic method, term frequency–inverse
document frequency (TFIDF) (Jones, 1972), to reflect the importance of words
in the corpus. In each phase, we collect all the documents as a corpus and we
generate a TFIDF matrix for it, then iterate over the resulting vectors to
extract top keywords. The top 10 keywords are shown in table 2, and they are
basically on the same topic in different phases. Therefore, we can conclude
that in the FNE dataset, the articles during different evolution phases are
largely focusing on the same subject. Since the top 10 keywords include
presidents’ names and politics-related nouns, we assume that the majority of
data in our dataset focuses on political topics.

###  3.4. Classification Accuracy

| Truth | Fake News | Evolved Fake News
---|---|---|---
Naive Bayes | 0.2084 | 0.8589 | 0.8432
Random Forest | 0.4684 | 0.6274 | 0.5853
Adaptive Boosting | 0.7126 | 0.1874 | 0.1579

Table 3. Classification accuracy by using different methods.

We train several standard machine learning models like Naive Bayes (Manning et
al., 2008), Random Forest (Breiman, 2004), and Adaptive Boosting (Freund and
Schapire, 1995) on the LIAR dataset (Wang, 2017). The LIAR dataset includes
manually labeled statements from political websites, and its topic is
consistent with our FNE dataset. Then, we show the classification accuracy of
these trained models on our FNE dataset in Table 3. The accuracy of the
evolved fake news is smaller than that of the fake news, which indicates that
detecting the evolved fake news is more intractable.

###  3.5. Part of Speech

Figure 2. Proportion of different parts of speech of words during the
evolution process.

We observe the proportion of various parts of speech of the articles in three
phases by using Natural Language Toolkit (NLTK) (Bird et al., 2008). There are
numerous parts of speech in the English language, and we only focus on those
who take up a large proportion. Here, we count 5 parts, and they are nouns,
adjectives, verbs, adverbs, and numbers. The result is shown in Figure 2, NN
represents nouns, JJ represents adjectives, VB represents verbs, RB represents
adverbs, and CD represents cardinal numbers. NN includes singular nouns,
plural nouns, and proper nouns and VB includes 3rd person verbs, non-3rd
person verbs and all tenses of verbs.

The proportion of parts of speech of the truth, the fake news, and the evolved
fake news are substantially consistent. Therefore, the authenticity of the
articles only makes a small contribution to grammatical features. However, we
notice that in the fake news and the evolved fake news, the behavior of
mentioning other users or media (through $@$ or $\\#$) increases. The total
frequency of tagging others is 368 in the truth, 696 in the fake news, and 619
in the evolved fake news. Due to human nature, people are vulnerable to being
deceived by more convincing and inflammatory news, which can be reflected by
the act of citing others’ example or exposition (Castillo et al., 2011).

###  3.6. Sentiment

We calculate the sentiment property of the articles using TextBlob to observe
the tendency during the evolution process. The sentiment property includes two
scores, polarity and subjectivity. For each text, the value of polarity is in
the range of -1 to 1. The value of -1 means very negative, and the score of 1
means very positive. Similarly, the value of subjectivity is in the range of 0
to 1, where 0 is very objective and 1 is very subjective.

To analyze the differences among the sentiment properties among the truth, the
fake news and the evolved fake news, we use analysis of variance (ANOVA),
which can decide whether the sample means are equal or not. The p-value
corresponding to the F-statistic of ANOVA is lower than 0.01 (equals to 99%
confidence coefficient), suggesting that one or more treatments are
significantly different.

Then, we use Tukey’s test, which applies simultaneously to the set of all
pairwise comparisons and can find means that are significantly different from
each other. We first establish the critical value $Q$ statistic of the Tukey’s
test based on $k=$ 3 samples and $v=$ 2847 degrees of freedom. For
significance level 99% ($\alpha=$ 0.01) in the Studentized Range distribution,
$Q_{critical}^{\alpha=0.01,k=3,\nu=2847}=$ 4.1237. Then we calculate a
parameter for each pair of samples being compared:

(3) $Q_{i,\,j}=\frac{\lvert\bar{x}_{i}-\bar{x}_{j}\rvert}{s_{i,\,j}}$ (4)
$\,\,{s_{i,\,j}}=\frac{\hat{\sigma}_{\epsilon}}{\sqrt{H_{i,\,j}}}\,\,\,\,\,i,\,j=1,\,\ldots,\,k;\,\,i\neq
j\,.$

The quantity ${H_{i,\,j}}$ is the harmonic mean of the number of observations
in samples labeled $i$ and $j$, and ${H_{i,\,j}}=$ 950\.
$\hat{\sigma}_{\epsilon}$ is the square root of the mean square error
determined in the precursor ANOVA procedure, and it is same across all pairs
being compared. We evaluate whether $Q_{i,\,j}>Q_{critical}$ to decide if we
can reject the null hypothesis. Here, reject the null hypothesis means that a
significant difference has been observed. The result is shown in Table 4.

| Truth vs Fake | Truth vs Evolved | Fake vs Evolved
---|---|---|---
Polarity | 0.1735 | 7.2598 | 7.0863
Subjectivity | 0.2696 | 6.8796 | 7.1492

Table 4. $Q$ statistic of the Tukey’s test among the three samples, the truth,
the fake news and the evolved fake news.

For both the polarity and the subjectivity scores, the evolved fake news is
the one that is significantly different from others. We calculate the average
scores, the polarity of the truth, the fake and the evolved fake is 0.0357,
0.0361, and 0.0523, while the subjectivity is 0.3474, 0.3482, and 0.3263.
Generally, the articles of this dataset are objective and positive. We use the
t-test mentioned in the previous section again and discover that we can say
with 99% confidence that the polarity score of the evolved fake news is larger
and the subjectivity score is smaller than that of the truth and the fake
news. Therefore, the evolved fake news is more positive and more objective
than the truth and the fake news. We assume that the evolved fake news is
designed to be formal and convincing, therefore it can mislead people
effectively (Guo et al., 2019), and this is consistent with prior
classification results.

##  4\. Conclusion

We introduce a new fake news evolution dataset. Compared with prior datasets,
our FNE dataset reflects the evolution process of fake news on the Internet.
Each piece of data is composed of the truth, the fake news, and the evolved
fake news, and all three articles are derived from the same event. During the
evolution process, the disinformation techniques, parts of speech, and
keywords keep consistent, while the text similarity and sentiment change. The
similarity score between the fake news and the evolved fake news is larger
than that between the truth and the fake news. For sentiment properties, the
evolved fake news is more objective and positive, and it is more difficult to
be detected. In future work, we would like to use this dataset on fake news
recognition models to promote classification performance when facing newly
generated rumors. We hope the release of this dataset could contribute to the
development of fake news detection and accelerate further investigation into
the evolution process.

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