Carrier refraction in quantum well waveguides

Richard A. Soref and Brian R. Bennett

Carrier-induced refractive index changes in forward-biased InGaAs-InAlAs quantum well waveguides arecalculated using a Kramers-Kronig transformation of Bar-Joseph's experimental absorption spectra [Phys.Rev. Lett. 59,1357 (1987)]. At the l.65-,um wavelength where the material is nominally transparent, an indexchange of -0.06 is found for an injection of 6 X 1017 electrons/cm 3 . A quantum well waveguide 2 X 2 reversed-A46 directional coupler switch with an active length of 480 ,um is proposed.

I. Introduction

The optical properties of III-V semiconductors canbe modified by the injection or depletion of chargecarriers (electrons or holes). The optical changes areespecially large in quantum well (QW) structures;thus, QWs are prime candidates for optical modulationapplications. A series of recent papers 1-3 describedcarrier-induced optical absorption in an InGaAs QW,although the refraction effects received little or noattention. The purpose of this paper is to examine theQW refraction effects in some detail. Because refrac-tion and absorption are linked by the dispersion rela-tions, we have used those relations to deduce the re-fractive index changes An from knowledge of thedifferential absorption spectra Aa. The dependenceof An upon electron density N is shown.

The main motivation for this work is to advance theart of integrated optics technology, mainly the art ofactive waveguide components. Such components canbe grouped into those that rely upon absorption effects(amplitude modulators) and those that use refractiveindex changes (phase modulators). An amplitudemodulator is usually a simple two-port device, while aphase modulator is often included as part of a moresophisticated device like a 2 X 2 interferometricswitch. That is why phase shifting is emphasized here.We shall describe how carrier-controlled QWs can beembedded in optical waveguides in order to make volt-

When this work was done both authors were with Rome AirDevelopment Center, Solid State Sciences Directorate, HanscomAir Force Base, Massachusetts 01731; Brian Bennett is now withMassachusetts Institute of Technology, Department of MaterialsScience & Engineering, Cambridge, Massachusetts 02139.

Received 16 May 1988.

age-controlled optical switches. A new 2 X 2 switchdesign is given, and the design tradeoffs are discussed.

II. Phase-Space Absorption Quenching

Experimental work by Chemla et al.1 and Bar-Jo-seph et al. 2 has revealed the effects of a free-electronconcentration upon the optical absorption of an In-GaAs quantum well. These researchers measured thedifferential absorption spectra of an Ino.53Gao.47Asquantum well between InAlAs barriers grown lattice-matched on an InP substrate. The differential ab-sorption Aa was measured as a function of photonenergy h at temperatures from 10 to 300 K. Theabsorption change a(hcv) is defined as a(-) - a(N),where a(°) is the absorption spectrum of the empty QWand (M) is the spectrum at an electron density N.

The principal effect of free carriers is to quench then = 1 exciton absorption by the process of phase-spacefilling and to red-shift higher lying states (n = 2,3,. . .)through electrostatic effects. Just above the bandgapEll(N), the positive Aa peak is quite large and reaches20,000 cm-l at large N. The complete physical expla-nation of the various spectral features is complicated.Phase-space filling",2 is a generalization of Burstein-Moss blue-shifting to include excitonic effects. Cou-lomb screening and exchange contribute to bandgaprenormalization effects that change the bandgap ener-gies.1,2

A set of 10 K spectra for five values of Nwas given inFig. lb of Ref. 2. These are reproduced here as Fig. 1.We believe that the Fig. 1 spectra are representative ofthe carrier-induced behavior of III-V MQW materials;therefore, we performed a Kramers-Kronig transfor-mation of these Aa-curves in order to find the differen-tial refraction spectra An(hw) = n()- n(N) for a typicalmaterial. In calling Fig. 1 representative, we are mak-ing an analogy between charge-induced and field-in-duced effects in multiple quantum wells. The chargespectra of GaAs/AlGaAs and InGaAsP/InP are not

1 September 1989 / Vol. 28, No. 17 / APPLIED OPTICS 3577

I - .1 1

N 2.1 x 1016.cm3

'10000

6000-

20000

1,000

'E 1000

4 000

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PHOTON ENERGY (eV)

oo0 I

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PHOTON ENERGY (eV)

250001

'E.0

.A .9 1.0 1.1 1.2 1.3 1.4 I

PHOTON ENERGY eV)-~~~ I

20000 - N-5.8 0o1 cm3

1000 _ )

E - I

-,,O.. - (e)

.0 1. ., 1.2 1.3 1. 1

PHOTON ENERGY eV)

Fig. 1. Differential absorption spectra produced by variation ofelectron density in a single InGaAs quantum well at 10 K. Data

from Ref. 2 are shown for five concentrations (a)-(e).

known. But, it is known that the field-induced spec-tra of InGaAs/InAlAs, GaAs/AlGaAs, and InGaAsP/InP have similar shapes and magnitudes.

A complete set of room-temperature Aa spectra wasnot given in Ref. 2, although one 300-K spectral curvewas presented in Fig. 2 of Ref. 1. A comparison ofthose data reveals that the main Aa peak at 300 K isabout half as large as the corresponding Aa peak at 10

.5 .7 .0B .9 1.0 1.1 1.2 1.3 1.4 1.5

PHOTON ENERGY (eV)

Fig. 2. Carrier-induced refraction-change corresponding to each ofthe five curves (a)-(e) in Fig. 1. Results were obtained from a

Kramers-Kronig analysis.

K, and that the 300 K Ao features are slightly broaderthan the 10 K features. Consequently, we expect thatthe values of An at 300 K will be approximately half aslarge as the 10 K An values found in this paper. In Ref.2, the sheet charge densities af were cited for curves (c),

3578 APPLIED OPTICS / Vol. 28, No. 17 / 1 September 1989

-5000 (a)

-1000 1 , I. I. I~ .PHOTON ENERGY ( eV )

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(a)

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PHOTON ENERGY (eV)

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%cm 3

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PHOTON ENERGY (eV)

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43

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I _

(d)

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PHOTON ENERGY (eV)

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......

I

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I

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(d), and (e) of Fig. 1: Yr = 8.0 X 1010 cm- 2, lad = 4.3 X

10"l cm- 2 , and e = 6.4 X 10"l cm-2 . We convertedthose densities into volume charge densities using N =/Lz where L, is the 110 A thickness of the InGaAs QW,

namely, N, = 7.3 X 1016 cm- 3 , Nd = 3.9 X 1017 cm-3 ,and N = 5.8 X 1017 cm- 3 . The carrier densities forcurves (a) and (b) of Fig. 1 were estimated by assumingthat the peak value of Aa at the n = 1 transition isproportional to N for curves (a), (b), and (c). Thisgives N = 2.1 X 1016 cm- 3 and Nb = 4.3 X 1016 cm- 3 .

11. Kramers-Kronig Transformation

The An value at a particular photon energy E = hw isgiven by the well-known formula:

ch(,N 0 pFAa(E',N) dE',r E' 2 -E 2

where E' = h' and P is the principal value. Eachspectrum in Fig. 1 was digitized and entered into thecomputer. Then, numeric integration of that data,per the above formula, was carried out. These resultsare shown in Fig. 2 where the refractive index change isplotted as a function of photon energy over the 0.6-1.5eV range for the five injection levels. A rich structureis seen at large N. Generally, the An values found forthe QW material are an order-of-magnitude largerthan the carrier-induced An values predicted for bulkIII-V materials with comparable bandgaps.4

To show the calculated values of An with more clar-ity, we made a log-log plot of An as a function of N atthe fixed photon energies 0.70, 0.75, 0.80 and 0.85 eV(see Fig. 3). Saturation behavior of An vs N is seen at0.85 eV where the peak value of An occurs, but the Ndependence is approximately linear at the other ener-gies which are within the nominally transparent re-gime of the InGaAs QW.

IV. Optical Switching Applications

If a QW structure is employed as the core of a single-mode channel waveguide, the carrier-induced opticalphase shift in that waveguide is given by A =2-FrAnL/X, where F is the spatial overlap of the guidedmode with the active QW material, and is the inter-action length.

We illustrate how carrier-induced A is applied to a2 X 2 directional coupler switch. Conceptually, theswitch is a guided-wave component comprised of twosingle-mode QW waveguides coupled by evanescentwaves. The cross section of each guide has the appear-ance of a laser diode, although optical reflections areminimized throughout the waveguide. Only the cou-pling region has segmented electrodes applied to thechannels; the rest of the guiding region is passive. Thedecrease in refractive index produced during forwardbiasing of the segments is -1%, but this antiguidingtendency is not large enough to overwhelm the perma-nent channeling in the heterostructure waveguides.

Figure 4 shows a top view of the proposed current-controlled optical switch in its cross and bar states.We have suggested a reversed-A switch that uses only

1 0

1 o-1

C.4

1 072

1 0

10 16 1 017

ELECTRON DENSITY (cm- 3)Fig. 3. Refractive index change at a fixed photon energy as afunction of injected electron density for the InGaAs/InAlAs QW

system.

rv -.e : . .

reversed A8

Fig. 4. Top view of a proposed 2 X 2 directional coupler switchconstructed from MQW channel waveguides. Shaded areas repre-sent forward-biased regions. The cross and bar states are shown.

one sign of phase shift, unlike the prior-art push-pullLiNbO3 reversed-A\ switch that uses both +An and-An. To our knowledge, the unipolar switch shown inFig. 4 has not been discussed before. Figure 4 shows

1 September 1989 / Vol. 28, No. 17 / APPLIED OPTICS 3579

_�

1 18

the alternating-AO3 condition for the cross state and theuniform-A3 condition for the bar state. In the uni-form-AO condition, we require that AO = Aiol = Vlr,or L = X/2rAn. It is important to choose a photonenergy for which the switch's QW material is quitetransmissive, such as hw = 0.75 eV. Then, from Fig. 3,we find that An(0.75 eV) = -0.060 at N = 5.8 X 1017

electrons/cm3 . (The index change at room tempera-ture would be about -0.030.) If we used several quan-tum wells in the waveguide core so that the activesemiconductor filled -10% of the waveguide thickness(r = 0.10), then the active portion of the switch wouldhave a length of 1.73 X 1.65 Am/2 X 0.1 X 0.06, or 238,m. At room temperature, the active length would be476 gm, and the transparency energy would be shiftedto a lower value.

For electrical control, the QW material is located inthe intrinsic region of a PIN diode. This diode can beforward or reverse biased. Thus, instead of using in-jection, we could address the switch by depleting local-ly doped regions of the QW material. In that case, theshaded areas of Fig. 4 would be reverse biased, yieldingregions of +An. A third possibility is to bias twosegments forward and two segments reverse in Fig. 4,thereby creating zones of -An and +An5 ' 6, reminiscentof a Pockels effect device.

Probably the most important issue for a QW elec-trooptic switch is the optical propagation loss in eachof the two switching states. To assure low loss, wewould select a photon energy below the bandgap: hc< E1l(N). In practice, there will be an absorption tailthat extends below the gap for both a(°) and a(N). Forexample, in Fig. 1, we see for curves (c), (d), and (e) thato(N) has finite values at 0.80-0.84 eV. The free-carrierplasma effect gives a background level of differentialabsorption, but we do not understand the origin of theresidual Aa in Fig. 1 because the experimental valuesare larger than the plasma-induced loss.

The key question for refractive index QW switchesis: How high and how broad are the absorption tails?At the moment this is an open question that will bedecided by future experiments. We do know thatthere are tradeoffs in the switch: the tailing loss willdecrease as hw is decreased and as E,,(N)-hco is in-creased. But IAnI decreases with decreasing hw in thetransparent realm, thereby increasing the activelength of the switch. Let us conclude this discussionwith an estimate of the tailing losses that can be toler-ated. If we assume that the overall length of theswitch is Co and the active length £1, we find that theswitch's insertion loss in dB is 10 log exp(-a(o)r[o -

Cl- ce(N)F). If we assume that r = o.10, £o = 900,m, and L1 = 476 Am, then the loss of the switch can bekept below 2 dB by keeping both a(O) and a(N) less than52 cm'1 [which is one of several solutions for a(0),ao(N)].

V. Summary

In summary, we have calculated carrier-induced re-fractive index changes in InGaAs/InAlAs multiplequantum well waveguides using a Kramers-Kronigtransformation of experimental Aa spectra taken fromthe literature. At the 750-meV photon energy, de-tuned 90 meV from the 840 meV differential absorp-tion edge, index changes of -0.003 to -0.06 are foundas the injected electron density ranges from 2 X 1016 to6 X 1017 cm-3, and An does not decrease rapidly withdecreasing hco in the sub-gap region. Near the n, = 1exciton resonance, we found that the dependence ofindex change upon carrier density is nonlinear, withsome evidence of saturation. We proposed an MQWchannel waveguide 2 X 2 unipolar reversed-Afl switchbased upon the carrier-induced electrooptic effect.This switch appears viable if tailing losses can be con-tained.

Note added in proof: Recently, room temperatureAa spectra for the InGaAs/InAlAs SQW were given byChemla et al. in IEEE J. Quantum Electron., QE-24,1664-1676 (1988) (Fig. 6). We infer that the 300 K Anresults are similar to those in Fig. 2 with the factor-of-two scaling mentioned above. Chemla et al. also givethe electron densities at 10 K for curves (a) and (b) inFig. 1 as: a = 1.3 X 1010 cm- 2 and Ub = 4.2 X 1010 cm- 2 .

Therefore, the Na and Nb values in Figs. 2 and 3 shouldbe amended to: Na = 1.2 X 1016 cm- 3 and Nb = 3.8 X1016 cm- 3.

References

1. D. S. Chemla, I. Bar-Joseph, C. Klingshirn, D. A. B. Miller, J. M.

Kuo, and T. Y. Chang, "Optical Reading of Field-Effect Transis-tors by Phase-Space Absorption Quenching in a Single InGaAsQuantum Well Conducting Channel," Appl. Phys. Lett. 50, 585-588 (1987).

2. I. Bar-Joseph, et al., "Absorption Spectroscopy of the Continu-ous Transition from Low to High Electron Density in a Single

Modulation-Doped InGaAs Quantum Well," Phys. Rev. Lett. 59,1357-1360 (1987).

3. J. H. Abeles, W. K. Chan, A. Kastalsky, J. P. Harbison, L. T.

Florez, and R. Bhat, "Guided-Wave GaAs/AlGaAs FET OpticalModulator Based on Free-Carrier-Induced Bleaching," Electron.Lett. 23, 1303-1305 (1987).

4. B. R. Bennett and R. A. Soref, "Bandfilling Electro-Optic Effect

in InP, GaAs, GaSb, InAs, and InSb," Proc. Soc. Photo-Opt.

Instrum. Eng. 994, 168-186 (1988).5. U. Koren, T. L. Koch, B. I. Miller, and A. Shahar, "An InGaAs/

InGaAsP Distributed Feedback Laser with an Intracavity PhaseModulator," in Technical Digest of Topical Meeting on Integrat-ed and Guided-Wave Optics (Optical Society of America, Wash-ington, DC, 1988), paper PD9.

6. R. A. Soref and K. Y. Lau, "A Proposed Carrier-Induced Elec-

trooptical Switch in III-V Quantum-Well Waveguides," Proc.Soc. Photo-Opt. Instrum. Eng. 993, 126-136 (1988).

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3580 APPLIED OPTICS / Vol. 28, No. 17 / 1 September 1989