1. Introduction

Silicon (Si) photonics has gained considerable research interest over the past decade because it is a promising technology to meet the growing demand for high data capacity in communications. An advantage of Si photonic devices is the fabrication compatibility with matured Si–CMOS technology. This compatibility made it possible to fabricate an optoelectronic integrated circuit monolithically on a Si substrate [1,2].

In recent years, the integration of optical and/or electronic functional materials with Si photonic devices has been intensively studied to add new functionalities [3–6]. In this regard, vanadium dioxide (VO₂) is one of the most promising candidates for integration with Si photonic devices because it exhibits a remarkable change in its optical constants at infrared wavelengths [7–10] as well as its electronic properties at temperatures above and below the metal–insulator transition (MIT) [11,12]. The MIT temperature (T_MI) of VO₂ is slightly higher than room temperature, ∼ 340 K, and the MIT is reversible and ultrafast [13–20].

Conventional Si photonic devices are based on a Si waveguide, and optical switches and modulators often consist of resonant structures or interferometer configurations. Therefore, the device size could be as large as tens of micrometers. The integration of VO₂ with Si waveguides possibly reduces the device footprint because the use of VO₂ simplifies the device structure. Several types of VO₂-integrated optical modulators have been developed, for example an optical modulator in which a 500-nm-long section of the Si waveguide was replaced with VO₂. Although the device had a large extinction ratio of ∼10 dB at a wavelength of 1550 nm, it experienced a large insertion loss of more than 5 dB, even in its ON state, because of the relatively large extinction coefficient of VO₂ (∼0.3) in its insulating phase [21]. Another type of device, i.e., a Si waveguide with a VO₂ cladding layer, has therefore been studied. In this geometry, light propagates through the Si waveguide and, consequently, insertion losses in the ON state are suppressed. In the OFF state when VO₂ is in the metallic phase, the metallic VO₂ cladding layer absorbs the light in the Si waveguide, resulting in a large extinction ratio.

In addition to downsizing the device, the integration of VO₂ with Si waveguide modulators is expected to realize high-speed modulation because VO₂ undergoes an ultrafast phase transition. However, hybrid Si/VO₂ modulators have been reported to exhibit switching time constants as long as hundreds of nanoseconds to microseconds [22,23]. The issue that remains unsolved is to identify the key factor that governs the switching speed of the device. This would explain the reason for the reported switching time constants being much longer than that of the MIT, which is of the order of sub-picoseconds, and which was estimated from the optical stimuli that induce the MIT of VO₂ [13,14,17].

In this study, we investigated the switching time of micrometer-scale modulators consisting of a Si waveguide with a VO₂ cladding layer in terms of the heat transfer in the devices. One of the characteristics of this switch is its known capability of undergoing photothermal switching: the insulator-to-metal transition of VO₂ can be induced by the photothermal effect of incident light [22,24]. Because the photothermal effect can heat VO₂ rapidly, we used it as a switching stimulus. Moreover, this characteristic provides the possibility of incorporating this switch in a surge protection device for which a high operating speed is required, and no electrode is needed in photothermal switching unlike in the case of electrical switching, resulting that the number of steps in the device fabrication process can be reduced. We evaluated the incident-light-power (P_i) dependence of the switching time by measuring the transient transmittance of the devices. The switching times obtained by numerically simulating the heat transfer in the devices were in good agreement with the experimental results, indicating that heat transfer governs the switching speed of these devices.

2. Device fabrication

A 500-µm-thick silicon-on-insulator (SOI) wafer was used to form the Si waveguide with a thickness of 220 nm and width of 400 nm on a buried oxide layer with a thickness of 2 µm. The first 1.8-µm-thick SiO­­₂ cladding layer was deposited by plasma-enhanced chemical vapor deposition. Subsequently, parts of the SiO₂ cladding were wet etched using a buffered hydrofluoric (BHF) acid solution to open windows ranging in length from 3 to 8 µm to expose the Si waveguide. A VO₂ layer with a thickness of 30 nm was fabricated on the waveguide by pulsed laser deposition, formed only on top of the Si waveguide and not on its sidewalls. The thickness of the VO₂ layer was determined from the computational simulations; the highest extinction ratio can be obtained in the VO₂ thickness range of 30–40 nm [24]. The deposition conditions and characterizations of the VO₂ layer on Si, such as surface roughness and crystallinity, have been reported previously [25]. Finally, the VO₂ layer was covered by a second 1-µm-thick SiO₂ cladding layer by sputtering. Details of the fabrication process were described elsewhere [24].

3. Transmission measurements

Two amplified spontaneous emission (ASE) light sources with an erbium-doped fiber amplifier (EDFA), hereafter referred to as L1 and L2, were used to measure the transient switching time as illustrated in Fig. 1. The wavelength was in the range of 1530 to 1610 nm. The continuous-wave light from L1 was controlled by an optical shutter consisting of a commercial fiber optical switch and a function generator for the photothermal heating of VO₂, and the light from L2 was used for the transmittance measurements when L1 was off. A square wave signal of 1 kHz was applied to the optical shutter with a duty cycle of 50%. The heating duration was long enough to achieve a thermal equilibrium state. The light beams from the two sources were coupled, and the transverse magnetic (TM) and transverse electric (TE) modes were decoupled by using a polarized beam splitter (PBS). The light in TM mode was used for the transmittance measurements because the VO₂ layer is located on top of the Si waveguide [24]. The light was input and output through a tip-lensed optical fiber from the chip-edge of the device under test (DUT) and the output signal was detected by a photodiode (PD; 1811-FC) or a power meter. The output voltage of the PD was recorded by an oscilloscope (Agilent DSO6104A). The light in TE mode was directly detected by another PD as an input reference. The devices were placed on a Peltier temperature-controlled stage and kept at T = 293 K.

 

Fig. 1. Schematic illustration of the experimental setup for measuring the switching dynamics of the optical modulators. ASE: amplified spontaneous emission; EDFA: erbium-doped fiber amplifier; PBS: polarization beam splitter; PD: photodiode; DUT: Device under test.

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4. Simulation

To explore the effect of heat transfer in the device on the switching dynamics, the local temperature of the VO₂ layer was characterized by numerical simulation. The switching times of the devices were deduced from the time constants within which the temperature of VO₂ reaches the T_MI. A three-dimensional waveguide structure with a length of 50 µm in all directions was assumed. The height and width of the Si waveguide were 220 nm and 400 nm, respectively. The waveguide was located on a 2-µm-thick SiO₂ layer and was covered by a 1-µm-thick SiO₂ layer. The finite element simulation of the device characteristics was conducted using a three-dimensional heat conduction model in COMSOL Multiphysics by solving the equilibrium and time-dependent heat equations. Photothermal heating was considered as a boundary heat source between the VO₂ layer and the Si core. The light was assumed to be absorbed by the 30-nm-thick VO₂ layer and that all the absorbed photon energy was converted to thermal energy. The absorption coefficient of the VO₂ layer was 2.1 × 10⁴ cm⁻¹ for the insulating phase and 2.9 × 10⁵ cm⁻¹ for the metallic phase at a wavelength of 1550 nm, deduced from the measured optical constants [25]. The T_MI of VO₂ was set as 340 K and 330 K for the heating and cooling processes, respectively. The thermal conductivity, mass density, and specific heat of VO₂ were 6 W/m·K, 4340 kg/m³, and 690 J/kg·K, respectively, for both the metallic and insulating phases [26–29]. Intuitively, the thermal conductivity of VO₂ may vary across the MIT. However, previous measurements demonstrated that this conductivity exhibits very little change or no observable discontinuity at the T_MI [30,31]. For the physical property values of Si and SiO₂, we used the default values in the COMSOL library. The temperature dependence of these values was not taken into account in this study. Here, we assumed a homogeneous transition of VO₂ and nanometer-scale phase separation was not considered. The transmittance was calculated from the lengths of the metallic (above T_MI) and insulating phases (below T_MI) of the VO₂ cladding layer by using transmission loss values of 4.55 dB/µm and 1.27 dB/µm for the metallic and insulating phases, respectively [24].

5. Results and discussion

 Figure 2(a) shows the P_i dependence of the transmittance for devices with different lengths. Here, the light from L1 was input to the device by operating the optical shutter manually. The measurements were performed for the thermal equilibrium state of the device as the time interval was as long as several seconds. The transmittance was derived by subtracting the contributions of the measurement system and those parts of the Si waveguide without a window. Note that the transmittance losses of the measurement system and the waveguide without a window were approximately 13 dB and 10 dB, respectively. The transmittance losses of the devices at T = 293 K and 353 K are plotted for comparison [24]. The transmittance decreased remarkably at a P_i of approximately 0 dBm as P_i increased. This result can be explained by the transition of the VO₂ cladding layer from the insulating phase to the metal phase. The insulating phase of VO­₂ corresponds to the ON state of the device and the metallic phase to the OFF state. The gradual transmittance change observed in the experiments is presumably due to the polycrystalline VO₂ film in the device. A polycrystalline VO₂ film usually has a great deal of dislocations and defects, which results in the spatial variation of the T_MIs. Below P_i of approximately 0 dBm, i.e., the threshold P_i, the photothermal effect raises the temperature of VO­₂ but is insufficient to increase it beyond the T_MI. On the other hand, above the threshold P_i, the photothermal effect raises the temperature of VO₂ to above the T_MI, resulting in the formation of the metallic phase of VO₂. In the reverse process, the transmittance recovered to the initial value at P_i of approximately −5 dBm. This hysteretic behavior is attributable to the MIT of VO₂.

 

Fig. 2. Transmittance with various device lengths as a function of P_i: (a) experimental and (b) simulated results. The transmittance values at temperatures of 293 K and 353 K are also plotted for comparison.

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For the device with a 3-µm-long window along the waveguide, referred to as the 3-µm-long device, the transmittance at a high P_i value (7 dBm) was coincident with that at T = 353 K. This indicates that the entire region occupied by the VO₂ cladding layer was in the metallic phase at high P_i. In contrast, for the devices with longer windows, the transmittance values at high P_i were smaller than those at T = 353 K, indicating that the VO₂ cladding layer partially remained unchanged from the insulating phase. While the transmittance is proportional to the device length at a P_i of −8 dBm, it is not at a P_i of 7 dBm. This also implies that the temperature of the VO₂ cladding layer with the longer windows was inhomogeneous at high P_i. We conducted numerical simulations of the P_i dependent transmittance of the devices, as shown in Fig. 2(b). As seen in Fig. 2, quantitatively, the simulations are in good overall agreement with the experimental results. This result implies that the switching characteristics of the devices can be explained by a simple heat transfer model, as is discussed later. The simulation results deviate from the experimental data especially in the 6- and 8-µm-long devices. This is presumably due to poor crystallinity, such as low density, dislocations, and defects, of the cladding layers [24], resulting that the thermal conductivity values of the cladding layers were not ideal in the actual devices.

Based on the results of the P_i dependence, the P_i from L1 was varied from 1 dBm to 7 dBm to induce the MIT of VO₂ and that from L2 was set to −8 dBm to avoid the photothermal effect. The optical switching characteristics of the 3-µm-long device for P_i = 7 dBm are shown in Fig. 3(a). Here, the input from L1 was intermittently turned on and off for 0.5 ms by the shutter while the input from L2 was continued during the measurement. Note that the P_i of 7 dBm does not include the contribution of L2 which is considerably smaller compared with that of L1. The output transmittance (red line) followed the input signal (blue line) with stability, indicating the continuous operation of the optical switching. The transmittance was derived from the ratio of the output voltage to the reference voltage. Higher transmittance denotes the insulating phase of VO₂ (L1 off, cooled state) and lower transmittance is associated with the metallic phase (L1 on, heated state). The extinction ratio was approximately 16 dB, consistent with the result in Fig. 2(a).

 

Fig. 3. (a) Time-dependent output transmittance of the 3-µm-long device (red) and input reference voltage (blue) of PD for P_i = 7 dBm. (b) PD voltages of output (red) and input (blue) vs. time for the heating process. Changes in the transient transmittance as a function of time with various P_i for the (c) heating process and (d) cooling process. Exponential fitting curves are also plotted.

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The switching dynamics were investigated in detail on a shorter time scale [Fig. 3(b)]. The output voltage (red line) increased in accordance with the input signal (blue line) and subsequently decreased owing to the insulator-to-metal transition of VO₂ induced by the photothermal effect. The input signal had a rise time of 100 ns, which was attributed to the performance of the optical shutter. The zero point (t = 0 s) was defined as the middle point of the rise time, where the output voltage exhibited a maximum value. Figure 3(c) shows the changes in the transient transmittance of the device with different P_i for the heating process, where VO₂ transits from the insulating phase to the metallic phase. For P_i = 1 dBm, the transmittance started to decrease at ∼0.8 µs after the zero point. Here, we define this delay time as τ₀, as indicated in Fig. 3(c). The value of τ₀ decreased with increasing P_i and was shorter than 10 ns at P_i ≥ 5 dBm. Note that because of the rise time of the shutter, values of τ₀ below 10 ns could not be evaluated in this study. After the delay time τ₀, the transmittance decreased markedly. We defined the time constant of the exponential fitting of the transmittance change [gray lines in Fig. 3(c)] as τ₁. The values of τ₀ and τ₁ are plotted as a function of P_i in Fig. 6 and are discussed with the simulation results later on. Note that an unusual increase of transmittance was observed at 0 < t < τ₀ (heating process) in Fig. 3(c). This is due to an underestimation of transmittance at t < 0 (cooled state). In order to reduce the photothermal effect from L2 as small as possible, the P_i of L2 was set as low as possible. As a result, the background noise of the PD affected the estimation of transmittance at t < 0. However, this has no effect on the evaluation of τ₀ and τ₁.

Figure 3(d) shows the changes in the transient transmittance of the device during the cooling process. The delay time was negligibly small compared with the switching time constant. In this case, we defined the time constant of the exponential fitting of the transmittance change [solid lines in Fig. 3(d)] as τ_c. The values of τ_c are plotted as a function of P_i in Fig. 6. Although the details are discussed later, it is interesting to note that τ_c is more than one order of magnitude longer than τ₁, meaning that the switching behavior during the cooling process is much slower than that during the heating process. This might be attributable to the thermal dissipation effect in the cooling process.

The dependence of the switching time on the device length was also examined. As shown in Fig. 4(a), the time-dependent transmittance was largely independent from the device length in the heating process. This result suggests that the switching dynamics of the device are governed by the light absorption in the VO₂ cladding layer near the edge of the device, as is discussed later. Figure 4(b) shows the time-dependent transmittance of the devices for the cooling process with different window lengths. The transient transmittance was almost coincident for all the devices.

 

Fig. 4. Changes in the transient transmittance for the (a) heating process as a function of time for P_i = 2 dBm and 7 dBm and (b) cooling process for P_i = 7 dBm for various devices.

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 Figure 5(a) shows the simulation results of the temperature distribution of the 3-µm-long device for P_i = 4 dBm in the state of thermal equilibrium. Note that the dimension of the device structure is shortened to emphasize the temperature profile around the Si core. Photothermal heating occurs at the VO₂/Si interface and a temperature gradient exists along the Y-direction. The propagating light wave is absorbed by the VO₂ layer and weakened as the Y-values increase. Figure 5(b) shows the time dependence of the temperature at representative points on the VO₂ layer along the Y-direction for the heating process for P_i = 4 dBm. The temperature of the device saturates at approximately t = 10 µs, indicating that the device is at thermal equilibrium. Figure 5(c) exhibits the temperature profile of the VO­₂ layer along the Y-direction in the time range from 1 ns to 10 µs. Here, the zero position (Y = 0 µm) was defined at the center of the device regardless of the device length. Even at thermal equilibrium (10 µs), temperature variation exists in the VO₂ layer along the Y-direction, and the temperature near the edge of the device (Y = −1.44 µm) is the highest at ∼590 K, which is much higher than the T_MI.

 

Fig. 5. (a) Temperature distribution of the 3-µm-long device across the device structure for P_i = 4 dBm. (b) Temperature-time profile at various points in the VO₂ layer during the heating process. The T_MI is also shown as a reference. (c) Temperature profile of the VO₂ layer along the Y-direction. (d) Temperature-time profile at representative points in the VO₂ layer during the cooling process.

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Assuming that the transmittance of the device starts to decrease when the temperature at the edge of the device reaches the T_MI, the value of τ₀ was estimated to be ∼22 ns from the simulation [Fig. 5(b)]. This value is in good agreement with that measured experimentally for the 3-µm-long device for P_i = 4 dBm [Fig. 6(a)]. As discussed previously, the switching dynamics in the heating process are governed by the light absorption in the VO₂ cladding layer in the vicinity of the device edge because the switching time is independent from the length of the device [Fig. 4(a)]. When the first part of the VO₂ cladding layer (within a distance of one micrometer from the edge) changes into the metallic phase, the transmittance of the device decreases to 1/e independently of the device length, as was estimated from the transmittance loss. Therefore, in the simulation, the switching time τ₁ corresponds to the time at which the temperature of the VO₂ cladding layer at Y = −0.5 µm reaches the T_MI for the 3-µm-long device. The value of τ₁ was estimated to be ∼27 ns from the simulation [Fig. 5(b)]. This value is also in good agreement with that evaluated experimentally [Fig. 6(a)].

Figure 5(d) shows the time dependence of the temperature of the VO₂ cladding layer for the cooling process for P_i = 4 dBm. Although the initial temperatures differ at each location, these temperatures decrease to below the T_MI at approximately 2 µs independently of the location. This cooling time might correspond to the time by which the switching is delayed during the cooling process. However, the delay time was negligibly small in the experiments, as mentioned previously [Fig. 3(d)]. Furthermore, the slow recovery process cannot be explained by the simulation results, which predict an abrupt change in the transmittance when the temperature of the VO₂ cladding layer reaches the T­_MI. A possible reason for this discrepancy is an inhomogeneous phase transition owing to VO₂ undergoing a first-order phase transition, which was not taken into account in the simulation. Therefore, τ_c cannot be estimated from the simulation in this study and would have to be investigated in future.

 

Fig. 6. P_i dependence of the switching time constants (τ₀, τ₁, τ_c) for devices with lengths of (a) 3 µm, (b) 4 µm, (c) 6 µm, and (d) 8 µm. The experimental data are indicated by closed circles and the simulated results are represented by open circles

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Figure 6 shows the dependence of the switching time constants [τ₀(exp), τ₁(exp), and τ_c(exp)] of the devices on P_i, as was evaluated from the experiments. Note that we averaged ten measurements and the standard deviation of the measurements is depicted by an error bar. We also plotted the time at which the temperature at the edge of the device (Y = −1.5 µm, −2.0 µm, −3.0 µm, and −4.0 µm for the 3-, 4-, 6-, and 8-µm-long devices, respectively) reaches the T_MI and that at which the temperature 1 µm from the edge of the device (Y = −0.5 µm, −1.0 µm, −2.0 µm, and −3.0 µm for the 3-, 4-, 6-, and 8-µm-long devices, respectively) reaches the T_MI in the simulation of the heating process. These values are denoted as τ₀(sim) and τ₁(sim), respectively. The simulated results of τ₀(sim) and τ₁(sim) were in good agreement with the experimental results of τ₀(exp) and τ₁(exp), respectively, for all the devices. This indicates that τ₀ and τ₁ are governed by the temperature changes at the edge of the device and within 1 µm from the edge of the device. Because τ₁ is the time at which the transmittance decreases to 1/e of the initial value, the result suggests that more than 63% of the propagation light in the waveguide was absorbed within ∼1 µm of the VO₂ cladding layer from the edge of the device. In fact, the experimental result of the light propagation of the device revealed that more than 78% of P_i is absorbed by the VO₂ cladding layer within 1 µm from the edge of the device when the VO₂ is in the metallic phase [24]. To improve the switching characteristics, the rate of change of the temperature in the VO₂ cladding layer should be increased. This means that heat transfer from the VO₂ cladding layer to the SiO₂ cladding layer should be suppressed. A possible solution would be the reduction of the thermal conductivity of the SiO₂ cladding layer. Considering that porous SiO₂ films reportedly have a lower thermal conductivity than dense SiO₂ films [32–35], the fabrication of a porous SiO₂ layer on the VO₂ layer could thus improve the switching characteristics of the heating process.

Here, it should be noted that the increase in the thickness of the VO₂ layer causes a stronger photothermal effect. The effect results in an improvement of the characteristics of the heating process due to the enhancement of thermal energy. However, it degrades the switching characteristics of the cooling process, which is an analogy to the P_i dependence of the switching characteristics.

For the cooling process, the τ_c slightly depended on P_i but was nearly independent of the device length. As mentioned previously, τ_c cannot be estimated from the simulations, but heat dissipation might play a critical role in the switching characteristics of the cooling process. The heat dissipation of the device is determined mainly by the thermal conductivity of the constituent materials. Improvement of the switching characteristics, therefore, would require the selection of a material with high thermal conductivity for the cladding layer. However, it would not be practically feasible to replace the SiO₂ cladding layer. In addition, an increase in the thermal conductivity of the cladding layer degrades the switching characteristics of the heating process, meaning that the improvements in the heating and cooling processes contradict each other. On the other hand, we believe that an improvement of the crystallinity of the cladding layer leads to faster switching speed for the cooling process. This is because the poor crystallinity of the cladding layer degrades the thermal conductivity of the device, as mentioned previously. If an epitaxial (single crystalline) VO₂ cladding layer with a sharp and homogeneous phase transition can be fabricated on Si waveguide, a switching speed would be faster for the cooling process.

6. Conclusions

We exploited the photothermal effect to investigate the switching time constants of micrometer-scale optical modulators consisting of a Si waveguide with a VO₂ cladding layer. Stable optical switching could be induced by turning the infrared light on and off, which induced the insulator-to-metal and metal-to-insulator transitions in the VO₂ cladding layer, respectively. For the heating process (insulator-to-metal transition), the delay time τ₀ for the incident light power P_i of 1 dBm was ∼0.8 µs. The value of τ₀ decreased with increasing P_i and was less than 10 ns for P_i ≥ 5 dBm. The switching time constant τ₁ was almost independent of the device length and decreased from ∼100 ns for P_i = 1 dBm to ∼10 ns for P_i = 7 dBm. The numerical simulations based on the heat transfer model revealed that τ₀ and τ₁ were determined by the temperature changes at the edge of the device and within ∼1 µm from the edge of the device, respectively. For the cooling process (metal-to-insulator transition), the switching time constant τ_c slightly depended on P_i and ranged from 3 µs to 15 µs.

This study revealed that the switching characteristics of the modulators driven by the photothermal effect are governed by heat transfer and thermal dissipation in the devices. These findings are applicable to cases of other thermal stimuli such as Joule heating because the thermal characteristics are determined mainly by the device structure and the thermal properties of the constituent materials rather than by thermal stimuli. We thus consider the findings of this study to provide a guideline according to which to design the thermal structure of the device to improve its switching dynamics.