Traveling SpatialQuantizedAnalog-to-digitalConversion

Traveling Wave Spatial Quantized Analog-to-digital ConversionMona Jarrahi, R. Fabian W. Pease, Thomas H. Lee

SMIRC Lab, Stanford University, Stanford, CA, 94305-4070

ABSTRACT An analog-to-digital converter (ADC)architecture that extracts the required quantization energydirectly from the input analog signal and sampling clock througha spatial quantization scheme is presented. We experimentallydemonstrate 8-level quantization consuming only 7.2pJper quantization operation with 18GHz bandwidth.Measured 8ps full-width half-maximum photodetectoroutput voltages, promises the potential of realizing a 3bit125GS/s ADC through this system.Index Terms - Analog-to-digital converter, mode-locked laser,quantum-confined Stark effect, INL, DNL, SNDR.

I. INTRODUCTION

With rapidly increasing signal bandwidths along withpredominance of digital technologies and techniques, the needfor higher speed analog-to-digital conversion arises in order tointerface between the analog and digital domains. Apart frommajor technical challenges in obtaining high samplingfrequencies, in combination with the increasing tendencytowards conservation of energy, the maximum availableenergy unfortunately, places an upper bound on the samplingfrequency in conventional interfaces between analog anddigital [ 1, 2]. To date, the fastest ADC that has beendemonstrated experimentally consumes 3.8W power toachieve 40GS/s sampling rate and 3bits of resolution [3] (i.e.,95pJ per sample), which is much higher than the availablepower for a battery-powered portable device.A number of photonic sampling techniques have beenproposed to overcome the limited timing jitter of electronicsampling circuits. Many of the proposed photonic ADCs takeadvantage of mode-locked lasers with sub-picosecond pulse-widths and aperture jitter of few tens of femtoseconds [4].Equally significant is the relative ease of optical clockdistribution without a consequential increase in amplitude andphase noise, due to the robust nature of photons fortransmitting information. Utilizing electronic quantizationcircuits in these optically sampled ADCs unfortunately limitsthe sampling speed due to the ambiguity of comparatorcircuits [2].Here, we present an analog-to-digital conversion technique,which in contrast to the conventional ADCs eliminates anyintermediate sample-and-hold and quantization circuit bydirectly launching the optical sampling pulses at spatialpositions corresponding to quantization levels, and isconsequently capable of achieving sampling frequencies ashigh as mode-locked laser pulse repetition rates. Theconversion technique is unique in the sense that the requiredsampling and quantization energy is obtained from the analoginput and sampling signal. We experimentally demonstrate 8-

level quantization consuming only 7.2pJ per quantizationoperation with 18GHz bandwidth. Measured 8ps full-widthhalf-maximum photodetector output voltages, promises thepotential of realizing a 3bit 125GS/s ADC through thissystem.

II. OVERVIEW OF THE ADC SYSTEM

The architecture of the proposed ADC is shown in Figure la.An optical input from a mode-locked laser is first coupled intoan input waveguide. The optical pulse is then split andpropagated down two waveguide branches of partial Mach-Zehnder-like interferometer. A phase modulator is integratedin one of the branches to vary the phase of the optical pulsesaccording to the electrical signal to be digitized.

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Photo-detectorarrays

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Fig. 1. (a) Schematic of the 3-bit spatially quantized ADC (b) Simulatedpower distribution on the image plane of a 350,um free propagation region

After passing through the interferometer arms, the opticalbeams from the two branches enter a slab waveguide regionallowing free propagation in the lateral direction in which thebeams from the two branches can diverge and interfere. Theresulting interference pattern from the two optical pulsesforms a spot on an effective image plane, a spot whoseposition varies as the phase difference between the two opticalpulses changes. In effect, the combination of the phasemodulator and the free-propagation region together constitutean imaging beam-deflection system whose deflection isdetermined by the phase difference between the two opticalpulses entering the free-propagation region and, morespecifically, by the modulating electrical signal. Placingphotodetectors at appropriate positions along the image plane

1-4244-0688-9/07/$20.00 C 2007 IEEE 225

enables measurement of the spatial distribution of opticalpower. Moreover, connecting photodetector arrays in a binaryfashion allows resolution of the output bits of the ADC. Figurelb shows the simulated optical power distribution on theimage plane of a 350gm free propagation region as a functionof the introduced phase shift.

III. PHASE MODULATOR AND PHOTODETECTOR

The phase modulation mechanism is based on the quantum-confined Stark effect, in which an applied perpendicularelectric field induces a shift in the absorption spectrum, and anaccompanying shift in the refractive index of a multiplequantum well structure [5]. In this work, multiple quantumwell layers are designed as integral parts of the intrinsic regionof a p-i-n diode integrated inside the optical waveguide, whichis designed for single transverse mode operation forwavelengths longer than 860 nm. The phase-modulatingelectric signal, which in combination with the substrate biasgenerates the electric field across the multiple quantum welllayers, propagates on a coplanar waveguide (CPW) along theoptical waveguide. Traveling wave phase modulation allows along modulation path while maintaining a small junction area[6]. Consequently, the bandwidth-efficiency tradeoff isreduced and higher modulation bandwidth and efficiency willbe achieved at the same time.a b

2 pmTi/Pt/Aup-Contact Au/Ni/Ge/Au

.m I n-contact

Fig. 2. Schematic of the traveling wave phase modulator

The schematic structure of the traveling wave phase modulator(TWPM) is shown in figure 2. Light is launched into theoptical waveguide formed in the junction of a p-i-n diode. Theepitaxial layers grown on a semi-insulating GaAs substrate arecomposed by a 0.1gm-thin layer of multiple quantum wellssandwiched between two nominally undoped Al0.05Gao.95Aslayers of 0.4gm thickness forming the intrinsic region of a p-i-n diode. A 1-gm thick, p (5X1017 cm3 Be) Al0o08Gao.92Aslayers followed by a 1-gm thick, p+ (2X10'9 cm-3 C)Al0o08Gao.92As layer, and a 2-gm thick, n (5X1017 cm-3 Si)Al0o08Gao.92As serve as upper and lower cladding layers,respectively.The CPW metal electrode structure comprised of metal on topof the optical waveguide and ground planes to either side isdesigned to have a characteristic impedance of 50Q and a

propagation constant set to allow for the phase modulatingelectric signal to travel in phase synchronism with the light.The complex characteristic impedance, Z0 (= IZ/Y), and thecomplex propagation constant, y, (= \ZY), can be determinedknowing the transmission line impedance per unit length, Z,and admittance per unit length, Y. The line impedance per unitlength is characterized by a conventional coplanar waveguideinductance and resistance per unit length. The line parallelplate capacitance and the waveguide diode depletion regioncapacitance, while operated at reverse bias, together with aseries resistance modeling the semiconductor losses associatedwith transverse current flow represent the line admittance perunit length. The 50Q CPW termination is fabricated using apart ofthe waveguide semiconductor.Photodetectors, monolithically fabricated along the outputwaveguides, consist of an active region terminated through6gm metal spacing on either side, equivalent to 50Q. Thegenerated photocurrent along the active region is a function ofMQW reverse bias set by substrate bias voltage. Absorption ofthe photodetector is calculated by the overlap of optical modewith the quantum well layers. The power absorption densityalong the waveguide photodetector is set to be locally low bythe small confinement factor of the guided light in the 0.1gm-thin multiple quantum well absorption layer. This improvesthe photodetector efficiency along large device lengths byreducing the field screening effect [7] caused by the highconcentration of photo-generated carriers at high optical pulsepeak powers. The simulation results suggest an opticalabsorption coefficient of 1.5 mm-' along the photodetectorunder 6V reverse-bias. The combination 0.218fF/gmcapacitive parasitic along the photodetector active region andthe 50Q termination resistance, suggests a bandwidth of36GHz and the corresponding FWHM pulse width of 5.5ps fora 400gm photodetector.

IV. FABRICATION AND EXPERIMENTAL RESULTS

GaAs/AlGaAs p-i-n layers are grown by molecular beamepitaxy on a (100) semi-insulating GaAs substrate. The 2gm-wide ridge waveguides are defined by Cl reactive ion etching.Au/Ni/Ge/Au n-contact metal region with total thickness ofabout 0.5gm was formed by standard lift-off and then rapid-thermal annealed (RTA) at 415°C for 30s. A Benzo CycloButene (BCB) layer was spun on the device and etched backup to the top of the waveguide for planarization of the etchedsurface such that the microwave coplanar waveguide (CPW)lines can be placed on top. A Ti/Pt/Au evaporation and lift-offstep forms the metallization of the CPW and the p-type metalcontact.CPW scattering parameters of a 1mm-long phase modulator,and the extracted characteristic impedance and propagationconstant are shown in figure 3.The extracted characteristic impedance is quite close to 50Q,within 6% deviation throughout the measurement range. Thisimpedance level allows the modulator input/output to be easily

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connected to conventional 50Q RF systems. The reasonablygood agreement between the experimental RF index and thedesired 3.2 optical index verifies less than 2% microwave-optical velocity mismatch for the frequencies lower than50GHz. The experimental RF attenuation is also shown infigure 3. The device performance would improve if theattenuation would be further reduced by increasing the centerstrip width to reduce the metal microwave loss.

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co 004 L-

0.02 ;0 2.5 co 3

0 0 1 2 210 122 1 210 10 10 10 10 10 10 10 10

Frequency (GHz) Frequency (GHz) Frequency (GHz)

Fig. 3. CPW characteristics calculated from CPW scattering parameters

The introduced phase shift AO in the optical mode is given by:

aLwhere %is the phase modulation efficiency (OVi'mmA), Vm isthe modulating electric voltage, L is the length of modulator,a is the microwave attenuation, and Tsettling iS given by L6]:T =tin2.2d+2ffP +2fL VO cV (2)setigv d V, V,where d is the depletion region depth, V is the carrier averagedrift velocity across the depletion region, p is the p-i-n diodecontact resistivity, and V0 and V, are the velocities of theoptical wave and the microwave, respectively. By calculatingthe CPW propagation constant from scattering parametermeasurements as a function of frequency an electric fieldsettling time of 2.1 ps is estimated for a 1.5 mm long phasemodulator. The expected operation bandwidth of thequantization system utilizing this phase modulator is 30 GHz,where the microwave attenuation of the CPW is the primarybandwidth-limiting mechanism.

In order to investigate the phase modulation characteristics,we convert phase modulation to intensity modulation byinserting a phase modulator in one arm of an asymmetricMach-Zehnder interferometer and observe 1800 phase shift ateach minimum/maximum intensity transition. Phasemodulation sensitivity as a function of reverse bias is obtainedby calculating interferometer Vr at each 1800 phase transitionand illustrated together with the associated intensitymodulation in figure 4. At the operating optical wavelength of870 nm, a relatively linear phase change of 2700Vi'mmi', andoptical loss variations of less than 0.28dBVilmmilareachieved, about a 2.1V reverse bias voltage. Using a 1.5mm-active region phase modulator allows the achievement of 2xphase shift over a +450mV input analog signal range.A die micrograph ofthe fabricated ADC is shown in figure 5a.The phase modulator is 1.5mm long and the free propagationregion is 350gm long. Lengths of 50gm, 150gm and 400gmare chosen for the I st, 2nd and 3rd bit detector arraysrespectively. Optical sampling pulses from a Ti-sapphiremode-locked laser operating at 870 nm, driving 150fs pulsesare coupled into the input waveguide. The resolved ADC bitswithin +lOOmV voltage range, at an input energy of 300fJ peroptical pulse are shown in Figure 5b. Depending on the digitaltechnology, we can adjust the optical pulse energy or utilizehigh gain stages prior to digital circuits to match the outputvoltage with the technology logic levels.

a b c

o1 2E 100 =

10 Vbit3 0

(U10 Cl)

100 40 00 FW

Aa0lbit2i

04

c 0 3060~~~600 -400 -200 0 200 400 600

Analog input voltage (mV) Time (ps)

Fig. 5. (a) ADC micrograph (b) ADC resolved bits at an input energy of68fJ per optical pulse (c) Photodetector transient response to a 150fs-wideoptical pulse

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Fig. 4. Traveling wavecharacteristics

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Reverse bias (V)

02

0

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phase modulator phase/amplitude modulation

Figure 5c shows the transient pulse response of a 400gmdetector, measured by pump-probe electro-optic (EO)sampling technique [8]. The measured 8ps full-width half-maximum (FWVHM) value at 6V reverse-bias indicates thecapability of photo-detector to detect optical pulse train withup to a 125GHz repetition rate.A performance summary of the fabricated ADC is shown infigure 6. Because of the limited mode-locked laser repetitionrate, the bandwidth performance ofthe ADC is investigated bymonitoring the frequency response ofADC LSB bit to a 6dBmsinusoidal analog source under laser continuous-waveoperation. The measured frequency response, shown in figure6a, indicates an instrument-limited operational bandwidth of18GHz. The linearity of the ADC is characterized by

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measuring the differential nonlinearity (DNL) and integralnonlinearity (INL) during ADC DC operation. Figure 6bshows the static INL and DNL error of less than 0.2LSB. Themain source of nonlinearity is the phase modulationnonlinearity with respect to the modulating voltage. Inaddition, optical loss in the phase modulator branch and allother sources of mismatch between two arms of the partialMach-Zehnder interferometer increase nonlinearity.a c

a)

0 5 10 15 20Analog frequency (GHz)

a)

0 1 2 3 4 5 6 7

Output Code

20

0

-20

-40

-60

-80

20

0

-20

Measured FFT Spectrum (fi/fs)

-40

_600-80

0 0.1 0.2 0.3 0.4 0.5

Measured FFT Spectrum (fi/fs)

traditional electrical quantization circuits with similarspecifications.

VII. CONCLUSION

The spatially quantized analog-to-digital conversion is anextremely power efficient technique for interfacing analog anddigital domains, while overcoming the sampling speedrestrictions of traditional ADCs. This is a valuable directionfor increasing flexibility of electronic systems by eliminatingmany performance limiting components along the way todigital processors. Realization of some of the electronicsystems, like software radio, which were previously notpractically feasible due to the need for directly digitizing a largeportion of the RF spectrum at the antenna will be possible byutilizing such an analog-to-digital conversion technique.

ACKNOWLEDGEMENT

The authors wish to acknowledge Prof. Yoshio Nishi, StanfordUniversity Center for Integrated Systems (CIS), Texas Instruments,and Agilent technologies for financial support. Special thanks go toR. Aldana and V. Abramzon for discussions and contributions to thiswork, H. Chin and 0. Fidaner for help with the measurement setup,and D. Mars, Agilent technologies, for wafer growth.

Fig. 6. (a) ADC LSB response to a 6 dBm analog input (b) INL and DNL(c) Measured FFT spectrum for f =80MS/s

For a mode-locked sampling clock of 80MHz, a signal-to-noise plus distortion ration (SNDR) of 17.8dB (equivalent to2.67 effective bits) and 18.5dB (equivalent to 2.78 effectivebits) is obtained for input signal frequencies of 1OMHz and30MHz, respectively (figure 6c). The limited repetition rate ofthe available mode-locked laser unfortunately did not allowSNDR measurements at sampling rates higher than 80MHz.Power consumption of the ADC is investigated by looking atthe quantization and sampling power consumptions,separately. The spatial quantization power is supplied by theinput analog signal performing the phase modulation withinthe +0.45V voltage range, corresponding 4mW maximumanalog input power, eliminating any static ADC power

consumption. As mentioned before, the optical pulses frommode-locked laser not only provide the low jitter ADCsampling clock, but are also recycled in the spatial quantizerto resolve ADC output bits. As a result, the input optical pulsepower directly affects the amplitude of the ADC resolved bitsand the ADC resolution. For an input optical energy of 300fJper pulse, about 25f is consumed to resolve 8 quantizationlevels, while the rest of the optical energy is dissipated alongmodulator waveguides and free propagation region. The totalenergy, including optical power for quantization operation andelectrical power dissipation in the photodetectors, is 7.2pJ per

quantization operation. Such energy consumption is more thantwo orders of magnitude lower than that predicted for a

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