We report the implementation of the XOR and XNOR operations using an electro-optic directed logic circuit based on two cascaded silicon microring resonators (MRRs), which are both modulated through the plasma dispersion effect. PIN diodes are embedded around the MRRs to achieve the carrier-injection modulation. The inherent resonance wavelength mismatch between the two nominally identical MRRs caused by fabrication errors is compensated by two local microheaters above each MRR through the thermo-optic effect. Two electrical modulating signals applied to the MRRs represent the two operands of the two operations. Simultaneous bitwise XOR and XNOR operations at 100 Mbit/s are demonstrated.
©2012 Optical Society of America
With the shrinking of transistors and metal interconnects, the power-consumption and transmission-bandwidth limitations of silicon electronics have been approached [1–3]. The convergence of optics and electronics at the chip level has become a necessity for the next generation processors. Recently, the field of silicon photonics is gaining more and more attention due to the potential of fabricating optical devices using standard semiconductor fabrication techniques and integrating them with microelectronic chips [4–11].
On the one hand, it has been widely regarded as a means for keeping on track with Moore’s Law by using optical interconnects to provide faster data transfer both between and within microchips [1–3]. For this purpose, various optical components have been developed such as the laser sources , electro-optic modulators , photodetectors , as well as the optical routers for networks-on-chips (NoC) [10, 11]. On the other hand, the advanced fabrication techniques and abundant silicon photonic device library have been leveraged to develop devices and subsystems to assist in high-speed signal processing [12–16]. It’s an attractive and promising solution to handle with high-bandwidth signals compared with traditional ways in terms of size, cost and power-dissipation.
Directed logic is a logic paradigm proposed by Hardy and Shamir , which takes advantage of the propagation of light to carry out Boolean functions [17–20]. In essence, the directed logic circuit is a network of switching elements which control the propagation direction of light passing through the network. Unlike traditional implementation of optical logic, the directed logic is specially adapted to the features and promises of optics since it depends on the propagation of light other than the nonlinear interactions between light and materials [21–23]. Compared to traditional digital logic circuit, directed logic circuit has markedly less state delay because the operands that determine the states of the switching elements do not pass through the preceding elements in the circuits. Therefore, all elements can perform their switching functions simultaneously and the results are given instantaneously.
In this paper we report an electro-optic directed logic circuit for XOR/XNOR operations. Compared to the previous demonstration presented in [24, 25], the plasma dispersion effect is utilized to modulate the microring-resonator-based optical switches. Degeneration of the spectra of the device shows up again as in . The XOR/XNOR operations are carried out correctly at 100 Mbit/s in both the degenerate and non-degenerate regions.
2. Design and fabrication
The schematic of the XOR/XNOR directed logic circuit is shown in Fig. 1(a) . The two MRRs function as 1 × 2 and 2 × 2 optical switches in the circuit, respectively. The four ports of each MRR are denoted as input, through, add and drop according to their functions. Monochromatic light with the wavelength of λ coupled into the input and add ports will be directed to the drop and through ports, respectively, if the MRR is on-resonance at λ. And if the MRR is off-resonance at λ, light coupled into the input and add ports will be guided to the through and drop ports, respectively (i.e. bypass the MRR).
Two electrical logic signals of X and Y are used to control the resonant states of the two MRRs, respectively. It’s assumed that the MRRs are on-resonance at λ if the applied electrical logic signals X and Y are at low levels (representing ‘0s’) and off-resonance at λ if X and Y are at high levels (representing ‘1s’). According to these rules, two logic outputs of and can be obtained at the drop and through ports of MRR2, respectively. Those two signals are just the results of and operations, where the symbols and represent the XNOR and XOR operators, respectively. Details on the principle are presented in . Those two output ports of the circuit are called drop port and through port hereinafter for simplicity. It can be noted in Fig. 1(a) that there are two arched segments in the waveguides connecting the four coupling areas of the two MRRs. Such two arched waveguides are designed on purpose to adjust the length difference between the two arms connecting the MRRs, which has a distinct impact on the response spectra of the device .
The device is fabricated on a silicon-on-insulator (SOI) wafer with 220-nm-thick top silicon and 2-μm-thick buried oxide layer. Rib waveguides with a height of 220 nm, a width of 400 nm and a slab thickness of 70 nm are used to construct the circuit, which only supports quasi-TE fundamental mode [24, 25]. The gaps between ring and straight waveguides are chosen to be 330 nm to achieve a balance between the extinction ratios of the drop and through ports of each MRR. The radii of the ring waveguides are both 10 μm. An elliptical structure (long axis = 6.25 μm, and short axis = 1.5 μm) is adopted to reduce the scattering at the crossing of the waveguides . 248-nm deep ultraviolet (UV) photolithography is used to define the device pattern. Inductively coupled plasma etching process is used to etch the top Si layer (Figs. 2(a) and 2(b)). Spot size converters (SSCs) are integrated on the input and output terminals of the waveguides to enhance the coupling between the waveguides and the fibers. The SSC is a 200-µm-long linearly inversed taper with 180-nm-wide tip . After the waveguide is etched, two PIN diodes are formed with the two ring waveguides as the intrinsic regions. The p- and n-doping concentrations are both 5.5 × 1020 cm−3, with both doped regions located 500 nm away from the sidewall of the ring waveguide ridge (Figs. 2(c) and 2(d)). After the doping, a 1500-nm-thick silica layer is deposited on the Si layer as the separate layer (SL) by plasma enhanced chemical vapor deposition (PECVD). Then a 150-nm-thick titanium nitride (TiN) layer is sputtered on the SL and two microheaters are fabricated by deep UV photolithography and dry etching (Fig. 2(e)) . Another silica layer of 300 nm is deposited by PECVD on the TiN heaters. Via holes to the PIN diodes and microheaters are etched on the silica layer in two steps (Figs. 2(f) and 2(g)). Then a 1000-nm-thick aluminum layer is sputtered and etched to be wires and pads connected to the microheaters and PIN diodes (Fig. 2(h)). Finally, the end-face of the SSC is exposed by a 110-µm-deep etching process as the world-to-chip interface (Fig. 2(i)) . The micrograph of the device is shown in Fig. 1(b). The 200-µm-long SSCs are not included in this micrograph. The side lengths of the two square pads located at the upper-left and upper-right of the micrograph are both 100 µm. The effective area of the device including the SSCs is about 1.2 × 0.4 mm2.
3. Experimental results
The fabricated device is characterized by an amplified spontaneous emission (ASE) source, an optical spectrum analyzer (OSA) and a tunable voltage source. The broadband light is coupled into the device through a lensed fiber. The output light is collected by another lensed fiber and fed into the OSA. The tunable voltage source is used to drive the microheater above the MRR with shorter resonance wavelengths. When this MRR is heated up, the effective refractive index of the optical mode in the ring waveguide increases and it will resonate at the same wavelengths as the other MRR.
The response spectra at the two output ports of the device are shown in Fig. 3 , with MRR2 being tuned by a heating voltage of 2.92 V to align the resonance wavelengths of the two MRRs. As the two arms connecting the two MRRs have the same lengths, the first and the third resonant regions in Fig. 3 are degenerate, which has been shown and explained in . The spectra of the drop ports at these two degenerate resonant regions should be flat due to the constructive interference between two light beams from two different paths . Shallow dips still appear at these two regions due to the difference of the two nominally identical MRRs and arms caused by fabrication errors.
The working wavelength can be chosen in either the non-degenerate or the degenerate regions, which will be shown in the next two subsections, respectively. Simultaneous operations of XOR and XNOR operations are achieved in both operating modes.
3.1 The first operating mode: working in the non-degenerate region
The working wavelength is determined from the spectra when neither of the two PINs is actuated (Fig. 3). According to the aforementioned principle, a maximum (representing a ‘1’) and a minimum (representing a ‘0’) should be obtained at the drop port and the through port, respectively, when the two applied electrical signals are both at low level (representing two ‘0s’). We choose 1556.38 nm in the second non-degenerate region as the working wavelength (Figs. 4(a) and 4(e)).
After the working wavelength has been chosen, the static operating principle is validated. As shown in Figs. 4(a)-4(d), a maximum is obtained at the drop port when the two applied electrical signals are both at low levels or high levels, and a minimum is obtained otherwise. As shown in Figs. 4(e)-4(h), a minimum is obtained at the through port when the two applied electrical signals are both at low levels or high levels, and a maximum is obtained otherwise. Therefore, the XNOR and XOR operations are performed correctly at the drop and through ports of the device, respectively. The diminishing of the extinction ratio of the activated MRRs is related to the loss induced by the injection of carriers to the ring waveguides. Such a phenomenon has no negative effect on the operation of the device since the optical signal circulating in the circuit will bypass the MRR with carriers injected .
After the static operating principle is validated, the analog voltage representing logic ‘0’ and ‘1’ for each MRR should be determined. Firstly, only an electrical signal at 100 Mbit/s is applied to the PIN diode of MRR1. The output optical signals at the drop and through ports are converted to electrical signals by a high-speed photodetector and observed with a real-time oscilloscope. Waveforms with the best extinction ratio are obtained when the applied signal has an amplitude of 350 mV with an offset of 405 mV. So the voltages representing logic ‘0’ and ‘1’ for MRR1 are 230 mV and 580 mV, respectively. Secondly, only an electrical signal at 100 Mbit/s is applied to the PIN diode of MRR2. The voltages representing logic ‘0’ and ‘1’ for MRR2 are found to be 356 mV and 544 mV, respectively. In both tests, MRR2 is always tuned by a heating voltage of 2.92 V.
A monochromatic light at 1556.38 nm from a tunable laser is coupled into the device and the output light at the through and drop ports of the circuit is fed into a high-speed photodiode. Two pseudo-random binary sequence (PRBS) non-return-to-zero (NRZ) signals at 100 Mbit/s with the aforementioned magnitudes are applied to the PINs of the two MRRs. The electrical signals converted by the photodetector and the two electrical signals applied to the two MMRs are fed into a four-channel real-time oscilloscope for waveform observation. The dynamic operation results are shown in Fig. 5 . It can be found that the XOR and XNOR operations are carried out correctly at the through and drop ports simultaneously.
As shown in Figs. 5(c) and 5(d), there are positive spikes between two consecutive outputs of ‘0s’, and negative spikes between two consecutive ‘1s’, which also appear and are explained in . The duration times of those spikes, as well as the rising and falling times of the output signals, which limit the working speed of the device, are determined by the diffusion and recombination time of the free carriers in the PIN diode.
The speed of the device can be greatly improved by engineering the NRZ driving signal to be the so-called pre-emphasized type . However, the carrier-depletion modulation mode has shown a much faster working speed over the carrier-injection modulation mode, and no pre-emphasized signal is required [30–32]. The improvement of the speed performance using the carrier-depletion mode is left for future work.
3.2 The second operating mode: working in the degenerate region
In the last operating mode, the working wavelength of 1556.38 nm is chosen from the fourth resonant region of the MRRs (Fig. 3). Actually, the working wavelength can also been chosen from the degenerate regions, i.e. the first and the third resonant regions according to the principle of the device [24,25]. To verify this point, the resonance wavelength of 1546.70 nm from the third resonant regions is chosen to be the working wavelength in the second operating mode (Figs. 6(a) and 6(e)).
After the working wavelength has been chosen, the static operating principle is validated. As shown in Figs. 6(a)-6(d), a maximum is obtained at the drop port when the two applied electrical signals are both at low levels or high levels, and a minimum is obtained otherwise. As shown in Figs. 6(e)-6(h), a minimum is obtained at the through port when the two applied electrical signals are both at low levels or high levels, and a maximum is obtained otherwise. Therefore, the XNOR and XOR operations are performed correctly at the drop and through ports of the device, respectively. The diminishing of the extinction ratio of the activated MRRs caused by the injected-carrier-induced loss also appears in Fig. 6, which does not hinder the operation of the device.
The characterization of the dynamic operation in the second operating mode is as same as the steps in the first operating mode except for the different working wavelength. Two PRBS NRZ signals at 100 Mbit/s are applied to the two MRRs. The modulating and result electrical signals are observed in a four-channel real-time oscilloscope. The results are shown in Fig. 7 . The XOR and XNOR operations are carried out correctly at the through and drop ports simultaneously. Spikes still show up in Fig. 7 as in Fig. 5 due to the speed-limited transitions of two different tuning statuses of the MRRs .
The quality factors (Q factor) of the two MRRs are both about 7,000 (with the 3-dB bandwidths of about 0.21 nm). For carrier-injection modulation, high Q factors are desirable for low-voltage and low-power operation. Higher Q factor means smaller 3-dB bandwidth, so smaller carrier concentration change can result in enough extinction. However, a too high Q factor will make a MRR be too sensitive to the environmental temperature change. So a moderate Q factor of 7,000 is suitable for the device shown in this paper. While for the MRR utilizing the carrier-depletion modulation or other advanced modulation schemes, the Q factor should not be too high for an extra reason. Higher Q factor means longer photon lifetime, which will further limit the working speed of the MRR in addition to the limitations imposed by the carrier dynamic process. This is also left for discussion in our future work utilizing more advanced modulation schemes to achieve faster operation.
We implement simultaneous XOR and XNOR operations using an electro-optic directed logic circuit based on two cascaded microring resonators. Bitwise operations at 100 Mbit/s are demonstrated in two different operating modes employing carrier-injection modulation. The carrier-induced loss in the modulating process does not impede the operation of the device. Further improvement of the working speed of the device relies on the utilization of more advanced modulation schemes, which is left for future work.
This work has been supported by the National Natural Science Foundation of China (NSFC) under grants 60977037 and 60907001 and the Beijing Municipal Natural Science Foundation under grant 4112059.
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