Abstract

Efficient tunable photonic integrated devices are important for the realization of reconfigurable photonic systems. Thermal tuning is a convenient and effective approach, and silicon’s large heat conductivity, thermo-optical coefficient, and CMOS fabrication compatibility make it a good candidate material for tunable optical microcavities, which are versatile elements in low-cost, large-scale photonic integrated circuits. Metal heaters are traditionally used for tuning, and a thick SiO2 upper-cladding layer is usually needed to prevent light absorption by the metal since that could reduce response speed and heating efficiency. In this paper, we propose and experimentally demonstrate thermally tunable silicon photonic microdisk resonators by introducing transparent graphene nanoheaters, which contact the silicon core directly without any isolator layer. The theoretical and experimental results show that the transparent graphene nanoheaters improve the heating efficiency, the temporal response, and the achievable temperature in comparison with a traditional metal heater. Furthermore, the graphene nanoheater is convenient for use in ultrasmall nanophotonic integrated devices due to its single-atom thickness and excellent flexibility. Both experiments and simulations show that the transparent graphene nanoheater is a promising option for other thermally tunable photonic integrated devices such as optical filters and switches.

© 2016 Optical Society of America

1. INTRODUCTION

Silicon photonics is one of the most promising technologies to realize low-cost, large-scale photonic integrated circuits (PICs) because of the ability to achieve ultrasharp bends, as well as the compatibility with CMOS fabrication processes [1,2]. Among various silicon photonic integrated devices, an optical microcavity is well known as a versatile element to realize many functionality components, including optical filters/switches [3,4], optical modulators [5], and optical sensors [6]. Since silicon has a large heat conductivity (149W/m·K) and a large thermo-optical (TO) coefficient (1.8×104/K at a wavelength of 1.55 μm) [7], it is possible and beneficial to achieve efficient thermal tuning in silicon photonic microcavities. Traditionally, metal heaters are usually used for thermally tunable silicon photonic microcavities, and a thick SiO2 upper-cladding layer is usually required between the metal heater and the silicon core to isolate the metal absorption. However, such a thick SiO2 upper-cladding layer will introduce some disadvantages due to its poor heat conductivity, e.g., low response speed and low heating efficiency. Furthermore, note that the temperature in the silicon core is much lower than that of the metal heater and consequently the temperature dynamics of the silicon core is limited to some degree. Therefore, the thermal tuning range is limited. In addition, silicon photonic microcavities of ultrasmall size are desired for large-scale integration, in which case the fabrication of nanoheaters becomes complicated with metal. Some approaches have been presented to improve the heating performance. One approach is to introduce free-standing silicon resonators with undercut structures so that the heating efficiency is enhanced significantly [8]. However, it is still difficult to achieve large thermal tuning range, as well as to realize nanoscale microcavities. Furthermore, the free-standing structure is usually not so robust mechanically. Its fabrication is also complicated and might be incompatible with the other elements on the same chip. An integrated silicon heater is another new type of heater formed by silicon regions with different doping levels, and has achieved low-power and high-speed thermal tuning [9,10]. The problem is that such a heater needs complicated fabrication processes to form heater regions with different doping levels, and it can be used only in some specific devices (e.g., adiabatic resonant microrings) whose heating sections need very careful design. Therefore, a simple and efficient heating approach is still desired for thermally tunable silicon photonic integrated devices (including microcavities).

Graphene has been extensively investigated worldwide because this two-dimensional (2D) sheet has many extraordinary properties [1114], such as a broadband absorption of 2.3% per layer for vertically incident light [11,12], a carrier mobility as high as 200,000cm2/V·s at room temperature (RT) [15,16], a “minimum” conductivity of 4e2/h even when the carrier concentration tends to zero [11,13], a high optical damage threshold value, and excellent mechanical stability [12]. Recent studies also suggest that graphene is expected to have high intrinsic thermal conductivity due to the long-wavelength phonon transportation in its 2D crystal lattices [17,18], and an experimental value of up to 5300W/m·K at RT has confirmed this conclusion [19]. The excellent thermal property of graphene coupled with its remarkable optoelectronic properties enables many potential applications in thermal management [20,21], such as efficient heat spreaders in electronic and photonic devices [22,23], and transparent and flexible heaters [2426].

In this paper, we experimentally demonstrate a thermally tunable silicon photonic microdisk resonator with transparent graphene nanoheaters. The graphene nanoheater is designed to contact the silicon core directly without the thick SiO2 upper-cladding layer required for traditional metal heaters, so that it is possible to achieve efficient thermal tuning and improved temporal response. In our previous work [27], we have demonstrated a graphene heat conductor to deliver heat from a traditional metal heater to nanophotonic integrated devices for realizing thermal tuning. In contrast, the graphene nanoheater demonstrated in this paper is used to generate heat by itself (instead of a metal heater), so that it works as a real “transparent graphene nanoheater.” Since there is no heat dissipation due to the delivery process, which exists in the graphene heat conductor, the heating efficiency for the present graphene nanoheater is greatly improved. Moreover, due to the single-atom thickness and excellent flexibility of graphene, it is convenient for the transparent nanoheater to be patterned in a nanoscale shape with CMOS-compatible fabrication processes. This is very useful for ultrasmall nanophotonic integrated devices that need thermal management, e.g., the thermally tunable microdisk resonator in our case. In this paper, thermally tunable silicon photonic microdisk resonators with transparent graphene nanoheaters are designed, fabricated, and characterized.

2. STRUCTURE, DESIGN, AND FABRICATION

Figure 1(a) shows the three-dimensional (3D) schematic illustration of the present thermally tunable silicon photonic microdisk with a transparent graphene nanoheater. The fabrication starts with a commercial SOI wafer with a 250 nm thick top silicon layer and a SiO2 buried oxide (BOX) layer of 3 μm. We use electron beam lithography (EBL) and inductively coupled plasma (ICP) etching processes to form the submicrometer-patterns. Then a second EBL process and a lift-off process are carried out to create some 100 nm thick titanium metal contacts on the top of the SiO2 BOX layer. A 1cm×1cm monolayer graphene sheet, grown by the chemical vapor deposition (CVD) method, is wet-transferred to cover the whole SOI chip (here no accurate alignment is required) [28,29]. A third EBL process followed by an oxygen plasma etching process is then utilized to pattern the graphene sheet [29], forming a circular nanoheater along the edge of the microdisk and two arms connecting the circular nanoheater with the metal contacts at the sides of the microdisk. As shown in Fig. 1(b), the radii of the microdisk and the graphene nanoheater are chosen as rd=5μm and rh=3.4μm, respectively, in this example. The widths for the circular nanoheater and the arms are wh=1.2μm and wa=2μm. These parameters are chosen to make the circular graphene nanoheater overlap less with the whispering gallery mode (WGM) of the microdisk resonator [see the bottom of Fig. 1(b)] [30], so that no significant loss is introduced from the graphene absorption.

 figure: Fig. 1.

Fig. 1. Thermally tunable silicon photonic microdisk resonator with a transparent graphene nanoheater. (a) Three-dimensional schematic illustration of a thermally tunable silicon photonic microdisk with a transparent graphene nanoheater. The circular graphene nanoheater is along the edge of the microdisk, and two graphene arms connect the circular nanoheater with the metal contacts at the sides of the microdisk. (b) Top: top view for the microdisk resonator with a graphene nanoheater. Bottom: cross-section view for the WGM of the microdisk resonator. The graphene nanoheater on the microdisk is shown with a green line. (c) Top: top-view microscope image of the fabricated thermally tunable microdisk resonator (scale bar: 100 μm). Bottom: zoom-in view for the black dashed square in the top image (scale bar: 10 μm). The graphene sheet is covered by a polymer film. (d) Top: top-view SEM image of the microdisk resonator covered by the patterned graphene nanoheater (scale bar: 2 μm). Bottom: zoom-in view for the black dashed square in the top image (scale bar: 1 μm). The outlines of the graphene nanoheater are shown by the green dashed lines.

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Figure 1(c) shows the microscope images of the fabricated devices, which have grating couplers at the input/output ends to achieve efficient coupling of the probe light [31]. To protect the patterned graphene from any damage or contamination, the photoresist for graphene patterning was left on the chip; it will not introduce any notable influence on the thermal behaviors of the devices since the guided-modal field is well confined to the silicon core. Moreover, the low thermal conductivity of photoresist could help decrease the heat convection of the graphene nanoheater, as shown in [26], and the heating efficiency can be even improved slightly. Figure 1(d) shows scanning electron microscope (SEM) images of the fabricated microdisk resonator with the graphene nanoheater. It can be seen that the graphene sheet flexibly crosses the step from the silicon core to the top surface of the SiO2–BOX layer. This makes the present flexible graphene nanoheater available for complex surfaces with nonplanar nanostructures.

3. RESULTS AND DISCUSSION

As is well known, the resonant wavelength λres of a microdisk resonator with a radius rd is described as [32]

λres=2πneffrdm,
where neff is the effective index of the WGM, and m is the resonant order. For the microdisk resonator in our case, we designed the coupling ratio to optimize the first-order mode with critical coupling theory [32]. For thermal tuning behaviors, when the current for heating is injected through the metal contacts, heat is generated mainly in the part of the graphene nanoheater where the resistance is higher than it is in other parts in the electric circuit. The heat is then transferred directly from the graphene nanoheater to the silicon photonic microdisk below, and consequently the temperature in the silicon region becomes increased. Due to the positive TO coefficient of silicon (1.8×104/K), the effective index neff for the WGM of the microdisk resonator increases. Accordingly, the resonant wavelength of the microdisk has a redshift, as indicated by Eq. (1).

Figure 2(a) shows the experimental result for the dynamic spectral responses of our fabricated microdisk resonator. When the heating power Pheating is 0, the free spectral range (FSR) and the Q-factor of the microdisk resonator are 22.5nm and 4000, respectively. With the heating power Pheating varies from 0 to 10.5 mW, the resonant wavelength λres of the microdisk resonator has a red-shift of 5nm. Meanwhile, both the Q-factor and the extinction ratio of the resonant peak also change. This is partially because the conductivity of graphene varies when the temperature increases [33,34], so that the light absorption of the graphene nanoheater and the propagation loss of the microdisk resonator change correspondingly [35]. The resonant-wavelength shifts Δλ with varying heating powers are shown in Fig. 2(b); it increases linearly with heating power Pheating. The corresponding heating efficiency ηd, which is defined as the ratio of the resonant-wavelength shift Δλ to the heating power Pheating, is estimated to be about ηd=0.48nm/mW. This value gives an evaluation for the conversion efficiency from the electrical heating power to the temperature change of the silicon photonic microdisk, which includes the processes of heat generation in the graphene nanoheater, heat transfer from the graphene nanoheater to the silicon core, and heat conduction in the silicon photonic microdisk.

 figure: Fig. 2.

Fig. 2. Characterization of the thermally tunable microdisk resonator with a transparent graphene nanoheater. (a) The measured spectral responses of the thermally tunable microdisk resonator as heating power Pheating varies from 0 to 10.5 mW. (b) The resonant-wavelength shift Δλ as the heating power varies. (c) The spectral responses of the thermally tunable microdisk resonator when Pheating is 0 mW (the solid line) and 4 mW (the dashed line). (d) The measured temporal responses of the modulated heating power Pheating (top) and the corresponding output signal of the photodetector (bottom).

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The temporal response of the thermally tunable microdisk resonator is also measured by fixing the wavelength of the probe light as λprobe=1543nm and applying a modulated heating power with an amplitude of 4mW. As shown in Fig. 2(c), when Pheating=0, the output power of the microdisk resonator has a minimal value (see the solid line), while the output becomes the maximum when Pheating=4mW (see the dashed line) because of the thermo-optic redshift. In this way, the probe light is modulated by varying the heating power, and the modulated light is then received by a photodetector (Conquer KG-HSP-04SMFP) in our experimental setup. Figure 2(d) shows the measured output signal from the photodetector when the modulation frequency is about 1 kHz. The 90% rising time and the decaying time of the thermal tuning are about 12.8 and 8.8 μs, respectively.

As heater resistance is the key for heat generation and power consumption, the resistance of the graphene nanoheater is analyzed and discussed below. For an electrical circuit with a total resistance Rtot between the two metal contacts, one has the following equation for the heating power Pheating when an electrical current I is injected [36]:

Pheating=I2Rtot.

For the present case, the total resistance Rtot includes three parts [3638], i.e., the resistance of the graphene circular nanoheater Rcircle, the resistance of the graphene arms Rarm, and the total contact resistance between the graphene arms and the metal pads Rcontact. Therefore, one has

Rtot=Rcircle+Rarm+Rcontact=πRsrh2wh+RsLawa+2Rcwc,
where Rs is the sheet resistance of graphene, La is the total length of the two graphene arms, Rc is the graphene–metal contact resistance, and wc is the width of the contact region. To obtain the values for Rs and Rc, we fabricated a series of test structures with graphene ribbons. The lengths for these graphene ribbons are chosen as Lribbon=10 or 20 μm while their widths wribbon vary from 0.5 to 6 μm. The measured total resistances Rtot for these graphene ribbons with Lribbon=10 and 20 μm are shown by the blue squares and the pink diamonds in Fig. 3(a), respectively, as the graphene-ribbon width wribbon varies. By fitting the experimental data by using Eq. (3) with Rcircle=0 (i.e., no circular nanoheater for the test structures with graphene ribbons), La=Lribbon, and wc=wa=wribbon, one obtains sheet resistance Rs=1.7/ϒ and contact resistance Rc=800Ω·μm for the graphene sheet in our case. With these values of Rs=1.7/ϒ and Rc=800Ω·μm, the calculated resistances for the present graphene nanoheater are Rcircle=0.64, Rarm=1.04, and Rcontact=0.025, respectively. Correspondingly, the theoretical total resistance Rtot(=Rcircle+Rarm+Rcontact) is about 1.68 kΩ, which is well consistent with the experimental result (1.63) from the I–V measurement. Since Rcontact is negligible, the power distribution to the circular nanoheater and the two arms can be obtained as Pcircle=PheatingRcircle/(Rcircle+Rarm) and Parm=PheatingRarm/(Rcircle+Rarm), respectively, when a heating power Pheating is applied.

 figure: Fig. 3.

Fig. 3. Theoretical calculation results for the thermally tunable microdisk resonator with a transparent graphene nanoheater. (a) 1/Rtot for the graphene ribbons with varying widths wribbon and lengths Lribbon. (b) Three-dimensional temperature distribution of the heated microdisk resonator by solving the Poisson equation with a 3D finite element method tool. RT is defined as 300 K. (c) Temperature distribution for the cross sections along Cut 1 (top) and Cut 2 (bottom) in (b). (d) Temperature distribution for the heated microdisk resonator. The outlines of the graphene sheet are shown by the black dashed lines.

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Figure 3(b) shows the simulated temperature distribution in the microdisk resonator with the graphene nanoheater by using a 3D simulation tool based on Poisson’s equation. In this simulation, the applied electrical power for heating is set as Pheating=10mW and it is assumed that the electrical energy is completely converted to thermal energy. The graphene sheet is considered to be a 0.34 nm thick layer with thermal conductivity of 2000W/m·K [39], which is for the graphene sheet supported on the substrate in our case (lower than that of a suspended graphene sheet [17,40]). The thermal conductivities of silicon, silica, and photoresist polymer are 80W/m·K, 1.38W/m·K, and 0.19W/m·K, respectively. The heat convection coefficient of air is set to 5W/m2·K [41]. From Fig. 3(b), it can be seen that both the silicon microdisk and the SiO2 BOX layer below are heated. More details can also be seen clearly from the temperature distributions of the cross sections along the cut lines (Cut 1 and Cut 2) shown in Fig. 3(c). Figure 3(d) shows the temperature distribution of the heated silicon microdisk, and the black dashed curves show the outlines of the graphene nanoheater on the silicon microdisk. It can be seen that the regions near the circular nanoheater along the edge of the microdisk have higher temperature than the center of the microdisk. Fortunately, the guided mode (WGM) of the microdisk is localized at the edge [see the bottom of Fig. 1(b)], which helps to have efficient thermal tuning. It can be also seen that the temperature distribution along the edge of the microdisk is not uniform due to the introduction of the graphene arms. In this case, the effective index of the WGM becomes nonuniform along the cavity. Therefore, when using Eq. (1) to estimate the resonant wavelength of the microdisk, one should replace the effective index neff by the average effective index n¯eff, which is given by

n¯eff=02πneff(θ)dθ2π,
where θ is the central angle along the microdisk. For the present case, the average effective index n¯eff is about 2.57. The corresponding resonant-wavelength shift is 10.6nm and the calculated heating efficiency is about ηt=1.06nm/mW, which is higher than the measurement result in our experiment (i.e., 0.48nm/mW). The primary reason might be that the quality degradation of the graphene sheet due to some contaminations and cracks during the fabrication process is not considered in the simulation. The contamination and cracks in the graphene sheet introduce some local large resistance, which creates some unexpected nonuniformity of the spatial distribution of heating. Particularly, the contamination and cracks might locate in the part of the graphene arms, and thus less heating power is applied to the part of the silicon microdisk. As a consequence, the heating efficiency becomes lower than the theoretical prediction. Another reason is that the big metal pads will dissipate a part of heat energy, which is also not included in the simulation. From the numerical simulation, we can also acquire the temporal response of the thermally tunable microdisk resonator. The theoretical 90% rising and decaying times are both 8.4μs, which are slightly faster than the measurement results (12.8μs for the rising process and 8.8μs for the decaying process).

In order to make a comparison, we also give a simulation for a thermally tunable silicon photonic microdisk resonator with a traditional metal heater. For this case, the metal heater is assumed to have the same shape as the present graphene nanoheater, and a 1 μm thick SiO2 upper-cladding layer is inserted between the metal heater and the silicon core to isolate the metal absorption [42]. The simulation result shows that the theoretical heating efficiency is about ηm=0.86nm/mW, and the 90% rising/decaying time is 13.8μs for the metal heater. In contrast, the theoretical heating efficiency for the design with the present graphene nanoheater is about ηt=1.06nm/mW, and the 90% rising/decaying time is 8.4μs. The reason for the difference between them is that the design with the graphene nanoheater does not have the thick SiO2 upper-cladding layer, which has poor heat conductivity and increases the heating volume significantly. The thick SiO2 upper-cladding layer also means that the silicon core cannot be as hot as the metal heater. For example, the temperature Tsilicon in the silicon core is 392K, which is 71K lower than that of the metal heater (i.e., Tmetal=463K) when the heating power is 10mW. For the design with the present graphene nanoheater, the temperature in the silicon core is almost the same as that of the heater. Therefore, the present graphene nanoheater potentially enables much higher temperature increase than the traditional metal heater assuming that they have the same damage threshold of temperature. This is very helpful to achieve a large thermal tuning range.

Noting that the dimension of the circular graphene nanoheater influences the temperature distribution of the microdisk and the heating efficiency of the device significantly, in the following we give a theoretical analysis for the dependence of the heating efficiency on the outer-edge position (rout=rh+wh/2) and width (wh) of the graphene nanoheater, as shown in Fig. 4(a). It can be seen that the heating efficiency has an enhancement as the width wh of the circular graphene nanoheater decreases. This can be explained as follows. According to the electrical circuit for heating, the heating power loaded in the circular graphene nanoheater is given by Pcircle=PheatingRcircle/(Rcircle+Rarm). Therefore, more heating power Pcircle will be loaded in the circular graphene nanoheater when using a narrower graphene nanoheater that has a larger resistance.

 figure: Fig. 4.

Fig. 4. Optimization of the transparent graphene nanoheater. (a) Heating efficiency ηt of the thermally tunable microdisk resonator as the outer-edge position (rout) and width (wh) of the graphene nanoheater vary. Inset, cross-section view for the WGM of the microdisk resonator. rout=rh+wh/2 and rin=rhwh/2 are the outer-edge and internal-edge positions of the graphene nanoheater, respectively. The parameters used in our experiments are indicated by a star. (b) Propagation loss α for the WGM of the microdisk as the outer-edge position (rout) and width (wh) of the graphene nanoheater vary. The value of 0.01 dB/μm is shown by the black dashed line. The parameters used in our experiments are indicated by a star. Inset, cross-section view for the WGM of the microdisk resonator. The parameters used in our experiments are indicated by a star. (c) Propagation loss α for the WGM of the microdisk when the graphene nanoheater is replaced by a metal (gold) heater. The thickness of the metal is 100nm. The gray regions show the conditions with only the plasmonic mode supported in the microdisk resonator. The values of 0.01 and 0.1 dB/μm are shown by black dashed lines. Inset, cross-section view for the WGM of the microdisk resonator when the metal heater has the same parameters (shown as a star) as the graphene nanoheater used in our experiment. (d) The heating efficiency ηt and the propagation loss α for the WGM of the microdisk when using the metal heater (top) and the graphene nanoheater (bottom), respectively. The outer-edge position is rout=4μm, while the width wh is varied from 0.2 to 2.6 μm, as indicated in the figure. (e) Heating efficiency ηt of the thermally tunable microdisk resonator as the width (wa) and the length (La) of the graphene arms vary. The parameters used in our experiments are indicated by a star.

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Figure 4(a) also shows that the heating efficiency is improved as the outer-edge position rout of the graphene nanoheater increases. This is because of the improved overlap between the thermal heating distribution and the WGM field [which locates at the edge of the microdisk; see Fig. 1(b)]. On the other hand, one should notice that the dimension of the circular graphene nanoheater also affects the propagation loss of the WGM field due to the graphene absorption in the microdisk. As shown in Fig. 4(b), when the outer-edge position rout of the circular graphene nanoheater increases, the propagation loss of the WGM is obviously increased due to the absorption of graphene. Therefore, the circular graphene nanoheater should not be too close to the edge of the microdisk. As shown in Fig. 4(b), the graphene propagation loss could also be reduced slightly by reducing the nanoheater width. However, a very narrow graphene strip is not so robust and fabrication should be done carefully. In our experiment, we choose rout=rh+wh/2=4μm and wh=1.2μm as a trade-off. In this case, the propagation loss is negligibly low (i.e., 0.00016dB/μm) and the heating efficiency is about ηt=1.06nm/mW, as indicated by the stars in Figs. 4(a) and 4(b). By using the optimized fabrication processes wet-transferring and patterning for the graphene, it is possible to make a narrow graphene nanoheater so that the heating efficiency can be greatly improved. However, a narrow graphene strip would decrease its breakdown current threshold [43] and limit the maximal operating current of the graphene nanoheater. Therefore, there is a trade-off when designing the graphene nanoheater.

As a comparison, we also consider the design of using a 100 nm thick gold thin film to replace the graphene sheet. In this case, the gold heater also contacts the silicon core directly. Figure 4(c) shows the calculated metal propagation loss as the dimension varies [4446]. It can be seen that the propagation loss α increases sharply when the outer-edge position of the metal heater increases to be rout>3.8μm. Particularly, when the metal heater further moves to be more close to the edge of the microdisk, surface plasmonic mode appears and the metal propagation loss becomes huge. As an example, for the design with rout=4μm and wh=1.2μm, the propagation loss is up to 0.011dB/μm for the metal heater, which is 70 times higher than the propagation loss (0.00016dB/μm) for the graphene nanoheater. Figure 4(d) shows the propagation loss α as well as the heating efficiency ηt for the metal heater (top) and the graphene nanoheater (bottom) as the width wh varies from 0.2 to 2.6 μm. Here rout=4μm. It can be seen that the metal heater always introduces a much higher propagation loss than the graphene nanoheater for the same heating efficiency. Therefore, the metal heater should be far away from the edge of the microdisk to avoid any significant loss. On the other hand, when considering the same requirement for low loss, a graphene nanoheater can be placed closer to edge of the microdisk than a metal heater and a higher heating efficiency is possibly achieved.

As discussed above, the heating efficiency can be improved by reducing the width wh of the circular nanoheater. Note that the fabrication for a narrow graphene nanoheater is relatively easy with a lithography process and an O2-plasma dry-etching process, in comparison with the lift-off process for a 100nm thick metal heater. According to the equation Pcircle=PheatingRcircle/(Rcircle+Rarm), one sees that another approach to improve the heating efficiency is reducing the resistance Rarm of the graphene arms by increasing width wa or decreasing the length of the graphene arms La. Figure 4(e) shows the calculated heating efficiency of the thermally tunable microdisk resonator as the width wa of the graphene arms increases. It can be seen that the heating efficiency is up to 1.34nm/mW when the graphene arm width and length are chosen as wa=4μm and La=4μm, respectively. We also notice that the propagation loss introduced by the graphene arms will increase as the width wa increases, which will influence the Q-factor and the extinction ratio of the resonator. Therefore, one should make a trade-off when choosing the width wa in practice. To decrease the graphene absorption, one approach is to tune its Fermi level by electrical gating or chemical doping [12]. This approach may cause some variation of graphene resistance [47] and the voltage (or current) applied to the graphene nanoheater should be tuned correspondingly. On the other hand, the heating efficiency of the graphene nanoheater will not decrease because the ratios of Rcircle/Rarm and Pcircle/Parm almost do not change, as discussed above.

It is well known that the heating efficiency can be improved further if the heating microdisk is shrunk to minimize the heating volume, which is also desired for realizing ultradense PICs. In this case, an ultracompact heater is usually needed. We realize that the present graphene nanoheater has the advantage of being patterned easily to be nanoscale with CMOS-compatible fabrication processes because of its single-atom thickness and excellent flexibility. This is very helpful for realizing ultrasmall thermally tunable silicon photonic microdisk resonators. As an example, we fabricated ultrasmall microdisks (rd=3μm and rd=2μm) with transparent graphene nanoheaters with varied parameters. Figure 5(a) shows the measured dynamic spectral responses of the fabricated 3 μm radius microdisk resonator as the heating power increases from 0 to 2.7 mW, where the transparent graphene nanoheater has parameters of rout=2.3μm, wh=0.5μm, and wa=2μm. From Fig. 5(b), which shows the resonance wavelength as the heating power varies, one sees the heating efficiency is about ηd=1.13nm/mW, which is much higher than the experimental result for the fabricated microdisk resonator with rd=5μm. Figure 6 shows the comparison of the experimental heating efficiency for the microdisk resonators (rd=2μm, 3 μm, and 5 μm) with transparent graphene nanoheaters with varied parameters. It can be seen that the heating efficiency is as high as 1.67nm/mW when the radius of the microdisk resonator is reduced to 2 μm. From the experimental and simulation results shown above, it can be seen that the present transparent graphene nanoheater provides an efficient method for thermal tuning for silicon photonic microdisk resonators. In this paper, we choose microdisks instead of microrings to demonstrate thermally tunable optical cavities with graphene nanoheaters because it is easier to transfer a graphene sheet to cover a microdisk than a microring. One should note that the heating efficiency can be further improved when using a microring resonator because of the reduced heating volume, which will be developed with an improved wet-transfer process of graphene in the future.

 figure: Fig. 5.

Fig. 5. Characterization of the 3 μm radius thermally tunable microdisk resonator with a transparent graphene nanoheater. (a) Spectral responses of the thermally tunable microdisk resonator as the heating power Pheating varies from 0 to 2.7 mW. (b) The shift of the resonant wavelength Δλ with varying heating powers. Inset: temperature distribution of the heated microdisk resonator simulated by solving the Poisson equation. The outlines of the graphene nanoheater are shown by black dashed lines. RT is defined as 300 K.

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 figure: Fig. 6.

Fig. 6. Summary of the heating efficiency for the microdisk resonators (rd=2, 3, or 5 μm) using transparent graphene nanoheaters. Inset, top-view microscope images of the fabricated thermally tunable microdisk resonators.

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4. CONCLUSION

In summary, we have demonstrated thermally tunable silicon photonic microdisk resonators with transparent graphene nanoheaters. Here the transparent graphene nanoheater is designed to contact directly with the silicon core region, and the excess loss due to graphene absorption is negligible (<0.0002dB/μm) when the position and dimensions of the graphene nanoheater sitting on the silicon core are optimized. This makes the present transparent graphene nanoheater potentially better than conventional metal heaters. Basically speaking, fabrication processes (like lithography and the dry-etching) for the transparent graphene nanoheaters are also easy in comparison with metal nanoheaters, particularly when used for nanophotonic integrated devices with very limited physical space. Even though the experimental result demonstrated here is not as good as theoretically predicted, it has been shown that the present transparent graphene nanoheater potentially provides high heating efficiency, fast temporal response, and large dynamic range of thermal tuning in comparison with traditional metal heaters. The heating efficiency for the present case can potentially be further improved by, e.g., making the graphene arms suspended [6,16] or inserting a layer of low heat conductivity material (e.g., polymer) between the graphene arms and the SiO2–BOX layer to prevent heat from dissipating. As a conclusion, the present heating approach with a graphene transparent nanoheater has the potential to be a very promising option for many applications of energy-efficient thermally tunable/switchable nanophotonic integrated circuits in the future.

Funding

National Natural Science Foundation of China (NSFC) (61422510, 11374263, 61431166001); The Program of Zhejiang Leading Team of Science and Technology Innovation (2010R50007); The Doctoral Fund of Ministry of Education of China (20120101110094); The Fundamental Research Funds for the Central Universities.

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5. Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005). [CrossRef]  

6. X. K. Wang, X. W. Guan, Q. S. Huang, J. J. Zheng, Y. C. Shi, and D. X. Dai, “Suspended ultra-small disk resonator on silicon for optical sensing,” Opt. Lett. 38, 5405–5408 (2013). [CrossRef]  

7. R. L. Espinola, M. C. Tsai, J. T. Yardley, and R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003). [CrossRef]  

8. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Z. Feng, G. L. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18, 20298–20304 (2010). [CrossRef]  

9. E. Timurdogan, E. S. Hosseini, G. Leake, D. D. Coolbaugh, and M. R. Watts, “L-shaped resonant microring (LRM) filter with integrated thermal tuner,” in Conference on Laser Electro-Optics (Optical Society of America, 2013), paper CTh4F.2.

10. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper CPDB10.

11. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010). [CrossRef]  

12. Q. L. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012). [CrossRef]  

13. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007). [CrossRef]  

14. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004). [CrossRef]  

15. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008). [CrossRef]  

16. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3, 491–495 (2008). [CrossRef]  

17. A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater. 10, 569–581 (2011). [CrossRef]  

18. D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, “Phonon thermal conduction in graphene: role of Umklapp and edge roughness scattering,” Phys. Rev. B 79, 155413 (2009). [CrossRef]  

19. A. A. Balandin, S. Ghosh, W. Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008). [CrossRef]  

20. M. M. Sadeghi, M. T. Pettes, and L. Shi, “Thermal transport in graphene,” Solid State Commun. 152, 1321–1330 (2012). [CrossRef]  

21. S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits,” Appl. Phys. Lett. 92, 151911 (2008). [CrossRef]  

22. S. Subrina, D. Kotchetkov, and A. A. Balandin, “Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,” IEEE Electron Device Lett. 30, 1281–1283 (2009). [CrossRef]  

23. R. Prasher, “Graphene spreads the heat,” Science 328, 185–186 (2010). [CrossRef]  

24. J. Kang, H. Kim, K. S. Kim, S. K. Lee, S. Bae, J. H. Ahn, Y. J. Kim, J. B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11, 5154–5158 (2011). [CrossRef]  

25. D. Sui, Y. Huang, L. Huang, J. J. Liang, Y. F. Ma, and Y. S. Chen, “Flexible and transparent electrothermal film heaters based on graphene materials,” Small 7, 3186–3192 (2011). [CrossRef]  

26. L. Yu, S. He, J. Zheng, and D. Dai, “Graphene-based transparent nano-heater for thermally-tuning silicon nanophotonic integrated devices,” in Progress in Electromagnetics Research Symposium (PIERS) Proceedings, Guangzhou, China, 2014, p. 1735–1738.

27. L. H. Yu, D. X. Dai, and S. L. He, “Graphene-based transparent flexible heat conductor for thermally tuning nanophotonic integrated devices,” Appl. Phys. Lett. 105, 251104 (2014). [CrossRef]  

28. L. Yu, Y. Xu, Y. Shi, and D. Dai, “Linear and nonlinear optical absorption of on-chip silicon-on-insulator nanowires with graphene,” in Asia Communications and Photonics Conference (Optical Society of America, 2012), paper AS1B.3.

29. L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8, 11386–11393 (2014). [CrossRef]  

30. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]  

31. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006). [CrossRef]  

32. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012). [CrossRef]  

33. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. 19, 026222 (2007).

34. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008). [CrossRef]  

35. M. Liu, X. B. Yin, E. Ulin-Avila, B. S. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011). [CrossRef]  

36. J. T. Smith, A. D. Franklin, D. B. Farmer, and C. D. Dimitrakopoulos, “Reducing contact resistance in graphene devices through contact area patterning,” ACS Nano 7, 3661–3667 (2013). [CrossRef]  

37. F. N. Xia, V. Perebeinos, Y. M. Lin, Y. Q. Wu, and P. Avouris, “The origins and limits of metal-graphene junction resistance,” Nat. Nanotechnol. 6, 179–184 (2011). [CrossRef]  

38. L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013). [CrossRef]  

39. A. N. Sidorov, D. K. Benjamin, and C. Foy, “Comparative thermal conductivity measurement of chemical vapor deposition grown graphene supported on substrate,” Appl. Phys. Lett. 103, 243103 (2013).

40. W. W. Cai, A. L. Moore, Y. W. Zhu, X. S. Li, S. S. Chen, L. Shi, and R. S. Ruoff, “Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition,” Nano Lett. 10, 1645–1651 (2010). [CrossRef]  

41. L. Yang, D. X. Dai, and S. L. He, “Thermal analysis for a photonic Si ridge wire with a submicron metal heater,” Opt. Commun. 281, 2467–2471 (2008). [CrossRef]  

42. M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17, 5502–5516 (2009). [CrossRef]  

43. R. Murali, Y. X. Yang, K. Brenner, T. Beck, and J. D. Meindl, “Breakdown current density of graphene nanoribbons,” Appl. Phys. Lett. 94, 243114 (2009). [CrossRef]  

44. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006). [CrossRef]  

45. R. Charbonneau and N. Lahoud, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005). [CrossRef]  

46. D. X. Dai and S. L. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009). [CrossRef]  

47. A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3, 210–215 (2008). [CrossRef]  

References

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  1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics 4, 492–494 (2010).
    [Crossref]
  2. M. Asghari and A. V. Krishnamoorthy, “Silicon photonics energy-efficient communication,” Nat. Photonics 5, 268–270 (2011).
    [Crossref]
  3. D. X. Xu, A. Densmore, P. Waldron, J. Lapointe, E. Post, A. Delage, S. Janz, P. Cheben, J. H. Schmid, and B. Lamontagne, “High bandwidth SOI photonic wire ring resonators using MMI couplers,” Opt. Express 15, 3149–3155 (2007).
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  4. V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, M. A. Foster, D. G. Ouzounov, and A. L. Gaeta, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869 (2004).
    [Crossref]
  5. Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
    [Crossref]
  6. X. K. Wang, X. W. Guan, Q. S. Huang, J. J. Zheng, Y. C. Shi, and D. X. Dai, “Suspended ultra-small disk resonator on silicon for optical sensing,” Opt. Lett. 38, 5405–5408 (2013).
    [Crossref]
  7. R. L. Espinola, M. C. Tsai, J. T. Yardley, and R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).
    [Crossref]
  8. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Z. Feng, G. L. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18, 20298–20304 (2010).
    [Crossref]
  9. E. Timurdogan, E. S. Hosseini, G. Leake, D. D. Coolbaugh, and M. R. Watts, “L-shaped resonant microring (LRM) filter with integrated thermal tuner,” in Conference on Laser Electro-Optics (Optical Society of America, 2013), paper CTh4F.2.
  10. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper CPDB10.
  11. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
    [Crossref]
  12. Q. L. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
    [Crossref]
  13. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
    [Crossref]
  14. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [Crossref]
  15. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146, 351–355 (2008).
    [Crossref]
  16. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, “Approaching ballistic transport in suspended graphene,” Nat. Nanotechnol. 3, 491–495 (2008).
    [Crossref]
  17. A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater. 10, 569–581 (2011).
    [Crossref]
  18. D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, “Phonon thermal conduction in graphene: role of Umklapp and edge roughness scattering,” Phys. Rev. B 79, 155413 (2009).
    [Crossref]
  19. A. A. Balandin, S. Ghosh, W. Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior thermal conductivity of single-layer graphene,” Nano Lett. 8, 902–907 (2008).
    [Crossref]
  20. M. M. Sadeghi, M. T. Pettes, and L. Shi, “Thermal transport in graphene,” Solid State Commun. 152, 1321–1330 (2012).
    [Crossref]
  21. S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, “Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits,” Appl. Phys. Lett. 92, 151911 (2008).
    [Crossref]
  22. S. Subrina, D. Kotchetkov, and A. A. Balandin, “Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,” IEEE Electron Device Lett. 30, 1281–1283 (2009).
    [Crossref]
  23. R. Prasher, “Graphene spreads the heat,” Science 328, 185–186 (2010).
    [Crossref]
  24. J. Kang, H. Kim, K. S. Kim, S. K. Lee, S. Bae, J. H. Ahn, Y. J. Kim, J. B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11, 5154–5158 (2011).
    [Crossref]
  25. D. Sui, Y. Huang, L. Huang, J. J. Liang, Y. F. Ma, and Y. S. Chen, “Flexible and transparent electrothermal film heaters based on graphene materials,” Small 7, 3186–3192 (2011).
    [Crossref]
  26. L. Yu, S. He, J. Zheng, and D. Dai, “Graphene-based transparent nano-heater for thermally-tuning silicon nanophotonic integrated devices,” in Progress in Electromagnetics Research Symposium (PIERS) Proceedings, Guangzhou, China, 2014, p. 1735–1738.
  27. L. H. Yu, D. X. Dai, and S. L. He, “Graphene-based transparent flexible heat conductor for thermally tuning nanophotonic integrated devices,” Appl. Phys. Lett. 105, 251104 (2014).
    [Crossref]
  28. L. Yu, Y. Xu, Y. Shi, and D. Dai, “Linear and nonlinear optical absorption of on-chip silicon-on-insulator nanowires with graphene,” in Asia Communications and Photonics Conference (Optical Society of America, 2012), paper AS1B.3.
  29. L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8, 11386–11393 (2014).
    [Crossref]
  30. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
    [Crossref]
  31. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
    [Crossref]
  32. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
    [Crossref]
  33. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. 19, 026222 (2007).
  34. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
    [Crossref]
  35. M. Liu, X. B. Yin, E. Ulin-Avila, B. S. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
    [Crossref]
  36. J. T. Smith, A. D. Franklin, D. B. Farmer, and C. D. Dimitrakopoulos, “Reducing contact resistance in graphene devices through contact area patterning,” ACS Nano 7, 3661–3667 (2013).
    [Crossref]
  37. F. N. Xia, V. Perebeinos, Y. M. Lin, Y. Q. Wu, and P. Avouris, “The origins and limits of metal-graphene junction resistance,” Nat. Nanotechnol. 6, 179–184 (2011).
    [Crossref]
  38. L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013).
    [Crossref]
  39. A. N. Sidorov, D. K. Benjamin, and C. Foy, “Comparative thermal conductivity measurement of chemical vapor deposition grown graphene supported on substrate,” Appl. Phys. Lett. 103, 243103 (2013).
  40. W. W. Cai, A. L. Moore, Y. W. Zhu, X. S. Li, S. S. Chen, L. Shi, and R. S. Ruoff, “Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition,” Nano Lett. 10, 1645–1651 (2010).
    [Crossref]
  41. L. Yang, D. X. Dai, and S. L. He, “Thermal analysis for a photonic Si ridge wire with a submicron metal heater,” Opt. Commun. 281, 2467–2471 (2008).
    [Crossref]
  42. M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17, 5502–5516 (2009).
    [Crossref]
  43. R. Murali, Y. X. Yang, K. Brenner, T. Beck, and J. D. Meindl, “Breakdown current density of graphene nanoribbons,” Appl. Phys. Lett. 94, 243114 (2009).
    [Crossref]
  44. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
    [Crossref]
  45. R. Charbonneau and N. Lahoud, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13, 977–984 (2005).
    [Crossref]
  46. D. X. Dai and S. L. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009).
    [Crossref]
  47. A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, and A. K. Sood, “Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor,” Nat. Nanotechnol. 3, 210–215 (2008).
    [Crossref]

2014 (2)

L. H. Yu, D. X. Dai, and S. L. He, “Graphene-based transparent flexible heat conductor for thermally tuning nanophotonic integrated devices,” Appl. Phys. Lett. 105, 251104 (2014).
[Crossref]

L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8, 11386–11393 (2014).
[Crossref]

2013 (4)

J. T. Smith, A. D. Franklin, D. B. Farmer, and C. D. Dimitrakopoulos, “Reducing contact resistance in graphene devices through contact area patterning,” ACS Nano 7, 3661–3667 (2013).
[Crossref]

L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, “One-dimensional electrical contact to a two-dimensional material,” Science 342, 614–617 (2013).
[Crossref]

A. N. Sidorov, D. K. Benjamin, and C. Foy, “Comparative thermal conductivity measurement of chemical vapor deposition grown graphene supported on substrate,” Appl. Phys. Lett. 103, 243103 (2013).

X. K. Wang, X. W. Guan, Q. S. Huang, J. J. Zheng, Y. C. Shi, and D. X. Dai, “Suspended ultra-small disk resonator on silicon for optical sensing,” Opt. Lett. 38, 5405–5408 (2013).
[Crossref]

2012 (3)

Q. L. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[Crossref]

M. M. Sadeghi, M. T. Pettes, and L. Shi, “Thermal transport in graphene,” Solid State Commun. 152, 1321–1330 (2012).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

2011 (6)

J. Kang, H. Kim, K. S. Kim, S. K. Lee, S. Bae, J. H. Ahn, Y. J. Kim, J. B. Choi, and B. H. Hong, “High-performance graphene-based transparent flexible heaters,” Nano Lett. 11, 5154–5158 (2011).
[Crossref]

D. Sui, Y. Huang, L. Huang, J. J. Liang, Y. F. Ma, and Y. S. Chen, “Flexible and transparent electrothermal film heaters based on graphene materials,” Small 7, 3186–3192 (2011).
[Crossref]

F. N. Xia, V. Perebeinos, Y. M. Lin, Y. Q. Wu, and P. Avouris, “The origins and limits of metal-graphene junction resistance,” Nat. Nanotechnol. 6, 179–184 (2011).
[Crossref]

A. A. Balandin, “Thermal properties of graphene and nanostructured carbon materials,” Nat. Mater. 10, 569–581 (2011).
[Crossref]

M. Asghari and A. V. Krishnamoorthy, “Silicon photonics energy-efficient communication,” Nat. Photonics 5, 268–270 (2011).
[Crossref]

M. Liu, X. B. Yin, E. Ulin-Avila, B. S. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref]

2010 (5)

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics 4, 492–494 (2010).
[Crossref]

P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Z. Feng, G. L. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18, 20298–20304 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

W. W. Cai, A. L. Moore, Y. W. Zhu, X. S. Li, S. S. Chen, L. Shi, and R. S. Ruoff, “Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition,” Nano Lett. 10, 1645–1651 (2010).
[Crossref]

R. Prasher, “Graphene spreads the heat,” Science 328, 185–186 (2010).
[Crossref]

2009 (5)

S. Subrina, D. Kotchetkov, and A. A. Balandin, “Heat removal in silicon-on-insulator integrated circuits with graphene lateral heat spreaders,” IEEE Electron Device Lett. 30, 1281–1283 (2009).
[Crossref]

D. L. Nika, E. P. Pokatilov, A. S. Askerov, and A. A. Balandin, “Phonon thermal conduction in graphene: role of Umklapp and edge roughness scattering,” Phys. Rev. B 79, 155413 (2009).
[Crossref]

D. X. Dai and S. L. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17, 16646–16653 (2009).
[Crossref]

M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17, 5502–5516 (2009).
[Crossref]

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R. L. Espinola, M. C. Tsai, J. T. Yardley, and R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).
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E. Timurdogan, E. S. Hosseini, G. Leake, D. D. Coolbaugh, and M. R. Watts, “L-shaped resonant microring (LRM) filter with integrated thermal tuner,” in Conference on Laser Electro-Optics (Optical Society of America, 2013), paper CTh4F.2.

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper CPDB10.

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M. Liu, X. B. Yin, E. Ulin-Avila, B. S. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
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L. Yu, J. Zheng, Y. Xu, D. Dai, and S. He, “Local and nonlocal optically induced transparency effects in graphene-silicon hybrid nanophotonic integrated circuits,” ACS Nano 8, 11386–11393 (2014).
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L. Yu, S. He, J. Zheng, and D. Dai, “Graphene-based transparent nano-heater for thermally-tuning silicon nanophotonic integrated devices,” in Progress in Electromagnetics Research Symposium (PIERS) Proceedings, Guangzhou, China, 2014, p. 1735–1738.

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W. W. Cai, A. L. Moore, Y. W. Zhu, X. S. Li, S. S. Chen, L. Shi, and R. S. Ruoff, “Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition,” Nano Lett. 10, 1645–1651 (2010).
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M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper CPDB10.

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Other (4)

E. Timurdogan, E. S. Hosseini, G. Leake, D. D. Coolbaugh, and M. R. Watts, “L-shaped resonant microring (LRM) filter with integrated thermal tuner,” in Conference on Laser Electro-Optics (Optical Society of America, 2013), paper CTh4F.2.

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2009), paper CPDB10.

L. Yu, S. He, J. Zheng, and D. Dai, “Graphene-based transparent nano-heater for thermally-tuning silicon nanophotonic integrated devices,” in Progress in Electromagnetics Research Symposium (PIERS) Proceedings, Guangzhou, China, 2014, p. 1735–1738.

L. Yu, Y. Xu, Y. Shi, and D. Dai, “Linear and nonlinear optical absorption of on-chip silicon-on-insulator nanowires with graphene,” in Asia Communications and Photonics Conference (Optical Society of America, 2012), paper AS1B.3.

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Figures (6)

Fig. 1.
Fig. 1. Thermally tunable silicon photonic microdisk resonator with a transparent graphene nanoheater. (a) Three-dimensional schematic illustration of a thermally tunable silicon photonic microdisk with a transparent graphene nanoheater. The circular graphene nanoheater is along the edge of the microdisk, and two graphene arms connect the circular nanoheater with the metal contacts at the sides of the microdisk. (b) Top: top view for the microdisk resonator with a graphene nanoheater. Bottom: cross-section view for the WGM of the microdisk resonator. The graphene nanoheater on the microdisk is shown with a green line. (c) Top: top-view microscope image of the fabricated thermally tunable microdisk resonator (scale bar: 100 μm). Bottom: zoom-in view for the black dashed square in the top image (scale bar: 10 μm). The graphene sheet is covered by a polymer film. (d) Top: top-view SEM image of the microdisk resonator covered by the patterned graphene nanoheater (scale bar: 2 μm). Bottom: zoom-in view for the black dashed square in the top image (scale bar: 1 μm). The outlines of the graphene nanoheater are shown by the green dashed lines.
Fig. 2.
Fig. 2. Characterization of the thermally tunable microdisk resonator with a transparent graphene nanoheater. (a) The measured spectral responses of the thermally tunable microdisk resonator as heating power P heating varies from 0 to 10.5 mW. (b) The resonant-wavelength shift Δ λ as the heating power varies. (c) The spectral responses of the thermally tunable microdisk resonator when P heating is 0 mW (the solid line) and 4 mW (the dashed line). (d) The measured temporal responses of the modulated heating power P heating (top) and the corresponding output signal of the photodetector (bottom).
Fig. 3.
Fig. 3. Theoretical calculation results for the thermally tunable microdisk resonator with a transparent graphene nanoheater. (a)  1 / R tot for the graphene ribbons with varying widths w ribbon and lengths L ribbon . (b) Three-dimensional temperature distribution of the heated microdisk resonator by solving the Poisson equation with a 3D finite element method tool. RT is defined as 300 K. (c) Temperature distribution for the cross sections along Cut 1 (top) and Cut 2 (bottom) in (b). (d) Temperature distribution for the heated microdisk resonator. The outlines of the graphene sheet are shown by the black dashed lines.
Fig. 4.
Fig. 4. Optimization of the transparent graphene nanoheater. (a) Heating efficiency η t of the thermally tunable microdisk resonator as the outer-edge position ( r out ) and width ( w h ) of the graphene nanoheater vary. Inset, cross-section view for the WGM of the microdisk resonator. r out = r h + w h / 2 and r in = r h w h / 2 are the outer-edge and internal-edge positions of the graphene nanoheater, respectively. The parameters used in our experiments are indicated by a star. (b) Propagation loss α for the WGM of the microdisk as the outer-edge position ( r out ) and width ( w h ) of the graphene nanoheater vary. The value of 0.01 dB/μm is shown by the black dashed line. The parameters used in our experiments are indicated by a star. Inset, cross-section view for the WGM of the microdisk resonator. The parameters used in our experiments are indicated by a star. (c) Propagation loss α for the WGM of the microdisk when the graphene nanoheater is replaced by a metal (gold) heater. The thickness of the metal is 100 nm . The gray regions show the conditions with only the plasmonic mode supported in the microdisk resonator. The values of 0.01 and 0.1 dB/μm are shown by black dashed lines. Inset, cross-section view for the WGM of the microdisk resonator when the metal heater has the same parameters (shown as a star) as the graphene nanoheater used in our experiment. (d) The heating efficiency η t and the propagation loss α for the WGM of the microdisk when using the metal heater (top) and the graphene nanoheater (bottom), respectively. The outer-edge position is r out = 4 μm , while the width w h is varied from 0.2 to 2.6 μm, as indicated in the figure. (e) Heating efficiency η t of the thermally tunable microdisk resonator as the width ( w a ) and the length ( L a ) of the graphene arms vary. The parameters used in our experiments are indicated by a star.
Fig. 5.
Fig. 5. Characterization of the 3 μm radius thermally tunable microdisk resonator with a transparent graphene nanoheater. (a) Spectral responses of the thermally tunable microdisk resonator as the heating power P heating varies from 0 to 2.7 mW. (b) The shift of the resonant wavelength Δ λ with varying heating powers. Inset: temperature distribution of the heated microdisk resonator simulated by solving the Poisson equation. The outlines of the graphene nanoheater are shown by black dashed lines. RT is defined as 300 K.
Fig. 6.
Fig. 6. Summary of the heating efficiency for the microdisk resonators ( r d = 2 , 3, or 5 μm) using transparent graphene nanoheaters. Inset, top-view microscope images of the fabricated thermally tunable microdisk resonators.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

λ res = 2 π n eff r d m ,
P heating = I 2 R tot .
R tot = R circle + R arm + R contact = π R s r h 2 w h + R s L a w a + 2 R c w c ,
n ¯ eff = 0 2 π n eff ( θ ) d θ 2 π ,

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