# High-Speed Optoelectronic Graphene Sampler at 1.55 µm Reaching Intrinsic Performances

Marin Tharrault, E. Grimaldi, Delphine Pommier, L. Hamidouche, P. Berger, S. Combrie, G. Baili, G. Baili, G. Baili, B Plaçais, et al.

► To cite this version:

Marin Tharrault, E. Grimaldi, Delphine Pommier, L. Hamidouche, P. Berger, et al. High-Speed Optoelectronic Graphene Sampler at 1.55 µm Reaching Intrinsic Performances. Advanced Electronic Materials, 2023, 9 (10), pp.2300260. 10.1002/aelm.202300260. hal-04785951

HAL Id: hal-04785951

https://hal.science/hal-04785951v1

Submitted on 15 Nov 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# High-Speed Optoelectronic Graphene Sampler at 1.55 µm Reaching Intrinsic Performances

M. Tharrault, E. Grimaldi, D. Pommier,* L. Hamidouche, P. Berger, S. Combrie, G. Baili, M. Rostischer, T. Taniguchi, K. Watanabe, B. Plaçais, E. Baudin, and P. Legagneux

Optoelectronic sampling is the ultimate method to perform ultra-high frequency analog-to-digital conversion. Thanks to the ps photo-thermo-bolometric effect in high mobility hexagonal boron nitride (h-BN) encapsulated graphene, a state-of-the-art optoelectronic sampler over a 40 GHz bandwidth using a 4 ps pulsed laser is demonstrated. The superior transport and optoelectronic linearities of this graphene sampler lead to very high harmonic rejections below –43 dB above 20 GHz. With a physics-based microscopic model, it is shown that harmonics are generated by optoelectronics saturation effects and only appear when carrier energy reaches that of optical phonons, which is very high in h-BN encapsulated graphene. This device is the first ultra-fast optoelectronic sampler based on the bolometric effect.

## 1. Introduction

Fast analog-to-digital converters (ADCs) are central in wireless communication and radar systems to transform radiofrequency (RF) signals into digital format. Demanding applications require high dynamic ADCs, which are limited to a few GHz, mainly due to non-linearity of components and jitter noise introduced by electrical clocks.[1–4] Therefore, the received signals at higher

frequency are first down converted to baseband and are then digitized. Sub-samplers based on a frequency comb allows performing this down-conversion operation at arbitrary high carrier frequency, but also requires low-jitter sources for high performances.

The rapid progress in low-jitter optical clocks[5,6] opened the possibility to perform optoelectronic sampling[7–13] with ultra-stable optical pulse trains having extremely low phase noise and jitter (generated by active mode-locked lasers). Optoelectronic subsampling of GHz and THz signals has been demonstrated with optical switches made of GaAs-based films grown at low-temperature[14–17] paving

the way for the efficient sampling of high-frequency signals. III-V semiconductor materials such as low temperature grown GaAs operating at either its optimal wavelength of 0.8 µm[15] or at 1.55 µm[16,17] are particularly studied. These studies highlighted that device linearity is crucial to mitigate harmonics generation, which introduces a parasitic signal in the sampling operation.

An efficient optoelectronic sampler requires simultaneously high-speed photodetection, fast carrier transport, and excellent linearity. It is one of the most demanding functions involving high-performance material and advanced theoretical modeling. Moreover, operating this optoelectronic sampler at 1.55 µm would give the opportunity of using all the already optimized photonic building blocks and integrated photonic platforms developed at this telecom wavelength.

Graphene fulfills all these requirements owing to its high carrier mobility,[18] broadband absorption,[19,20] low photocarrier lifetime and ultrasmall heat capacity.[21] Its properties have been exploited for high-frequency electronics[22–25] and photodetection.[26–29] Moreover, high frequency optoelectronic mixers have recently been demonstrated.[30,31]

The recent advances in boron nitride-encapsulated graphene provide nearly ballistic transport[32,33] where photodetection and optoelectronic mixing mechanisms approach the intrinsic limit.[34] Furthermore, compared to photoconductive switches, the ability to tune the Fermi energy allows determining the microscopic mechanism at play. In this article, we exploit the extraordinary properties of boron nitride-encapsulated graphene to demonstrate the first graphene-based optoelectronic sampler. Remarkably, we obtain state-of-the-art optoelectronic sampling, using a device based on bolometric effect.

M. Tharrault, M. Rostischer, B. Plaçais, E. Baudin
Laboratoire de Physique de l'Ecole normale supérieure

ENS
Université PSL, CNRS

Sorbonne Université
Université de Paris

24 rue Lhomond, Paris 75005, France

E. Grimaldi, D. Pommier, L. Hamidouche, P. Berger, S. Combrie, G. Baili,

P. Legagneux

Thales Research & Technology
Palaiseau 91767, France

E-mail: delphine.pommier@thalesgroup.com

T. Taniguchi, K. Watanabe
Advanced Materials Laboratory
National Institute for Materials Science

Tsukuba, Ibaraki 305-0047, Japan

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/aelm.202300260

© 2023 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/aelm.202300260
<figure><img src="image_3.png" /><figcaption>**Figure 1.** a) Picture of the graphene-based optoelectronic sampler with RF probes and lensed optical fiber. b) Experimental scheme: a 1.55 µm-lensed fiber fed by an active mode-locked laser illuminates the graphene channel embedded in a coplanar waveguide. RF probes allow both the injection of the high-frequency RF input signal along with DC channel biasing, and the measurement of the down-converted output RF signal. A Si backgate controls the graphene doping. c) Principle of optoelectronic subsampling: the optical clock signal (top panel) is mixed with the input RF signal (middle panel), generating harmonics in baseband (bottom panel, light blue area).</figcaption></figure>

We first present the operation principle of optoelectronic sampling and detail our sampler performances, featuring a 40 GHz bandwidth with harmonic rejection below -43 dB at 20 GHz. We then proceed with presenting the microscopic origin of ultrafast photodetection in graphene, explaining its extraordinary characteristics for optoelectronic sampling and its intrinsic limits, and demonstrating the harmonic rejections origins in graphene.

## 2. Results and Discussion

### 2.1. Optoelectronic Sampling Principle and Performances

The graphene-based optoelectronic sampler is made of a $L \times W = 3 \times 3 \mu m^2$ high-mobility graphene (28 000 cm$^2$.V$^{-1}$.s$^{-1}$) embedded into a 50 Ω-impedance coplanar waveguide (CPW) fabricated on 2 µm SiO$_2$/high-resistivity Si substrate, as sketched in Figure 1b (see Experimental Section for fabrication details). A lensed fiber fed by a 1.55 µm active mode-locked laser illuminates the graphene channel over a 2.5 µm-diameter spot with 4 ps-long optical pulses at a clock repetition rate of $f_{cl} = 4$ GHz. The input monochromatic RF signal is injected with a frequency $f_{RF} = 2 - 40$ GHz, a power $P_{RF} = 0$ dBm, and the down-converted output RF signal is measured in the baseband frequency range ($f < f_{cl} / 2 = 2$ GHz).

#### 2.1.1. Working Principle of Optoelectronic Subsampling

Down conversion in baseband is ensured by mixing a RF-signal and an optical frequency comb, via the photodetection process in graphene. The down-conversion efficiency is defined as the ratio $P_1/P_{RF}$ between the down-converted output RF-signal power $P_1$ at the intermediate frequency (e.g., $f_1 = f_{RF} - 2f_{cl}$ for the example shown in Figure 1c and the input RF-signal power $P_{RF}$.

Due to unavoidable device nonlinearities, spurious harmonics are also generated in baseband. In usual samplers, harmonics are generated by the device nonlinear electronic response. In contrast, our graphene-based sampler shows excellent linearity in electronic and optical responses.[35] so that non-linearities originate solely from the mixing process. Harmonics generation arises from the mixing of one tooth of the frequency comb at $k f_{cl}$ and of n times the microwave at $f_{RF}$:

$$I_{IF}^{(n)}[k f_{cl} - n f_{RF}] = \frac{1}{2^n} G_{ph}^{(n)}[f_{cl}] (V_{RF}[f_{RF}])^n \quad (1)$$

where $f_{IF}^{(n)} = |k f_{cl} - n f_{RF}| < f_{cl} / 2$ is the intermediate frequency of the harmonic converted in baseband, and the $1/2^n$ factor accounts for the $(n + 1)$ waves mixing. For instance, on Figure 1c, the 3rd harmonic results from the mixing of the optical comb and of 3 microwaves, and is downconverted to the frequency $f_{IF}^{(3)} = 3f_{RF} - 7f_{cl}$.

The nonlinear processes for the 2nd and 3rd harmonics can be conveniently represented as resulting from virtual electronic harmonics at $2f_{RF}$ and $3f_{RF}$, thus shown as dashed arrows in Figure 1c. These parasitic signals are detrimental to the subsampling performance, hence their suppression are sought, associated with low $P_2/P_1$ and $P_3/P_1$ rejections values.

#### 2.1.2. Subsampling Performances of Graphene-Based Sampler

In Figure 2a, the measured conversion efficiency $P_1/P_{RF}$ is shown as a function of $f_{RF}$. The graphene-based sampler presents an almost flat conversion efficiency up to 40 GHz, which corresponds to the cut-off of the 4 ps-optical pulses. Its step-like decrease originates from the drop of the comb power at high frequency.

As the input RF power is not converted to baseband during the off-cycle, the clock duty cycle limits the conversion efficiency.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Performances of the graphene optoelectronic sampler, for an average optical power $P_{opt} = 30$ mW and a RF power $P_{RF} = 0$ dBm. a) Conversion efficiency $P_1 / P_{RF}$ varying the input frequency $f_{RF}$. Mixing of laser comb teeth of decreasing power at high-frequency results in a staircase pattern. In inset: conversion efficiency as function of the average optical power for $f_{RF} = 20$ GHz, showing a linear evolution. b) 2nd and 3rd harmonic rejections $P_2 / P_1$ and $P_3 / P_1$ varying the input frequency $f_{RF}$. Rejections reach -43 dBm at 20 GHz.</figcaption></figure>

As $T_p = 4$ ps, this limit reaches $20 \log(T_p f_{cl}) = -36$ dB. The inset of Figure 2a shows the linear evolution of conversion efficiency with respect to average optical power for $f_{RF} = 20$ GHz. The corresponding second and third harmonic rejections ($P_2 / P_1$ and $P_3 / P_1$, respectively) are shown on Figure 2b. The parasitic signal is dominated by the 3rd harmonic over the whole investigated frequency range. Like the first harmonic, the third harmonic power decreases with frequency due to the finite optical pulse duration, but with a frequency cut-off at 40 GHz/3 ≈ 13 GHz.

## 2.2. Microscopic Origin of Photodetection and Optoelectronic Nonlinearities in Graphene

The heart of the graphene-based optoelectronic sampler relies on the photo-thermo-bolometric effect in doped graphene: the incoming optical power heats up the graphene electron gas, and as a consequence the channel conductance decreases. This bolo-

metric process is used in conventional room-temperature ultra-broadband photodetectors, but its µs-long thermalization time limits its application to slow devices. Comparatively, in graphene, thermalization occurs in only 1 ps, which allows reaching the 220 GHz switching speed.[34,36]

**Figure 3** schematizes the generation of a photocurrent: when the channel is illuminated at constant bias $V_{ch}$, the carrier temperature rise $\Delta T$ results in a current change, that we identify as the photocurrent $I_{ph}$. In the linear response regime under illuminated conditions, we have the relation:

$$I_{ph} = I_{ch}^{light} - I_{ch}^{dark} \approx \frac{\partial I_{ch}}{\partial T} \Delta T \quad (2)$$

The source of non-linearity lies thus in the DC response of the graphene channel $I_{ch}(V_{ch})$, and requires understanding the microscopic phenomena at play.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Microscopic origin of the photocurrent in graphene. a) DC response $I_{ch}(V_{ch})$ of the graphene channel for dark and illuminated conditions. Two domains are highlighted. For low $V_{ch}$ (green area), Coulomb scattering is dominant, thus under illumination carriers heating causes stronger scattering and the current decreases. At high $V_{ch}$ (blue area), phonon scattering is dominant. As it does not depend on the carrier temperature, the current under both illuminated and dark conditions saturates at the same value $I_{sat}$. b) A RF signal, drawn as a varying DC signal on the $I_{ch}(V_{ch})$ curve, is applied on the device, which results in c) a varying $I_{ch}$ signal. d) The difference between the dark and the illuminated current curves results in the photocurrent, which can be decomposed in the contributions of the different harmonics.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 4. Experimental validation of the photodetection microscopic model. a) DC $I_{ch}$ – $V_{ch}$ transfer curves of a high-mobility graphene field-effect transistor ($L \times W = 3 \times 3 \mu m$, mobility $\mu = 28 000 cm^2 V^{-1} s^{-1}$, $R_c = 130 \Omega$) for various gate voltages $V_G$ (color scalebar on the right, gate capacitance $C_G = 15.7 \mu F \cdot m^{-2}$). On the explored bias range, the onset of current saturation is almost invisible. Panel b) From this transport response, we predict the photocurrent $I_{ph} = -\alpha \frac{dI_{ch}}{dV_{ch}} V_{ch}$, where $\alpha = -4 \%$ is the relative photodetection sensitivity. Panel c) represents the measured photocurrent $I_{ph} = \frac{I_{ch}^{light} - I_{ch}^{dark}}{I_{ch}}$ as a function of bias and doping and shows excellent agreement with the expected behavior of panel (b). Insets of b,c) represents the saturation voltage as a function of $V_G$, as deduced from transport (a and b), and experimental photoresponse (c) Voltage saturation $V_{sat} \approx I_{sat}/G_{ch}$ extracted using Equation 4. All data are obtained for an average optical power of 24 mW.</figcaption></figure>

At low bias, graphene current-to-voltage response follows Ohm's law (green region of Figure 3a). In this regime, carrier mobility is dominated by quasi-elastic scattering which is temperature-dependent. Indeed, a rise in temperature implies a reduced screening of Coulomb-like defects and thus inducing the thermobolometric effect. Conversely, at large bias (blue region in Figure 3a), conduction electrons reach saturation velocity $v_{sat}$. The saturation velocity microscopically originates from inelastic electron-optical phonon scattering[33,37] and is mostly temperature-independent. The corresponding saturation current reads $I_{sat} = W n e v_{sat}$, where n is the charge carrier density, and W is the transistor channel width. The I-V response in the dark and under illumination is schematically modeled in Figure 3a. This simplified model ignores interband tunneling and channel pinch-off effects at large bias,[33] as in practical situations the graphene sampler is always operated at low to moderate bias where these two effects are absent.

To understand the origin of photocurrent nonlinearity, we start from the low bias development of channel DC current up to third order in bias voltage, where we introduce a voltage saturation $V_{sat}$ that can be related to the previous saturation current through the device conductance $I_{sat} \approx G_{ch} V_{sat}$:

$$I_{ch} \approx G_{ch}^{(1)} V_{ch} \left( 1 - \frac{1}{2} \left( \frac{V_{ch}}{V_{sat}} \right)^2 \right) \approx G_{ch}^{(1)} V_{ch} \left( 1 - \frac{1}{2} \left[ \frac{G_{ch}^{(1)} V_{ch}}{I_{sat}} \right]^2 \right) \quad (3)$$

where $G_{ch}^{(1)}$ is the first order channel conductance term in the channel voltage expansion. Note that the channel current does not have any second order contribution with bias due to the symmetry of the configuration. The saturation current $I_{sat}$ being independent of the temperature, the only temperature dependence of $I_{ch}$ lies in the term $G_{ph}^{(1)}$. One can therefore rewrite Equation 2 as:

$$I_{ph} \approx G_{ph}^{(1)} \frac{\partial I_{ch}}{\partial G_{ch}^{(1)}} \approx G_{ph}^{(1)} V_{ch} \left( 1 - \frac{3}{2} \left[ \frac{G_{ch}^{(1)} V_{ch}}{I_{sat}} \right]^2 \right) \quad (4)$$

with $G_{ph}^{(1)}$ the first photoconductance order in channel voltage. In addition to explain the amplitude of the photodetection efficiency

(see Ref. [34] for a detailed discussion), Equation 4 reveals that the cause of the photodetection nonlinearity lies solely in the nonlinear DC response of the transistor.

In Figure 4, we confront our photo-thermo-bolometric model to experimental results. The channel current-voltage response is represented in Figure 4a varying the gate voltage. The drain-bias voltage is corrected to express the voltage across the channel $V_{ch}$ de-embedded from contact resistances (see Section S1, Supporting Information). We model the low-bias photoconductance with a simple law $G_{ph}^{(1)} = \alpha G_{ch}^{(1)}$, with an experimentally inferred relative sensitivity of the photodetection mechanism $\alpha = -4 \%$ (linear in optical power as demonstrated in Figure 2a inset, in this case 24 mW). Using Equations 3 and 4 an expression for the photocurrent can be derived more details in Section S2, Supporting Information):

$$I_{ph} \approx \alpha \frac{\partial I_{ch}}{\partial V_{ch}} V_{ch} \quad (5)$$

The photocurrent inferred from the DC I-V response of the transistor on Figure 4a with this relation is drawn in Figure 4b. It can be compared with the experimental photocurrent on Figure 4c. Despite being designed in the large doping limit, the model correctly captures the photocurrent amplitude,[38] even for low doping ($V_{CNP} = -194V < V_G < -100V$, SI-1). In particular the saturation behavior of photoconductance is remarkably predicted, with an absolute accuracy on saturation voltage $V_{sat} \approx I_{sat}/G_{ch}$ better than 8%. In Section S2 (Supporting Information), we additionally show that the saturation current is well captured by the optical-phonon velocity saturation model.[33]

In conclusion, our model allows predicting the photocurrent generation in graphene from the DC behavior of the device and the illuminated/dark current ratio. It also accurately predicts the non-linear photoresponse arising from optical phonon saturation in graphene, responsible for rejections generation and intrinsically limiting the device performances.

## 2.3. Parasitic Harmonics Generation Mechanisms

As pictured in Figure 2, the 3rd order rejection dominates the 2nd order rejection. We will show that 3rd order rejection is
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Comparison between the projected performances of high-speed optoelectronic sampling inferred from DC photoresponse of Figure 4 and measured performances. Top panels (a,b) are harmonics powers for fundamental $P_1/P_{RF}$ (red), and 3rd order $P_3/P_{RF}$ (blue), while bottom panels (c,d) are relative power rejection $P_3/P_1$. Left panels (a,c) compare projected (dots) and measured at 5 GHz (crosses) performances as a function of gate voltage for $P_{RF} = 0$ dBm, $P_{opt} = 24$ mW. In right panels (b,d) they are compared while varying optical input power at fixed gate voltage $V_G = 0$ V and RF input power $P_{RF} = -10$ dBm. The photocurrent data used for the projection from DC is measured on a range of drain-source voltage $V_{DS} \in [-20 \text{ mV}, 20 \text{ mV}]$, corresponding to RF powers reaching typically 0 dBm.</figcaption></figure>

intrinsically related to phonon-limited current saturation. In this case, the photoresponse nonlinearity quantitatively predicts the 3rd harmonics rejection. In contrast, 2nd order rejection is instrumental and relates to the device and setup asymmetry, and can consequently be controlled and cancelled using appropriate biasing.

### 2.3.1. Third-Order Harmonic Rejection

Let us first show that the DC response seamlessly predicts the RF high-frequency harmonic generation, because of graphene photodetection ultrafast response time.

The harmonics rejections powers can be predicted from the DC photocurrent-voltage polynomial decomposition following Equation 1 (procedure detailed in Section S3, Supporting Information). The high frequency nature of the third harmonic generation can be verified by comparing the reconstituted $P_1$ and $P_3$ harmonics and their corresponding rejections on **Figure 5** to the ones measured by sampling at 5 GHz. Projected harmonics from DC differ up to 5 dB from measured ones, and rejections are at most 2 dB apart. In Figure 5c, deviation occur close to the charge neutrality point (around -194 V, SI-1), where photocreated carriers start to compete with bolometric effect.[34,39] Importantly, the excellent model-experiment agreement over the whole investigated gate voltage range, where the saturation voltage features a four fold decrease (see insets of Figure 4), confirms the central role of the phonon-limited saturation as the third order rejection origin.

Finally, we propose a closed-form formula for the third order rejection function of the voltage saturation of the transistor (using Equation 4; Equation S7, Supporting Information):

$$ \frac{P_3}{P_1} = \frac{9}{4} \left( \frac{1}{(1 + 2G_{DS}Z_0)^2} \right)^2 \frac{P_{RF}^2}{(V_{sat}^2/Z_0)^2} \quad (6) $$

where $Z_0 = 50 \Omega$ is the line impedance. We can notice in particular that the 3rd order rejection is independent of the channel photoconductance $G_{ph}$. From this equation we can find[40] the dependency $P_3/P_1 \propto [P_1/Z_0(aI_{sat})^2]^{1/2} \propto 1/n_s^2$ in the carrier surface density $n_s$. To reduce the third rejection while keeping the same conversion efficiency $P_1/P_{RF}$, it is thus beneficial to seek the highly-doped regime, as already visible on Figure 5c.

It is interesting to compare the graphene optoelectronic sampler to common photoconductive optoelectronic samplers, for example, based on LT-GaAs. In the latter case, the saturation voltage is strongly reduced with increasing optical power[41] which both precludes to reproduce the simple analysis we developed for graphene, and sets a performance limit when the sampler is operated at large optical power.

### 2.3.2. Second-Order Harmonic Rejection

The second harmonic originates from device asymmetries, among which bias voltage and laser position play a crucial role. In contrast with third harmonic generation, its origin is extrinsic to the graphene channel which hinders the prediction of its amplitude, but enables its cancellation a posteriori by tuning the sampler working point.

The main source of second harmonic generation is the presence of drain-source bias as pictured in **Figure 6a,b.** Offsetting the input RF by a value of $V_{DS} = 0.2$ V rises the 2nd harmonic by about 30 dB. Setting a zero bias is thus crucial to insure good 2nd harmonic suppression. Residual asymmetries can even be compensated by a finer tuning of the bias: in the inset of Figure 6b, a bias of $V_{DS} = 5$ mV can lower the 2nd rejection by an extra 10 dB.
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Second harmonic generation mechanisms. a) Working principle of harmonics generation under voltage bias: the bias induces top-down asymmetries in the outgoing signal that differs whenever light is applied or not. This induces 2^nd^ order harmonic in the generated photocurrent. The scheme is pictured for constant light excitation, but is representative of the mixing phenomenon at high-frequency. b) Rise of the P_2 2^nd^ harmonic with the applied voltage bias V_DS amplitude. In inset: a finer tuning of the bias can lead to a further decrease of the 2^nd^ harmonic. Data has been measured at 5 GHz, with P opt = 24 mW, V G = 0 V and P RF = -10 dBm. c) Illustration of the effect of displacing the spot position. The relatively large spot size makes difficult to precisely center on the 3 × 3 µm channel. Apart from the active channel region, contacts act as junctions where generation of photovoltaic currents occurs. d) Modulation of the 2^nd^ harmonic when displacing the spot position along the channel. The grey region corresponds to the active channel area. Data taken at 5 GHz for P opt = 24 mW, V G = -30 V, and P RF = 0 dBm.</figcaption></figure>

Another source of asymmetry can be revealed by displacing the spot position (already explored in Ref. [41]). The contacts act as a junction where the high electric fields can lead to carriers creation and separation, leading to extra photovoltaic currents, as pictured on Figure 6c. Hence, displacing the spot position along the channel modulates the 2^nd^ harmonic, whose variation is shown on Figure 6d. It can be noticed that its minimal value is not reached for a spot centered on the sampler channel (corresponding to the

grey area on the plot), but at another position. This means that further thermoelectric effects are present in the device, leading as well to P_2 generation.

Nevertheless as detailed earlier a fine tuning of the voltage bias can suppress the second harmonic. At this point the rejections being dominated by the third harmonic, the understanding and tailoring of the graphene sampler saturation is the tipping point for device optimization.

<table><caption>**Table 1.** Comparison with state-of-the-art optoelectronic samplers based on LT-GaAs.[15,16] λ opt is the optical wavelength, f cl the clock frequency, T p the pulse width, P RF the RF power, f RF the RF frequency, τ the carrier lifetime, and P opt the optical power. Measured conversion efficiency (Meas.) P 1 / P RF is compared to the maximum conversion efficiency limited by the clock duty cycle (Max), from which the corresponding ratio (Meas./Max) is derived. The last columns report the measured rejections ratios of 2^nd^ (P 2 / P 1 ) and 3^rd^ (P 3 / P 1 ) harmonics.</caption><thead><tr><th rowspan="2">Work units</th><th rowspan="2">Material</th><th rowspan="2">λ<sub>opt</sub> [μm]</th><th rowspan="2">f<sub>cl</sub> [GHz]</th><th rowspan="2">T<sub>p</sub> [ps]</th><th rowspan="2">P<sub>RF</sub> [dBm]</th><th rowspan="2">f<sub>RF</sub> [GHz]</th><th rowspan="2">τ [ps]</th><th rowspan="2">P<sub>opt</sub> [mW]</th><th colspan="3">Efficiency P<sub>1</sub>/P<sub>RF</sub></th><th rowspan="2">P<sub>2</sub>/P<sub>1</sub> [dBc]</th><th rowspan="2">P<sub>3</sub>/P<sub>1</sub> [dBc]</th></tr><tr><th>Meas. [dB]</th><th>Max [dB]</th><th>Ratio [dB]</th></tr></thead><tbody><tr><td rowspan="2">[15]</td><td rowspan="2">LT-GaAs</td><td rowspan="2">0.8</td><td rowspan="2">2</td><td rowspan="2">7</td><td>5.7</td><td>20</td><td rowspan="2">10</td><td rowspan="2">25</td><td>-48</td><td>-37</td><td>-11</td><td>-43</td><td>-31</td></tr><tr><td>12</td><td>5.8</td><td>-41</td><td>-4</td><td>-53</td><td>-26</td></tr><tr><td>[16]</td><td>LT-GaAs</td><td>1.55</td><td>1</td><td>1.5</td><td>[-20,+5]</td><td>67</td><td>0.5</td><td>30</td><td>-65</td><td>-56</td><td>-9</td><td>/</td><td>/</td></tr><tr><td rowspan="2">This work</td><td rowspan="2">hBN/Gr/hBN</td><td rowspan="2">1.55</td><td rowspan="2">4</td><td rowspan="2">4</td><td>0</td><td>20</td><td rowspan="2">&lt;1</td><td rowspan="2">30</td><td>-47</td><td>-36</td><td>-11</td><td>-53</td><td>-43</td></tr><tr><td>5.8</td><td>-52</td><td>-21</td></tr></tbody></table>
## 2.4. Comparisons with Subsampling Made on LT-GaAs

We show that our hBN-encapsulated sampler features competitive performances with state-of-the-art LT-GaAs based samplers. High-linearity and ultrafast optoelectronic mechanisms in graphene make it particularly suitable for high-rejections and high-frequency applications.

In Table 1, we compare the performances of our graphene-based sampler to those based on LT-GaAs.[15,16] The ratio between the measured efficiency and the corresponding maximum conversion efficiency limited by the clock duty cycle quantifies the intrinsic efficiency. Graphene sampler measured efficiency is better than LT-GaAs sampler at $\lambda_{opt} = 1.55$ µm and similar at 0.8 µm. Moreover at high-frequency (20 GHz) it outperforms the LT-GaAs sampler in terms of harmonics rejections in its optimal working conditions at 0.8 µm.

The choice of a 7 ps pulse width laser comb for the LT-GaAs sampler at 0.8 µm inducing a cutoff frequency at 25 GHz is particularly suitable, it highly suppresses the rejections generation while preserving the conversion efficiency.[42] The graphene sampler performances at 20 GHz would as well benefit from such a laser pulse width, leading to even greater rejections reduction.

In addition, LT-GaAs high frequency samplers require a short photocarrier lifetime made possible by increasing the defect density at the expense of reduced efficiency. This is illustrated by the device of Ref. [16] which operates at 67 GHz owing to its 0.5 ps carrier lifetime. In contrast, graphene has an intrinsically low photocarrier lifetime (≈ 1 ps) and is therefore already compatible with frequencies up to 220 GHz.[34,36]

Finally, reduced spatial and power footprint can be easily reached by using the large absorption of an integrated photonic circuit configuration (45%)[43] instead of free space coupling of graphene to the pulsed excitation (≈ 1%).[44]

## 3. Conclusion

We reported the first demonstration of a graphene-based sampler, operating at the telecom wavelength of 1.55 µm, and featuring a 40 GHz bandwidth with conversion efficiency ratio of -11 dB and harmonic rejection below -43 dB at 20 GHz. This device is competitive with state-of-the-art LT-GaAs based samplers. Its performances rely on an hBN encapsulated channel design providing intrinsic graphene performances, among which superior linearity and high-frequency photodetection based on picosecond photo-thermo-bolometric effect. Our analysis showed that our optoelectronic sampler performances, in particular the dominant third order rejection, reaches hBN-encapsulated graphene intrinsic limits set by the optical phonon-induced saturation velocity.

This work opens the possibility to engineer and optimize graphene samplers, in particular, we showed that controlling graphene doping is beneficial both for the mixing efficiency and rejection damping. We showed that second order rejection originates from device asymmetries and can be suppressed using a small DC bias. In addition, we have seen that careful choice of the optical laser comb for a given frequency range would enable optimized rejections. The next step is to integrate such graphene sampler on a silicon photonic wafer. Indeed, coupling graphene to an optical waveguide increases its optical absorption by 2 orders of magnitude.

This will allow to reduce optical power and/or to improve further the conversion efficiency.

## 4. Experimental Section

*Device Fabrication:* Contacts made of Cr/Au (5/100 nm) connect the graphene channel to the CPW signal line. The high mobility was obtained by encapsulating the graphene between two hexagonal-boron nitride flakes, as described in Ref. [32]. More details on the sample fabrications are given in Ref. [34].

*Sampling Measurements:* A lensed fiber fed by a 1.55 µm active mode-locked laser illuminates the graphene channel over a 2.5 µm-diameter spot with 4 ps-long optical pulses at a clock repetition rate of $f_{cl} = 4$ GHz. The average optical power $P_{opt}$ is controlled using an optical powermeter (Thorlabs S132C), and could be varied up to 37 mW. Apart from Figure 2a inset, all measures were conducted with optical powers of 24 – 30 mW to maximize efficiency. The RF power is controlled using a Rohde & Schwarz VNA (ZVA 67) whose losses from the input and output RF cables have been compensated. Sampling harmonics expressed at 5 GHz in Figures 5 and 6 were averaged from the frequency window [4.75 GHz – 5.25GHz].

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

The authors acknowledge the financial support from the European Union's Horizon program under grant agreement no. 785219 (Core2) and no. 881603 (Core3) Graphene Flagship.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Keywords

bolometer, field effect transistors, graphene, optoelectronics

Received: April 18, 2023

Revised: June 9, 2023

Published online: July 10, 2023

[1] R. H. Walden, *IEEE J. 1999*, **17**, 539.

[2] A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popovic, J. Sun, G.-R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, F. X. Kärtner, *Opt. Express* **2012**, *20*, 4454.
[3] B. Jonsson, ADMS Design AB 2013, https://wwwsemanticscholar.org/paper/A-D-converter-performance-evolution-Jonsson/d75480e0d260278dd704acb654440225eb70c01?p2df (accessed: May 2023).

[4] B. Murmann, IEEE Solid-State Circuits Mag. 2015, 7, 58.

[5] P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O'Donnell, K. G. Ray, R. C. Williamson, *IEEE Trans. Microwave Theory Tech.* **2001**, *49*, 1840.

[6] G. C. Valley, *Opt. Express* **2007**, *15*, 1955.

[7] K. J. Weingarten, M. Rodwel, D. M. Bloom, *IEEE J. Quantum Electron.* **1988**, *24*, 198.

[8] D. H. Auston, *Appl. Phys. Lett.* **1975**, *26*, 101.

[9] R. Castagne, S. Laval, R. Laval, *Electron. Lett.* **1976**, *17*, 438.

[10] R. Lawton, J. Andrews, *Electron. Lett.* **1975**, *11*, 138.

[11] F. Leonberger, P. Moulton, *Appl. Phys. Lett.* **1979**, *35*, 712.

[12] B. Kolner, D. Bloom, *IEEE J. Quantum Electron.* **1986**, *22*, 79.

[13] T. Clark, J. Kang, R. Esman, *IEEE Photonics Technol. Lett.* **1999**, *11*, 1168.

[14] R. Horváth, J.-F. Roux, J.-L. Coutaz, J. Poette, B. Cabon, C. Graham, in *2017 Int. Conf. on Opt. Network Design and Modeling (ONDM)*, IEEE, Piscataway, NJ, USA **2017**, pp. 1–5.

[15] C. Tripon-Canseliet, M. Zegaoui, G. Jestin, C. Coinon, P. Berger, G. Baili, A. Descamps-Mandine, I. Maksimovic, D. Decoster, J. Hodé, D. Dolfi, J. Chazelas, *Electron. Lett.* **2016**, *52*, 237.

[16] M. Billet, Y. Desmet, F. Bavedila, S. Barbieri, W. Hänsel, R. Holzwarth, G. Ducournau, J.-F. Lampin, E. Peytavit, *Electron. Lett.* **2017**, *53*, 1596.

[17] M. Billet, Y. Desmet, F. Bavedila, S. Barbieri, W. Hänsel, R. Holzwarth, G. Ducournau, J. Lampin, E. Peytavit, in *2018 43rd Int. Conf. on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz)*, IEEE, Piscataway, NJ, USA **2018**, pp. 1–2.

[18] A. Schmitt, P. Vallet, D. Mele, M. Rosticher, T. Taniguchi, K. Watanabe, E. Bocquillon, G. Féve, J. Berroir, C. Voisin, J. Cayssol, M. O. Goerbig, J. Troost, E. Baudin, B. Plaçais, *Nat. Phys.* **2023**, *19*, 830.

[19] K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, T. F. Heinz, *Phys. Rev. Lett.* **2008**, *101*, 196405.

[20] A. C. Ferrari, F. Bonaccorso, V. Fal'Ko, K. S. Novoselov, S. Roche, P. Bøggild, S. Borini, F. H. Koppens, V. Palermo, N. Pugno, J. A. Garrido, R. Sordan, A. Bianco, L. Ballerini, M. Prato, E. Lidorikis, J. Kivioja, C. Marinelli, T. Ryhänen, A. Morpurgo, J. N. Coleman, V. Nicolosi, L. Colombo, A. Fert, M. Garcia-Hernandez, A. Bachtold, G. F. Schneider, F. Guinea, C. Dekker, M. Barbone, et al., *Nanoscale* **2015**, *7*, 4598.

[21] M. Massicotte, G. Soavi, A. Principi, K.-J. Tielrooij, *Nanoscale* **2021**, *13*, 8376.

[22] Y.-M. Lin, C. Dimitrakopoulos, K. A. Jenkins, D. B. Farmer, H.-Y. Chiu, A. Grill, P. Avouris, *Science* **2010**, *327*, 662.

[23] E. Pallecchi, C. Benz, A. Betz, H. v. Löhneysen, B. Plaçais, R. Danneau, *Appl. Phys. Lett.* **2011**, *99*, 113502.

[24] W. Wei, E. Pallecchi, S. Haque, S. Borini, V. Avramovic, A. Centeno, Z. Amaia, H. Happy, *Nanoscale* **2016**, *8*, 14097.

[25] L. Viti, A. R. Cadore, X. Yang, A. Vorobiev, J. E. Muench, K. Watanabe, T. Taniguchi, J. Stake, A. C. Ferrari, M. S. Vitiello, *Nanophotonics* **2021**, *10*, 89.

[26] F. Koppens, T. Mueller, P. Avouris, A. Ferrari, M. Vitiello, M. Polini, *Nat. Nanotechnol.* **2014**, *9*, 780.

[27] S. Schuler, D. Schall, D. Neumaier, L. Dobusch, O. Bethge, B. Schwarz, M. Krall, T. Mueller, *Nano Lett.* **2016**, *16*, 7107.

[28] D. Schall, C. Porschatis, M. Otto, D. Neumaier, *J. Phys. D: Appl. Phys.* **2017**, *50*, 124004.

[29] Z. Wang, A. Hemmetter, B. Uzlu, M. Saeed, A. Hamed, S. Kataria, R. Negra, D. Neumaier, M. C. Lemme, *Adv. Electron. Mater.* **2021**, *7*, 2001210.

[30] A. Montanaro, S. Mzali, J.-P. Mazellier, O. Bezencenet, C. Larat, S. Molin, L. Morvan, P. Legagneux, D. Dolfi, B. Dlubak, P. Seneor, M.-Bl. Martin, S. Hofmann, J. Robertson, A. Centeno, A. Zurutuza, *Nano Lett.* **2016**, *16*, 2988.

[31] A. Montanaro, W. Wei, D. De Fazio, U. Sassi, G. Soavi, P. Aversa, A. Ferrari, H. Happy, P. Legagneux, E. Pallecchi, *Nat. Commun.* **2021**, *12*, 2728.

[32] L. Banszerus, M. Schmitz, S. Engels, J. Dauber, M. Oellers, F. Haupt, K. Watanabe, T. Taniguchi, B. Beschoten, C. Stampfer, *Sci. Adv.* **2015**, *1*, e1500222.

[33] Q. Wilmart, M. Boukhicha, H. Graef, D. Mele, J. Palomo, M. Rosticher, T. Taniguchi, K. Watanabe, V. Bouchiat, E. Baudin, J.-M. Berroir, E. Bocquillon, G. Féve, E. Pallecchi, B. Plaçais, *Appl. Sci.* **2020**, *10*, 446.

[34] L. Hamidouche, A. Montanaro, M. Rosticher, E. Grimaldi, B. Poupet, T. Taniguchi, K. Watanabe, B. Plaçais, E. Baudin, P. Legagneux, ACS *photonics* **2020**, *8*, 369.

[35] Rejections resulting from electronic-only non-linearities at $2f_{RF}$ and $3f_{RF}$ have been measured to be below -50 dBc for the considered RF powers. Optical response linearity is treated thereafter in the inset of 2a.

[36] K. Yoshioka, T. Wakamura, M. Hashisaka, K. Watanabe, T. Taniguchi, N. Kumada, *Nat. Photonics* **2022**, *16*, 718.

[37] In hBN-encapsulated graphene, the relevant phonons for velocity saturation are the remote out-of-plane optical phonons of hBN, which have an energy of 0.1 eV.[33]

[38] It can be noted that the measured photocurrent features an offset at $V_{ds} = 0$ V for low doping, originating from carriers creation at device contacts acting as junctions (detailed in part 3.2).

[39] P. Huang, E. Riccardi, S. Messelot, H. Graef, F. Valmorra, J. Tignon, T. Taniguchi, K. Watanabe, S. Dhillon, B. Plaçais, R. Ferreira, J. Mangeney, *Nat. Commun.* **2020**, *11*, 863.

[40] Using Equation S7 (Supporting Information) again for $P_1$, the relation $G_{ph}^{(1)} = -\alpha G_{ch}^{(1)}$ and $I_{sat} \propto 1/\sqrt{n_S}$ from Equation S5 (Supporting Information) in the high doping regime.

[41] Y. Desmet, Theses, Université de Lille, **2018**, https://theses.hal.science/tel-03623290.

[42] See the reasoning of part 1.2, a 25 GHz cutoff on $P_1$ induces a 25 GHz/3–8 GHz cutoff on $P_3$.

[43] D. Schall, E. Pallecchi, G. Ducournau, V. Avramovic, M. Otto, D. Neumaier, in *Optical Fiber Communication Conference, Optica Publishing Group*, Washington, DC, USA **2018**, pp. M21–4.

[44] M. Romagnoli, V. Sorianello, M. Midrio, F. H. Koppens, C. Huyghebaert, D. Neumaier, P. Galli, W. Templ, A. D'Errico, A. C. Ferrari, *Nat. Rev. Mater.* **2018**, *3*, 392.