8. S. Uysal, Non-Uniform Line Microstrip Directional Couplers andFilters, Artech House, Norwood, MA, 1993.

9. R. N. Simons and G. E. Ponchak, ‘‘Modeling of Some CoplanarWaveguide Discontinuities,’’ IEEE Trans. Microwa e TheoryTech., Vol. 36, Dec. 1988, pp. 1796]1803.

10. K. M. Rahman and C. Nguyen, ‘‘On the Analysis of Single- andMultiple-Step Discontinuities for a Shielded Three-Layer Copla-nar Waveguide,’’ IEEE Trans. Microwa e Theory Tech., vol. 41,Sept. 1993, pp. 1484]1487.

Q 1997 John Wiley & Sons, Inc.CCC 0895-2477r97

PHOTOLUMINESCENCE STUDY OFHIGHLY DOPED, TENSILE-STRAINEDGaAs ///// In Al As0.07 0.93QUANTUM WELLSVishnu Balan,1 Theda Daniels-Race,1 and Laurie E. McNeil21Department of Electrical and Computer EngineeringDuke University, Durham, North Carolina 277082Department of Physics and AstronomyUniversity of North CarolinaChapel Hill, North Carolina 27599

Recei ed 18 April 1997

ABSTRACT: A photoluminescence study of highly doped tensile-strainedGaAs quantum wells is made to in¨estigate the feasibility of achie ingpolarization-independent photodetection. A simulation procedure to pre-dict the photoluminescence peaks is also de¨eloped which shows goodagreement with the experimental results. A primiti e structure for achie -ing polarization-independent photodetection is also proposed. Q 1997John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 7]11, 1997.

Key words: tensile strain; polarization independence; photolumines-cence; GaAs r InAlAs quantum wells

1. INTRODUCTION

The integration of optics and electronics, called ‘‘opto-electronics,’’ is still a relatively new technology offering greatpotential for major breakthroughs in the speed of communi-cation. The field of optoelectronics draws expertise frommany basic fields including lasers and electro-optics, electrondevices, circuits and systems, components packaging, andmanufacturing technology. The main objective of optoelec-tronics is to transmit information with light as the carrier.Advances in fiber optics and lasers have enabled this objec-tive to be realized.

Optical switching and modulation employing III]V semi-conductor multiple quantum well structures are very attrac-tive because of the large field-induced refractive index andabsorption variations observed in these structures as com-pared to conventional bulk materials. However, several short-

w xcomings are present 1 . One such challenge is the strongpolarization dependence characteristic of normal lattice-matched systems. This is due to the fact that the dipolemoments of the electron]heavy hole and electron]light holeshow a strong polarization dependence. Transverse electricŽ .TE mode light, with its electric field vector in the planeof the quantum well layers, can interact with both

electron]heavy hole and electron]light hole transitions. OnŽ .the other hand, the transverse magnetic TM mode polariza-

tion, with its electric field vector perpendicular to the quan-tum well, can interact only with electron]light hole transi-tions. Moreover, in normal unstrained quantum wells, theheavy-hole and light-hole band edges are degenerate. Hence,the electron]heavy hole transition always leads theelectron]light hole transition at the absorption edge due tothe larger effective mass of the heavy holes.

Polarization-independent optical switching utilizing quan-tum well structures was first demonstrated with parabolicpotential quantum wells where the energy shift is indepen-

w xdent of the effective mass of the particle 2 . Another methodof achieving polarization independence involves bringing theelectron]light hole transition peak to the absorption edge.

w xThis can be achieved by tensile strain 3 where it is possibleto adjust the relative positions of the heavy-hole and light-holequantum energy levels with respect to one another. If theheavy-hole and light-hole quantum energy levels are broughtto meet at the absorption edge, both TE and TM polarizationwill display identical absorption edges. An interesting featureof the heterostructure is the synthesis of an epitaxial layer on

w xa substrate with different lattice constants 4 . If the epitaxiallayers are thin enough, then the whole structure can have thesame in-plane lattice constant such that the epitaxial layer isunder strain. The strain will shift the positions of the conduc-tion and valence band edges, and have a significant effect onthe relative positions of the light-hole, heavy-hole, and split-off hole bands. If the bulk lattice constant of the quantumwell is larger than that of the substrate, then the quantumwell will be under compressive strain. However, if the sub-strate has a larger lattice constant than the quantum well, thequantum well will be tensile strained. The two different typesof strain have opposite effects on the relative shifts of thevarious valence bands.

In a compressively strained quantum well, the topmostvalence band is always the heavy hole irrespective of the wellthickness. In a tensile-strained quantum well, the relativeposition of the light and heavy hole can be changed byvarying the amount of strain and the quantum well thickness.For example, the light-hole band can be made to be thetopmost valence band. Thus, it can be arranged so that evenif the topmost valence band is the light-hole band due to thestrain-induced shift, the well width may be properly adjustedto place the heavy-hole energy level above the light-hole leveldue to the confinement effect.

Therefore, it is possible to accomplish band structureengineering with elastic strain and control of layer thicknesswhich can lead to drastic improvements in the performanceof optical devices. Moreover, devices operating at wave-lengths which are not conceivable with any existing un-strained semiconductor material systems can now be realized.In particular, tensile strain is especially favorable for bandgapcontrol as the relative positions of the heavy- and light-holequantum energy levels can be adjusted at will.

So far, undoped quantum wells have been extensivelystudied, and a number of successful devices have been tested.In this work, the photoluminescence of heavily dopedtensile-strained InAlAsrGaAsrInAlAs quantum wells isstudied. A simulation procedure to predict the peaks from PLmeasurements is also developed. Single quantum well struc-tures are examined in order to explore the physics of de-vice operation with respect to the feasibility of polarization-independent photodetection.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 16, No. 1, September 1997 7

2. EXPERIMENT

w xThe samples studied in this work were grown on 001 -ori-ented GaAs substrates using molecular-beam epitaxy. Thesubstrate temperature was 600 and 5408C for the growthGaAs and In Al As, respectively. A 0.5 mm GaAs buffer0.07 0.93was first grown on the substrate. This was followed by a 1 mmIn Al As layer. A GaAsrIn Al As quantum well0.07 0.93 0.07 0.93was then grown on the thick In Al As layer and capped0.07 0.93

˚with 100 A GaAs. A schematic of the sample PL structure isshown in Figure 1, and the structure of the electrical sampleis shown in Figure 2. The growth rates of the various epilay-ers are based on RHEED oscillation calibration prior togrowth. Three sets of samples grown in different growthsequences were measured. Other sample information is listedin Table 1.

The PL measurements were excited by the 488 nm line ofan Arq laser. The PL intensity was detected using a SPEX-1403 double monochromator equipped with a photomultipliertube and photon-counting electronics.

To predict the PL peak position, the Poisson and Schro-¨dinger equations are solved by discretizing in space with a

˚grid of 0.5 A. The Poisson equation is first solved to obtainthe energy band diagram. This energy band diagram is thentaken as the 1-D potential distribution for electrons, heavyholes, and light holes to solve for the confinement energiesthrough the Schrodinger equation. So we have for e]h re-¨

Figure 1 Structure of the PL samples

Figure 2 Structure of electrical sample

TABLE 1 Sample Details

W W W N N N0 1 2 A0 D1 A2y3 y3 y3˚ ˚ ˚Ž . Ž . Ž . Ž . Ž . Ž .A A A cm cm cm

23518 18 18Set I 450 450 3.3 = 10 1 = 10 1.4 = 10225

205

9518 17 17Set II 1100 800 5 = 10 2 = 10 2 = 1089

84

6518 17 17Set III 1100 800 5 = 10 2 = 10 2 = 1050

35

combination,

EU s E y dEg g g

E s EU q E q Ee ] h g h e

E s E y Esim e ] h ex

where EU, E , E , E are the renormalized bandgap, hole,g h e exand electron confinement energies and exciton binding en-ergy, respectively.

To solve the Poisson and Schrodinger equation, the¨strain-induced band shifts, effective masses in the variousepilayers, and the band offsets in the heterostructure arerequired. For the relaxed In Al As, the bandgap and0.07 0.93effective masses are obtained by linear interpolation of thevalues known for InAs and AlAs. For the tensile-strainedGaAs, the band edge shifts calculated from the four-band

Ž .k ? p Hamiltonian k s k s 0 , which also incorporatesx ystrain in the epilayer, are added to the intrinsic values. The

w xband edge shifts are given by 5

D E s dEcc h

D E s dE¨ y dEhh h s

D E s dE¨ y 1r2D q 1r2dElh h so s

2 2Ž .'q 1r2 D q dE q 8dEso s s

D E s dE¨ y 1r2D q 1r2dEso h so s

2 2Ž .'y 1r2 D q dE q 8dEso s s

where the strain-induced shifts are

c, ¨ Ž .dE s a 2e q eh c, ¨ x x z z

Ž .dE s yb e y es x x z z

and a and b are the hydrostatic and valence band shearc, ¨deformation potentials. We have

a y as ee s e sx x y y ae

e s yDez z x x

c12w001xD s 2c11

where c and c are elastic moduli of the epilayer, and a12 11 sand a are the lattice constants of the substrate and epilayer,erespectively. The material parameters of interest are given in

w x w x w xTable 2 5 and Table 3 5 . The reader is referred to 5 fortheoretical calculations in greater detail.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 16, No. 1, September 19978

TABLE 2 Material Parameters of GaAs, AlAs, and InAs

m m m E E De h h lh G X soŽ . Ž . Ž .m m m eV eV eV0 0 0

GaAs 0.067 0.35 0.082 1.519 2.00 0.341AlAs 0.015 0.48 0.200 3.13 2.23 0.28InAs 0.023 0.35 0.026 0.418 2.06 0.380

TABLE 3 Elastic Moduli, Hydrostatic, and Valence BandShear Deformation Potentials for GaAs

c c a a b11 12 c ¨Ž . Ž . Ž . Ž . Ž .Mbar Mbar eV eV eV

1.18 0.54 y9.3 y1.0 y1.7

The effective masses in GaAs are also calculated theoreti-cally from the Hamiltonian. The effective masses in the

w x Utensile-strained GaAs are found to be 6 m s 0.062m ,e 0mU s 0.07726m , and mU s 0.35m , respectively, where mlh 0 h h 0 0is the free electron mass. The valence band offset is esti-

w xmated via the model-solid theory 7 . An experimental valuew xof 0.55 eV for the GaAsrIn Al As system 5 , which0.07 0.93

agrees well with the model-solid theory, is used in this study.The heavy doping in the GaAs well results in an effective

w xreduction in the bandgap 8 . The bandgap narrowing de-pends both on quantum well thickness and on the doping inthe well. The renormalization for various dopings are given inw x 18 y38 . For a typical doping of 5 = 10 cm with a well width

˚of 100 A, the bandgap narrowing is 30 " 5 meV. An accuratew xtheory of excitons in quantum wells is given in 9 . The

binding energy of the excitons depends on the well thickness,the type of dopant in the well, the concentration of dopant,

w xthe quality of the interface, and the barrier material 10]12 .Also, the exciton energies for doped GaAsrInAlAs quantumwells have not yet been investigated. Thus, values from

w xGaAsrAlAs quantum wells were extrapolated 10 . A typical˚binding energy for a well width of 100 A is 14 " 7 meV with

the range of uncertainty necessitated by the selected simpli-fication of the calculation.

3. RESULTS AND ANALYSIS

The PL spectrum obtained from the sample with well width˚ Ž .of 235 A is shown in Figure 3 a . The signal is noticeably

weak and noisy. This may be because of the heavy doping ofthe GaAs quantum well as well as the heavy doping in the

w xbarrier 13 . Given the heavy doping, light is scattered as itenters the sample and proceeds to the quantum well. There-after, the weak luminescence intensity produced further de-creases as the light travels back to the surface. To obtain the

ŽPL energy information, the signal is smoothed running aver-.ages of length 15 . The smoothed signal is shown in Figure

Ž .3 b . A peak around 1.511 eV is observed. This is most likelythe excitonic peak in the bulk GaAs of the substrate giventhat the energy of the exciton recombination in bulk GaAs isabout 1.514 eV at 25 K. A smaller satellite peak in thespectrum is also seen. This peak at 1.523 eV is most likelyfrom the quantum well, while the value expected from simu-lation is at 1.544 eV.

Figure 4 shows the spectra from the next set of samples˚ ˚with well widths of 95, 89, and 84 A, respectively. The 95 A

sample was grown on nq substrate, while the other two weregrown on semi-insulating substrates. All of the samples show

˚Figure 3 PL spectrum from sample with well width of 235 A

Figure 4 PL spectrum from samples with well widths of 95, 89, and˚84 A

a very distinct peak at the free excitonic energy of 1.515 eV.Superposed on these strong peaks, we observe smaller peakswhich are from the quantum well. The peaks for the 89 and

˚84 A samples occur at 1.502 and 1.506 eV, respectively, whilethe values predicted by simulations are 1.497 and 1.510 eV,respectively. The signal-to-noise ratio is much improved inthis set of samples as compared to the previous set. This maybe due to the reduced doping of the barrier layer. The line

˚widths of the peaks from the 89 and 84 A samples are 6 and 8meV, respectively. This line width is characteristic of good

w xabrupt interfaces and good crystalline quality 14 . In the case˚of the 95 A sample, we note two features which are different

from the other two samples. First, the intensity of the bulkpeak is much less than that in the other samples. Also, thepeak from the well is much broader than the line widths ofthe other two samples.

The lower intensity of the bulk peak is presumed due tothe nq substrate used for the sample. The nq substrate is

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 16, No. 1, September 1997 9

much thinner than the semi-insulating substrate used for theother samples. Also, the high doping in the nq substratecauses more scattering of light, as described earlier, and thussupports the reason for the observed low intensity of the peakat 1.515 eV. A line width of 25 meV for this sample suggestsbad interface and crystalline quality. Since the structures ofthe samples used in this study do not have superlattice

w xdislocation filters 15 , dislocations can be formed on thesurface of the strained InAlAs buffer layer, which can alsopropagate into the GaAs quantum well. In turn, dislocationsin the GaAs could result in lower strain or no strain at all inthe well. To verify this, simulations are performed with arelaxed GaAs quantum well. Accordingly, a peak is predictedat 1.581 eV, within the expected margin of error, correspond-ing to the experimental peak at 1.541 eV. Furthermore, thesimulations predict a peak at 1.530 eV for a strained GaAswell. The above values indicate that the GaAs layer mayindeed be partially strained, as postulated.

˚For the samples with well widths 95, 89, and 84 A, inten-sity scans at three different incident powers were performed.These plots are shown in Figure 5. These plots serve to givemore information on the PL peaks observed. All the peaks inthe spectrum show a nonlinear increase in intensity withincreasing incident power. Also, a very slight decrease in the

Ž .PL peak energy by about 1 meV or less with increasingincident power is noted. This is consistent with type-I transi-

w xtions 8 under high excitation, and is attributed to bandgapshrinkage due to the exchange and many-body effects ofelectron]hole plasma in quantum wells. Type-I transitionsimply that the electron]hole pair responsible for the peakoriginates from the same physical location in the sample.Thus, these peaks are mainly from the quantum wells in thesamples.

Figure 6 shows the smoothed PL spectrum from samples˚with well widths of 35, 50, and 65 A, respectively. The

absence of a peak at 1.515 eV, observed in previous samples,˚is noted. In the case of the 35 A sample, the peak energy

from the quantum well is 1.662 eV, while the simulations˚predict the peak at 1.669 eV. In the case of the 50 A sample,

simulations predict a peak at 1.584 eV corresponding to an

Figure 5 Intensity scans at I, 2 I, and 4I where I s 1 Wrcm2 forsample set II

Figure 6 Smoothed PL spectrum from samples with well widths of˚65, 50, and 35 A

˚observed peak at 1.563 eV. For the 65 A sample, a predictedpeak at 1.538 eV corresponds to the observed peak at 1.544eV.

It will be relevant here to discuss the discrepancies pres-ent while comparing experimental data with the values pre-dicted by simulations. First, there may be slight deviations inthe exact doping values for the wells. It is known that dopingconcentrations in MBE growths depend both on the celltemperature and the growth rate. There may be slightŽ .two]three monolayers fluctuations in the growth rate dur-ing the course of the run. Hence, the designed well andbarrier widths as well as their doping may not be exactlyachieved. When simulations were performed on a structure, itwas noticed that there were differences on the order ofseveral millielectronvolts in transition energies predicted forminor variations in widths and doping of the various layers.Thus, the device structure considered in this study has highsensitivity to process variations. Another implication of thefluctuations in growth rate is the possible minute change inthe indium mole fraction of In Al As during growth,x 1yxthereby giving slightly different values of strain in the GaAsquantum well. While simulating, the strain is taken to be a

w xconstant value equal to 0.005 16 . Also, the excitonic ener-gies in the strained quantum wells and the bandgap narrow-ing effect due to the high doping can only be estimated fortypical values. In simulations, the bandgap narrowing effectwas taken into account by simply reducing the bandgap foundafter strain-induced shifts by an amount estimated from the

w xliterature 8 . It is to be noted that there is a built-in electricfield in the quantum well because of the doping. Thus, theelectron]hole pairs generated in the quantum well by theincident light will be swept out of the quantum well ifthe transit time is smaller than the recombination lifetime at25 K. Carriers swept out of the quantum well do not con-tribute to the luminescence intensity from the quantum well.This, compounded by the high doping, may be the reason forthe weak signals mixed with the noise characteristic in manyof the spectra seen.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 16, No. 1, September 199710

Figure 7 Theoretical calculations showing the crossover of LH andHH energy levels by the application of a reverse bias across thestructure

ŽIt is possible to build a primitive photodetector reverse-.biased p]n junction by embedding the basic structure con-

sisting of the doped barriers and strained well in a structureŽsimilar to the PL samples using doped buffer layers for low

.series resistance and contacts on the top and bottom surfaceŽof the sample as shown in Figure 2. Fabrication of this

.structure will be the topic of a future publication. To achievepolarization independence, the ratio of the photocurrents for

Žhorizontal and vertical polarizations of incident light at a.given power for a certain reverse bias should approach 1.0. It

is shown by simulations that it is indeed possible to superposethe light-hole and heavy-hole energy levels by the applicationof a reverse bias across the structure.

It is observed that simulation results for the PL measure-ments agreed reasonably well with the experimental values inmost cases, indicating that the simulations performed are agood approximation to actual phenomena. The simulationprocedure developed is used to show the crossover of thelight-hole and heavy-hole energy levels with applied biasacross the structure. A structure with dopings of 2 = 1017

cmy3 Be and Si in the barriers, respectively, and 5 = 1018

cmy3 Be in the GaAs quantum well is considered for this˚purpose. The widths of the barriers are 800 and 1100 A,

˚respectively, with a well width of 53 A. The crossover of thelight- and heavy-hole energy levels is shown in Figure 7. Theenergy axis uses the top of the valence band as reference,with hole energies increasing below the top of the valenceband. It is observed that, as bias is applied, there is amovement of the confinement energies of the light and heavyholes with a crossover occurring at 156 mV, reverse bias.Therefore, by appropriately choosing the doping and thick-ness of the different layers, it is possible to superpose light-hole and heavy-hole energy levels for a certain reverse biasacross the structure.

4. CONCLUSIONS

Optical properties of highly doped, tensile-strained GaAsquantum wells were studied. A general simulation scheme for

studying device structures which have strained as well asrelaxed layers is developed. From this study, it is observedthat it is possible, in theory, to superpose the heavy-hole andlight-hole energy levels in a strained quantum well by theproper choice of doping concentrations, thickness of thelayers, and reverse bias across the structure. The devicestructure used in this study is a primitive photodetector.Further work is indicated to improve optical efficiency.

ACKNOWLEDGMENTS

The authors wish to thank Richard Kendall for his assistancein the MBE growth of the samples. This work was supportedby the NSF under Grant DMR-92-08381.

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Q 1997 John Wiley & Sons, Inc.CCC 0895-2477r97

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