Thermo-electro-optical analysis of modulator embedded in all-silicon structure

Silicon is the most diffused material for microelectronic industry. We propose a thermo-electrical simulation of an integrated optical modulator realized by ion implantation in SOI wafer. This structure allows to obtain an easier integration with electronic devices.


I. INTRODUCTION
An increasing interest has been devoted in the last years to the fabrication of all-silicon active photonic devices, as modulators, switches, filters and so on.Among the different principles exploited to realize these devices, the variation of the complex refractive index with the injected free carriers, i.e. the plasma dispersion effect, has been shown to be particularly effective, and in fact several electro-optic modulators have been proposed and developed in all-Si and SOI waveguides.
In this work we propose an exhaustive analysis of a device already described in our previous work [1], in particular with the aim to investigate the thermal impact on the electrical and optical behavior, both in static and dynamic conditions.
The chosen process flow allows to realize a planar device, fully compatible with standard bipolar and CMOS circuits.

II. DEVICE STRUCTURE AND OPTICAL ANALYSIS
In Fig. 1 is sketched the whole structure, made up by incoming and outcoming waveguides, needed to carry the light to and from the modulator along the chip, and by the modulator itself.Both the passive waveguides and the free carrier modulator are realizable on the same Silicon-on-Insulator (SOI) wafer, with compatible technological steps.The optical properties of SOI structures are well-described in detail in [1−3].
Modulator single-mode rib structure is obtained with two lateral implanted regions, that allows to obtain a planar device.The process-flow of this optoelectronic device is analyzed using 2-D process simulations software by SILVACO International ATHENA [4].It's necessary to utilize multiple implantations to obtain 1-µm-deep lateral doped regions and spike annealing thermal process, in order to activate the dopant, avoiding to exceed with depth of diffusion.The substrate is a standard SOI wafer and an upper thin SiO 2 cladding can be realized by thermal oxidation, in order to reduce the scattering losses on the air-silicon rib surface.
The active region cross section of the structure, where the free carriers plasma is generated in order to achieve the desired modulation effect, is the elementary cell of a lateral p-i-n diode.

III. ELECTRICAL AND THERMAL ANALYSIS
The 2-D semiconductor device simulation package SILVACO has been employed to investigate the static and dynamic behavior of the modulator, to optimize the interaction between the injected free carriers and the propagating optical guided mode, and to minimize the thermal impact on the optical and electrical characteristics of the device.In particular, ATLAS [8] package has been used to calculate the injected free carriers profiles and temperature distribution into the n -optical channel, for different driving conditions.By means of these data, we can calculate the complex refractive index 2D distribution inside the channel waveguide at λ = 1.55 μm, generated at the same time by plasma-optic and thermo-optic effects.Our first goal is to perform the injection efficiency analysis, in order to find the bias condition for an uniform injected carriers density throughout the region in which the optical mode propagates, suitable to give rise to an useful modulation depth, with the smallest electrical power consumption and thermal dissipation.We must specify thermal boundary conditions for ATLAS lattice heat flow equation solver: in particular, we have imposed two perfect thermal contacts at 300°K on top and bottom of the device, putting us in the optimal condition, although realistic, of good integrated heat sinks on the device, while we have considered adiabatic conditions on the sidewalls.
The novelty of such analysis is in the evaluation of the lattice heat flow in the modulator structure, generated by the electrical operation itself, and related influences on free carriers transport and diffusion dynamic inside the device.Numerical processing of thermo-electric simulations, carried out by MATLAB procedures, returns the spatial distribution of the refractive index with or without thermal effects, according to the following equation, where the distinct plasma-dispersion and thermo-optical effects are clear.
The comparison between the refractive index variations in the center of the optical channel for both cases, reported in Fig. 2 as a function of p-i-n anode voltage, allows us to verify how the thermal effects influence the pure electrical behavior.In particular, from Fig. 2 it can be noted that also for relatively low applied voltage (around 1.5 V), the thermo optic effect can be remarkable, and so it has to be taken in account to simulate the right behavior of an electro-optical devices.Despite that, a right choice of the driving signal level can minimize thermal effects and guarantee correct and useful optical performances.With regard to the proposed devices, for an applied bias of V anode = 1.0 V, which generates a free carriers injection of p ≈ n = 1.67 × 10 +18 cm -3 , the induced temperature increase into the channel is about 2°C.For this driving signal, the discrepancy between refractive index variation with and without thermal effects is very small, because the temperature increasing is limited.At such low bias level the plasma-dispersion effect dominates and the resulting refractive index distribution of the whole structure doesn't support any fully confined mode, but only slab modes are returned from simulations.This fact can be explained looking to the reduced physical refractive index difference between lateral highly-doped regions and central channel filled by free carriers.At V anode = 1.0 V this difference can not guarantee lateral confinement for optical radiation and for this reason it is not possible to find a fully-confined optical mode.Moreover, the optical channel exhibits also a significant attenuation induced by free carriers injection into it.The resulting behavior combines the optical radiation attenuation with the lateral confinement vanishing.
In Fig. 3 are reported the optical power distributions at the center of the channel, for input beam, output beam when the modulator is turned off and when the modulator is driven at V anode = 1.0 V, normalized to the peak input power.It is possible to observe that the output beam for V anode = 0 V shows an attenuation of about 1 dB, as expected from mode-solver analysis, while the modulator in ON state induces a global attenuation of about 46.5 dB or, in other word, generates a modulation depth M ≈ 100%.
Another interesting feature to note in Fig. 3 is the leakage of optical power at left side of the central peak, due to the asymmetric lateral confinement vanishing.At this bias point the total electrical power consumption is 470 μW and the corresponding current I anode = 470 μA.The maximum current density flowing in the modulator is about 47 A/cm 2 , supposing the anode contact area of 1×1000 μm 2 .

IV. DYNAMIC BEHAVIOR
The last phase is the simulation of the dynamic operation of the proposed device.This investigation consists in the evaluation of the plasma injection and depletion time in our electrical structure, and in its heating and cooling dynamic behavior.We carried out the analysis to obtain the switching characteristic of modulator biased with the driving signal applied to the anode and the cathode grounded.In particular, we refer to the steady state condition relative to an applied voltage V anode of 1.0 V, which induces, for a 1000-μm-long active region, an uniform carriers concentration of about 1.67×10 +18 cm -3 .In order to evaluate the turn-on dynamic, the applied driving signal is a step going from V anode = −1.0V to V anode = 1.0 V with a rise time of about 500 ps.In the same way, for the turn-off dynamic analysis, the voltage step goes from 1.0 V to −1.0 with similar fall time.In Fig. 4 is reported a detail of the switching dynamic for both electrical and thermal phenomena.It is worthwhile to notice that the free carriers concentration evolves with typical time of some tenths of nanoseconds, while the temperature arises in some tenths of microseconds.It is possible to define the electrical and thermal rise (fall) time τ r (τ f ) as the time required to move from 10% to 90% (from 90% to 10%) of the maximum value.In our case, we have τ rE ≈ 30 ns and τ rT ≈ 60 μs for the turn-on transient, τ fE ≈ 10 ns and τ fT ≈ 70 μs for the turn-off one.
Through this analysis it is possible to individuate the cut-off frequencies with the aim to decouple the fast electrical performance from slower thermal transient dynamic.Indeed, the free carriers injection in the channel is a very fast process, compared to the thermal heating diffusion inside the guiding layer.In particular, we have a -3dB bandwidth of about 11.6 Mhz for electrical dynamic (limited by the rise time) and 5.8 kHz for thermal one.Given the different cut-off frequency for the two effects, a suitable input signal can reduce the unwanted effect of the temperature when the device is driven to high frequencies.In this section we have dealt the digital operation of the device, that induces an ON/OFF optical switching in which the band limit can be deducted from the rise or fall time.A first possible improvement of this operation method, can be obtained from the device overdrive, for instance with V anode = 2.0 V for a limited time, to allow a most effective filling up of free carriers in the optical channel.
-0.On the contrary, a higher reverse bias can produce faster turn-off transient.A different driving technique, useful to speed up the dynamics, exploiting an analog driving signal, consists in a sort of small signal operation, using bias AC signal superimposed to a DC offset which drives the device to a proper operating point.

V. CONCLUSION
We have analyzed the performance of a Si waveguidevanishing-based optical modulator, based on free-carrier dispersion effect to produce the desired refractive index and absorption coefficient variations.In particular, we have analyzed the thermal impact on the device behavior, both static and dynamic.The SILVACO two-dimensional semiconductor device simulator has been used to analyze the microelectronic process to obtain the modulator structure and electrical operation of the device, with reference to the injected free carriers concentration into the optical channel, its uniformity and the required current density, electrical power dissipation and thermal induced distribution.We have also analyzed the propagation characteristics, that is the insertion losses and the modal operation of the SOI waveguide and the modulator structure.We have optimized the device for maximum injection level for a given applied voltage, that is for the maximum modulation efficiency.The proposed device shows an uniform refractive index variation over the region in which the optical mode propagates, and a high injection efficiency.For a 1000-μm-long active region, we have a M ≈ 100% (waveguide-vanishing effect) for an injection power of 470 μW, and switching time of about 30 ns.All analyzed performances are very promising, compared to similar structures reported in literature.A dimensional scaling of the electrical structure can improve the injection efficiency and increase the bandwidth of the device.
In telecommunication applications there are some interesting areas where a modulator with a bandwidth up to some hundreds of MHz is suitable.In the fiber-to-home and fiber-in the-loop applications, or in the local area network (LAN), a bandwidth of a few tenths MHz is adequate and the very low cost and the integrability with electronic devices are very attractive characteristics.

Fig. 1 .
Fig. 1.Sketch of the whole structure composed by the input SOI waveguide, the active device and the output SOI waveguide.

Fig. 2 .
Fig. 2. Refractive index profile in the middle point of the optical channel versus anode bias, with and without thermal effects.

Fig. 4 .
Fig. 4. Rise time of free charge density and temperature in the optical channel versus time.