Active semiconductor microdisk devices

IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 1, JANUARY 2002 105

Active Semiconductor Microdisk DevicesKostadin Djordjev, Sang-Jun Choi, Seung-June Choi, and P. D. Dapkus, Fellow, IEEE

Abstract—The design of active semiconductor microdiskswitches, modulators, or wavelength routers enabled by mod-ulating the transfer characteristics of a resonant cavity isinvestigated. A simple theoretical model based on coupled-modetheory is used to elucidate design trends and constraints in thecases where electroabsorption, gain, and free carrier injection areemployed to modulate the resonator characteristic.

Index Terms—Active microresonators, electroabsorption effect,integrated optics, modulators, optical switches, optical waveguidefilters, wavelength division multiplexing (WDM).

I. INTRODUCTION

MANY practical passive devices incorporating mi-crodiscs and microrings have been demonstrated lately,

including channel dropping filters [1], WDM demultiplexers[2], and notch filters [3]. The spectral selectivity inherent inthese resonant structures makes them attractive for applicationsto wavelength division multiplexed (WDM) systems. Bycoupling to bus waveguides, a single ring may completelytransfer a resonant wavelength [4] from the input waveguide toanother waveguide and offer superior performance comparedto standing-wave resonators. The passive devices fabricated todate from semiconductors range in radius from 4 to 30 m,illustrating that such devices can be very compact and areamenable to large-scale integration. Passive devices, such asthe ones described here, have many limitations when consid-ered for incorporation into large-scale systems using a fixedmanifold of wavelengths. Their inherent wavelength selectivityplaces unrealistic demands on fabrication uniformity andreproducibility, and their temperature sensitivity suggests thata static system design would be thermally unstable. For thesereasons alone, it is interesting to consider active resonator de-vices that can be configured as tunable elements. Active devicesalso enable switching and tuning elements to be incorporatedinto an optical circuit that greatly increases the functionalityof such circuits. Furthermore, with slight modifications ofthe device design, one can easily envision that the same basicstructure can be used to incorporate tunable lasers, detectors,and modulators into the system. In view of the potential ofthese elements in WDM systems, it is surprising that so littleattention has been paid to analyze their performance. In thispaper, we will analyze the operation and design of activesemiconductor microresonator devices to determine the mostpromising mechanisms to incorporate into the resonator toachieve the desired tunability and switching characteristics.

Manuscript received May 31, 2001; revised October 12, 2001. This work wassupported by DARPA under Contract N00014-00-C-0292.

The authors are with the Department of Electrical Engineering and Electro-physics, University of Southern California, Los Angeles, CA 90089 USA.

Publisher Item Identifier S 0733-8724(02)00374-2.

(a)

(b)

Fig. 1. Schematic diagrams of resonator–waveguide device with (a) laterallyand (b) vertically coupled microdisk resonator.

Our design perspective is to focus on those mechanisms thatmaintain high system throughput and require low electricalpower to effect.

There are two main configurations utilizing the coupling be-tween the disk and bus waveguides. The first approach uses lat-eral coupling [see Fig. 1(a)], with waveguide–resonator sepa-rations on the order of 0.1 m, fabricated by high-resolutionlithography. This small separation is a result of the high-indexcontrast ( ) at the semiconductor–air interface and, inthis design, the coupling coefficient is very difficult to control.The second approach uses a vertical geometry [5] and has theadvantage of precise control of the coupling coefficient by epi-taxial growth [see Fig. 1(b)]. Another advantage is that waveg-uides and resonator can be grown with different material com-positions. This facilitates the design of active microdisk de-vices—ON–OFF switches, modulators, and microdisk lasers.

The precise simulation of an active microdisk device is arather challenging task. This includes solving for the resonantmodal-field distribution and for the coupling between the diskand the waveguides under given pumping conditions, and, atthe same time, accounting for all of the properties of the ac-tive media. The finite difference time domain (FDTD) methodsolves Maxwell’s equations exactly, but it is not intuitive, and iscomputationally intensive and time consuming. It is also diffi-cult to incorporate gain–absorption in this model. It can be used,however, for the simulation of – fields in the final device.The conformal transformation approach for finding the modalfields (for example, [6]) is rather fast, with reasonable accuracy,and can be used to solve parts of the problem such as the opticalcoupling coefficient between the resonator and the waveguidesbuses.

0733–8724/02$17.00 © 2002 IEEE

106 IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 1, JANUARY 2002

In this article, we will analyze the effect of incorporatingan active region inside a semiconductor microdisk resonatorand will find certain design constraints and material parame-ters leading to optimal device performance. Gain and electroab-sorption (EA) regions are considered as means for tuning theresonator and for affecting its losses (and, therefore, its qualityfactor ). Free carrier (FC) injection–absorption is also investi-gated as means to tune the resonator–switch. The losses that ac-company the FC-induced index changes, in this case, are detri-mental but small. In the case where practicality of the modula-tion mechanism is strongly dependent on the specifics of the ac-tive region design (electroabsorption), we have also included anoptimization of the active region design. The theory of couplingmodes in time [coupled-mode theory (CMT)] [1] is used as amain theoretical approach because of its simplicity and speed.Also, the main objective of this work is not to find the exact so-lution, but to elucidate some trends and general design criteria.This approach does not distinguish between polarizations (CMTlooks at the devices as lumped circuits), but the effects of polar-ization can be calculated by utilizing the appropriate couplingcoefficients and effective indices of refraction for each polar-ization to model them separately. Although this is an importantconsideration, it is not the objective of this paper.

The article is organized as follows. In Section II, CMT is re-viewed because it is the main tool used. Section III discussesthe main factors limiting the device frequency bandwidth. Sec-tions IV–VI discuss the properties of an active microdisk devicewith electroabsorption, gain, and free-carrier active regions, re-spectively.

II. CMT

The CMT formalism [1] looks on the resonator as a lumpeddevice and only considers the total energy and power in the ring.All structural parameters are taken into account by the couplingcoefficient and the model assumes single-mode operation. Thering has an energy amplitude , normalized so thatrepresents the total energy stored. This energy is supplied bythe incident wave of amplitude . The output wave travelsto the detector, and the power not coupled to the ring travels asa transmitted wave . Here, is normalized so that is thepower in the waveguides.

The oscillator has a resonant frequency and an ampli-tude decay time constant . This decay rate is related to: i) theenergy leaving the disk toward the detector by ; ii) theenergy coupled to the transmitted wave by ; and iii) theenergy lost inside the disk due to scattering by :

. From energy-flow considerations,, where is the mutual coupling coeffi-

cient. After solving the coupled equations for the resonator andwaveguides assuming a harmonic input, the amplitude transmis-sion coefficient is

(1)

The quality factor of a resonant cavity defines the spectralselectivity of the device, , where is the spectral

Fig. 2. Frequency bandwidth of a microresonator as limited by the capacitanceand quality factor Q.

linewidth of the resonance. is proportional to the amplitudeloss rate by . Thus, the associated with internalloss and scattering can be defined as (is the distributed absorption coefficient [ ], and is theeffective refractive index). Also, the associated with couplingloss is found to be ; is the ringradius and is the power coupling coefficient between theinput , output waveguide , and the ring). Using these relation-ships, (1) can be rewritten as

(2)

where is the detuning from the resonance and the changeof the refractive index, , causes a change of the resonantfrequency (terms in the order of are neglected).

The transmittance of the resonator-waveguide coupler can beaffected by: i) changing the absorption, i.e., , by the EAeffect ( and are fixed by the device geometry); ii) in-troducing gain into the medium ( ); and iii) changingthe refractive index by FC injection. In this paper, we willinvestigate all three mechanisms.

III. FREQUENCY BANDWIDTH

There are three limiting factors that determine the frequencybandwidth (the response time) of an active microdisk device:i) the parasitic capacitance from the bond-pads and the junctioncapacitance; ii) the quality factor of the cavity (the energy buildsup and decays with a certain time constant); and iii) the modu-lating mechanism itself.

Fig. 2 shows a plot of the bandwidth imposing restric-tions on the maximum allowed junction capacitance and loaded

. Assuming a load resistance of and intrinsiclayer thickness of m (a typical value for thesedevices— scales linearly with ), a bandwidth of 40 GHzlimits the disk radius to less than 10 m. Because this is based

DJORDJEV et al.: ACTIVE SEMICONDUCTOR MICRODISK DEVICES 107

Fig. 3. Quality factor and transmission of a microresonator with radius R = 5 �m as a function of the internal loss � and power coupling coefficient �.

purely on area considerations, can be increased by not cov-ering the whole disk with an electrode (as the optical field isconcentrated close to the disk edge) or by the use of a microring.

Certain semiconductor devices, such as add-drop filters andswitches, require both large free spectral range (FSR) and high

. Large FSR can be obtained by decreasing the cavity dimen-sions. For example, a cavity with m has FSR nm,which is larger than the communication window defined by theEr-doped amplifier. On the other hand, increasing the loadedleads naturally to decrease of the bandwidth–speed of the de-vice. Fig. 2 shows that a of 5000 limits the bandwidth to40 GHz. The maximum available value of is determined bythe bending radiation losses [7], and they are less than 1% perround trip for diameters greater than 1 m [6] for high-indexcontrast semiconductor devices. Therefore, for any practical de-vices with radii less than 10 m, is limited by the loadedquality factor of the cavity.

The bandwidth may also be restricted by the modulationmechanism. For example, an active region employing EAlimits the device speed much less than an active region withgain or free carrier injection modulation. In the latter cases, theminority carrier lifetime on an order of ns constrains thebandwidth to GHz.

IV. EA LOSS ACTIVE REGION

The EA effect is widely used in practice for designing mod-ulators [8], but in the case of a microdisk device, the absorptivemechanism can be used to suppress the resonant power transferrather than to promote loss. Thus, the input signal only suf-fers small attenuation. The potential advantages of this approachhave been described by Little et al. [9]. The design methodology

we have employed here minimizes the required applied voltageto affect a certain ON–OFF contrast ratio (CR). This approachmay result in some residual loss in the high transmission statethat would be viewed as insertion loss. If the applied voltage isnot a constraint, choosing another design can reduce this inser-tion loss.

To investigate the influence of the loss on the resonator, per-formance contours of equal power transmission andderived from (2) are plotted at resonance for m disk inFig. 3 against two independent variables. The first independentvariable is the coupling coefficient , which can becontrolled by choosing the appropriate vertical separation be-tween the waveguide and disk; the second variable is the loss inthe disk, .

The intersection values for the and contours on theaxis (when ) are for a stand-alone disk, i.e., when the diskis not coupled to the waveguides. Increasing the losses insidethe device leads to decrease of the quality factor, which is losslimited. The values of and on the axis are for the caseof an ideal disk without internal losses ( ). is couplinglimited and the input energy is completely transferred ( )to the output waveguide independent of (assuming symmetriccoupling). Any practical configuration ( ) can befound somewhere in between.

Note that the disk can tolerate moderately large losses andstill provide useful performance as an add–drop filter. For ex-ample, to obtain power transmission of (90% of theinput power is extracted from the bus waveguide) with loss co-efficient cm , we can design the power coupling coeffi-cient to be and the resulting . To obtain thesame transmission at higher losses, cm , the couplingefficiency needs to be increased, , to compensate for


Fig. 4. Quality factor and transmission of a microresonator with constant power coupling coefficient of � = 0:02 as a function of the internal loss �.

the power lost. This, of course, will decrease the quality factorof the cavity to .

A larger disk is less sensitive to the coupling, meaning that atthe same and , the larger disk has larger quality factor butalso larger transmission (we want small, possibly zero, trans-mission at resonance). Thus, going to bigger disks, we trade CRfor quality factor (or ).

Fig. 3 also shows the possibility of designing an activedevice by using absorption as a modulating mechanism.For acceptable, practical values of the contrast ratio ofCR lg dB, and , this graphcan be used for design considerations. Let us assume that thecoupling coefficient is , and we would like to vary thelosses in order to achieve a change of transmission .For , the loss has to be cm and the resulting

, for , we need cm and theresulting . Thus, to achieve the desired contrast ratio,the electroabsorption parameter must be .This is also shown in Fig. 4, where and are plotted as afunction of at (the intersection points indicated bythe dashed line in Fig. 3).

In bulk materials, EA is achieved by the Franz–Keldysh (FK)effect, and in two-dimensional (2-D) quantum-well materials,EA is achieved by the quantum confined stark effect (QCSE).The QCSE is more sensitive to the applied voltage and the ab-sorption change is much larger than in the case of the FK ef-fect. Thus, the QCSE is the preferred choice [10]. We follow themethod outlined in [13], where the quantum-well (QW) statesunder applied field are calculated via the transfer matrix ap-proach for solving the effective mass equation, and the excitondiscrete states are found by the variational method. The com-plete absorption spectrum can be calculated as a sum of bound-

state excitonic transitions and continuum-state quantum wellcontributions.

The purpose of this section is to investigate the applicabilityof the QCSE in active microdisk devices. As shown in Fig. 3, amicrodisk resonator is very sensitive to any kind of loss. Thus,the challenge is to optimize the active region in such a way as tomeet all of the design targets. Positioning the mode frequencycloser to the bandgap increases the absorption change and, thus,decreases the required switching voltage. The closer positionalso increases the background absorption at zero voltage and de-creases the CR. Thus, the tradeoff is between drive voltage andCR, and the challenge is to find the appropriate QW compo-sition and size which will give maximum transmission changeand CR at m.

To accomplish this task, we developed a procedure forQW optimization, which is similar to the one outlinedin [8] but differs in that, here, the task is to find the op-timal conditions for electroabsorption microdisk devices.The results are shown in Figs. 5–6. The procedure for theIn Ga As P –In Ga As P system as follows.

1) Assume barrier strain and wavelength, for exampleand m. The composition parametersare then found.

2) Assume QW strain ( ), and calculate the QCSEat wavelength m for different (0.66to 0.77) and different QW sizes (70 to 150 ). Theapplied field is kV/cm, which corresponds to

V for an intrinsic layer thickness m.The bandgap energy and the overlap integral (65 kV/cm)between the conduction band (CB) and the first valenceband (VB) bound state are given in Fig. 5. The overlap inte-gral and, thus, theoscillator strengthdependsmainlyon the


Fig. 5. QCSE optimization. Bandgap energy and overlap integral between the CB and the first V B ground state as a function of the QW size L and QWAscomposition y .

Fig. 6. QCSE optimization. Change in transmission�T and transmission in OFF state T of a microresonator with radius R = 5 �m as a function of the QWsize L and QWAs composition y .

QW size, and it is weakly dependent on the composition.The smaller the QW size, the stronger the particle confine-ment. Under an applied electric field, the and wavefunctions shift toward the opposite ends of the QW. Thus,the stronger confinement leads to larger overlap integral.

3) Calculate the absorption coefficient at zero bias and atkV/cm.

4) Use the results from the previous step and calculate thechange in absorption (maximum value is

cm ) and the change in refractive index (max-


Fig. 7. Contours of constant transmission T and quality factor Q for a R = 5 �m microdisk with gain-active region. The concomitant change of the refractiveindex �n is not taken into account.

imum change at m dueto the applied field.

5) Assuming an average optical confinement of ,two QWs, , and using (2), the calculatedtransmission in the OFF state ( ) and are given inFig. 6.

The best values are achieved at and, which corresponds to a bandgap energy of

eV ( m). This composition does notcoincide with the one where is maximum ( ,

). This is because, under these conditions, the highbackground absorption decreases the contrast ratio. Thus, theobjective is to find a composition with a high absorption changeand, at the same time, with a small background absorption.The transmission achieved in the OFF state is and

, which corresponds to CR dB. From theseresults, it can be concluded that the design of an EA activemicrodisk will require precise tuning of all the parameters, diskdimensions, and active region composition.

The performance of a single-disk EA devices is limited bythe minimum achievable loss in the ON state, which determinesthe quality factor (the bandwidth) of the unbiased device, andthe available dynamic range of the active EA region. A rea-sonably high on-resonance extinction could be achieved and thedevice could be useful for modulator and ON–OFF switch appli-cations. Further improvement of the performance could be real-ized by designing higher order filters [11].

V. ACTIVE REGION WITH GAIN

Waveguide circuits inevitably introduce losses that limit thescale of the system or that require the use of optical amplifica-tion for compensation. In this section, we consider the effects

and implications of introducing gain as a mechanism to varythe transfer function of the resonant coupler. Because electricalexcitation of the resonant medium changes both the loss andthe index of refraction, it is expected and found that the func-tionality of the device is altered over the EA case studied in theprevious section, where the dominant effect is variation of theloss. To separately demonstrate the effects resulting from the in-troduction of gain into the resonator, we have plotted, in Fig. 7,contours of equal transmission and using (2) for a gain-ac-tive region ( ) where we have not included the inevitablechanges in the refractive index. The contours are plotted, as-suming a rather high value of residual loss in the resonator of

cm . We have chosen a value that is at the limit ofusable device performance to show that even a lossy cavity canprovide a useful performance with small driving powers whengain is used as the active region modulation mechanism.

In this case, the gain compensates for losses and the in-creases with gain, which is accompanied by a decrease of thetransmission at resonance (in the presence of gain, the definitionof is questionable and, in this case, the linewidth is a betterquantity for consideration). The cavity views the coupling to thewaveguides as an additional loss, and, thus, with an increase of

, for given gain, decreases. Above a certain gain value, thestimulated emission from the cavity adds to the mode energy,and, thus, the transmission begins to increase rapidly. The clearmaximum in the ( goes to infinity) and in the transmissioncoefficient along the line connecting the coordinates ( ,

) and ( , ) expresses the threshold condi-tion: GAIN LOSS. At that point, the device is a laser. Thedata on the right of this line is invalid because that line marksthe condition for which the gain is pinned to its threshold value.

Of course, in practice, a pure gain medium is impossiblebecause there is inevitably a concomitant change in the index


Fig. 8. Material gain and the associated �n as a function of the carrier density, calculated for an In Ga As P QW/B.

Fig. 9. Contours of constant transmission T and quality factor Q for a R = 5-�m microdisk with gain-active region. The concomitant change of the refractiveindex �n is taken into account.

of refraction. Furthermore, the devices we model are high-resonant cavities and any change, even a small one, inleads to detuning of the resonant frequency and decreaseof the transmission. Thus, the inclusion of by a morerealistic active region in the calculations is an importantissue. The gain spectrum and the total recombination rate foran In Ga As P –In Ga As P active region iscalculated [12], and the results are shown in Fig. 8 for the caseof m, gain peak positioned at m, andQW compressive strain [13]. The index change iscalculated using Kramers–Kronig (KK) relationships.

The calculation of and for a fixed-wavelength input areshown in Fig. 9. The maximum in the transmission around thecoordinate ( ) is due to the inclusion of the re-fractive index change , which shifts the resonance and, thus,affects . In this case, the coupling coefficient has to be properlytuned in order to achieve the desired transmission change. Forthe application of this device as a modulator or switch, hasto be at least 70% to achieve CR dB. Applying a couplingof and having the initial modal gain of cmand final modal gain of cm , we can meet this target.If we assume only one well, confinement factor of ,


Fig. 10. Contours of constant transmission T and quality factor,Q for a R = 5 �m microdisk with active FC active region.

and load resistance of , calculated drive currentsresult in voltage changes of less than 0.2 V to achieve thesegain and transmission changes. Again, this is based on activearea considerations, and, thus, by varying the disk and electrodesizes, different voltage-to-gain characteristics can be achieved.The bandwidth of the device will be limited by the minority car-rier lifetime.

A microdisk device with a gain active region could be usefulas a laser, ON–OFFswitch, modulator, and add–drop filter. Thegain compensates for the loss, and a high extinction ratio anddrop efficiency could be obtained with low power consumptionat the expense of a speed limited by the carrier lifetime. Thedevice can be operated in two regimes. The first is in the limitof small coupling coefficient and small index change, where in-creasing the gain compensates for the loss, increases the loaded

, and decreases the transmission. The second regime is whenthe device is used with a bias point set to achieve zero trans-mission and increase of the gain leads to increase of . Ei-ther mode is potentially useful and requires very low switchingpower. Each also permits the bias tuning of the operating pointnecessary to compensate for fabrication or temperature varia-tions.

VI. FREE CARRIERS ACTIVE REGION

In cases where gain is not desired or required, processes thatmerely tune the resonant frequency offer an interesting counterexample to loss modulation considered previously. In this sec-tion, we investigate the behavior of a region into which free car-riers are injected. To maximize the effects of the free carrierdensity on the effective index of the mode in the resonator weconsider a thick, highly confining waveguide with a bandgapenergy higher than the operating photon energy. This region is

an intrinsic, high refractive index layer sandwiched between -and -doped low-index layers. Free carriers are injected into the

region by applying forward voltage to the p-i-n junction. Werestrict the injection level to levels low enough to avoid popula-tion inversion and gain in the region. The first task is to find thecarrier density in steady-state condition from the rate equationwithout the stimulated recombination

(3)

Here, we assume , cm /s is the spon-taneous emission rate coefficient, cm /s is theAuger recombination rate coefficient, [A/cm ] is the currentdensity, and m is the intrinsic layer thickness.Solving for , we obtain carrier densities up to 4 10 cmfor current densities up to 200 A/cm .

The next task is to obtain the refractive index change due tothe free carriers injected into the intrinsic region. For this hy-pothetical device, we choose to estimate the free carrier effectsusing an empirical relationship that captures the magnitude ofthe effect in the absence of a specific design. The empirical for-mula used is [14] .Here, is the confinement factor of the mode, which is ap-proximately 50%, and is the carrier density in cm . For thecurrent density change mentioned previously, index changes areon the order of .

The injected carriers absorb light. The free carrier absorption(FCA) coefficient, in this case, is also found by using anempirical relation, FCA

. Here, is in cm and is in cm . Thisrelationship was empirically determined for GaAs at an energybelow the bandgap. The magnitude is not expected to be


strongly dependent on the materials choice for energies belowthe bandgap. The change in the absorption found for the carrierdensities of interest is cm , which does not stronglyaffect the .

The performance of an active microdisk with this active re-gion is calculated by assuming a background absorption of

cm , which is a typical value measured in semiconductorlaser diodes and includes the material absorption and the absorp-tion from the - and -doped regions. Fig. 10 shows a calcula-tion of the transmission change and the total quality factor ofthe cavity. The change of the refractive index affects the cavityperformance more than the FCA, and switching is achieved, forexample, with A/cm at . At these condi-tions, remains almost constant , , and ,which gives CR dB.

This result shows the attractive features of a free carrier in-jection region as an active material. Another attractive feature isthat the device could be fabricated in a variety of direct bandgapmaterials without the need to match the energy gap to the inputwavelengths.

FC injection could be an useful approach for building activesemiconductor microdisk devices. The index change has muchlarger influence than the absorption change and the device couldbe tuned without substantially degrading the quality factor andthe filter bandwidth. This may find application in photonic cir-cuits, where an active tuning of the resonant frequency is re-quired in order to compensate for fabrication imperfections andaging processes. Also, this shift of the resonant frequency couldbe used in modulator, ON–OFF switch, and add–drop filter appli-cations, where large contrast ratios could be achieved with smallpower consumption.

VII. SUMMARY

In this article, active microdisk resonators have been analyzedby the use of CMT, and, at the same time, the optical propertiesof the media have been taken into account. These active res-onators may serve as building blocks for microdisk lasers, mod-ulators, and ON–OFF switches. For high-speed operation, diskswith radii less than 10 m have to be considered and the band-width is limited either by the quality factor of the cavity or by theactive region itself. When the electroabsorption effect is used,contrast ratios of more than 10 dB can be achieved. The deviceis loss modulated and will require precise tuning of both themultiple QW region and the fabrication process. Any additionalloss, i.e., due to scattering from sidewall roughness, will tend todecrease the CR. The active region with gain, on the other hand,is able to tolerate much higher losses while achieving high CR,but the bandwidth is limited by the minority carrier lifetime.Furthermore, the device has to be designed carefully becausethe corresponding refractive index change has considerable ef-fect on the transmission. Another promising mechanism is mod-ulation of the resonance by free carrier injection into an intrinsicwaveguiding region, the resonator. The effect of change of therefractive index on the transmission is larger then the effect ofFCA, and, thus, high-contrast ratios can be achieved at almostconstant . Also, another attractive feature of the FC injection

region is that a device, operating at 1.55 m, could be built ineither the InP or GaAs material systems.

ACKNOWLEDGMENT

The authors wish to thank T. Sadagopan for technical discus-sions and Dr. J. Lorenzo for support during the early stage ofthis work.

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Kostadin Djordjev, photograph and biography not available at the time of pub-lication.

Sang-Jun Choi, photograph and biography not available at the time of publica-tion.

Seung-June Choi, photograph and biography not available at the time of pub-lication.

P. D. Dapkus (SM’80–F’87), photograph and biography not available at thetime of publication.

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Active semiconductor microdisk devices