Introduction

With metal interconnects being a bottleneck for integrated circuits in various aspects such as capacitance and speed, there has been much interest in replacing them with optical interconnects. However, the integration of optoelectronic and electronic components require a coherent light source whose dimensions are comparable to electronic components. Much attention has, therefore, been given recently to reducing the size of such light source to nanoscale dimensions. At first, in order to achieve sub-wavelength nanolasers, focus was on the development of novel geometries, including microdisk cavities [1–4], photonic crystals [5], and nanowires [6–8], in order to maximize photon confinement in the smallest possible space. However, as more recently demonstrated, one of the most promising schemes to reduce the physical dimension of a laser seems to be the use of metal. Light penetrates little into the metal layer and can, therefore, be confined in a much tighter space. With the presence of metal, optical modes can take on various shapes: pure surface plasmon, standing-wave hybrid dielectric-plasmonic, and traveling hybrid dielectric-plasmonic. State-of-the-art standing wave hybrid dielectric-plasmonic lasers include bowtie cavity lasers [9,10], metal-clad nanopillar and Fabry-Perot lasers [11,12], and plasmonic nanowire lasers [13]. Examples of pure surface plasmon nanolasers include spacer-based nanolasers [14], and surface plasmon-enabled sub-wavelength injection laser (SPESIL) [15]. In all of the three cases, use of metal increases absorption loss significantly, with pure surface plasmon cavities suffering the greatest metal loss owing to the large overlap between the lasing mode and the metal. By shifting the peak of the electric field away from metal, the hybrid dielectric-plasmonic modes are able to lessen the burden of metal loss. However, the hybrid mode requires a larger laser cavity. Hence the trade-off needs to be understood in order to optimize the semiconductor laser structures while scaling. This paper addresses this need.

2. Proposal of the semiconductor nanoring laser

Of the two hybrid dielectric-plasmonic modes – standing and traveling – traveling wave optical modes are more attractive for on-chip operation because they require no extra gratings or mirrors. For this reason, most of state-of-the-art integrated optical components currently utilize whispering gallery mode, a type of traveling wave optical mode. A prime example of such cavity is a semiconductor ring resonant cavity. Semiconductor ring lasers (SRLs) possess several advantages that are critical for photonics integration [16,17]. These are in-plane orientation for easy coupling to output waveguides and capability of controlling emission wavelength and laser dimension independently. In addition, the SRLs can exhibit bistability due to de-generate clockwise and counter-clockwise modes. This bistability has been exploited for the on-chip optical memory application [18–20].

In this paper, we propose a new type of metal-clad nanolaser structure—semiconductor nanoring laser—that exhibits superior scaling properties and possesses desired features for on-chip integration. The metal-clad semiconductor nanoring laser is expected to preserve the advantages of their metal-free microring laser counterpart while enabling scaling to the sub-wavelength dimension. In addition, the small laser dimension can considerably increase the free-spectral range, allowing single longitudinal operation to be attained without additional feedback structures.

We will present the scaling properties of metal-clad nanoring laser which supports a hybrid dielectric-plasmonic traveling wave optical mode. Due to two degrees of design freedom, ring width and diameter, it will also be shown that metal-clad nanoring laser possesses superior properties of scalability and is highly desirable for integration with electronic components. As a comparison, we will compare the scaling properties of the metal-clad nanoring laser with two other similar nanolaser structures that have been previously proposed, namely metal-clad nanopillar lasers and SPESILs. The cross-sectional view of all three laser structures is shown in Figs. 1(a) , 1(b) and 1(c), respectively. The metal-clad nanopillar laser possesses only one design parameter, the pillar diameter, and has hybrid dielectric-plasmonic standing wave optical mode [11]. Furthermore, nanolasers can exhibit a very low threshold carrier density owing to the highly efficient coupling of spontaneous emission into the lasing modes due to the ultrasmall mode volume [21]. Hence, when one compares the nanoring laser against the nanopillar laser, assuming identical Q factor and diameter, the nanoring structure can allow a smaller active region volume, and therefore, can reduce the threshold current or pump power. For example, for nanopillar and nanoring lasers of 1.2-μm diameter, their respective mode volumes are 0.068 μm³ and 0.04 μm³. The SPESIL has pure surface plasmon confinement at the interface between metal and semiconductor [15].

 

Fig. 1 (a). Side view of the sub-wavelength ring laser. The semiconductor ring is covered with metal everywhere. Hybrid dielectric-plasmonic traveling wave. (b). Side view of the metal-coated pillar laser used in simulations. The semiconductor pillar is covered with metal everywhere. Hybrid dielectric-plasmonic standing wave. (c). Surface plasmon-enhanced sub-wavelength injection laser used in simulations. The top layer is metal sitting in close proximity to quantum well gain medium. Pure surface plasmonic wave.

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3. Theoretical modeling and results

The sub-wavelength nanoring laser can be formed by conformally depositing a metal layer over a semiconductor ring structure. The metal enables tight optical confinement and improves heat conduction of the device, resulting in a device that can be scaled to sub-wavelengths in all three directions. Figures 2(a) and 2(b) show the calculated lateral and transverse optical modes, respectively. The radial mode profile shows the hybrid nature of dielectric and surface plasmonic confinement as manifested by the electric field profile near the metal-semiconductor interface. The transverse mode is from the conventional dielectric confinement with the active region acting as the waveguide core. Simulations were performed using MEEP, which is a finite-difference time-domain (FDTD) simulator [22]. Cavity resonant frequencies were calculated using the filter diagonalization method [23]. For simulations, InGaAs thickness was 400nm and the total height of the ring was 1μm. Gold (Au) was used as the metal of choice. 10nm of silicon nitride with a refractive index of 2 was used as an insulator material to separate the InGaAs active region from the Au. To reach the lasing threshold, the optical gain must overcome all the losses including metal absorption, diffraction, and scattering loss. In our simulations, the scattering loss is simulated by the grid size of the FDTD calculations. The total cavity loss was represented by a cavity Q factor. Because the optical mode propagates parallel to the substrate in this device, the laser output is expected to be primarily from the circumference of the ring via diffraction and scattering losses.

 

Fig. 2 (a). WGM lateral confinement of sub-wavelength ring laser. (b). Transverse confinement of sub-wavelength ring laser, done via refractive index differences between InP and InGaAs layers. The left side of the graph is the top of the ring and the right side is the InP substrate.

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To show that the meta-clad nanoring laser indeed exhibits a superior scaling property, Fig. 3 compares the cavity Q factors versus the device dimension, normalized to the free-space wavelength λ₀, for the three metal-clad nanolaser structures—the nanoring, nanopillar, and SPESIL—and the conventional microdisk laser. In SPESILs, the transverse mode is a pure surface plasmon polariton (SPP) mode whose propagation loss is limited by the metal loss rather than by the diffraction loss for a device dimension greater than 0.5λ₀. As a result, the cavity Q factor in a SPESIL structure shows a saturation behavior even with an increasing device size for D/λ₀ > 0.5 where D is the device diameter. Although the diffraction loss is even larger in this regime as shown by the cavity Q factor of the microdisk laser, the combination of dielectric and metal confinement can considerably increase the cavity Q. This is attributed to better dielectric confinement as a result of the metallic interface which suppresses the diffraction loss. Both metal-clad nanopillar and nanoring lasers show benefits of the hybrid dielectric-plasmon mode. However, owing to one extra design parameter, the nanoring laser shows a superior scaling property compared to the nanopillar laser. In the simulation, lasers of some diameters did not have a resonance at λ_o. Additionally, as the resonant wavelength is constant, the mode type is not always the lowest order mode. For example, for D/ λ_o = 1.2, nanopillar laser has a TE mode with m = 4 and n = 2.

 

Fig. 3 Cavity Q factor vs. D/λo for subwavelength ring laser, metal-coated pillar laser and SPESIL. Lines are for visual guidance only.

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In addition to the superior cavity Q behavior for D/λo > 0.5, the metal-clad nanoring laser also possesses the desired features of optoelectronic integration previously mentioned. First, the nanoring laser can be electrically injected from the top by insulating the sidewalls of the ring. The bottom contact can be made from the substrate. The nanoring laser also has an in-plane orientation. It can be epitaxially grown and the output can be easily coupled to an in-plane waveguide. The output coupling will be discussed in more detail later. Furthermore, the ring structure has two design parameters—the ring diameter and width—which allow independent control of the resonance wavelength and cavity Q factor. Figure 4(a) shows how cavity Q factor changes for various ring widths given a ring diameter for the resonance wavelength of 1μm. It can be seen that the cavity Q can be optimized at a different ring width for a given laser dimension. The simultaneous optimization of the cavity Q factor and control of the resonance wavelength is critical for the practical applications of nanolasers. Without such a capability, it will be extremely difficult to fix the output wavelength of a nanolaser due to the large free spectral range that is typical for a nanolaser. According to Fig. 4(a), as the laser dimension becomes larger, the optimal ring width also becomes larger. For example, the optimal ring width for a 700nm diameter laser is 125nm whereas that for a 900nm diameter laser is 200nm. However, as the optimal nanoring laser design below 500nm diameter becomes a nanopillar laser, this trend disappears for smaller devices. Figure 4(b) shows how tolerable a nanoring laser of a given diameter is to non-optimal ring widths. As the ring diameter increases, ring width tolerance for FWHM of cavity Q factor decreases significantly. For ring diameter equal to 700nm, the Q decreases to half of the maximum value within 50nm on either side of the optical ring width. However, as the diameter increases to 1100nm, the tolerance is only 10nm on either side. Therefore, there is a stricter design requirement for a larger diameter sub-wavelength ring laser.

 

Fig. 4 (a). Cavity Q factor vs. ring width for 4 different ring diameters. λres = 1μm. (b). Ring width tolerance for FWHM of Q factor in nm for a given ring diameter. Lines are for visual guidance only.

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Conventional semiconductor lasers use bulky optics for output coupling into an optical waveguide. An ideal nanolaser must have a nanoscale output coupling scheme so that it can be easily integrated with other nanoscale optoelectronic components. In order to achieve this, an opening in the metal layer at the outer edge of the nanoring cavity can be introduced and an optical waveguide can be inserted from such an opening. To keep the opening as small as possible, the beginning segment of the output waveguide can also be metal-clad to improve confinement. The same output coupling scheme can be used in the nanopillar laser structure too. Inevitably, the output coupling of a nanolaser is going to decrease the cavity Q factor. Figures 5(a) and 5(b) show the cavity Q factors of both the nanoring and nanopillar lasers versus the width of the output waveguide. It can be seen that the nanoring laser exhibits a higher cavity Q factor than the nanopillar laser does with output waveguides attached to them for all sizes. In addition, a smaller nanoring laser has a better tolerance to the perturbation created by the presence of a waveguide. This is attributed to the results shown in Fig. 4(b) that a larger nanoring laser has a more stringent design requirement.

 

Fig. 5 (a). Cavity Q factor vs. waveguide width for D/λ_o = 0.6 and ring width = 150nm. (b). Cavity Q factor vs. waveguide width for D/λ_o = 0.9 and ring width = 200nm.

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As mentioned above, a metal-clad nanolaser exhibits better photon confinement than a microdisk laser does owing to the metal confinement. It is, therefore, important to optimize the metal layer thickness. As shown in Fig. 6(a) , when the metal layer is too thin, the optical mode cannot be tightly confined inside the semiconductor region, causing more metal absorption and diffraction losses and resulting in a low cavity Q factor. As the metal layer thickness increases, more and more field is confined inside the semiconductor, therefore increasing the cavity Q. Figure 6(b) shows the electric field profiles with 3 different metal layer thicknesses (50nm, 90nm and 200nm). In Fig. 6(b), x = 0 denotes the center of the ring and the semiconductor region is located between x = −200nm and −400nm. Due to the boundary condition and the exponentially decaying electric field profile inside the metal, more electric field lies within the semiconductor for devices with a thicker metal coverage. Furthermore, with a thinner metal thickness such as 50nm, the optical mode is concentrated more toward the inner perimeter of the ring. Because the grid size used in FDTD calculations, 12nm, simulates the surface scattering loss, this causes a higher loss for a ring with a thinner metal thickness.

 

Fig. 6 (a). Cavity Q factor vs. metal thickness for semiconductor (excluding metal thickness) ring diameter = 800nm and ring width = 200nm. Resonance = 1μm. (b). E-field profile with varying metal thickness.

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In fabricating the sub-wavelength nanoring laser, it is critical to form a conformal coverage of the metal on the semiconductor ring structure. If there are sidewalls that are not covered with metal, the field confinement inside the semiconductor will be weakened, resulting in a smaller cavity Q factor. However, with the presence of a deep cylindrical trench in the middle of the ring, much attention must be given to filling the trench completely without forming a pinhole. One potential solution is electrodeposition [24]. Electrodeposition reduces the metallic cations in the liquid electrolyte to the conducting surface of the substrate. Because liquid-semiconductor interface can be formed conformally, it is expected that the electrodeposition can give us a uniform coating of the metal onto the semiconductor. To initiate the electrodeposition process, the semiconductor nanoring surface must be made conducting. This can be achieved by depositing a few monolayers using electron beam evaporation or atomic layer deposition. Figure 7 shows a cross sectional view of the nanoring device fabricated using electrodeposition. A seed layer of Au was at first evaporated using electron beam evaporation after which the rest of Au was deposited using electrodeposition. The scanning electron micrograph was taken after milling away half of the ring geometry using focused ion beam (FIB). It shows that the center trench of a sub-wavelength ring laser device can indeed be filled uniformly without forming a pinhole using the combination of electron beam evaporation and electrodeposition.

 

Fig. 7 Scanning electron micrograph of a sub-wavelength laser geometry, illustrating uniform metal coverage of a center trench via electrodeposition.

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4. Conclusion

In summary, a metal-clad semiconductor nanoring laser structure was proposed, theoretically analyzed, and compared to two other similar metal-clad nanolaser structures. Each of the nanolasers compared possesses a different metal-confined optical mode. The proposed sub-wavelength nanoring laser, exhibiting a traveling hybrid dielectric-plasmonic mode, was shown to exhibit superior scaling properties for D/λ_o > 0.5. Moreover, it possessed desired features for photonic integration and scaling—electrical injection, in-plane orientation, independent control of resonance wavelength and laser dimensional, and output coupling. Two design parameters including ring diameter and ring width allow for the optimization of the cavity Q factor to be independent from the control of the resonance wavelength. It was found that a larger nanoring laser requires a more stringent control on the design parameters to achieve the optimal cavity Q. The output coupling of a metal-clad nanolaser was discussed. A nanoscale waveguide inserting into the nanoring and nanopillar lasers was found to be feasible. Finally, we presented a potential fabrication strategy to the metal-clad nanoring cavity by electrodeposition.