We explore the design space for optimizing CMOS compatible waveguide crossings on a silicon photonics platform. This paper presents simulated and experimental excess loss and crosstalk suppression data for vertically integrated silicon nitride over silicon-on-insulator waveguide crossings. Experimental results show crosstalk suppression exceeding −49/-44 dB with simulation results as low as −65/-60 dB for the TE/TM mode in a waveguide crossing with a 410 nm vertical gap.
© 2013 OSA
Device density in photonic interconnection networks continues to grow at a rapid pace as the bandwidth limitation of electrically connected networks makes photonics economically viable in long and medium-haul applications such as tele- and data communications [1,2]. This increase in device density and corresponding increase in on-chip network complexity naturally leads to a significant increase in the number of optical waveguide crossings required to perform the desired signal routing [3,4]. Waveguide crossings reduce system performance in two significant ways. First, the signal is attenuated at each crossing due to scattering from the intersection. This leads to increased system loss and differential path loss based on the number of crossings traversed, both of which negatively impact the power budget of the optical system. If enough crossings are present in the system, this factor alone leads to the requirement for optical amplifiers and signal grooming components which ultimately increase system cost and complexity. Second, as the optical signal scatters from the intersection, power is coupled into the waveguide being crossed leading to unintended effects on the optical power distribution. For a large number of waveguide crossings, this crosstalk can cause a substantial unintended signal power in a given waveguide leading to a power penalty and increased communication errors. An example schematic of the routing portion of a 16 port Banyan switch is shown in Fig. 1.
Because the scattered power scales directly with index contrast, excess loss and crosstalk suppression are especially poignant issues in high-index-contrast systems. For example, in silicon-on-insulator (SOI) waveguides, the core-cladding refractive index contrast is near 2.0 in the near infrared. Several authors have made strides in optimizing in-plane waveguide crossing performance via modification of the waveguide dimensions in the region near the crossing. Approaches include the use of photonic crystals [5,6], subwavelength diffraction gratings [7,8], resonant cavities [9–11], wavefront matching [12,13], multimode interference regions [14–16], mode transformation [17–20] and others [21–23] with the best broadband, fabrication tolerant results reported by Bogaerts, et.al . with demonstrated crossing excess loss as low as −0.16 with −40 dB crosstalk suppression at 1550 nm. Bock, et. al.  demonstrated superior broadband loss performance in subwavelength grating waveguides with < −0.1 dB per crossing reported. These structures, however, may require advanced lithography nodes due to the small feature size and relatively large aspect ratio.
However, many of the highest performance waveguide crossings reported in the literature are resonant in nature and therefore suffer from narrow optical bandwidths and strict fabrication tolerances. As an alternative, vertically separated waveguides present a design tolerant option for achieving low loss, low crosstalk waveguide crossings. This approach has been discussed in the literature [4,24] with vertical transitions , vertically coupled resonators , waveguide crossings in low index contrast systems  and active optical materials  demonstrated for specific use-cases.
In this paper, we present a numerical and experimental study of the performance of silicon nitride over SOI vertical waveguide crossings for photonic interconnection networks. We have chosen a silicon nitride over SOI system because both materials are: 1) present in most modern CMOS lines enabling direct integration with current electronics fabrication processes and economies of scale, 2) exhibit low loss across the S, C, and L optical telecommunication transmission bands given proper processing conditions and waveguide geometries, and 3) are capable of low loss, small radii bends due to the large index contrast of both waveguide systems. The use of silicon nitride as a secondary optical layer is particularly advantageous in that propagation losses as low as 2.9 dB/m have been reported . In addition, proper tapering of the silicon nitride layer at the end-facets of the chip can yield fiber-to-waveguide coupling losses as low as 0.5 dB  for standard single mode fiber, thereby enhancing the commercial viability of the presented technology via reduced packaging cost.
2. Device geometry
The optical system analyzed here is a four port nitride-over-silicon (NOS) waveguide crossing as shown in Fig. 2. Silicon is used as the primary optical routing layer with vertical transitions into and out of silicon nitride in the crossing region. Adiabatic vertical waveguide transitions  100 μm in length were used, yielding low-loss transitions between optical layers. Five μm radii bends are used to produce minimal bending loss and a perpendicular crossing geometry. The silicon waveguides were 400 nm wide and 230 nm thick while the silicon nitride waveguides were 250 nm thick with a 1.2 μm width. These geometries were chosen to ensure single mode operation while minimizing propagation loss in each layer.
All fabrication was carried out using a silicon photonic process developed within the CMOS foundry at Sandia National Laboratories’ MESA facility. The silicon waveguides were fabricated via optical lithography followed by dry etching of the silicon device layer. A subsequent reduction of sidewall roughness via thermal oxidations, which consumed 20 nm, yielded a final device layer thickness of 230 nm. PECVD oxide was then deposited followed by CMP to planarize the structure leaving the desired thickness oxide as a vertical buffer between the silicon and silicon nitride waveguides. After CMP, silicon nitride was deposited via CVD followed by a second lithography process and subsequent dry etch to create the silicon nitride waveguides. Finally, PECVD oxide was deposited to passivate and protect the structure while also serving as an upper cladding.
The thickness of the buffer oxide between waveguide layers was critical in determining device performance. Variance limitations in the CMP process resulted in a vertical gap variability of ± 100 nm from the targeted thickness. In order to ensure the validity of the resulting data, a Rudolf AutoEL III ellipsometer with a vertical thickness resolution of ± 3Å was used to measure the thickness of the buffer oxide. Utilizing this technique, error in the analysis due to variability in the CMP process was significantly reduced; however, variation in the flatness of the planarized surface and differential performance of the process over structures of different size resulted in a vertical measurement error of ± 50 nm.
Advances in CMP technology including reticle modification, endpoint monitoring, and multi-zone polishing heads have enabled process standard deviations of less than 5 nm over a set of 5000 wafers . This level of process control will ultimately enable performance repeatability rivaling that of lithographically defined structures and supports the validity of using this approach in novel systems and commercial products alike.
3. Crosstalk calculation
Crosstalk in a passive four port optical system, as depicted in Fig. 2, is defined as the ratio of the output power in the cross state to the sum of the signals in the cross and bar states. Defining the power coupling coefficient from input port ‘i’ to output port ‘j’ as kij, the crossing-induced crosstalk for input ports 1 and 2 may be calculated asEq. (1).
In real systems, the crossing cannot be directly probed and factors such as coupling and propagation loss must be taken into account when attempting to extract the power coupling coefficients. The externally measured (port-to-port) crosstalk for input ports 1 and 2 may be written as
By taking the product of the externally calculated crosstalk values, the path and coupling losses cancel leaving the product of the crossing-induced crosstalk, given by:Eq. (4) yields the geometric mean of the crosstalk which may be rigorously compared to the data with no assumptions or approximations applied to the result. For systems in which the crossing waveguides have similar mode volumes and propagation constants, the crosstalk values for both input ports converge and the results from the above treatment reduce to those produced by simplified formulations of coupled mode theory (CMT) .
While CMT treatments have been developed , these results cannot be used directly in this case, even if scattering loss is accounted for. Although reciprocity dictates that each , it does not require the transmission coefficients for input ports 1 and 2 ( and here) to be equal. Due to reduced confinement of the silicon nitride mode in NOS crossings, the magnitude of the interaction of the optical mode in silicon nitride with the crossing silicon waveguide is far stronger than the inverse case. In addition, the magnitude of the field coupled to radiation modes caused by interaction with an index perturbation is directly proportional to the index contrast of the perturbation. The index contrast of the SOI waveguide is approximately a factor of four larger than its silicon nitride counterpart. Thus, significantly increased scattering of the optical modes in the silicon nitride waveguide is expected. These factors combine to invalidate the assumptions made in typical coupled mode theory treatments and thus indicate the need for a rigorous treatment of the crossing region interaction for this system.
4 FDTD simulation results
4.1 Modal field calculations
The devices tested were simulated in three dimensions using the commercially available finite difference time domain (FDTD) software FDTD Solutions (Lumerical Inc.) . The simulations were performed at the highest density grid setting using a conformal mesh to enhance the speed and accuracy of the result. The optical modes of the isolated silicon and nitride waveguides are presented in Fig. 3 for the fundamental TE and TM modes. Figure 4 shows the TE and TM modes in a cross-section through the crossing region perpendicular to the silicon waveguide as shown in Fig. 2(c) for structures with various vertical gaps between the silicon and silicon nitride waveguides. Analogous mode simulations for cross-sections perpendicular to the silicon nitride waveguides (as in Fig. 2(b)) are presented in Fig. 5.
Due to high confinement, the TE mode in the silicon guide experiences little modification as the vertical gap decreases, retaining its fundamental shape with minor modification of the exponential decay in the vertical direction. Qualitatively, the expected magnitude of the field scattered by the waveguide crossing is proportional to the level of disturbance experienced by the optical mode. Because of this, we expect the TE mode in silicon to demonstrate very low crosstalk and excess loss values. Conversely, the TM field shifts significantly and begins to strongly overlap the silicon nitride waveguide as the two waveguides are brought into proximity. This is expected due to the reduced confinement of the TM optical mode in the silicon waveguide. It is further expected that the crosstalk and excess loss values for the TM optical mode will be larger than those of the TE mode.
In the nitride waveguide, the response is somewhat counterintuitive; the crossing exhibits superior performance for the TM mode. Field confinement within the high index regions is reduced for the TM field with peaks at the upper and lower boundaries of the high index region, much like isolated silicon and nitride waveguides. This reduces the magnitude of the field in the crossing waveguide, which ultimately leads to improved crosstalk. The large size of the TM mode also leads to a reduction in excess loss as the response to the index perturbation is effectively reduced. This phenomenon is well demonstrated in structures such as those developed by Bogaerts  and others [14,15].
4.2 E-field propagation
Images of the E-field propagating through the silicon and silicon nitride waveguides are presented in Figs. 6 and 7 respectively. These images show the differential in magnitude of the field coupled to radiation modes upon interaction with the coupling region for each input. Also of import is the reflected field, which is made visible by the interference pattern to the left of the interaction region. While difficult to see for the silicon input, the response from the silicon nitride input creates a clear standing wave pattern.
4.3 Crosstalk and excess loss simulations
Crosstalk and excess loss simulations were performed using mode monitors in FDTD Solutions . These monitors capture the electric field passing through a given region and numerically evaluate the overlap integral with the modal field of the waveguide thus eliminating errors due to stray fields present in the simulation window. Using this technique, the excess loss and crosstalk values were predictively modeled for a wide range of vertical gaps and signal wavelengths. The results of these simulations for optical inputs in the silicon (port 1) and silicon nitride (port 2) waveguides are presented in Figs. 8 and 9 respectively.
The following graphs contain a good deal of data and are organized as follows. The simulated response of the system over the 1500 to 1600 nm wavelength range is represented as a set of filled patches with the boundaries at 1500 and 1600 nm represented as dashed and solid lines, respectively. Points shown along each line are simulation data points with the line between points generated by spline interpolation. In all cases, the system varied approximately linearly with wavelength. Each experimental data point is represented by a circle showing the response at 1550 nm with error bars used to show the response of the system within the 1500 to 1600 nm wavelength range. The filled patches surrounding each data point indicate measurement error of both throughput and interlayer thickness. Excluding the TM response of the silicon nitride input for buffer thicknesses less than 550 nm, the excess loss of the crossing was directly proportional to wavelength. The inset in Fig. 8(b) shows the crossing point for this behavior with a number of simulations performed around this point to ensure the validity of the simulation data.
Crosstalk performance trends the same for both waveguide systems with a convergence of the crosstalk values as the vertical gap increases. This result is important in that it validates the use of the geometric mean in approximating the calculated crosstalk values for both waveguide systems for sufficient gap sizes.
These simulations indicate that the crosstalk reaches exceptionally low values for relatively modest vertical gap sizes. Specifically, −40 dB crosstalk suppression is achieved for TE and TM polarizations for both input waveguides with a vertical gap as low as 125 nm. Using a gap size of 400 nm produces crosstalk suppression values exceeding −60 dB, leading to significantly superior crosstalk suppression when compared to in-plane approaches.
The excess loss for the silicon input is an order of magnitude lower than that of the silicon nitride input. While the excess loss for the silicon input quickly approaches zero with excess losses well below 0.1 dB for vertical gaps exceeding 400 nm, the excess loss for the silicon nitride input is significant for small gap sizes increasing to maxima of 15 and 3.4 dB for TE and TM polarizations, respectively, at a wavelength of 1550 nm. In order to achieve excess losses below 0.1 dB, the vertical gap must be increased to over 1 μm. At this gap size, the excess loss for the silicon input is negligible; reaching values below 0.003 and 0.03 dB for TE and TM polarizations. The drawback of arbitrarily increasing the vertical gap between the waveguides is that doing so may have unintended consequences in the design of multi-layer optical networks such as an increase in the taper length required to efficiently transition between layers, which ultimately affects the required on-chip footprint and the number of crossings required to achieve superior system performance over single layer networks. In Fig. 10, we provide a comparison of vertical transition and crossing excess loss for the silicon nitride input port. In examining this data, we see that as the vertical gap and taper lengths change, the regime in which the excess loss is dominated by the crossing changes. This behavior results in a design optimization process that must be carried out on a case-by-case basis based on the crosstalk, excess loss, and on-chip area requirements of the system.
As an alternative to increasing the gap between optical layers, the excess loss of the silicon nitride guide may be reduced via modification of the waveguide geometry in the crossing region using one of several approaches in the literature [7–23]. This design and optimization is outside the scope of this paper and will be pursued in future work.
5. Experimental method and results
An Agilent 81600B tunable laser source was used to test the response of waveguide crossings with silicon-to-nitride vertical gaps between zero and 400 nm with wavelengths ranging from 1500 to 1600 nm at a resolution of 10 pm. The polarization of the signal was controlled via a Thorlabs FPC560 Three Paddle Polarization Controller that was used to reduce polarization crosstalk to well below −30 dB. The optical measurement was performed in a fiber-to-fiber configuration using OZ Optics tapered and lensed fiber with a spot size of 2 μm to enhance coupling efficiency to the on-chip waveguides. The signal was then detected using an Agilent 81635A Dual Optical Power Sensor with an intrinsic optical noise floor of −80 dBm. A schematic of the optical test setup is presented in Fig. 11.
Calculating the crosstalk requires accurate alignment of optical paths with signals near the optical noise floor. This sort of alignment cannot be done using the standard technique (i.e. translating each fiber until the maximum power is transmitted) as stray light often causes local maxima in the transmitted power that do not correspond to optimal coupling to the on-chip waveguide. Instead, we used a 10X objective with an optical axis normal to the surface of the chip coupled to a Sensors Unlimited, Inc. InGaAs SWIR camera to image the crossing region of the device. Light is preferentially scattered by the crossing region only when the input signal is efficiently coupled to the waveguide. This method enables efficient coupling of low-throughput optical paths with a high degree of confidence and repeatability yielding an estimated alignment error of + \- 0.5 dB.
The noise floor of the crosstalk measurement is defined as the minimum external crosstalk measurable with this setup. While the noise floor of the detector is −80 dBm, the noise floor for the crosstalk measurement is defined as the ratio of the minimum measureable cross state power to the average transmitted power in the bar state given by
Of the < −30 dB excess loss present in the system, around −12 dB is attributed to fiber-to-waveguide coupling loss at each end facet with < 0.1 dB predicted by 3D FDTD simulation for each vertical transition. Propagation loss is estimated to be 1.4 and 4.0 dB/cm with bending losses estimated to be < 0.1 and ~1.5 dB per turn for TE and TM, respectively.
As depicted in Fig. 9 the data agrees well with the predictions of the 3D FDTD simulations for small vertical gaps. For gaps larger than 200 nm, the measurements are near the noise floor and may exhibit lower crosstalk than reported here. Port 1 of the device with a 400 nm vertical gap exhibited −49.4 and −44.3 dB crosstalk at a wavelength of 1550 nm for TE and TM polarized inputs respectively. This represents the lowest crosstalk measured in a high-index-contrast system to date. Simulation data suggests that crosstalk values as low as −65 dB for TE and −60 dB for TM polarized inputs may be expected for these structures with crosstalk continuing to decrease as the vertical separation of the guides is increased. For vertical separations greater than 1 μm, these structures are predicted to exceed −100 dB crosstalk suppression for both the TE and TM polarizations.
Excess loss measurements were performed using the same equipment and wavelength range as above; however, alignment here was performed in the standard way using the power meter to ensure optimal throughput. Loss of the silicon nitride input of structures with 0, 2, and 4 NOS crossings was measured on a wafer 305 nm vertical gap. Crossing excess loss was then calculated by taking the slope of the line connecting the three data sets. While alignment error was less than 0.2 dB, small differences in the optical path length of each structure and the lack of data points with a large number of waveguide crossings led to an overall measurement error of 0.5 dB as reflected in the data in Fig. 8(b).
We have reported on the use of NOS crossings as low loss crossing structures exhibiting exceptional crosstalk suppression and excellent uniformity across the S, C, and L optical transmission bands. Experimental results show crosstalk values as low as −49.40 and −44.34 dB for a device with a vertical separation of 410 nm at a wavelength of 1550 nm with excess losses predicted by high resolution 3D FDTD to be below 0.001 and 0.05 dB per crossing for TE and TM polarizations respectively for the silicon input waveguide. Crosstalk values for both inputs and polarizations are expected to exceed −60 dB in this geometry. The excess loss of the silicon nitride input is nearly 1 dB for a 400 nm vertical gap with an un-modified crossing region. We expect this loss to be significantly mitigated via intelligent engineering of the crossing region geometry and/or increasing the vertical gap between optical layers.
A typical planar SOI waveguide crossing  requires 36 μm2 on-chip area and produces excess loss and crosstalk values of 0.16 dB and −40 dB respectively for a single polarization. The structure reported here requires an on-chip area of 0.3 μm2 with comparable loss performance and < −90 dB crosstalk suppression for a 1 μm vertical gap. Performance is expected to greatly exceed the current state-of-the-art once the crossing geometry is optimized. It should be noted, however, that one cannot simply assume the device will exhibit superior performance because the crossing waveguide systems are physically disjoint. Intelligent design and optimization of the crossing is still required to achieve suitable results.
Our results suggest that NOS waveguide crossings can be used as compact, efficient, easily integrable structures in densely integrated photonic interconnection networks.
Sandia National Laboratories is a multi-program lab managed and operated by Sandia Corp., a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. R.A. Norwood acknowledges the support of the CIAN ERC under grant #EEC-0812072.
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