1. Introduction

Although silicon ring resonators have been a core component of silicon photonics with potential applications to modulators [1,2], amplifiers and lasers [3–7], wavelength converters [8,9], switches and wavelength-division multiplexing (WDM) filters [10–15], the performance of silicon ring-based components is far below acceptable specifications for simple photonic on-chip networks. To our investigation, all the papers describing on-chip optical networks make use of ring resonators, especially, for switching and routing, which forces to solve the following three problems.

The first problem is fabrication-induced resonant wavelength errors of the ring resonators of which primary sources are the waveguide width and thickness variations. The width variation, causing a typical resonance wavelength error of ~ ± 0.5 nm in multi-channel ring filters [10–12], is induced by pattern density distributions, reactive ion etching (RIE), lithography, defects and impurities, particle drops, and so on, in very complicated ways. The thickness variation is induced by the radial slope of thickness of the silicon layer in a silicon-on-insulator (SOI) wafer, thicker in center, which causes a wavelength variation, 0.992 nm per 1 cm radial distance from our measurements.

The second problem is compatibility of the fabrication processes with complementary metal-oxide semiconductor (CMOS) integrated chip technology. Investigating high order ring resonators [10,11,14,15], E-beam lithography which is not CMOS compatible has been used in most demonstrations, owing mainly to the small gaps in coupled rings and partly to low cost and easy availability of E-beam lithography. A typical gap distance, 100 nm, of ring resonators is smaller than a typical foundry-guaranteed space size, ~160 nm, of ArF photolithography.

The third problem is the temperature-dependent resonant wavelength shift to red, ~8 nm/100 °C for the typical design of ring waveguides, width 500 nm and height 220 nm [16,17]. No confirmative solutions have been proposed for CMOS compatible athermal silicon ring filters. As an alternative, a polymer of which temperature dependence of refractive index is opposite to that of silicon has been used as an upper cladding material on a silicon waveguide to compensate for refractive index change with temperature [16,17].

Our research has been focused on finding a best compromising solution for the three problems. We found that, though having a small footprint from tight confinement of light, a silicon waveguide based on the fundamental transverse electric (TE) mode is not a good candidate for the best compromising solution, first because, for the channel-type waveguide, we found from our fabrications and measurements that its confinement of light is too strong to ease the three problems, second because, for the rib-type waveguide to reduce the confinement of light, the thickness uncertainty and variation of the unetched silicon layer are added to the existing variations. For the rib-type waveguides based on the fundamental TE mode, it is also difficult to find a proper thickness of the unetched silicon layer to meet the target free spectral range (FSR) of ring filters. We have studied silicon waveguides based on the fundamental transverse magnetic (TM) mode, theoretically and experimentally, to find the most optimized ring resonator dimensions leading to a best compromising solution for the three problems.

2. Design and fabrication

The transmission spectra of 3^rd order ring resonators were calculated by using the transfer matrix equations and parameters, the coupling coefficient t² = 0.3 between the bus lines and the side rings and the coupling coefficient t² = 0.07 between the side rings and the center ring, the intensity attenuation factor α = 0.995 for a typical loss 2 dB/cm, the ring radius 9 μm, FSR 12.8 nm at 1550 nm [13]. To design the waveguide dimensions and the ring radius for the TM mode to obtain the parameter values, instead of using commercial beam-propagation programs, we calculated the light beam size in the waveguide by the classical spot-size equation D≈λ/N.A., N.A. = (n_h-eff ²-n₀ ²)^1/2, with the effective index of refraction, n_h-eff, extracted from the vertical structure of the waveguide. For a vertical structure, for example, silicon layer thickness 200 nm in between oxide claddings, our approximate empirical calculation, 40% of electric field intensity in Si and the remaining 60% in oxide cladding, leads to the effective index n_h-eff (0.4x3.45 + 0.6x1.45) = 2.25 with n_si = 3.45 and n_oxide = 1.45 and leads to the beam size D≈0.9 μm for λ = 1.55 μm. As the waveguide width and height are designed 900 nm x 200 nm, the evanescent beam shape in the waveguide is close to a circle with a diameter D≈0.9 μm.

The rough estimation on the dimensions of waveguides and ring resonators was refined and optimized by many series of fabrications, measurements, and feedbacks. The waveguide width, 1.0 μm and 1.2 μm, was tested and the height was varied from 150 nm to 260 nm by 10 nm steps for each width, and the gap between bus lines and side rings was varied from 400 nm to 600 nm by 100 nm steps, the gap between center ring and side rings from 500 nm to 800 nm by 100 nm steps. First order ring filters with the gap varied from 600 nm to 1200 nm were also fabricated on the same wafer as 3^rd order filters. Our optimized values are 1 μm for the waveguide width, 190 nm for the waveguide height, 400 nm for the gap between bus lines and the side rings, and 500 nm for the gap between the center ring and side rings. Figure 1(a) and (b) show a microscope image and a scanning electron microscope image of our optimized design.

 

Fig. 1 (a) A microscope image and (b) a scanning electron microscope image of our optimized design, and (c) a fundamental TM mode shape simulated by a FDTD program

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With the optimized dimension of the waveguide, the radius of a ring resonator was varied from 8 μm to 12 μm, and the coupling region from 2 μm to 4 μm, finding, as optimal values, the radius 9 μm and the coupling region 2 μm and an addition of a small adjustment 28 nm to the ring periphery to get an exact number 12.8 nm of FSR to accommodate 50 GHz-spaced 32 channels and 100 GHz-spaced 16 channels in the filter. The group index was calculated n_g = 3.1 from our measured FSR 12.8nm, ring radius 9μm, and using the equation FSR = λ²/Ln_g for λ = 1.550 μm, where L is ring periphery, L = 2πR + 2x2, and the length of coupling region is 2x2 μm. Total 6 times mask revisions and 15 times processing runs were performed to optimize those dimensions and to minimize fabrication-induced resonant wavelength errors. One remarkable fact is that, as far as the fundamental TM mode is concerned, all the dimensions optimized are in the range that the Hg-I line photolithography can manage. We actually used Hg-I line photolithography to make all the TM mode-based ring resonators, though ArF photolithography is available to us. Another fact is that the fundamental TM mode only was allowed to propagate into the drop port because the gap width in the coupling region is too wide for TE modes to be coupled, though the dimension of the waveguide is wide to allow TE multi-modes. Our empirical design of waveguide was confirmed by a commercial simulation tool, Fullwave/ FDTD, showing a fundamental TM mode shape in Fig. 1(c) and allowing only one mode for TM and four modes for TE.

3. Measurements and analysis

To minimize fabrication-induced resonant wavelength errors, we compared and analyzed the resonant wavelength measurements from different channels, different dies, different wafers, different runs to extract quantifiable contributions from various sources, different pattern densities, imperfectness of line and space on the photo-mask, non-uniform waveguide width induced by a combination of photolithography and RIE, thickness variation of the Si-layer of a SOI wafer, irregular large jumps mainly due to defects and particles. Although it is difficult to isolate the exact value of contribution from each item, rough estimations can be obtained by some specified comparisons between various measurements, comparing the resonance wavelengths at different pattern densities and the repeated occurrence of the errors, and comparing the data from different sets of filters, dies and wafers, etc.

Different pattern densities induce a non-uniform etching rate of RIE and non-uniform exposure and development of photolithography. Resonant wavelength errors induced by different pattern densities can be measured by comparing the data from the ring resonators located at different pattern densities. Our measurement for this error with ring resonators based on TM mode showed an average 0.364nm, which was minimized to 0.005 nm by arranging patterns uniformly with some insertions of dummy patterns in less dense areas, which have required multiple revisions of photo-masks.

Photo-mask-induced resonant wavelength errors can be extracted by measuring the resonant wavelength errors of ring filters for different dies at the same wafer and by observing the repeated occurrence of the errors for the different dies. Our measurement on this error showed ~0.023 nm on average which is smaller than the other errors. Because lines and spaces in photo-mask are 5 times bigger than those in the wafer due to 5:1 magnification of our photolithography illumination system, the photo-mask-induced-errors must be smaller by a factor of 5 roughly.

Resonant wavelength errors from the waveguide width variation induced by the combination of photolithography and RIE can also be extracted by measuring the resonant wavelength errors of the channels in the center of the ring filters and comparing with each other for different sets of filters which have the same condition for the pattern density and by subtracting the photo-mask-induced frequency error. Our measurement showed 0.091 nm on average which accounts for a considerable part of the standard deviation of frequency errors. To minimize this error, all the conditions for photolithography and RIE, exposure time, illumination intensity, development time, etching time, RF power, were taken to optima by repeated processes.

A wavelength shift induced by the thickness variation of the Si-layer of a SOI wafer was measured 0.992 nm/cm on average for 3 different wafers. The resonance wavelength of a filter at the center die was compared with the corresponding filter at the next die, where a die size is 1x1 cm².

Irregular large jumps, >0.4 nm, occur at an average of 4 channels out of 32 channels, which is not accounted for by any of comparative analysis above. As we investigate the surface of the rings, a particle or a clear irregularity on the surface was not often found, so it may be attributed to crystal defects or an irregular behavior of fabrication processes at that point. We had no ways to minimize this error except maintaining a clean state of wafer.

For spectral measurements of the ring filters, amplified spontaneous emission (ASE) of erbium-doped fiber amplifier (EDFA) was injected into the input port and collected from the drop ports of the ring filters. Lensed fibers were used to couple light into the input port and out of drop port waveguides. The end facets of waveguides were prepared by sawing and polishing. The waveguides of the input port and the drop port were tapered to be 10μm-wide near the facets. A typical coupling loss, ~3dB, at each facet was measured. The lensed fibers were aligned accurately by an auto-aligner which has a minimum step of moving, 0.05μm.

Figure 2 and Table 1 describe our demonstration of 3^rd order ring resonator filters. Figure 2(a) represents the spectra of 50 GHz-spaced 32 channels transmitted through the drop ports of a filter. The bottoms of curves are shifted to have the same level of tops for a better comparison of peak positions and for neatness. Different peak heights can be attributed to various reasons, fiber coupling efficiencies, alignment accuracies, resonant wavelength mismatch of 3^rd order rings, a data point near the peak height, etc. Figure 2(b) represents some odd number channels of Fig. 2(a), channels 15 ~31, to show the raw data of spectral shapes and adjacent channel crosstalks. Figure 2(c) represents a distribution of channel positions for the filter in Fig. 2(a), where the straight line represents the target wavelength of the filter. Figure 2(d) shows a histogram graph of resonant wavelength deviations. A total number of 160 channel spectra collected from the last three processing runs were used to draw the histogram graph.

 

Fig. 2 Measurements of Si micro-ring filters. (a) Spectra of 50 GHz-spaced 32 channel filter, (b) Spectral shapes of odd channels, (c) Channel positions with respect to the target wavelengths, (d) Histogram graph of resonant wavelength deviations

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Table 1. Performance of 16 channel ring filters

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The performance of the filters is summarized in Table 1, where 100 GHz-spaced 16 channel filters, odd number channels in Fig. 2(b), were compared with a commercial silica 16 channel arrayed waveguide grating (AWG). Most specifications, FSR, channel space, adjacent channel crosstalk, bandwidth, 1 dB pass band, insertion loss, are comparable to those of the commercial AWG except the deviation of channel center wavelengths. The performance of odd or even number channels selected from a 50 GHz-spaced 32 channel filter has no difference with a stand-alone 100 GHz-spaced 16 channel filter fabricated on the same processing run. As shown in Fig. 2(a) and 2(c), some channels are nearly stacked up and 50 GHz-spacing (0.4 nm) is too close for the filter to be useful. It is because the filter is designed, in a primary objective, for 100 GHz-spaced 16 channel 3^rd order rings, and we expect that, if necessarily demanded in the future, improvements to produce a useful 50 GHz-spaced filter can be achievable, as gap distances in coupling regions are adjusted and the fabrication-induced error is further decreased.

One remarkable fact is that the standard deviation, 0.237 nm, of resonant wavelengths which includes the irregular large jumps is an acceptable value to be used for an on-chip network, as far as dummy channels are arranged. If the irregular large jumps are uncounted on the statistics, the standard deviation, 0.185 nm, is smaller than the 2 dB passband, 0.5 nm, and 120 channels out of 160 channels are within 2 dB passband. It means that the deviation might not make an obstacle, if channels are arranged as 12 main channels and 4 dummy channels out of 16 channel filters. In optical fiber communications, 1 dB passband is often used for AWG specification. In the on-chip optical networks shown in the next section the distance between transmitter and receiver is less than a few millimeters and the passband doesn’t have to be so strict. Here, we use 2 dB passband for the purpose to show a potential of the filter. Another remarkable fact with ring resonators based on the TM mode waveguide is that the missing channels caused by resonance mismatch among 3 rings were not observed in more than 10 filters of 32 channels, while a considerable rate, more than 10%, were missing with the ring resonators based on the fundamental TE mode waveguide, width 500nm and height 220nm, in our early experiments. Ring resonators based on the TM mode waveguide are much more tolerable to the resonance mismatch than those based on the TE mode waveguide, because the light on the TM mode waveguide is confined much loosely.

Figure 3 represents the temperature dependence of resonant wavelengths for the 3^rd order ring filters in Fig. 2(a). The spectral curves were collected experimentally by an optical spectrum analyzer as the temperature of the filter was changed, 26.6, 40.5, 54.5, 75.6, 93, 111, 122°C, in which the temperatures were measured by a digital thermometer and a thermo-couple. The spectral curves of 3^rd order ring filter in Fig. 3(a) are closer to Gaussian, while those of 1^st order ring filter, Airy function, are closer to Lorentzian [13]. The resonant wavelength moves by 0.043 nm/°C to the long wavelength direction, which is remarkably smaller than the temperature dependence, ~0.08 nm/°C, of silicon ring resonators based on the TE mode [16]. The temperature dependences of Si and SiO₂ are known as Δn = 1.8x10⁻⁴/°C and Δn = 0.1x10⁻⁴/°C, respectively, which makes the TM mode waveguide more durable to the temperature change. Considering 2 dB passband of 0.5 nm, a tolerant local temperature difference is ΔT>10 °C. The maximum local temperature difference of 10 °C in a single chip is an optimistic range, if the chip is in contact with a metal block of heat sink and instantaneous powers consumed by cores are arranged uniformly. As far as the temperature is uniform in the whole area of the chip, the absolute temperature or temperature change is not a matter, because all the resonant wavelengths of rings move to the same direction by the same amounts.

 

Fig. 3 Temperature dependence of resonant wavelengths. (a) Shifts of spectrum at different temperatures, (b) A graph of resonant wavelength vs temperature.

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4. On-chip optical network

The ring resonators have been key devices to implement the on-chip optical networks for many cores CPU [18–21]. The on-chip optical networks which consist of many waveguide crossings and ring resonator switches might be far from realization due to the low performance of the ring resonator switches and loss at the waveguide crossings. It is very difficult for the resonant frequencies of hundred or thousand ring switches to be matched, even in the case of tuning their wavelengths actively. A non-blocking point-to-point on-chip optical network to interconnect many CPUs and DRAMs which does not contain waveguide crossings and ring resonator switches has been proposed by Ashok V. Krishnamoorthy, et. al. [19], where 8 channel WDM filters are used to route and demux the optical signal of 8 wavelengths. We believe that our 3^rd order 16 channel ring filter has a performance to meet the requirement, only if a channel space, 0.8 nm, is tuned by such a micro-heater as in ref [22–25]. A difficulty with this on-chip optical network would be the integration of many transmitters and receivers, more than 4000s each, to interconnect 64 blocks (256 cores) in addition to aligning passively thousands of optical proximity connects, all without fails.

Here we propose an on-chip optical network to realize with our 3^rd order 16 channel ring filters and the currently available technology, without containing waveguide crossings and ring resonator switches, though the network is neither non-blocking nor point-to-point. Figure 4(a) shows the hierarchical network structure of which a fundamental block consists of 12 cores and a control unit (CU) connected by a ring-shape bus line. The second level block containing 144 cores also consists of the 12 fundamental blocks and a control unit, and the third level block containing 1728 cores also consists of the 12 second level blocks and a control unit, and so on. To communicate, for example, between core 1 and core 10 within the fundamental block, core 1 sends an optical signal to the control unit. After receiving the signal, the control unit decides the address to resend the signal. Core 10 receives the signal from the control unit via O-E and E-O conversions. To communicate from core 1 to any core outside the fundamental block, the optical signal is transceived by the same way as within the fundamental block except passing through more control units.

 

Fig. 4 A hierarchical on-chip network structure. (a) Schematic structure of the network, (b) Device configuration of core 1. (c) Device configuration of control unit.

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Figure 4(b) shows a device configuration of core 1 to send and receive optical signals. A spectrum from the broadband light source (BLS) is sliced by the 3^rd order ring resonator, R1, and then modulated by a modulator (MOD), then transmitted through another 3^rd order ring resonator, R2, and coupled to the bus line. The transmitted signal is received by the corresponding channel of a monolithic integrated germanium photodiode (GPD) in the control unit. If needed, the signal can be amplified by the hybrid-integrated semiconductor optical amplifier (SOA) and monitored by the few-percent-coupling grating coupler (GC) before the control units. The GPD in core 1 receives a signal sent by the control unit through the ring resonator R2. The 16 channel ring filters are used as 12 main channels for 12 cores and 4 dummy channels, and each core has one main channel and one or two dummy channels, where dummy channels can be overlapped by the different cores. Considering the waveguide propagation loss 2 dB/cm, the insertion loss ~5 dB to the drop port in Table 1 transmits ~68% of light to the through port, allowing 3 channels to be overlapped.

Figure 4(c) shows a device configuration of the control unit. The transmitter part has 12 main channels and 4 dummy channels corresponding to the channels for 12 cores, and has one BLS, where each channel has two ring resonators and one MOD. The receiver part also has 12 main channels and 4 dummy channels, and each channel has one GPD. The bus line is disconnected between the transmitter part and the receiver part to prevent signal overlaps. To communicate with the higher level block, there should be the same kind of channel configurations in the control unit as those in core 1.

A resonant wavelength shift, 0.992 nm/cm, induced by the thickness variation of the Si-layer of a SOI wafer can be avoided by adjusting FSR to 12.8 nm and choosing 16 resonant wavelengths spanned from one FSR to the next FSR. Because of fabrication-dependent random wavelengths between different filters, it is still necessary to tune one channel space, 0.8 nm, possibly by using a micro-heater as in ref [22–25].

Although a silicon ring modulator or a silicon Mach-Zehnder modulator which has a speed of >10 Gbps might be used [26], a hybrid-integrated electro-absorption modulator (EAM) would be better, if BLS is necessarily used to avoid wavelength mismatch between the light source and the filters. Phase-controlled modulators do not have a good speed with spectrum-sliced light. The hybrid integration of InP-based laser diode on silicon waveguides are established [27,28], and BLS, EAM, and SOA which have similar structures and less sensitive conditions of thresholds than a laser diode could be integrated on the silicon waveguide with the same technology as the InP-based laser diode. Furthermore, they can be replaced by the monolithic integrated Ge-based ones, considering that the Ge-based light source is regarded most promising among possible group IV light sources [29–31]. In our calculation, the power consumption, the total waveguide loss, and the total area for required devices and waveguides are much smaller than those of the networks in ref [18]. and [19]. Although our network is neither non-blocking nor point-t-point, an overall latency and bandwidth are comparable to the network containing waveguide crossings and ring resonator switches.

5. Conclusion

We report our demonstration of 3^rd order silicon ring filters, 100 GHz-spaced 16 channels and 50 GHz-spaced 32 channels. The second problem, CMOS-compatibility of lithography, is solved by our ring resonator design. Fabrication-induced resonant wavelength errors and the temperature-dependent wavelength shift are also reduced to the record values, which could realize an on-chip optical network for many cores CPU with the currently available technology, if 12 main channels and 4 dummy channels out of 16 channels are arranged.