WAVEGUIDE-INTEGRATED PHOTODETECTOR
20200119205 ยท 2020-04-16
Inventors
Cpc classification
H01L31/1085
ELECTRICITY
H01L31/02005
ELECTRICITY
H01L31/028
ELECTRICITY
H01L31/022408
ELECTRICITY
H01L31/02327
ELECTRICITY
International classification
Abstract
An exemplary photodetector can be provided, which can include, for example, a metal contact, a metal stripe coupled to the metal contact, and a photon absorbing material(s) surrounding the metal stripe on at least four sides of the metal stripe. The photon absorbing material(s) can be germanium. The photon absorbing material(s) can be configured to absorb photons in a wavelength range of about 1.1 m to about 1.7 m.
Claims
1. A photodetector, comprising: a metal contact; a metal stripe coupled to the metal contact; and at least one photon absorbing material surrounding the metal stripe on at least four sides of the metal stripe.
2. The photodetector of claim 1, wherein the at least one photon absorbing material is germanium.
3. The photodetector of claim 1, wherein the at least one photon absorbing material is configured to absorbs photons in a wavelength range of about 1.1 m to about 1.71 m.
4. The photodetector of claim 1, further comprising a further metal contact disposed on the at least one photon absorbing material.
5. The photodetector of claim 4, further comprising at least one voltage generator configured to apply a bias voltage between the metal contact and the further metal contact to generate an electric field in the at least one photon absorbing material.
6. The photodetector of claim 1, wherein the metal contact is disposed on the at least one photon absorbing material.
7. The photodetector of claim 1, further comprising a semiconductor layer, wherein the at least one photon absorbing material is disposed on the semiconductor layer.
8. The photodetector of claim 7, wherein the semiconductor layer is silicon dioxide.
9. The photodetector of claim 7, further comprising at least one further photon absorbing material disposed on the semiconductor layer adjacent to the at least one photon absorbing material.
10. The photodetector of claim 9, wherein the at least one further photon absorbing material is silicon.
11. The photodetector of claim 10, wherein the at least one further photon absorbing material includes a slab and a ridge extending from the slab.
12. The photodetector of claim 10, further comprising a low refractive index substrate, wherein the semiconductor layer is disposed on the low refractive index substrate.
13. The photodetector of claim 1, wherein the at least one photon absorbing material includes a slab and a ridge extending from the slab, and wherein the metal contact is disposed on the slab and the metal strip is one of (i) disposed between the ridge and the slab, (ii) disposed entirely in the ridge, or (iii) inside the slab.
14. The photodetector of claim 1, wherein the metal contact and the metal strip are composed of one of Titanium nitride, aluminum, copper, silver, gold, or zirconium nitride.
15. A photodetector, comprising: a metal contact; a metal stripe coupled to the metal contact; and at least one layer of graphene located between the metal stripe and a semiconductor layer.
16. The photodetector of claim 15, wherein the at least one layer of graphene is coupled to the metal contact.
17. The photodetector of claim 15, further comprising at least one further metal contact, wherein the at least one layer of graphene is coupled to the at least one further metal contact.
18. The photodetector of claim 15, further comprising at least one photon absorbing material surrounding the metal stripe on at least four sides of the metal stripe
19. The photodetector of claim 18, wherein the at least one photon absorbing material is germanium.
20. The photodetector of claim 19, wherein the metal contact is disposed on the at least one photon absorbing material.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] Further objects, features and advantages of the present disclosure will become apparent from the following detailed description taken in conjunction with the accompanying Figures showing illustrative embodiments of the present disclosure, in which:
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[0086] Throughout the drawings, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the present disclosure will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments and is not limited by the particular embodiments illustrated in the figures and the appended claims.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
Exemplary Waveguide-Integrated Photoconductive Plasmonic Photodetector
[0087] The exemplary plasmonic photodetector can be based on a surface plasmon polariton (SPP) waveguide arrangement with the germanium absorbing material as one of the examples of photoconductive materials. However, it should be noted that other suitable photoconductive materials can also be used.
[0088] SPPs are electromagnetic (EM) waves that can be coupled to surface collective oscillations of free electrons in a metal bounded to the metal and propagating along metal-dielectric/semiconductor interfaces. (See, e.g., References 9-11). They can range from localized surface plasmons (LSPs) of individuals particles to various propagating SPPs existing at flat, curved, single or multiple surfaces. (See, e.g., Reference 9). LSP modes bring about unique plasmonic phenomena of subwavelength light confinement and EM field enhancement resulting in extreme light concentration. SPP modes can also be strongly localized in the cross-section perpendicular to the propagation direction. However, they suffer from inevitable EM absorption in metals. SPP-based waveguides can transport the same huge bandwidth of information as conventional photonics waveguides, while not limited by diffraction limit. (See, e.g., Reference 9).
[0089] As indicated above, one of the challenges shared by plasmonic structures can be considerable plasmonic losses due to absorption by the metal that increases drastically for better confinement modes. The presence of a metal within the structure introduces losses simultaneously, which facilitates the co-propagation of overlapping electric and photonic signals and thus can be of great interest. It can provide ways to generate, modulate and detect light shrinking dimensions towards the scale of electronic. (See, e.g., References 4 and 9). The presence of a metal electrode at the electric field maximum of the propagating SPP mode greatly enhances the sensitivity to an applied electrical signal. An obstacle for realization of plasmonic devices can be a limited propagation length of the optical signal within a plasmonic waveguide, which can be a direct result of light absorption in the metal. In the last decade, various plasmonic waveguide configurations were proposed and demonstrated to tackle this problem. These include gap (e.g., metal-insulator-metal) (see, e.g., References 8 and 9), metal stripe (see, e.g., Reference 9), V-groove (see, e.g., Reference 9), nanowires (see, e.g., Reference 9), dielectric-loaded SPP (DLSPP) (see, e.g., References 9 and 14), and long-range SPP (LR-SPP). (See, e.g., Reference 9). However, they have either poor more confinement or short propagation length; for example, long propagation length of the signal can be achieved at the expense of weak spatial confinement.
Exemplary Long-Range Dielectric Loaded Surface Plasmon Polariton (LR-DLSPP)
[0090] LR-DLSPP inherits many advantages of having a very long propagation length from long-range SPP (LR-SPP) waveguide, and good mode confinement from the DLSPP waveguide. (See, e.g., References 9-13). LR-DLSPP includes a semiconductor/dielectric ridge deposited on top of a thin metal stripe/electrode, which can be supported by other semiconductor slab from a bottom. The entire structure can be supported by a low-index substrate which can ensure mode confinement to the semiconductor/dielectric ridge and underlying semiconductor/dielectric slab. Due to the thin metal film, the SPPs on the two metal-semiconductor/dielectric interfaces can couple to each other and form a supermode with symmetric and anti-symmetric transverse components. The symmetric mode, long-range mode, can be characterized by low longitudinal component of the electric field in the metal, thus lowering the absorption losses. Long propagation distance can be achieved when mode effective indexes on both metal-semiconductor/dielectric interfaces can be close to each other such that they can couple together minimizing an electric field in the metal. Thus, LR-DLSPP can provide very high propagation length and reasonable mode confinement. In comparison, a gap SPP (MIM) can support very high confined SPP mode, but absorption losses arising from a metal can limit the propagation distance to tens of the corresponding mode wavelengths. LR-DLSPP can facilitate superior mode field confinement and high propagation length. (See, e.g., References 9-13). It can have the highest evaluated a figure of merit (FoM) among any other plasmonic waveguides that takes into account mode size, wavelength, and propagation length (see, e.g., Table 1 below) (see, e.g., References 9 and 11). Thus, for example:
where w.sub.0 can be the lateral mode width, L.sub.p can be the mode propagation length, n.sub.eff can be the mode effective index, and .sub.0 can be the excitation wavelength.
[0091] The FoM for LR-DSLPP was much higher, at least of two orders magnitude, compared to any other plasmonic waveguide configurations (see, e.g., Table 1 below). (See, e.g., References 9 and 11).
TABLE-US-00001 TABLE 1 FoM for plasmonic waveguides. Wave- Gap guide LR-DLSPP LR-SPP DLSPP (MIM) V-grove FoM 3.2 .Math. 10.sup.6 3.2 .Math. 10.sup.4 3.4 .Math. 10.sup.3 1.1 .Math. 10.sup.4 2.9 .Math. 10.sup.4
[0092] Furthermore, the LR-DLSPP mode profile matches very well the mode of the photonic waveguide, thus facilitating efficient coupling between photonics and plasmonic platforms. LR-DLSPP waveguide mode supporting a TM mode can have a similar mode profile to the photonic TM mode with the overlap integral between them showing up to 98% coupling efficiency with superior tolerance to the offset of the metal stripe supporting the LR-DLSPP mode. (See, e.g., References 12 and 13)
Exemplary Ge Photodetector
[0093]
Exemplary Quantum Efficiency
[0094] Neglecting the scattering losses, the responsivity of the photodetector can depend only on the absorption coefficient of Ge, .sub.Ge, and metal, .sub.m. The material absorption of Ge and the confinement factor of the mode in the Ge waveguide can be used to determine .sub.Ge. Also, the overlap of the mode with the metal can be used to determine .sub.m. (See, e.g., Reference 7). To calculate the absorption coefficients of metal (e.g., Au), .sub.Au, and Ge, .sub.Ge, the 3D FDTD and FEM simulations were performed. To determine .sub.Au, the Ge absorption coefficient was set to 0 and Au stripe/electrode (see, e.g., diagrams shown in
[0095]
[0096] In the exemplary arrangement, the absorption coefficient of Ge, .sub.Ge, can be at least 7 times higher compared to the absorption coefficient of Au, .sub.Au, for a wavelength of =1550 nm, and over 43 times higher for a wavelength of =1310 nm where Ge shows a higher absorption. (See, e.g., graph shown in
Exemplary Speed (Bandwidth)
[0097] In telecommunication systems, photodetectors can be used to detect optical signals modulated at high data rates. Thus, an important metric can be the opto-electrical 3 dB bandwidth, which can be defined as the frequency range from DC to cut-off frequency f.sub.3dB, for example, the frequency at which the electrical output power drops by 3 dB below power value at very low frequency. The opto-electronic bandwidth of a photodetector can depend on the carrier transit time and RC response time. To reduce the carrier transit time, the distance between the collecting electrodes can be small. In comparison, RC time reduction can be obtained by lowering the contact resistance of the metal electrodes and by reducing the detector length what reduce the photodetector capacitance. (See, e.g., Reference 15). The RC-limited 3 dB cut-off frequency can be expressed as, for example:
where R.sub.eff can be the effective overall resistance and C.sub.pd can be the junction capacitance. The carrier transit time, that defines the time of photogenerated electron or hole to travel through the active region prior to being collected by the contacts, can be estimated using, for example:
where d.sub.abs can be a distance between areas where carriers generate and the electrode collecting those carriers, and v can be the average carrier velocity.
[0098] As discussed above, only L=5 m long photodetector may be used to achieve a quantum efficiency exceeding 95% at wavelength of 1310 nm. Taking into account a distance between both electrodes in the range of 450 nm, for example, the second electrode can be placed around 300 nm from the Ge waveguide, the capacitance in a range of a few fF can be suspected. The second electrode placed 300 nm from the waveguide may not disturb a propagating mode in the waveguide, what can translate into small propagation losses and can be associated with small absorption by a metal electrode supporting a propagating mode, which gives a rise to enhanced quantum efficiency and responsivity. If the device/photodetector can be connected with a 50 load, the RC cut-off frequency exceeding a 1 THz can be achieved.
[0099] In the exemplary design/configuration, all carriers can be generated in the area limited by the semiconductor ridge. Thus, the maximum distance between photogenerated carriers and the electrode, collecting those carriers, being at the same time the metal stripe supporting a propagating mode, can be around d.sub.abs=200 nm. Taking a drift velocity of 600 m/s, the bandwidth of f.sub.t=160 GHz can be achieved. However, as it can be observed from the field plots and graph 5 shown in
[0100] As discussed herein, the bandwidth of the photodetector is not limited by a RC time constant; however, the transit time used for carriers to drift to contact electrode collecting the carriers can be beneficial. By decreasing the distance between the two contacts, a large electric field can be obtained at low bias voltage, which improves the carriers' collection.
Exemplary Symmetric and Asymmetric Electrodes
[0101]
[0102] Previously, a new class of plasmonic materials appeared, so called transition metal nitrides (TMNs) that offer the optical properties close to that of noble metals. (See, e.g., graphs shown in
Exemplary Waveguide-Integrated Plasmonic Graphene Photodetector
[0103] The PDs are one of the basic building blocks of an optoelectronic link that convert light into an electrical signal. The monolithic, on-chip, optoelectronic integration utilizes development of CMOS compatible PDs operating in the telecom wavelengths (1.1-1.7 m) based on the CMOS technology. (See, e.g., References 22-24). Although sensitivity can be an important attribute for photodetectors in long distance communications, for short distance interconnects an important factor can be the total energy dissipated per bit. The optical energy received at a photodetector can be directly related to the transmitter optical output power and the total link loss power budget, which can include total link attenuation, coupling losses and eventually, a power margin. Therefore, for 10 fJ/bit transmitted optical energies, the received optical energy can be 1 fJ/bit. Thus, minimizing the optical losses at the photodetector can be beneficial for overall performance of the system. Photodetectors usually operate on the basis of the photoelectric effect or exhibit an electrical resistance dependent on the incident radiation. The operation principal can be based on the absorption of photons and the subsequent separation of photogenerated charge carrierselectron-hole (e-h) pairs. They suffer, however, from low efficiency either because the NIR photons energy at telecom wavelengths (e.g., 0.79-0.95 eV) may not be sufficient to overcome the Si bandgap (e.g., 1.12 eV) or low detection area in the case of Ge-based photodetectors (e.g., bandgap 0.67 eV). The alternative approach utilizes the intrinsic absorption of graphene integrated with a photonic platform for photodetection.
[0104] Graphene can be very attractive material for photonic and optoelectronics because it offers a wide range of advantages compared to other materials. Single-layer graphene absorbs 2.3% of the incident light, which can be remarkably high for an atomically thin material. Graphene can be gapless what can facilitate charge carrier generation by light absorption over a very wide energy spectrum. It can have ultrafast carrier dynamics, wavelength-independent absorption, tunable optical properties, high mobility, and the ability to confine electromagnetic energy to very small volumes. (See, e.g., Reference 4). The high carrier mobility (e.g., both electrons and holes) can facilitate ultrafast conversion of photons or plasmons to electrical currents or voltages. By integration with local gates, this process can be in situ tunable and can facilitate submicron detection resolution. (See, e.g., References 5-7). Furthermore, graphene can be integrated onto silicon-based systems on wafer-scale. By integration of graphene with the propagating photonic mode, the interaction length of the mode with graphene can be greatly enhanced compared to the normal incidence situation in which the interaction length can be limited by the thickness of graphene. These graphene photodetectors have the additional advantage of process compatibility with standard photonic integrated circuits. (See, e.g., References 29-22). The absorption of graphene is described in terms of the optical conductivity which can be calculated from the Kubo formula that can depend on the angular frequency , the charge particle scattering rate F, the chemical potential , and temperature T. Thus, the relative conductivity .sub.eff of graphene can be calculated from, for example:
where here can be the thickness of graphene being 0.335 nm.
[0105]
[0106] Previous waveguide-based graphene photodetectors were based on the Si integrated photonic waveguide arrangement, where the optical mode couples to the graphene layer through the evanescence field, leading to optical absorption by graphene and a generation of photocurrent. (See, e.g., References 29-33). In this case, the photocurrent was collected by two metal electrodes located on opposite sides of the waveguide. To create a lateral metal-doped junction, either different metal electrodes have to be implemented (see, e.g., Reference 34) or an asymmetry in the electrode's distance from the waveguide have to be introduce. (See, e.g., Reference 32). For the exemplary arrangement, it can be used to create a graphene-metal junction close enough to the waveguide to efficiently separate the photoexcited electron-hole pairs at zero bias. The guided mode approach can facilitate longer interaction between graphene and the optical waveguide mode than free-space illumination. Waveguide-integration can facilitate an increase in the optical absorption in the exemplary photodetector beyond 2.3% and, by increasing the interaction length, 100% light can be absorbed and contribute to photocurrent. (See, e.g., Reference 33). However, as the metal electrode can be placed very close to the waveguide, it can disturb a propagating mode. (See, e.g., References 29-33). Furthermore, because of the evanescence coupling, the typical length needed to achieve complete absorption can be 60-100 m. Thus, the target can be to increase the light absorption of graphene, and address the difficulty of extracting photoelectrons, as only a small area of the p-n junction close to the metal-graphene contact can contribute to current generation. (See, e.g., References 26 and 35).
[0107] To generate a photocurrent, the photogenerated carries exits the photogeneration region before they recombine. Assuming strong E-field and carrier saturation velocity of 5.5.Math.10.sup.5 m/s at low carrier density, it can take only 0.36 ps for the carrier to travel out of the 200 nm current generation region. Thus, the photogenerated carriers have a good chance of exiting the photogeneration region, resulting in reasonably good internal efficiency within the high E-field photodetection region, although the lifetime can be short. The transit time limited bandwidth of the photodetector can be given by f.sub.t=3.5/2t.sub.tr, where t.sub.tr can be the transit time through the photodetection region. Thus, a value of 1.5 THz can be obtained, which shows that a huge bandwidth that can be achieved with a graphene-based photodetector. Thus, the main challenge for realization of graphene-based photodetectors can be increasing the graphene absorption. Absorption of graphene can be improved by exploit the strongly enhanced electro-magnetic near-fields associated with LSPRs. (See, e.g., References 28, 36 and 37). LSPRs originate from the resonant coherent oscillation of a metal's conduction electrons in response to incident radiation. The resulting enhanced near-field surrounding the nanostructure can promote light absorption in the materials around them. Incident light, absorbed by plasmonic nanostructures, can be converted into plasmonic oscillations, with an enhancement of the local electric field. Such field enhancement, which can be in the area of the p-n junction formed in graphene, can result in a significant performance improvement. (See, e.g., Reference 39).
[0108] Additionally, this can be achieved by exciting SPP and then guiding it into the junction region at the contact edge with a graphene. (See, e.g., References 38-42). SPPs are surface bound waves propagating on a metal-dielectric interface and originate from the coupling of light with the metal's free electrons. SPPs can be delivered to the active region, junction at the contact edge, thus enhancing the overall absorption. The same electrode can be used as a contact and metal electrode supporting a collected and propagating mode.
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[0111] For a photodetection purpose, a graphene or 2D material can be placed either below a metal stripe or on top. A metal electrode inside a waveguide can work as a metal stripe supporting a propagating mode and as a metal electrode that can create a junction between graphene and metal. Depending on the needs, this plasmonic waveguide can support either TM or TE modes. (See, e.g., electric field plots shown in
[0112] In particular,
[0113] The exemplary arrangement provides superior coupling efficiency from a photonic waveguide to a photodetector calculated at 98% for both aluminum (see, e.g., Reference 45) and gold (see, e.g., Reference 46) stripes compared to MIM gap plasmon arrangement (see, e.g., Reference 47) and inverse-DLSPP arrangements (see, e.g., Reference 48) where the coupling efficiencies were estimated at 50-60%. The improved coupling efficiency for the LR-DLSPP mode can result from the similar mode profile of the photonic and fundamental LR-DLSPP modes. (See, e.g., contour plots shown in
[0114] The photodetection in the exemplary plasmonic waveguide arrangement can be achieved by photo-voltaic, photo-conductive, photo-thermoelectric, photo-bolometric or photo-gating effect and a preferred mechanism can depend on the specific design, fabrication and integration needs.
Exemplary Photovoltaic Effect
[0115] Photovoltaic (PV) photocurrent generation can be based on the separation of photogenerated electron-hole (e-h) pairs by built-in electric fields at junctions between positively (e.g., p-type) and negatively (e.g., n-type) doped regions of graphene or between differently doped sections. The same effect can be achieved by applying a source-drain bias voltage V.sub.bias producing an external electric field. This can generally be avoided in the case of graphene as it can be a semimetal, and therefore it can generate a large dark current. The built-in field can be introduced either by local chemical doping, electrostatically by the use of gates (e.g., split gates), or by taking advantages of the work function difference between graphene and a contacting metal. In the case of graphene-metal junction, the doping in the contact area can be fixed. This can typically bep-type for metals with a work function higher than that of intrinsic graphene (e.g., 4.45 eV), whereas the graphene channel can be p or n. The photocurrent direction can depend only on the direction of the electric field, not on the overall doping level.
Exemplary Photo-Thermoelectric Effect
[0116] Hot-carrier-assisted transport can play an important role in graphene. Because of strong e-e interactions, a photoexcited e-h pair can lead to ultrafast (e.g., 10-50 fs) heating of the carriers in graphene. Because the optical photon energy in graphene can be large (e.g., 200 men, hot carriers created by the radiation field can remain at a temperature T.sub.e and thus energy k.sub.BT.sub.e, with k.sub.B the Boltzmann constant higher than that of the lattice for many picoseconds. Final equilibration of the hot electrons and the lattice can occur via the slower scattering between charge carriers and acoustic phonons. These processes can take place on a nanosecond timescale, although they can experience a substantial speed-up attributed to disorder-assisted collisions. The photogenerated hot electrons can produce a photovoltage, V.sub.PTE, by the photo-thermoelectric (PTE) effect (e.g., Seebeck effect): V.sub.PTE=(S.sub.1S.sub.2)T.sub.e, where S.sub.1,2 (in V.Math.K.sup.1) can be the thermoelectric power (e.g., Seebeck coefficient) in the two graphene regions with different dopings, and T.sub.e can be the electron temperature difference between the regions. The PTE effect can be dominate in graphene p-n junctions or in suspended graphene. Because hot electrons, rather than lattice heating, can generate the electronic response under these conditions, PTE graphene detectors can achieve high bandwidths, as in the case of PV detectors.
[0117] As discussed above, the photocurrent generation can be based on the photo-thermoelectric effect. However, the exemplary arrangement can also utilize a photo-voltaic effect, a photo-conductive effect, a photo-gaining effect, and a photo-bolometric effect.
Exemplary Bolometric Effect
[0118] The bolometric effect can be associated with the change in the transport conductance produced by heating associated with the incident photons. A bolometer can measure the power of electromagnetic radiation by absorbing the incident radiation (dP) and reading out the resulting temperature increase dT. The parameters of a bolometer can be the thermal resistance R.sub.h=dT/dP, which ultimately can define its sensitivity, and the heat capacity C.sub.h which can determine its response time =R.sub.hC.sub.h. Graphene can have a small volume for a given area and low density of states, which can result in low C.sub.h, thus a fast device response. The cooling of electrons by acoustic phonons can be inefficient, owing to the small Fermi surface, and cooling by optical phonons can utilize high T.sub.e. Thus R.sub.h can be relatively high, giving rise to high bolometric sensitivity.
[0119] As this photodetection mechanism can be based on a light-induced change in conductance, instead of direct photocurrent generation, it can utilize an externally applied bias and can operate on homogeneous graphene, without the need to introduce a p-n junction. The conductance change induced by the incident light can be due to two mechanisms: (i) a change in carrier mobility due to the associated temperature change, or (ii) a change in the number of carriers contributing to the current. The two can coincide with the PV effect, with the electric field generated by the external bias.
[0120] Two mechanisms result in bolometric photocurrents with opposite sign; the photoinduced excess carrier induces an enhancement of the conductance, whereas the temperature dependence of the mobility leads to a reduction of the conductance. By changing the energy Fermi level E.sub.F, which mechanism dominates can be controlled. Near the Dirac point, where the carrier density can be lowest, PV effects dominates, whereas far away PTE effects dominate. (See, e.g., Reference 7).
Exemplary Photogating Effect
[0121] The photogating process can be associated to a light-induced change of the carrier density n of a conductor, therefore of its a. For graphene, this change in can be given by the relation: =n.Math.e.Math.. Under the optical illumination, the absorption process can lead to the generation of e-h pairs. It can induce a conductance modulation through photoinduced gate voltage. Thus, compared to the bolometric effect, which can be based on the change in carrier mobility due to heating, the photogating effect can be based on a light induced change in the carrier's density.
[0122] Compared to the previously reported waveguide arrangements (see, e.g., References 29-33), a 2D material can be placed in the maximum electric field of the mode, thus the interaction of a mode's electric field with a 2D material can be much stronger. (See, e.g., electric field plots and graphs shown in
[0123] The relaxation of photoexcited carrier to equilibrium in graphene can include three processes. In the first procedure, photoexcited carriers can lose energy through e-e and electron-phonon scattering on a 10 fs time scale. Subsequently, this distribution thermalizes through electron-phonon scattering toward a hot Fermi-Diract distribution, with the time scale of hundreds of femtoseconds. The hot Fermi-Diract distribution relaxes to equilibrium by e-h recombination, which can lead to plasmon emission, phonon emission, and Auger scattering on a picosecond time scale. (See, e.g., Reference 42).
[0124] For the photovoltaic and photo-thermoelectric effects where the separation of photo-generated e-h pair by built-in field at junction between negatively (e.g., n-type) and positively (e.g., p-type) doped regions of graphene can be used, the doping can be introduced either by local chemical doping, electrostatically, by the use of two gates (e.g., split gates), or by taking advantage of the work function difference between graphene and a contacting metals. This doping can typically be p-type for metals with a work function higher than the work function of intrinsic graphene (e.g., 4.45 eV), while the graphene channel can be p or n. (See, e.g., diagrams shown in
[0125] As shown in
[0126] In the exemplary waveguide arrangement, a strong potential gradient located close to a metal stripe/electrode overlaps with the LR-DLSPPWs mode while there can be the absence of an overlap between the optical field and potential difference created by the second electrode. (See, e.g., electric field plots and graphs shown in
[0127] As shown in from
[0128] Compared with a metal electrode placed on top of the waveguide (see, e.g., Reference 41) where metal electrode contributed for most of the power absorbed by a Si waveguide, the exemplary waveguide can achieve superior guiding properties of the mode even with a metal electrode placed inside a waveguide, in the maximum electric field of the propagating mode. This becomes even clearer when propagation lengths of the modes are compared. For a structure with metal on top of the Si waveguide (see, e.g., Reference 41), the propagation length reduced to 7 m for wider electrodes, while in the exemplary arrangement it reached 156 m for wide metal electrodes supporting a TM mode (see, e.g., contour plots shown in
[0129] Increased absorption on the metal stripe that can be at the same time on one of the photodetector's contacts, leads to a temperature rise on the metal stripe, thus heating the p-n junction at the contact edge, and producing a thermoelectric contribution to the photovoltage. Considering gold's (e.g., 300 W/mK) and graphene's (e.g., up to 5000 W/mK) thermal conductivities, the heat can be transported to the p-n junction from within the metal stripe, leading to a temperature gradient across the device and producing a thermoelectric contribution to the photovoltage. (See, e.g., Reference 40).
[0130] As shown in
[0131] The second mechanism that can contribute to the bolometric effect can be based on a change in carrier mobility due to the temperature change through a heating. As shown in
[0132] The exemplary geometry of the exemplary arrangement facilitates a realization of ground-source-ground configurations as well as a doubling of the total photocurrent as compared to the simple ground-source case, where the source electrode can be at the same time a metal stripe supporting a propagating LR-DLSPP mode. Compared to the previous configurations (see, e.g., Reference 41) with the metal electrode placed on top of the photonic waveguide, the exemplary metallic source electrode can be a part of the waveguide supporting the LR-DLSPP mode. The source electrode placed on top of the photonic waveguide can be close to the photonic's mode electric field to dope a graphene channel, however when it can be placed in close proximity to the waveguide, it can induce light absorption that can degrade device performance significantly. (See, e.g., Reference 41). In the exemplary arrangement, the source electrode simultaneously can be part of the waveguide, and can be placed in the maximum of the mode's electric field, and does not disturb the propagating mode.
[0133] Unlike previous waveguide-integrated graphene photodetectors, the metal electrode that can be a part of the LR-DLSSPW mode can facilitate independently tune graphene Fermi level and electric field across the waveguide mode in the source-drain-gate electrode arrangement where metal pad 2 serve as a source, metal pad 3 as a drain, and metal stripe, metal pad 1, as a gate. (See, e.g., diagram shown in
[0134] As the photogenerated carrier in graphene can have very high mobility, the photodetection speed is not limited by the transit time of the carriers, but rather by the RC characteristic of the photodetector. Small metal electrodes can contribute to the small capacitance enhancing a photodetector speed. Furthermore, a small photodetector footprint can facilitate a response speed of hundreds of GHz. Moreover, graphene's two-dimensional nature can enable the generation of multiple electron-hole pairs for high-energy photon excitation. High in-plane electric field component on the graphene can generate such pairs giving rise to the carrier multiplication process even without external bias.
[0135] A waveguide-integrated plasmonic graphene photodetector in an exemplary arrangement can combine advantages of compact size, zero-bias operation, and ultrafast response over a broad range of wavelength and can enable novel architecture for on-chip communications. Together with a high coupling efficiency of a light coupling from a photonic waveguide to the photodetector, LR-DLSPPW, it facilitates very high external quantum efficiency and, in consequence, very high external responsivity.
Exemplary Waveguide-Integrated Photodetector
[0136] Compared to lasers and modulators that can be combined into one device element, thus avoiding in the optical link, photodetectors can be elements that cannot be replaced. Such photodetectors convert light into an electrical signal, making it essential for integrating small but slow electronic components with fast but large sized photonic elements. Furthermore, these photodetectors can be the last elements in the optical link, so they can operate effectively under low input power. (See, e.g., References 52-56). The optical energy received at a photodetector can be directly related to transmitter optical output power and the total link loss. Thus, for 10 fJ/bit transmitted optical energies, the received optical energy can be 1 fJ/bit. (See, e.g., References 54 and 56). Therefore, minimizing the optical losses at the photodetector can be beneficial for the overall performance of the system. Photodetectors usually operate on the basis of the photoelectric effect, or exhibit an electrical resistance dependent on the incident radiation. The operation principal can be based on the absorption of photons and the subsequent separation of photo-generated charge carrierselectron-hole (e-h) pairs. They suffer, however, from low efficiency either because the photon's energy at telecom wavelengths (e.g., 0.79-0.95 eV) may not be sufficient to overcome the Si bandgap (e.g., 1.12 eV), a low detection area in the case of Ge-based photodetectors (e.g., bandgap 0.67 eV), or fabrication problems in the case of graphene-based photodetectors. (See, e.g., References 52-56). To overcome some of these problems, much attention in recent years has been focused on plasmonics-based photodetectors.
[0137] Plasmonics photodetectors are attractive because they have the ability to confine light below the diffraction limit, facilitating light-matter interaction on a deep sub-wavelength scale. (See, e.g., Reference 57). This can facilitate considerable shrinking of device size, which brings the technology one step closer to the fusion of optical and electronic components of the same size. Plasmonics can serve as a bridge between photonics and electronics by providing components with sizes similar to electronics and speeds characterized by photonics. (See, e.g., References 58 and 59). As with all other plasmonic devices, plasmonic photodetectors naturally include metallic elements that can either constitute the absorber in hot-carrier devices, or provide enhancement of the electromagnetic field inside an absorber or both. (See, e.g., References 55 and 57). Waveguide-integrated photodetectors can be beneficial for on-chip optical communication as they can be monolithically integrated with electronics. Furthermore, such devices can be placed at the terminal end of a waveguide and can utilize one of the photo detection [illegible]. (See, e.g., Reference 57). As the carrier collection path and the light propagation direction can be orthogonal in this type of photodetector, the trade-off between bandwidth and responsivity can be avoided. Additionally, they can provide a significant advantage in terms of noise reduction that scale directly with the photodetector active volume that can be kept small for a single-mode operation. (See, e.g., Reference 56).
Exemplary Plasmonic Photodetectors
[0138] Recently, the surge of research in waveguide-integrated plasmonic photodetectors has produced results that show very promising performance improvements. In plasmonic photodetectors relying on a hot carrier photodetection schema, a bandwidth of 40 GHz and a responsivity of 0.12 A/W at 1550 nm was measured at a bias voltage of 3.5 V in a MIM waveguide arrangement with a footprint below 1 m2. (See, e.g., Reference 60). Another exemplary arrangement relies on the inverse DLSPP waveguide design where a responsivity of 0.085 A/W at 1550 nm wavelength was measured. (See, e.g., References 61 and 62). However, by placing a graphene sheet between the metal and the semiconductor, it can be possible to enhance the efficiency of internal photoemission due to a prolonged carrier life-time in the graphene. Thus, a responsivity improvement of 0.37 A/W at 1550 nm wavelength was achieved. (See, e.g., Reference 63). Further improvements have been predicted for a thin metal stripe placed entirely inside a semiconductor and operating based on a LR-DLSPP waveguide arrangement. (See, e.g., Reference 64). Taking advantage of this arrangement, a responsivity exceeding 1 A/W was predicted while still keeping bandwidth above 80 GHz. In addition, it has been shown that by replacing noble metals with a TiN as a metal stripe, the improvement in terms of the signal-to-noise ratio (SNR) was predicted as a result of an optimum Schottky barrier height of 0.697 eV. Similar to the inverse-DLSPP, further improvement can be possible by placing graphene below or above a metal stripe in LR-DLSPP arrangements.
[0139] Additionally, interest has grown in graphene-based photodetectors that can operate based on PTE, photovoltaic (PC) or bolometric effects. (See, e.g., References 65 and 66). Each of these mechanisms can become dominant in different photodetector configurations. Recent work on plasmonic graphene photodetectors utilizing a bolometric effect showed a responsivity of 0.5 A/W at 1550 nm operating at 100 Gbit/s. (See, e.g., Reference 67). Another study utilized a narrow asymmetric MIM plasmonic waveguide to provide enhanced light-graphene interaction and enable effectively separate photo-generated carriers. (See, e.g., Reference 68). In this case, the responsivity was 0.36 A/W with bandwidth exceeding 110 GHz. In the similar, but symmetric, MIM arrangement, another group was able to measure a responsivity of 0.35 A/W and 0.17 A/W for bolometric and photovoltaic effect, respectively. (See, e.g., Reference 69). To achieve a responsivity of 0.35 A/W, a bias voltage of only 0.2 V was utilized. (See, e.g., Reference 69).
[0140] The ideal waveguide-integrated photodetector can have high responsivity (e.g., quantum efficiency), fast response time, and reduced power consumption, defined by the voltage utilized to achieve high responsivity. Furthermore, such device can be implemented into the process flow of photonic foundries. State-of-the-art waveguide-integrated photodetectors need to be at least comparable with available Ge photodetectors that offer a responsivity of 1 A/W at an operating wavelength of 1550 nm. Finally, the bandwidth can exceed 50 GHz, and a device can be CMOS compatible.
Exemplary Germanium Photodetectors Overview
[0141] Germanium is used in a MSM configuration as it is compatible with the CMOS process, and it is a good active material for photodetection in the telecom wavelength range. (See, e.g., References 55, 57, 70 and 71). Germanium belongs to the same group IV materials as Si, so it can be easily integrated with silicon platforms. Compared to Si, which has a relatively large bandgap of 1.12 eV corresponding to an absorption cutoff wavelength of 1100 nm, Ge has a direct bandgap of 0.8 eV, which is only 0.14 eV above the dominant indirect bandgap (e.g., 0.66 eV), providing a much higher optical absorption in the 1300-1550 nm wavelength range. (See, e.g., graph shown in
[0142] Conventional Ge waveguide photodetectors utilize deposition of metal contacts on Ge. This process, however, introduces a significant losses what influence device responsivity. (See, e.g., References 72-74). To reduce these losses, modified Ge PIN waveguide photodetectors were introduced that exploited lateral Silicon/Germanium/Silicon (Si/Ge/Si) heterojunctions. (See, e.g., References 72-74). These results were achieved through improved optical confinement in the Ge layer, yielding a reduction of optical loss in doped contacts. However, the difference in refractive index between doped Si and intrinsic Ge regions can still be small, which makes the mode relatively large. As a consequence, for a Ge width of w=0.3 m, the fraction of optical power inside Ge can be estimated to be 54%, while the fraction of optical power inside doped Si can be 32%. (See, e.g., References 72 and 73). To achieve more power inside Ge, the width of Ge has to be increased. Accordingly, for a Ge width of w=1 m, around 86% of optical power stays inside the Ge while only 8% of power is situated in the highly doped Si regions. (See, e.g., References 72 and 73). For a device with Ge width of w=1 m and a photodetector length of 10 m, the device responsivity was measured to be 0.5 A/W, which is in agreement with calculations showing 0.63 A/W. (See, e.g., Reference 72). For a photodetector length of 40 m, responsivity was measured at 1.2 A/W under low reverse bias voltage of 1 V. (See, e.g., Reference 72). However, for a Ge width of 1 m, the bandwidth barely reaches 30 GHz under even a high voltage of 3 V, and it can be independent of the device length as the frequency response can be limited by the carrier transit time. (See, e.g., References 72 and 73). In order to achieve a higher bandwidth, the Ge width needs to be reduced. Combining these results, a 50 GHz bandwidth has been obtained at a reverse bias voltage of 2 V for a Ge width of 0.3 m and at 3 V for a Ge width of 0.5 m. (See, e.g., Reference 73).
[0143] To enhance the electric field in the Ge, an exemplary MIM plasmonic waveguide has been introduced where the electric field can be highly enhanced in the slot between the two metals. (See, e.g., Reference 75). Compared with other SPP waveguide arrangements, the MIM fundamental mode does not exhibit a cut-off, even for very small thicknesses of semiconductor layer. Thus, an extremely small mode much below the diffraction limit can be obtained. However, as the gap size reduces, the energy begins to enter the metallic layer, reducing the mode propagation length due to an increase in field localization to the metal-semiconductor interface. As a result, absorption in the metal takes place. Thus, to minimize the losses related to absorption into the metal, it can be desired to operate a photodetector in the regime where the absorption in the Ge can be high. Therefore, absorption in the Ge can dominate over absorption losses in the metal. The resulting internal quantum efficiency (IQE) can be estimated to be 36% for 1310 nm wavelength and dropping below 10% for the wavelength of 1550 nm. However, to achieve even such results, a very large voltage exceeding 10 V can be utilized. As the MIM field can be confined in a narrow Ge region, 100-200 nm, short drift paths for photogenerated carriers can be achieved, producing a high speed photoresponse exceeding 100 GHz. (See, e.g., Reference 75).
Exemplary Long-Range Dielectric-Loaded SPP Germanium Photodetectors
[0144] To evaluate the performance of the exemplary plasmonic waveguide in terms of applications for a germanium photodetector, the propagation length and mode field confinement can be considered. The former provides information how long the mode can be transmitted, for example, absorption losses into a metal, and the latter determines the electric field strength inside a waveguide, for example, interaction between a mode and material.
[0145]
[0146] The exemplary photoconductive germanium photodetector can be based on the absorption of a LR-DLSPP mode (See, e.g., References 76 and 77) propagating in a germanium waveguide 2105. (See, e.g., diagrams and electric field plots shown in
[0147] LR-DLSPP inherits the advantages of a very long propagation length from LR-SPP waveguides and superior mode confinement from DLSPP waveguides. (See, e.g., References 76-79). LR-DLSPP can include of a semiconductor ridge deposited on top of a thin metal stripe/electrode, which can be supported by another semiconductor slab beneath. The entire structure can be supported by a low refractive index substrate which can facilitate mode confinement to the semiconductor ridge and underlying semiconductor slab. Due to the thin metal film, the SPPs on the two metal-semiconductor interfaces can couple to each other and form supermodes with symmetric and anti-symmetric transverse components. The symmetric mode and long-range mode can be characterized by a low longitudinal component of the electric field in the metal, thus lowering absorption losses. The long propagation distance can be achieved when the effective mode refractive indices on both metal-semiconductor interfaces can be close in value to each other such that they can couple together to minimize the electric field in the metal. Thus, the exemplary LR-DLSPP configuration facilitates high propagation length and reasonable mode confinement. In comparison, a gap SPP MIM can support a very high confined SPP mode but absorption losses from the metal arises, limiting the propagation distance to tens of the corresponding mode's wavelengths. The exemplary LR-DLSPP waveguide facilitates superior mode field confinement and high propagation length. (See, e.g., References 76-79). It has the highest evaluated FoM among all other plasmonic waveguides, taking into account mode size, wavelength, and propagation length. (See, e.g., Table 2 below). For example:
where w.sub.0 can be the lateral mode width, L.sub.p can be the mode propagation length, n.sub.eff can be the mode effective index, and .sub.0 can be the excitation wavelength.
[0148] The FoM for LR-DSLPP can be at least two orders magnitude higher than other plasmonic waveguide configurations. (See, e.g., Table 2 below). (See, e.g., References 58, 77 and 80). Recently, another plasmonic waveguide was introduced, the so-called hybrid photonic-plasmonic waveguide, which offers extremely long propagation length. However, the mode confinement exceeds 7 m so it may not be practical for on-chip integration. (See, e.g., Reference 80). Furthermore, the FoM for this waveguide exceeds other plasmonic waveguides, but it still over 30 times lower compared to the LR-DLSPP waveguide. Thus, in terms of the absorption losses into metal, mode field confinement, and possible integration with other on-chip components, the exemplary LR-DLSPP waveguide can be a perfect candidate for photodetection applications.
TABLE-US-00002 TABLE 2 FoM for plasmonic waveguides. Waveguide LR-DLS LR-SPP DLSPP Gap (MIM) HPP FoM 3.2 .Math. 10.sup.6 3.2 .Math. 10.sup.4 3.4 .Math. 10.sup.3 1.1 .Math. 10.sup.4 2.9 .Math. 10.sup.4 1.0 .Math. 10.sup.5
[0149] The exemplary LR-DLSPP mode profile matches the mode of the photonic waveguide, facilitating efficient coupling between photonics and plasmonic platforms. (See, e.g., contour plots shown in
[0150] The exemplary LR-DLSPP configuration therefore demonstrates great potential for creation of photoconductive photodetectors based on germanium and other absorbing materials where superior mode confinement and low absorption losses in metal can be beneficial.
Exemplary LR-DLSPP Waveguide for a Photodetection
[0151] In a state-of-the-art PIN photodetector, the cross-sectional area of the waveguide has to be big enough to minimize or otherwise reduce absorption losses in a doped Si, so waveguide dimensions of w=1 m and h=260 nm can be utilized to achieve good mode field confinement in the Ge, low absorption into the doped Si, with high responsivity as a result. (See, e.g., References 72 and 73). The cross-sectional area for such a waveguide can be 0.26 m.sup.2. In contrast, the plasmonic MIM photodetector offers an extremely small cross-sectional area of 0.016 m.sup.2, although at the cost of absorption losses into the metal that significantly limit its photodetector quantum efficiency. (See, e.g., Reference 75). Calculations show that the quantum efficiency of a MIM photodetector operating at 1310 nm does not exceed 70%, and drops to 30% for 1550 nm. For the MIM photodetector with Ge between the metals and on top of the MIM structure, the quantum efficiency does not exceed 10%.
[0152] Compared to the MIM structure, the exemplary Ge photodetector based on the LR-DLSPP waveguide arrangement provides a cross-sectional area of 0.129 m.sup.2 even when far from optimization. Such a cross-section was chosen to facilitate efficient coupling of light from the Si waveguide to the photodetector through a butt-coupling arrangement. (See, e.g., diagrams and contour plots shown in
[0153]
[0154] The calculated electric field profile of the fundamental TM mode (See, e.g., electric field plot shown in
Exemplary Quantum Efficiency of the LR-DLSPP Ge-Based Photodetector
[0155] Neglecting the scattering losses, the responsivity and the IQE of a photodetector can depend only on the absorption coefficient of Ge, .sub.Ge, and metal, .sub.m:
where L.sub.Ge and L.sub.m can be the total length of the Ge waveguide and metal contact, respectively. Here L.sub.Ge=L.sub.m. The absorption of Ge and the confinement factor of the mode in the Ge waveguide can determine .sub.Ge. Also, the overlap of the mode with the metal can determine .sub.m. (See, e.g., Reference 58). To calculate the absorption coefficients of metal (e.g., Au), .sub.Au, and Ge, .sub.Ge, 3D FDTD and FEM simulations were performed. To determine .sub.Au, the Ge absorption coefficient was set to 0 and the Au stripe/electrode (See, e.g., diagrams and contour plots shown in
[0156] The calculated effective absorptions of Ge was .sub.Ge=920 cm.sup.1 and .sub.Ge=7956 cm.sup.1 for wavelengths of =1550 nm and =1310 nm (See, e.g., graph shown in
[0157] In the exemplary arrangement according to the present disclosure, the absorption coefficient of Ge, .sub.Ge, can be at least 7 times higher compared to the absorption coefficient of Au, .sub.Au, for a wavelength of =1550 nm, and over 43 times higher for a wavelength of =1310 nm where Ge shows a higher absorption. (See, e.g., graph shown in
Exemplary Responsivity of the LR-DLSPP Ge-Based Photodetector
[0158] The light propagating in the Ge LR-DLSPP waveguide can be absorbed mostly by the Ge and only partially by a metal. (See, e.g., graph shown in
P.sub.abs=0.5 Re(.Math.
)=0.5|E|.sup.2Im(()) (7)
[0159]
[0160] As a result, an absorption as a function of space and frequency can depend only on the electric field intensity and the imaginary part of the material permittivity. Performed simulations showed that 97% of the power can be absorbed in the first 5 m of the LR-DLSPP waveguide for a wavelength of 1310 nm and over 88% of the power coupled to the photodetector can be absorbed in the first 30 m of the photodetector for a wavelength of 1550 nm. (See, e.g., graph shown in
[0161] These exemplary results fit very well with the data shown in the graph of
[0162] The frequency-dependent photon absorption rate can be equivalent to the generation rate under the assumption that each absorbed photon can excite an electron-hole pair. The generation rate for wavelengths of 1310 nm and 1550 nm with different photodetector lengths was calculated using Lumerical FDTD simulations and then exported to Lumerical Devices, where it was used to calculate a responsivity for each photodetector configuration. (See, e.g., graph shown in
[0163] The dark current achieved in the exemplary devices was around 0.6 A for a 3 m long photodetector operating at wavelength of 1310 nm. As shown
Photodetector Speed and Bandwidth
[0164] In telecommunication systems, photodetectors can be utilized to detect optical signals modulated at high data rates. Thus, an important figure of merit can be the opto-electrical 3 dB bandwidth, which can be defined as the frequency range from DC to cut-off frequency f.sub.3dD i.e., the frequency at which the electrical output power drops by 3 dB below power value at very low frequency. The opto-electronic bandwidth of a photodetector can depend both on the carrier transit time and RC response time. To reduce the carrier transit time, the distance between the collecting electrodes can be small. In comparison, RC time reduction can be obtained by lowering the contact resistance of the metal electrodes and by reducing the detector length which reduces the photodetector capacitance. (See, e.g., Reference 81). The RC-limited 3 dB cut-off frequency can be expressed as, for example:
where R.sub.eff can be the effective overall resistance and C.sub.pd can be the junction capacitance. The carrier transit time, that defines the time of photo-generated electrons or hole to travel through the active region prior to being collected by the contacts, can be estimated using, for example:
where d.sub.abs is the distance between the site where carriers can be generated and the electrode collecting those carriers, and v can be the average carrier velocity. (See, e.g., References 64, 81, and 88).
[0165] As discussed above, a L=5 m long photodetector can be utilized to achieve a quantum efficiency exceeding 95% at a wavelength of 1310 nm. Taking into account the distance between both electrodes to be approximately 450 nm i.e., the second electrode can be placed around 300 nm from the Ge waveguide, a capacitance in the range of a few fF can be suspected. The second electrode placed 300 nm from the waveguide may not disturb a propagating mode in the waveguide. (See, e.g., contour plot shown in
[0166] In the exemplary design, all carriers can be generated in the area limited by the germanium waveguide. Assuming a distance between electrodes of 450 nm and a drift velocity of 6.5.Math.10.sup.6 cm/s (See, e.g., Reference 88), a bandwidth of f.sub.t=80 GHz can be achieved. However, as it can be observed from
[0167] Therefore, a bandwidth exceeding 100 GHz can be achieved even for an electrode spacing of 540 nm (See, e.g., contour plot shown in
[0168] As previously discussed, the bandwidth of the photodetector may not be limited by the RC time constant, but the transit time utilized for carriers to drift to the contact electrode collecting the carriers. By decreasing the distance between the two contacts, a very high electric field can be obtained at low bias voltage what additionally improves carrier collection.
[0169] The exemplary Ge plasmonic photodetector provides a combination of advantages and a huge flexibility in terms of design and integration with other materials. Due to the difference in velocity of the carriers, electrons and holes, the response of the photodetector can usually be asymmetric as holes can be delayed compared to electrons. However, in the exemplary LR-DLSPP photodetector arrangement, carriers can be photogenerated in the region surrounding the metal stripe that serves simultaneously as a collection electrode. (See, e.g.,
Exemplary Symmetric and Asymmetric Electrodes
[0170] Compared to previous waveguide arrangements where carriers were generated in the entire area limited only by metal contacts (See, e.g., diagrams shown in
Exemplary Plasmonic Graphene Photodetector Based on Channel Photo-Thermoelectric Effect
Exemplary Photo-Thermoelectric Effect
[0171] Three exemplary effects can contribute to a photodetection in waveguide-integrated graphene devices (see, e.g., References 113-116): (i) photo-voltaic (PV) or photo-conductive (PC) (see, e.g., References 117-122), (ii) photo-bolometric (PB) (see, e.g., References 123-127) and (iii) photo-thermoelectric (PTE) (see, e.g., References 128-131) effects. The choice of the effect depends on device configuration, design and operation conditions. (See, e.g., References 113, 116, 122, and 128). PTE photodetectors in recent studies showed that PTE effect dominates over PV the photocurrent generation in graphene devices. (See, e.g., References 132 and 133).
[0172]
[0173] Graphene is a very attractive material for such a photodetector. Apart from the excellent properties, it can sustain a very high temperature; thus far the highest of all materials exceeding 4550 K or even 6000 K under short period of time (See, e.g., Reference 136), thus, enhancing a photocurrent. (See, e.g., Reference 135). Furthermore, the response time dominated by the phonons interaction is in the range of about 2-4 picoseconds. (See, e.g., References 137-140). The operation of such a photodetector utilizes spatially in-homogeneous doping profile that is created by local heating of p-n junction by the incident laser power. (See, e.g., References 104, 109, 128-131, and 141). As a result, the non-equilibrium hot carriers can be excited with an electron temperature T.sub.e higher than that of the lattice, giving rise to the electron temperature gradient across a junction. This increases in the temperature of photoexcited carriers is a direct consequence of the large optical phonon energy in graphene (e.g., 200 eV) and low scattering rate of electrons by acoustic photons. (See, e.g., References 138-144). The latter give rise to an increased temperature of the photoexcited carriers for picoseconds, while the lattice stays close to room temperature. In such a photodetector, the photovoltage is generated from hot electrons through the Seebeck coefficient that varies in the graphene sheet as result of different doping or the temperature gradient. For different doping levels on both sides of the junction, and the temperature profile in the graphene, the Seebeck coefficient can vary across graphene, which can generate a photo-thermoelectric voltage. Due to the non-monotonous dependence of the difference of the Seebeck coefficient in the two different doped regions of the junction, the resulting photovoltage exhibits multiple sign reversals in dependence of the gate voltage. The characteristic 6-fold pattern is the result of the two doping levels on either side of the junction. Another approach relies on heating of one contact that can lead to a temperature gradient across a graphene channel resulting in a photo-thermoelectric contribution to the photovoltage. (See, e.g., References 128 and 144).
Exemplary Graphene Photodetector Arrangement
[0174] The exemplary photodetector can be based on an exemplary metal-graphene-metal (MGM) arrangement (See, e.g., References 117, 118, and 131) with a graphene channel contacted by two electrodes, either of the same (See, e.g., Reference 118) or two different metals. (See, e.g., References 117 and 122). The difference in work function between the metal pads and graphene leads to charge transfer with a consequent shift of the graphene Fermi level that is in contact with the metal. (See, e.g., References 117, 122, and 145). As the Fermi level of the metal-free graphene channel can be different, this can result in a potential gradient between the metal-free graphene and graphene that can be in contact with metal. (See, e.g., References 117 and 122). This inhomogeneous doping profile (See, e.g., References 144 and 145) can create a junction along the channel that can be beneficial in the photodetection process, as it can result in an internal electric field capable of separating the light induced e-h pairs.
[0175]
[0176] As the electron-electron scattering in graphene can be ultrafast on the order of 10 fs, and electron-phonon scattering relatively slow on the order of picoseconds (See, e.g., References 137-140, 142, and 143), the photoinduced carriers can be thermalized by the electronic system, and can dissipate the heat very slowly to the lattice. Because of the linear electronic dispersion and its low dimensionality, the electron-electron scatterings can be substantially stronger than the electron-phonon scatterings. Typically, the cooling length of hot electrons in graphene exceeds hundreds of nanometers. Thus, the electrons in graphene may not reach thermal equilibrium with the lattice before being collected. (See, e.g., References 114 and 137-140).
[0177] In the exemplary photodetector arrangement, the electric field reaches a maximum at the interface between metal stripe and semiconductor along graphene sheet, and can decay fast in the direction of second electrode. This can lead to an asymmetric temperature distribution between metal contacts, and can be transduced into an electrical signal through the Seebeck effect. This can be beneficial in excitation of currents in graphene, the in-plane electric field component (Ey) of the LR-DLSPP mode is very strong close to the graphene surface even for TM supported mode (See, e.g., References 147-150) and arise from a sharp metal stripe corners. (See, e.g., contour plot shown in
Exemplary Calculation of Power Absorbed by Graphene Sheet
[0178]
[0179] To evaluate the performance of the photodetector, the amount of power absorbed by a graphene sheet needs to be calculated. Power absorbed by the graphene sheet can be calculated from, for example:
P.sub.abs=P.sub.ine.sup..Math.L(11)
[0180] For example, around P.sub.in=165 W of power coupling to a photodetector was simulated. For the absorption coefficient for graphene .sub.G and metal am obtained from a simulation, the length dependency of fraction of light absorption in graphene can be calculated by, for example:
where L can be the length of photodetector. The results are shown in the graph of
[0181] The absorption coefficient of graphene .sub.G can be calculated from a formula that relates a 2D graphene absorption .sub.2D with the effective thickness of the waveguide t through the expression. Thus, for example:
.sub.G=.sub.2D/t(13)
[0182] Taking .sub.2D=2.3% and the effective thickness of the waveguide at t=100 nm, the absorption of graphene was calculated at .sub.G=0.23 dB/m. Thus, to achieve 50% absorption of power by graphene around 13 m-long waveguide can be utilized.
Exemplary Channel PTE Current Generation Principle
[0183] Most of the previously reported PTE effects usually refer to the junction formed either by monolayer and bilayer graphene or between regions of graphene with different Fermi energies E.sub.F, such as p-n junctions with buried split-gates or with a top-gated control. As discussed above, the main principle of the PTE effect can be creating an asymmetry in the device. Such asymmetry can be created by using two different contact metals (See, e.g., Reference 117) or by using two adjacent graphene regions of different doping.
[0184] The photovoltage in this exemplary case can be generated at the junction, and can be driven by the difference in graphene's Seebeck coefficients S=S.sub.1S.sub.2 on either side of the junction through, for example:
V.sub.ph=ST=(S.sub.1(.sub.i)S.sub.2(.sub.2))T(14)
where T can be the electron temperature increase within the junction after photoexcitation and can be the chemical potential. The dependence of the photocurrent defined as, for example:
on S, which results in multiple photocurrent sign reversals over a gate voltage sweep due to the non-monotonic dependence of S.sub.1 and S.sub.2 on E.sub.F.
[0185] Compared to PTE effect, the PV effect relies on the separation and then collection of photoinduced electrons and holes by a built-in electric field leading to a net photocurrent. Thus, for example:
where .sub.mob can be the carriers mobility, the width of the neutrality region in the channel graphene, .sub.0 the minimum conductivity, R the total resistance, and n.sub.x the steady state density of photoexcited carrier. Here, .sub.1 and .sub.2 suggest a chemical potential shift that can result from a different doping level introduced by different metals or biased voltage.
[0186] From above photocurrent equation, it can be determined that photoresponse can maximize in the presence of a p-n junction when .sub.1 and .sub.2 can have an opposite sign. As the polarity of the PV current can be determined solely by the sign of field gradient, there may only be one sign reversal occurring at .sub.1=.sub.2. Thus, the photovoltage induced by the PV can effect change monotonically with the gate voltage.
[0187] For example, the graphene-metal (G-M) interface where chemical potential of graphene that can be in contact with metal can be shifted compared to the graphene channel that can be related to the difference in work functions of the materials. (See, e.g., References 144-146). In the exemplary arrangement, the temperature difference can be established across the entire device channel. This can provide a few advantages over narrow p-n junction, as more of the electron heat can be converted into a photovoltage giving rise to a responsivity increase. (See, e.g., References 108 and 109). In contrast to p-n junction PTE, the channel PTE voltage can be driven by entire temperature across the channel as, for example:
V.sub.ph=ST=S()T(17)
[0188] The Seebeck coefficient S of the graphene channel can be defined as, for example:
where k.sub.B can be the Boltzman constant, T can be the lattice temperature, e can be the electron charge, can be the conductivity of graphene, and can be the chemical potential. Consequently, the channel PTE exhibits a single sign change in the channel due to the monotonic dependence of S on .
[0189]
[0190] The operation principle of the exemplary LR-DLSPP graphene photodetector can be as follows. The propagating plasmonic mode can reach a maximum in the metal-semiconductor interface (e.g., Contact 2 shown in
where R can be the resistance of the graphene sheet. Thus, for example:
[0191] Assuming L=400 nm spacing between electrodes, photodetector length of W=40 m, and a photodetector operating based on the G-M channel photo-thermoelectric effect (.sub.1=.sub.2), the graphene sheet resistance was calculated at R50 at chemical potential =0 eV (See, e.g., graph shown in
Exemplary Temperature Distribution
[0192] The electron temperature of hot electrons in graphene can be governed by the heat transfer equation, which can be, for example:
.sup.el.sup.2T.sub.eC.sup.el(T.sub.eT.sub.0)+P*=0(21)
where .sup.el can represent the lateral 2D thermal conductivity and C.sup.el the vertical heat loss, T.sub.e can be the electron temperature at a given position, To can be the temperature of the substrate and P* can be the input power density provided by the LR-DSLPP mode. Thermal conductivity .sup.el can be calculated from the Wiedemman-Franz relation (See, e.g., Reference 138) and expressed by, for example
where k.sub.B can be the Boltzman constant, e can be the electron charge, T can be the operation temperature and can be the electrical conductivity of the graphene. The 2D electrical conductivity of graphene can depend on the chemical potential/Fermi level shift and can be expressed by, for example:
where .sub.0 can denote the minimum conductivity and the spreading of the transfer characteristics. Here .sub.0 it was assumed that .sub.0=0.193 mS, which can be close to the experimentally achieved value of 0.21 mS.
[0193] As the electrons in graphene can be thermally isolated from the lattice, the electrons thermal conductivity .sup.el and the thermal coupling between electrons and lattice C.sup.el can govern the heat dissipation, and can determine the electron temperature distribution. Because of much higher heat capacity of a photon system compared to an electronic one, the photon system can be treated as an ideal thermal bath with T.sub.0 staying constant. Here can represent the electron-lattice cooling rate and C.sup.el the electron heat capacity. In graphene with a linear electronic dispersion, both parameters can be very small, meaning that the vertical heat dissipation can be mainly limited by the electron-lattice cooling.
[0194] The distance between the peak position of the electron temperature T.sub.e and the metal contact can be characterized by the cooling length of hot electrons given by =(.sup.el/C.sup.el).sup.1/2.
[0195] In comparison, for the lower electron-photon coupling strength g=0.0513, the cooling rate exceeds 0.6 ns.sup.1 even for the charge neutrality point =250 meV in the entire Fermi energies range from 0 eV to 0.5 eV. (See, e.g., graph shown in
[0196] The temperature distribution in the photodetector was calculated using the analytical solution to the heat equation, which can be, for example:
where P* can be the rate at which heat enters the system and L can be the photodetector length, for example, a distance between electrodes. As seen from above equation, material parameters that can affect the temperature profile include the thermal conductivity .sup.el, the electronic specific heat C.sup.el, and the electron-lattice cooling rate . The combination of these three parameters generates a characteristic cooling length for hot-carrier propagation in the system. As can be seen from
Exemplary Photocurrent MapOperation Regime
[0197] The exemplary photodetector can operate without a need for a bias voltage as the electronic gradient across a graphene channel can be incorporated through an asymmetric electrical contact arrangement. Here one of the photodetector electrodes can serve simultaneously as a metal stripe supporting a propagating mode. Thus, a highly enhanced electric field can be present around this electrode with the maximum localized at the metal, which can decay fast into graphene channel in a direction of the external electrode. As a result, an electronic temperature difference can be established across the channel with built-in potential difference in a channel.
[0198] In
[0199] As shown in
Exemplary Evaluating PTE Performances
[0200] For a W=40 m long photodetector and a distance between electrodes L=400 nm, the resistance of the graphene was calculated as a function of chemical potential for different widths of the neutrality region A. (See, e.g., graph shown in
Exemplary Asymmetric Metal Arrangement and Operation Speed
[0201] It was previously observed that for the exemplary MGM arrangement, with a metal being the Au, a p-type doping of graphene beneath the metal can be observed that can be lower than the intrinsic doping of the graphene channel. A doping induced by a metal can be related with a difference in the work functions of the metal and graphene (.sub.G=4.5 eV) (See, e.g., Reference 145) that leads to charge transfer at the contact interface. Depending on the metal, a different type and doping level can be achieved. (See, e.g., References 110, and 144-146). As a results, Ti (.sub.G=4.3 eV) can shift the Fermi energy for E.sub.F=230 meV while Au (.sub.G=4.7 eV) for E.sub.F=250 eV. (See, e.g., Reference 145). This can confirm that Ti contacts can result in n-type doping of graphene while Au contacts can result in p-type doping. (See, e.g., References 144-146).
[0202] The transit-time-limited bandwidth of the photodetector can be given by, for example:
where t.sub.r can be the transit time between metal stripe and external electrode. The exemplary photodetector can operate even at the zero bias voltage as the result of a difference in the Fermi level between two contacts on graphene that can be doped by different metallic electrodes. (See, e.g.,
[0203] As discussed herein, the exemplary photodetector can be based on photo-voltaic, photo-conductive, photo-thermoelectric, photo-bolometric or photo-gaining effect. It can take advantage of additional hot carriers generated in the metal stripe that can be transferred to the graphene or 2D material. Graphene or other 2D material can be below or above a metal stripe, and it can consist of one layer of graphene or 2D material or two or more layers. The exemplary photodetector can be separated by another dielectric material. It can be made of only graphene or a 2D material, or it can be made of graphene and a 2D material together in order to take advantage of the absorption properties of 2D material and the transport properties of graphene. The metal stripe can be in the center of the waveguide or displaced in the waveguide. An external metal electrode can be only on one side of the waveguide or it can be two or more metal electrodes placed on both sides of the waveguide. The metal stripe can be placed directly on top of the semiconductor buffer or inside a semiconductor buffer or inside a semiconductor ridge. The metal stripe and metal electrode(s) can be made from the same material or they can be made from different metallic materials. The external electrodes can be made from the same material or they can be made from different materials. The semiconductor ridge and the semiconductor buffer can be made from the same material or they can be made from different materials. The semiconductor ridge and the semiconductor buffer can be made from any material that meets the requirements of integration with other photonic and electronic components. The semiconductor ridge can have any suitable characteristics (e.g., it can be wider or higher) to meet requirements of coupling efficiency from a photonic waveguide.
[0204]
[0205] As shown in
[0206] Further, the exemplary processing arrangement 3505 can be provided with or include an input/output ports 3535, which can include, for example a wired network, a wireless network, the internet, an intranet, a data collection probe, a sensor, etc. As shown in
[0207] The foregoing merely illustrates the principles of the disclosure. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements, and procedures which, although not explicitly shown or described herein, embody the principles of the disclosure and can be thus within the spirit and scope of the disclosure. Various different exemplary embodiments can be used together with one another, as well as interchangeably therewith, as should be understood by those having ordinary skill in the art. In addition, certain terms used in the present disclosure, including the specification, drawings and claims thereof, can be used synonymously in certain instances, including, but not limited to, for example, data and information. It should be understood that, while these words, and/or other words that can be synonymous to one another, can be used synonymously herein, that there can be instances when such words can be intended to not be used synonymously. Further, to the extent that the prior art knowledge has not been explicitly incorporated by reference herein above, it is explicitly incorporated herein in its entirety. All publications referenced are incorporated herein by reference in their entireties.
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