analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked...

Analysis of free-space optical interconnects for thethree-dimensional optoelectronic stacked processor

Guoqiang Li*, Emel Yuceturk, Dawei Huang, Sadik C. Esener

Department of Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla,

CA 92093-0407, USA

Received 19 July 2001; received in revised form 5 November 2001; accepted 6 December 2001

Abstract

Performance of free-space optical interconnect for the three-dimensional optoelectronic stacked processor

(3DOESP) has been analyzed. The wave propagation in the optical interconnection system has been investigated by

utilizing rigorous scalar diffraction theory. The effects of ghost talk caused by the superposition of the delayed re-

flections of the original signal due to the multiple propagation of the wave between the vertical-cavity surface-emitting

laser (VCSEL) and metal-semiconductor-metal (MSM) detector have been analyzed. The conducted study indicates

that even in the presence of significant amount of ghost talk a high performance free-space optical interconnect can be

realized in this system by employing a receiver architecture that allows for DC level adjustment of the signal at the input

of the transimpedance amplifier stage. � 2002 Published by Elsevier Science B.V.

Keywords: Optical interconnects; Optical switching; 3D VLSI; Optoelectronics; VCSELs

1. Introduction

Current electronic interconnection technologycannot keep pace with the continuous perfor-mance improvement of VLSI circuits enabled bythe scaling down of device feature size and theincrease of integration density and processor clockspeed. The bandwidth of the electronic intercon-nection is limited by the inherent characteristics of

the electronic circuit and its two-dimensional (2D)topology. Optical interconnection using 2D denseoptoelectronic device arrays and the third dimen-sion for beam propagation has been proved to be asolution to this problem [1,2]. In the last decade,technologies such as array fabrication of vertical-cavity surface-emitting lasers (VCSEL) and metal-semiconductor-metal (MSM) detectors, hybridintegration of GaAs optoelectronic device arrayswith silicon transmitter and receiver circuits, fab-rication and integration of micro-optical compo-nents, system packaging, etc. have experiencedtremendous progress and improvement [3–11].Moreover, advances in 3D VLSI packaging tech-nologies have enabled the integration of multiple

15 February 2002

Optics Communications 202 (2002) 319–329

www.elsevier.com/locate/optcom

*Corresponding author. On leave from Shanghai Institute of

Optics and Fine Mechanics, Academia Sinica, Shanghai

201800, China.

E-mail address: [email protected] (G. Li).

0030-4018/02/$ - see front matter � 2002 Published by Elsevier Science B.V.

PII: S0030-4018 (01 )01735-7

electronic chips into a smaller volume by stackingthem on top of each other [12,13]. By combiningthe powerful processing capability of the 3D sili-con chip stacks and the high bandwidth of the freespace optical modules, a scalable optoelectronicswitching system [14] (Fig. 1) has been built underthe 3D optoelectronic stacked processor(3DOESP) consortium. In this system, a foldedmicro-/macro-optical module with a concave re-flection mirror that can tolerate a relative largemisalignment of the components has been de-signed.

The interconnection density and the data bit-rate of the free space interconnect systems are af-fected by the maximum optical power incident onthe photodetector and the associated circuits,which, in turn, depends on the power of theemitter and the efficiency of the optical system. Itis desired that all the energy emitted from the laseris confined within the micro-optical channel thatguides light from the VCSEL to the detector.However, due to the diffraction of the beam infree-space propagation, part of the energy may beclipped by the aperture of the microlens. Clippingof the beam at the aperture not only causes a lossof energy and thus decreases the efficiency of theoptical system, but also results in cross talk if the

beam is incident on the adjacent detectors. Fur-thermore, when the surfaces of the detector andthe VCSEL have high reflection coefficients thelight will bounce back and forth between the twodevices, a phenomenon called ghost talk [15], andmay therefore limit the maximum speed of oper-ation. For these reasons, accurate analysis of thebeam propagation through the optical system issignificant for characterization of the optical link.Three numerical models, namely ray tracing,Gaussian beam propagation, and scalar diffractiontheory have been utilized for this purpose [16].When subwavelength structures are involved, theutilization of vector diffraction theory that takesinto account the polarization dependence of dif-fraction is necessary for achieving accurate char-acterization of the optical interconnect [17,18]. Forthe aforementioned modeling tools, it has beenshown that simulation based on the rigorous scalardiffraction theory is more accurate and matcheswell with the experimental results. In this paper,the scalar diffraction theory has been employed toanalyze the microbeam propagation in folded hy-brid micro-/macro-optical system. The effects ofghost talk on the performance of high-speed free-space interconnect have been investigated viaSPICE simulations that take into account the high

Fig. 1. Schematic diagram of the 3D optoelectronic processor using 3D chip stacks and free-space optical interconnects.

320 G. Li et al. / Optics Communications 202 (2002) 319–329

reflectivity of the optoelectronic devices. By usinga receiver architecture that allows for DC leveladjustment of the signal at the input of the tran-simpedance amplifier stage, the ghost talk effect inthis system can be compensated.

2. Optical simulation

Our demonstration system (Fig. 1) includesthree assembled 3D VLSI functional chip stacksand an optical module for global communication.It is designed for data switching with low power,small volume, high-density, and high bandwidth.Each stack consists of 16 VLSI chips and a single16� 16 VCSEL/MSM detector array flip-chipbonded on top of the chip stack and each chip inthe stack supports 16 optical I/Os at 1 Gb/s.Furthermore, the 16� 16 electronic crossbarswitch that can arbitrarily route data packets be-tween its inputs/outputs and the associated driver/receiver circuits have all been implemented in thesame electronic layer. Processors with more pow-erful functionality can also be embedded into thechip for various application specific systems. Thechips in the central stack are perpendicular tothose in the other two stacks so that a signal inone end stack can be routed to any chip on theopposite end stack. To realize communicationwith both the left and the right neighbors, theoptoelectronic array is separated into two logicalhalves and the beams in the two halves are di-rected to the left and the right neighbors, respec-tively. The main advantages of this opticalinterconnection layer are that it provides means ofimplementing a global communication amongneighboring stacks and achieves more scalable andhigher bandwidth interconnect compared to theall-electronic systems. The adoption of a 3D ar-chitecture and the use of chip stack enable a sig-nificant footprint area reduction of the overallsystem in comparison with the 2D implementa-tion. The general requirements of a high-densityfree-space optical system are high resolution(small spot size), low loss (high link efficiency),low cross talk, large field of view, low cost, smallvolume, large misalignment tolerance, cascadabil-ity (modular design). To satisfy these require-

ments, a novel hybrid micro/macro-optical systemusing a concave reflection mirror is designed. Themethodology adopted in the system design is veryversatile and can therefore be easily extended toaccommodate the design constraints of similarapplications.

The schematic diagram of the optical modulethat interconnects the two neighboring stacks isshown in Fig. 2. The system is a combination of apair of small field, low f/number microlenses, a pairof large field, high f/number macrolenses, a pair ofdeflecting elements (prisms or gratings), and aconcave reflection mirror. In this system, the mi-crolens array collimates the beams emitting fromthe VCSELs and refocuses the beams onto thedetectors whereas the macrolenses adjust the in-terconnection distance. Both the microlens andmacrolens are used at infinite conjugates and thebeams are focused at the common focal plane ofthe two macrolenses. The performance require-ments on the macrolenses are greatly reduced dueto the fact that the microlenses provide high res-olution and therefore the macrolenses need onlyresolve the aperture of the microlenses. By com-bining the strengths of macro- and micro-opticalconfigurations the system not only outperformsthe conventional macro-optical imaging in appli-cations that utilize large dilute arrays with largefield but also overcomes the cross talk imposedlimitations on the interconnect length that arepresent in purely microoptical imaging.

Since the choice of optical elements has signif-icant performance impact, a careful considerationof various performance trade-offs imposed by theselected optical components is essential forachieving a high performance system. In our sys-tem the deflecting elements have been inserted inthe collimated beam path between the micro- andmacro-lenses so that they do not generate addi-tional aberrations. Since the aberrations of animaging system increase with increasing numericalaperture, it is helpful to utilize a large f/numbermacrolens to improve the imaging quality. Themicrolens should be chosen to match the VCSELbeam property so that there is no beam clipping atthe aperture of the microlens. However, in thisconfiguration the small f/number microlenses thatare necessary for satisfying the VCSELs beam

G. Li et al. / Optics Communications 202 (2002) 319–329 321

characteristics have severe mechanical toleranceconstraints and hence a small alignment error ofthe microlens may greatly deteriorate the images.To compensate the aberrations caused by themisalignment of the microlens, instead of using aflat reflection mirror, a concave reflection mirrorwith radius close to the focal length of the mac-rolens has been employed. Both the f/2.9 macro-lens (KPX088) and the concave mirror (KPC031,with reflection coating on the concave side) havebeen selected among readily available Newportoptical components.

Based on Huygen’s scalar diffraction theory, ageneralized form of paraxial wave optics [19] hasbeen developed to analyze the wave propagationthrough an arbitrary complex optical system con-sisting of a cascaded series of optical elements. Theparaxial optical system can be characterized by an

overall ray matrix or ABCD matrix, which can bederived according to geometric optics. The wavepropagation from plane z1 to plane z2 can bemathematically expressed by

u2ðx2; y2Þ ¼ � jkB

ejkLZ Z

u1ðx1; y1Þ

� exp ðjk=2BÞ½Aðx21�

þ y21Þþ Dðx22 þ y22Þ � 2ðxxx2 þ y1y2Þ

�dx1 dy1

ð1Þin which u1ðx1; y1Þ and u2ðx2; y2Þ are the opticalfield distributions in plane z1 and plane z2, re-spectively, k is the optical wavelength in free space,k ð¼ 2p=kÞ is the wave number, L is the total op-tical path length for a ray travelling exactly on theaxis through the system, and A, B, D are the ele-ments of the ray matrix

Fig. 2. Schematic diagram of the folded hybrid optical system with a top concave mirror for interconnect. The inset depicts a mag-

nified view of the beam focused on the detector.


A BC D

� �

representing the optical system between plane z1and plane z2. The ray matrix of a system com-prising various cascaded optical components isobtained by multiplying the individual ray matri-ces for the individual components including free-space sections, and these matrices are arranged inreverse order from the one in which the ray en-counters the components. The transfer matrix forfree space is written as

1 d=n0 1

� �; ð2Þ

where d is the thickness and n is the refractive in-dex of the medium, and the refraction matrix for arefractive surface takes the form

1 0�ðnt � niÞ=r 1

� �; ð3Þ

where nr and nt are the indices of refraction forthe incident medium and the transmittingmedium, respectively, r is the radius of therefracting surface and it obeys the commonlyused sign convention. Therefore the ray matrixof a lens is the product of the transfer andthe two refraction matrices in the reverse order.The ray matrix for a reflecting surface can bereadily obtained by substituting nr ¼ �nt intoEq. (3).

In our system, the VCSEL works at 850 nm andthe beam has a waist of 1:03 lm. The substratebetween the VCSEL and the microlens has athickness of about 637 lm and a refraction indexof 1.523. The plano-convex microlens has a sag of50 lm, a radius of )250 lm, a diameter of about330 lm, and a refraction index of 1.52. The pa-rameters for the plano-convex macrolens ared4 ¼ 5:122 mm, n ¼ 1:51, and r4 ¼ �39:07 mm.The radius of the concave reflection mirror isr5 ¼ �75:69 mm. The aperture of the VCSEL andthat of the detector are 5 and 50 lm, respectively.For simplicity, we consider the coaxis wave prop-agation through the system. The system matrix canbe written as

M ¼ T10M9T8M7T6R6T5M4T3M2T1; ð4Þ

in which T is for the transfer matrix of a layer ofmedium, M the functional matrix of a lens, and Rthe reflection matrix of a mirror. The amplitude ofthe beam emitted from the VCSEL is assumed tosingle-mode Gaussian function as

u0ðx; yÞ ¼ exp

� ðxþ yÞ2

w20

!; ð5Þ

where w0 is the waist of the Gaussian beam.The beam emitted from the VCSEL plane is

first collimated by a microlens and after thepropagation through the optical channel it is fi-nally refocused to the detector by another micro-lens. To check the beam clipping at the aperture ofthe microlenses, the ray matrices for the subsys-tems between the VCSEL plane and the respectivefront surfaces of the two microlenses can becalculated separately and substituted into Eq. (1)to observe the field distribution at the frontsurfaces. In our case, the energy loss due to thebeam clipping is negligible. The intensity distri-bution when the beam arrives at the detector planefor the first time is shown in Fig. 3. The diameter isabout 18 lm, which is much smaller than theaperture of the detector. Note that the detector hasperiodic electrodes deposited on the GaAssubstrate, and the reflectances of the electrodesand the substrate are approximately 81% and 36%,respectively. Thus, part of the beam will bereflected from the MSM detector. The detector canbe regarded as an amplitude grating with theamplitude response

gðxÞ ¼ rectxa

� r1 comb

xp

�� rect x

p1

� ��

þ r2 combxp

�� rect x� p1

p � p1

� ��; ð6Þ

where a is the aperture size of the detector, r1 ¼ 0:9and r2 ¼ 0:6 are the reflection coefficients of themetal and the substrate, respectively, p and p1 arethe pitch and the width of the electrodes, respec-tively, and the symbol � represents convolution.The reflected field is assumed to be the conjugateof the incident wave modulated by the grating andsince the link is symmetric, the system matrix forback propagation is the same as that for frontpropagation. The simulated density distribution of


the reflected beam that reaches the VCSEL plane(Fig. 4) indicates that the size of beam is not biggerthan the window of the device. Moreover, becauseof the significant distortion of the reflected beam ina real system, the coupling of the reflected beaminto the VCSEL cavity mode is expected to be low.Subsequently, the effect of coupling between thereflected beam and the VCSEL has not been in-

cluded in the ghost talk analysis. Since in generalthe VCSEL’s top surface has a high reflectance, theworst case ghost talk analysis is conducted underthe assumption that the reflectivity is 100%. Thebeam incident on the VCSEL will be reflected andpropagated through the system to the detectoragain. Fig. 5 shows the intensity distribution whenthe beam arrives at the detector for the second

Fig. 4. Intensity distribution when the reflected beam hits the VCSEL.

Fig. 3. Intensity distribution when the beam hits the detector for the first time.


time. The beam will be transmitted back and forthseveral times until it is totally absorbed at the de-tector. According to the numerical simulations andthe experimental results, in this system the crosstalk among adjacent channels is negligible.Therefore, the ghost talk, which is caused by su-perposition of signals of different delays, will havea dominant effect on the high-speed optical inter-connection.

3. Effect of the ghost talk on optical interconnection

To study the effect of the ghost talk in oursystem, a SPICE model of the optical link thatincludes the characteristics of the VCSEL/MSMdevices and their corresponding driver/receivercircuits and surface refelectivities has been devel-oped. In the link, the VCSEL has a 0.45 mAthreshold current and 0.8 W/A efficiency whereasthe MSM detector has 0.25 A/W responsivity at 5V. The performance of the transmitter/receivercircuits also plays a critical role in the optical in-terconnection. The primary criteria for transmit-ter/receiver are high speed, small area and lowpower dissipation. The current mirror style trans-mitter (Fig. 6) employed in our system providesthe flexibility of individually controlling the

threshold and modulation currents of the laser,characteristics that are very useful in prototypesystems. The transimpedance receiver (Fig. 7)converts the weak photocurrent generated by thedetector to voltage. Then the signal is amplifiedand the thresholding stage restores the CMOSlogic levels of the data. The detector dark currentfrom the input of the transimpedance amplifier isredirected with a feedback provided by an NMOStransistor and the gain of the transimpedance stageis regulated by the control voltage Vrs. Local gen-eration of reference voltage for thresholdingmakes the receiver self-adapted to power fluctua-tions. The eye diagrams of the transmitter and the

Fig. 5. Intensity distribution when the beam hits the detector for the first time.

Fig. 6. Current mirror style transmitter.


receiver both working at 1 Gb/s are shown in Figs.8 and 9, respectively.

The optical path length from the VCSEL to thedetector is 175 mm, so the delay of a single round-trip is about 1.2 ns. The numerical simulationsdescribed in the last section indicate that 40% ofthe beam incident on the detector will be reflected.Assuming that the intensity of the beam hitting thedetector for the first time is 1, then the intensityvalues for the successive delayed signals are 0.4,0.16, etc. The total optical signal received by thedetector is the summation of the original and thedelayed waveforms. The responses of the MSMdetector and its corresponding receiver operatingat 500 Mb/s for the cases when the ghost talk is/notpresent in the system are summarized in Fig. 10.Depending on the delay in the optical path and the

period of the transmitted signal, the effect of thereflections of one symbol can extend to next fewsymbols and thus cause intersymbol interference(Fig. 10(a)). This, on the other hand, results in achange of the DC level and the amplitude of thephotogenerated current (Fig. 10(b)) and masquer-ades as a duty cycle variation (24% instead of 50%)at the output of the receiver (Fig. 10(c)). The dutycycle variation can be balanced by adjusting theDC level of the photogenerated current throughthe NMOS transistor at the front stage of thetransimpedance amplifier. Figs. 11 and 12 depictsimulations of free-space links operating at 500Mb/s and 1 Gb/s in which the effects of ghost talkhave been compensated for by increasing thebias voltage of the NMOS transistor from 1.6 to2.05 V.

The analysis conducted in this study indicatesthat the intersymbol interference caused by thepresence of significant amount of ghost talk in afree-space optical interconnect can be compen-sated for by employing a receiver architecturethat allows for DC level adjustment of thephotocurrent. The ghost talk effect depends onseveral system parameters such as the transmis-sion efficiency, the surface reflectance of theFig. 8. Transmitter eye diagram at 1 Gb/s.

Fig. 9. Transimpedance receiver eye diagram at 1 Gb/s.

Fig. 7. Transimpedance receiver.


optoelectronic devices, and the delay of the sig-nals incident on the detector, which is related tothe optical path length from the VCSEL to thedetector. Actually in the case when each channelis operated at the speed of 1 Gb/s, the ghost talk

effect in the above simulation is very severe, sincethe single round-trip delay is close to the half ofthe signal period. The method has also beenproved to be effective for our system when thedelay is smaller.

Fig. 11. Compensation of the effect of ghost talk by shifting the DC level of the photocurent in a high-speed optical interconnection at

500 Mb/s. The bias voltage has been increased from 1.6 to 2.05 V. Dashed line, without ghost talk; Solid line, with ghost talk.

Fig. 10. Ghost talk and its effect on high-speed optical interconnection at 500 Mb/s: (a) photocurrent components generated by the

original signal (solid line) from the VCSEL and round-trip reflections (dashed lines); (b) total photodetector current in a system with/

without ghost talk. In the presence of ghost talk, the overall photocurrent is the sum of those components; (c) output signals at the

logic circuit with/without ghost talk. The bias voltage of the NMOS transistor is set to be 1.6 V. The duty cycle of the output signal in

the presence of ghost talk is changed.


4. Conclusion

In this paper, we have analyzed the perfor-mance of free-space optical interconnect for thethree-dimensional optoelectronic stacked proces-sor (3DOESP). The wave propagation in the op-tical interconnection system has been studiedbased on rigorous scalar diffraction theory. Withsuitable design of the optical system, the cross talkcan be negligible. By employing a receiver archi-tecture that allows for DC level adjustment at theinput of the transimpedance amplifier stage, theeffects of the ghost talk in the system can becompensated for and thus a high performancefree-space optical interconnect at high speed canbe achieved even in the presence of significantamount of ghost talk.

Acknowledgements

This effort is sponsored by the Defense Ad-vanced Research Projects Agency (DARPA) andAir Force Research Laboratory under agreementnumber F30602-97-2-0122.

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Fig. 12. High-speed optical interconnection at 1 Gb/s in the presence of ghost talk: (a) photocurrent components generated by the

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