1. Introduction

With the continued development of higher-power chip-scale lasers and frequency combs, and the improvement of more sensitive integrated photo-detectors, including avalanche photo-diodes and even waveguide-integrated single-photon detectors, there is increasing need in integrated photonics for high dynamic range optical power control (OPC) through a variable optical attenuator (VOA). Applications include simultaneous transmit-and-receive (STAR) [1–3], optical remote sensing and lidar [4], optical radios [5], and optical communication formats such as pulse position modulation which use a high peak-to-average power ratio [6]. Other emerging applications are in integrated quantum and nonlinear photonics, where there are strong residual pump beams that should be diverted (rather than totally blocked) [7], and signals that are many tens of dB weaker allowed to propagate.

A component is needed which allows a strong signal (typically, the transmitted waveform) to exist for some duration of time or in certain pathways, which is well isolated from weak signals (typically, the received waveform) that exit in the same pathway at other times, or in adjacent portions of the microchip. Such a component should be compact, since many of these applications now require arrays of such components, and footprint on a microchip is expensive (in silicon photonics, at a typical cost of $2,000 per cm² [8]).

The traditional silicon photonics VOA technology consists of a p-i-n electronic diode designed for current injection across the cross-section of a silicon photonic waveguide [9–11]. A basic design [12, 13] results in a typical attenuation of 25 dB/mm, and therefore, achieving 40 dB on-off dynamic range contrast requires a long device [9, 14] (an order-of-magnitude larger than here). Driving such large electrodes also results in a slow response from the driver circuits.

An alternative is to use the combination of a traditional p-i-n VOA and an optical component such as a Mach-Zehnder interferometer (MZI) or a microring resonator (MRR), which for the purposes of this discussion, are two examples of optical lattice planar waveguide filters. Such designs fall into two types: the MZI based designs are moving-average (MA) filters, and the single-stage MA filter has a sinusoidal response, which can act as a notch filter by rejecting a narrow range of frequencies [15, pp. 237–303]. In contrast, an MRR is an auto-regressive (AR) filter, and the single-stage AR filter typically has a bandpass response. Both MA and AR structures in silicon photonics can be tuned at microsecond speeds [16], and Si MRR’s are especially compact devices. (In fact, here, we show they are small enough to be able to share the heat generated by the p-i-n VOA situated nearby, and do not require additional direct heating.)

Why not use only a filter structure for OPC? Some researchers are indeed proposing to do so [17,18]. However, the MA rejection notch is narrowband, and cascading MA stages is possible but challenging and requires numerous tuning elements and space on the microchip [18]. Usually, significantly better roll-off and passband rejection can be achieved with the AR design over the MA design [15]. However, AR filters also have a fundamental tradeoff between extinction ratio and the full-width at half-maximum, which can be somewhat easily mitigated by high-order MRR filters with flat-top response [19]. However, as the poles moves close to the unit circle to improve the performance of the AR filter, the group delay (GD) increases (poles inside the unit circle contribute positive GD), which can cause problems in the aforementioned applications. Therefore, the filter order should not be too high (even though very long silicon MRR chains have been demonstrated [20]), and we may not wish to rely solely on the filter structure for OPC.

A two-stage approach is now used for high-performance filtering [19, 21]; here we show a two-stage approach can be used for compact-footprint OPC using both a VOA and a flat-top filter structure, as in Fig. 1. Although it is not surprising that a two-part device provides more extinction than a conventional VOA, a point of interest here is that the second stage did not need any control, and harvested the heat generated in the first section. As with any filter, we sacrifice continuous spectral coverage (typical with the bare VOA), for band-selective enhanced VOA functionality. This may be adequate for many applications where the laser wavelengths are known, or lie on a grid, or can be searched for dynamically (the passbands of the device can be tuned within microseconds). Data is presented here to help the designer decide whether to adopt this type of dual-stage approach for the intended applications, or the cascaded filter architecture discussed elsewhere [19].

 

Fig. 1 Schematic of the two-part optical power control (OPC) device, consisting of a current-injection VOA, formed by a p-i-n junction fabricated across a waveguide, followed by a second-order coupled-microring filter. The microrings are designed such that, when no current is driven through the p-i-n junction, they are on-resonance with the laser wavelength, and hence, transmit light with minimal loss. When current is driven through the p-i-n junction, the dissipated power converted into heat is used to shift the resonances of the microrings. The achievable extinction comprises two contributions: free-carrier absorption in the first section, and the out-of-band extinction of the filter in the second section.

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2. Fabrication

The device was designed on a silicon photonics process at the Sandia National Laboratories on a silicon-on-insulator wafer with 250 nm active-layer silicon thickness and 3 µm buried oxide. After oxidation to reduce sidewall roughness, the silicon waveguide height was 230 nm. The waveguide cross-section was designed to support a single transverse electric (TE) mode relative to the device plane. The p-i-n diode in the device was formed by adiabatically transitioning from a fully-etched strip waveguide to a ridge waveguide, as shown in Fig. 1(b). The 150 nm thick slab tapers were designed with 25 µm length, and with a 25 µm constant-width mid-section and doped regions of length 50 µm. The two sides of the slab were implanted n and p over a length of 50 µm, with a 900 nm separation from the edge of the 400 nm wide intrinsic waveguide core. Facets for edge-coupling were exposed by a deep silicon etch, and the wafer was singulated into chips for testing. Electrical contacts were made by wirebonding to a printed circuit board (PCB) made of FR-4 material (epoxy laminate sheets, thickness 3.1 mm) using Hysol QMI538NB die-attach paste, with the die being situated on an ENEPIG (gold) pad (approximate thickness 150 µm).

3. Optical measurements of attenuation and spectral selectivity

Variable optical attenuation available from the p-i-n junction is spectrally wideband and offers the most flexibility in controlling power levels of light at any wavelength. However, in many applications, the spectral locations of the lasers are approximately known (or can be tuned to). We can then tradeoff spectral coverage for extra attenuation gained by using a second method of variable attenuation after the p-i-n junction, such as tuning a filter or interferometer on and off resonance. As shown in Fig. 1, the output of the p-i-n VOA connects to a second-order filter (cascaded double ring) with major diameter 29 µm, major diameter 25 µm, and whose waveguide width varied between 400 nm and 800 nm. These rings were measured to have a free spectral range (FSR) of 850 GHz. At the port labeled ‘out’ in Fig. 1, the light is attenuated, with respect to the input at the port labeled ‘in’, by the combination of the extinction from free-carrier absorption in the p-i-n VOA segment and the extinction of the filter.

Microring AR filters can be designed to have high extinction ratios in two ways, either by increasing the size and cavity quality factor, or by using higher-order structures. In the first case, achieving higher extinction ratios reduces the bandwidth of the passband or stopband. Here, we used a second-order coupled-microring filter after the p-i-n VOA stage, from which an on-off contrast was obtained by shifting the resonance wavelengths thermally. Thermal tuning, rather than current injection, of microrings results in a higher achievable on-off contrast because current injection induces free carrier absorption in the microrings (enhanced by the multiple round trips made by light in the resonator).

Figure 2 shows the optical transmission in the ‘on’ and ‘off’ states for the measured device at wavelengths around 1550 nm and 1590 nm. The total fiber-to-fiber measured insertion loss in the zero-voltage state was −29 dB, the majority of which (−18 dB) was due to the fiber-to-waveguide couplers, which have not been optimized. An on-off contrast of up to 40 dB was achievable by injecting current into the p-i-n section. Approximately 15 dB of the on-off contrast was achieved by the diode segment alone, and the rest (approximately 25 dB) was achieved by thermally shifting the microring resonance to longer wavelengths. The indicated bandwidth ΔB is determined by the passband width of the microring resonators, and Fig. 3 shows that high extinction ratio can be achieved over many bands within the measured wavelength range of 1520 nm to 1620 nm.

 

Fig. 2 Transmission spectrum data measured with zero current through the p-i-n diode (optical transmission‘on’ state) is shown by the dashed (black) line, and when current is applied to forward-bias the p-i-n junction (optical transmission ‘off’ state) is shown by the solid (red) line. Two representative bands are shown: panel (a) shows wavelengths around 1550 nm, and panel (b) shows wavelengths areound 1590 nm. (Other spectral bands are shown in Fig. 3.)

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Fig. 3 The available on-off contrast ΔT (dB) versus bandwidth is shown across the C and L transmission bands. Higher attenuation is achievable over narrower bandwidths, as visually represented by the height and width of the colored bars. Refractive index dispersion results in slightly lower attenuation in the L-band, compared to the C-band.

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To operate the device between the ‘on’ and ‘off’ states, an electrical current was injected only into the p-i-n section. The heat generated by electrical dissipation when forward-biasing the p-i-n diode is normally wasted; here, that heat was harvested to shift the filter spectrum and provide additional on-off contrast. Thus, the enhanced variable attenuation obtained from microring tuning consumed no additional power. The temporal characteristics (discussed later) clearly showed different time constants for the carrier injection / depletion and the heating / cooling effects. Because the latter effects are relatively slow, the p-i-n section can be designed with a wide intrinsic region to enable low-loss optical propagation.

Optical attenuation was measured by tuning the laser to the resonance peaks of the ring filter (when no current was driven through the device), and then sweeping the current through the anode and cathode of the PIN diode in forward-bias from 0 to 100 mA. The measured transmission spectrum was used to fit a matrix model for microrings [22], in which the wavelength range was segmented into individual FSR’s and a nonlinear curve-fitting algorithm was used to extract the round-trip propagation and transmission coefficients of the second-order ring filter. Data measured for the peak wavelength shift versus current was then fit with a weighted-linear-least-squares local regression model. The sum of the attenuation obtained from the microring and that obtained by the p-i-n diode provided the analytical form for the total attenuation in this two part device, and is shown by the continuous black lines in Fig. 4.

 

Fig. 4 Panel (a) shows the total attenuation through the entire device versus current applied to forward bias the p-i-n junction in VOA A. Panel (b) shows that the non-monotonically increasing trend is different for VOA B, and a higher attenuation is reached because the ring is shifted more (tuning efficiency is higher) to where the highest contrast coincides with the highest attenuation from the p-i-n.

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The left panel of Fig. 4 shows the attenuation achieved by a device, labeled VOA A, in which the distance between the p-i-n junction and the microring section was longer by 140 µm than in VOA B, which is shown in the right panel. Since the available contrast from a microring filter is maximized by tuning from the peak to the valley (i.e., by one-half of the FSR), we expect that the microrings in VOA A would be tuned less efficiently by the injected current than in VOA B, and would result in a smaller dynamic range. Experimental measurements Fig. 4 confirm this intuition, and VOA B achieves 40 dB of ‘on’ - ‘off’ contrast, whereas that of VOA A was slightly lower. For VOA B, the attenuation efficiency was measured to be 0.14 dB/mA, with the maximum attenuation at 100 mA (electrical power 286 mW) resulting in a power-consumption efficiency of 7.2 mW/dB.

It is simple to explain this behavior by observing the wavelength-resolved transmission spectra, which were measured at 6 discrete values of the injection current for structure A and B, as shown in Fig. 7 and Fig. 8 in Appendix A1. When the microring resonance has thermally red-shifted past the (fixed) input laser wavelength, then it no longer contributes an attenuation to the total until the next resonance, one free-spectral-range away, is thermally tuned into the input laser wavelength.

Based on the known value of the thermo-optic coefficient for silicon and the measured spectral shift, we can estimate the temerature rise experienced by the microrings. The microrings in VOA A were situated 495 µm from the p-i-n segment, and experienced 55K increase in temperature when 100 mA current was injected, whereas the microrings in VOA B were situated 355 µm from its respective p-i-n segment and experienced 62K increase in temperature when 100 mA current was injected.

No thermo-electric controller was used in these measurements. As described earlier, the chips were mounted on a printed circuit board made of FR4 material which is a poor thermal conductor. No thermal vias or heat dissipation pathways were incorporated in the PCB. These experimental conditions encouraged lateral spreading of heat through the Si handle layer (thickness 0.68 µm), since the lateral thermal resistance between two Si segments of length 100 µm separated by a distance of 400 µm is 400 times smaller than the vertical thermal resistance of the FR4 layer between the hot side and the convective boundary to air. In a more complicated, multi-component device, thermal spreading from hot components such as current-injection VOA’s will cause crosstalk between other optical devices unless heat management pathways are designed carefully on both the device stack and the PCB.

4. p-i-n junction measurements and simulations

The attenuation from the p-i-n waveguide section was calculated by identifying the peak-to-valley spectral contrast in the measured transmission spectra (which was due to the microrings alone, since the p-i-n segement has no wavelength dependency) using a swept-wavelength tunable laser between 1520 nm to 1620 nm at each current level. Figure 5(c) shows the p-i-n attenuation for VOA A versus current through only the forward biased p-i-n junction of the device from free carrier absorption. The attenuation due to the p-i-n diode only was measured to reach 15 dB at 100 mA, with an attenuation efficiency measured to be 0.0523 dB/mA. Figure 5(d) shows the IV curve measured with no guided light, using a Source Measurement Unit (SMU, Keithley 2450). To fit the data, the p-i-n diode was modeled as an ideal diode (Shockley equation) in series with a resistor; we extracted a series resistance of 17.6 Ω. Device destruction occurred when injecting more than 110 mA.

 

Fig. 5 (a) Optical microscope image of VOA, showing the metalization above the p- and n-doped slab regions surrounding the optical waveguide. (b) Simulation of the injection current into the waveguide cross-section calculates the current density profile (Silvaco ATLAS). (c) Comparison of the simulated and the measured results of optical attenuation versus injected current when light was transmitted in the waveguide. (d) Comparison of the simulated and the measured I–V curves for the p-i-n junction in the absence of guided light.

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To compare the measurement with a theoretical model, we performed a simulation using Silvaco Atlas of the cross-section shown in Fig. 5(b). The intrinsic region in the waveguide core was assumed to be lightly p-doped with a concentration of 1.0 × 10¹⁵ cm⁻³ (consistent with the sheet resistivity of the SOI wafer). The p and n regions were implanted to a concentration of 2.1 × 10²⁰ cm⁻³ and 2.9 × 10²⁰ cm⁻³, respectively. Figure 5(b) shows the current density calculated from the electron and hole concentrations when a voltage of 1.6 V was applied across the contacts. Next, Lumerical MODE Solutions eigenmode-expansion solver was used to calculate the optical mode, given the perturbed refractive index profile as a result of the injected carriers. From the imaginary part of the modal index, we calculated the attenuation through the pi-n diode. Despite accounting for a large variety of physical phenomena (concentration-dependent Shockley-Read-Hall recombination, Fermi-Dirac statistics for reduced carrier concentration in heavily-implanted regions, surface recombination velocities, band-gap narrowing with Klaassen’s unified low-field mobility model for heavy implantation [23], and Auger recombination), the simulation results predicted a lower attenuation efficiency than was measured. While we do not know the definite reason for the discrepancy at this time, one possible reason might be that the experimentally-achieved carrier mobilities were lower than simulated, and may have resulted in a longer carrier lifetime, which is known to increase the optical attenuation [11].

5. Dual time-constant frequency response

The frequency response of the device was obtained by driving the device with a sine wave (generated by a Stanford Research SG380 Series RF Signal Generator), and measuring the waveform of the transmitted light using a fiber-coupled avalanche photodetector with 7 GHz bandwidth (Terahertz Technology TIA 4000). Voltage was app lied to a non-wire-bonded device using a multi-contact wedge (Cascade Eyepass). Figure 6 shows a two-plateau type of response, with a 3 dB bandwidth of the thermo-optic response limited to 8.3 kHz (rise/fall time τ = 19 µs, typical for thermally-tuned microrings), corresponding to the range in switching speed where the full attenuation was still possible. Beyond that, attenuation from the PIN diode exhibited a carrier-lifetime limited response of around 28 MHz (rise/fall time τ = 5.7 ns, comparable to standard, non-defect-implanted p-i-n diodes). These measurements clearly show that both the thermal and the current-injection effects play a significant role in the overall operation of the VOA.

 

Fig. 6 The frequency response measured by driving a sinusoindal waveform into the p-i-n diode, thus modulating the transmitted light, and measuring the optical waveform at the output on a photodiode and oscilloscope. The data shows two roll-offs, with the lower frequency roll-off attributed to the thermal effect, and the higher-frequency roll-off attributed to carrier injection.

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6. Discussion

This work demonstrated a way to achieve higher on-off extinction ratios in a compact footprint than a conventional silicon photonic VOA. We demonstrated a two-part device which achieved 40 dB of attenuation by enhancing a short-length (75 µm) p-i-n diode VOA, which achieved about 15 dB of extinction, with a second-order ring filter (footprint approximately 29 µm × 50 µm), whose resonance was shifted thermally.

With the current design, a VOA-alone approach to achieve 40 dB contrast, the same overall on-off contrast as the VOA-and-ring combination, would require a 2× longer structure, and consume 3× higher power. The footprint overhead is actually larger than 2×, since we would require more careful planning to mitigate thermal crosstalk on the chip (e.g., moving components further away from the hotter VOA structures). Thus, the VOA + ring combination can be an attractive alternative. However, if footprint and power consumption are not limitations, or if speed is the highest priority, it is undoubtedly simpler to make the VOA longer than to rely on a combination of a VOA and a parasitically-heated resonator.

In this version of the chip, four p-i-n diodes of the same design were placed at different distances from their respective rings, and the heating of the rings by the current in the p-i-n junction was not optimized. Future optimization will focus on minimizing the insertion loss, which depends not only on the width of the intrinsic region of the p-i-n waveguide segment, but also on the design and loss of the microring and ring-waveguide couplers, and on improving the speed and efficiency of the thermal heating, which depends on the overall physical layout of chip, including heat-diffusion and dissipation. Modeling all these combined multi-scale and multi-physics effects—carrier injection, thermal heating and diffusion, and optical propagation through both waveguide and resonant structures—requires advances in simulation techniques and algorithms. A preliminary model based on the concept of thermal resistance is presented in Appendix A2.

Appendix

A1. Transmission spectra

 

Fig. 7 Measured transmission spectra for VOA A, at six values of the VOA injection current, showing the progressive red-shifting of the microring spectra, as well as the increasing baseline attenuation from the p-i-n diode section alone. The combination of these two effects give rise to the behavior at a fixed wavelength shown in Fig. 4.

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Fig. 8 Measured transmission spectra for VOA B, at six values of the VOA injection current, showing the progressive red-shifting of the microring spectra, as well as the increasing baseline attenuation from the p-i-n diode section alone. The combination of these two effects give rise to the behavior at a fixed wavelength shown in Fig. 4.

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A2. Circuit model of heat transfer

Although a complete thermal model lies beyond the scope of this paper, we present some relevant insights here, using the simple concept of thermal resistance circuits. There are three questions we address:

1. How hot does the VOA section typically get?
2. How is the heat transferred from the hot VOA to the cooler rings,
3. How hot do the rings get, as a consequence?

Figure. 9(a) shows the circuit model of a heater with oxide cladding, terminated in perfect heat sinks on both the upper and lower surfaces. We take the dimensions of the heater to be the same as the planar footprint of the VOA with electrodes, i.e., L = 50 µm in length and W = 16 µm in (edge-to-edge) width. The thickness of the oxide layer, both above and below the surface of the silicon, is taken to be t_ox = 3 µm. Using the thermal conductivity of oxide, k_ox = 1.5 W/(m.K), we define the thermal resistance θ_ox = t_ox/(k_ox A) where the cross-section area A ≈ 50 µm × 16 µm. (We will refine this approximation shortly.) Thus, θ_ox ≈ 2 × 10³ K/W. Assuming perfect termination (“electrical ground” is analogous to ideal heat-sinking to room-temperature), the two resistances are in parallel and the equivalent resistance is halved. Therefore, when 300 mW of power is dissipated in the heater (the upper-limit of the horizontal axis in Fig. 4 is 100 mA current injection at approximately 3 V forward bias), the temperature of the heater rises by 300 K. Additional thermal impedances at the boundary will raise the temperature further. This simple calculation shows the need to account for temperature-dependent effects in calculations such as shown in Fig. 5. (Answer to question 1).

 

Fig. 9 (a) Simple model of a heater (diode section of VOA), modeled as a hot plate surrounded by a thickness t_ox of silicon dioxide. (b) Model of the separated diode-microring structure. Constitutive parameters are defined in the text. (c) Heat-spreading model.

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To answer the other two questions, we need to model the separated diode-microring structure, and account for additional layers, and in particular, the silicon handle [k_Si = 150 W/(m.K), thickness t_ox = 675 µm], the FR4 PCB [k_Si = 0.25 W/(m.K), thickness t_ox = 3.2 mm], and convection to air [h = 10 W/(m².K)]. (We did not include the ENEPIG (gold) pad or die-adhesive epoxy in this model.) The heater section (diode) and the microrings (monitor) are assumed to be separated by a distance L_wg of fully-etched silicon waveguide, whose cross-section area is A_wg = 0.5 µm × 0.25 µm.

In drawing Figure. 9(b), we have separated the vertical and horizontal pathways; this greatly simplifies the model. However, because of the large thicknesses of the Si substrate and the FR4 region, we need to model heat spreading in order to better define area, A, which is necessary for the calculation of each thermal resistance.

In an unbounded three-dimensional medium (coordinate label r ∊ ℝ³), the steady-state solution of the heat diffusion equation is u′ + ℒ [u] = F where u is the temperature, u′ is its temporal derivative, the operator ℒ = −α∇² (α is the thermal diffusivity, i.e., the thermal conductivity divided by the product of the specific heat and mass density) and the source F is taken as concentrated at the origin and constant-valued in time. As t → ∞, the solution converges to the potential-type distribution, $u(\mathbf{r})\simeq \sqrt{\pi }/(4\alpha |\mathbf{r}|)$.

Given this 1/|r| spreading factor in three-dimensional space, a point-localized heat source located at a distance t from a plane will create a hot spot whose full-width (diameter) at half-maximum (temperature) is 2t, i.e., the heat spreads approximately at a 45-degree angle, as shown in Figure. 9(c) between each pair of interfaces e.g., between the oxide-substrate interface and the substrate-PCB interface, and also between the upper and lower PCB interfaces.

Since the dimensions of the hot diode are much smaller than the Si substrate thickness, this approximation is justified. Defining A simply as 2t × 2t would over-estimate the area near the constricted end of the cone; thus, we take one-half of the spreading factor along each dimension, and define A ≈ t × t in the calculation of θ. (It is hard to justify this strong approximation too much further; however, for elliptic partial differential equations, when discretized, the value at the central lattice point is the arithmetic mean of the values at the neighbors.) Of course, we used the full spreading factor to define the baseline area for the “image” of the heat source on each planar boundary outwards from the diode.

In this way, we calculate the various thermal resistances shown in Figure. 9(b), so that

(1)$${\theta }_{\text{Si},\mathrm{V}}=\frac{t_{\text{Si}}}{k_{Si}(L+2t_{\text{ox}}+t_{\text{Si}})(W+2t_{\text{ox}}+t_{\text{Si}})}=8.8K/W$$

(2)$${\theta }_{\text{FR}4}=\frac{t_{\text{FR}4}}{k_{Si}(L+2t_{\text{ox}}+2t_{\text{Si}}+t_{\text{FR}4})(W+2t_{\text{ox}}+2t_{\text{Si}}+t_{\text{FR}4})}=608K/W$$

The convection resistance is calculated as

(3)$${\theta }_{\text{conv}}=\frac{1}{h(L+2t_{\text{ox}}+2t_{\text{Si}}+2t_{\text{FR}4})(W+2t_{\text{ox}}+2t_{\text{Si}}+2t_{\text{FR}4})}=1648K/W.$$

To model the heat spreading horizontally along the silicon substrate, we use the approximation that the relevant area is that defined by the image of the heater at the oxide-silicon interface (i.e., as it that heat source were simply turned by 90 degrees).

(4)$${\theta }_{\text{Si},\mathrm{H}}=\frac{L_{\text{wg}}}{k_{Si}(L+2t_{\text{ox}})(W+2t_{\text{ox}})}=2.7\times {10}^{3}K/W.$$

(Since the resultant A in the FR4 layer already encompasses a distance greater than L_wg, we did not include a lateral “θ_FR4−H” resistance in this model.) The thermal resistance of (lateral) heat transfer along the silicon waveguide itself is

(5)$${\theta }_{\text{Si},\text{wg}}=\frac{L_{\text{wg}}}{k_{Si}{A}_{\text{wg}}}=2.7\times {10}^{7}K/W,$$

which, for L_wg = 500 µm (or, in fact, any reasonable value, L ≫ λ, the optical wavelength) is much higher than the resistance of the alternative path through the substrate. Therefore, the heating between the diode section of the VOA and the microring section does not occur along the silicon optical waveguide, but through the substrate layer. (Answer to question 2).

Finally, we solve the circuit model shown in Figure. 9(b) when 300 mW is dissipated at the diode section for two cases, L_wg = 500 µm (VOA A) and L_wg = 350 µm (VOA B), calculating that the temperature V_X at the microring section should be 55 K (VOA A) and 64 K (VOA B). As stated earlier, the measured temperature shifts (from the resonance shift and the simulated waveguide effective index) were 55 K (VOA A) and 62 K (VOA B). The simple model therefore gives a useful approximation to the behavior seen in the measurements, and can serve as a guide to more detailed simulations. (Answer to question 3).

Thus, using an FR4 PCB (a poor conductor of heat) rather than a metal-backed thermo-electric cooler has a significant effect on heat sharing between the diode and the microring sections. In principle, efficient heat conduction pathways can be designed between different portions of the microchip layout in the PCB to harvest heat only where desired, and heat-sink the rest pf the chip. (Heat sharing traces can also be designed in the metal wiring embedded in the oxide above the device layer).

Funding

National Science Foundation (NSF) (EEC-0812072, 1525090); National Aeronautics and Space Administration (NASA, Space Technology Research Grants Program, Early Stage Innovations); Texas Instruments Kilby Labs.

Acknowledgments

Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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