High-responsivity graphene photodetectors integrated on silicon microring resonators

Abstract

Graphene integrated photonics provides several advantages over conventional Si photonics. Single layer graphene (SLG) enables fast, broadband, and energy-efficient electro-optic modulators, optical switches and photodetectors (GPDs), and is compatible with any optical waveguide. The last major barrier to SLG-based optical receivers lies in the current GPDs’ low responsivity when compared to conventional PDs. Here we overcome this by integrating a photo-thermoelectric GPD with a Si microring resonator. Under critical coupling, we achieve >90% light absorption in a ~6 μm SLG channel along a Si waveguide. Cavity-enhanced light-matter interactions cause carriers in SLG to reach ~400 K for an input power ~0.6 mW, resulting in a voltage responsivity ~90 V/W, with a receiver sensitivity enabling our GPDs to operate at a 10⁻⁹ bit-error rate, on par with mature semiconductor technology, but with a natural generation of a voltage, rather than a current, thus removing the need for transimpedance amplification, with a reduction of energy-per-bit, cost, and foot-print.

Optical receivers based on graphene still suffer from low responsivity. Here, the authors integrate a photo-thermoelectric graphene photodetector with a Si micro-ring resonator, and obtain a voltage responsivity ~ 90 V/W and a reduction of energy-per-bit consumption, enabling performance on par with mature semiconductor technology.

Introduction

The same-chip integration¹ of active and passive optical components with electronics offers a cost- and energy-efficient solution for short- and long-reach optical interconnects^2,3. Single layer graphene (SLG) is an ideal material for integrated photonics^4,5, promising e.g. high-speed (>200 GHz)^6,7 and broadband (ultraviolet to far-infrared)^8,9 operation that could lift bandwidth (BW) (~100 GHz)^10,11 and spectral (<1600 nm)¹² limitations of existing technologies, such as Ge/Si^13,14 and InGaAsP/InP^15,16. A variety of waveguide (WG)-integrated SLG-based photonic devices have been reported^17–34, including electro-absorption (EAMs)^17–19 and electro-refraction modulators (ERMs)²⁰, optical switches^4,21, and photodetectors (GPDs)^22–33. SLG and layered materials can be integrated with passive Si photonic WGs^22–27 or any other passive WG technology⁴, including Si₃N₄^29,34,35, sapphire³⁶, Ge³⁷, and polymers^38,39, extending the spectral range and scope of possible applications^37,40.

SLG’s optical absorption is ~2.3% under normal incidence⁴¹, which limits the photoresponse in top-illuminated GPDs⁸. This can be increased in a WG configuration through the interaction with the evanescent field of the optical WG mode⁴². However, since the mode-overlap with SLG’s monatomic cross-section typically restricts absorption to ~0.01–0.1 dB/μm (~0.2–2%/μm)⁴, device lengths ~100 μm are needed for near-complete (>90%) absorption, with adverse effects on foot-print and capacitance⁷. The resulting trade-off between length and absorption has implications for GPDs that operate via the photo-thermoelectric effect (PTE)^43–45: Due to slow (~ps⁴⁶) heat dissipation to the lattice via phonon mediated cooling^46,47, photo-excitation leads to the formation of a hot-carrier distribution in SLG^8,43,44. The associated electron temperature, T_e, can be substantially above the lattice temperature, T₀⁴⁸, and leads to a photovoltage^43–45:

$$V_{\mathrm{PTE}}=\int S\left(x\right)\cdot \nabla T_e\left(x\right)\mathrm{d}x$$ 1

if both a T_e gradient and a spatially varying Seebeck coefficient, S, (controlled by the chemical potential, μ_c) are present⁴³. In order to achieve a high (>mV) V_PTE, it is better to absorb the incident electromagnetic energy over small (<10 μm) lengths, leading to localised electronic heating for a higher (~tens K) T_e and ∇ T_e(x).

Different approaches have been explored to increase and confine light absorption in free-space-coupled^49–51 and WG-integrated GPDs^26–29, e.g. by embedding SLG into optical cavities^50,51, slot WGs²⁶, plasmonic structures^28,29,31,49, or by enhancing the light-matter interaction using sub-wavelength structures²⁷, but these have coupling and propagation losses³¹, limitations in field enhancement^25,30, or in carrier mobility μ^26,32, fabrication flows incompatible with complementary metal-oxide-semiconductor (CMOS) processing^25,31,32, bias-induced dark currents^30,31, or a combination thereof^25,31,32. Thus, the demonstration of GPDs on photonic integrated circuits (PICs) that leverage SLG’s unique hot-carrier dynamics and maximise the voltage responsivity R_[V/W] = V_PTE/P_in, with P_in the incident optical power in the WG, is challenging.

Here, we report GPDs integrated on looped WGs, known as microring resonators⁵², which act as PIC-embedded resonant cavities. The conversion of incident light into an electrical signal occurs via the PTE effect. The GPDs directly generate a voltage, which allows us to operate them without bias and dark currents, limiting the GPD noise to thermal Johnson-noise, due to fluctuations of the carrier density⁵³. Other sources of noise, in particular low (~Hz-kHz) frequency contributions, such as 1/f and generation-recombination⁵⁴, are not relevant for bias-free high-speed PTE-GPDs operating in the GHz regime³³. This removes the need of transimpedance amplifiers (TIA) in the read-out electronics, with a reduction of the energy-per-bit cost and system foot-print. With R_[V/W] ~ 90 V/W, our GPDs pave the way towards SLG integration on Si photonic receivers, overcoming the limitation of photocurrent (I_ph) generating GPDs with current responsivities R_[A/W] = I_ph/P_in lower than mature Ge PDs^25,30,31. We attribute this to our high (>10⁴ cm²/Vs) μ, and the combination with the Si microring resonator giving a ~10-fold enhancement of electric field strength and >90% light absorption in just ~6 μm SLG on Si WGs.

Results

Device concept

Figure 1 a is a scheme of our GPDs, which comprise a layered materials heterostructure (LHM) of SLG and hexagonal boron nitride (hBN). To increase the generated V_PTE upon optical illumination according to Eq. (1), encapsulation of the SLG channel in hBN ensures a high (>10⁴ cm²/Vs) μ⁵⁵ for large (~200 μV/K) peak S²⁹, according to Mott’s formula^43,44:

$$S=-\frac{{\pi }^2{k}_{\mathrm{B}}^2{T}_e}{3e\sigma \left(\mu ,{\mu }_c\right)}\frac{\mathrm{d}\sigma \left(\mu ,{\mu }_c\right)}{\mathrm{d}{\mu }_c}$$ 2

where k_B is the Boltzmann constant, e the electron charge, σ = nμe the conductivity, and n the carrier concentration. Dual-gate SLG electrodes, separated from the LMH by an Al₂O₃ layer, are employed to tune S in adjacent regions of the device²⁶. The LMH is contacted on opposite sides and centrally aligned to the WG of a microring resonator fabricated on a Si-on-insulator (SOI) wafer. The resonator serves a two-fold purpose. First, the higher (compared to the bus WG) intra-cavity energy density⁵² results in ~10-fold enhanced light-matter interaction⁵⁶ and can enable near-complete light absorption in the SLG channel if its coverage of the resonator is optimised. Second, the wavelength, λ, selectivity of the resonator^56,57, makes the GPD suitable for wavelength division multiplexing (WDM)¹⁴, whereby the data rate of a single optical channel is increased by combining signals of different λ at the transmitter, and separating them at the receiver^58–60.

Fig. 1. Si ring resonator integrated GPD.

a Sketch of device. b Transmission spectra of a ring cavity with SLG on top, indicating the effects of varying W on ER and Q. For clarity, the spectra are aligned at the resonance wavelength closest to 1553.55 nm. c Corresponding transmission at resonance. The black line is the calculated transmission for κ = 10%. The coloured dots mark the transmission for various loss coefficients.

To find the SLG length, W, over the ring that enables maximum absorption inside the resonator, we perform an initial experiment on a reference microring cavity with identical parameters (WG thickness t_WG = 220 nm, WG width w_WG = 480 nm, ring radius R = 40 μm). Coupling to the resonator occurs through a 200 nm gap via a single bus WG, Fig. 1a, which has grating couplers (GCs) on either end, with coupling efficiency¹⁴ $\eta =P_{\mathrm{in}}/P_{\mathrm{fibre}}~$0.28, with $P_{\mathrm{fibre}}$ the optical power in the fibre connecting source and SOI chip, determined from transmission measurements on reference WGs on the same chip. The power coupling between these two structures depends on the coupling and transmission coefficients, i.e. the scattering matrix elements relating incoming and outgoing electric fields from the coupling region^56,57. The choice of the power coupling coefficient, κ, affects both the optical (frequency) bandwidth f_FWHM and the quality factor Q = f_FWHM/f_res, with f_res the resonance frequency⁵⁹ of the resonator, resulting in a trade-off between achievable extinction ratio (ER, defined as the ratio of minimum (at resonance) and maximum transmitted optical power⁵⁰), thus R_[V/W], and the maximum achievable electrical bandwidth, f_3dB. For our GPD, we select κ = 10% (with a measured optical (wavelength) bandwidth λ_FWHM ~ 150 pm at λ_res ~ 1.55 μm, corresponding to f_FWHM ~ 18.7 GHz. This, according to⁶¹:

$$f_{\mathrm{3dB}}=\sqrt{\sqrt{2}-1}\times f_{\mathrm{FWHM}}$$ 3

allows for f_3dB ~ 12 GHz in our design, sufficient for applications in data centre optical interconnects².

The wavelength-dependent transmitted power, P_trans, of a ring resonator can be written as⁵²:

$$P_{\mathrm{trans}}=P_{\mathrm{in}}\frac{\left(1-\kappa \right)+\xi -2\sqrt{\left(1-\kappa \right)\xi }\cos \left(\theta \right)}{1+\left(1-\kappa \right)\xi -2\sqrt{\left(1-\kappa \right)\xi }\cos \left(\theta \right)}$$ 4

where θ = 4π²Rn_eff/λ is the round-trip phase shift of the circulating mode and the effective mode index n_eff = β_m/k₀, with β_m the propagation constant of the mode, defined as the wavevector component along the WG, and k₀ the free-space wavevector^60,62. Omitting negligible losses caused by coupling between bus and ring, the term:

$$\xi =e^{-W{\alpha }_{\mathrm{SLG}}}{e}^{-2\pi R{\alpha }_{\mathrm{WG}}}$$ 5

describes the round-trip propagation loss in the ring, with α_SLG and α_WG, in dB/μm, the power attenuation coefficients in SLG and Si WG, respectively. When θ = 2πm (m = 1, 2, 3…), the light in the ring constructively interferes with itself and the cavity is in resonance⁵². From Eq. (4), the transmission drops to zero if ξ = 1 − κ. Under this so-called critical coupling⁵⁷, as the transmission approaches zero, maximum absorption inside the ring resonator is achieved. With all other parameters fixed in Eq. (5), changing the SLG-induced losses by changing W can therefore be used to tune ξ and achieve critical coupling.

Coupling and absorption optimisation

To find the optimum W, we first measure the transmission of an unloaded (no SLG, i.e. W = 0 μm) resonator by coupling light (continuous-wave (CW), TE-polarised) from a tunable laser (Newport TLB6700) into the bus WG, using an optical single-mode fibre, and measuring the transmitted power at the output GC as a function of λ, around one of the resonance peaks close to main Telecom wavelength at 1.55 μm, Fig. 1b. Due to SLG’s broadband absorption⁸, there will be identical behaviour for the other resonances, apart from a shift in P_in with GC response envelope¹⁴. The results, after calibration for the coupling losses, are shown by the dark-blue line and symbols in Figs. 1b, c, respectively. The microring resonator is not critically coupled at resonance for λ ~ 1553.55 μm, as P_trans does not vanish, but only part of the incident power is dissipated in the WG. From Eqs. (4), (5), α_WG ~ 1.4 dB/cm.

We then proceed to study the effect of SLG with varying W on the power dissipated in the resonator. We first place a W = 20 μm SLG flake, prepared by micro-mechanical cleavage (MC)⁶³ of bulk graphite, transferred using a micro-manipulator and a stamp consisting of polycarbonate (PC) and polydimethylsiloxane (PDMS), and cleaned by immersion in chloroform, over the ring, and measure the transmission as before. Using successive electron beam lithography (EBL, Raith e-LINE) runs to define a poly(methyl methacrylate) (PMMA) etch mask and reactive ion etching in O₂ to remove excess material, we then reduce W further in several steps down to 2.5 μm, with transmission measurements in between. The results, Figs. 1b, c, show an initial transmission decrease at resonance with decreasing W, before the trend is inverted as W tends to zero. The minimum transmission, indicating critical coupling, is for W = 6 μm. From Eq. (5) we extract α_G ~ 0.07 dB/μm, in agreement with measured¹⁷ and simulated⁴ values from literature. Using these and the comparison of the transmission curves for W = 6 μm, we estimate the fraction of absorbed light in the SLG channel to be ~92% under critical coupling. Figure 1b can also be used to monitor the effects of changing W on Q, as discussed in Supplementary Note 1. Supplementary Fig. 1 plots the degradation of Q as losses are increased with W. We further use Q^56,64 to confirm the absorption in our devices.

LMH characterisation

Based on these findings, we fabricate the GPD in Fig. 1a with W = 6 μm from a LMH (hBN encapsulated SLG as channel layer) on top of the ring resonator, as shown in Fig. 2 and described in Methods. A microscope image of hBN/SLG/hBN on the WG is in Fig. 3a. We perform Raman spectroscopy (Renishaw inVia at 514.5 nm, power <0.5 mW) and atomic force microscopy (AFM, Bruker Dimension Icon) to monitor the SLG quality. A typical Raman spectrum before further processing of the stack is in Fig. 3b. The position of the combined hBN E_2g peaks⁶⁵ from top and bottom flakes is Pos(E_2g) ~ 1366 cm⁻¹ with full-width half maximum, FWHM(E_2g) ~ 9.5 cm⁻¹, as expected considering the top flake is bulk and that the planar domain size in MC-produced hBN crystals is limited by the flake size^55,66. Pos(2D) ~ 2693 cm⁻¹, FWHM(2D) ~ 18 cm⁻¹, Pos(G) ~ 1583 cm⁻¹, FWHM(G) ~ 14 cm⁻¹, confirming the presence of SLG and low n < 10¹² cm⁻²⁶⁷. The area (A(2D)/A(G) ~ 10.7) and intensity (I(2D)/I(G) ~ 7.6) ratios indicate a Fermi level E_F < 100 meV^67–69.

Fig. 2. Device fabrication.

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

Fig. 3. LMH characterisation.

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

The AFM scan of the overlap region between LMH and microring in Fig. 3c shows blister-free SLG/hBN interfaces, confirming successful cleaning⁵⁵, apart from a bubble trapped in a cladding trench above the WG. The FWHM(2D) map in Fig. 3d, taken from a 20 × 30 μm² area in the centre of the LMH, shows a region with homogeneous (spread < 1 cm⁻¹) and narrow (≤18 cm⁻¹) FWHM(2D) and spots of increased (>21 cm⁻¹) FWHM(2D) that coincide with the blister position, as revealed by AFM. Based on these findings, we then select the channel position (marked red in Figs. 3a, c, d) to be in a blister-free region. The final device has an active area L × W ~ 2.5 × 6 μm². We use L ~ 2.5 μm, of the order of twice the cooling length L_cooling in SLG (~1 μm^25,70, related to electron thermal conductivity κ_e (see Methods) and interfacial heat conductivity Γ ~ 0.5–5 MWm⁻²K^−1 71,72, via $L_{\mathrm{cooling}}=\sqrt{{\kappa }_e/\mathrm{\Gamma }}$⁴⁴), to fully exploit the T_e profile with expected maximum at L/2^26,29, i.e. the WG centre.

Electrical characterisation

An image of the full GPD after fabrication, obtained by SEM, is in Fig. 4a, revealing a well-aligned WG, LMH, and split-gate structure. We first verify gate tunability of the SLG channel by measuring the drain-source current (I_DS) at a fixed drain-source voltage (V_DS) while varying the two gate-voltages. The resulting resistance map (Fig. 4b) shows a cross pattern, which confirms that four junction constellations (p-n, n-p, n-n, p-p) can be generated in the channel²⁶. In order to extract the contact resistance, R_contact, and μ from the GPD directly (rather than from a four-probe reference structure made from a second LMH), then used to estimate S, we utilize the measured transfer curve at homogenous channel doping in Fig. 4c and plot the device resistance as function of the inverse carrier concentration (1/n) for electron (Fig. 4e) and hole (Fig. 4f) doping. By fitting the linear part (as 1/n → 0) of these plots, as for ref. ⁷³, R_contact can be obtained from the intersection of the fit curve and y-axis, while the residual carrier concentration, n₀, is found from the intersection between the fit curve and a horizontal line through the maximum. Using these values, we then model the total device resistance as for ref. ²⁶: R_total = R_contact + $\frac{L}{W}\frac{1}{e\mu n}$, with $n=\sqrt{n_0^2+{\left[C_{\mathrm{ox}}/e\left(V_{\mathrm{G}}-V_{\mathrm{CNP}}\right)\right]}^2}$, where R_contact includes the contacts and the contribution from the ungated region, V_CNP is the gate voltage corresponding to the charge neutrality point (CNP, E_F = 0 meV), C_ox is the gate capacitance, and μ is used as a fit parameter. The original data (solid line) and the model (dashed line) are compared in Fig. 4c. We get R_contact ~ 400 Ω and ~530 Ω, as well as μ_e ~ 17, 700 cm²/Vs and μ_h ~ 11, 800 cm²/Vs for electrons (red lines) and holes (blue lines), respectively. This demonstrates a PIC-integrated, LMH-based PD with high (>10⁴ cm²/Vs) μ, while refs. ^25,74 used hBN encapsulation for alternative detection concepts.

Fig. 4. GPD characterisation.

a False-colour SEM image of our GPD, showing Cr/Au contacts (yellow), Si WG (green), contacted hBN/SLG/hBN (blue, dashed line under contacts), and SLG gates (red). Scale bar: 2 μm. b Resistance map demonstrating independent tunability of charge carrier concentration in the SLG channel via V_G1 and V_G2. c Electrical characterization at homogeneous channel doping (solid lines, measured data; dashed lines, model). d Calculated S based on the electrical data in c. e, f) Resistance vs. inverse carrier concentration for e electron and f hole doping. g Photoresponse at zero bias on resonance (λ = 1555.87 nm). h Frequency response. The 3-dB cutoff frequency, marked by intersecting dashed lines, is ~12 GHz.

Steady-state photoresponse

For optical characterisation, we first couple modulated light (ON-OFF) with a duty cycle of 50% from a tuneable laser source (Agilent 81680A) into the bus WG using an optical single-mode fibre. While varying the potential at the two gate electrodes (V_G1, V_G2), the photoresponse of the unbiased GPD (V_DS = 0 mV, to avoid dark currents impairing the noise performance) is recorded using a lock-in amplifier. Since the PTE effect as electromotive force is intrinsically best read-out as open circuit potential difference^4,75, we record the response as V_PTE, rather than measuring the resulting short-circuit photocurrent, which depends on external factors, such as R_contact. Figure 4g shows a photoresponsivity map measured on resonance at 1555.87 nm, from which we extract a maximum R_[V/W] ~ 90 V/W. The six-fold pattern, with the highest photoresponse for bipolar (p-n, n-p) junctions, and a sign-change across the diagonal (V_G1 = V_G2) for unipolar (n-n, p-p) junctions in the SLG channel, confirms that the PTE effect dominates the conversion of photons into electrical signal (rather than a photovoltaic conversion with a two-fold pattern in photovoltage over the same measurement range)^43,44. Our R_[V/W] outperforms the current state-of-the-art for waveguide-integrated PTE-GPDs, R_[V/W] ~ 3–12 V/W^25,29,33,76, by around one order of magnitude.

High-speed photoresponse

To determine the BW, we modulate CW light at 1555.87 nm from the same source using a commercial (Thorlabs LN05S-FC) intensity modulator (lithium niobate, f_3dB = 40 GHz) and couple it into the device. While tuning the modulation frequency of the external modulator, we monitor the GPD response with an electrical spectrum analyzer (Agilent PSX N9030A), while the gate bias (V_G1 = −0.5 V, V_G2 = −2.1 V) is set at an operating point where R_[V/W] is largest. This gives a 3-dB bandwidth ~12 GHz, Fig. 4h, as expected from the design of the passive photonic structure and the cavity-imposed limit calculated via Eq. (3).

Power and wavelength dependence

Figures 5a, b plot the wavelength dependence of optical transmission and photovoltage for V_G1 = 1 V, V_G2 = −1 V and various P_in. The maxima of the V_PTE traces match the resonance minima in P_trans, confirming the proportionality between the two, as SLG dominates absorption for our resonator-based PDs. This is also shown in Supplementary Note 2 and Supplementary Fig. 2, where we plot the estimated absorption and resulting V_PTE at low (<0.1 mW) P_in on a linear scale. The shift of the resonance and its asymmetry for higher P_in (>0.2 mW) are attributed to the power-dependent change of the effective refractive index of the Si WG through a thermo-optic effect^52,77. Extracting the power-dependent maxima in V_PTE allows us to estimate T_e at resonance, and plot the R_[V/W] power dependence.

Fig. 5. Wavelength and power dependence.

a Transmitted power for various P_in. b Photovoltage for a fixed gate voltage combination (V_G1 = 1 V, V_G2 = − 1 V) for various input powers (same color code as for the transmission in a). c T_e calculated from the photoresponse in b and S in Fig. 4d. d Power-dependent R_[V/W].

The junction carrier temperature, T_e,j, can be written as (see Methods):

$$T_{\mathrm{e,j}}=\sqrt{2∣\frac{V_{\mathrm{PTE}}}{{\zeta }_1-{\zeta }_2}∣+T_0^2}$$ 6

where T₀ = 294 K is the room temperature and ${\zeta }_{1,2}=\frac{{\pi }^2{k}_{\mathrm{B}}^2}{3e\sigma }\frac{\mathrm{d}\sigma }{\mathrm{d}ϵ}$ at ϵ = E_F, in analogy to Eq. (2). In order to estimate ζ_1,2, following the same method used to determine S in Fig. 4d, we use R_contact and μ as obtained from the electrical measurements at homogeneous channel doping. The resulting T_e extracted for different P_in is in Fig. 5c. The carriers reach T_e ~ 400 K for P_in ~ 0.6 mW, due to cavity-enhanced light-matter interaction. The T_e power dependence can be fitted by the heat equation^44,70, neglecting diffusive cooling through the contacts (see Methods):

$$T_{\mathrm{e},\mathrm{j}}={\left(\beta P_{\mathrm{IN}}+T_0^{\delta }\right)}^{\frac{1}{\delta }}$$ 7

with δ ~ 3⁷⁸ and β a fitting parameter.

The associated, power-dependent, R_[V/W] is in Fig. 5d. For small P_in (<0.2 mW), we get a constant R_[V/W]. For P_in > 0.2 mW we have sublinear scaling between V_PTE and P_in, giving a R_[V/W] drop according to $R_{\left[\mathrm{V}/\mathrm{W}\right]}\propto P_{\mathrm{in}}^{-1/3}$ due to the T_e dependence of the electronic heat capacity^78,79.

Discussion

In order to assess our GPD performance against non-SLG-based ones, where typically a photocurrent I_ph is generated¹⁴, we compare two representative optical receiver implementations: a conventional (i.e. non-SLG) system based on a wafer-scale, commercial, high-speed (>50 GHz) Ge photodiode with R_[A/W] ~ 0.5 A/W⁸⁰, and a receiver based on our GPD. In both systems the same amplifier is employed to obtain a >200 mV output voltage swing (V_OUT), as required for driving the subsequent clock and data recovery CMOS circuit. For simplicity we assume that the amplifier represents a capacitive load.

Our GPDs are based on the PTE effect, where an electromotive force directly provides a voltage, rather than a current^8,79. In case of Ge, an additional TIA is needed to convert the photocurrent into a voltage for further signal processing⁸¹. In the TIA we consider a feedback resistor R_F = (90 V/W)/(0.5 A/W) = 180 Ω, which assures the same V_OUT for same optical input power in both cases. Neglecting any noise other than thermal noise produced by R_F, we estimate for the conventional receiver a lower limit for the sensitivity ${\overline{P}}_{\mathrm{sens}}=Q{i}_{\mathrm{n}}/R_{\mathrm{[A/W]}}=12.6\mu$W ~ −19 dBm at a bit-error-rate (i.e. probability of false identification of a bit by the receiver decision circuit⁸²) BER = 10⁻⁹. We calculate the thermal noise current as i_n = $\sqrt{4k_{\mathrm{B}}\cdot T\cdot BW/R_{\mathrm{F}}}$ with BW = 12 GHz, as in our GPDs, and a Q factor (i.e. required signal-to-noise ratio to get a specific BER⁸³) ~6 from⁸² BER = $\frac{1}{2}\mathrm{erfc}\left(Q/\sqrt{2}\right)$. For our GPDs, we estimate ${\overline{P}}_{\mathrm{sens}}$=Qv_n/R_[V/W] ~ −16 dBm for same BER and BW, where v_n=$\sqrt{4k_{\mathrm{B}}\cdot T\cdot BW\cdot R_{\mathrm{G}}}$, and R_G ~ 800 Ω is the total device resistance. Thus, in contrast to previous reports of both PTE^{25–27,29,33,76} and non-PTE^30–32 GPDs for integrated photonics, ${\overline{P}}_{\mathrm{sens}}$ of our GPD-based receiver is on par with mature semiconductor technology, and could be further improved by reducing R_contact, which dominates the total device resistance, thus being the primary source of thermal noise. The natural generation of a voltage makes the need for a TIA obsolete, with a reduction of energy-per-bit cost and system foot-print.

In summary, we reported photo-thermoelectric GPDs, integrated on Si microring resonators. By tuning the SLG coverage on top of the resonator, we optimised the round-trip propagation losses inside the cavity to get critical coupling, achieving >90% light absorption in ~6 μm SLG. The resulting carrier heating on such compact lengths enables high peak T_e ~ 400 K in the GPDs. In combination with high (>10⁴ cm²/Vs) mobility, obtained by encapsulating the SLG channel in hBN, this allowed us to get R_[V/W] ~ 90 V/W. Our bias-free, Johnson-noise limited GPDs, with voltage output, are a more power-efficient alternative to state of the art commercial PDs used in optical interconnects. Hot-carrier effects in SLG can be exploited for receiver architectures where current-to-voltage conversion, traditionally performed by transimpedance amplifiers, can be bypassed for a reduction in energy-per-bit cost and system foot-print.

Methods

Sample fabrication

The LMH is made as follows⁵⁵: SLG and hBN flakes of different thicknesses (t_bottom ~ 3 nm, t_top ~ 20 nm) are prepared on Si/SiO₂ ($t_{{\mathrm{SiO}}_2}$ = 285 nm) by MC of bulk graphite (Graphenium) and hBN single crystals grown at high pressure and temperature as detailed in ref. ⁸⁴. The thickness of the bottom hBN, t_bottom, is chosen with the following trade-off: sufficiently thin (<5 nm) to ensure α_SLG (thus ξ) comparable to the initial experiment used to find W, but sufficiently thick (~nm) that high (>10⁴ cm²/Vs) μ is achieved, due to reduced (in comparison to SiO₂) carrier inhomogeneities, roughness, and charge impurities^55,85,86. A micro-manipulator and a PC/PDMS stamp are then used to pick up and stack the flakes at 50 °C (Fig. 2a). In order to clean the LMH interfaces, the target photonic chip is then heated to 180 °C⁵⁵, while we align the LMH to the Si WG. We then laminate the PC film onto the target substrate, pushing contamination blisters, formed at the SLG/hBN interfaces, out of the GPD channel region and placing the LMH on the WG, Fig. 2b.

After the PC film is dissolved in chloroform, we perform EBL (Raith EBPG 5200) to define the GPD channel geometry via a PMMA etch mask. To transfer this pattern to the LMH, we use two dry etching steps. First, to achieve etch selectivity between LMH and underlying photonic circuit, we use a reactive ion etcher (RIE, Plasma-Therm) with a forward radio frequency power ~80 W and an SF₆ flow ~80 sccm. As reported by ref. ⁸⁷, these conditions allow fast (>200 nm/min) etching of hBN, slow (<7 nm/min) etching of SiO₂, while SLG is not etched, serving as etch stop on the bottom hBN flake (Fig. 2c). We then expose the LMH to low power (3W) O₂ plasma to remove all excess SLG, leaving behind the fully shaped GPD channel (Fig. 2d). A second EBL step, electron beam evaporation (5nm Cr/50nm Au), and lift-off in acetone are then used to contact the exposed SLG channel edges (Fig. 2e). To fabricate the split-gate structure on top of the LMH, required to create a p-n juntion in the GPD channel, a transparent (at λ ~ 1.55 μm) conductor that does not affect ξ (thus W) is needed. A second layer of SLG, sufficiently high (~tens nm) above the WG to leave α_SLG unaltered, can be used for this. We therefore thermally evaporate 1nm Al as seed layer on the top hBN, and atomic layer deposit (ALD, Savannah) t_ox ~ 20 nm Al₂O₃ as additional gate dielectric and spacer between channel and gate electrodes (Fig. 2f). The combined thickness of the top-gate dielectric (t_top + t_ox) ensures both low (~2 V or less) gate biases at the operating point of the GPD and, from eigenmode Lumerical simulations, a change in α_SLG < 25%.

To ensure alignment between LMH and gate SLG, we transfer a continuous film of SLG, grown by chemical vapor deposition (CVD) on Cu, following the process described in ref. ⁸⁸, using a PMMA support membrane⁸⁹ on the SLG/Cu substrate. We etch Cu in ammonium persulfate, transfer the PMMA/SLG stack onto the photonic chip (Fig. 2g), and remove the PMMA by immersion in acetone. We then use two additional EBL steps, O₂ plasma etching, and electron beam evaporation, to define the SLG split-gate geometry (Fig. 2h) and fabricate metal contacts to these gates (Fig. 2i). Finally, we perform optical lithography on a laser writer (MicroTECH LW405) and wet etching in HF to get access to drain and source contact pads.

Temperature estimation

The junction T_e can be extracted from power-dependent photovoltage measurements. Rewriting Eq. (2) as S = ζT_e, where $\zeta =-\left({\pi }^2{k}_{\mathrm{B}}^2\right)/3e\sigma \mathrm{d}\sigma /\mathrm{d}ϵ$ at ϵ = E_F, and using this in Eq. (1), we get V_PTE = ∫S(x) ∇ T_e(x)dx = ∫ζ(x)T_e(x) ∇ T_e(x)dx. Integration over the p-n-junction gives $V_{\mathrm{PTE}}={\zeta }_1{\int }_{-\frac{L}{2}}^0{T}_{\mathrm{e}}\left(x\right)\frac{\mathrm{d}{T}_{\mathrm{e}}}{\mathrm{d}x}\mathrm{d}x+{\zeta }_2{\int }_0^{\frac{L}{2}}{T}_{\mathrm{e}}\left(x\right)\frac{\mathrm{d}{T}_{\mathrm{e}}}{\mathrm{d}x}\mathrm{d}x=\frac{{\zeta }_1-{\zeta }_2}{2}\left(T_{\mathrm{e,j}}^2-T_0^2\right)$. From this, we extract the junction T_e from the measured photovoltage as T_e,j=$\sqrt{2∣\frac{V_{\mathrm{PTE}}}{{\zeta }_1-{\zeta }_2}∣+T_0^2}$. In the most general case, the T_e profile can be calculated from the heat equation^44,70, including diffusive cooling through contacts and cooling through the phonon bath: $\frac{\mathrm{d}q}{\mathrm{d}x}=-\frac{\mathrm{d}}{\mathrm{d}x}\left({\kappa }_{\mathrm{e}}\frac{\mathrm{d}}{\mathrm{d}x}{T}_{\mathrm{e}}\right)+\frac{{\kappa }_{\mathrm{e}}}{L_{\mathrm{cooling}}^2}\left(T_{\mathrm{e}}^{\delta }-T_{\mathrm{0}}^{\delta }\right)$, where $\frac{\mathrm{d}q}{\mathrm{d}x}$ describes the heating of the system. The electronic thermal conductivity is given by ${\kappa }_{\mathrm{e}}=\sigma {\mathcal{L}}_0{T}_{\mathrm{e}}$⁹⁰, with Lorenz number ${\mathcal{L}}_0$, while a $T_e^{\delta }$ dependence with δ ~ 3 is characteristic for SLG^70,91. Assuming the distance from the heat source to the heat sink larger than the cooling length (L_channel > 2L_cooling), the heat equation becomes $\frac{\mathrm{d}q}{\mathrm{d}x}=\frac{{\kappa }_{\mathrm{e}}}{L_{\mathrm{cooling}}^2}\left(T_{\mathrm{e}}^{\delta }-T_{\mathrm{0}}^{\delta }\right)$, with $\frac{\mathrm{d}q}{\mathrm{d}x}=\alpha P_{\mathrm{in}}/A$, αP_in the fraction of the absorbed power, and A the heated area. We thus get $T_{\mathrm{e,j}}={\left(\beta P_{\mathrm{in}}+T_0^{\delta }\right)}^{\frac{1}{\delta }}$, with β a fit parameter.

Author contributions

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

Data availability

Data supporting the findings of this study are available from the corresponding authors upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-021-23436-x.