Abstract

Graphene has emerged as an ultrafast optoelectronic material for on-chip photodetector applications. The 2D nature of graphene enables its facile integration with complementary metal–oxide semiconductor (CMOS) microelectronics and silicon photonics, yet graphene absorbs only ${\sim}2.3\%$ of light. Plasmonic metals can enhance the responsivity of graphene photodetectors, but may result in CMOS-incompatible devices, depending on the choice of metal. Here we propose a plasmon-enhanced photothermoelectric graphene detector using CMOS-compatible titanium nitride on the silicon-on-insulator platform. The device performance is quantified by its responsivity, operation speed, and noise equivalent power. Its bandwidth exceeds 100 GHz, and it exhibits a nearly flat photoresponse across the telecom C-band. The photodetector responsivity is as high as 1.4 A/W (1.1 A/W external) at an ultra-compact length of 3.5 µm, which is the most compact footprint reported for a graphene-based waveguide photodetector. Furthermore, it operates at zero-bias, consumes zero energy, and has an ultra-low intrinsic noise equivalent power (${\rm{NEP}} \lt 20\;{\rm{pW/}}\sqrt {{\rm{Hz}}}$).

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The integration of optical interconnects with CMOS microelectronics for ultra-high-speed links has become an industrial necessity [1]. Unlike lossy metallic links, integrated optical interconnects can sustain the transmission of ultrafast signals with losses as low as 0.1 dB/cm using the silicon-on-insulator (SOI) platform [2]. Moreover, silicon photonics and CMOS microelectronics are both based on silicon, and can in principle function hand in hand within a single chip. However, the size disparity between diffraction-limited photonics and advanced CMOS technology nodes, in addition to fabrication and co-integration challenges, impedes this progress. Introducing plasmonic metals to photonic devices to excite surface plasmon polaritons (SPPs) is one viable solution to this problem, at least for some functionalities, such as photodetection. SPPs are electromagnetic (EM) excitations that exist at the interface between a metal and a dielectric (or a semiconductor). These unique EM excitations result in a significant enhancement of the EM field at the metal–dielectric interface, where light can also be confined beyond its diffraction limit [3].

Integrated optical interconnects consist of a transmitter, waveguide, and a receiver. The receiver contains a photodetector that converts optical signals to electrical ones. A photodetector is differentiated by its responsivity, speed, footprint, dark current, energy consumption, and ease of integration with standard industrial platforms. Most photodetectors employed in silicon photonics are based on germanium [4]. However, these photodetectors are limited either by the resistance-capacitance (RC) product or by the carrier-transit time. Incorporating plasmonic waveguides and applying a large bias voltage can push the speed of germanium photodetectors up to 110 GHz [5]; however, high energy consumption and large dark currents are associated with this boost. Plasmonic Schottky photodetectors have been proposed for their ease of integration with silicon photonics and their ability to absorb photons at telecom wavelengths, with a demonstrated responsivity of 0.37 A/W at 3 V bias [6]. Nonetheless, huge dark currents are associated with plasmonic Schottky photodetectors, which could hinder their implementation in applications where high signal-to-noise ratios (SNRs) are essential, e.g., telecom. III-V compound semiconductors, which are heterogeneously integrated on silicon, can exhibit a decent performance in terms of speed and responsivity [7], yet their performance is degraded when integrated with CMOS microelectronics due to packaging parasitics. Besides that, heterogeneous integration techniques are expensive [8,9]. Furthermore, the monolithic integration of III-V compound semiconductors with silicon is hindered by the large mismatches in their lattice constants and thermal expansion coefficients [10].

Two-dimensional (2D) materials recently emerged as alternative active materials for modulation and photodetection with a special set of inherent features including high-speed, small-footprint, low-cost manufacturing, low-power consumption, and CMOS compatibility [4]. More specifically, graphene photodetectors have gained extraordinary attention for their ultrafast speed and broadband absorption, despite the innate, relatively low optical absorption of graphene [1118]. Several techniques have been proposed to boost the responsivity of high-speed graphene photodetectors including waveguide-integrated configurations where light continuously interacts with the graphene sheet as it propagates through the waveguide, combining graphene with other 2D materials in composite heterostructures, and enhancing graphene’s absorption by plasmonic means. So far, the demonstrated waveguide-integrated plasmonic graphene photodetectors have all been based on gold [1922], which in spite of its outstanding plasmonic performance, is not CMOS compatible [23].

In this work, we propose an on-chip, compact-footprint, ultrafast, and high-responsivity plasmon-enhanced graphene photodetector that operates at the telecom C-band and that can be realized using CMOS-compatible processes. The proposed device employs titanium nitride (TiN) as the plasmonic material. TiN is a refractory metal nitride that has optical properties very similar to gold [24] and an electrical conductivity higher than titanium [25]; yet unlike gold, TiN is CMOS compatible [2628]. The device performance is studied and quantified in terms of its responsivity, operation speed, energy consumption, and noise equivalent power (NEP).

2. DEVICE STRUCTURE

The structure of the on-chip photodetector is illustrated in Fig. 1. A silicon rib waveguide on top of a 2 µm bottom oxide (BOX) layer guides the incoming light to the photodetector section at the terminating end of the optical link, where the optical signal is absorbed and reverted to its electrical form. The waveguide supports a transverse magnetic (TM) mode. Within the photodetector section, silicon dioxide (${\rm{Si}}{{\rm{O}}_2}$) is placed on the sides of the waveguide ridge to facilitate the placement of the graphene monolayer on top of the waveguide. The generated electrical signal is collected by the two TiN films that are deposited on top of the graphene. Besides collecting the signal, the center TiN film plasmonically enhances the interaction of the propagating TM mode with graphene, which boosts the optical absorption of the latter, resulting in a high photoresponse at an ultra-compact device length of 3.5 µm. Details of the device geometry, optimization procedure, propagation modes, plasmon-induced losses, and the impact of potential fabrication variations are provided in Supplement 1, Section 1.

 figure: Fig. 1.

Fig. 1. (a) On-chip photodetector structure. (b) Front view of the photodetector device.

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3. OPERATION PRINCIPLE

Graphene detects light mainly through three physical effects: photovoltaic [2931], bolometric [3234], and photothermoelectric (PTE) [3537] effects. The bolometric effect is observed only for devices under bias [38], which is not the case for our device. The PTE effect dominates over the photovoltaic effect at zero-bias [39]; thus, the photodetection process in our device is predominantly determined by the PTE effect. This effect is based on the phenomenon of photogenerated hot carriers in graphene. Due to the unique conical dispersion of graphene, the density of states fades away at the Dirac point. As a consequence, carriers have a low heat capacity near the Dirac point, and when excited, they immediately scatter with other carriers within a few tens of femtoseconds. These carrier–carrier scattering events result in an ephemeral Fermi–Dirac distribution of hot thermalized carriers, which can be described by a chemical potential ($\mu$) and a carrier temperature (${{\rm{T}}_c}$) [40]. Afterwards, the hot thermalized carriers cool down in picoseconds by emitting optical and acoustic phonons, coupling with surface optical phonons, and most importantly through disorder-assisted scattering, which dominates at room temperature [4143].

Within the photodetector section, the propagating TM mode experiences a near-field plasmonic enhancement at the TiN–graphene–Si interface due to the presence of the TiN stripe. This near-field enhancement results in a plasmon-enhanced effective absorption of graphene, and hot carriers are generated as the propagating mode interacts with the graphene sheet. An uneven distribution of hot carriers across the graphene sheet induces a PTE voltage [44,45]:

$${V_{{\rm{PTE}}}} = \int_0^{{x_0}} S\nabla {T_c}{\rm{d}}x.$$

The Seebeck coefficient is a function of the chemical potential, and resembles the curve shown in Fig. 2(a). According to Eq. (1), an asymmetric profile of the Seebeck coefficient across the graphene sheet induces a PTE voltage. Graphene is effectively doped when placed in contact with a metal, which in turn affects the Seebeck coefficient and the PTE voltage. The resulting shift in chemical potential ($\Delta\mu$) is related to the Shottky barrier height (${\Phi _B}$) at the metal–graphene junction, which is approximated using the Schottky–Mott rule [46,47]:

$${\Phi _B} = {\Phi _M} - {X_S},$$
where ${\Phi _M}$ is the metal work function, and ${X_S}$ is the electron affinity of the semiconductor given by
$${X_S} = {\Phi _S} - ({E_c} - {E_F}),$$
where ${\Phi _S}$ is the work function, ${E_c}$ is the energy of the conduction band edge, and ${E_F}$ is the Fermi energy of the semiconductor. Here we consider TiN, a metal nitride, as the metal, and graphene, a zero-bandgap semiconductor, as the semiconductor. Considering the case of an ideally undoped graphene gives $({E_c} - {E_F}) = 0$ and ${X_S} = {\Phi _S}$. Taking work function values of ${\sim}4.6\;{\rm{eV}}$ for graphene [48,49] and 4.2–4.5 eV for TiN [50,51] gives ${\Phi _B} \lt 0$, leading to electrons flowing from graphene to TiN, or graphene being effectively p-doped by TiN, and the Seebeck coefficient varies as a result [Fig. 2(b)]. For this device, however, the Seebeck coefficient does not contribute to the generated photovoltage, since TiN is placed on both sides of the graphene sheet, giving a symmetric doping profile across it. A difference in the Seebeck coefficient across the graphene sheet is required to generate a ${V_{{\rm{PTE}}}}$ for a fixed ${T_c}$ profile based on [39]
$${V_{{\rm{PTE}}}} = ({S_1} - {S_2})\,\Delta T ,\quad \Delta T = {T_c} - {T_0},$$
where ${S_1}$ and ${S_2}$ represent the Seebeck coefficient at each side of the graphene sheet, and ${T_0}$ is the lattice temperature. Therefore, the photodetector operates based solely on the plasmonic thermoelectric effect. The previous analysis assumes an ideal metal–semiconductor interface. In practice, ${\Phi _B}$ is experimentally extracted as described in [46], since the Schottky–Mott rule does not take into account the presence of charged impurities at the metal–semiconductor interface. Even so, a similar conclusion can be reached because of the symmetric doping profile induced by the TiN–graphene–TiN configuration.
 figure: Fig. 2.

Fig. 2. (a) Seebeck coefficient as a function of chemical potential. (b) Band diagram representing the doping profile across the graphene sheet; graphene is effectively p-doped by TiN. Black circles and white circles represent electrons and holes, respectively. Gr, graphene.

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The carrier temperature profile across the graphene sheet is given by solving the heat transport equation [39,52,53]

$${-}\kappa \frac{{{\partial ^2}{T_c}}}{{\partial {x^2}}} + \gamma C({T_c} - {T_0}) = {A_G}I(x),$$
where $\gamma$ is the carrier cooling rate, $C$ is the carrier heat capacity, ${A_G}$ the effective optical absorption of graphene (see Methods), and $I(x)$ is the intensity profile of the excitation waveguide mode (see Supplement 1, Section 4). The product of the carrier temperature profile and the Seebeck coefficient is later integrated to find the induced PTE voltage, according to Eq. (1). Finally, the voltage responsivity of the photodetector is calculated by dividing the PTE voltage by the total input optical power in the waveguide. In this work, we plug in parameters taken from experimental reports to the heat transport equation. First, the electrical conductivity ($\sigma$) of graphene is calculated as [39,52,53]
$$\sigma = {\sigma _0}\left({1 + \frac{{{\mu ^2}}}{{{\Delta ^2}}}} \right),\quad {\sigma _0} = 5\left({\frac{{{e^2}}}{h}} \right),$$
where ${\sigma _0}$ is the minimum conductivity taken from [53], $h$ is Planck’s constant, and $\Delta$ is the minimum conductivity plateau; $\Delta \approx 55 \;{\rm{meV}}$ for graphene-on-${\rm{Si}}{{\rm{O}}_2}$ [53,54]. The thermal conductivity ($\kappa$) is related to the electrical conductivity ($\sigma$) through the Wiedemann–Franz law
$$\kappa = \frac{{{\pi ^2}k_B^2T}}{{3{e^2}}}\sigma .$$

The carrier cooling rate ($\gamma$) can be expressed as [42,53]

$$\gamma = b\left({T + \frac{{T_*^2}}{T}} \right),$$
$$b = 2.2\,\frac{{{g^2}\rho {k_B}}}{{\hbar {k_F}\ell}},\;{T_*} = {T_{{\rm BG}}}\sqrt {0.43{k_F}\ell} ,$$
$$\begin{split}g& = \frac{D}{{\sqrt {2\rho {s^2}}}},\;\rho = \frac{{2\mu}}{{\pi {\hbar ^2}v_F^2}},\;{k_F} = \frac{\mu}{{\hbar {v_F}}},\\ {k_F}\ell &= \frac{{\pi \hbar \sigma}}{{{e^2}}},\;{T_{{\rm BG}}} = \frac{{s\hbar {k_F}}}{{{k_B}}}.\end{split}$$

The first term in the right-hand side of Eq. (8) is related to intrinsic scattering processes that dominate at low temperatures, while the second term is related to disorder-assisted scattering, which dominates at high temperatures, including room temperature ($T$). $g$ is the electron–phonon coupling constant, $\rho$ is the density of states, ${k_F}\ell$ is the mean free path, ${k_F}$ is the Fermi wave vector, ${T_{{\rm BG}}}$ is the Bloch–Grüneisen temperature, $D = 20 \;{\rm{eV}}$ is the deformation potential constant [41], $\rho = 7.6 \times {10^{- 7}} \;{\rm{Kg}}/{{\rm{m}}^2}$ is the mass density of graphene, and $s = 2 \times {10^4} \;{\rm{m}}/{\rm{s}}$ is the speed of longitudinal acoustic phonons [45]. The carrier heat capacity ($C$) is given by [55]

$$C = \frac{{{\pi ^2}k_B^2T}}{3}\rho .$$

The carrier cooling length ($\xi$) is related to $\kappa$, $\gamma$, and $C$ by the following relation:

$$\xi = \sqrt {\frac{\kappa}{{\gamma C}}} .$$

Now we have the ingredients required to solve the heat transport equation. The carrier temperature profile is calculated using the analytical solution to the heat transport equation [42,56]

$$\Delta T = {T_c}(x) - {T_0} = \frac{{\xi \,{\sinh}(({x_0} - |x|)/\xi)}}{{2\,{\cosh}({x_0}/\xi)}}\left({\frac{{{A_G}I(x)}}{\kappa}} \right),$$
where ${x_0}$ is the distance from the peak of $I(x)$ to the side electrode. The carrier temperature is multiplied by the Seebeck coefficient, which is given by the Mott formula
$$S = - \frac{{{\pi ^2}k_B^2T}}{{3e}}\frac{1}{\sigma}\frac{{d\sigma}}{{d\mu}}.$$

The photocurrent is calculated by dividing the resultant PTE voltage by the resistance of the graphene sheet (${R_G}$):

$${R_G} = \frac{w}{L}{\sigma ^{- 1}}(x),$$
where $w$ is the electrode spacing, and $L$ is the photodetector length. The equivalent electric circuit model is given in Supplement 1, Section 7. Finally, the current responsivity is calculated by dividing the photocurrent by the total input optical power in the waveguide.

4. METHODS

The optimization procedure, presented in Supplement 1, Section 1, was carried out for the graphene-on-${\rm{Si}}{{\rm{O}}_2}$ waveguide photodetector. The refractive index of TiN was taken as $n = 2.54 + 7.84i$ at $\lambda = 1550 \;{\rm{nm}}$ [27,57] (see Supplement 1, Section 3). Simulations were conducted using Lumerical, where graphene is modeled as a 2D material with a surface optical conductivity ($\tilde \sigma$) given by [58,59]

$$\tilde \sigma (\omega ,\Gamma ,\mu ,T) = {\tilde \sigma _{{\rm{intra}}}}(\omega ,\Gamma ,\mu ,T) + {\tilde \sigma _{{\rm{inter}}}}(\omega ,\Gamma ,\mu ,T),$$
$$\begin{split}{\tilde \sigma _{{\rm{intra}}}}(\omega ,\Gamma ,\mu ,T) &= \frac{{- j{e^2}}}{{\pi {\hbar ^2}(\omega + j2\Gamma)}}\\&\quad\times\int_0^\infty E \left({\frac{{\partial f(E)}}{{\partial E}} - \frac{{\partial f(- E)}}{{\partial E}}} \right)\,{\rm{d}}E,\end{split}$$
$$\begin{split}{\tilde \sigma _{{\rm{inter}}}}(\omega ,\Gamma ,\mu ,T)& = \frac{{- j{e^2}(\omega + j2\Gamma)}}{{\pi {\hbar ^2}}}\\&\quad\times\int_0^\infty \frac{{f(- E) - f(E)}}{{{{(\omega + j2\Gamma)}^2} - 4(E/\hbar {)^2}}}{\rm{d}}E,\end{split}$$
$$f(E) = ({e^{(E -\mu)/{k_B}T}} + {1)^{- 1}}.$$

${\tilde \sigma _{{\rm{intra}}}}$ and ${\tilde \sigma _{{\rm{inter}}}}$ account for the surface optical conductivity due to intraband and interband transitions, respectively. $\omega$ is the angular frequency of incident photons, $\Gamma$ is the scattering rate of graphene, $T$ is the operation temperature, $e$ is the electron charge, $\hbar$ is the reduced Planck constant, $f(E)$ is the Fermi–Dirac distribution, and ${k_B}$ is the Boltzmann constant. The surface electric permittivity ($\tilde \epsilon$) and the surface electric susceptibility ($\tilde \chi$) are related to $\tilde \sigma$ through the following relation [45]:

$$\tilde \epsilon = {\epsilon _0}\tilde \chi + j\frac{{\tilde \sigma}}{\omega}.$$

In general, graphene samples are unintentionally doped when placed on a substrate, which results in a chemical potential in the range of $0.1 {-} 0.2\;{\rm{eV}}$ [60,61]. In this work, we model graphene with a 0.15 eV chemical potential and 1 ps scattering time. The scattering time is related to the scattering rate by $\tau = 1/2\Gamma$. An incident photon has a ${\sim} 0.8\;{\rm{eV}}$ energy at $\lambda = 1550\;{\rm{nm}}$; this photon induces an interband transition when absorbed by graphene since $\hbar \omega \gt 2\mu$ (see Supplement 1, Section 2). The optical absorption of graphene is dominated by interband transitions at telecom wavelengths for the aforementioned chemical potential range. Therefore, variations in the scattering rate, which is related to intraband transitions, will have a negligible effect on the optical absorption of graphene for $0.1\;{\rm{eV}} \le\mu\le 0.2\;{\rm{eV}}$. Our simulations revealed that the optical absorption of graphene was similar for 100 fs, 500 fs, and 1000 fs scattering times, as explained in Supplement 1, Section 2. On the other hand, chemical potential variations have a significant impact on the device performance, where the responsivity degrades for large $\mu$ values. In our case, the responsivity reduction associated with larger $\mu$ is determined mainly by the drop in ${T_c}$ and $S$ at higher carrier densities, as explained in Section 5.

The computed propagation loss is $3.67\;{\rm{dB}}/{\rm{\unicode{x00B5}{\rm m}}}$ for the TM mode presented in Fig. S5 of Supplement 1. Here the propagation loss ($\alpha$) is defined as [62]

$$\alpha = - 20\,{\rm{lo}}{{\rm{g}}_{10}}\,({E_f}/{E_i}),$$
where ${E_i}$ and ${E_f}$ represent the electric field intensity before and after propagating through the photodetector waveguide, respectively. The absorbed power (${P_{{\rm{abs}}}}$) in the photodetector waveguide can be calculated using the Beer–Lambert law
$${P_{{\rm{abs}}}}(L) = 1 - {10^{- 2(\alpha /20)L}}.$$

Figure 3(a) shows ${P_{{\rm{abs}}}}$ as a function of the photodetector length for $\alpha = 3.6\;{\rm{dB}}/{\rm{\unicode{x00B5}{\rm m}}}$. ${P_{{\rm{abs}}}} = 95\%$ for $L = 3.5\;{\rm{\unicode{x00B5}{\rm m}}}$, as given in Supplement 1, Section 1. To find the effective absorption of graphene (${A_G}$), we extract the computed mode shown in Supplement 1, Fig. S5, and then import it into a Lumerical FDTD simulation of the same device structure shown in Fig. 1(a), but without the TiN stripe. The presence of the TiN stripe introduces a plasmonic near-field enhancement of the EM field at the graphene sheet plane. To find the power absorbed solely by graphene, we follow the aforementioned approach, where the only absorbing material in the Lumerical FDTD simulation is graphene, which “sees” the plasmonically enhanced EM field at the graphene sheet plane due to the presence of the TiN stripe in the imported mode. Figure 3(b) plots ${A_G}$ as a function of the photodetector length for the imported plasmonic TM mode with TiN, where ${A_G} = 5.2\%$ for $L = 3.5\;{\rm{\unicode{x00B5}{\rm m}}}$. We find that the effective absorption of graphene is ${\gt}2 \times$ larger purely because of the presence of the TiN stripe, where the absorption of the graphene–silicon waveguide without the TiN stripe is only 2.4% for $L = 3.5\;{\rm{\unicode{x00B5}{\rm m}}}$ (see Supplement 1, Section 1). Hence, the effectively enhanced absorption is a consequence of the plasmonic near-field enhancement of the TiN stripe, which the TM mode experiences as it propagates in the photodetector section.

 figure: Fig. 3.

Fig. 3. (a) Optical power absorbed as a function of the photodetector length for the optimized waveguide geometry, and (b) effective absorption of graphene as a function of the photodetector length for the imported optimum mode at $\lambda = 1550 \;{\rm{nm}}$. Data were extracted from power monitors in Lumerical FDTD for the structure that is shown in the inset.

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5. RESULTS AND DISCUSSION

A. Carrier Cooling and Thermoelectric Performance

Figure 4 shows the carrier cooling rate and cooling length as a function of chemical potential. It is noted that carriers cool down faster in graphene with higher disorder, i.e., higher $\Delta$, resulting in a faster operation speed. The highest demonstrated bandwidth for a PTE graphene on-chip detector is 67 GHz [63], which is a setup-limited bandwidth. A bandwidth of ${\sim} 110 \;{\rm{GHz}}$ has been demonstrated for graphene photodetectors operating based on the photovoltaic and bolometric effects [19,22]. A bandwidth exceeding 100 GHz is not inconceivable for PTE graphene photodetectors considering the ultrafast cooling dynamics of photoexcited hot carriers in graphene. Experimentally, the cooling time of graphene is on the order of a few picoseconds [64,65], corresponding to a cooling rate in hundreds of ${\rm{G}}{{\rm{s}}^{- 1}}$. Furthermore, it is experimentally reported that highly disordered graphene sheets exhibit faster carrier cooling dynamics than less disordered sheets [66], which is in agreement with our conclusions. The cooling length is $\xi \sim 1/\sqrt \gamma$; hence, the higher the cooling rate, the shorter the cooling length.

 figure: Fig. 4.

Fig. 4. Carrier cooling rate and cooling length as a function of chemical potential for $\Delta = 60 \;{\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 40 \;{\rm{meV}}$.

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As previously mentioned, carrier cooling mechanisms are dominated by disorder-assisted scattering at room temperature. Disorder can come in the form of ripples, charged impurities, or strain fluctuations [43,67]. Low-disorder graphene has a lower resistance and higher mobility than high-disorder graphene, as shown in Fig. 5, where the mobility ($\eta$) is taken as the Drude mobility $\eta = \sigma /en$, and $n = {\mu ^2}/\pi {\hbar ^2}v_F^2$ is the density of carriers in graphene [68]. High-mobility carriers in low-disorder graphene experience less scattering, resulting in a slower cooling rate for photoexcited hot carriers. On the other hand, in high-disorder graphene, the mobility is relatively low, and carriers are more likely to scatter and cool down rapidly as a result. Disorder is accounted for through the minimum conductivity plateau ($\Delta$). Higher disorder is manifested in the form of a wider charge neutrality region in the conductivity plot of graphene [43], as shown in Fig. 6(a). To extract the $\Delta$ parameter, the conductivity plot of graphene is experimentally measured, and then analytically fitted with the appropriate $\Delta$ value. This was the approach reported by other groups [44,53]. The electron mobility in graphene can be higher than the hole mobility [54]. In case further modeling of this phenomenon is intended, two distinct $\Delta$ values should be adopted, where the electron-related $\Delta$ would be lower than the hole-related $\Delta$, since the electron mobility is higher. Depending on whether the graphene sheet is p- or n-doped, the appropriate $\Delta$ value should be used.

 figure: Fig. 5.

Fig. 5. Graphene sheet resistance and mobility as a function of the chemical potential for $\Delta = 60 \;{\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 40 \;{\rm{meV}}$.

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The normalized ${T_c}$ profiles of the high-disorder ($\Delta = 60 \;{\rm{meV}}$) and low-disorder ($\Delta = 40 \;{\rm{meV}}$) graphene photodetectors are shown in Fig. 7. The maximum ${T_c}$ is located at the waveguide center, and decays as one approaches the waveguide sides. Therefore, a strong ${T_c}$ gradient is present across the graphene sheet, resulting in the generation of a PTE voltage according to Eq. (1). It is noted that ${T_c}$ drops with rising $\mu$, which is expected since the PTE effect is more dominant in the low $\mu$ regime, as explained in Section 3. It is observed that the carrier temperature is slightly more concentrated at low chemical potentials for the low-disorder sheet. A similar trend is seen in the Seebeck coefficient ($S$) plots shown in Fig. 6(b), where $S$ is higher for low-disorder sheets at low chemical potentials. The Seebeck coefficient, and hence the thermoelectric performance, is enhanced in low-disorder graphene [69].

 figure: Fig. 6.

Fig. 6. Electrical conductivity of graphene and Seebeck coefficient as a function of the chemical potential for $\Delta = 40 \;{\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 60\; {\rm{meV}}$.

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 figure: Fig. 7.

Fig. 7. Normalized temperature profiles for a varying chemical potential for high-disorder ($\Delta = 60 \;{\rm{meV}}$) and low-disorder ($\Delta = 40 \;{\rm{meV}}$) graphene sheets.

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Photovoltaic graphene photodetectors function based on the flow of photoexcited carriers in graphene, which makes such photodetectors carrier transit-time limited [70]. On the other hand, PTE graphene photodetectors operate based on the generation of a thermoelectric voltage induced by photoexcited hot carriers in graphene. The operation speed of PTE graphene photodetectors is limited by the carrier cooling rate [56,63,65], where carriers can re-participate in the photodetection process after adequately cooling down. Interestingly, a high mobility graphene sheet is favorable for photovoltaic photodetectors, since a low mobility sheet limits the speed of carrier flow across graphene, while a low mobility sheet is preferable for PTE graphene photodetectors, as long as the device bandwidth is the only concern. On the other hand, the Seebeck effect, and consequently the thermoelectric performance, is degraded at higher disorder [69], resulting in a responsivity–bandwidth trade-off for graphene-on-${\rm{Si}}{{\rm{O}}_2}$ PTE detectors that is dictated by the disorder strength. For instance, a suspended graphene sheet is characterized by an ultrahigh electron mobility, e.g., ${\sim}200{,}000 \;{\rm{cm}}^2/{\rm{Vs}}$ [71]. A waveguide-integrated PTE detector with suspended graphene was reported in [72], where the use of high-mobility suspended graphene on top of a silicon slot waveguide achieved a high responsivity ($0.273 \;{\rm{A}}/{\rm{W}}$) without relying on plasmonic nanostructures. However, the photodetector response time was limited to tens of microseconds due to the relatively slow carrier heating and cooling dynamics in suspended graphene, where substrate-induced disorder-assisted scattering is absent.

B. Photoresponsivity and Noise Performance

The voltage responsivity (${R_v}$) and current responsivity (${R_i}$) of the photodetector are shown in Fig. 8. The enhanced thermoelectric performance of low-disorder graphene augments the detector’s photoresponse. The voltage responsivity exceeds 350 V/W and 650 V/W for $\Delta = 60 \;{\rm{meV}}$ and $\Delta = 40 \;{\rm{meV}}$, respectively. It is observed that the responsivity depends strongly on the chemical potential, which is related to the dependence of ${T_c}$ and $S$ on $\mu$. The device performance is optimal when $0 \lt \mu \lt 0.1\;{\rm{eV}}$, where the Seebeck coefficient and the carrier cooling rate are both high. Consequently, chemical potential tuning is required to acquire the optimum responsivity. The chemical potential of graphene on a substrate can be tuned by thermal annealing [41,61,73]. The current responsivity is as high as 1.4 A/W (1.1 A/W external) for $\Delta = 40 \;{\rm{meV}}$, and 0.7 A/W (0.6 A/W external) for $\Delta = 60 \;{\rm{meV}}$.

 figure: Fig. 8.

Fig. 8. Voltage and current responsivity of the photodetector as a function of the chemical potential for $\Delta = 40\; {\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 60 \;{\rm{meV}}$.

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Table 1 presents a summary of the performance metrics and features of some recently reported on-chip graphene photodetectors. The highest external responsivity of a demonstrated waveguide-integrated graphene-based photodetector is 0.67 A/W at 0.5 V bias, for a 5 µm long device [74]. Using high-mobility graphene ($\Delta = 40 \;{\rm{meV}}$), the herein proposed device can deliver ${\gt}1.5 \times$ that responsivity (1.1 A/W external) for a smaller footprint (3.5 µm), and is the most compact graphene-based waveguide photodetector reported to date. Moreover, this device operates at the zero-bias condition, while offering CMOS compatibility and ultrahigh speed beyond 100 GHz. Theoretical responsivities up to 1000 A/W have been reported in [56] for a waveguide-integrated graphene photodetector, which may be overestimated considering the highest external responsivity that has been demonstrated so far, namely, 0.67 A/W.

Tables Icon

Table 1. Performance Metrics and Features of On-Chip Graphene Photodetectors

The photodetector exhibits a nearly flat photoresponse across the telecom C-band, as illustrated by the blue markers in Fig. 9(a). Here we consider the maximum external responsivity of the photodetectors for comparison, where the external responsivity is defined as the product of the responsivity with the coupling efficiency. It is observed that the responsivity slightly increases at shorter wavelengths following the trend of the coupling efficiency, which is represented by the red markers in Fig. 9(a). Certainly, graphene’s absorption of the propagating mode increases at longer wavelengths, since the propagating mode becomes more confined in the photodetector waveguide, and the graphene sheet absorbs more of the propagating mode as a result (see Supplement 1, Section 3). However, at long wavelengths in this band, the coupling efficiency reduces at a higher rate than the increasing rate of the graphene absorption, which explains the results that we obtain in this study.

 figure: Fig. 9.

Fig. 9. (a) Maximum external current responsivity and coupling efficiency as a function of wavelength and (b) noise equivalent power (NEP) as a function of chemical potential for $\Delta = 40 \;{\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 60 \;{\rm{meV}}$.

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Further improvement of the device performance can be achieved by placing graphene on a hexagonal boron nitride (hBN) substrate, or encapsulating graphene between two hBN layers. The Seebeck coefficient of graphene is enhanced by ${\sim}2 \times$ when placed on a hBN substrate [44]. This is due to the charge screening role of the hBN spacer layer, which mitigates the influence of the substrate impurities [75]. In addition, the carrier cooling dynamics in graphene–hBN Van der Waals (vdW) heterostructures is dominated by hot carrier coupling to hyperbolic phonon polaritons, not disorder-assisted scattering [7678]. Experimentally, graphene-on-hBN demonstrated faster cooling dynamics than graphene-on-${\rm{Si}}{{\rm{O}}_2}$ [76,79]. Therefore, the cooling pathway introduced by hyperbolic phonon polaritons is more efficient than disorder-assisted scattering, which opens up the possibility for faster optoelectronic devices based on graphene–hBN vdW heterostructures.

A transimpedance amplifier is an electronic circuit that converts an input electric current into voltage, and is typically employed in receiver circuits to convert the photodetector current into a voltage reading [80]. The proposed device can be operated without a transimpedance amplifier [4], since a photovoltage is already generated across the graphene sheet, and can be collected through the two TiN films, as shown in Fig. 8. Moreover, this device does not consume energy, has a zero dark current, zero flicker ($1/f$) noise, and zero shot noise, because of its zero-bias operation [63,8185]. Therefore, its NEP is determined by the Johnson–Nyquist (thermal) noise:

$${\rm{NEP}} = \frac{{{V_{{\rm{th}}}}}}{{{R_v}}} = \frac{{\sqrt {4{k_B}T{R_G}}}}{{{R_v}}},$$
where ${V_{{\rm{th}}}}$ is the variance of the thermal noise voltage per 1 Hz of bandwidth. The NEP is defined as the input signal power that results in an SNR ratio of one in a 1 Hz output bandwidth. A low NEP value corresponds to a lower noise floor and a more sensitive detector [86,87]. Therefore, a low NEP value is an attractive feature for photodetector devices. Figure 9(b) shows the NEP as a function of $\mu$ for $\Delta = 40 \;{\rm{meV}}$, $\Delta = 50 \;{\rm{meV}}$, and $\Delta = 60 \;{\rm{meV}}$. It is noted that the NEP for low-disorder photodetectors is initially low at low chemical potentials. That is attributed to the remarkably high ${R_v}$ and small ${R_G}$ of the low-disorder graphene photodetector in that regime. Nevertheless, the NEP becomes comparatively lower for the high-disorder graphene photodetector at high chemical potentials, where the voltage responsivity of the low-disorder graphene photodetector is relatively low. The voltage responsivity of the high-disorder graphene photodetector becomes slightly higher than that of the low-disorder graphene photodetector at large $\mu$ values, as illustrated in Fig. 8. The resistance of low-disorder graphene is lower than that of high-disorder graphene at all chemical potentials, as shown in Fig. 5; this is supposed to give a lower NEP for the low-disorder graphene at large $\mu$ values, but the graphene sheet resistance term (${R_G}$) is under the square root in Eq. (23), making the ${R_v}$ term more effective in determining the NEP.

Considering that the photodetectors are operating in the optimal chemical potential range, $0 \lt \mu \lt 0.1\;{\rm{eV}}$, the corresponding NEP values are nearly $5 \lt |{\rm{NEP}}| \lt 20\;{\rm{pW}}/\sqrt {{\rm{Hz}}}$ for both photodetectors, where we deliberately exclude the NEP values at $\mu= 0$, in addition to NEP values in its very close proximity, since the chemical potential cannot be exactly zero, as explained in Section 4. These NEP values are an order of magnitude lower than the reported values for other plasmonically enhanced graphene photodetectors [20,21]. Therefore, the zero-bias operation of the proposed photodetector eliminates flicker noise, shot noise, and dark current, and as a result, the NEP is minimal. However, in an actual measurement setup, noise from the photodetector makes up a fraction of the total noise, where contributions by other components in the system may be dominant, e.g., amplifier noise [19], and taking that into account may invalidate the previous comparison. Nonetheless, the intrinsic NEP introduced by this photodetector is ultra-low (${\lt}20\;{\rm{pW/}}\sqrt {{\rm{Hz}}}$).

6. CONCLUSION

To sum up, we present a waveguide-integrated graphene photodetector that is based on the plasmon-induced PTE effect. The photodetector relies on the plasmonic response of TiN, which is a CMOS-compatible metal nitride that exhibits plasmonic properties that are similar to gold. The photodetector response and bandwidth depend on graphene disorder. High-disorder graphene enables higher operation speeds, while a superior thermoelectric performance and photoresponse are achievable using low-disorder graphene. For low-disorder graphene ($\Delta = 40 \;{\rm{meV}}$), the responsivity is as high as 1.4 A/W (1.1 A/W external), and it is 0.7 A/W (0.6 A/W external) for high-disorder graphene ($\Delta = 60 \;{\rm{meV}}$), at an ultra-compact length of 3.5 µm. This device has the most compact footprint reported for an on-chip graphene photodetector. Moreover, it exhibits a nearly flat photoresponse across the telecom C-band. Its intrinsic NEP is ultra-low (${\lt}20\;{\rm{pW/}}\sqrt {{\rm{Hz}}}$) because of its bias-free operation, and it consumes zero energy. Further advances in graphene deposition methods and quality control of samples will be key in realizing graphene-based optoelectronics as a mainstream industrial technology.

Funding

New York University Abu Dhabi.

Acknowledgment

Support from the NYUAD research grant is gratefully acknowledged.

Disclosures

The authors declare no conflicts of interest.

Supplemental Document

See Supplement 1 for supporting content.

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90. D. Schall, C. Porschatis, M. Otto, and D. Neumaier, “Graphene photodetectors with a bandwidth >76 GHz fabricated in a 6′′ wafer process line,” J. Phys. D 50, 124004 (2017). [CrossRef]  

91. S. Schuler, D. Schall, D. Neumaier, L. Dobusch, O. Bethge, B. Schwarz, M. Krall, and T. Mueller, “Controlled generation of a p–n junction in a waveguide integrated graphene photodetector,” Nano Lett. 16, 7107–7112 (2016). [CrossRef]  

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2020 (7)

J. Guo, J. Li, C. Liu, Y. Yin, W. Wang, Z. Ni, Z. Fu, H. Yu, Y. Xu, Y. Shi, Y. Ma, S. Gao, L. Tong, and D. Dai, “High-performance silicon-graphene hybrid plasmonic waveguide photodetectors beyond 1.55 µm,” Light Sci. Appl. 9, 29 (2020).
[Crossref]

J. Gosciniak, M. Rasras, and J. B. Khurgin, “Ultrafast plasmonic graphene photodetector based on the channel photothermoelectric effect,” ACS Photon. 7, 488–498 (2020).
[Crossref]

V. Miseikis, S. Marconi, M. A. Giambra, A. Montanaro, L. Martini, F. Fabbri, S. Pezzini, G. Piccinini, S. Forti, B. Terres, I. Goykhman, L. Hamidouche, P. Legagneux, V. Sorianello, A. C. Ferrari, F. H. L. Koppens, M. Romagnoli, and C. Coletti, “Ultrafast, zero-bias, graphene photodetectors with polymeric gate dielectric on passive photonic waveguides,” ACS Nano 14, 11190–11204 (2020).
[Crossref]

L. Wang, P. Makk, S. Zihlmann, A. Baumgartner, D. I. Indolese, K. Watanabe, T. Taniguchi, and C. Schönenberger, “Mobility enhancement in graphene by in situ reduction of random strain fluctuations,” Phys. Rev. Lett. 124, 157701 (2020).
[Crossref]

Z. Ma, K. Kikunaga, H. Wang, S. Sun, R. Amin, R. Maiti, M. H. Tahersima, H. Dalir, M. Miscuglio, and V. J. Sorger, “Compact graphene plasmonic slot photodetector on silicon-on-insulator with high responsivity,” ACS Photon. 7, 932–940 (2020).
[Crossref]

P. Huang, E. Riccardi, S. Messelot, H. Graef, F. Valmorra, J. Tignon, T. Taniguchi, K. Watanabe, S. Dhillon, B. Placais, R. Ferreira, and J. Mangeney, “Ultra-long carrier lifetime in neutral graphene-hBN van der Waals heterostructures under mid-infrared illumination,” Nat. Commun. 11, 1 (2020).
[Crossref]

A. Yurgens, “Large responsivity of graphene radiation detectors with thermoelectric readout: results of simulations,” Sensors 20, 1930 (2020).
[Crossref]

2019 (10)

S. Naghdi, G. Sanchez-Arriaga, and K. Y. Rhee, “Tuning the work function of graphene toward application as anode and cathode,” J. Alloys Compd. 805, 1117–1134 (2019).
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Y. Lin, Q. Ma, P.-C. Shen, B. Ilyas, Y. Bie, A. Liao, E. Ergeçen, B. Han, N. Mao, X. Zhang, X. Ji, Y. Zhang, J. Yin, S. Huang, M. Dresselhaus, N. Gedik, P. Jarillo-Herrero, X. Ling, J. Kong, and T. Palacios, “Asymmetric hot-carrier thermalization and broadband photoresponse in graphene-2D semiconductor lateral heterojunctions,” Sci. Adv. 5, eaav1493 (2019).
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J. E. Muench, A. Ruocco, M. A. Giambra, V. Miseikis, D. Zhang, J. Wang, H. F. Y. Watson, G. C. Park, S. Akhavan, V. Sorianello, M. Midrio, A. Tomadin, C. Coletti, M. Romagnoli, A. C. Ferrari, and I. Goykhman, “Waveguide-integrated, plasmonic enhanced graphene photodetectors,” Nano Lett. 19, 7632–7644 (2019).
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Y. Ding, Z. Cheng, X. Zhu, K. Yvind, J. Dong, M. Galili, H. Hu, N. A. Mortensen, S. Xiao, and L. K. Oxenløwe, “Ultra-compact integrated graphene plasmonic photodetector with bandwidth above 110 GHz,” Nanophotonics 9, 317–325 (2019).
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D. Akinwande, C. Huyghebaert, C.-H. Wang, M. I. Serna, S. Goossens, L.-J. Li, H.-S. P. Wong, and F. H. L. Koppens, “Graphene and two-dimensional materials for silicon technology,” Nature 573, 507–518 (2019).
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K. Sun and A. Beling, “High-speed photodetectors for microwave photonics,” Appl. Sci. 9, 623 (2019).
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P. Ma, Y. Salamin, B. Baeuerle, A. Josten, W. Heni, A. Emboras, and J. Leuthold, “Plasmonically enhanced graphene photodetector featuring 100 Gbit/s data reception, high responsivity, and compact size,” ACS Photon. 6, 154–161 (2019).
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J. Gosciniak, F. B. Atar, B. Corbett, and M. Rasras, “Plasmonic Schottky photodetector with metal stripe embedded into semiconductor and with a CMOS-compatible titanium nitride,” Sci. Rep. 9, 6048 (2019).
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R. Jago, E. Malic, and F. Wendler, “Microscopic origin of the bolometric effect in graphene,” Phys. Rev. B 99, 035419 (2019).
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Y. Chen, Y. Li, Y. Zhao, H. Zhou, and H. Zhu, “Highly efficient hot electron harvesting from graphene before electron-hole thermalization,” Sci. Adv. 5, eaax9958 (2019).
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2018 (8)

Y. Salamin, P. Ma, B. Baeuerle, A. Emboras, Y. Fedoryshyn, W. Heni, B. Cheng, A. Josten, and J. Leuthold, “100 GHz plasmonic photodetector,” ACS Photon. 5, 3291–3297 (2018).
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X. Chen, M. M. Milosevic, S. Stanković, S. Reynolds, T. D. Bucio, K. Li, D. J. Thomson, F. Gardes, and G. T. Reed, “The emergence of silicon photonics as a flexible technology platform,” Proc. IEEE 106, 2101–2116 (2018).
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C. Xie, Y. Wang, Z.-X. Zhang, D. Wang, and L.-B. Luo, “Graphene/semiconductor hybrid heterostructures for optoelectronic device applications,” Nano Today 19, 41–83 (2018).
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A. Di Bartolomeo, G. Luongo, L. Iemmo, F. Urban, and F. Giubileo, “Graphene–silicon Schottky diodes for photodetection,” IEEE Trans. Nanotechnol. 17, 1133–1137 (2018).
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V. Shautsova, T. Sidiropoulos, X. Xiao, N. A. Güsken, N. C. G. Black, A. M. Gilbertson, V. Giannini, S. A. Maier, L. F. Cohen, and R. F. Oulton, “Plasmon induced thermoelectric effect in graphene,” Nat. Commun. 9, 5190 (2018).
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S. Schuler, D. Schall, D. Neumaier, B. Schwarz, K. Watanabe, T. Taniguchi, and T. Mueller, “Graphene photodetector integrated on a photonic crystal defect waveguide,” ACS Photon. 5, 4758–4763 (2018).
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K.-J. Tielrooij, N. C. Hesp, A. Principi, M. B. Lundeberg, E. A. Pogna, L. Banszerus, Z. Mics, M. Massicotte, P. Schmidt, D. Davydovskaya, D. G. Purdie, I. Goykhman, G. Soavi, A. Lombardo, K. Watanabe, T. Taniguchi, M. Bonn, D. Turchinovich, C. Stampfer, A. C. Ferrari, G. Cerullo, M. Polini, and F. H. L. Koppens, “Out-of-plane heat transfer in van der Waals stacks through electron–hyperbolic phonon coupling,” Nat. Nanotechnol. 13, 41–46 (2018).
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Y. Gao, L. Tao, H. K. Tsang, and C. Shu, “Graphene-on-silicon nitride waveguide photodetector with interdigital contacts,” Appl. Phys. Lett. 112, 211107 (2018).
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2017 (5)

A. Principi, M. B. Lundeberg, N. C. Hesp, K.-J. Tielrooij, F. H. Koppens, and M. Polini, “Super-Planckian electron cooling in a van der Waals stack,” Phys. Rev. Lett. 118, 126804 (2017).
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D. Golla, A. Brasington, B. J. LeRoy, and A. Sandhu, “Ultrafast relaxation of hot phonons in graphene-hBN heterostructures,” APL Mater. 5, 056101 (2017).
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K. J. A. Ooi, P. C. Leong, L. K. Ang, and D. T. H. Tan, “All-optical control on a graphene-on-silicon waveguide modulator,” Sci. Rep. 7, 12748 (2017).
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A. Catellani and A. Calzolari, “Plasmonic properties of refractory titanium nitride,” Phys. Rev. B 95, 115145 (2017).
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D. Schall, C. Porschatis, M. Otto, and D. Neumaier, “Graphene photodetectors with a bandwidth >76 GHz fabricated in a 6′′ wafer process line,” J. Phys. D 50, 124004 (2017).
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2016 (10)

S. Schuler, D. Schall, D. Neumaier, L. Dobusch, O. Bethge, B. Schwarz, M. Krall, and T. Mueller, “Controlled generation of a p–n junction in a waveguide integrated graphene photodetector,” Nano Lett. 16, 7107–7112 (2016).
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J. A. Briggs, G. V. Naik, T. A. Petach, B. K. Baum, D. Goldhaber-Gordon, and J. A. Dionne, “Fully CMOS-compatible titanium nitride nanoantennas,” Appl. Phys. Lett. 108, 051110 (2016).
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Y. Wang, W. Yin, Q. Han, X. Yang, H. Ye, Q. Lv, and D. Yin, “Bolometric effect in a waveguide-integrated graphene photodetector,” Chin. Phys. B 25, 118103 (2016).
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A. Lefebvre, D. Costantini, I. Doyen, Q. Lévesque, E. Lorent, D. Jacolin, J.-J. Greffet, S. Boutami, and H. Benisty, “CMOS compatible metal-insulator-metal plasmonic perfect absorbers,” Opt. Mater. Express 6, 2389–2396 (2016).
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I. Goykhman, U. Sassi, B. Desiatov, N. Mazurski, S. Milana, D. de Fazio, A. Eiden, J. Khurgin, J. Shappir, U. Levy, and A. C. Ferrari, “On-chip integrated, silicon–graphene plasmonic Schottky photodetector with high responsivity and avalanche photogain,” Nano Lett. 16, 3005–3013 (2016).
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Y. Jung, J. Shim, K. Kwon, J.-B. You, K. Choi, and K. Yu, “Hybrid integration of III-V semiconductor lasers on silicon waveguides using optofluidic microbubble manipulation,” Sci. Rep. 6, 29841 (2016).
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J. Gosciniak, J. Justice, U. Khan, and B. Corbett, “Study of tin nanodisks with regard to application for heat-assisted magnetic recording,” MRS Adv. 1, 317–326 (2016).
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J. Abu-Taha and M. Yazgi, “A 7 GHz compact transimpedance amplifier TIA in CMOS 0.18 µm technology,” Analog Integr. Circuits Signal Process. 86, 429–438 (2016).
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J. Duan, X. Wang, X. Lai, G. Li, K. Watanabe, T. Taniguchi, M. Zebarjadi, and E. Y. Andrei, “High thermoelectricpower factor in graphene/hBN devices,” Proc. Natl. Acad. Sci. USA 113, 14272–14276 (2016).
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J. Wang, Z. Cheng, Z. Chen, X. Wan, B. Zhu, H. K. Tsang, C. Shu, and J. Xu, “High-responsivity graphene-on-silicon slot waveguide photodetectors,” Nanoscale 8, 13206–13211 (2016).
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2015 (5)

R.-J. Shiue, Y. Gao, Y. Wang, C. Peng, A. D. Robertson, D. K. Efetov, S. Assefa, F. H. L. Koppens, J. Hone, and D. Englund, “High-responsivity graphene–Boron nitride photodetector and autocorrelator in a silicon photonic integrated circuit,” Nano Lett. 15, 7288–7293 (2015).
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B. Zhou, B. Zhou, Y. Zeng, G. Zhou, and T. Ouyang, “Spin-dependent Seebeck effects in a graphene nanoribbon coupled to two square lattice ferromagnetic leads,” J. Appl. Phys. 117, 104305 (2015).
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K. J. Tielrooij, L. Piatkowski, M. Massicotte, A. Woessner, Q. Ma, Y. Lee, K. S. Myhro, C. N. Lau, P. Jarillo-Herrero, N. F. van Hulst, and F. H. L. Koppens, “Generation of photovoltage in graphene on a femtosecond timescale through efficient carrier heating,” Nat. Nanotechnol. 10, 437–443 (2015).
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P. Patsalas, N. Kalfagiannis, and S. Kassavetis, “Optical properties and plasmonic performance of titanium nitride,” Materials 8, 3128–3154 (2015).
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J. Wang, Z. Cheng, Z. Chen, J.-B. Xu, H. K. Tsang, and C. Shu, “Graphene photodetector integrated on silicon nitride waveguide,” J. Appl. Phys. 117, 144504 (2015).
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2014 (5)

X. Cai, A. B. Sushkov, R. J. Suess, M. M. Jadidi, G. S. Jenkins, L. O. Nyakiti, R. L. Myers-Ward, S. Li, J. Yan, D. K. Gaskill, T. E. Murphy, H. D. Drew, and M. S. Fuhrer, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9, 780–793 (2014).
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N. Youngblood, Y. Anugrah, R. Ma, S. J. Koester, and M. Li, “Multifunctional graphene optical modulator and photodetector integrated on silicon waveguides,” Nano Lett. 14, 2741–2746 (2014).
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F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9, 780–793 (2014).
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Q. Ma, N. M. Gabor, T. I. Anderse, N. L. Nair, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, “Competing channels for hot-electron cooling in graphene,” Phys. Rev. Lett. 112, 247401 (2014).
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D. Schall, D. Neumaier, M. Mohsin, B. Chmielak, J. Bolten, C. Porschatis, A. Prinzen, C. Matheisen, W. Kuebart, B. Junginger, W. Templ, A. L. Giesecke, and H. Kurz, “50 gbit/s photodetectors based on wafer-scale graphene for integrated silicon photonic communication systems,” ACS Photon. 1, 781–784 (2014).
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2013 (2)

X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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X. Wang, Z. Cheng, K. Xu, H. K. Tsang, and J.-B. Xu, “High-responsivity graphene/silicon-heterostructure waveguide photodetectors,” Nat. Photonics 7, 888–891 (2013).
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2012 (5)

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D 45, 113001 (2012).
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H. Vora, P. Kumaravadivel, B. Nielsen, and X. Du, “Bolometric response in graphene based superconducting tunnel junctions,” Appl. Phys. Lett. 100, 153507 (2012).
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J. C. W. Song, M. Y. Reizer, and L. S. Levitov, “Disorder-assisted electron-phonon scattering and cooling pathways in graphene,” Phys. Rev. Lett. 109, 106602 (2012).
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M. Freitag, T. Low, F. Xia, and P. Avouris, “Photoconductivity of biased graphene,” Nat. Photonics 7, 53–59 (2012).
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L. Lima, J. Diniz, I. Doi, and J. Godoy Fo, “Titanium nitride as electrode for MOS technology and Schottky diode: alternative extraction method of titanium nitride work function,” Microelectron. Eng. 92, 86–90 (2012).
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2011 (5)

J. Yan and M. S. Fuhrer, “Correlated charged impurity scattering in graphene,” Phys. Rev. Lett. 107, 206601 (2011).
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W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. F. Crommie, and A. Zettl, “Boron nitride substrates for high mobility chemical vapor deposited graphene,” Appl. Phys. Lett. 98, 242105 (2011).
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J. C. W. Song, M. S. Rudner, C. M. Marcus, and L. S. Levitov, “Hot carrier transport and photocurrent response in graphene,” Nano Lett. 11, 4688–4692 (2011).
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D. Basko, “A photothermoelectric effect in graphene,” Science 334, 610–611 (2011).
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G. Rao, M. Freitag, H.-Y. Chiu, R. S. Sundaram, and P. Avouris, “Raman and photocurrent imaging of electrical stress-induced p–n junctions in graphene,” Nano Lett. 5, 5848–5854 (2011).
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2010 (2)

E. C. Peters, E. J. H. Lee, M. Burghard, and K. Kern, “Gate dependent photocurrents at a graphene p-n junction,” Appl. Phys. Lett. 97, 193102 (2010).
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V. E. Dorgan, M.-H. Bae, and E. Pop, “Mobility and saturation velocity in graphene on SiO2,” Appl. Phys. Lett. 97, 082112 (2010).
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2009 (5)

Y.-J. Yu, Y. Zhao, S. Ryu, L. E. Brus, K. S. Kim, and P. Kim, “Tuning the graphene work function by electric field effect,” Nano Lett. 9, 3430–3434 (2009).
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Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
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T. Mueller, F. Xia, M. Freitag, J. Tsang, and P. Avouris, “Role of contacts in graphene transistors: a scanning photocurrent study,” Phys. Rev. B 79, 245430 (2009).
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X. Xu, N. M. Gabor, J. S. Alden, A. M. van der Zande, and P. L. McEuen, “Photo-thermoelectric effect at a graphene interface junction,” Nano Lett. 10, 562–566 (2009).
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F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
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2008 (5)

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92, 042116 (2008).
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L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
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H. E. Romero, N. Shen, P. Joshi, H. R. Gutierrez, S. A. Tadigadapa, J. O. Sofo, and P. C. Eklund, “N-type behavior of graphene supported on Si/SiO2 substrates,” ACS Nano 2, 2037–2044 (2008).
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J.-H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nat. Phys. 4, 377–381 (2008).
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K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
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2006 (1)

S. J. Koester, S. Member, J. D. Schaub, G. Dehlinger, and J. O. Chu, “Germanium-on-SOI infrared detectors for integrated photonic applications,” IEEE J. Sel. Top. Quantum Electron. 12, 1489–1502 (2006).
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2005 (1)

F. Fillot, T. Morel, S. Minoret, I. Matko, S. Maîtrejean, B. Guillaumot, B. Chenevier, and T. Billon, “Investigations of titanium nitride as metal gate material, elaborated by metal organic atomic layer deposition using TDMAT and NH3,” Microelectron. Eng. 82, 248–253 (2005).
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Abu-Taha, J.

J. Abu-Taha and M. Yazgi, “A 7 GHz compact transimpedance amplifier TIA in CMOS 0.18 µm technology,” Analog Integr. Circuits Signal Process. 86, 429–438 (2016).
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I. D. Sousa and L.-M. Achard, “The future of packaging with silicon photonics,” in Chip Scale Review (2016).

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J.-H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, “Charged-impurity scattering in graphene,” Nat. Phys. 4, 377–381 (2008).
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Akhavan, S.

J. E. Muench, A. Ruocco, M. A. Giambra, V. Miseikis, D. Zhang, J. Wang, H. F. Y. Watson, G. C. Park, S. Akhavan, V. Sorianello, M. Midrio, A. Tomadin, C. Coletti, M. Romagnoli, A. C. Ferrari, and I. Goykhman, “Waveguide-integrated, plasmonic enhanced graphene photodetectors,” Nano Lett. 19, 7632–7644 (2019).
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Akinwande, D.

D. Akinwande, C. Huyghebaert, C.-H. Wang, M. I. Serna, S. Goossens, L.-J. Li, H.-S. P. Wong, and F. H. L. Koppens, “Graphene and two-dimensional materials for silicon technology,” Nature 573, 507–518 (2019).
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Alden, J. S.

X. Xu, N. M. Gabor, J. S. Alden, A. M. van der Zande, and P. L. McEuen, “Photo-thermoelectric effect at a graphene interface junction,” Nano Lett. 10, 562–566 (2009).
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Amin, R.

Z. Ma, K. Kikunaga, H. Wang, S. Sun, R. Amin, R. Maiti, M. H. Tahersima, H. Dalir, M. Miscuglio, and V. J. Sorger, “Compact graphene plasmonic slot photodetector on silicon-on-insulator with high responsivity,” ACS Photon. 7, 932–940 (2020).
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Anderse, T. I.

Q. Ma, N. M. Gabor, T. I. Anderse, N. L. Nair, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, “Competing channels for hot-electron cooling in graphene,” Phys. Rev. Lett. 112, 247401 (2014).
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Andrei, E. Y.

J. Duan, X. Wang, X. Lai, G. Li, K. Watanabe, T. Taniguchi, M. Zebarjadi, and E. Y. Andrei, “High thermoelectricpower factor in graphene/hBN devices,” Proc. Natl. Acad. Sci. USA 113, 14272–14276 (2016).
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Ang, L. K.

K. J. A. Ooi, P. C. Leong, L. K. Ang, and D. T. H. Tan, “All-optical control on a graphene-on-silicon waveguide modulator,” Sci. Rep. 7, 12748 (2017).
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Anugrah, Y.

N. Youngblood, Y. Anugrah, R. Ma, S. J. Koester, and M. Li, “Multifunctional graphene optical modulator and photodetector integrated on silicon waveguides,” Nano Lett. 14, 2741–2746 (2014).
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R.-J. Shiue, Y. Gao, Y. Wang, C. Peng, A. D. Robertson, D. K. Efetov, S. Assefa, F. H. L. Koppens, J. Hone, and D. Englund, “High-responsivity graphene–Boron nitride photodetector and autocorrelator in a silicon photonic integrated circuit,” Nano Lett. 15, 7288–7293 (2015).
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X. Gan, R.-J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7, 883–887 (2013).
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J. Gosciniak, F. B. Atar, B. Corbett, and M. Rasras, “Plasmonic Schottky photodetector with metal stripe embedded into semiconductor and with a CMOS-compatible titanium nitride,” Sci. Rep. 9, 6048 (2019).
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K. Tielrooij, S. Castilla, B. Terres, M. Autore, L. Viti, J. Li, A. Nikitin, M. S. Vitiello, R. Hillenbrand, and F. H. L. Koppens, “Highly sensitive, ultrafast photo-thermoelectric graphene thz detector,” in 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2018), pp. 1–3.

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F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9, 780–793 (2014).
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M. Freitag, T. Low, F. Xia, and P. Avouris, “Photoconductivity of biased graphene,” Nat. Photonics 7, 53–59 (2012).
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G. Rao, M. Freitag, H.-Y. Chiu, R. S. Sundaram, and P. Avouris, “Raman and photocurrent imaging of electrical stress-induced p–n junctions in graphene,” Nano Lett. 5, 5848–5854 (2011).
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T. Mueller, F. Xia, M. Freitag, J. Tsang, and P. Avouris, “Role of contacts in graphene transistors: a scanning photocurrent study,” Phys. Rev. B 79, 245430 (2009).
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F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
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V. E. Dorgan, M.-H. Bae, and E. Pop, “Mobility and saturation velocity in graphene on SiO2,” Appl. Phys. Lett. 97, 082112 (2010).
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P. Ma, Y. Salamin, B. Baeuerle, A. Josten, W. Heni, A. Emboras, and J. Leuthold, “Plasmonically enhanced graphene photodetector featuring 100 Gbit/s data reception, high responsivity, and compact size,” ACS Photon. 6, 154–161 (2019).
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Y. Salamin, P. Ma, B. Baeuerle, A. Emboras, Y. Fedoryshyn, W. Heni, B. Cheng, A. Josten, and J. Leuthold, “100 GHz plasmonic photodetector,” ACS Photon. 5, 3291–3297 (2018).
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K.-J. Tielrooij, N. C. Hesp, A. Principi, M. B. Lundeberg, E. A. Pogna, L. Banszerus, Z. Mics, M. Massicotte, P. Schmidt, D. Davydovskaya, D. G. Purdie, I. Goykhman, G. Soavi, A. Lombardo, K. Watanabe, T. Taniguchi, M. Bonn, D. Turchinovich, C. Stampfer, A. C. Ferrari, G. Cerullo, M. Polini, and F. H. L. Koppens, “Out-of-plane heat transfer in van der Waals stacks through electron–hyperbolic phonon coupling,” Nat. Nanotechnol. 13, 41–46 (2018).
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Bao, Q.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
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D. Basko, “A photothermoelectric effect in graphene,” Science 334, 610–611 (2011).
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Baum, B. K.

J. A. Briggs, G. V. Naik, T. A. Petach, B. K. Baum, D. Goldhaber-Gordon, and J. A. Dionne, “Fully CMOS-compatible titanium nitride nanoantennas,” Appl. Phys. Lett. 108, 051110 (2016).
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L. Wang, P. Makk, S. Zihlmann, A. Baumgartner, D. I. Indolese, K. Watanabe, T. Taniguchi, and C. Schönenberger, “Mobility enhancement in graphene by in situ reduction of random strain fluctuations,” Phys. Rev. Lett. 124, 157701 (2020).
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K. Sun and A. Beling, “High-speed photodetectors for microwave photonics,” Appl. Sci. 9, 623 (2019).
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Bethge, O.

S. Schuler, D. Schall, D. Neumaier, L. Dobusch, O. Bethge, B. Schwarz, M. Krall, and T. Mueller, “Controlled generation of a p–n junction in a waveguide integrated graphene photodetector,” Nano Lett. 16, 7107–7112 (2016).
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Bie, Y.

Y. Lin, Q. Ma, P.-C. Shen, B. Ilyas, Y. Bie, A. Liao, E. Ergeçen, B. Han, N. Mao, X. Zhang, X. Ji, Y. Zhang, J. Yin, S. Huang, M. Dresselhaus, N. Gedik, P. Jarillo-Herrero, X. Ling, J. Kong, and T. Palacios, “Asymmetric hot-carrier thermalization and broadband photoresponse in graphene-2D semiconductor lateral heterojunctions,” Sci. Adv. 5, eaav1493 (2019).
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Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1. (a) On-chip photodetector structure. (b) Front view of the photodetector device.
Fig. 2.
Fig. 2. (a) Seebeck coefficient as a function of chemical potential. (b) Band diagram representing the doping profile across the graphene sheet; graphene is effectively p-doped by TiN. Black circles and white circles represent electrons and holes, respectively. Gr, graphene.
Fig. 3.
Fig. 3. (a) Optical power absorbed as a function of the photodetector length for the optimized waveguide geometry, and (b) effective absorption of graphene as a function of the photodetector length for the imported optimum mode at $\lambda = 1550 \;{\rm{nm}}$ . Data were extracted from power monitors in Lumerical FDTD for the structure that is shown in the inset.
Fig. 4.
Fig. 4. Carrier cooling rate and cooling length as a function of chemical potential for $\Delta = 60 \;{\rm{meV}}$ , $\Delta = 50 \;{\rm{meV}}$ , and $\Delta = 40 \;{\rm{meV}}$ .
Fig. 5.
Fig. 5. Graphene sheet resistance and mobility as a function of the chemical potential for $\Delta = 60 \;{\rm{meV}}$ , $\Delta = 50 \;{\rm{meV}}$ , and $\Delta = 40 \;{\rm{meV}}$ .
Fig. 6.
Fig. 6. Electrical conductivity of graphene and Seebeck coefficient as a function of the chemical potential for $\Delta = 40 \;{\rm{meV}}$ , $\Delta = 50 \;{\rm{meV}}$ , and $\Delta = 60\; {\rm{meV}}$ .
Fig. 7.
Fig. 7. Normalized temperature profiles for a varying chemical potential for high-disorder ( $\Delta = 60 \;{\rm{meV}}$ ) and low-disorder ( $\Delta = 40 \;{\rm{meV}}$ ) graphene sheets.
Fig. 8.
Fig. 8. Voltage and current responsivity of the photodetector as a function of the chemical potential for $\Delta = 40\; {\rm{meV}}$ , $\Delta = 50 \;{\rm{meV}}$ , and $\Delta = 60 \;{\rm{meV}}$ .
Fig. 9.
Fig. 9. (a) Maximum external current responsivity and coupling efficiency as a function of wavelength and (b) noise equivalent power (NEP) as a function of chemical potential for $\Delta = 40 \;{\rm{meV}}$ , $\Delta = 50 \;{\rm{meV}}$ , and $\Delta = 60 \;{\rm{meV}}$ .

Tables (1)

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Table 1. Performance Metrics and Features of On-Chip Graphene Photodetectors

Equations (23)

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V P T E = 0 x 0 S T c d x .
Φ B = Φ M X S ,
X S = Φ S ( E c E F ) ,
V P T E = ( S 1 S 2 ) Δ T , Δ T = T c T 0 ,
κ 2 T c x 2 + γ C ( T c T 0 ) = A G I ( x ) ,
σ = σ 0 ( 1 + μ 2 Δ 2 ) , σ 0 = 5 ( e 2 h ) ,
κ = π 2 k B 2 T 3 e 2 σ .
γ = b ( T + T 2 T ) ,
b = 2.2 g 2 ρ k B k F , T = T B G 0.43 k F ,
g = D 2 ρ s 2 , ρ = 2 μ π 2 v F 2 , k F = μ v F , k F = π σ e 2 , T B G = s k F k B .
C = π 2 k B 2 T 3 ρ .
ξ = κ γ C .
Δ T = T c ( x ) T 0 = ξ sinh ( ( x 0 | x | ) / ξ ) 2 cosh ( x 0 / ξ ) ( A G I ( x ) κ ) ,
S = π 2 k B 2 T 3 e 1 σ d σ d μ .
R G = w L σ 1 ( x ) ,
σ ~ ( ω , Γ , μ , T ) = σ ~ i n t r a ( ω , Γ , μ , T ) + σ ~ i n t e r ( ω , Γ , μ , T ) ,
σ ~ i n t r a ( ω , Γ , μ , T ) = j e 2 π 2 ( ω + j 2 Γ ) × 0 E ( f ( E ) E f ( E ) E ) d E ,
σ ~ i n t e r ( ω , Γ , μ , T ) = j e 2 ( ω + j 2 Γ ) π 2 × 0 f ( E ) f ( E ) ( ω + j 2 Γ ) 2 4 ( E / ) 2 d E ,
f ( E ) = ( e ( E μ ) / k B T + 1 ) 1 .
ϵ ~ = ϵ 0 χ ~ + j σ ~ ω .
α = 20 l o g 10 ( E f / E i ) ,
P a b s ( L ) = 1 10 2 ( α / 20 ) L .
N E P = V t h R v = 4 k B T R G R v ,

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