In this article a new method is presented that allows for low loss implementation of fast carrier transport structures in diffraction limited photonic crystal resonators. We utilize a ‘node-matched doping’ process in which precise silicon doping results in comb-like shaped, highly-doped diode areas that are matched to the spatial field distribution of the optical modes of a Fabry-Pérot resonator. While the doping is only applied to areas with low optical field strength, the intrinsic diode region overlaps with an optical field maximum. The presented node-matched diode-modulators, combining small size, high-speed, thermal stability and energy-efficient switching could become the centerpiece for monolithically integrated transceivers.
©2013 Optical Society of America
Electronic data processing relies on charge carrier transport in silicon-based integrated transistors which have experienced a feature size reduction by three orders of magnitude over the last 40 years. This was possible due to the fact that the fundamental limit given by the small electron wavelength (few nanometers) has not been reached in today’s fabrication processes. The carrier distribution and their dynamics can thus be controlled very precisely even in very small areas via the doping geometry and the applied voltage.
While the benefit of electronics lies in the small feature size of highly complex circuitry for data processing, efficient data transmission over distances of more than a few meters suffers from very high signal attenuation for bandwidths of more than several gigahertz. Photonics on the other hand provides high bandwidth data transmission over hundreds of kilometers. Silicon as a medium for integrated optics, allows for complex photonic integrated circuits with highest integration levels . Due to the high mode confinement in silicon waveguides the minimal feature size amounts to a few hundred nanometers and bending radii of 5 µm at an optical wavelength of typically 1.55 µm . In comparison to the feature size of electronic transistors, the guided mode size is still more than an order of magnitude larger. Integration of small electronic structures into active photonic circuits usually leads to a conflict with the optical mode size inside the nano-waveguides causing high free-carrier absorption and scattering losses for the optical wave.
As a consequence, the goal for developing integrated electro-optic components must be to find the optimum merge between electronics and photonics, combining the extreme compactness of electronic structures with the ability to control light for ultra-high bandwidth transmission. Here, we present a novel method and its application in a device that allows for spatially and temporally controlled carrier transport in and out of an optical standing wave. Precise carrier injection into the anti-nodes of the field distribution results in highly efficient light modulation, enabling extremely compact and power efficient modulators.
Photonic-electronic integration is a core technology for mastering the ever increasing bandwidth demands in many network and interconnect applications. Low-cost electro-optic modulators are key components for electronic-to-optical bit pattern translation in next generation high-speed optical interconnects . Although the dramatic improvement of silicon photonic technology has shown its potential for these applications, a fully integrated modulator, combining small size, high-speed and stability, has yet to be demonstrated. On the background of silicon based electronics industry, it would be attractive to develop a single fabrication process for both electronic and photonic elements which can be directly derived from the silicon CMOS technology. For this work we used standard electronic fabrication technologies. The devices were processed in a high-performance BiCMOS foundry.
In this article we outline the principle of the node-matched doping method before presenting experimental results of spectral resonator characteristics, free-carrier dynamics and optical modulation capabilities of electro-optically matched modulator structures.
Light modulation in the silicon devices presented in this article is achieved via the free-carrier plasma dispersion effect (PDE), which describes the change of the absorption and the medium refractive index with the free-carrier density . In order to control the injection or depletion of electrons and holes inside the propagation volume of the guided light, diode structures are placed around the waveguide, where the applied voltage level determines the free-carrier density. High doping levels in the diode contacts lead to a stronger PDE but are limited by the detrimental impact on the optical insertion losses.
Two methods to exploit the PDE for amplitude modulation need to be considered. Firstly, the induced absorption change directly translates into an amplitude modulation of the transmitted radiation which can be observed by an offset in the peak transmission. Secondly, the refractive index change acts on the signal phase and thus requires an interferometric structure, like a resonator, to be utilized for amplitude modulation as well. In a resonator, the optical field forms a standing wave with alternating localized zones of low and high intensity, called nodes and anti-nodes, respectively (see Fig. 1(a)). The corresponding transmission peak is determined by the mirror reflectivity as well as their spacing and shifts with changes in the refractive index. Thus, the applied modulation voltage allows modifying the transmission at a given wavelength apart from the absorption changes. This relation is referred to as the spectral transfer function . The modulator device presented in this article includes periodic structures consisting out of etched holes inside a silicon rib waveguide that lead to a variation of the effective refractive index [6,7]. These one-dimensional photonic Bragg-gratings serve as mirrors of a Fabry-Pérot (FP) micro-cavity .
The crucial point of this work was to match the diode geometry to the spatial distribution of the optical field inside the FP-resonator. This was achieved by placing alternating comb-shaped p+- and n+-doped p-i-n-diode regions inside the waveguide core (see Fig. 1(a)) with the comb segments being located in the nodes of the optical standing wave, whereas the free-carrier distribution induced by the driving voltage is overlapping with the anti-nodes, where the optical field strength is maximal (see Fig. 1(b)). This doping arrangement, for which we propose the term node-matched diode (NMD), significantly reduces the optical losses and the optical field tolerates very high doping levels of 1020 cm−3 without suffering high loss penalty. As a consequence, the small overlap of the light field with the doped volume enabled us to reduce the width of the intrinsic region below the size limit given by the optical mode. The realization of our modulator approach was motivated by previous simulations  and has resulted in the smallest gigabaud injection modulator structure demonstrated so far. A vertical cross-sectional cut through the device and a schematic illustration are shown in Fig. 1(c) and Fig. 1(d). Both, size reduction of the intrinsic region and high electric field strength strongly increase the kinetics of the carriers and finally the achievable modulation bandwidth. The electro-optic effect is significantly enhanced through the high dopant concentration which can be exploited to shorten the modulator length. Additionally, the NMD device can be operated with low power consumption and driving voltage that can be readily provided by standard silicon driver electronics, which is essential for monolithic co-integration of silicon photonic structures and electronic circuits.
2. Device fabrication and characterization
The modulators were fabricated in a 0.13 µm SiGe BiCMOS production line at IHP GmbH in Frankfurt (Oder), Germany using 200 mm SOI wafers and 248 nm DUV lithography. Within the 220 nm thick silicon device layer of the SOI substrate the nano-wires are embedded (Fig. 1(c) and 1(d)). The SOI rib-waveguides with dimensions of 220 × 450 nm2 , including the micro-cavity components are designed using a single mask and fabricated in a shallow trench process. The etching depth of the photonic structures is 170 nm, with a 50 nm high remaining slab for carrier injection/depletion on top of the underlying BOX layer with a thickness of 2 μm. The doping level inside the p+- and n+-doped regions was 1·1020 cm−3. Input and output light coupling is achieved via grating couplers, each with 5 dB losses and optimized for 1550 nm wavelength. The micro-cavities are formed by one-dimensional photonic crystals in a FP-structure consisting of tapered holes  with a lattice constant of 350 nm and diameters of up to 180 nm. The taper section leads to a mode adaptation between the waveguide and the photonic crystal mirror due to a gradual refractive index transition, thus decreasing the losses.
Block I in Fig. 2 represents the generation of the linearly polarized cw light. The tunable cw laser source used in our measurements is an Agilent ECL model 81940A with a tuning range from 1520 nm to 1630 nm in 1 pm steps and maximum 14 dBm output power. The output radiation is transmitted through a single mode fiber with 125 µm cladding and 9 µm core diameter, an optical isolator, polarization controllers (PC) and a polarizer. It is coupled into the waveguide including the DUT via a grating coupler (GC) (Block IV). Thermal stabilization is provided by placing the DUT on a copper block whose temperature is regulated by a Peltier element and a Profile LDC 400 temperature controller.
The sources for the electrical signals applied to the DUT vary depending on the performed experiments. Signal transmission for recording of eye diagrams is shown in Block III. It is controlled by a 4-channel Anritsu data generator MP1800A (Data Gen.) with 12.5 GBaud symbol rate per channel. The four channels are combined by an Anritsu M1821A Multiplexer (MUX) to one channel with a maximum symbol rate of 50 GBaud. The signals are attenuated (Att.) to prevent saturation, before being passed to an SHF 806E amplifier (Amp.) in order to obtain signals with maximum amplitude of 5 V. We then use a variable attenuator (var. Att.) and a Picosecond PulseLabs 5575A bias tee (Bias) to vary the amplitude and the DC voltage offset. For cut-off frequency determination we employed a Hittite sine wave generator HMC T2100 (SWG) and the above mentioned bias tee (Block II). The signal is fed to the DUT by an RF ground-signal-ground probe.
The modulated signal is then coupled out via the same type of grating coupler. One per cent of the signal is tapped via an 1%/99%-optical coupler (OC) to a power meter. The coupling stability is improved by a feedback system (Thorlabs Nanotrak TNA001) consisting of the power meter (PM), a translation stage controller (TSC) and the two 3-axis translation stages (TS) on which the coupling fibers are mounted.
The spectral intensity distribution for passive and temporally integrated transmission properties is recorded by an optical spectrum analyzer (OSA) (HP 70952B) (Block V).
For temporal measurements (Block VI) the remaining 99% of the modulated signal are amplified in an erbium doped fiber amplifier (EDFA) (Amoco 1.5-Amp). An optical tunable band-pass filter Yenista Xtract 150 to 650 (BPF) is used to filter the amplified signal before detection by a Newport D15-IR photo diode (PD). The electrical diode signal is amplified by using an SHF 806E (Amp.). The extinction ratio of the signal is determined without the electrical amplifier. Finally, the output signal is analyzed and recorded with an Agilent Infiniium DCA J86100C oscilloscope with 70 GS/s sampling rate.
Considerations about the longitudinal mode matching for the doping regions led to a period of p+- (or n+-) doped comb segments of 590 nm, according to the optical wavelength inside the waveguide (λ0/neff), where λ0 is the free-space wavelength of 1550 nm. The cavity length of higher order filters is calculated by lc,m = lc,1 + (m - 1)λ0/2neff. The integer m gives the order of the higher order cavities. For cavities with non-tapered mirrors lc,1 can be estimated to 1.5a where a denotes the lattice constant. The distance between the centers of the innermost holes of the cavity defines the cavity length lc,x . Implementing tapered mirror structures introduces changes of the photonic band gap as well as the transmission peak positions which cannot be easily considered by this simple expression. In this case 3D simulations are required. Each comb segment has a width of 130 nm with a penetration depth into the waveguide of 200 nm.
The experiments have been performed using a linearly polarized cw light source, coupled to the device-under-test (DUT) via grating couplers as described in the device fabrication section above. Rectangular modulation signals for the recording of eye diagrams were produced from a data generator with 50 GBaud bandwidth.
Subtraction of the passive NMD-modulator transmission spectrum from a similar blank waveguide without modulator yields the calibrated output spectrum with a loss related to the modulator structure of 3.5 dB. DC measurement of the shifted peak position in the modulator on-state is prevented by the fact that the injection process is accompanied by an increase of temperature resulting in opposing spectral shifts. However, due to inertia, thermal effects at modulation bandwidths higher than a few hundred kHz lead to a non-oscillating voltage dependent shift of the transmission spectrum and the PDE becomes the dominating mechanism for spectral modulation which was recorded by an optical spectrum analyzer during modulation operation at 50 MBaud.
3.1 Fabry-Pérot micro-resonator properties
In order to effectively exploit the diode related bandwidth improvements when implementing an NMD into a waveguide structure, the presence of a standing wave with according nodes and anti-nodes in a resonator is required. As an additional benefit, resonator structures allow for a dramatic reduction of the modulator footprint while maintaining long effective interaction lengths by multiple roundtrips.
The applied injection voltage effectively changes the optical length of the resonator and consequently its spectral transfer function so that optical radiation with a wavelength at a resonator transmission maximum experiences high losses during the driver signal high-state when the transmission peak is shifted by carrier injection. This additional increase of modulation contrast compared to the intrinsic absorption loss modulation by the diode alone is particularly helpful to obtain faster switching rise times for the transmitted signals. Within a DC voltage range from 0 V to 2 V, a linear refractive index change Δn and a linear wavelength shift Δλ can be approximated as shown in Fig. 3(c). The voltage dependent spectral blue-shift amounts up to 14 nm at 2 V for a corresponding resonator cavity with a length of 1.9 μm amounting to 8.8 μm for the complete FP-structure including the photonic crystal mirrors. The photonic structures are embedded in a single-mode nano-waveguide with dimensions of 450 × 220 nm2 and an effective area of the fundamental TE mode of approximately 0.12 µm2. Figures 3(a) and 3(b) depict the longitudinal and transversal distribution of the optical field inside the FP-resonator waveguide obtained from Finite-difference time-domain method simulations.
The shown wavelength shift was determined by temporally integrating the spectral transmission from a broad-band continuous wave light source during modulation operation with a rectangular signal at 50 MBaud. The recorded spectrum, depicted by the black line in Fig. 3(d), shows the sum of the driver low-state spectrum and the driver high-state spectrum. The peak at 1546 nm wavelength corresponds to the driver low-state while the 1537 nm peak belongs to the driver high-state at 1.6 V forward bias voltage, respectively. A wavelength difference of Δλ = 9 nm has been determined between both states. The carrier transport during modulation leads to a heating related red-shift which occurs on a much longer time scale in the microsecond range. Regarding the passive cw transmission spectrum without applied voltage (see grey line in Fig. 3(d)), this thermal effect can be estimated to about Δλth = 6 nm. During modulation operation this red-shift can be assumed as a quasi-uniform spectral shift.
The peak transmission in the passive spectrum yields 3.5 dB insertion losses for this modulator structure. A 3 dB offset to the driver low-state transmission peak (black line in Fig. 3(d)) can be associated to the 50% duty cycle between high- and low-states, assuming negli-gible transition times between both states. When driving voltage is applied to the NMD, free-carrier absorption causes optical losses of 5 dB as is evident from the difference in maximum transmission of the high- and low-state peak in the integrated transmission spectrum, designated by the dashed red and black vertical lines, respectively. The additional 5 dB losses at the modulation wavelength of 1546 nm are attributed to the wavelength shift of the transmission spectrum. This amounts to a total modulation contrast of 10 dB which was verified by corresponding eye diagrams.
3.2 Comparison of homogeneous and node-matched diodes
The appropriate choice which diode type to implement in our concept was based on the consideration to combine a strong PDE inside a small structure with low insertion loss at fast modulation speed. The diode in electro-optic modulators is commonly realized as a p-n-type  which requires a reverse bias voltage to actively deplete the free-carrier concentration or as a p-i-n-diode  where carriers are injected into the intrinsic region. Hence, these two device classes were coined depletion and injection type modulators. The depletion of carriers allows for intrinsic modulation bandwidths of around 50 GHz  but the weakness of the electro-optic effect requires large structures with high absorption of the transmitted radiation inside the p-n-junction area. The node-matched diode designs are based on p-i-n-type diodes so that the intrinsic region allows guiding the light in a volume with very low free-carrier density when no voltage is applied. Injection based modulation allows for high doping concentrations of up to 1020 cm−3, resulting in refractive index changes of Δn ≈10−2 which is about three orders of magnitude higher than for carrier depletion. Diode structures can thus berealized with much shorter length. The carrier dynamic in p-i-n-diodes depends on the electric field strength and the recombination distance which are affected by the width of the intrinsic diode region, the waveguide geometry, and the applied voltage in relation to the electron and hole mobility of about 1400 cm2V−1s−1 and 450 cm2V−1s−1 in silicon, respectively [15,16]. In previous approaches, excessive optical loss due to high doping levels could only be avoided if the waveguide was positioned in the intrinsic region and the doped regions are placed outside the waveguide so that the absorption of the guided mode is minimized. Therefore, low loss operation could only be achieved at the expense of limited intrinsic modulation bandwidth of about 250 Mbps due to the large area of the intrinsic region of the implemented p-i-n diodes . For a similar p-i-n-diode inside an asymmetric Mach-Zehnder structure, Green et al. already demonstrated transmission of data signals at forty times the intrinsic diode bandwidth. A data rate of 10 Gbps could be achieved by using an appropriate electrical driver design . Downsizing of the intrinsic region leads to higher diode speed – however at the cost of extremely high absorption loss penalty. NMD modulators are not subject to this restriction allowing a reduction of the intrinsic region width down to 190 nm which corresponds to the undoped space between two neighboring p+- and n+-doped NMD comb segments.
The unique geometries of these modulator p-i-n-diodes suggested the characterization of the frequency dependent optical response of the diode. We experimentally compared the intrinsic small signal cut-off frequencies of an NMD and a conventional state-of-the-art injection diode with a homogeneous intrinsic gap of 1.2 μm  in order to demonstrate the respective diode performance independently from additional improvements by the resonator spectral transfer function. Both diodes with a length of 1.9 µm are implemented in identical resonator structures with 8.8 μm length. Additional losses from the NMD compared to the homogeneous diode amount to 0.9 dB. The penetration depth of the NMD comb segments into the waveguide is 200 nm which was found to be the optimal balance between residual absorption from the doped comb regions and fast transition times. The corresponding resonator footprint is about 4 µm2. Including the diode contacts with the vias to the metal layer, the footprint was still kept below 100 µm2. Thereby, the presented NMD modulator is the smallest silicon electro-optic modulator with gigabaud bandwidth so far.
The low-pass filter characteristics in Fig. 4(a) of the intrinsic speed of the diode structures have been investigated by an S21-parameter test of the optical response at low driver signal amplitude of 0.2 Vpp and 1.1 Vbias from a sine wave generator in order to decouple the electrical from the spectral resonator properties. In this way, the influence of the spectral transfer function is minimized and the modulation takes place within an approximately linear regime of the transmission peak shift. These measurements have been performed without reverse bias voltage to determine the NMD bandwidth in pure injection operation. At 12.5 GHz, the sensitivity of the photo diode limited the bandwidth measurements.
The −3 dB cut-off frequency of 850 MHz for the NMD was found to be 4.6 times higher than for the homogeneous diode with a cut-off frequency of 185 MHz (Fig. 4(a)). Higher frequency signals above the cut-off frequency experience less attenuation in the NMD than in homogeneous diodes which is expressed by the respective attenuation slopes of −7.95 dB/decade and −9.73 dB/decade. The attenuation level of the NMD at 12 GHz is met by the homogeneous diode already at ten times lower frequencies. As a consequence, the signal to noise ratio (SNR) at high frequencies is greatly improved, thus enabling high bandwidth data transmission. The effective bandwidth limits of conventional and NMD-modulators with 8.8 μm length have been investigated in Fig. 4(b) and 4(c) at 12.5 GBaud and an applied voltage of 2.7 Vpp with 0.45 Vbias. In agreement to the large attenuation difference between both devices for small signal driving voltage especially at high bandwidths, the modulator with the homogeneous diode does not provide sufficient modulation contrast. The NMD-modulator however operated at an extinction ratio of 1.7 dB and SNR of 8.9. It should be mentioned that for large driving voltage, the modulation bandwidth does not solely depend on the intrinsic diode properties anymore. It is rather governed by a combined effect comprising the diode bandwidth together with a voltage dependent increasing impact of the spectral transfer function on the overall modulation bandwidth . These bandwidth improving effects of the NMD concept are becoming increasingly more pronounced compared to homogeneous diodes towards higher modulation speeds. Although the resonator geometry is identical for both modulators, the NMD improves the diode bandwidth as well as the spectral transfer function due to larger carrier concentration changes inside the intrinsic region.
The discussions up to this point are based on a FP-resonator with an unloaded Q-factor of 244 according to the Q-factor definition given by ν0/Δν, with a resonance frequency ν0 of 194 THz and a transmission linewidth Δν of 794 GHz. Higher modulation contrast and steeper edges can be achieved from larger Q-factors. On account of the increased intrinsic bandwidth of node-matched diodes, the demands for bandwidth improvements by the spectral transfer function are moderate so that the Q-factor can be about hundred times lower than for ring resonators with Q-factors being typically in the tens of thousands when used for high bandwidth modulation . This results in low temperature sensitivity. In general, a compromise must be found between modulation bandwidth enhancement by the spectral transfer function and practical considerations regarding thermal stability and fabrication tolerances .
3.3 Transition times of an NMD modulator
In order to translate the fast electrical switching capabilities into high speed optical modulation, the resonator geometry was tailored to provide a higher Q-factor of 390 for improved transition times  while keeping the temperature sensitivity on a tolerable level. For this purpose, we designed an extended NMD modulator with 35 µm length and 30 µm cavity length. The NMD p-i-n-junction geometry is the same as was used in the shorter devices with equal small-signal cut-off frequencies. Detailed studies of the temporal transition behavior between on- and off-states have been performed. The rise and fall times of the modulated optical signal result from the injection and depletion process, respectively in combination with the spectral transfer function. Both are voltage dependent due to the increase in the electrical field strength, so that signal edges with a faster time constant are obtained for higher applied voltage [19,20] (see Fig. 5(a) and 5(b)). The possibility of significant transition time reduction through implementing an NMD compared to ahomogeneous diode had already been indicated by dynamic simulations, preceding the fabrication of the presented devices. Experimental transition times and eye diagrams have been measured and are described in the following.
A periodic ‘10’ signal without pre-emphasis was applied to the devices to determine the voltage dependence of the 90%-10% rise and fall times at 400 MBaud modulation bandwidth as shown in Fig. 5(c). The bandwidth was sufficiently high to avoid oscillations of the transmission spectrum from thermal variations. Nevertheless, a constant thermal shift with increasing voltage still needs to be compensated at each voltage step by tuning of the wavelength and thus operating with a similar spectral transfer function. Carrier injection into the waveguide is obtained by applying a voltage Ufb in forward direction while a reverse bias voltage Urb is used to sweep out the carriers. A minimum forward bias voltage of 0.8 V is required to obtain a distinct modulation pattern. Consequently, pure injection operation was performed for forward bias voltages between 0.8 V and 2.2 V without reverse bias voltage. In the opposite case, a fixed forward bias voltage of 1.4 V has been applied and the reverse bias voltage was tuned from 0 V to 3.6 V.
In order to reduce the influence of detector noise, the eye diagrams in Fig. 5(d) and 5(e) and the SNR have been measured with a periodic ‘010’ electrical signal after electrical amplification while the extinction ratios are calculated from measurements without amplification. The same conditions have been applied to obtain the eye diagrams presented in Fig. 4(b) and 4(c).
The fall time at a Urb of 0 V in Fig. 5(a) rises with higher forward bias voltage since a higher free-carrier density inside the intrinsic zone must be depleted and causes strong Coulomb scattering which prolongs the depletion process. Active carrier depletion by applying a reverse bias voltage as shown in Fig. 5(b) reduces the free-carrier lifetime and therefore the fall time. Applying a Ufb of 1.4 V and a Urb of 3.6 V leads to a minimum rise time of 141 ps and a minimum fall time of 46 ps representing a fourfold reduction of the fall times compared to a Urb of 0 V. Here, the reverse bias voltage leads to an increasing contrast of the carrier concentration between the on- and off-state which in turn increases the blue-shift of the transmission peak so that the rise time is lowered even further. Rise and fall times both benefit from the NMD design which can be attributed to different effects. During the rise time, carriers are injected into the intrinsic region which requires a voltage in forward bias direction exceeding the height of the potential barrier. The reduction of the intrinsic region size in NMD devices increases the electric field strength and therefore the acceleration of the injected carriers. Furthermore, the propagation distance of the carriers to the optical mode centre is shortened. The modulator fall time is defined by the recombination time of the injected carriers. In homogeneous diodes with large intrinsic regions, the recombination is mainly determined by interface recombination during the large path length between the optical mode field and the doped regions . Under the conditions given in Fig. 5(b), the fall time in similar conventional FP-modulators was always above 290 ps which is about six times slower than for NMD modulators, showing the intrinsic limitations of the homogeneous diode design. In NMDs on the contrary, recombination predominantly takes place in the doped p+- and n+-regions inside the waveguide core. Consequently, node-matched doping shows a way to overcome the mode size limitation for the integration of diode and waveguide, hence pushing the modulation bandwidth limit.
NMD-modulators exhibited high eye diagram performance with an extinction ratio of 2.9 dB and an SNR of 12 at 12.5 GBaud. The device operated even at 25 GBaud with an extinction ratio of 1.3 dB and a SNR of 9. In both cases the operation voltage was set to 3 Vpp with 0.5 Vbias. Corresponding eye diagrams are presented in Fig. 5(d) and 5(e). Within a temperature range of 20°C to 40°C, the SNR of 9.5 of the NMD-modulator at 10 GBaud is very constant and its variation ΔSNR is below one.
The high refractive index changes, observed in our devices (see Fig. 3(c)) exceed the values reported for other p-i-n-diode injection modulators in silicon [7,17], mainly due to a lower contact resistance. The corresponding wavelength shift leads to a pronounced temporal transmission variation, which is expressed by the spectral transfer function. Additional insertion losses of less than 1 dB for an NMD in a micro-cavity FP-resonator compared to a homogeneous diode confirmed that node-matched doping is a suitable method to drastically reduce the intrinsic diode region size without the extremely high losses that would otherwise prevent miniaturization of conventional homogeneous diodes from practical applications.
Between the comb segment centers and edges, the doping concentration decreases gradually by diffusion processes. Thus, the absorption losses result from the overlap integral of the doping profile and the intensity distribution of the standing wave. For the described structures with 130 nm segment width, a tolerance of about 50 nm for the comb segment positions in relation to the optical field nodes ensures that the losses are not increased significantly. However, the absolute values depend on several additional parameters like the segment and resonator length, the resonator Q-factor, doping concentration, and the operating wavelength. In the 8.8 µm long modulator presented in Fig. 3, 1.6 dB loss difference between node-matched and λ/4 shifted comb segments occurs. For longer resonators and higher Q-factors this value can be significantly higher. In case of the 35 µm long modulator used for the results shown in Fig. 5, the loss difference amounts to 3 dB.
The advantages of a smaller intrinsic diode region have been demonstrated by about five times higher cut-off frequencies as shown in Fig. 4(a). The slope of the NMD indicates the efficient injection and depletion of the charge carriers. Hence, lower driver voltage is required to obtain modulation at the same signal quality. In reverse, for a given voltage the maximal modulation bandwidth is extended. Optimization of the resonator geometry with an improved spectral transfer function is an additional way to achieve higher modulation speed which is supported by the experimental results presented in Fig. 5. The gain in modulation performance in comparison to the shorter NMD modulator is related to the difference in their spectral transfer functions.
At present we have focused on the investigation of the fundamental modulator properties. High bandwidth modulation of periodic signals was demonstrated, but in order to achieve data transmission, an appropriate electronic driver design for non-return-to-zero (NRZ) operation needs to be employed. Such a design encompasses control algorithms for an overdrive forward bias voltage at the rising edge of the electrical modulation signal which is routinely utilized to increase the modulation bandwidth of injection modulators and is referred to as pre-emphasis .
A few remarks regarding the power consumption in our NMD modulators will be given at this point to clarify the associated operating conditions. The total power consumption is calculated for a non-return-to-zero on-off-keying modulation format at a typical bandwidth of 10 Gbps. It comprises the energy for switching from driver low- to driver high-state plus the energy that is required to hold the high-state for the duration of one bit. The required energy scales strongly with the applied voltage. A power consumption of 207 fJ/bit for the 8.8 µm long NMD modulator has been determined, with 31 fJ/bit related to switching and 176 fJ/bit to holding energy per bit. The NMD modulator with 35 µm length operated at an Es of 476 fJ/bit and an Eh of 533 fJ/bit amounting to 1 pJ/bit power consumption. The power consumption must be considered as a worst case scenario where the holding voltage coincides with the switching voltage. This is not the case for non-return-to-zero data transmission due to the implementation of pre-emphasis which allows applying significantly lower injection voltage for holding the driver high-state than for performing the transition to it . Both NMD modulator structures discussed in this article leave room for further developments, especially with regards to the resonator geometry  and the optimal spectral transfer function. Future plans involve monolithic co-integration of photonic circuits and electrical driver units within the BiCMOS process which allows driving signal voltage of up to 3 Vpp.
The NMD modulator concept combines high bandwidth of 12.5 GBaud with resonator footprints of about 4 µm2 and low power consumption of 207 fJ/bit, making it the smallest gigabaud silicon modulator reported so far. The bandwidth potential has been demonstrated in an NMD modulator with 25 GBaud bandwidth utilizing a spectral transfer function with higher edge steepness. Considering furthermore the mature fabrication process of the presented devices on a BiCMOS pilot line, we consider NMD-modulators as future key components for ultra-fast signal modulation in photonic integrated circuits with the possibility to monolithically co-integrate driver electronics and photonics.
This work was supported by the German Federal Ministry of Education and Research (BMBF) under the grants “SiliconLight” (no. 13Ν9734) and “SILIMOD” (no.16V0382). We acknowledge C. Meuer, K. Jamshidi and B. Kuhlow for fruitful discussions, as well as S. Schrader and V. Ksianzou for their support.
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