### Machine idea

Determine 1 a is a scheme of our GPDs, which comprise a layered supplies heterostructure (LHM) of SLG and hexagonal boron nitride (hBN). To extend the generated *V*_{PTE} upon optical illumination in line with Eq. (1), encapsulation of the SLG channel in hBN ensures a excessive (>10^{4 }cm^{2}/Vs) *μ*^{55} for giant (~200 *μ*V/Okay) peak *S*^{29}, in line with Mott’s formulation^{43,44}:

$$S=-frac{{pi }^{2}{ok}_{{rm{B}}}^{2}{T}_{e}}{3esigma (mu ,{mu }_{c})}frac{{rm{d}}sigma (mu ,{mu }_{c})}{{rm{d}}{mu }_{c}}$$

(2)

the place *ok*_{B} is the Boltzmann fixed, *e* the electron cost, *σ* = *n**μ**e* the conductivity, and *n* the service focus. Twin-gate SLG electrodes, separated from the LMH by an Al_{2}O_{3} layer, are employed to tune *S* in adjoining areas of the system^{26}. The LMH is contacted on reverse 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 objective. First, the upper (in comparison with the bus WG) intra-cavity power density^{52} leads to ~10-fold enhanced light-matter interplay^{56} and may allow near-complete mild absorption within the SLG channel if its protection of the resonator is optimised. Second, the wavelength, *λ*, selectivity of the resonator^{56,57}, makes the GPD appropriate for wavelength division multiplexing (WDM)^{14}, whereby the info price of a single optical channel is elevated by combining alerts of various *λ* on the transmitter, and separating them on the receiver^{58,59,60}.

To search out the SLG size, *W,* over the ring that permits most absorption contained in the resonator, we carry out an preliminary experiment on a reference microring cavity with similar parameters (WG thickness *t*_{WG} = 220 nm, WG width *w*_{WG} = 480 nm, ring radius *R* = 40 *μ*m). Coupling to the resonator happens by a 200 nm hole through a single bus WG, Fig. 1a, which has grating couplers (GCs) on both finish, with coupling effectivity^{14 }(eta ={P}_{{rm{in}}}/{P}_{{rm{fibre}}} sim)0.28, with ({P}_{{rm{fibre}}}) the optical energy within the fibre connecting supply and SOI chip, decided from transmission measurements on reference WGs on the identical chip. The facility coupling between these two buildings is dependent upon the coupling and transmission coefficients, i.e. the scattering matrix components relating incoming and outgoing electrical fields from the coupling area^{56,57}. The selection of the energy coupling coefficient, *κ*, impacts each the optical (frequency) bandwidth *f*_{FWHM} and the standard issue Q = *f*_{FWHM}/*f*_{res}, with *f*_{res} the resonance frequency^{59} of the resonator, leading to a trade-off between achievable extinction ratio (ER, outlined because the ratio of minimal (at resonance) and most transmitted optical energy^{50}), thus *R*_{[V/W]}, and the utmost achievable electrical bandwidth, *f*_{3dB}. For our GPD, we choose *κ* = 10% (with a measured optical (wavelength) bandwidth *λ*_{FWHM} ~ 150 pm at *λ*_{res} ~ 1.55 μm, comparable to *f*_{FWHM} ~ 18.7 GHz. This, in line with^{61}:

$${f}_{{rm{3dB}}}=sqrt{sqrt{2}-1}instances {f}_{{rm{FWHM}}}$$

(3)

permits for *f*_{3dB} ~ 12 GHz in our design, adequate for purposes in knowledge centre optical interconnects^{2}.

The wavelength-dependent transmitted energy, *P*_{trans}, of a hoop resonator could be written as^{52}:

$${P}_{{rm{trans}}}={P}_{{rm{in}}}frac{(1-kappa )+xi -2sqrt{(1-kappa )xi }cos (theta )}{1+(1-kappa )xi -2sqrt{(1-kappa )xi }cos (theta )}$$

(4)

the place *θ* = 4*π*^{2}*R**n*_{eff}/*λ* is the round-trip part shift of the circulating mode and the efficient mode index *n*_{eff} = *β*_{m}/*ok*_{0}, with *β*_{m} the propagation fixed of the mode, outlined because the wavevector part alongside the WG, and *ok*_{0} the free-space wavevector^{60,62}. Omitting negligible losses brought on by coupling between bus and ring, the time period:

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

(5)

describes the round-trip propagation loss within the ring, with *α*_{SLG} and *α*_{WG}, in dB/*μ*m, the facility attenuation coefficients in SLG and Si WG, respectively. When *θ* = 2*π**m* (*m* = 1, 2, 3…), the sunshine within the ring constructively interferes with itself and the cavity is in resonance^{52}. From Eq. (4), the transmission drops to zero if *ξ* = 1 − *κ*. Underneath this so-called vital coupling^{57}, because the transmission approaches zero, most absorption contained in the ring resonator is achieved. With all different parameters mounted in Eq. (5), altering the SLG-induced losses by altering *W* can subsequently be used to tune *ξ* and obtain vital coupling.

### Coupling and absorption optimisation

To search out the optimum *W*, we first measure the transmission of an unloaded (no SLG, i.e. *W* = 0 *μ*m) resonator by coupling mild (continuous-wave (CW), TE-polarised) from a tunable laser (Newport TLB6700) into the bus WG, utilizing an optical single-mode fibre, and measuring the transmitted energy on the output GC as a operate of *λ*, round one of many resonance peaks near essential Telecom wavelength at 1.55 *μ*m, Fig. 1b. As a consequence of SLG’s broadband absorption^{8}, there will likely be similar behaviour for the opposite resonances, other than a shift in *P*_{in} with GC response envelope^{14}. The outcomes, after calibration for the coupling losses, are proven by the dark-blue line and symbols in Figs. 1b, c, respectively. The microring resonator isn’t critically coupled at resonance for *λ* ~ 1553.55 *μ*m, as *P*_{trans} doesn’t vanish, however solely a part of the incident energy is dissipated within the WG. From Eqs. (4), (5), *α*_{WG} ~ 1.4 dB/cm.

We then proceed to check the impact of SLG with various *W* on the facility dissipated within the resonator. We first place a *W* = 20 *μ*m SLG flake, ready by micro-mechanical cleavage (MC)^{63} of bulk graphite, transferred utilizing 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 earlier than. Utilizing successive electron beam lithography (EBL, Raith e-LINE) runs to outline a poly(methyl methacrylate) (PMMA) etch masks and reactive ion etching in O_{2} to take away extra materials, we then scale back *W* additional in a number of steps right down to 2.5 *μ*m, with transmission measurements in between. The outcomes, Figs. 1b, c, present an preliminary transmission lower at resonance with reducing *W*, earlier than the pattern is inverted as *W* tends to zero. The minimal transmission, indicating vital coupling, is for *W* = 6 *μ*m. From Eq. (5) we extract *α*_{G} ~ 0.07 dB/*μ*m, in settlement with measured^{17} and simulated^{4} values from literature. Utilizing these and the comparability of the transmission curves for *W* = 6 *μ*m, we estimate the fraction of absorbed mild within the SLG channel to be ~92% below vital coupling. Determine 1b will also be used to observe the results of adjusting *W* on *Q*, as mentioned in Supplementary Be aware 1. Supplementary Fig. 1 plots the degradation of *Q* as losses are elevated with *W*. We additional use *Q*^{56,64} to verify the absorption in our gadgets.

### LMH characterisation

Based mostly on these findings, we fabricate the GPD in Fig. 1a with *W* = 6 *μ*m from a LMH (hBN encapsulated SLG as channel layer) on high of the ring resonator, as proven in Fig. 2 and described in Strategies. A microscope picture of hBN/SLG/hBN on the WG is in Fig. 3a. We carry out Raman spectroscopy (Renishaw inVia at 514.5 nm, energy <0.5 mW) and atomic drive microscopy (AFM, Bruker Dimension Icon) to observe the SLG high quality. A typical Raman spectrum earlier than additional processing of the stack is in Fig. 3b. The place of the mixed hBN E_{2g} peaks^{65} from high and backside flakes is Pos(*E*_{2g}) ~ 1366 cm^{−1} with full-width half most, FWHM(*E*_{2g}) ~ 9.5 cm^{−1}, as anticipated contemplating the highest flake is bulk and that the planar area measurement in MC-produced hBN crystals is proscribed by the flake measurement^{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* < 10^{12} cm^{−2}^{67}. The realm (A(2D)/A(G) ~ 10.7) and depth (I(2D)/I(G) ~ 7.6) ratios point out a Fermi stage *E*_{F} < 100 meV^{67,68,69}.

The AFM scan of the overlap area between LMH and microring in Fig. 3c exhibits blister-free SLG/hBN interfaces, confirming profitable cleansing^{55}, other than a bubble trapped in a cladding trench above the WG. The FWHM(2D) map in Fig. 3d, taken from a 20 × 30 *μ*m^{2} space within the centre of the LMH, exhibits a area with homogeneous (unfold < 1 cm^{−1}) and slender (≤18 cm^{−1}) FWHM(2D) and spots of elevated (>21 cm^{−1}) FWHM(2D) that coincide with the blister place, as revealed by AFM. Based mostly on these findings, we then choose the channel place (marked pink in Figs. 3a, c, d) to be in a blister-free area. The ultimate system has an lively space *L* × *W* ~ 2.5 × 6 *μ*m^{2}. We use *L* ~ 2.5 *μ*m, of the order of twice the cooling size *L*_{cooling} in SLG (~1 *μ*m^{25,70}, associated to electron thermal conductivity *κ*_{e} (see Strategies) and interfacial warmth conductivity Γ ~ 0.5–5 MWm^{−2}Okay^{−1} ^{71,72}, through ({L}_{{rm{cooling}}}=sqrt{{kappa }_{e}/{{Gamma }}})^{44}), to completely exploit the *T*_{e} profile with anticipated most at *L*/2^{26,29}, i.e. the WG centre.

### Electrical characterisation

A picture of the total GPD after fabrication, obtained by SEM, is in Fig. 4a, revealing a well-aligned WG, LMH, and split-gate construction. We first confirm gate tunability of the SLG channel by measuring the drain-source present (*I*_{DS}) at a hard and fast drain-source voltage (*V*_{DS}) whereas various the 2 gate-voltages. The ensuing resistance map (Fig. 4b) exhibits a cross sample, which confirms that 4 junction constellations (p-n, n-p, n-n, p-p) could be generated within the channel^{26}. To be able to extract the contact resistance, *R*_{contact}, and *μ* from the GPD straight (relatively than from a four-probe reference construction produced from a second LMH), then used to estimate *S*, we make the most of the measured switch curve at homogenous channel doping in Fig. 4c and plot the system resistance as operate of the inverse service focus (1/*n*) for electron (Fig. 4e) and gap (Fig. 4f) doping. By becoming the linear half (as 1/*n* → 0) of those plots, as for ref. ^{73}, *R*_{contact} could be obtained from the intersection of the match curve and y-axis, whereas the residual service focus, *n*_{0}, is discovered from the intersection between the match curve and a horizontal line by the utmost. Utilizing these values, we then mannequin the full system resistance as for ref. ^{26}: *R*_{whole} = *R*_{contact} + (frac{L}{W}frac{1}{emu n}), with (n=sqrt{{n}_{0}^{2}+{left[{C}_{{rm{ox}}}/eleft({V}_{{rm{G}}}-{V}_{{rm{CNP}}}right)right]}^{2}}), the place *R*_{contact} consists of the contacts and the contribution from the ungated area, *V*_{CNP} is the gate voltage comparable to the cost neutrality level (CNP, *E*_{F} = 0 meV), *C*_{ox} is the gate capacitance, and *μ* is used as a match parameter. The unique knowledge (strong line) and the mannequin (dashed line) are in contrast in Fig. 4c. We get *R*_{contact} ~ 400 Ω and ~530 Ω, in addition to *μ*_{e} ~ 17, 700 cm^{2}/Vs and *μ*_{h} ~ 11, 800 cm^{2}/Vs for electrons (pink traces) and holes (blue traces), respectively. This demonstrates a PIC-integrated, LMH-based PD with excessive (>10^{4} cm^{2}/Vs) *μ*, whereas refs. ^{25,74} used hBN encapsulation for various detection ideas.

### Regular-state photoresponse

For optical characterisation, we first couple modulated mild (ON-OFF) with an obligation cycle of fifty% from a tuneable laser supply (Agilent 81680A) into the bus WG utilizing an optical single-mode fibre. Whereas various the potential on the two gate electrodes (*V*_{G1}, *V*_{G2}), the photoresponse of the unbiased GPD (*V*_{DS} = 0 mV, to keep away from darkish currents impairing the noise efficiency) is recorded utilizing a lock-in amplifier. Because the PTE impact as electromotive drive is intrinsically greatest read-out as open circuit potential distinction^{4,75}, we report the response as *V*_{PTE}, relatively than measuring the ensuing short-circuit photocurrent, which is dependent upon exterior components, comparable to *R*_{contact}. Determine 4g exhibits a photoresponsivity map measured on resonance at 1555.87 nm, from which we extract a most *R*_{[V/W]} ~ 90 V/W. The six-fold sample, with the very best photoresponse for bipolar (p-n, n-p) junctions, and a sign-change throughout the diagonal (*V*_{G1} = *V*_{G2}) for unipolar (n-n, p-p) junctions within the SLG channel, confirms that the PTE impact dominates the conversion of photons into electrical sign (relatively than a photovoltaic conversion with a two-fold sample in photovoltage over the identical measurement vary)^{43,44}. Our *R*_{[V/W]} outperforms the present state-of-the-art for waveguide-integrated PTE-GPDs, *R*_{[V/W]} ~ 3–12 V/W^{25,29,33,76}, by round one order of magnitude.

### Excessive-speed photoresponse

To find out the BW, we modulate CW mild at 1555.87 nm from the identical supply utilizing a business (Thorlabs LN05S-FC) depth modulator (lithium niobate, *f*_{3dB} = 40 GHz) and couple it into the system. Whereas tuning the modulation frequency of the exterior modulator, we monitor the GPD response with {an electrical} spectrum analyzer (Agilent PSX N9030A), whereas the gate bias (*V*_{G1} = −0.5 V, *V*_{G2} = −2.1 V) is ready at an working level the place *R*_{[V/W]} is largest. This provides a 3-dB bandwidth ~12 GHz, Fig. 4h, as anticipated from the design of the passive photonic construction and the cavity-imposed restrict calculated through Eq. (3).

### Energy 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 varied *P*_{in}. The maxima of the *V*_{PTE} traces match the resonance minima in *P*_{trans}, confirming the proportionality between the 2, as SLG dominates absorption for our resonator-based PDs. That is additionally proven in Supplementary Be aware 2 and Supplementary Fig. 2, the place we plot the estimated absorption and ensuing *V*_{PTE} at low (<0.1 mW) *P*_{in} on a linear scale. The shift of the resonance and its asymmetry for larger *P*_{in} (>0.2 mW) are attributed to the power-dependent change of the efficient refractive index of the Si WG by a thermo-optic impact^{52,77}. Extracting the power-dependent maxima in *V*_{PTE} permits us to estimate *T*_{e} at resonance, and plot the *R*_{[V/W]} energy dependence.

The junction service temperature, *T*_{e,j}, could be written as (see Strategies):

$${T}_{{rm{e,j}}}=sqrt{2left|frac{{V}_{{rm{PTE}}}}{{zeta }_{1}-{zeta }_{2}}proper|+{T}_{0}^{2}}$$

(6)

the place *T*_{0} = 294 Okay is the room temperature and ({zeta }_{1,2}=frac{{pi }^{2}{ok}_{{rm{B}}}^{2}}{3esigma }frac{{rm{d}}sigma }{{rm{d}}epsilon }) at *ϵ* = *E*_{F}, in analogy to Eq. (2). To be able to estimate *ζ*_{1,2}, following the identical technique used to find out *S* in Fig. 4d, we use *R*_{contact} and *μ* as obtained from {the electrical} measurements at homogeneous channel doping. The ensuing *T*_{e} extracted for various *P*_{in} is in Fig. 5c. The carriers attain *T*_{e} ~ 400 Okay for *P*_{in} ~ 0.6 mW, as a consequence of cavity-enhanced light-matter interplay. The *T*_{e} energy dependence could be fitted by the warmth equation^{44,70}, neglecting diffusive cooling by the contacts (see Strategies):

$${T}_{{rm{e}},{rm{j}}}={(beta {P}_{{rm{IN}}}+{T}_{0}^{delta })}^{frac{1}{delta }}$$

(7)

with *δ* ~ 3^{78} and *β* a becoming parameter.

The related, power-dependent, *R*_{[V/W]} is in Fig. 5d. For small *P*_{in} (<0.2 mW), we get a relentless *R*_{[V/W]}. For *P*_{in} > 0.2 mW we have now sublinear scaling between *V*_{PTE} and *P*_{in}, giving a *R*_{[V/W]} drop in line with ({R}_{[{rm{V}}/{rm{W}}]}propto {P}_{{rm{in}}}^{-1/3}) as a result of *T*_{e} dependence of the digital warmth capability^{78,79}.