Highly Sensitive Wavelength-scale Amorphous Hybrid Plasmonic Detectors

Hybrid integration of plasmonics and Si photonics is a promising architecture for global microprocessor interconnects. To this end, practical plasmonic devices not only should provide athermal, broadband operation over wavelength-scale footprint, but also support non-intrusive integration with low-loss Si waveguides as well as CMOS back-end-of-line processes. Here, we demonstrate a hybrid plasmonic photodetector with a single active junction fabricated via back-end deposited amorphous materials coupled to Si nanowires with only 1.5dB loss. Utilizing internal photoemission, our detectors measured sensitivity of -35dBm in a 620nm by 5{\mu}m footprint at 7V bias. Moreover, responsivity up to 0.4mA/W and dark current down to 0.2nA were obtained. The high process tolerance is demonstrated between {\lambda}=1.2-1.8{\mu}m and up to 100{\deg}C. The results suggest the potential towards plasmonic-photonic optoelectronic integration on top of Si chips without costly process modifications.


ANALYSIS OF THE HYBRID-SPP WAVEGUIDE
Compared to conventional TIR structures, SPP modes are capable of confining light on subwavelength scales, thus enabling photonic devices with very compact footprint and much higher density. The complex permitivity of metals at optical frequencies lead to significant losses, limiting propagation lengths to a few microns before power is attenuated below detectable levels. Due to these losses, it seems that plasmonic modes may never outperform their all-dielectric counterparts to transport light between different points. However, if these losses are reduced beyond a certain level, plasmonic structures may provide the optimum medium to accommodate truly nano-scale devices in all three dimensions, thereby empowering a contender to the all-dielectric Si platform used at present.
The hybrid-SPP waveguide shown in Fig. S1 is formed by a superposition of single-sided HPW with SPP mode coupled through a thin metal film. The asymmetry does not only come from permittivity differences, but the original modes are also fundamentally different. When decoupled, both HPW and SPP modes have drastically different propagation constants and evolve differently when the dimensions are varied. Yet, coupled supermodes can still be excited when the metal film is sufficiently thin. As Fig. S1 shows, the hybrid-SPP waveguide can be treated as two individual decoupled HPW and SPP waveguides when the metal film is thicker than its skin depth. As the thickness is reduced below skin depth, coupled supermodes between HPW and SPP arise as the evanescent fields extend to the opposite side and perturb each other, as long as the effective index difference is small. The combination of HPW and SPP into one structure also suggests light-matter interaction on two types of plasmonic interfaces, metal with high-index and metal with low-index, allowing one waveguide to support multiple applications.
In Fig. S2, the dispersion properties of the various supermodes are plotted. To illustrate the effects of field matching, Fig. S1. Hybrid-SPP waveguide can be treated as superposition of two individual decoupled HPW and SPP modes when the metal film is thicker than its skin depth.
HPW side is kept constant as thickness of the SPP-side highindex Si layer (t ε4 ) is varied from 100nm to 300nm. Coupling of the HPW and SPP forms a fundamental antisymmetric and a higher-order symmetric supermodes similar to a thin metal film embedded in a homogeneous dielectric bulk. From coupled mode theory analysis, antisymmetric corre-https://doi.org/10.6084/m9.figshare.5421598 sponds to in-phase coupling of the HPW and SPP modes, resulting in overlap with the metal leading to significant absorption losses. On the opposite, the out-of-phase coupling of the symmetric mode minimizes overlap as a result of destructive interference, lending support for long-range propagation with losses much lower than either SPP and HPW. In this 1D analysis, the optimal t ε4 thickness is 148nm for a slab mode extending to infinity in the horizontal direction.
The hybrid-SPP waveguide displays interesting effects as we move to 2D confinement. The mode effective index and propagation loss of the symmetric supermode are plotted in Fig. S3 as function of width and wavelength for a hybrid-SPP structure with t ε4 of 185nm. This thickness is based on loss optimization analysis for a minimum realizable width of 200nm due to limitations in our fabrication processes. From the dispersion plot, it is observed that the symmetric supermode of a 200nmwide waveguide can operate up to a wavelength of 1.8µm, after which the optical mode becomes leaky as the mode index drops below the substrate index. In Fig. S3, it is observed that the absorption losses of the symmetric mode increases dramatically as width approaches 620nm due to the combined effects of field symmetry breaking and modal evolution asymmetry. This behavior enables the design of devices that benefit from both low and high absorption for the same mode under the same fabrication steps. The field profiles for E x , D y and E z are shown in Fig. S4 as the mode changes from a width of 200nm to 620nm. For E x and E z , only fields inside the metal are shown in order to highlight field symmetry and overlap. The loss contribution from the x and z components is dependent on the location of zero-crossing and indicates the amount of overlap with the metal. At wider widths, E z overlap with the metal is stronger as the position for zerocrossing does not extend to the edges as in the narrow case.
For E x at 200nm, a deformed quadrupole field distribution is formed from fields extending inwards from the metal corners, thus expanding the zero-crossing and reducing field overlap in two axes. As width increases, E x becomes a dipole instead and the horizontal zero-crossing is entirely shifted out of the metal, thus maximizing E x overlap. The modal evolution asymmetry in the hybrid-SPP waveguide is also evidenced in the D y profile. The higher effective index of the SPP side allows it to start supporting higher order modes at much reduced widths than the HPW side. As a result of the evolution asymmetry, the HPW can couple to higher order SPP modes to form hybridized supermodes, which further enhances the field symmetry breaking in order to increase field overlap with the metal. In the 620nm case, TM s0 hybridizes with TM a2 as their effective indices cross, but absorption drops again at wider dimensions as the contrast becomes larger until the next hybridization point is reached.

PHOTODETECTOR MODELING
Modeling of the hybrid-SPP photodetector consists of two parts, optically-induced internal photodetection and dark current generation. Internal photoemission is the optical excitation of photocarriers in a metallic emitter and subsequent generation of photocurrent as these excited carriers have enough energy to cross a Schottky barrier. The total optical absorptance of the hybrid-SPP waveguide is given by the mode attenuation α multiplied by the detector length L d . As the mode loss γ dB is expressed in units of dB/µm, the attenuation coefficient α and absorptance A are given by: The internal quantum effiency η i or internal photoyield is the amount of absorbed photons per second that can be efficiently converted to carriers that contribute to photocurrent. This metric determines how many of the hot carriers generated by absorption have enough energy to cross Φ B when they arrive at the Schottky interface. Scattering events due to collisions with phonons, imperfections, and cold electrons can contribute carrier energy loss within the metal, and modelled via the hot carrier attenuation length L, defined as the distance travelled before energy decays by a factor of e −1 . From the models proposed by Berini [1,2], the internal quantum efficiency of a thinfilm single-barrier Schottky detector is given by: where P t (E 0 ) is the sum of carrier emission probability with energy level E 0 > Φ B , given as: The probability P k for energy level E k after k round trips between the two interfaces of the metal is: where t is the metal thickness and total number of round trips between the interfaces before E k falls below Φ B is given by: In Eq. S4, the emission probability of a photogenerated carrier is determined by whether it has enough escape momentum component normal to the interface to overcome Φ B . Eq. S5 suggests an increase of emission probability for hot carriers in metal films with a thickness much lower than its attenuation length and describes the probability of a carrier to be emitted over the barrier even after multiple reflections within the metal interfaces.
The external quantum efficiency is the internal quantum efficiency multiplied by the optical absorptance (η e = Aη i ). Herein exists a trade-off between η i and A, as the former benefits from a thin metal layer in order to increase carrier escape probability through multiple interface reflections, but optical absorption is reduced due to the decreased overlap, which increases the detector footprint in typical cases. However, it was shown earlier that the hybrid-SPP waveguide can alleviate this trade-off and achieve high absorption for a 10nm-thin metal layer by breaking field symmetry and maximizing metal overlap instead.
The responsivity of a photodetector is the photoresponse or amount of photocurrent generated from incident optical power in units of A/W, given by: Therefore, in order to obtain a large photoresponse, both a low Schottky barrier height and high absorptance are essential. However, a lower barrier height also leads to increased dark currents and idle power consumption. The dark current density of a reverse biased Schottky junction is given by thermionic emission theory [3]: where A * * is the carrier effective Richardson constant in the semiconductor, T is the operation temperature and V T is the thermal voltage k B T. The dark current is then I d = A c J d , where A c is the active contact junction area. The sensitivity or minimum detectable power under CW illumination is defined in the model proposed by Berini as 1dB above the incident power required to generate a photocurrent equal to the dark current, in units of dBm: The dark current of a photodetector is an important metric as it not only leads to increased power consumption, but also in operation temperature as the additional power dissipates through the sample and feedbacks positively into the device. Design of the electrical contacts is based on the MSM configuration, which consists of two back-to-back reverse biased Schottky junctions separated by a semiconductor of thickness L s . While MSM structures typically exhibit large dark currents due to thermionic emission over two junctions, suppression of dark currents can be achieved by designing small contact areas.
For a lightly doped semiconductor, under increasing reverse voltage, there exists a flat-band condition for which free carriers are fully depleted, allowing for photogenerated carriers to be quickly swept from emitter to collector. The corresponding flatband voltage is given by: where N is the semiconductor doping, ε s is the material permittivity of Si, and L s is the top-side Si thickness. Under the flat-band condition, dark current density is given by the summation of electron injection at the cathode and hole injection at the anode: The total dark current is then given by I d = A cn J dn + A cp J dp , in which A cn and A cp are the contact junction areas of the cathode and anode respectively. It should also be noted that at applied voltages greater than flat-band, the effective Schottky barrier height decreases due to image force lowering effects, given by: where ∆Φ B is the potential barrier lowering due to applied voltage: observing that by applying the image force lowering effect, higher η i can be achieved but at the same time, I d also increases. For computational modeling of a 10µm-long hybrid-SPP photodetector, the carrier attenuation length L of Al is assumed to be 100nm and Schottky barrier heights for Al/p-Si junctions are taken as Φ Bn0 = 0.54eV and Φ Bp0 = 0.58eV [3]. In order to utilize the lower n-barrier for carrier emission, the 10nm-thick Al emitter is biased at a negative potential with respect to the collector on top. To suppress dark currents from the collector, contact junction area is reduced to 1 × 1µm 2 . Given an absorption of 1.0dB/µm for the symmetric supermode, the internal responsivity, dark currents and minimum sensitivity are plotted in Fig. S5. With this design, a responsivity of 30mA/W can be achieved under 2V. The dark current density is on the order of 1nA/µm 2 and using the proposed contact junction designs, total dark currents can be reduced to nA range or lower, enabling a sensitive detector at −50dBm at low bias.

A. Series Resistance
The model provided in Section 2 modeled the voltage drop to be across the reversed bias junction with negligible series resistance in the silicon film and forward junction contact. However, in our experimental devices the series resistance acted as a voltage divider and caused the effective bias at the reverse junction Fig. S5. Internal responsivity, dark currents and minimum sensitivity for the proposed hybrid-SPP photodetector design with a detector length of 10µm and 90% absorption. A reverse voltage bias is applied above the computed V FB = 0.3V.
to be much lower. This can be attributed to the poor conductivity in the film quality and insufficient doping of the amorphous silicon sputtering target used.
The series resistance of two back-to-back Schottky junctions can be approximated via R s = dV/dI at the linear high voltage bias regime of the I-V curves. Using this approximation, the static series resistance for the devices of various lengths are plotted in Fig. S6. The large series resistance is the primary factor for the increase in bias required to observe photocurrents as well as the low responsivity in the experimental devices compared to theory. The performance of our photodetectors can improve by applying controlled doping concentrations on the αSi film.

B. Minimum Sensitivity
The minimum sensitivity is given by Eq. S8 and allows us to express device performance as trade-off between responsivity and dark currents, which is a more representative metric for design of low-power devices in system applications. The sensitivity derived from the responsivity and dark current measurements is plotted in Fig. S7.   Fig. S7. Minimum sensitivity derived from experimentally measured dark currents and responsivity.

C. Sample Variations
The variations in currents measured can be attributed to factors such as non-uniform formation of Schottky junctions which are known to be difficult to control and contact pad resistance due to damage from device probing. The dark currents of the devices are plotted in Fig. S8 with the standard deviation across multiple devices.

D. Frequency Response
Measurement of the experimental frequency response was limited within a range of 100MHz to 2.5GHz due to the bandwidth of the optical modulator, amplifiers and signal source. To estimate the RC-limited bandwidth, the parasitic capacitances were measured for devices of various lengths using a HP4280 1MHz C Meter, shown in Fig. S9. Based on these parasitics, the RC bandwidth of the shortest device is 400GHz for a 50Ω load. However, the speed is also limited by the carrier transit time in the αSi film between the two metals. The saturation drift velocity is approximately 10 6 cm/s at the bias range applied [4].

COMPARISON OF EXPERIMENTAL IPE PHOTODE-TECTORS
In Table S1, the hybrid-SPP photodetector is placed in comparison with previous experimental works reported in literature. These devices are traveling-wave detectors based on the internal photoemission process and do not include surfaceilluminated photodetection. The following metrics are compared: materials used to form the active junction, device length, optical power coupling efficiency, responsivity, dark currents, minimum sensitivity, operating wavelength range and tested temperature range. Our device is the first report of a hybrid plasmonic waveguide used for photodetection based on amorphous materials and still be able to achieve better performance in various metrics compared to crystalline counterparts, most notably the lowest minimum sensitivity reported experimentally due to low dark currents. The use of aluminum as a metal layer compatible with CMOS processes and deposited amorphous silicon allow non-intrusive back-end integration of on-chip optoelectronics.

Materials
Length