1. Introduction

Silicon photonics is attracting the attention of both researchers and engineers because of its capacity for integration, low operating power, and ease of combination with existing silicon electronic devices. An on-chip all-optical switch has been demonstrated using silicon micro-ring resonators [1, 2], and also with even smaller photonic crystal (PhC) nanocavities [3, 4]. These devices enable us to achieve all-optical switching with extremely low energy, which is essential if we want to integrate these devices into a chip. Optical memory operation has also been demonstrated using these small cavities [5, 6], and this paves the way for the development of on-chip digital photonics. In addition to the all-optical devices, combination with existing silicon electronic devices offers the possibility of adding the functionality for controlling light.

PhC technologies allow the strong confinement of photons in a small area, and can enhance the interaction between light and matter [7]. Indeed, a very small mode volume V of just ~2.1(λ/2n)³ is fabricated in a PhC nanocavity [8]. A smaller V leads to a lower operating power, which gives PhC nanocavities an advantage over other types of micro-cavities. In fact the demonstrated operating energy for an all-optical PhC nanocavity switch is a few orders of magnitude smaller than that of other types of micro sized switches [3].

In this paper, we demonstrate low-power electro-optic (EO) modulation by using a high-Q photonic crystal nanocavity integrated with a lateral p-i-n diode structure. The key idea behind the device operation is based on the pioneering work undertaken by X. Qu et al. [9], in which they demonstrated fast EO modulation using a silicon micro-ring resonator. Similar demonstrations using silicon wire waveguide based devices have also been reported by a number of groups [10–12]. But here, we aim to achieve reduced operating power through the use of a smaller p-i-n structure and a PhC nanocavity with a higher Q. EO modulation in a small device has been attempted using an ultrasmall Fabry-Pérot cavity in a rib waveguide, but it is difficult to achieve an ultrahigh-Q with this device [13]. On the other hand, a PhC nanocavity is a good candidate for realizing a high Q and a small size simultaneously [14–16], and should be capable of demonstrating EO modulation at a significantly reduced power.

Although a vertical p-n structure enables us to pump PhC nanocavity lasers electrically [17], this structure does not allow us to achieve a high Q, because of the large absorption at the p and n layers that overlaps the optical mode. Therefore, a lateral p-i-n structure is needed to obtain a high Q since this means we can reduce the overlap between the optical mode and the p or n region. A lateral p-i-n structure has already been fabricated with PhC waveguides on SiO₂ [18, 19], but the use of SiO₂ cladding usually makes it impossible to fabricate high-Q nanocavities [20]. Therefore, an air-bridged p-i-n structure is needed to allow us to perform various studies based on high-Q cavities. Although the fabrication of a p-i-n structure on an air-bridged PhC is challenging, it will be of benefit as regards achieving a high Q and a small V. The realization of a high Q/V would mean that this structure should offer the possibility of low-power EO modulation and EO Q-switching [21] or ultrasensitive opto-electric detection [22]. A high-Q cavity with a p-i-n structure in silicon may even allow the development of opto-electrical circuits that can operate with only a few photons and electrons.

2. Fabrication and description of device structure

The fabrication process is illustrated in Fig. 1 . It starts with a conventional silicon-on-insulator wafer, in which we selectively implant p and n type ions by opening windows using an electron-beam resist. Boron and phosphorus ions are implanted at a dose of 10¹⁴ cm⁻², with a target projection range of 0.05 μm. The wafer is then annealed for 30 min at a temperature of 1000°C in a nitrogen atmosphere to activate the ions. The target doping density for both p⁺ and n⁺ regions is 5×10¹⁸ cm⁻³. After patterning the PhC using electron beam lithography and dry etching, we form aluminum contact pads by employing evaporation and lift-off techniques. Finally, the aluminum contacts are protected with a resist, and the scarifying SiO₂ layer is selectively removed by wet etching using buffered hydrofluoric acid.

 

Fig. 1 Fabrication process of a silicon PhC with a p-i-n structure. (1) Ion implantation. An electron beam resist is used to selectively implant ions. (2) Annealing for activation of implanted ions. (3) Fabrication of PhC by electron-beam lithography and dry etching. (4) Forming an aluminum contact by electron beam evaporation and lift-off. (5) Remove scarifying layer with BHF wet etching. The aluminum contact is protected with a resist. (6) Illustration of a fabricated air-bridged PhC with a p-i-n structure.

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Figure 2(a) shows an example scanning electron microscopic image of the fabricated device. Figure 2(b) is a schematic illustration of the device structure. The width modulated line-defect PhC nanocavity [14, 15] is fabricated in the i region, which lies between the n ⁺ and p ⁺ regions. This type of PhC nanocavity enables us to achieve an ultrahigh unloaded Q, which is advantageous as regards fabricating a device with a high transmittance at a high Q.

 

Fig. 2 (a) Scanning electron microscope image of a fabricated PhC nanocavity with a p-i-n structure. This is an inline type width-modulated line defect PhC nanocavity. (b) Schematic illustration of the structure. The PhC nanocavity is fabricated by shifting the air-holes slightly outwards as shown in the picture. The lattice constant a, hole radius r, and slab thickness t, are 420, 216 and 204 nm, respectively. The distances between the two contacts and between the p ⁺ and n ⁺ ion-implanted regions are shown as w _c and w _i, respectively. The contact pad size is about 200×200 μm (not shown here). The input and output waveguides with a width of $1.05\sqrt{3}a$ (W1.05) are optically connected with the cavity through barrier line defects that have a width of $0.98\sqrt{3}a$ (W0.98). The length d of the barrier W0.98 line defect determines the coupling between the cavity and the input/output waveguides.

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3. Spectrum characteristics

3.1 CW operation

The transmittance spectrum of a PhC nanocavity with w _w=2.5 μm, w _i=4.4 μm, w _c=11.1 μm, and d=9a is shown in Fig. 3(a) . It exhibits a very high loaded Q of 5.4×10⁵ with a transmittance of about 22%. This corresponds to an unloaded Q of about 1.0×10⁶. Since the highest Q achieved with the same design is 1.8×10⁶ [23], the optical absorption and scattering loss caused by the neighboring implanted p and n regions are considered to be small. The V of this cavity is very small at ~1.5(λ/n)³. We would like to emphasize that such a high Q and small V is possible because we fabricate the PhC nanocavity on an air-bridged slab.

 

Fig. 3 (a) Transmittance spectrum of a PhC nanocavity with a p-i-n structure when no voltage is applied. The structural parameters are described in the text. (b) Transmittance spectrum when a forward DC bias v is applied to the electrodes. The applied voltage is shown in the panel.

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Now, we apply a forward DC bias to the electrodes, and measure the transmittance spectrum of the cavity using a continuous-wave (CW) laser light. p ⁺ is grounded and a negative voltage –v is applied to the n ⁺ region. The result is shown in Fig. 3(b).

Figure 3(b) shows that the transmittance spectrum shifts towards a shorter wavelength when a forward bias is applied. This tells us that the refractive index of silicon has been reduced. It is known that the thermo-optic effect in silicon increases the refractive index; however, the carrier-plasma dispersion effect decreases it [24]. Therefore, Fig. 3(b) shows directly that carrier-plasma dispersion overcomes the thermo-optic effect when carriers are injected through a p-i-n diode. It should be noted that this has now became possible using the p-i-n structure, because it injects carriers but extracts them before they recombine and generate significant heating. Moreover, Fig. 3(b) also shows that the transmittance is lower with higher carrier injection, which is probably due to the free carrier absorption. The observation of a carrier-dispersion induced shift is promising in terms of achieving a fast EO modulation because the modulation through the carriers is much faster than that through heat.

As shown in Fig. 3(b), the spectrum exhibits a negligible shift when a reverse bias (–3 V) is applied. In fact, the current is below the measurement limit. In contrast, a very small shift is already visible at an applied voltage of 1 V. In this case, the measured current injected into the p-i-n device is only 0.12 μA (series resistance R_s between electrical probes are 8.3 MΩ), which tells us that only 0.12 μW is required to modulate the resonance shift of the PhC nanocavity. A clearer resonant shift is visible when 1.5 V is applied. In this case the cavity will be capable of a very high 14.2 dB optical signal modulation when the wavelength of the input light is set at the cavity resonance. Here, the current is still very small at 1.4 μA (R_s=1.1 MΩ), and the result is that a very small electrical power of 2.1 μW is required for high-contrast operation. This value is about 4.6 times smaller than that reported for a silicon micro-ring resonator [9]. Since the cavity has a high Q, a large optical modulation depth is possible with a small index shift. In addition, the index shift is determined by the carrier density. Because the width of the p-i-n junction is very small while the slab thickness is very thin, we can obtain a high carrier density with a small current. Hence a small operating power is achieved owing to the high Q and small V of the PhC nanocavity device. While the contact resistance between the probe and the aluminum contact pad is negligible, the measured R_s were somewhat higher than we expected. We found that an unfavorable Schottky barrier is created between n ⁺ and aluminum contact. Also, p ⁺ and n ⁺ regions exhibit relatively high sheet resistances of 1.3 kΩ/sq and ~8.9 kΩ/sq, respectively. These problems can be improved by optimizing such as the doping densities and annealing conditions. Therefore we should be able to further improve the operating power.

3.2 RF operation

Next, we investigate the radio-frequency (RF) characteristic of the p-i-n nanocavity modulator by measuring the time averaged transmittance spectrum. We generate a 2-ns wide square pulse train with a pulse interval of 2 ns. We send the signal to n ⁺ and ground p ⁺. The top and bottom of the square pulse is set at±v to enable carrier injection and extraction by turns. The spectrum is measured by employing the method used in Fig. 3, and is shown in Fig. 4(a) .

 

Fig. 4 (a) Transmittance spectrum measured by sweeping a CW laser light when applying a square shaped pulse with an amplitude of ±v, a pulse width of 2 ns, and a pulse interval of 2 ns. The amplitude ±v is shown in the panel. (b) The same as (a) but with square pulses with a width of 1 ns and a pulse interval of 1 ns. The spectrum for 0 V is not shown because it is identical to that shown in panel (a).

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The spectrum now shifts towards a longer wavelength, which indicates that in general the thermo-optic effect dominates the carrier-plasma dispersion effect. We think this occurs for the following reason. When we inject carriers for only half the time and extract carriers for the remaining time, their visible effect decreases and results in a smaller blue shift in the measured spectrum. On the other hand, when we inject carriers for a relatively long time of 2 ns, so the carriers can diffuse quickly far away from the p-i-n region [25], there is inefficient extraction of the carriers though the electrodes. As a result, the carriers recombine around the cavity, which leads to a temperature increase. In fact, as shown in Fig. 4(b), when we performed the same measurement but with twice the modulation speed there was a smaller red shift at the same applied voltage. We believe this is due to the shorter carrier diffusion time.

More importantly, when we consider the shape of the spectrum, we see that the peak is split into two. This indicates that the spectrum peak of the cavity performs a successful to-and-fro motion as a result of the RF voltage applied to the electrodes. It should be noted that the spectrum should become blurred when the transition time at which we switch the voltage is long compared with the flat-top time of the 2-ns square pulse, because we measure this spectrum with a CW laser light. Since we can still observe two clear peaks in Fig. 4(b), we know that the fabricated p-i-n PhC nanocavity switch can operate at a speed faster than 1 GHz, which is comparable to the first demonstration in a silicon micro-ring EO modulator [9].

4. Demonstration of electro-optic modulation

Next, we discuss a time-domain demonstration of our p-i-n PhC nanocavity EO modulator. We performed the EO modulation using the same cavity that we used for Fig. 4. The results are shown in Fig. 5 . If we set the input laser light at the first resonance peak, we should be able to observe on-to-off switching. Off-to-on switching is possible by changing the laser light to a shorter wavelength peak.

 

Fig. 5 (a) Output optical signal when a 2-ns square pulse (forward bias period) with a 2-ns interval (reverse bias period) is applied to n ⁺. The black and red lines indicate input wavelengths of 1589.93 nm and1589.83 nm, respectively. (b) The same as (a) but the electrical signal has a width of 1 ns with a 1-ns interval. The input CW laser light for the black curve (on-to-off type modulation) is 1589.893 nm and 1589.872 nm for the red (off-to-on type modulation).

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Figure 5(a) shows the modulated output when a 2-ns square pulse with a 2-ns interval is applied to n ⁺ at an amplitude of ±1.5 V, while p ⁺ is grounded. The output waveforms are shown for two input CW laser lights at different wavelengths. The wavelengths of each CW laser input are set to match one of the two peaks of the transmittance spectrum for ±1.5 V shown in Fig. 4(a). The obtained waveform shows clear on-to-off and off-to-on modulation of the optical signal. The switching contrast for Fig. 5(a) is larger than 10 dB, where the value is only limited by our measurement apparatus. Figure 5(b) shows the output for double the speed with an amplitude of ±1.6 V. The result obtained in Fig. 5 shows that successful GHz modulation is possible with our PhC nanocavity EO modulator.

Here we would like to emphasize that this is the first demonstration of EO modulation in a silicon PhC nanocavity, based on the carrier-dispersion effect. As a result of cavity resonance, the modulation depth is much greater, and the device size is significantly smaller than that of previously demonstrated MZI type PhC waveguide based EO switches [18]. By comparison with silicon micro-ring resonator based switches, PhC nanocavity based EO modulators should enable us to achieve an even lower operating power at a higher contrast owing to their smaller size and higher Q.

To investigate the carrier extraction efficiency during the reverse voltage period, we compared two output waveforms as shown in Fig. 6 . The forward voltage amplitude for these two waveforms was the same at +1.5 V, and was used to inject the same number of carriers into the device. But in one case we applied −1.5 V during the 2-ns square pulse interval (reverse bias period) and applied no voltage (0 V) in the other case. The waveform clearly reveals that the light quickly recovers to the on state when a reverse voltage is applied, but the recovery speed is much slower when no reverse voltage is applied. This shows directly that carriers are efficiently extracted though a p-i-n nanocavity, when a negative pulse is applied. However, Fig. 5 still shows that carrier injection is faster than carrier extraction. As discussed above, we believe this is due to carrier diffusion. The injected carriers quickly diffuse outside the p-i-n region even during the injection period, which makes them difficult to extract from the device when applying a switched voltage. A possible solution to this problem is to use a pre-emphasized non-return-to-zero signal, as used with micro-ring resonators, to enhance its modulation speed [26].

 

Fig. 6 Output optical signal for on-to-off type modulation when a 2-ns square pulse with a 2-ns interval is applied to n ⁺. The forward voltage is 1.5 V and the reverse voltage is −1.5 V for the red line and 0 V for the black line. Although we used a different sample for this measurement, the overall optical characteristics are similar to those of the sample used for Fig. 3-5. The sample design parameters are the same except that w _i=5.8 μm.

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When we estimate the capacity C of this device by using a simple model as described by C=ε _si S/d, where S = t×w _w, d = w_i, and ε _si is the dielectric constant of silicon, we should obtain 5.6 × 10⁻¹⁸ F. Obviously, this extremely small value is obtained owing to the smallness of this device, which is an advantage of PhC devices. Because of this small C and considering the discussion in the previous section, the required operating RF power should be at a very low (μW) level. This is a great advance in terms of silicon EO modulators, which we achieved because we employed a very small PhC nanocavity. In addition, the small C should allow even faster operation, if we utilize, for example, the depletion technique [27], whose speed is dependent on resistance capacitance limitations.

Finally, we would like to add some words about the ultimate operating speed and the cavity Q. Obviously the maximum speed will be limited with the high Q of the cavity. As discussed before, the presence of free carrier absorption during the operation lowers the Q. Figure 4(b) shows that the Q is about 3.6×10⁵ under the condition of GHz signal with an amplitude of ±1.6 V. This Q corresponds to a photon lifetime of about 0.3 ns, which gives the maximum operating speed. Since the modulation speed demonstrated in Figs. 5 and 6 are still far beyond this value, we should be able to improve the operating speed, while keeping the operating power about the same, by optimizing the electrical properties. We need to use lower Q only when we want to have much higher speed. In that case, we can achieve higher speed at a cost of increasing operating power, because we can roughly assume a linear relationship between the refractive index shift and the injected current.

5. Summary

We demonstrated GHz EO modulation in a silicon chip by employing a PhC nanocavity with a p-i-n structure. The modulation is based on the carrier-plasma dispersion effect, which enables us to achieve a fast modulation in silicon. The high Q of the cavity makes a sufficiently large optical modulation possible even when the refractive index modulation is small, and the small V allows us to employ a low current. As a result, the PhC nanocavity EO modulator made it possible to achieve modulation at a low (μW level) electrical operating power.

Finally, we would like to comment on the possibility of using a p-i-n PhC nanocavity for a different purpose to emphasize the progress made with this technology. For example, we may be able to trap and release photons with arbitrary timing from an ultrahigh-Q PhC nanocavity by changing the voltage applied to the p-i-n junction. The Q switching of PhC nanocavities has been demonstrated by utilizing carrier injection optically [21], but this will limit the high Q owing to the existence of free carrier absorption. Now, since a p-i-n junction can both inject and extract carriers at with an arbitrary timing, we should be able to demonstrate Q switching with an ultrahigh contrast. Since the high Q of PhC nanocavities is superior to that of other micro-cavities, the demonstration of Q switching with a p-i-n junction in a PhC nanocavity constitutes a significant advance by comparison with other technologies, and will offer the possibility of fabricating a true photonic memory.