1. Introduction

Silicon (Si) microring resonators are important building blocks for integrated photonic devices, including filters, modulators, resonantly-enhanced detectors, wavelength converters, classical and quantum light sources [1–13]. Usually, the resonator must be tuned, i.e., its resonance wavelength shifted, to align to a spectral grid, or to a desired operating wavelength. A variety of methods for tuning Si microring resonators have been shown, including photo-sensitive trimming [14], nano-scale oxidation [15], stress/strain effects and the incorporation of other materials as cladding [16] etc. but the most popular approach is to use either the electro-optic effect or the thermo-optic effect, i.e., the change of the refractive index with injection or removal of charge carriers [17] or with change of temperature [18–20]. Since field effects in Si waveguides, though fast, are fairly weak, they are used mainly for data modulation, and the thermal tuning effect is used for microring tuning.

Here, we describe p-n junction field-effect (JFE) thermo-optic micro-heaters embedded into silicon microring resonators and used in tunable optical filter banks. This research is based on two communication trends: (a) Modern data networks need micro-second scale reconfigurability [21], and (b) to realistically enable wavelength-division multiplexing, optical components need to be able to tune over a fairly wide wavelength range (tens of nanometers) [22]. In addition, the fabrication technology should be simple, and photonic components should be robust to various kinds of driver circuits, including to over-driving techniques such as pre-emphasis which are used to extract higher performance from speed-limited systems ranging from audio frequencies to optical frequencies.

Figure 1 shows a sketch of a microring resonator with a tuning resistor near it; in this paper, the electrical current (I) and voltage (V) refer to the quantities indicated in the figure, and the optical measurements shown are those at the ‘thru’ or ‘drop’ optical ports of the device as indicated. The typical power levels are approximately 0.1–1 mW optical power in the waveguide, and 1–100 mW electrical power driving the resistor. The most common approach to incorporating heaters in a foundry-fabrication Si photonics process flow, now well-described in textbooks [23], is to use a metal layer (i.e., after the silicon waveguide etch, dopant and contact formation steps) to define a structure such as a serpentine resistor above or near the Si microring, and drive current through the resistor. However, the hottest portion structure is separated from the optical mode by a distance of 1 μm or more, and the intervening oxide is a poor conductor of heat. Consequently, such heaters are typically slow and inefficient.

 

Fig. 1 (a) Schematic diagram of a waveguide-coupled optical microring resonator near an electrical tuning micro-heater. The latter may be integrated into the microring (when the resistor is formed using doped Si segments), or may be a separate structure (when the resistor is formed using metal traces). The current (I) - voltage (V) relationship can take several forms, including (i) Ohmic, (ii) non-Ohmic, leading to runaway, breakdown and destruction at a voltage labeled V_D, and (iii) transistor-like behavior with a ‘saturated’ constant-current source I_SAT. Panels (c)–(d) show experimental I-V data from structures on the chip for types (ii) and (iii).

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Alternatively, the heater can be formed using a doped section of Si itself, through which current can be conducted. One approach is to form the heater (and the current path) transverse to the direction of light propagation [23, pp. 236–240]. Alternatively, a heater can be formed within the microring (or microdisk) resonator itself. Light stays on the outside of a bend [24,25] or a ring [26] (e.g., a whispering gallery mode is confined to the periphery of a disk), and thus, a portion of the inner diameter can be formed into a resistor without incurring excessive optical loss by sitting directly in the lightpath. In this case, the current propagates along the microring resonator in the same direction as the light. Since the heating element is separated from the optical mode by only a few tens of nanometers (and heat has to propagate only through silicon, not oxide), the resulting thermo-optic tuning effect is faster, and typically on micro-second scales.

Driving significant amounts of current (typically, 1 mA) through a small region (typically, a 0.1 − 0.2 μm) of resistive silicon (or even metal, [19]) for prolonged periods of time can lead to degradation, electro-migration and device failure. Deep-sub-micron-scale heaters are highly nonlinear and show signs of runaway and catastrophic breakdown [see the sketch in Fig. 1(b) marked trace ‘ii’ and the experimental data on a test structure shown in Fig. 1(c)]. One reason this occurs is that the doped section of the microring is already designed to be more resistive than the tethers so that the applied voltage is dropped mostly in that section, and the decrease in carrier mobility with increasing temperature further raises its resistivity, leading to even more heating. A transistor-like I-V relationship, with constant current beyond a certain saturation voltage [see the sketch in Fig. 1(b) marked trace ‘iii’ and the experimental data on a test structure shown in Fig. 1(d)] would not only serve to protect the device, but also allow a voltage pre-emphasis spike to be used for speeding up the response (as often seen, e.g., [18, Fig. 4]), and will linearize the wavelength shift with electrical power. Here, we show that such a structure can be achieved quite readily within the standard foundry fabrication processes used today in silicon photonics. We demonstrate the junction field effect (JFE) used in conjunction with bend-integrated micro-heaters in Si microring resonators, both for wide-range and narrow-range tuning, and with microsecond-scale time constants.

2. Experimental details

2.1. Component design and simulation

The components were designed on silicon nanophotonic chip (see Fig. 2) that was fabricated as part of a multi-project run using deep ultra-violet lithography and Complementary Metal-Oxide-Semiconductor (CMOS) compatible processes at the Microsystems and Engineering Sciences Applications (MESA) facility at the Sandia National Laboratory. A p-type, 14 − 24 Ω.cm resistivity (acceptor doping concentration approximately 1 × 10¹⁵ cm⁻³) silicon-on-insulator wafer with 250 nm active-layer Si thickness and 3 μm buried SiO₂ thickness was used. A sequence of silicon etch steps was used to form the fully-etched and rib waveguides which were used in different parts of the chip, along with multiple steps of oxidation smoothening for waveguide sidewall roughness reduction and optical propagation loss mitigation. The waveguides were designed for low-loss transmission in the lowest-order mode of the transverse electric (TE) polarization defined relative to the device plane, and measurements of the transmission spectra confirm that only a single mode-family was supported. Dopant implants were followed by a rapid thermal anneal (RTA) activation process, and by additional processing steps to form contact vias. A single metal layer was used for low-resistance ohmic contacts, electrical connection pads, and test resistor structures. After a deep silicon etch to expose facets for edge-coupling, the wafer was singulated into chips for testing. Electrical contacts were made by wirebonding to a printed circuit board.

 

Fig. 2 (a) A silicon photonic chip, which contained several banks of tunable microring filters (locations indicated by the white boxes), was designed and fabricated using the Sandia photonics process. (b) Diagrams of the two types of microheater-integrated microrings studied here; only the silicon mask layer is shown. The n-doped regions are indicated by red color within the gray regions which indicate the p-doped Si in the starting wafer. Numerical values of the major diameter (MD) and doped length (L) are provided in the text. The dotted red lines schematically indicate the electrical connections made to drive current through the microheaters.

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Of interest here are two types of microheater-integrated microring resonators shown in Fig. 2. The smaller microring resonators have a major diameter (MD) of 4.8 μm, and a waveguide width which varied between 325 nm and 650 nm. These microrings have a free spectral range (FSR) exceeding 40 nm (i.e., only one resonance within the C-band telecommunications wavelength), and a passband wide enough to drop at least 800 GHz. Another type of microring resonator was larger, with major diameter (MD) 29 μm, and whose waveguide width varied between 400 nm and 800 nm. these rings had a smaller FSR (850 GHz) and narrower (but still flat-top) passbands, wide enough for only one channel on the 100 Ghz ITU-T telecommunications grid. (The FSR and bandwidth specifications were inherited from the specifications of the “MORDIA” network testbed [27] for which project the chip shown in Fig. 2 was designed.) At the widest points of the waveguide, a fraction of the waveguide width was implanted with n-type dopants over a length (L) of approximately 1.7 μm and 3.4 μm for the smaller and larger microrings, respectively, to form resistive heaters. Both microrings received Arsenic (As) dopants with implant energy 380 keV and at an areal concentration of 4 × 10¹³ cm⁻², which results in nominal resistivity of 1300 Ω/sq. Also shown in Fig. 2 are the outlines of the Si segments labeled “tethers” which were doped more heavily and with a different dopant species to provide a lower-resistivity contact (approximately 30 Ω/sq.) to the via and metal wiring. From separate test measurements on a different part of the chip, we measured a contact / wire-bonding resistance of less than 10 Ω. In this configuration, nearly all the applied voltage was dropped over the integrated micro-heaters.

Figure 3(a) shows the cross-section of a representative implanted waveguide (schematic drawing, not to scale). Note that in the fabricated microrings, only n-implants were used in the microring section itself, and the n+ implants, tungsten (W) vias and metal traces were used near the tethers. Figure 3(b) shows results of a cross-sectional 2D process simulation (net doping, calculated using ATHENA Silvaco software) of the n-implant in the region indicated by the solid box with light yellow transparent coloration which is labeled ‘n implant’ in Fig. 3(a). The p-doped starting-wafer and n-implant conditions result in the formation of a p-n junction within the cross-sectional extents of the waveguide. The optical mode in the microring thus “sees” both net p- and n-doped regions with not dis-similar concentrations (approximately an order-of-magnitude higher on the n side, but the optical mode sits closer to the outer edge, i.e., the p-side).

 

Fig. 3 (a) Schematic diagram of the waveguide cross-section (not to scale). By partially counter-implanting (n-type) a section of the p-doped wavguide, a quasi-lateral p-n junction is created. (b) Simulation of the doped profile using ATHENA (Silvaco) for a representative waveguide section of width 800 nm in which the right-side one-half width (400 nm) was masked off for the implant. Spreading and diffusion of the implanted species results in a metallurgical junction that lies inside (under) the masked-off region. The colorbar shows the exponent of the net carrer density (units: cm⁻³).

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This section is part of the waveguide cross-section in the widest portion of the microrings, and the direction of current flow is along the n-implanted region only, and perpendicular to the cross-sectional cut that is shown. The device thus resembles a depletion-mode junction-field effect transistor (JFET) and the diffused pinch-resistor [28], which are formed by implanting a conducting channel with a counter-doped layer deposited over it, thus narrowing or “pinching” the resistive channel depending on the base voltage. The “drain” and “source” terminals are the two contact points to the implanted resistor, across which the I-V data presented below was measured. The “gate” consists of the large island of p-doped Si which forms the un-implanted portion of the microring. We have fabricated no explicit gate contact, since doing so would significantly perturb the optical mode, which propagates around the outer periphery of the circular optical pathway. Nevertheless, carriers have a finite lifetime in the ring, in part due to recombination with the photons of the resonant mode, as well as collisions with the etched sidewalls (width-to-height aspect ratio is approximately 3:1 or 4:1 in the two types of microrings). The gate may be considered to be weakly (capacitively) coupled to ground, as indeed are floating gates used in memory or logic cells. Depletion regions are not totally devoid of carriers, and in the saturated regime of a JFET, drain-source current continues to flow as the drain-source voltage is increased. Indeed, this is a most useful regime of operation, in which the device operates as a constant-current source.

2.2. Measurement of electrical characteristics

I-V measurements of these integrated micro-heaters were carried out using a Source Measurement Unit (Keithley 2450). Whereas I-V measurements in Fig. 1(d) were taken without optical light, the data shown using square- and diamond-shaped markers in Fig. 4 were acquired when optical light was being guided on the chip, and at the same time as swept-wavelength optical transmission data was being recorded. Dashed red lines in Fig. 4(a) show the I-V relationship for microrings fabricated on a previous run (using the same physical geometry but a different species and energy of dopants) which resulted in a much higher (4–5 orders of magnitude) net carrier concentration on the donor side, compared to the acceptor side. Because of this imbalance, the impurities were not fully depleted, and the device behaved like a normal (nonlinear) resistive heater. Attempts to tune those microrings widely resulted in the current quickly exceeding the desired value, and the device was easily destroyed without much tuning. Here, not only was a much wider tuning range possible, but the driving voltages could be pre-emphasized for sharper rising transitions (as discussed below) without damaging the device.

 

Fig. 4 (a) The I-V measurement (small squares) for the small microrings was well fitted by the JFET I-V equation as described in the text. The dashed red line shows the I-V measurements of a similar microring but with different dopants (and no channel pinch-off) which exhibited device destruction before saturation. (b) The larger microrings, with a longer ‘channel’ L, also were fitted by the same equation, with different parameters. (c) At low frequencies (< 75 Hz), the capacitance for 3 banks of dual-ring filters driven in parallel (red data points and sigmoidal fit) showed an increase with voltage. At high frequencies (100 kHz), the effect was less noticeable (blue points and fit). The black trace shows there was no change in capacitance with voltage of a loading circuit used in parallel with the device under test (see text for description). Errorbars show the uncertainty (noise) in the measurement.

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There are several points of similarity between the I-V relationship of the integrated micro-heater and that of a JFET. The fitted lines in Figs. 4(a) and 4(b) follow the usual JFET equation, $I=k\left(\raisebox{1ex}{$V_{\mathit{GT}}{V}_{\mathit{min}}-V_{\mathit{min}}^2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$, where k is called the gain factor in JFETs and is a fitted parameter in our model describing the heater efficiency (i.e., the slope of the conductance at small voltages), V_GT = V_G − V_T in terms of the gate voltage V_G and threshold voltage V_T (neither quantity is defined in the geometry of our device, and therefore, V_GT is a fitting parameter here), and V_min = min(V_GT, V_D, V_DSAT), where V_D is the applied voltage to the heater, and V_DSAT, the drain-source saturation voltage in the JFET here refers to the fitted parameter value at which the I-V relationship saturates (V_DSAT = 5.4 V and 14 V for the small and large microrings, respectively). As expected, the longer length of the resistive section in the larger microrings shows “long-channel” I-V relationships compared to the smaller microrings, which saturates earlier. Furthermore, the fitted gain factor k can be used to define an equivalent transconductance g = 2k V_GT = 0.6 mA/V which is not far from the typical transconductance value (1–2 mA/V) for MOSFETs in a similar technology process node, and is also comparable with the estimate g ≈ 2(kI_DSAT)^1/2 ≈ 0.44 mA/V [29]. The applied drain voltage in excess of V_DSAT is dropped across the depleted section of the channel. In both microrings, I_DSAT is limited to less than 1 mA, which protects against the catastrophic damages experienced in earlier measurements [see red line in Fig. 4(a) and also see Fig. 1(c)].

Since the p-doped ‘gate’ region is physically much larger in size than the n-implanted channel (e.g., the circumference of the small microring is 30 μm of which the doped regions account for 3.3 μm), the former accumulates sufficient charges, at room temperature, on the opposite side of the metallurgical junction to form a measurable capacitor, i.e., positive and negative charges separated by a short distance. Accordingly, we expect to see increased capacitance with increased voltage as the channel gets pushed further into pinch-off. In agreement with this intuition, Fig. 4(c) shows measurements of three such dual-microring filters (a total of six microrings) driven in parallel, so that the capacitances add. (We have verified that driving fewer, e.g., one or two, microrings proportionately decreases the magnitude of the change.) This measurement was performed using a precision LCR meter (Quadtech 7600 Model B) with the device-under-test placed in parallel with a loading circuit that consisted of a polyster film capacitor and a series resistor, which did not change over the range of applied voltages [black markers in Fig. 4(c)]. The average value of these measurements was taken as the reference value from which the change in capacitance of the micro-heaters was defined. The data is plotted along with error bars defined as one standard deviation of the measured values over 64 averages. The fitted lines are based on the following functional form ΔC(V) = (b + exp[−a(V − V₀)])⁻¹.

The red-colored data points were measured at a low frequency (67 Hz) whereas the blue-colored data points were measured at a higher frequency (100 kHz) where the effect was less noticeable (as typical with field-effect impacted electron transport channels), but still evident. Notice that the measured capacitance increases with voltage, whereas the voltage of a capacitor affected by ferroelectricity or crystalline stress, such as a ceramic disc capacitor made of barium titanate decreases with voltage, an effect not observed here in any microring.

2.3. Temporal characteristics

When driven by a pulsed waveform, an order-of-magnitude estimate of the intrinsic switching times can be calculated from a linearization of the resistance and capacitance change over the range of applied voltages, R_eff ≈ (R_min + R_max)/2 ≈ (1.7 kΩ + 5.9 kΩ)/2 ≈ 3.8 kΩ, and ΔC = 0.12 nF, which predicts a rise/fall time (10%–90% transition) of approximately τ = 2.2 R_effΔC = 1.0 μs. This is of the same order-of-magnitude as the rise and fall times of the measured optical transmission through the devices at a fixed wavelength.

Under both large-signal and small-signal driving conditions, we measured the transmission of a semiconductor laser tuned to a wavelength on the shorter-wavelength edge of a filter resonance (near 1535 nm). For the large-signal driving waveforms (amplitude 10 V), voltage pulses were provided by a pulse generator (BNC Nucleonics, Model 6040/201E, 100 Hz trigger, 4 ms pulse width), with a pre-emphasis on the leading edge as shown in Fig. 5(a). As discussed earlier, since current is approximately constant over the voltage values that define the pre-emphasis peak (approximately a 5 volt range from 10 V to 15 V), the devices are not damaged, unlike the previous generation of microheaters without the JFE effect. To avoid loading the time-constants by the relatively long wirebonds in the packaged devices, a bare-die chip was used for these measurements, and voltage was applied using a multi-contact wedge (Cascade Eyepass). Data was acquired using a fiber-coupled detector with 100 MHz bandwidth d.c.-coupled to an oscilloscope. Stored data was processed offline to extract 10%–90% rise and fall transition times from the signal after smoothing (moving window consisting of 2% of the dataset) using weighted-linear-least-squares local regression (quadratic polynomial model).

 

Fig. 5 Pulsed electrical waveform driving the microheater (black line showing a vertically-scaled replica for comparison; original waveform was 10 Vpp excluding pre-emphasis), and measured optical response (blue line, measured amplitude at oscilloscope). (a) For the smaller microrings, the 10%–90% transition rise and fall times were measured to be 0.6 μs and 19 μs. The optical waveforms in regions indicated by dotted boxes are shown in detail in subsequent panels. (b) The larger microring resonators (consistent with the smaller-sized heaters relative to their size) showed 10%–90% transition times of 24 μs and 47 μs for the rise and fall transitions. (c), Magnified view of the optical waveform (squares) and fitted line for the falling edge, with a 10%–90% transition time of 19 μs (16 μs from an exponential fit). (d) Magnified view of the optical waveform (square) and fitted line for the rising edge, with a 10%–90% transition time of 0.6 μs.

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The measured 10%–90% transition time was 0.6 μs and 19 μs for the rise and fall transitions. When driven by voltage pulses, the rising-edge transition corresponds to the ‘forced response’ of the device to the voltage step, whereas the falling-edge transition is measured when the device relaxes to its original state, and thus, corresponds to the ‘natural response’. Heat dissipation pathways on this chip have not been optimized and can be improved. (Alternatively, two devices can be used in combination to achieve sub-microsecond transitions on both the rising and falling edges [30].) For a lower-amplitude (small-signal) driving voltage (2 V peak-to-peak, without pre-emphasis), the rising-edge 10%–90% transition time was 4 μs. As discussed below, the large-signal driving transitions result in a wavelength shift of about 25 nm; and the resulting tuning speed of 25 nm in 0.6 μs is the fastest reported for thermally tuned microrings. (Carrier-injection or depletion effects can be faster still, but result in much smaller wavelength shifts [31].) We did not measure the temporal characteristics of the larger microrings since they were designed only for quasi-d.c. shifts, and not for fast tuning.

2.4. Measurement of the optical characteristics

As part of the integrated Si photonic chip, both the small and the large microrings were used in second-order (cascaded) filter configuration. For coupling from sub-micron scale waveguides to fibers at one edge of the chip, the silicon waveguides were designed with a taper down to a tip width of about 0.2 μm for mode-matching to lensed, tapered fibers. At the present time, we used a standard fiber array (fiber core diameter 9 μm) and incurred substantial coupling losses (estimated 10 dB/facet). These measurements were carried out mostly over the wavelength range corresponding to the C-band telecommunications wavelengths used in our testbed (1520 nm to 1565 nm, extended past 1580 nm to clearly show the FSR of the small microrings). A single-polarization swept-wavelength laser was used to characterize optical transmission. The state-of-polarization (SOP) of the light entering the chip was scrambled, and since the waveguides only transmit TE polarization, this incurred 3 dB insertion loss.

Shown in Fig. 6(a) are transmission measurements of a wide-passband filter made using the smaller thermally-tuned microring shown in Fig. 3(b), at voltage levels of 0 V, 5 V, 10 V and 15 V. We observe the peak shifting to longer wavelengths and no decrease in the height of the peak, which is consistent with the thermo-optic phase-shifting mechanism, whereas the carrier-injection mechanism results in a shift to shorter wavelengths, and considerable attenuation of the peak transmission [23]. The 0 dB baseline in Fig. 6(a) was measured by a separate calibration path on the chip using similar photonic components in the lightpath except for the ring filter. The zero-voltage loss is −8.4 dB per ring, much higher than designed; we believe that the positioning of the n-type implants in these microrings was too close to the optical mode, and the waveguide-ring coupling coefficient was incorrect (see Section 3). By fitting a Lorentzian to the data, we measured the peak shift with applied power (voltage times current) to the microheater. The fitted line in Fig. 6(b) has the functional form $\mathrm{\Delta }\lambda =a{P}_{mW}^b$, with fitted parameters a = 3.6 nm/mW and b = 0.55. Taking a linear approximation to the tuning curve between Δλ = 0 and 25 nm, we calculate a tuning efficiency of each heater to be 3.2 μW/GHz, a factor-of-two improvement on other recent reports [31] and nearly a factor-of-ten improvement on traditional metal heaters [23]. Another way of stating the efficiency is in (inverted) units of nm/mW: these heaters have an efficiency of 2.9 nm/mW up to a shift of about 12 nm, which is about one-half the reported value of 4.8 nm/mW for highly-optimized conventional heaters but with heat-confinement trenches over a similar tuning range [32] (similar work was reported in [33]).

 

Fig. 6 (a) Transmission spectrum at the drop’port of a dual-ring tunable filter made using the smaller microrings. Shown in panels (i)–(iv) are four measurements of wide range tuning at voltage levels of 0 V, 5 V, 10 V and 15 V, respectively. Measurements are shown by dots, and a Lorentzian fit by a solid line of the same color. (b) The peak wavelength of the fitted Lorentzian is plotted versus electrical driving power (V × I). (c) Transmission spectrum at the drop port of a dual-ring tunable filter made using the larger microrings. (d) Shown are four measurements of fine-tuning of the filter with increasing voltage levels (0 V, 5 V, 10 V and 15 V, respectively). (e) The peak wavelength of the fitted Lorentzian is plotted versus electrical driving power (V × I).

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A similar dual-ring filter, but formed using the larger thermally-tuned microrings, was also measured. Because the circumference was larger, the FSR was smaller, as shown in Fig. 6(c), but the filter exhibits uniform response with a peak-valley contrast of 25 dB over a wide wavelength range for reasons explained in Section 3. Figure 6(d) shows measurements of thermally-tuned responses around one resonance, with flat top characteristics preserved during tuning. The zero-voltage insertion loss IL was about −2.5 dB per ring. The tuning characteristics are shown in Fig. 6(e); we calculate an efficiency of 33 μW/GHz, which while comparable to standard designs [23], does not represent maximum heater efficiency. Here, the length of this current-carrying segment (approximately 7 μm) was only a small fraction of the circumference (approximately 160 μm); this dual-bank filter was designed for finely-tunable flat-band transmission, e.g., tracking dynamic wavelength shifts over a few nanometers in transceivers without precise stabilization.

3. Discussion

An iterative cycle of design, fabrication and measurement can be used to improve the performance of components when parameter extraction can be performed reliably and robustly from the data. The transmission spectrum of a microring resonator can be analyzed using a matrix model [34] to identify two dimensionless coefficients: |t|, the magnitude of the transmission coefficient of the ring-waveguide coupling matrix, and the single-pass round-trip propagation coefficient of the microring, α, which is related to the per-length propagation coefficient a (units: cm⁻¹) by α = exp(−aL) where L is the circumference of the microring. The measured spectrum was segmented into each individual FSR, and a nonlinear curve-fitting algorithm was used to fit the matrix model, extracting a value of |α| and |t| for each FSR, by minimizing the sum of squared-errors on a linear scale (since the transmission peaks are measured with less noise). Although a simple matrix model cannot reproduce every artifact of the measurement, the fit shown in Fig. 7 is satisfactory near all peaks, and in most valleys as well.

 

Fig. 7 (a) Transmission spectrum of filter using the larger microrings at 0 V (blue dots) and the fit (black line) using the model described in the text. Shown are the extracted values of (b) the round-trip loss |α| and (c), the magnitude of the ring-waveguide coupler’s transmission coefficient |t| versus wavelength.

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Data extraction from the transmission spectrum of the larger microring shows successful design close to the desirable critical-coupling condition (single-pass round-trip loss in the ring equals in magnitude the transmission coefficient of the ring-waveguide coupler which results in maximum on-off filtering contrast. The slopes of the wavelength variation (i.e., dispersion) of the loss and coupling coefficients were also matched, and consequently, the transmission spectrum in Fig. 6(a) showed a clean response with more than 25 dB peak-valley contrast over more than 40 nm. We achieved this by measuring a first fabricated batch of devices ([27], which had lesser contrast, approximately 10 dB), performing parameter-extraction and analysis, and then fabricating a second batch of devices with improved performance.

However, the small microring has a very large FSR, and there is insufficient information in the transmission spectra measured with our tunable laser [there is only one FSR shown in Fig. 5(a) to clearly separate the role of the coupling coefficients and the propagation loss. Our measurement and design effort here is not yet complete: although we achieved an on-off contrast exceeding 15 dB at a wavelength separation of ±10 nm from the peak, the insertion loss was high as discussed earlier. With improved designs, we may be able to demonstrate higher-order filters using the small microrings, with flat-top transmission characteristics, similar to the performance shown here for the larger microrings, or improved results obtained elsewhere [3,8].

Since the change of the refractive index of silicon with temperature is known (dn/dT = 1.9 × 10⁻⁴ /K), and the waveguide cladding, made of silicon dioxide, is a poor conductor of heat, it may be argued that measurement of the transmission spectrum taken at different temperatures can be used to estimate the temperature [19, 35]. However, these heaters only cover a small portion of the circumference, and heating is highly non-uniform and local. On the other hand, quantities measured from the optical spectrum like FSR, resonance-shift etc. are intrinsically averaged over the light path, including the hot and the cold sections. Thus, although temperature increases of 250°C and 17°C can be calculated for the widest tuning ranges in Figs. 6(b) and 6(e), respectively, they do not actually correspond to the devices under test.

Heating results in a change of the index of refraction of the constituent waveguides, and therefore, also of the FSR of microring resonators. If the temperature-induced change in the effective refractive index, n_eff, is large compared to the temperature-induced change in the dispersion of the effective refractive index (i.e., of λ × dn_eff/dλ), which is the case for these waveguides, then the fractional change of the FSR due to the temperature change is equal in magnitude, and opposite in sign, to the fractional change of the effective index, i.e., ΔFSR/FSR ≈ −(Δn_eff/n_eff). The latter quantity is itself equal to the fractional (wavelength) shift of the resonance peak, i.e., Δλ/λ₀, where Δλ is the measured wavelength shift of a resonance as shown in the vertical axis of Figs. 6(b) and 6(e), and the resonance wavelength λ₀ ≈ 1.55 μm. Thus, the fractional change in the FSR is approximately 2% in the case of Fig. 6(b), and less than 0.1% in the case of Fig. 6(e).

In summary, we have presented a design for integrated micro-heaters incorporated inside silicon microring resonators which are used in filter banks, which include a junction field effect. These structures achieved a transistor-like I-V relationship, and allow driving the heaters with a pre-emphased pulsed waveform without damage. We demonstrated microsecond scale rise/fall times, and tunability over both wide and narrow spectral ranges with attractive characteristics (tuning range, efficiency, filter shape, ease of fabrication etc.) that are desirable for integrated silicon photonic components used in future microsecond-scale circuit-switched data networks. Although more work remains to be done in both measurement analysis and component re-design to improve the insertion loss and demonstrate higher-order filtering using the large-FSR tunable microrings, we believe that these types of micro-heaters may be a useful component in the silicon photonics toolkit.