Photonic Analog-to-Digital Conversion with ... - Semantic Scholar
Invited Paper
Photonic Analog-to-Digital Conversion with Electronic-Photonic Integrated Circuits F. X. Kärtnera,b, R. Amatyaa,b,d, M. Araghchini a,b, J. Birgea,b, H. Byuna,b, J. Chena,b, M. Dahlema,b, N.A. DiLelloa,d, F. Gana,b, C. W. Holzwarthb,c, J. L. Hoyta,d, E. P. Ippena,b, A. Khiloa,b, J. Kima,b, M. Kima,d, A. Motamedia,b, J. S. Orcutta,b,d, M. Parka,d, M. Perrotta,d, M. A. Popovića,b, R. J. Rama,b,d, H. I. Smitha,b, and G. R. Zhoub a
Department of Electrical Engineering and Computer Science, bResearch Laboratory of Electronics, cDepartment of Material Science and Engineering, d Microsystems Technology Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein Massachusetts Institute of Technology, Lincoln Laboratory, 244 Wood St.,Lexington, MA 02420 ABSTRACT Photonic Analog-to-Digital Conversion (ADC) has a long history. The premise is that the superior noise performance of femtosecond lasers working at optical frequencies enables us to overcome the bottleneck set by jitter and bandwidth of electronic systems and components. We discuss and demonstrate strategies and devices that enable the implementation of photonic ADC systems with emerging electronic-photonic integrated circuits based on silicon photonics. Devices include 2-GHz repetition rate low noise femtosecond fiber lasers, Si-Modulators with up to 20 GHz modulation speed, 20 channel SiN-filter banks, and Ge-photodetectors. Results towards a 40GSa/sec sampling system with 8bits resolution are presented. Keywords: Electronic photonic integrated circuits, silicon photonics, high index contrast, optical sampling, optical analog-to-digital conversion
1. INTRODUCTION The major limitation to electronic ADCs stems from aperture jitter set by the timing jitter or phase noise of the local clock used in the sampler. It was shown by Walden [1], that electronic jitter is limiting the progress in more advanced electronic ADCs to an increase in resolution-sampling speed product to about 2 effective number of bits (ENOB) per decade. The hope is that photonic technologies, such as femtosecond lasers, optical integration and multiplexing enables the miniaturization of high repetition rate modelocked lasers, electro-optic conversion, filter and detector technologies to overcome the electronic bottleneck [2,3,4,5]. Femtosecond lasers are providing a stream of sampling pulses with much reduced timing jitter, when compared to integrated microwave oscillators, approaching attosecond jitter levels over milliseconds of measurement time [6]. Therefore, photonic ADCs have been the subject of extensive research in recent years. In this paper, we analyze and pursue experimentally a new approach towards photonic ADCs based on a wavelength division multiplexing approach to parallelize and demultiplex the stream of sampling pulses into lower rate channels, that can then be digitized with conventional electronic ADCs [5]. The layout of the wavelength-demultiplexed photonic sampling ADC being considered here is shown in Fig. 1. A low-jitter pulse train with repetition rate fR generated by a mode-locked laser passes through a dispersive fiber with length L and dispersion coefficient β2 , which imposes chirp so that a frequency component ω gets delayed by τ (ω)=β2ω L. This chirped pulse train is modulated by a Mach-Zehnder (MZ) modulator whose RF driving voltage V(t) is the signal to be sampled. The modulator effectively imprints the time dependence of V(t) onto the optical spectrum. The optical signal is demultiplexed into N channels by a filter bank, so that every pulse is split into N sub-pulses. Each sub-pulse is detected by a photodetector and digitized by an electronic ADC taking one sample per pulse. This sample
Silicon Photonics III, edited by Joel A. Kubby, Graham T. Reed Proc. of SPIE Vol. 6898, 689806, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.767926
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represents the RF signal at time moment tn = τ (ωn), where ωn is the filter center frequency. N samples VADC(tn) are obtained, which are spaced uniformly across the repetition period TR if β2L∆ω N = TR, where ∆ω is the channel frequency spacing. This approach allows us to improve the sampling rate over what is available in electronic ADCs by a factor of N. By using both outputs of the MZ modulator we can also linearize its transfer function which is otherwise sinusoidal and factor out pulse-to-pulse amplitude fluctuations [4].
Figure 1: High-speed, high resolution optical sampling system and EPIC chip. A low-jitter femtosecond laser with repetition rate fR=1/TR is emitting a stream of 100-200 fs pulses that is spectrally dispersed in regular single-mode fiber. Dispersion is chosen such that the chirped pulses cover the time interval between pulses with a smooth spectrum. The optical spectrum is limited by a bandpass filter. The RF-waveform to be sampled is imprinted on the chirped pulse stream via a dual-port silicon-based electro-optic modulator. The differential optical output is channelized via a dual-WDM-filter bank with precisely-tuned center frequencies that map each optical frequency component to certain sampling time slots. The signals from each channel corresponding to time interleaved sample sequences are then separately digitized in low-rate high-resolution ADC’s. The EPIC chip may comprise the silicon optical modulator, filter banks, detector arrays, the low-rate electronic ADCs and feedback circuitry that is necessary to stabilize the optical filter bank.
Table 1 summarizes the system parameters to achieve an overall sampling rate fS of 40GSa/sec. with 8 bit resolution or 100GSa/sec. with 10 bit resolution of an analog signal with a bandwidth equal to the Nyquist frequency of the sampler, i.e. fS/2. For successful sampling of such signals the required timing jitter levels are 30 fs and 3 fs, respectively. In the following we consider system components, devices and signal sources that will enable the successful implementation of the first example given in table 1. As we will see later, recovery of the original signal from the samples is highly non trivial and without a strategy for elimination of device variations and device nonlinearities virtually impossible with high resolution. Therefore, we consider first signal extraction to better understand the performance required by each individual component of the system. Table 1: Summary of system parameters for overall sampling rates of 40 or 100 GSa/sec.
Overall Sampling Rate f S = 1/ TS
Laser Rep. Rate
Filter Bandwidth
Channel Spacing ∆f
f R = 1/ TR
Number Total Optical Resolution of Bandwidth Filters ∆V / V N
Max. Jitter ∆t
Center Frequency Precision
40 GSa/sec
2 GHz
25 GHz
80 GHz
20
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30 fs
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100 GSa/sec
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50
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10 bit
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2. SIGNAL RECOVERY The measured signal VADC(tn) can differ from the real RF signal V(tn) for many reasons. Even if all components of the system are perfect, the effective number of bits (ENOB) is limited by dispersion picked up by the RF signal from the chirped optical pulses and by the fact that VADC(tn) is defined by a convolution of V(t) with the optical filter transfer function. Errors can also arise due to various imperfections of system components, such as (a) in the filter bank: errors
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in filter frequencies, mismatch between frequencies of the two filter banks, crosstalk between channels, channel-tochannel filter shape variations; (b) in MZ modulator: nonlinear dependence of phase shift on the driving voltage, loss dependence on the driving voltage (as in carrier-injection Si modulators), error in bias voltage, unequal splitting in MZ couplers; (c) detection system imperfections: crosstalk between different sub-pulses for slow photodetectors, different sensitivities of photodiodes and individual ADCs, unequal channel path losses, etc. An algorithm which allows us to compensate such ADC errors numerically in the data post-processing stage has been developed. The relation between input and output voltage of the ADC is written as VADC = (1+ εˆ )V, where εˆ is a nonlinear operator describing the distortion introduced by the system; εˆ should be much smaller than 1 for a reasonable ADC system. The RF signal we want to find can then be expressed as V = VADC – εˆ V, (1) where the error εˆ V is unknown. We start with a guess V(1) for the RF signal assuming that this error is zero, i.e. V(1) = VADC. Using this guess V(1) as the RF driving voltage, we then run a system simulation and find the samples V(1)ADC which would be obtained from the ADC in this case. Because V(1)ADC = (1+ εˆ )V(1), the error can be calculated as εˆ V(1)= V(1)ADC –V(1). As our guess is close to the real RF signal, the error ε V(1) is also close to the real error εˆ V. Therefore, we substitute εˆ V(1) instead of εˆ V into (1) and get an an improved guess V(2) = V(1) + (VADC – V(1)ADC) (2) The new guess can be further improved by running the ADC simulation and applying (2); this can be repeated until the desired accuracy is reached. As an example we consider the ADC system with the parameters given in Table 1 for the 40GSa/sec case. The length of SMF-28 fiber is approximately 2.4km. For this system, the ENOB is limited to about 4 by dispersion and filter bandwidth even if all other system components are perfect. As a test case for the error compensation algorithm, we assume rather poor ADC components: photodetectors with 1 GHz bandwidth only, leading to overlap between the detected pulses, filter banks with randomly spaced center frequencies with a variance of 15GHz, and a MZ modulator with 30/70 splitting ratio in the output coupler. The samples directly out of such ADC do have ENOB~1bit; the proposed algorithm allows us to improve ENOB to 10 bits in 11 iterations. Fig. 2 illustrates how the error is reduced with initial iterations. An ADC with better components requires fewer iterations. The proposed algorithm was verified to be effective against the error sources listed above. The errors which cannot be compensated are the random errors due to laser jitter and photodetection noise. For sufficiently low jitter and large en enough power on the photodetectors, the ENOB achievable using the proposed algorithm is limited only by the precision with which the ADC components are calibrated by periodic sampling of appropriate test signals derived from the modelocked laser itself. The proposed approach is generic and is expected to be effective for other photonic ADC configurations as well. 1 iteration
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Figure 2: Example of error compensation by the proposed iterative algorithm. The error is defined as VADC(tn)-V(tn).
3. HIGH REPETITION RATE, LOW JITTER FEMTOSECOND LASERS Key to the sampling system is a high repetition rate (2 GHz) femtosecond laser. For testing and initial feasibility studies, we have developed a low jitter 200 MHz femtosecond fiber laser that is then multiplied in repetition rate by locking to an external Fabry-Perot (FP) cavity [7]. In this paper, we review the generation of low timing jitter, 150 fs
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Balance Detector
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pulse trains with a repetition rate of 2 GHz, by locking a 200 MHz fundamentally mode-locked erbium doped fiber laser (ErFL) to external FP cavities. The experimental setup is shown in Fig. 3(a). A fundamentally passively mode-locked ErFL in a sigma cavity configuration was constructed as the seed laser to generate 130 fs pulses at a repetition rate of 200 MHz. The output of the laser is coupled and mode-matched into a free space FP cavity. The Hänsch-Couillaud locking scheme is used to lock the mode comb of the laser to the transmission maxima of the external FP cavity by controlling the piezo-mounted mirror on the sigma arm of the ErFL cavity. A second feedback loop is implemented to reduce the output intensity noise by feeding the error signal of the intensity fluctuations at the output to the driving current of the pump diode of the seed laser. Two sets of mirrors are used to generate a high finesse (F) cavity (F=2000) and a low finesse cavity (F=200). All of the mirrors used in the FP cavities are dispersion flattened around 1550 nm.
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Figure 3: (a) Experimental setup. (b) Optical spectra of the pulse train before (solid) and after (dashed) the external FP cavity. (c) RF spectra of the pulse train after the external FP cavity with F=2000 detected with a 10 GHz photodetector.
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The optical spectra of the pulse train before and after the external FP cavity with 2 GHz free spectral range are shown in Fig. 3(b) for the case of F=200 and F=2000. The 3 dB spectral bandwidths of the 200-MHz pulse train, the 2-GHz pulse train are 22.5 nm (F=200) and 17 nm (F=2000), respectively, corresponding to more than 2THz bandwidth, which is necessary for the sampling application. Fig. 3(c) shows that the FP cavity (F=2000) suppresses the 200 MHz fundamental by 40 dB in the RF domain, corresponding to 46 dB in the optical domain. Fig. 4 shows both the phase noise of the 200-MHz seed pulse train at its 10th harmonic (2 GHz) and the 2-GHz Figure 4: Phase noise of 2-GHz (harmonic) of seed pulse train at its fundamental, measured with an HP5052a laser, fundamental (2GHz) of the repetition rate signal source analyzer. The 2-GHz pulse trains exhibit multiplied pulse train, and progressively integrated essentially the same phase noise as the 200-MHz seed timing jitter starting from 10 MHz down to 10 Hz, pulse train. The timing jitter progressively integrated RIN=0.27%. starting from 10 MHz down to 1 Hz is also shown. The timing jitter integrated from 1 kHz to 10 MHz is 27 fs [7]. Work is in progress to demonstrate a similar laser source as an integrated planar lightwave circuit using Er:glass waveguides as the gain medium.
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4. SILICON ELECTRO-OPTIC MODULATORS Another important component of the sampling system is a high-speed silicon optical modulator that transfers the electronic signal into the optical domain. Fig. 5(a) illustrates the Mach-Zehnder interferometer device architecture used for our modulator. The interferometer arms contain diode sections, see Fig. 5(b), with an intrinsic region serving as the waveguide core. The refractive index of the intrinsic region is changed by electronic carrier injection and the resulting plasma effect [8], which induces the phase shifts in each arm of the interferometer and modulates the output light intensity. It is possible to drive the modulator using both arms in push-pull arrangement, but in this paper only the results from a single driven arm will be reported. This type of modulator can be operated either as a forward biased or as a reverse biased PIN diode. In forward biased operation the device is more sensitive to the applied voltage, but under reverse bias the modulator exhibits greater bandwidth. -10
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Figure 5: Mach-Zehnder modulator. (a) Interferometer shown in plane view. (b) Cross section of the phase shifter diode structure.
Figure 6: Measured frequency response of the modulator under reverse bias and forward bias operation.
The modulators were fabricated with a standard CMOS-compatible lithography process. The sidewalls of the waveguide are moderately doped to a concentration of 1018 cm-3, and the center of the waveguide is doped n-type to a lighter concentration of 1017 cm-3. These doping concentrations were chosen to produce a diode that would simultaneously cause a reasonable phase shift without excessive optical loss [9]. When operated in reverse bias, a depletion region forms at the junction at one sidewall of the waveguide. As the reverse bias voltage is increased, this depletion region becomes larger and extends into the center of the waveguide. A highly doped (1019 cm-3), 50-nm-thick silicon layer connects the waveguide to electrical contacts located 1 µm from the waveguide. Even higher doping concentrations of 1021 cm-3 are used under the metal contacts to assure good ohmic contacts. The modulators were tested under DC operation, and, as expected, the devices had much greater sensitivity when operated in forward bias than in reverse bias. Under forward bias a device with only 0.25-mm long diode section can achieve a π phase shift with a change in input voltage of 0.1 V (with a bias of 1V). This corresponds to an extremely low (low frequency RF) VπL of 0.0025 V·cm. Because this is a low impedance device, the current increases from 3 mA to 10 mA for this π phase shift. Under reverse bias, a 5mm long device can achieve a π phase shift with a change in input voltage of 10.5 V, corresponding to a VπL of 5.3 V·cm. This is comparable to vertical diode devices reported in the literature where a VπL of 4 V·cm was achieved [10]. Fig 6 shows the measured small signal response of a 0.5-mmlong modulator under forward bias operation and 1.0-mm-long modulator under reverse bias operation. The response curve for forward bias shows a relatively small bandwidth of about 100 MHz. When operated in reverse bias the device shows a relatively flat response to 18 GHz but at the expense of a strongly reduced sensitivity. The numerical simulations were performed with the software SENTAURUSTM (Synopsys) with which an induced carrier density can be calculated as a function of the applied DC voltage by solving the Poisson equation coupled to the electron and hole continuity equations that govern carrier transport. The measured and simulated currentvoltage characteristics of the Mach-Zehnder modulator with 0.25 mm phase shifters are shown in Fig. 7(a). After obtaining the induced refractive index and absorption change due to the free-carrier plasma effect, the resulting phase shift is then found by solving for the optical mode (its intensity distribution is shown in the inset of Fig. 7(b)) and its propagation constant. Good agreement with the experiment is obtained by choosing for the doping dependent carrier lifetime profile τ0/(1+N/N0) with τ0=2.4 ns, N0 =5×1017 cm3. Fig. 7(b) shows the normalized optical transmission as a function of the applied voltage for the same silicon modulator. The static Vπ L-product obtained from the simulations is 0.024 V·cm, and the low frequency RF Vπ L-product is as small as 0.002V·cm. This excellent fit for the DC-
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characteristics and static optical transmission characteristics of the modulator confirms that the choice for the lifetime profile is consistent, as it is further illustrated in Fig. 8. Fig. 9 shows the measured and modeled small signal response of a 0.5 mm long modulator under forward biased operation for two types of devices. The device (#1) has been described before; the device #2 is identical except it has been implanted with silicon to reduce the carrier lifetime. The analytical model is based on semiconductor pn-junction theory combined with its small signal equivalent circuits (GD in conjunction with CD and in series with Rs). Note that both GD and CD are functions of angular frequency ω. We evaluate the normalized power response |S21|2 by calculating the stored charge Q on CD under the applied voltage (Vdc+ vsinωt). A constant effective lifetime of 1.0 ns is used in the analytical model and Rs is chosen to be 5Ω (as extracted from DC characteristics). The numerical modeling of the AC characteristics is based on calculating the induced AC carrier densities for the small signal AC input similar to the DC modeling. The DC bias voltage is chosen as 0.9 V and 3 mV of AC amplitude is used in the simulations and in the experiments. For the simulations the lifetime doping profile extracted from the DC characteristics is used. The proper choice of this lifetime profile is found to be crucial in predicting the response accurately. Both analytical and numerical models predict an accurate 3-dB bandwidth of ~0.3 GHz for this forward-biased modulator and the numerical model results agree very well with measurements up to 20 GHz where the RF parasitic circuitry starts to limit the response bandwidth. It is also demonstrated in Fig. 9 both in modeling (using the lifetime profile #2 shown in Fig. 8) and measurement that after lifetime reduction the frequency bandwidth can be increased to ~2 GHz with a reduced response level at lower frequencies. An alternative technique of using a pre-compensation filter has been presented previously to extend the bandwidth to ~5 GHz [11]. In reverse biased operation up to ~20GHz of bandwidth has been achieved as shown in Fig 6.
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Figure 9: Modeled and measured frequency responses for modulators with 0.5mm long phase shifters. Device #1 is the baseline and #2 has reduced carrier lifetime.
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5. HIGH INDEX CONTRAST FILTER BANK The next essential component of the optical analog-to-digital converter is the dual filter bank, which consists of two identical filter banks to be used for demultiplexing two MZ modulator outputs. Microring-resonator filters, utilizing high-index contrast (HIC) materials, are ideal for filter banks in large scale EPIC systems because of their ability to achieve the required low loss and large free spectral range (FSR) needed while maintaining wavelength-scale dimensions. Design and fabrication of HIC microring resonators has proved to be very challenging due to the decrease in critical feature size as well as increased sensitivity to roughness and dimensional errors [12-15]. The proposed ADC chip requires two identical twenty-channel filter banks composed of second-order microring-resonator filters with 2 THz free spectral range, 25 GHz bandwidth, and 80 GHz channel spacing. We have previously reported success in the fabrication of an eight-channel second-order microring-resonator filter bank using silicon-rich silicon nitride (SiNx), n =2.2 at 1550 nm, as the core material, SiO2 as the undercladding, and an air overcladding. The fabrication process for these filters, based on scanning-electron beam lithography and reactive-ion etching, was optimized to achieve high absolute dimensional accuracy and smooth vertical sidewalls [16]. Using the method of dose modulation, as described in [17], we were able to control the resonant frequency of the filters with a precision of 5 GHz (1σ), which corresponds to controlling the average ring-waveguide width with a precision of 0.15 nm. For the proposed analog-to-digital converter to produce 8 effective bits at 40 GSa/sec without subsequent postprocessing, it is necessary to control the resonant frequencies of these filters within 100 MHz. To achieve this level of precision, thermal tuning with integrated microheaters must be used to correct for the picometer-scale dimensional errors that occur during fabrication. However, before microheaters can be integrated the rings need to be overcladded to isolate the optical mode from the metallic heaters. The material chosen for the overcladding was hydrogen silsesquioxane (HSQ) using an optimized annealing process. HSQ, a spin-on dielectric, is ideal for an overcladding material since it has excellent gap filling and self-planarization properties and by optimizing the annealing process the same optical properties as SiO2 are achievable [18]. Using the HSQ overcladding, dose modulation, and a new secondorder filter design, optimized to achieve the performance needed for the ADC, a dual, twenty-channel filter bank was fabricated and tested (Fig. 10).
Figure 10: (a) Measured frequency response for the dual twenty-channel filer bank with all non-filter related losses factored out. (b) Cross-section of waveguide overcladded with HSQ. (c) Top-view optical micrograph of the dual filter bank.
The filter bank’s optical response shows an average channel spacing of 83 GHz (1σ = 8.5 GHz) just slightly larger than the target spacing of 80 GHz. The bandwidth of the filters was much larger than the 25 GHz designed due to a frequency mismatch between the two rings in a single filter. This mismatch, measured to be 29 GHz on average, results in an increase in the drop loss of approximately 4 dB. This frequency mismatch can be easily corrected with
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thermal tuning by implementing individually controlled heaters above each ring. After subtracting this component of the drop loss it is found that there is still ~6 dB of drop loss left. This drop loss was found to be caused by a larger than expected propagation loss of 38 dB/cm. This large of a propagation loss can not be accounted for by sidewall roughness alone and is thought to be due to absorption loss in the material. The SiNx used for these devices has been optimized for low-stress, not optical quality. Also the non-stoichiometric nature of this material makes it more prone to substantial variations from batch-to-batch than other photonic core materials such as SOI and Si3N4. The same fundamental fabrication technique can be used to fabricate this device using SOI where propagation losses below 3 dB/cm are now routinely achieved, eliminating the high drop loss of this device [19,20]. As mentioned previously, efficient post-fabrication trimming is required to correct for the small resonant frequency errors caused by the picometer-scale fabrication errors. Thermal tuning using microheaters can be used for this post-fabrication trimming taking advantage of the thermal dependence of the SiNx index of refraction. Low power thermal tuning with efficiency of 80µW/GHz/filter has been demonstrated for a second-order SiNx microring resonator. According to the 3-D finite element thermal simulation, the optimized heater design was to provide tuning efficiency of 60µW/GHz/filter. Due to heater misalignment of 6 µm during fabrication, the thermal impedance of the ring decreases from 4800K/W to 3570K/W, thus, decreasing the tuning efficiency to 80µW/GHz/filter (Fig. 11). This is still a dramatic improvement for the tuning efficiency of a SiN ring resonator than earlier reported value of 400µW/GHz [21]. For the photonic enhanced ADC application, the thermal stability of the resonant frequency is an important parameter. A Wheatstone bridge is utilized for the temperature controller circuit. The heater is the unknown resistor in the bridge and the other three resistors are assumed to be temperature independent. One of the resistors is a potentiometer which sets the resistance value for the heater. Once the bridge is balanced, if there is any temperature change in the ring/heater, the resistance of the heater changes according to its temperature coefficient. The error in the voltage between the set resistor and the heater is measured by an instrumentation amplifier (low noise, low offset voltage) which then passes through a proportional-integral-derivative (PID) controller and through a summing junction where it contributes to the total voltage across the bridge. If the heater resistance is higher than the set value, the current flow decreases through the heater which reduces the power, thus reducing its temperature rise due to joule heating, and lowering the overall resistance to maintain the temperature. Similarly, if the heater resistance is lower, the current flow increases which causes larger power dissipation and increase in temperature and its resistance. The open-loop thermal stability for the microring resonator has been measured to be within 400MHz of the resonant frequency, which corresponds to the ring temperature fluctuation of 160mK (Fig. 12). A lock-in technique was used for the thermal stability measurement. For the experiment, two optical signals are coupled into the waveguide. One signal has its wavelength at the steepest slope in the pass-band of the filter and another is a reference signal away from the pass-band. Both signals are modulated at two different frequencies and measured through a photodetector and a lock-in amplifier in dual-frequency mode. The drop port spectrum is shown in the inset of Fig. 12 with the slope estimate at the wavelength of interest. I-'i
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Figure 11: Shift in resonant wavelength of the second-order filter due to on-chip heating. The inset shows the drop port spectra during tuning.
Figure 12: Thermal stability for the resonant frequency of the ring resonator to within 160mK.
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input I —
19 more filters drop2 drop I--
Channel
Figure 13: (left) sketch illustrating how one filer can be in both filter banks by using the couter-propagating resonant mode. (right) frequency response from a single channel of a twenty channel filter bank.
Once of the most stringent requirement of the dual filter bank is that the complementary filters in each filter bank need to have the same resonant frequency and frequency response. One way to achieve this is to use the same filter for each filter bank. This can be done by using counter-propagating modes in the ring for the different filter banks as illustrated in Fig. 13. Using this method the resonant frequencies are intrinsically aligned. The only requirement for this to work is that there is low crosstalk between the adjacent filters and counter-propagating modes. A crucial, but often overlooked, component to the filter bank and all EPIC components is an efficient fiber-towaveguide coupler to get light on and off the chip. We have designed such a coupler using a low-index contrast polymer waveguide, which has the same mode size as the fiber, sitting above an inverse taper (Fig. 14). Previously designed horizontal couplers based on tapers have all used linear tapers to achieve adiabatic mode conversion from the large fiber mode to the strongly confined waveguide mode. We are working on designs with highly non-linear taper shapes that can achieve the same coupling efficiency as the linear tapers over a significantly smaller distance.
S j02
j:y
cyclotene
--
5.Oam
Small-con
fiber
Si02
Figure 14: (left) schematic of designed horizontal coupler. (center) simulations of the mode cross-section as it propagates through the coupler. (right) scanning-electron micrograph of the cyclotene polymer waveguide.
In addition to the filter banks fabricated in silicon nitride, there is an additional effort to fabricate ring resonator filter banks in silicon. These filters are fabricated using the same fabrication process and SOI material as the silicon modulators, and therefore these components should be simple to integrate together. Because silicon has a higher index of refraction compared to silicon nitride, the fabrication of silicon filters is more challenging. Greater dimensional control is necessary to control the resonance of the filters, and any sidewall roughness will cause greater loss. In addition, optical lithography was used in the process, which does not have the resolution of e-beam lithography or the ability to easily fine-tune the exposure of different features. However, optical lithography has much higher throughput, which will ultimately be necessary for manufacturing of these EPIC chips. A ten channel silicon filter bank has been created using coupled ring resonators, similar to the silicon nitride filter bank the silicon filters use two coupled rings per channel. The rings are approximately 5 µm in diameter. The input and output waveguides are nominally 360 nm wide and the ring waveguides are 450 nm wide. The gaps between the input/output waveguides and the rings are nominally 225 nm, and the gap between the two rings is nominally 504 nm. All the waveguides are 210 nm thick. The smaller width of the input and output waveguides improves the coupling
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between the waveguide and the ring by pushing more of the mode outside the waveguide. This design is expected to give 45 GHz of bandwidth and 30 dB of extinction of the adjacent channel (assuming a channel spacing of 150 GHz). To create the desired response from the filter bank requires precise control of the resonant frequency of each ring. Rather than trying to precisely control the fabrication of each ring, each ring is thermally tuned. After the waveguides are etched in silicon, oxide is deposited by PEVCD and planarized by CMP (chemical-mechanical polishing). Approximately 1 µm of oxide remains above the waveguide after CMP. Heaters are fabricated in a 100 nm thick layer of polysilicon which is in-situ doped. The heaters are 4 µm wide, and have a resistance of 220 Ω. Fig. 15 shows an optical image of one of the channels in the filter bank. Because the two rings are in such close proximity, each heater will heat the adjacent ring in addition to the ring beneath it. The tuning was measured to be 0.68 nm/mW for the ring beneath the heater and 0.19 nm/mW for the adjacent ring.
Drop Port Intensity (dB)
0
Input
1 2 3 4 5 6 7 8 9 10
-10
-20
-30
A:: i Drop Figure 15: Optical image of one channel of the filter bank. Dashed lines are drawn-in to highlight the position of the waveguides, which are overwise overshadowed by metal heaters and contacts.
1526
1530
1534 1538 Wavelength (nm)
1542
Figure 16. Drop port response of the filter bank.
Fig. 16 shows the drop port response of each of the 10 channels of the filter bank when tuned to its nominal center frequency and each of the two rings were aligned in frequency. The accuracy of the tuning of the filter bank was limited by the measurement, and was 2 pm. The power necessary to tune each channel was between 1 and 5 mW. There is good extinction for all the channels, although a few channels do not reach the design goal of 30 dB of extinction. The cause for this discrepancy has not been established yet. The bandwidth is smaller than expected, typically about 30 GHz, and the filter shape is not always single peaked. Some of the irregularities in the filter shape are believed to be due to reflections in the rings which are known to cause peak splitting in single ring devices [22]. The measurement equipment currently being used only allows one channel to be tuned at a time, so some of the measured filter shape irregularity is caused by the interference from the through-port response of the untuned rings located along the light path before the measured filter. The devices are fairly stable in an uncontrolled environment. Only 9 pm of drift occurred after 2 hours without any adjustment of the tuning.
6. SILICON AND GERMANIUM INFRARED PHOTODIODES Both germanium and silicon photodiodes are being pursued for this application. The Ge diode technology is well established, but requires careful attention to process integration issues when used in a silicon CMOS process. In pursuit of easier process integration, we have developed a novel all-silicon infrared diode device. It has been reported [23] that radiation damaged Si contains mid-bandgap states that produce optical absorption and photocurrents for wavelengths as large as 4 µm. This infrared photocurrent was thought to be of little practical value until Knights et al. [24,25] in 2003 reported that diodes formed in ion-implant-damaged Si rib waveguides exhibit photo response of 0.008 A W-1 at 1550 nm with an electrical bandwidth of 2 MHz. We have developed an optimized submicrometer scale version of this device that achieves photoresponse of up to 0.5 A W-1 at 5 V and 20 GHz bandwidth [26,27]. As shown in Fig. 17, these p-i-n diodes are similar to the diode structure of the modulator. The central region of the waveguide has a cross section of 0.52×0.22 µm with 50-nm-thick Si wings connecting the
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waveguide to electrical contacts 900 nm away. The thin Si wings have little effect on the mode of the waveguide, which has the strong optical confinement of a strip waveguide. The p+ and n+ regions are doped to 1×1019 cm-3 and the p and n region are doped to 1×1018 cm-3. The diodes were then implanted with 1×1013 cm-2, 190-keV Si+ to form the photosensitive damaged silicon region in the waveguide. TiN-Al Contact Pads
Al Contact Pad
Si02
/
Si Wavegui1e LPCVD
_____
TiN-W plug
Al Contact Pad
0.25mm _________
500 nm Intrinsic Si,
5i02
/ ion damage
p p ( i' n________
______
• -— b.
n
SiWing
Figure 17: Waveguide photodiode. (a) Top-view optical micrograph of 0.25-mm-long waveguide photodiode. (b) Schematic drawing of the p-i-n diode cross section. The waveguide is the intrinsic silicon rib in the center of the sketch.
Ion implantation induces a variety of crystal defects including divacancies and interstitial clusters that can be considered as nano-crystal structures imbedded in the single-crystal Si matrix. These defects are affected by processing temperature and electrical operating point. Devices processed to 475 °C, as required for a typical CMOS metallization process, can be in one of two stable optically-active states, arbitrarily labeled L1 and L2. After device fabrication the interstitials are in state L1 with a waveguide photodiode optical absorption of 8 dB cm-1. If the diode is forward biased for several minutes the defects change their character into the L2 configuration with absorption of 18 dB cm-1. The L2 state can be transformed back to the L1 by annealing the diode to 250 °C for 10 s in air. Diodes have been cycled between these two states without any measurable character change. The L1 and L2 states have an affect on the electrical performance of the devices as described below. The leakage and photocurrents for a 3-mm-long diode in the L2 state are shown in Fig. 18(a). The ratio of 10
mW of 1539 nm light
0
0.01
E a)
-20
= 0 a)
= 0 CI)
-30
Fourier transform
106
Network analyzer
-40
0.25 mm diode, 20 V -50 0.01
10-8
0.1
Bias voltage (V)
1
10
100
Frequency (GHz)
Figure 18: Measured photoresponse. (a) Diode current in the dark and illuminated with ~ 1 mW of 1539 nm radiation as a function of bias voltage for a 3-mm-long diode. (b) Frequency response of 0.25-mm-long Si photodiode in the L1 and L2 states. A network analyzer was used to measure response from 0.01 to 60 GHz, dashed red curves. Fourier transform analysis of the pulse response was used to obtain the response from 0.1 to 150 GHz, solid blue curves. All the curves were shifted vertically to allow the L2 state set-ofcurves to coincide with 0 dB at 10 GHz. The cause of the discrepancy for diodes in the L2 state between the network analyzer and the Fourier transform analysis of the pulse response is described elsewhere [27].
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cal-to-Electrical S2 1 (dB)
photocurrent generated by 1 mW of 1539 nm radiation to leakage current is >1x106 at 1 V and is comparable to commercial 1550-nm InGaAs PIN photodiodes. Although several groups have reported two photon absorption and photocurrents proportional to the light intensity squared [28], all the diodes reported here, implanted and otherwise, exhibit a photocurrent linear with light intensity [26,27]. The frequency response of these diodes is limited by pad parasitics. The driving resistance, 50 Ω, and the pad capacitance, 0.15 pF for the 0.25-mm-long devices, result in a 7 ps time constant and a 20 GHz bandwidth. Fig. 18(b) shows the measured frequency response. The longer 3-mm devices achieve greater photo sensitivity, but are limited to 2 GHz bandwidth. We have also been working on germanium photodiodes. As reported previously [5] Ge-on-Si films were grown in a low-pressure chemical vapor deposition epitaxial reactor and subsequently fabricated into vertical PIN photodiodes. A cross-sectional schematic of these diodes is shown in the inset to Fig. 19. Typical 50 µm circular diodes have a dark current of 3 µA at -1 V and a responsivity of 0.4 A/W at 1550 nm. These diodes are limited to a
Photonic Analog-to-Digital Conversion with Electronic-Photonic Integrated Circuits F. X. Kärtnera,b, R. Amatyaa,b,d, M. Araghchini a,b, J. Birgea,b, H. Byuna,b, J. Chena,b, M. Dahlema,b, N.A. DiLelloa,d, F. Gana,b, C. W. Holzwarthb,c, J. L. Hoyta,d, E. P. Ippena,b, A. Khiloa,b, J. Kima,b, M. Kima,d, A. Motamedia,b, J. S. Orcutta,b,d, M. Parka,d, M. Perrotta,d, M. A. Popovića,b, R. J. Rama,b,d, H. I. Smitha,b, and G. R. Zhoub a
Department of Electrical Engineering and Computer Science, bResearch Laboratory of Electronics, cDepartment of Material Science and Engineering, d Microsystems Technology Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein Massachusetts Institute of Technology, Lincoln Laboratory, 244 Wood St.,Lexington, MA 02420 ABSTRACT Photonic Analog-to-Digital Conversion (ADC) has a long history. The premise is that the superior noise performance of femtosecond lasers working at optical frequencies enables us to overcome the bottleneck set by jitter and bandwidth of electronic systems and components. We discuss and demonstrate strategies and devices that enable the implementation of photonic ADC systems with emerging electronic-photonic integrated circuits based on silicon photonics. Devices include 2-GHz repetition rate low noise femtosecond fiber lasers, Si-Modulators with up to 20 GHz modulation speed, 20 channel SiN-filter banks, and Ge-photodetectors. Results towards a 40GSa/sec sampling system with 8bits resolution are presented. Keywords: Electronic photonic integrated circuits, silicon photonics, high index contrast, optical sampling, optical analog-to-digital conversion
1. INTRODUCTION The major limitation to electronic ADCs stems from aperture jitter set by the timing jitter or phase noise of the local clock used in the sampler. It was shown by Walden [1], that electronic jitter is limiting the progress in more advanced electronic ADCs to an increase in resolution-sampling speed product to about 2 effective number of bits (ENOB) per decade. The hope is that photonic technologies, such as femtosecond lasers, optical integration and multiplexing enables the miniaturization of high repetition rate modelocked lasers, electro-optic conversion, filter and detector technologies to overcome the electronic bottleneck [2,3,4,5]. Femtosecond lasers are providing a stream of sampling pulses with much reduced timing jitter, when compared to integrated microwave oscillators, approaching attosecond jitter levels over milliseconds of measurement time [6]. Therefore, photonic ADCs have been the subject of extensive research in recent years. In this paper, we analyze and pursue experimentally a new approach towards photonic ADCs based on a wavelength division multiplexing approach to parallelize and demultiplex the stream of sampling pulses into lower rate channels, that can then be digitized with conventional electronic ADCs [5]. The layout of the wavelength-demultiplexed photonic sampling ADC being considered here is shown in Fig. 1. A low-jitter pulse train with repetition rate fR generated by a mode-locked laser passes through a dispersive fiber with length L and dispersion coefficient β2 , which imposes chirp so that a frequency component ω gets delayed by τ (ω)=β2ω L. This chirped pulse train is modulated by a Mach-Zehnder (MZ) modulator whose RF driving voltage V(t) is the signal to be sampled. The modulator effectively imprints the time dependence of V(t) onto the optical spectrum. The optical signal is demultiplexed into N channels by a filter bank, so that every pulse is split into N sub-pulses. Each sub-pulse is detected by a photodetector and digitized by an electronic ADC taking one sample per pulse. This sample
Silicon Photonics III, edited by Joel A. Kubby, Graham T. Reed Proc. of SPIE Vol. 6898, 689806, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.767926
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6U!SSe3OJd-;SOd
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represents the RF signal at time moment tn = τ (ωn), where ωn is the filter center frequency. N samples VADC(tn) are obtained, which are spaced uniformly across the repetition period TR if β2L∆ω N = TR, where ∆ω is the channel frequency spacing. This approach allows us to improve the sampling rate over what is available in electronic ADCs by a factor of N. By using both outputs of the MZ modulator we can also linearize its transfer function which is otherwise sinusoidal and factor out pulse-to-pulse amplitude fluctuations [4].
Figure 1: High-speed, high resolution optical sampling system and EPIC chip. A low-jitter femtosecond laser with repetition rate fR=1/TR is emitting a stream of 100-200 fs pulses that is spectrally dispersed in regular single-mode fiber. Dispersion is chosen such that the chirped pulses cover the time interval between pulses with a smooth spectrum. The optical spectrum is limited by a bandpass filter. The RF-waveform to be sampled is imprinted on the chirped pulse stream via a dual-port silicon-based electro-optic modulator. The differential optical output is channelized via a dual-WDM-filter bank with precisely-tuned center frequencies that map each optical frequency component to certain sampling time slots. The signals from each channel corresponding to time interleaved sample sequences are then separately digitized in low-rate high-resolution ADC’s. The EPIC chip may comprise the silicon optical modulator, filter banks, detector arrays, the low-rate electronic ADCs and feedback circuitry that is necessary to stabilize the optical filter bank.
Table 1 summarizes the system parameters to achieve an overall sampling rate fS of 40GSa/sec. with 8 bit resolution or 100GSa/sec. with 10 bit resolution of an analog signal with a bandwidth equal to the Nyquist frequency of the sampler, i.e. fS/2. For successful sampling of such signals the required timing jitter levels are 30 fs and 3 fs, respectively. In the following we consider system components, devices and signal sources that will enable the successful implementation of the first example given in table 1. As we will see later, recovery of the original signal from the samples is highly non trivial and without a strategy for elimination of device variations and device nonlinearities virtually impossible with high resolution. Therefore, we consider first signal extraction to better understand the performance required by each individual component of the system. Table 1: Summary of system parameters for overall sampling rates of 40 or 100 GSa/sec.
Overall Sampling Rate f S = 1/ TS
Laser Rep. Rate
Filter Bandwidth
Channel Spacing ∆f
f R = 1/ TR
Number Total Optical Resolution of Bandwidth Filters ∆V / V N
Max. Jitter ∆t
Center Frequency Precision
40 GSa/sec
2 GHz
25 GHz
80 GHz
20
1.6 THz
8 bit
30 fs
100 MHz
100 GSa/sec
2 GHz
25 GHz
80 GHz
50
4.0 THz
10 bit
3 fs
10 MHz
2. SIGNAL RECOVERY The measured signal VADC(tn) can differ from the real RF signal V(tn) for many reasons. Even if all components of the system are perfect, the effective number of bits (ENOB) is limited by dispersion picked up by the RF signal from the chirped optical pulses and by the fact that VADC(tn) is defined by a convolution of V(t) with the optical filter transfer function. Errors can also arise due to various imperfections of system components, such as (a) in the filter bank: errors
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in filter frequencies, mismatch between frequencies of the two filter banks, crosstalk between channels, channel-tochannel filter shape variations; (b) in MZ modulator: nonlinear dependence of phase shift on the driving voltage, loss dependence on the driving voltage (as in carrier-injection Si modulators), error in bias voltage, unequal splitting in MZ couplers; (c) detection system imperfections: crosstalk between different sub-pulses for slow photodetectors, different sensitivities of photodiodes and individual ADCs, unequal channel path losses, etc. An algorithm which allows us to compensate such ADC errors numerically in the data post-processing stage has been developed. The relation between input and output voltage of the ADC is written as VADC = (1+ εˆ )V, where εˆ is a nonlinear operator describing the distortion introduced by the system; εˆ should be much smaller than 1 for a reasonable ADC system. The RF signal we want to find can then be expressed as V = VADC – εˆ V, (1) where the error εˆ V is unknown. We start with a guess V(1) for the RF signal assuming that this error is zero, i.e. V(1) = VADC. Using this guess V(1) as the RF driving voltage, we then run a system simulation and find the samples V(1)ADC which would be obtained from the ADC in this case. Because V(1)ADC = (1+ εˆ )V(1), the error can be calculated as εˆ V(1)= V(1)ADC –V(1). As our guess is close to the real RF signal, the error ε V(1) is also close to the real error εˆ V. Therefore, we substitute εˆ V(1) instead of εˆ V into (1) and get an an improved guess V(2) = V(1) + (VADC – V(1)ADC) (2) The new guess can be further improved by running the ADC simulation and applying (2); this can be repeated until the desired accuracy is reached. As an example we consider the ADC system with the parameters given in Table 1 for the 40GSa/sec case. The length of SMF-28 fiber is approximately 2.4km. For this system, the ENOB is limited to about 4 by dispersion and filter bandwidth even if all other system components are perfect. As a test case for the error compensation algorithm, we assume rather poor ADC components: photodetectors with 1 GHz bandwidth only, leading to overlap between the detected pulses, filter banks with randomly spaced center frequencies with a variance of 15GHz, and a MZ modulator with 30/70 splitting ratio in the output coupler. The samples directly out of such ADC do have ENOB~1bit; the proposed algorithm allows us to improve ENOB to 10 bits in 11 iterations. Fig. 2 illustrates how the error is reduced with initial iterations. An ADC with better components requires fewer iterations. The proposed algorithm was verified to be effective against the error sources listed above. The errors which cannot be compensated are the random errors due to laser jitter and photodetection noise. For sufficiently low jitter and large en enough power on the photodetectors, the ENOB achievable using the proposed algorithm is limited only by the precision with which the ADC components are calibrated by periodic sampling of appropriate test signals derived from the modelocked laser itself. The proposed approach is generic and is expected to be effective for other photonic ADC configurations as well. 1 iteration
|Error|, a.u.
Signal, a.u.
No correction
3 iterations
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Figure 2: Example of error compensation by the proposed iterative algorithm. The error is defined as VADC(tn)-V(tn).
3. HIGH REPETITION RATE, LOW JITTER FEMTOSECOND LASERS Key to the sampling system is a high repetition rate (2 GHz) femtosecond laser. For testing and initial feasibility studies, we have developed a low jitter 200 MHz femtosecond fiber laser that is then multiplied in repetition rate by locking to an external Fabry-Perot (FP) cavity [7]. In this paper, we review the generation of low timing jitter, 150 fs
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Balance Detector
Loop Filter
PBS
Output
λ/4 4% glass slide Mode Matching Optics Mirror λ/4
4% glass slide M1
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Diode Driver
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Brewster Plate
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Piezo Driver
Mirror
Normalized Intensity (AU)
pulse trains with a repetition rate of 2 GHz, by locking a 200 MHz fundamentally mode-locked erbium doped fiber laser (ErFL) to external FP cavities. The experimental setup is shown in Fig. 3(a). A fundamentally passively mode-locked ErFL in a sigma cavity configuration was constructed as the seed laser to generate 130 fs pulses at a repetition rate of 200 MHz. The output of the laser is coupled and mode-matched into a free space FP cavity. The Hänsch-Couillaud locking scheme is used to lock the mode comb of the laser to the transmission maxima of the external FP cavity by controlling the piezo-mounted mirror on the sigma arm of the ErFL cavity. A second feedback loop is implemented to reduce the output intensity noise by feeding the error signal of the intensity fluctuations at the output to the driving current of the pump diode of the seed laser. Two sets of mirrors are used to generate a high finesse (F) cavity (F=2000) and a low finesse cavity (F=200). All of the mirrors used in the FP cavities are dispersion flattened around 1550 nm.
-30
(c)
-40 -50 -60 -70 0
2
4
6
8
10
Frequency (GHz)
Figure 3: (a) Experimental setup. (b) Optical spectra of the pulse train before (solid) and after (dashed) the external FP cavity. (c) RF spectra of the pulse train after the external FP cavity with F=2000 detected with a 10 GHz photodetector.
(sj)
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0
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0 0 0 0 0
0 0 0
0
0)
Phase Noise (dBcIHz)
The optical spectra of the pulse train before and after the external FP cavity with 2 GHz free spectral range are shown in Fig. 3(b) for the case of F=200 and F=2000. The 3 dB spectral bandwidths of the 200-MHz pulse train, the 2-GHz pulse train are 22.5 nm (F=200) and 17 nm (F=2000), respectively, corresponding to more than 2THz bandwidth, which is necessary for the sampling application. Fig. 3(c) shows that the FP cavity (F=2000) suppresses the 200 MHz fundamental by 40 dB in the RF domain, corresponding to 46 dB in the optical domain. Fig. 4 shows both the phase noise of the 200-MHz seed pulse train at its 10th harmonic (2 GHz) and the 2-GHz Figure 4: Phase noise of 2-GHz (harmonic) of seed pulse train at its fundamental, measured with an HP5052a laser, fundamental (2GHz) of the repetition rate signal source analyzer. The 2-GHz pulse trains exhibit multiplied pulse train, and progressively integrated essentially the same phase noise as the 200-MHz seed timing jitter starting from 10 MHz down to 10 Hz, pulse train. The timing jitter progressively integrated RIN=0.27%. starting from 10 MHz down to 1 Hz is also shown. The timing jitter integrated from 1 kHz to 10 MHz is 27 fs [7]. Work is in progress to demonstrate a similar laser source as an integrated planar lightwave circuit using Er:glass waveguides as the gain medium.
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4. SILICON ELECTRO-OPTIC MODULATORS Another important component of the sampling system is a high-speed silicon optical modulator that transfers the electronic signal into the optical domain. Fig. 5(a) illustrates the Mach-Zehnder interferometer device architecture used for our modulator. The interferometer arms contain diode sections, see Fig. 5(b), with an intrinsic region serving as the waveguide core. The refractive index of the intrinsic region is changed by electronic carrier injection and the resulting plasma effect [8], which induces the phase shifts in each arm of the interferometer and modulates the output light intensity. It is possible to drive the modulator using both arms in push-pull arrangement, but in this paper only the results from a single driven arm will be reported. This type of modulator can be operated either as a forward biased or as a reverse biased PIN diode. In forward biased operation the device is more sensitive to the applied voltage, but under reverse bias the modulator exhibits greater bandwidth. -10
λ
Forward Bias Reverse Bias
-20
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Si Waveguide: 500 x 220 nm
oxide
-50 -60 -70
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1 µm
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(b) 50 nm
-80 0.01
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10
100
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Figure 5: Mach-Zehnder modulator. (a) Interferometer shown in plane view. (b) Cross section of the phase shifter diode structure.
Figure 6: Measured frequency response of the modulator under reverse bias and forward bias operation.
The modulators were fabricated with a standard CMOS-compatible lithography process. The sidewalls of the waveguide are moderately doped to a concentration of 1018 cm-3, and the center of the waveguide is doped n-type to a lighter concentration of 1017 cm-3. These doping concentrations were chosen to produce a diode that would simultaneously cause a reasonable phase shift without excessive optical loss [9]. When operated in reverse bias, a depletion region forms at the junction at one sidewall of the waveguide. As the reverse bias voltage is increased, this depletion region becomes larger and extends into the center of the waveguide. A highly doped (1019 cm-3), 50-nm-thick silicon layer connects the waveguide to electrical contacts located 1 µm from the waveguide. Even higher doping concentrations of 1021 cm-3 are used under the metal contacts to assure good ohmic contacts. The modulators were tested under DC operation, and, as expected, the devices had much greater sensitivity when operated in forward bias than in reverse bias. Under forward bias a device with only 0.25-mm long diode section can achieve a π phase shift with a change in input voltage of 0.1 V (with a bias of 1V). This corresponds to an extremely low (low frequency RF) VπL of 0.0025 V·cm. Because this is a low impedance device, the current increases from 3 mA to 10 mA for this π phase shift. Under reverse bias, a 5mm long device can achieve a π phase shift with a change in input voltage of 10.5 V, corresponding to a VπL of 5.3 V·cm. This is comparable to vertical diode devices reported in the literature where a VπL of 4 V·cm was achieved [10]. Fig 6 shows the measured small signal response of a 0.5-mmlong modulator under forward bias operation and 1.0-mm-long modulator under reverse bias operation. The response curve for forward bias shows a relatively small bandwidth of about 100 MHz. When operated in reverse bias the device shows a relatively flat response to 18 GHz but at the expense of a strongly reduced sensitivity. The numerical simulations were performed with the software SENTAURUSTM (Synopsys) with which an induced carrier density can be calculated as a function of the applied DC voltage by solving the Poisson equation coupled to the electron and hole continuity equations that govern carrier transport. The measured and simulated currentvoltage characteristics of the Mach-Zehnder modulator with 0.25 mm phase shifters are shown in Fig. 7(a). After obtaining the induced refractive index and absorption change due to the free-carrier plasma effect, the resulting phase shift is then found by solving for the optical mode (its intensity distribution is shown in the inset of Fig. 7(b)) and its propagation constant. Good agreement with the experiment is obtained by choosing for the doping dependent carrier lifetime profile τ0/(1+N/N0) with τ0=2.4 ns, N0 =5×1017 cm3. Fig. 7(b) shows the normalized optical transmission as a function of the applied voltage for the same silicon modulator. The static Vπ L-product obtained from the simulations is 0.024 V·cm, and the low frequency RF Vπ L-product is as small as 0.002V·cm. This excellent fit for the DC-
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Normalized Transmission
Current (mA)
characteristics and static optical transmission characteristics of the modulator confirms that the choice for the lifetime profile is consistent, as it is further illustrated in Fig. 8. Fig. 9 shows the measured and modeled small signal response of a 0.5 mm long modulator under forward biased operation for two types of devices. The device (#1) has been described before; the device #2 is identical except it has been implanted with silicon to reduce the carrier lifetime. The analytical model is based on semiconductor pn-junction theory combined with its small signal equivalent circuits (GD in conjunction with CD and in series with Rs). Note that both GD and CD are functions of angular frequency ω. We evaluate the normalized power response |S21|2 by calculating the stored charge Q on CD under the applied voltage (Vdc+ vsinωt). A constant effective lifetime of 1.0 ns is used in the analytical model and Rs is chosen to be 5Ω (as extracted from DC characteristics). The numerical modeling of the AC characteristics is based on calculating the induced AC carrier densities for the small signal AC input similar to the DC modeling. The DC bias voltage is chosen as 0.9 V and 3 mV of AC amplitude is used in the simulations and in the experiments. For the simulations the lifetime doping profile extracted from the DC characteristics is used. The proper choice of this lifetime profile is found to be crucial in predicting the response accurately. Both analytical and numerical models predict an accurate 3-dB bandwidth of ~0.3 GHz for this forward-biased modulator and the numerical model results agree very well with measurements up to 20 GHz where the RF parasitic circuitry starts to limit the response bandwidth. It is also demonstrated in Fig. 9 both in modeling (using the lifetime profile #2 shown in Fig. 8) and measurement that after lifetime reduction the frequency bandwidth can be increased to ~2 GHz with a reduced response level at lower frequencies. An alternative technique of using a pre-compensation filter has been presented previously to extend the bandwidth to ~5 GHz [11]. In reverse biased operation up to ~20GHz of bandwidth has been achieved as shown in Fig 6.
Simulation Measurement 0.25mm Modulator
1.0
(b) Simulation Measurement 0.25mm Modulator
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1.0
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0.4
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1.2
Voltage (V)
Figure 7: Measured and simulated (a) current-voltage characteristics and (b) optical transmission for the MZ-modulator with 0.25-mm-long phase shifters. Insets show (a) waveguide cross section and (b) simulated optical mode. 10
-10
|S21| (dB)
Extracted From DC Measurement Lifetime #1: Fit by τ0/(1+N/N0)
2
Carrier Lifetime τ (ns)
0 1
3
(τ0=2.4ns, N0=4.9e17cm )
0.1
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Lifetime #2: (τ0=100ps, N0=5e17cm )
-20 -30 -40 -50 -60
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Measurement 1 Measurement 2 Analytical Modeling 1 Numerical Modeling 1 Numerical Modeling 2 0.5mm Modulator 0.1
Carrier Concentration N (cm )
1
f (GHz)
Figure 8: Variation of carrier lifetime as a function of carrier concentration: fit for device #1 (Red); lifetime profile for device #2 (Green).
10
Figure 9: Modeled and measured frequency responses for modulators with 0.5mm long phase shifters. Device #1 is the baseline and #2 has reduced carrier lifetime.
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5. HIGH INDEX CONTRAST FILTER BANK The next essential component of the optical analog-to-digital converter is the dual filter bank, which consists of two identical filter banks to be used for demultiplexing two MZ modulator outputs. Microring-resonator filters, utilizing high-index contrast (HIC) materials, are ideal for filter banks in large scale EPIC systems because of their ability to achieve the required low loss and large free spectral range (FSR) needed while maintaining wavelength-scale dimensions. Design and fabrication of HIC microring resonators has proved to be very challenging due to the decrease in critical feature size as well as increased sensitivity to roughness and dimensional errors [12-15]. The proposed ADC chip requires two identical twenty-channel filter banks composed of second-order microring-resonator filters with 2 THz free spectral range, 25 GHz bandwidth, and 80 GHz channel spacing. We have previously reported success in the fabrication of an eight-channel second-order microring-resonator filter bank using silicon-rich silicon nitride (SiNx), n =2.2 at 1550 nm, as the core material, SiO2 as the undercladding, and an air overcladding. The fabrication process for these filters, based on scanning-electron beam lithography and reactive-ion etching, was optimized to achieve high absolute dimensional accuracy and smooth vertical sidewalls [16]. Using the method of dose modulation, as described in [17], we were able to control the resonant frequency of the filters with a precision of 5 GHz (1σ), which corresponds to controlling the average ring-waveguide width with a precision of 0.15 nm. For the proposed analog-to-digital converter to produce 8 effective bits at 40 GSa/sec without subsequent postprocessing, it is necessary to control the resonant frequencies of these filters within 100 MHz. To achieve this level of precision, thermal tuning with integrated microheaters must be used to correct for the picometer-scale dimensional errors that occur during fabrication. However, before microheaters can be integrated the rings need to be overcladded to isolate the optical mode from the metallic heaters. The material chosen for the overcladding was hydrogen silsesquioxane (HSQ) using an optimized annealing process. HSQ, a spin-on dielectric, is ideal for an overcladding material since it has excellent gap filling and self-planarization properties and by optimizing the annealing process the same optical properties as SiO2 are achievable [18]. Using the HSQ overcladding, dose modulation, and a new secondorder filter design, optimized to achieve the performance needed for the ADC, a dual, twenty-channel filter bank was fabricated and tested (Fig. 10).
Figure 10: (a) Measured frequency response for the dual twenty-channel filer bank with all non-filter related losses factored out. (b) Cross-section of waveguide overcladded with HSQ. (c) Top-view optical micrograph of the dual filter bank.
The filter bank’s optical response shows an average channel spacing of 83 GHz (1σ = 8.5 GHz) just slightly larger than the target spacing of 80 GHz. The bandwidth of the filters was much larger than the 25 GHz designed due to a frequency mismatch between the two rings in a single filter. This mismatch, measured to be 29 GHz on average, results in an increase in the drop loss of approximately 4 dB. This frequency mismatch can be easily corrected with
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thermal tuning by implementing individually controlled heaters above each ring. After subtracting this component of the drop loss it is found that there is still ~6 dB of drop loss left. This drop loss was found to be caused by a larger than expected propagation loss of 38 dB/cm. This large of a propagation loss can not be accounted for by sidewall roughness alone and is thought to be due to absorption loss in the material. The SiNx used for these devices has been optimized for low-stress, not optical quality. Also the non-stoichiometric nature of this material makes it more prone to substantial variations from batch-to-batch than other photonic core materials such as SOI and Si3N4. The same fundamental fabrication technique can be used to fabricate this device using SOI where propagation losses below 3 dB/cm are now routinely achieved, eliminating the high drop loss of this device [19,20]. As mentioned previously, efficient post-fabrication trimming is required to correct for the small resonant frequency errors caused by the picometer-scale fabrication errors. Thermal tuning using microheaters can be used for this post-fabrication trimming taking advantage of the thermal dependence of the SiNx index of refraction. Low power thermal tuning with efficiency of 80µW/GHz/filter has been demonstrated for a second-order SiNx microring resonator. According to the 3-D finite element thermal simulation, the optimized heater design was to provide tuning efficiency of 60µW/GHz/filter. Due to heater misalignment of 6 µm during fabrication, the thermal impedance of the ring decreases from 4800K/W to 3570K/W, thus, decreasing the tuning efficiency to 80µW/GHz/filter (Fig. 11). This is still a dramatic improvement for the tuning efficiency of a SiN ring resonator than earlier reported value of 400µW/GHz [21]. For the photonic enhanced ADC application, the thermal stability of the resonant frequency is an important parameter. A Wheatstone bridge is utilized for the temperature controller circuit. The heater is the unknown resistor in the bridge and the other three resistors are assumed to be temperature independent. One of the resistors is a potentiometer which sets the resistance value for the heater. Once the bridge is balanced, if there is any temperature change in the ring/heater, the resistance of the heater changes according to its temperature coefficient. The error in the voltage between the set resistor and the heater is measured by an instrumentation amplifier (low noise, low offset voltage) which then passes through a proportional-integral-derivative (PID) controller and through a summing junction where it contributes to the total voltage across the bridge. If the heater resistance is higher than the set value, the current flow decreases through the heater which reduces the power, thus reducing its temperature rise due to joule heating, and lowering the overall resistance to maintain the temperature. Similarly, if the heater resistance is lower, the current flow increases which causes larger power dissipation and increase in temperature and its resistance. The open-loop thermal stability for the microring resonator has been measured to be within 400MHz of the resonant frequency, which corresponds to the ring temperature fluctuation of 160mK (Fig. 12). A lock-in technique was used for the thermal stability measurement. For the experiment, two optical signals are coupled into the waveguide. One signal has its wavelength at the steepest slope in the pass-band of the filter and another is a reference signal away from the pass-band. Both signals are modulated at two different frequencies and measured through a photodetector and a lock-in amplifier in dual-frequency mode. The drop port spectrum is shown in the inset of Fig. 12 with the slope estimate at the wavelength of interest. I-'i
Ill-I
IU • —
Figure 11: Shift in resonant wavelength of the second-order filter due to on-chip heating. The inset shows the drop port spectra during tuning.
Figure 12: Thermal stability for the resonant frequency of the ring resonator to within 160mK.
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input I —
19 more filters drop2 drop I--
Channel
Figure 13: (left) sketch illustrating how one filer can be in both filter banks by using the couter-propagating resonant mode. (right) frequency response from a single channel of a twenty channel filter bank.
Once of the most stringent requirement of the dual filter bank is that the complementary filters in each filter bank need to have the same resonant frequency and frequency response. One way to achieve this is to use the same filter for each filter bank. This can be done by using counter-propagating modes in the ring for the different filter banks as illustrated in Fig. 13. Using this method the resonant frequencies are intrinsically aligned. The only requirement for this to work is that there is low crosstalk between the adjacent filters and counter-propagating modes. A crucial, but often overlooked, component to the filter bank and all EPIC components is an efficient fiber-towaveguide coupler to get light on and off the chip. We have designed such a coupler using a low-index contrast polymer waveguide, which has the same mode size as the fiber, sitting above an inverse taper (Fig. 14). Previously designed horizontal couplers based on tapers have all used linear tapers to achieve adiabatic mode conversion from the large fiber mode to the strongly confined waveguide mode. We are working on designs with highly non-linear taper shapes that can achieve the same coupling efficiency as the linear tapers over a significantly smaller distance.
S j02
j:y
cyclotene
--
5.Oam
Small-con
fiber
Si02
Figure 14: (left) schematic of designed horizontal coupler. (center) simulations of the mode cross-section as it propagates through the coupler. (right) scanning-electron micrograph of the cyclotene polymer waveguide.
In addition to the filter banks fabricated in silicon nitride, there is an additional effort to fabricate ring resonator filter banks in silicon. These filters are fabricated using the same fabrication process and SOI material as the silicon modulators, and therefore these components should be simple to integrate together. Because silicon has a higher index of refraction compared to silicon nitride, the fabrication of silicon filters is more challenging. Greater dimensional control is necessary to control the resonance of the filters, and any sidewall roughness will cause greater loss. In addition, optical lithography was used in the process, which does not have the resolution of e-beam lithography or the ability to easily fine-tune the exposure of different features. However, optical lithography has much higher throughput, which will ultimately be necessary for manufacturing of these EPIC chips. A ten channel silicon filter bank has been created using coupled ring resonators, similar to the silicon nitride filter bank the silicon filters use two coupled rings per channel. The rings are approximately 5 µm in diameter. The input and output waveguides are nominally 360 nm wide and the ring waveguides are 450 nm wide. The gaps between the input/output waveguides and the rings are nominally 225 nm, and the gap between the two rings is nominally 504 nm. All the waveguides are 210 nm thick. The smaller width of the input and output waveguides improves the coupling
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between the waveguide and the ring by pushing more of the mode outside the waveguide. This design is expected to give 45 GHz of bandwidth and 30 dB of extinction of the adjacent channel (assuming a channel spacing of 150 GHz). To create the desired response from the filter bank requires precise control of the resonant frequency of each ring. Rather than trying to precisely control the fabrication of each ring, each ring is thermally tuned. After the waveguides are etched in silicon, oxide is deposited by PEVCD and planarized by CMP (chemical-mechanical polishing). Approximately 1 µm of oxide remains above the waveguide after CMP. Heaters are fabricated in a 100 nm thick layer of polysilicon which is in-situ doped. The heaters are 4 µm wide, and have a resistance of 220 Ω. Fig. 15 shows an optical image of one of the channels in the filter bank. Because the two rings are in such close proximity, each heater will heat the adjacent ring in addition to the ring beneath it. The tuning was measured to be 0.68 nm/mW for the ring beneath the heater and 0.19 nm/mW for the adjacent ring.
Drop Port Intensity (dB)
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A:: i Drop Figure 15: Optical image of one channel of the filter bank. Dashed lines are drawn-in to highlight the position of the waveguides, which are overwise overshadowed by metal heaters and contacts.
1526
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1534 1538 Wavelength (nm)
1542
Figure 16. Drop port response of the filter bank.
Fig. 16 shows the drop port response of each of the 10 channels of the filter bank when tuned to its nominal center frequency and each of the two rings were aligned in frequency. The accuracy of the tuning of the filter bank was limited by the measurement, and was 2 pm. The power necessary to tune each channel was between 1 and 5 mW. There is good extinction for all the channels, although a few channels do not reach the design goal of 30 dB of extinction. The cause for this discrepancy has not been established yet. The bandwidth is smaller than expected, typically about 30 GHz, and the filter shape is not always single peaked. Some of the irregularities in the filter shape are believed to be due to reflections in the rings which are known to cause peak splitting in single ring devices [22]. The measurement equipment currently being used only allows one channel to be tuned at a time, so some of the measured filter shape irregularity is caused by the interference from the through-port response of the untuned rings located along the light path before the measured filter. The devices are fairly stable in an uncontrolled environment. Only 9 pm of drift occurred after 2 hours without any adjustment of the tuning.
6. SILICON AND GERMANIUM INFRARED PHOTODIODES Both germanium and silicon photodiodes are being pursued for this application. The Ge diode technology is well established, but requires careful attention to process integration issues when used in a silicon CMOS process. In pursuit of easier process integration, we have developed a novel all-silicon infrared diode device. It has been reported [23] that radiation damaged Si contains mid-bandgap states that produce optical absorption and photocurrents for wavelengths as large as 4 µm. This infrared photocurrent was thought to be of little practical value until Knights et al. [24,25] in 2003 reported that diodes formed in ion-implant-damaged Si rib waveguides exhibit photo response of 0.008 A W-1 at 1550 nm with an electrical bandwidth of 2 MHz. We have developed an optimized submicrometer scale version of this device that achieves photoresponse of up to 0.5 A W-1 at 5 V and 20 GHz bandwidth [26,27]. As shown in Fig. 17, these p-i-n diodes are similar to the diode structure of the modulator. The central region of the waveguide has a cross section of 0.52×0.22 µm with 50-nm-thick Si wings connecting the
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waveguide to electrical contacts 900 nm away. The thin Si wings have little effect on the mode of the waveguide, which has the strong optical confinement of a strip waveguide. The p+ and n+ regions are doped to 1×1019 cm-3 and the p and n region are doped to 1×1018 cm-3. The diodes were then implanted with 1×1013 cm-2, 190-keV Si+ to form the photosensitive damaged silicon region in the waveguide. TiN-Al Contact Pads
Al Contact Pad
Si02
/
Si Wavegui1e LPCVD
_____
TiN-W plug
Al Contact Pad
0.25mm _________
500 nm Intrinsic Si,
5i02
/ ion damage
p p ( i' n________
______
• -— b.
n
SiWing
Figure 17: Waveguide photodiode. (a) Top-view optical micrograph of 0.25-mm-long waveguide photodiode. (b) Schematic drawing of the p-i-n diode cross section. The waveguide is the intrinsic silicon rib in the center of the sketch.
Ion implantation induces a variety of crystal defects including divacancies and interstitial clusters that can be considered as nano-crystal structures imbedded in the single-crystal Si matrix. These defects are affected by processing temperature and electrical operating point. Devices processed to 475 °C, as required for a typical CMOS metallization process, can be in one of two stable optically-active states, arbitrarily labeled L1 and L2. After device fabrication the interstitials are in state L1 with a waveguide photodiode optical absorption of 8 dB cm-1. If the diode is forward biased for several minutes the defects change their character into the L2 configuration with absorption of 18 dB cm-1. The L2 state can be transformed back to the L1 by annealing the diode to 250 °C for 10 s in air. Diodes have been cycled between these two states without any measurable character change. The L1 and L2 states have an affect on the electrical performance of the devices as described below. The leakage and photocurrents for a 3-mm-long diode in the L2 state are shown in Fig. 18(a). The ratio of 10
mW of 1539 nm light
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E a)
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Figure 18: Measured photoresponse. (a) Diode current in the dark and illuminated with ~ 1 mW of 1539 nm radiation as a function of bias voltage for a 3-mm-long diode. (b) Frequency response of 0.25-mm-long Si photodiode in the L1 and L2 states. A network analyzer was used to measure response from 0.01 to 60 GHz, dashed red curves. Fourier transform analysis of the pulse response was used to obtain the response from 0.1 to 150 GHz, solid blue curves. All the curves were shifted vertically to allow the L2 state set-ofcurves to coincide with 0 dB at 10 GHz. The cause of the discrepancy for diodes in the L2 state between the network analyzer and the Fourier transform analysis of the pulse response is described elsewhere [27].
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cal-to-Electrical S2 1 (dB)
photocurrent generated by 1 mW of 1539 nm radiation to leakage current is >1x106 at 1 V and is comparable to commercial 1550-nm InGaAs PIN photodiodes. Although several groups have reported two photon absorption and photocurrents proportional to the light intensity squared [28], all the diodes reported here, implanted and otherwise, exhibit a photocurrent linear with light intensity [26,27]. The frequency response of these diodes is limited by pad parasitics. The driving resistance, 50 Ω, and the pad capacitance, 0.15 pF for the 0.25-mm-long devices, result in a 7 ps time constant and a 20 GHz bandwidth. Fig. 18(b) shows the measured frequency response. The longer 3-mm devices achieve greater photo sensitivity, but are limited to 2 GHz bandwidth. We have also been working on germanium photodiodes. As reported previously [5] Ge-on-Si films were grown in a low-pressure chemical vapor deposition epitaxial reactor and subsequently fabricated into vertical PIN photodiodes. A cross-sectional schematic of these diodes is shown in the inset to Fig. 19. Typical 50 µm circular diodes have a dark current of 3 µA at -1 V and a responsivity of 0.4 A/W at 1550 nm. These diodes are limited to a
