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A novel structure is proposed to electrically detect the plasmonic waves from a subwavelength plasmonic waveguide. By locating two L-shaped metallic nanorods in close proximity of each other at the end of the plasmonic waveguide, a metal-semiconductor-metal plasmonic detector is constructed. The L-shaped nanorods also form a dipole nanoantenna and a nanocavity to focus the photonic power into the active volume of the detector. The dimensions and locations of the L-shaped nanorods are studied to maximize the transmission efficiency of the photonic power from the plasmonic waveguide to the detector. Impedance matching with a sub is investigated to further improve the power transmission. Possible leads of the detector are discussed and their effects are investigated. Proposed detector has an ultra-compact and easy-to-fabricate planar structure, and a potentially THz speed, high responsivity as well as low power dissipation.
©2009 Optical Society of America
Integrating optics with electronics could simultaneously achieve both the ultra-compactness of electronics and the super-wide bandwidth of optics [1,2]. A critical challenge we face when attempting to integrate dielectric optics with electronics is that the micrometer scales of optical devices are significantly larger than the corresponding nanometer scales of modern electronic counterparts. Plasmonics, which is concerned with the manipulation of the flow of light at subwavelength scales by using metallic nanostructures [3,4], shows a great potential for the realization of integrated optical and electric circuitry in a nanometer scale [3–7]. A wide range of ultra-compact plasmonic devices have been demonstrated to generate [8–10], guide [6,11–17] and detect [18–20] light far below the optical diffraction limit. Plasmonic waveguides, taking the advantages of the plasmon-enabled modal confinement, offer promise for overcoming the bandwidth limitations of the classical electric interconnects [6,11–17]. It’s therefore necessary to develop high-bandwidth, high-responsivity, and nanoscale optical-electric converters to integrate the plasmonic waveguides with the electronic circuits.
Traditional photodetectors are large in dimensions since they generally have low responsivity per unit volume [21]. Localized surface plasmon polaritons, which are associated with the oscillations of the conduction electrons of metallic nanoparticles, have been used to concentrate light into a subwavelength volume [22–25], consequently making it possible to construct a photodetector in a subwavelength scale [18,19]. Recently, a nanoscale plasmonic detector has been successfully integrated with a metal–insulator–metal plasmonic waveguide to detect the surface plasmon polaritons [20]. However, there is still a far way to apply the plasmonic detector to modern electronic circuits. The grant challenges are faced when attempting to detect the plasmonic waves propagating along a metallic waveguide. Firstly, the plasmonic waves are generally very weak at the open end of the waveguide because of high losses in the metallic waveguides [3]. Secondly, a strong reflection may exist at the interface between the plasmonic waveguide and the detector, owing to a large contrast between the permittivities of the media forming the waveguide and the detector. Thirdly, plasmonic waves decay rapidly when they move away from the metallic waveguide into the surrounding dielectric medium. Only a small fraction of the plasmonic energy can reach the active region of a butt-connected plasmonic detector. Consequently, the efficient coupling of the optical energy between the plasmonic waveguide and the nanoscale detector becomes a critical issue in the design of a plasmonic detector.
A dipole nanoantenna, formed by placing two nanoparticles in close proximity of each other, can significantly enhance the field strength in the gap [22–28]. Paper [29] presents how plasmonic waves propagate through a plasmonic waveguide coupled with a nanocavity formed by a pair of metallic nanorods. In this paper, we postulate to use a pair of L-shaped metallic nanorods to form a nanocavity coupled with a plasmonic waveguide to effectively focus the power of the plasmonic waves, and thereafter convert them into electric signals. The L-shaped nanorods, which form a half-wavelength dipole nanoantenna as well as the nanocavity, are used to couple, concentrate as well as enhance the electromagnetic fields from the plasmonic waveguide. The L-shaped nanorods are also designed as a half-wavelength waveguide in the propagation direction to further enhance the electric fields in the nanocavity where the peak of the standing waves is generated. Furthermore, the L-shaped nanorods are also functioned as the electrodes of the plasmonic detector, leading to an ultra-compact planar detector structure yet easy to be fabricated. The plasmonic waveguide and the plasmonic detector are electrically isolated, enabling a complex optical-electric circuitry on a nanoscale footprint.
Figure 1 shows the proposed structure of a plasmonic detector, which is realized by means of a metal-semiconductor-metal (MSM) photodetector, coupled with a metal-insulator-metal (MIM) subwavelength waveguide. The MIM waveguide consists of a 100nm silica slot sandwiched between two pieces of Ag (ε = −86.24 + 8.74i [30]) thin films with a thickness of 50nm. This type of waveguide is able to support a spatial field-confined surface plasmonic polariton mode [17]. The MSM plasmonic detector, which uses a pair of L-shaped silver nanorods as the electrodes, is located 50nm away from the MIM waveguide. The nanocavity aligned by the two L-shaped nanorods is filled with the absorption material Ge (ε = 18.28 + 0.0485i [30]), which is compatible with the standard silicon technology [31]. The leads of the MSM plasmonic detector are two conducting wires made of transparent conduction oxide (TCO) ZnO (ε = 3.712), which has less impact on the resonant fields in the nanocavity. The entire structure is embedded in SiO2 (ε = 2.085), for practical experimental considerations, e.g., to avoid external contaminations. The operating wavelength is 1.55μm in our study. The simulation is carried out using finite integral time domain method in the transient solver with CST Microwave Studio [32]. Only the fundamental transverse-magnetic mode, which is excited by the waveguide port, is considered due to the nature of the MIM waveguide. 2.5nm and 5nm mesh steps are applied in the critical and non-critical regions, respectively. Open boundary conditions are applied with SiO2 as the background material. Furthermore, the final results are verified using Ansoft in frequency domain via the finite element method.
Fig. 1 Schematics of a plasmonic detector coupled with a plasmonic waveguide. The plasmonic waves, propagating along the waveguide, are focused in a nanocavity and converted into photocurrent via the plasmonic detector.
The electromagnetic fields propagated from the MIM waveguide are localized and enhanced in the nanocavity. A nanoantenna is formed by the two arms of the L-shaped nanorods in the y-direction, which corresponds to the direction of the electric fields in the MIM waveguide because of the transverse-magnetic nature of the surface plasmons [17]. When the nanoantenna operates at the resonant frequency, the maximum electromagnetic energy will be received from the MIM waveguide and concentrated in the nanocavity between the two nanorods. The gap width has a high impact on the resonant fields in the nanocavity [24]. The two nanorods together with the material inside the nanocavity form a planar capacitor. The smaller the gap, the larger the capacitance is; therefore, the stronger the electric fields are. However, a smaller gap implies a smaller active volume and hence less absorption of the detector. The integration of the electric-field intensity over the nanocavity or the power absorption is more interesting for a plasmonic detector. Figure 2 shows the power absorption in the nanocavity as a function of the length of the nanoantenna for various gaps. The resonant length of the nanoantenna increases with an increase of the gap width owing to the decrease of the coupling between two arms of the nanoantenna [24]. The power absorption at the resonant length does not increase monolithically with the decrease of the gap width. The maximum value appears when the length of the nanoantenna is 350nm and the gap width is 50nm. These dimensions agree with those used in the Ge photodetector demonstrated by Miller’s Group [19]. Note that the resonant length of the nanoantenna is substantially shorter than the half of the free-space wavelength, which is the resonant length of a traditional half-wave dipole antenna at radio or microwave frequencies. This is because that the metallic nanorods are no longer perfect electric conductors at optical frequencies. In addition, two arms of the nanoantenna are strongly coupled by the interaction of the localized surface polaritons. As a result, the effective wavelength of the near-field around the nanorods is much shorter than the free-space one and hence the resonant length of the nanoantenna becomes shorter [26].
Fig. 2 Power absorption in the nanocavity as a function of the length of the nanoantenna, for various widths of gaps (g) between two L-shaped nanorods.
The fields in the nanocavity are further enhanced through a nanorod waveguide, which is formed by the other two arms of the L-shaped nanorods in the x-direction. A standing wave propagates along the nanorod waveguide as a result of the interference of the forward wave and the reflection wave from the opened right-end of the nanorod waveguide. Specifically, if the length of the nanorod waveguide is one-half the effective wavelength, the electric fields will exhibit a cosine distribution along the nanorod waveguide [33], and the fields in the nanocavity can be enhanced. Figure 3a shows the averaged electric-field intensity in the nanocavity as a function of the length of the nanorod waveguide. The maximum of the fields are obtained when the length of the nanorod waveguide is 190nm, and the averaged electric-field intensity in the nanocavity is enhanced by 42% comparing to the case where two straight nanorods are used (waveguide length = 50 in Fig. 3a). Figure 3b shows the distribution of the electric and magnetic fields in the xy-plane crossing the center of the nanorods when the length of the nanorod waveguide is 50nm (straight nanorods) and 190nm (L-shaped nanorods), respectively. We see that the electric fields are concentrated in the nanocavity and the magnetic fields are focused in the center of the nanorod waveguide with the L-shaped nanorods; while strong electric fields are observed in far ends, and the strong magnetic fields are located at the sides, of the dipole nanoantenna with the straight nanorods. Poynting vector calculation shows that 81% of the optical power in the MIM waveguide is transmitted to the nanocavity when the L-shaped nanorods are used.
Fig. 3 Normalized averaged electric-field intensity in the nanocavity as a function of the length of the nanorod waveguide. The maximum value appears when the length is 190nm. (b) The distribution of the electric and magnetic fields in the xy-plane crossing the center of the nanorods when the nanorod waveguide is 50nm (straight nanorods) and 190nm (L-shaped nanorods), respectively.
The optical power received in the nanocavity is converted into electric signals with a plasmonic detector by means of an inherently fast MSM structure [19,34]. Two electrodes are needed to apply bias voltage, and to conduct the photocurrents generated by the detector. Instead of using two additional electrodes as in the literature [19], we design the electrodes by connecting two additional conduction wires − the leads of the detector − to the nanorods as shown in Fig. 1. Such a configuration leads to an ultra-compact planar structure, which is easy to fabricate. However, the bias voltage applied to, and the photocurrents flowing through, the nanorods will vary their electron distribution, particularly at the surfaces facing to the absorption materials. Such variation of the electron density in the nanorods may alter the plasmonic behavior of the nanorods [3]. For our plasmonic detector, the saturation bias is far less than 1V, and the photocurrents are in a nanoampere range as shown in Fig. 7 . The caused variation of the electron density in the two nanorods is less than 0.01% [35]. Previous experimental studies have also implied that the bias voltage and the photocurrents do not have an obvious effect on the near-fields generated around the metallic electrodes of MSM photodetectors [20,36].
Fig. 7 Photocurrents of the plasmonic detector as a function of the applied bias voltage. Inset is photogeneration distribution inside the nanocavity in the xy-plane.
The additional detector leads may slightly affect the resonance of the nanoantenna. To minimize the effects, the leads should be connected to the nanorods in the directions perpendicular to the y-direction as it is the critical direction in the antenna design [33]. Moreover, TCO leads are preferred to metallic leads as a metallic waveguide will be formed to guide the received energy to leave the nanocavity if the leads are in the xy-plane. Figure 4 shows the normalized averaged electric fields in the nanocavity as a function of the length of the leads connected to the L-shaped nanorods at three different locations shown in the inset. The leads are made of two ZnO wires and the cross-section of each is 50nm × 50nm. We see, for all three cases, that the averaged electric fields in the nanocavity reduce slightly with increasing the length of the leads at the beginning and the decrease is saturated when the length is further increased. The saturation feature is favored in real applications. The decrease of the electric fields is less than 3% in all three cases. This trivial effect could be compensated as shown in the following section. However, the resistance of the TCO leads may need to be taken into further consideration in the experimental realization of the detector.
Fig. 4 Normalized averaged electric fields in the nanocavity as a function of the length of the leads (ZnO wires) connected to the L-shaped nanorods at three different locations shown in the inset. The effect of the ZnO leads on the electric fields in the nanocavity is less than 3%.
Figure 5 shows the electric fields propagating along the center of the plasmonic waveguide to the nanocavity with three nanoantenna structures: the straight nanorods, the L-shaped nanorods, and the L-shaped nanorods plus the detector leads, respectively. The shaded area corresponds to the location of the nanocavity. The electric fields without nanorods are also shown as a reference. We see that the electric fields are greatly enhanced in the nanocavity by the nanorods, especially by the L-shaped nanorods. However, we also see a large reflection of the electric fields along the MIM waveguide due to mismatched impedance between the MIM waveguide and the plasmonic detector. A stub shown in Fig. 1, which has been widely used for impedance matching at microwave frequencies [33], is extended here to perform the impedance matching at optical frequencies.
Fig. 5 Electric fields propagating along the center of the plasmonic waveguide in the x-direction to the nanocavity in four different cases: with no nanorod, with the straight nanorods, with the L-shaped nanorods, and with the L-shaped nanorods plus the leads. The electric fields are enhanced the most in the nanocavity with the L-shaped nanorods. The origin of the coordinates is located in the central end of the MIM waveguide.
The MIM waveguide and the plasmonic detector can be modeled as a transmission line, which has a propagation constant γ, characteristic impedance Z0, and a load with impedance ZL. If ZL = Z0, there will be no power reflection from the load. For an arbitrary load ZL, we can match the load ZL to the characteristic impedance Z0 by using a stub located near the end of the waveguide. The transmission line model for the MIM waveguide and the stub is shown in the upper inset in Fig. 6 . Suppose that the stub is located a distance d from the right end of the waveguide, has the same slot width as that of the plasmonic waveguide, and has a depth l. The impedance of the waveguide between the stub and the load can be expressed as Z1 = Z0(ZL + Z0th(γd))/(Z0 + ZLth(γd)); and the impedance of the stub is given by Z2 = Z0th(γl) [33]. To match the characteristic impedance Z0 and the load ZL, we set Z1 + Z2 = Z0. This is a nonlinear complex equation. An analytic solution can only be obtained when the transmission line is lossless. A numerical method is needed herein to obtain the solutions as the losses in the plasmonic waveguides cannot be ignored. The bottom inset in Fig. 6 shows the comparison of the electric field distribution along the central line in the matched and un-matched MIM waveguides, where the d and l for the stub are found to be 382nm and 58nm, respectively. It is evident that insignificant portion of power is reflected to the source in the matched waveguide and higher power transmission (around 6%) is achieved from the matched MIM waveguide to the nanocavity as shown in Fig. 6.
Fig. 6 The real part of Poynting vectors along the central line of the MIM waveguide in the x-direction for impedance matched/unmatched MIM waveguide with the L-shaped nanorods plus the leads. Upper inset shows the transmission-line model for the MIM waveguide and the stub for the impedance matching. Bottom inset shows the electric fields of the matched and unmatched MIM waveguides along the central line.
The electric characteristics of the plasmonic detector are studied with a 2-D model of a MSM photodetector. In this model, the MSM photodetector is formed by the absorption material Ge, which is filled in the nanocavity, and the two L-shaped nanorods. The photogeneration rates in the absorption material are calculated by using η|E|2λα/(2πћc), where η is the internal quantum efficiency, ħ the Planck’s constant, λ the free space wavelength, c the speed of light, α the absorption coefficient and E the integrated electric fields. The photogeneration rate calculated is subsequently inserted into the Luminator and Atlas solvers in the Silvaco TCAD software [37], where the electric characteristics of the plasmonic detector are simulated.
Figure 7 shows the photocurrents of the plasmonic detector as a function of the applied bias voltage, and the photogeneration rates inside the plasmonic detector are shown in the inset, where the internal quantum efficiency η is taken 50%, for simplicity. The photogeneration distribution in the absorption material is proportional to the electric-field intensity in the nanocavity as shown in Fig. 3b. The curve of photocurrents shows that the plasmonic detector works pretty well. Note that the saturated bias voltage of the plasmonic detector is in a level of mille-volts. This implies that the power dispersion of the plasmonic detector will be much smaller than the traditional butt-coupled waveguide photodetectors in which the bias voltage is generally larger than 10 volts [21].
The transit time of the excited carriers across the 50-nm-long active area is estimated to be 0.5ps, assuming the drift velocity of the carriers to be 1 × 107 cm/s in Ge material [38]. This implies that the cutoff frequency of the plasmonic detector can reach one THz. The capacitance between two nanorods is about 10aF based on the simple parallel-plate model, assuming the distance between the two electrodes is 50nm, and the cross-section of 50nm × 50nm filled by Ge and 50nm × 140nm filled by silica. Such a small internal capacitance of the detector allows a relatively larger external resistance even for high-speed operations. The rough estimation suggests that the detector has a ~THz bandwidth. In addition, the short depletion layer between the two electrodes will greatly reduce the chances for the excited carriers to be recombined. This is helpful to achieve a high responsivity for the plasmonic detector.
In conclusion, we have demonstrated a technique to electrically detect plasmonic waves from a MIM plasmonic waveguide remotely by means of an ultra-compact MSM plasmonic detector. The detector is designed such that its two metallic electrodes − a pair of L-shaped nanorods − are used to form a nanoantenna, a nanocavity as well as a half-wavelength waveguide to efficiently couple the electromagnetic fields from the plasmonic waveguide to the detector. By optimizing the geometric dimensions of, and the distance between, the two electrodes, 81% of the optical power in the MIM waveguide can be transmitted to the active volume (50nm × 50nm × 50nm) of the detector. The leads of the detector are proposed to be made of transparent conduction oxide, which cause negligible effects on the antenna. The stub, traditionally used for impedance matching at radio and microwave frequencies, has been successfully extended to match the impedance of the plasmonic waveguide and the plasmonic detector at optical frequencies, leading to 6% improvement of the power transmission. Electric analyses show that the detector has a potential THz speed, high responsivity and low power dissipation. The proposed plasmonic detector has an ultra-compact yet realistic planar structure which can be easily fabricated. We firmly believe this work will advance for the integration of nanophotonics with modern nanoelectronic circuitry. In addition, this technique may also find applications in plasmonic biosensors, by replacing bulky near-field detection equipments such as scanning near-field spectroscopy with tiny and portable electric output systems.
Acknowledgment
This work was partially supported by Singapore Agency for Science Technology and Research (A*STAR) SERC Research Grant No.082 1410039. The authors also thank Dr. Yuriy Akimov for his valuable discussion on the bias effects on the nanoantenna.
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