The strong thermooptic effect in silicon enables low-power and low-loss reconfiguration of large-scale silicon photonics. Thermal reconfiguration through the integration of metallic microheaters has been one of the more widely used reconfiguration techniques in silicon photonics. In this paper, structural and material optimizations are carried out through heat transport modeling to improve the reconfiguration speed of such devices, and the results are experimentally verified. Around 4 µs reconfiguration time are shown for the optimized structures. Moreover, sub-microsecond reconfiguration time is experimentally demonstrated through the pulsed excitation of the microheaters. The limitation of this pulsed excitation scheme is also discussed through an accurate system-level model developed for the microheater response.
©2010 Optical Society of America
The promise of silicon (Si) photonics for large-scale and low-cost integration of photonic devices for different applications such as, intra-chip optical interconnects, fiber optics components, and optical signal processing has attracted a lot of attention recently [1–3]. The possibility of large-scale integration of photonic devices enables functionalities with an unprecedented level of flexibility and scalability. A major requirement in such Si photonics devices is the possibility of tuning of individual photonic devices not only to correct for fabrication inaccuracies but also for the reconfiguration of the characteristics of the system. Previous works for reconfiguration of Si photonic devices have been mainly focused on three major physical effects, namely, free-carrier-plasma dispersion [4, 5], electrooptic , and thermooptic [7–17] effects. Although the free-carrier-plasma dispersion effect enables a fast reconfiguration speed (typically ≤1 ns), this fast reconfiguration comes at the cost of an inherent optical loss caused by the injection of free carriers. For many applications, especially signal processing, the introduced loss can be detrimental to the performance of the device. Another method of reconfiguration is through hybrid Si-polymer devices based on the electrooptic effect, which has the advantage of being low-loss and low-power with relatively fast response time (typically, in the order of nanoseconds) . However, realization of these devices is technologically challenging as they require large drive voltages and at the same time their fabrication is not CMOS-compatible. On the other hand, the thermooptic effect, which is inherently lossless, can be utilized to efficiently tune photonic devices with negligible insertion loss. The only shortcoming of these devices is their slow response time, which is usually limited to a few to tens of microseconds as a result of slow heat diffusion process. The thermooptic effect in Si-based devices has been used extensively before for the implementation of reconfigurable filters , reconfigurable add-drop multiplexers (ROADMs) [8, 9], dispersion compensators [10, 11], and switches [12–17].
Heating of photonic devices for the utilization of the thermooptic effect has been mainly demonstrated using two approaches: 1) direct Joule-heating of the Si device , and 2) integration of metallic microheaters close to the Si device [7–17]. The former approach requires doping of the Si slab to reduce the resistivity of the intrinsic Si which leads to optical absorption and higher insertion loss. Also, with moderate doping levels of the Si layer, heater electrical resistance is high and therefore, the required drive voltage is relatively high (typically, tens of Volts) in these devices. The latter approach has been more widely used to this date as the metallic microheater can be placed far enough from the photonic device to reduce the optical absorption by the metal. However, this method usually has slower response time because of a larger heating volume and therefore, a larger heat capacity. This slow reconfiguration time can be an obstacle in many signal processing application. Hence, a detailed study of heat transport in such structures is necessary for more optimum designs.
In this work, we experimentally and numerically study the effect of different geometrical parameters for the improvement of the reconfiguration speed of the thermally-tuned Si photonic devices. It is shown that by using a cladding material with better thermal properties (e.g., higher thermal conductivity as in low-pressure chemical vapor deposition (LPCVD) silicon nitride (SiN)) the speed of the device is improved. For more accurate device modeling, thermal properties (i.e., thermal conductivity and specific heat capacity) of the deposited materials are fine-tuned by fitting the experimental and simulation data. In this work, a simple model is presented, which can perfectly describe the transients of the thermal response of these devices. It is also shown that through pulsed-excitation of these devices sub-microsecond reconfiguration time is possible.
The organization of this paper is as follows. In Section 2, the architecture and numerical modeling of microheaters are presented. Fabrication and experimental characterization details are presented in Section 3. Device optimization along with the comparison of modeling and experimental results are discussed in Section 4. The system-level model for metallic microheaters along with their pulsed-excitation performance is studied in Section 5; and the paper is concluded in Section 6.
2. Device architecture and numerical modeling
The performance of microheaters, which is mainly studied in terms of power consumption and tuning speed, is usually calculated either through analytical/semi-analytical methods [19, 20] or through numerical modeling of the heat-transport equation [12, 21]. Although the former approach provides physical insight into the heat transport, it is usually not accurate enough for the optimization purpose. Hence, in this work our modeling is performed by numerical simulation of the heat-transport equation with material thermal properties, which are optimized to minimize the error between simulation and experimental results.
Figure 1(a) shows the architecture of the waveguide-microheater configuration on an silicon-on-insulator (SOI) substrate, which is considered in this work. Here, the metallic microheater is placed on top of the Si waveguide and is separated from the Si device layer by a cladding material with the thickness tclad to avoid optical loss. The details of structural parameters are shown in Fig. 1(b) and are tabulated in Table 1. Heat transport in this device is simulated by numerically solving the heat conduction equation
using the finite-element method (FEM)  in the COMSOL software package by applying appropriate boundary conditions. Here k, c, and ρ, are the thermal conductivity, specific heat capacity, and density of the material, respectively; and qs and T are the density of the heat power generation and the temperature, respectively. In these simulations, the structure is assumed to have translational symmetry and thus the cross-section of the device shown in Fig. 1(a) is modeled (see Fig. 1(b)). Heat convection boundary condition, −k ∂T/∂n = hair, is applied to the top surface of the device, where n is the direction normal to the surface and hair is the convection heat coefficient to the surrounding air. Also, the right, left and bottom boundaries of the simulation window are placed 20 µm away from the microheater device so that the temperature rise is negligible at these boundaries. This large simulation window allows approximating the temperature at the boundaries with the ambient temperature (Tamb) with very good accuracy.
Figure 1(b) shows the distribution of temperature at the cross-section of waveguide-microheater configuration. White arrows show the heat flux in this structure. The thicknesses of the buried oxide (BOX) layer and the cladding layer are both 1 µm and the waveguide cross-section is 220×480 (nm)2, in this example. The cladding material is SiO2 and the microheater material is nickel (Ni). To maximize the overlap of microheater temperature profile with the optical mode of the waveguide, a simple single-strip microheater, which is laterally co-centered with the waveguide, is considered in this work as shown in Fig. 1(a). The list of physical parameters used in our simulations can be found in Table 2. Thermal conductivity and specific heat capacity of the cladding material depend on the deposition condition  and are optimized by fitting the modeling to the experimental results presented in Section 3.
Two of the most important geometrical parameters in the optimization of the response of metallic microheater devices are the thicknesses of the BOX and the cladding layers. Figures 2(a) and 2(b) show the rise/fall time and the steady-state temperature rise at the center of the Si device for different thicknesses of the BOX layer, respectively; while the thickness of the cladding layer is fixed at tclad = 1 µm. The rise-time (fall-time) is defined as the time by which the temperature rises (falls) from 10% to 90% (90% to 10%) of the steady-state value when a step signal is applied to the microheater. It should be noted the heat transport equation is linear and time-invariant and therefore, the rise-time and fall-time of the device are equal. This is observed in Fig. 2(a), in which the rise/fall-time curves lie on top of each other. It is seen in Figs. 2(a) and 2(b) that the response of the microheater becomes faster at the price of less temperature rise or higher power consumption. Since, in this work we are aiming to increase the reconfiguration speed of microheaters, thin BOX layers are chosen. It should also be noted that the BOX should be kept thick enough to avoid leakage of the optical field into the underneath Si substrate. The BOX thickness required to keep the propagation loss below 0.08 dB/cm (corresponding to a resonator intrinsic quality factor (Q) of 107) is around 700 nm . We have chosen a BOX thickness of tBOX = 1 µm, because of the availability of SOI wafers with this BOX layer thickness, with a little compromise over the device performance. Moreover, the thickness of the cladding layer, tclad, has to be above 800 nm to satisfy the same level of propagation loss (i.e., 0.08 dB/cm) caused by the absorption by the metallic microheaters . Throughout this work, we have chosen a slightly larger cladding thickness, tclad=1 µm, so that the possible variations in the cladding thickness in the fabrication process do not introduce metal absorption loss in the device.
3. Fabrication and characterization
The performance of the microheater-waveguide configuration studied in the previous section can be characterized by fabricating a device based on this configuration and by monitoring its transmission properties as heat is dissipated in the microheater. Here, we fabricated 20 µm diameter microring resonators with same radial cross-section as shown in Fig. 1(b). As the radius of the bend is much larger than the variations of both optical field and temperature distribution, previous simulations for devices with translational symmetry can be used for the microring device with cylindrical symmetry (numerical modeling results showed very small error (≈0.5%)). The device in fabricated on Soitec SOI wafer with Si slab thickness of 220 nm, and a BOX layer of 1 µm thickness. The widths of the bus waveguide and the microring are 480 nm to assure single-mode operation. First, the pattern of the device is written on ZEP electron-beam resist using electron-beam lithography (JEOL 9300) and etched into Si by inductively-coupled-plasma etching (STS ICP) using a combination of Cl2 and HBr gases. After this step, 1 µm SiO2 is deposited using plasma-enhanced chemical-vapor-deposition (PECVD) and microheater patterns are defined by a lift-off process using poly(methyl methacrylate)(PMMA) electron-beam resist and electron-beam evaporation. Microheaters are formed by the deposition of 75 nm thick Ni layer, and contact pads are covered with 150 nm gold (Au) for better electrical contact. To increase the yield in fabrication, we perform one step lift-off of both Ni and Au at the locations of microheaters and contact pads. Later, in another lithography step, areas over photonic device are opened using ZEP resist, where Au is removed using a Ni-safe Au etchant, GE-8148 (Transcene Inc.). This Au is removed for higher electric resistance and higher power dissipation over the photonic device. Figure 3(a) shows the optical micrograph of the fabricated microring with integrated microheaters. Dashed lines depict the edges of the photonic device. Figure 3(b) shows the scanning-electron micrograph of a 500 nm wide microheater over the microring.
The performance of the microheater is characterized by measuring the transmission of the fabricated microring using a standard optical characterization test setup similar to the one described in , while different drive signals are applied to the microheater. The optical transmission is measured by coupling the TE-polarized light from a swept-wavelength tunable laser into the input waveguide, while the output of the device is coupled into a photodetector and the data is transferred to a PC using a data-acquisition card. The drive signal of the microheater is applied using an RF probe (Microtech Inc.). Figure 4(a) shows the transmission spectra of the microring for different power dissipations in the 500 nm wide microheater. The intrinsic Q of the fabricated microring resonator is around 60k. It is observed that resonance wavelength of microring is red-shifted as power dissipation is increased in the microheater. The resistance of this microheater is 590 Ω at small power dissipations and increases almost linearly with power consumption by 34 Ω/mW. This can be translated to 0.36 K/Ω change in the temperature of the microheater. Hence, the microheater can also be used as a thermistor in this device .
To measure the step-response of the microheater, laser wavelength is fixed at the linear region of the microring resonance line-shape. Then a small-signal step voltage is applied to the microheater and the output of the microring is monitored on an oscilloscope. The applied signal should be small enough so that the laser wavelength remains in the linear region of the resonance. Figure 4(b) depicts the measured normalized step-response of the microheater along with the simulation results. Good agreement is obtained between measurement and simulation results. It is observed that the rise-time and fall-time of the microheater is around 4 µs.
4. Microheater Optimization
A single-strip microheater co-centered with the underlying photonic device is studied in this work as the microheater of choice. The effect of the width of this microheater is studied in this section. Also, as shown in Section 2, to assure faster reconfiguration time, the minimum possible thickness of the BOX and cladding layers (≈ 1 µm) should be used. Although the thermal properties of the BOX layer are always fixed, the choice of the cladding material will affect the thermal response of the device, and its effect is studied in this section.
4.1. Effect of Microheater Width
Figure 5(a) shows the simulation and experimental results of temperature rise in the center of the Si device for 1 mW power dissipation in the microheaters with different widths (Wh) over a 20 µm diameter microring. It is observed that temperature rise is higher for the narrower microheaters and hence they are more power efficient. To compare the experimental and simulation results, power dissipation in Au pads and thin-film connectors are extracted and numerical results are adjusted to take this power loss into account. The thermooptic coefficient of Si, dnSi/dT = 1.8×10−4, is used to relate the resonance wavelength shift to the temperature change of the microring. We see that relatively good agreement between simulation and experimental results is obtained. The vertical axis on the right side of Fig. 5(a) also shows the amount of frequency shift of the microring for 1 mW power dissipation.
Rise-time and fall-time of microheaters are also measured and shown in Fig. 5(b) for different microheater widths along with the simulation results. It is observed that as the width of the microheater is reduced, its reconfiguration time is decreased as a result of smaller heating volume. The frequency response of these microheaters are also measured. For this measurement, a small-signal sinusoidal voltage with frequency f is applied to the microheater and the optical output of the microring which has a 2f frequency content (optical response is linear with respect to power dissipation) is locked to the double frequency of the drive signal in a lock-in amplifier. From these measurements, the 3dB bandwidth of microheaters with widths of 2 µm, 1 µm, and 0.5 µm are measured to be 109 kHz, 132 kHz, and 139 kHz, respectively. These results support our previous observation that narrower microheaters reconfigure faster along with more heating efficiency.
It is observed from the temperature response of the microheater device (Figs. 5(a) and 5(b)) that the performance measures of such a device do not change considerably with the microheater width. This is mainly caused by the lateral diffusion of the heat in the cladding and BOX layers (approximately 1–2 µm on each side of the microheater), which is comparable to the size of the microheater . Hence, to further reduce the heating volume, trenches can be etched on the sides of the microheater. The effect of side trenches is significant in the performance of the thermooptic device and has to be studied for different applications. For instance, a 500 nm wide microheater with two 1 µm wide trenches located 500 nm to the sides of the microheater and etched down to the underlying Si substrate shows an increase in the rise/fall time to 6.2 µs while the power consumption is reduced by half compared to the case without trenches. Other simulations on the effect of trenches showed an increase in the response time of the device and since, the focus of this work is to increase the reconfiguration speed, we avoid trenches on the sides of the microheater.
4.2. Effect of cladding material
One other important factor in the performance of microheaters that is usually ignored is the effect of cladding material. Usually, PECVD SiO2 is used for cladding because of the ease of fabrication and CMOS-compatibility. An alternative material that can be used as the cladding is SiN. It has been shown before that SiN films deposited using LPCVD have high thermal conductivities  (10 to 20 times higher than PECVD SiO2). Our numerical results show that if the thermal conductivity of cladding is increased while its specific heat capacity is kept unchanged, response of the microheater becomes faster at the price of higher power consumption. Since the physical parameters of LPCVD SiN films that were reported in the literature were not consistent as a result of different deposition conditions, we fabricated the same devices as explained in Section 3 with LPCVD SiN cladding and then we measured the thermal properties of the deposited SiN. Figure 6(a) shows the frequency response of the 1 µm wide microheater with PECVD SiO2 and LPCVD SiN claddings. It is seen that the 3dB bandwidth is increased by 23% in the LPCVD SiN cladding device to 162 kHz. Figure 6(b) compares the normalized step-response of these microheaters at the rise and fall of the drive signal. It is observed that the response of these devices are almost the same at large time-scales. However, devices with LPCVD SiN cladding showed faster response at small time-scales which can be advantageous for pulsed excitation of microheaters as discussed in Section 5. The steady-state heating property of these devices are also measured, and it is found that devices with SiO2 cladding have 35% less power consumption compared to devices with SiN cladding as a result of lower thermal conductivity of the SiO2 layer.
5. System-level model and pulsed excitation of microheaters
One approach to increase the reconfiguration speed of microheaters is through applying high-energy-pulsed drive signals [18,26]. To predict the performance of microheaters using this type of excitation, an accurate model capable of predicting the microheater response at short time-scales (hundreds of nanosecond) is needed. Despite the good agreement between the simulation and experimental results at t ≥ 1 µs (as shown in Section 3 and Fig. 4(b)), the accuracy of modeling reduces for t ≤ 1 µs as a result of second order heat propagation effects. In this section, a system-level model is introduced which is capable of perfectly predicting the response of microheaters in the whole time-span.
Figure 7(a) shows the proposed model, which is composed of a block with a delay-like response cascaded by a first-order linear-time-invariant (LTI) system. The delay is caused by the heat propagation from the microheater to the Si waveguide whose response is chosen so that the model best fits the experimental data. The effective delay of this block is τdelay and is shown in the delay response. Also, the first-order LTI system with a time-constant of τdiff models the heat diffusion in a simple layered structure. The parameters of this model are extracted for a 1 µm wide microheater by fitting the experimentally measured response to that of the model.
As a result τdelay and τdiff are found to be 400 ns and 1.5 µs, respectively. Figure 7(b) shows the experimental result for the normalized impulse-response of the described microheater along with the impulse-response of the proposed model. Experimental impulse response is evaluated by taking the derivative of the step-response of the system. It is observed that there is a good agreement between the experimental and modeling results. We also observe a 725 ns delay in the impulse-response of this structure. This reveals that even by applying a high-energy pulse at the beginning of the excitation, reconfiguration time less than 725 ns is impractical. This limitation which is shown for the first time in this work is the ultimate reconfiguration speed limit in these type of microheaters for the given device parameters.
It is important to note that the 725 ns is the delay in heat transfer from the microheater to the Si layer, and it is not necessarily the response time of the microheater. It is known that an LTI system can reach its steady state step response fast, if it is excited by a short pulse (ideally an impulse) combined with a step function. We have used our theoretical model to optimize the pulsed excitation signal. Using the results of our model we have developed an experiment to test the effect of such excitations. Figure 8 shows the experimental results for the structure shown in Fig. 3(a) with a microheater width of 1 µm. The other geometrical parameters of the structure are the same as those in Table 2. The two curves in Fig. 8 show the normalized temperature at the center of the Si microring for the excitation with a step function with and without an added pulse. For the pulsed-excitation, we have considered a 500 ns high-energy pulse at the beginning of the excitation signal to enhance the rise-time of the system (inset of Fig. 8). It is observed that the rise-time of the device is reduced from 4.2 µs to below 1 µs through pulsed-excitation. By shortening the duration of the pulse and increasing its peak-power, rise-times as low as 725 ns can be achieved with practical peak-power levels.
The heat propagation delay from the microheater to the device layer plays a crucial role in the thermal reconfiguration time and device optimization for reducing the heat propagation delay is of great significance. We studied the impact of the following device parameters on the heat propagation delay (i) microheater width and (ii) thermal conductivity of the cladding material. As seen in Section 4.1, the width of the microheater does not play a major role in the settling time of the device. On the other hand, the thermal diffusivity (α = k/ρc) of the cladding material plays a significant factor in reducing the heat propagation delay. Figure 9 shows the modeling results for heat propagation delay of a 500 nm wide microheater versus the cladding material thermal diffusivity constant. All other device parameters are the same as in Table 2. It is observed that the heat propagation delay is inversely proportional to the thermal diffusivity of the material, which is in agreement with the analytical results for a one-dimensional system . The locations of PECVD SiO2, LPCVD SiN and crystalline Si (c-Si) on the thermal diffusivity axis are marked. As observed, heat propagation delay of a cladding material with a heat diffusivity close to c-Si can result into heat propagation delay of less than 10 ns. We have experimentally demonstrated in Ref.  that we can utilize this to our advantage through a novel thermally reconfigured device, in which the high thermal diffusivity of c-Si is used to reduce the heat propagation delay and also the reconfiguration time to below 75 ns.
It should be noted that the pulsed excitation of microheaters can be used to reduce the rise-time of the device. However, this approach cannot be used to reduce the fall-time and cooling usually proceeds at the natural thermal time constant of the device. However, as shown in , through differentially addressable device architecture, pulsed-excitation can be used to reconfigure the device in opposite directions at high speed.
In this work, a numerical study of heat transport in metallic microheater structures is performed for the purpose of improving reconfigurable speed of Si photonic devices. It is experimentally shown that through geometrical optimizations, ≈4 µs rise/fall times are achieved in such structures. Also, the effect of the cladding material is studied and it is shown that high-thermally-conductive LPCVD SiN cladding can improve the reconfiguration speed compared to the conventional SiO2 cladding by approximately 20%. Moreover, sub-microsecond reconfiguration time is experimentally demonstrated through pulsed-excitation of microheaters. A modified model is also proposed that can accurately predict the transients of the microheater response. Using this model, it is shown that the fastest reconfiguration time for the demonstrated microheater structure is around 725 ns using pulsed-excitation.
This work was supported by the Air Force Office of Scientific Research under Grant No. FA9550-09-1-0572 (G. Pomrenke) and by Defense Advanced Research Projects Agency under Grant No. HR0011-09-1-0014 (M. Haney).
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