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INTRODUCTION

It has been shown recently that beryllium-basedII-VI semiconductor alloys form high-degree covalentbonds that result in lower defect densities and, con-sequently, increase the lifetimes associated with op-toelectronic devices.1 Due largely to these advan-tages, BexZn1−xTe alloys have been recently proposedfor applications in lasers and light-emitting diodesthat operate in the visible wavelength range.2,3 Inaddition to its application benefits, there is also atheoretical interest in studying the BexZn1−xTeternary-alloy system because it undergoes a tran-sition from a direct-gap material to an indirect-gapmaterial at x = 0.28.4 If these alloys are to be used tofabricate novel optical devices, their optical proper-ties must be well understood. Although there are afew studies reported on the bandgap and the exci-tonic properties of BexZn1−xTe, very little knowledgeof the dispersion of the index of refraction, n, ispresently available.

Although there are numerous experimental meth-ods available to determine the n of thin films, such asinterferometry, reflection spectroscopy, ellipsometry,and prism coupler, all of these techniques seem to suf-fer from deficiencies associated with their respectivemeasuring technique or their analysis procedure. Forinstance, in both interferometry and reflection spec-troscopy, one needs the prior knowledge of the filmthickness to obtain accurate values for n.5 Althoughin the prism-coupler technique one is able to deter-mine both n and the thickness, this method is limitedby its inability to obtain n as a function of wave-length.6 This is because, due to experimental con-straints, the prism-coupler method is most conve-niently performed with a laser source, as opposed to acontinuous source. Similarly, although it is possible toobtain the dispersion of n and the thickness from el-lipsometric data, because of the large number of un-known parameters, this method can be nontrivial.7Because each of these techniques by itself has inher-ent problems (as well as strengths), to obtain accuratevalues for the dispersion of n, one needs to implementa couple of these techniques concurrently.

The Indices of Refraction of Molecular-Beam Epitaxy–GrownBexZn1–xTe Ternary Alloys

F.C. PEIRIS,1,3 M.R. BUCKLEY,1 O. MAKSIMOV,2 M. MUNOZ,2and M.C. TAMARGO2

1.—Department of Physics, Kenyon College, Gambier, OH 43022. 2.—Department of Chemistry,City College and Graduate Center, CUNY, New York, NY 10031. 3.—E-mail: peirisf@kenyon.edu

We have used a combination of prism-coupling, reflectivity, and ellipsometrictechniques to investigate the indices of refraction, n, of a series of BexZn1−xTethin films grown on InP substrates. After determining the concentrations ofeach of the BexZn1−xTe alloys using x-ray diffraction measurements, we mea-sured their n at discrete wavelengths using a prism-coupler setup. In addition,we used reflectivity measurements to complement the prism-coupler data andarrive at the dispersion relations of n for the BexZn1−xTe alloys below their fun-damental energy gaps. We then employed a rotating analyzer-spectroscopicellipsometer to measure the complex reflection ratio for each of the films atangles of incidence of 65°, 70°, and 75°. By using the n values obtained fromboth the prism-coupler and the reflection-spectroscopy techniques to guide theellipsometric analysis, we were able to obtain accurate results for the disper-sion of n for the BexZn1−xTe alloys, not only below their fundamental energygaps, but also above their energy gaps (up to 6.5 eV) using these three comple-mentary techniques.

Key words: BexZn1−xTe, molecular-beam epitaxy (MBE), index of refraction,prism coupler, reflectivity, ellipsometry

Journal of ELECTRONIC MATERIALS, Vol. 32, No. 7, 2003 Special Issue Paper

(Received October 20, 2002; accepted November 13, 2002)

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In this article, we have combined the prism-coupler, reflection-spectroscopy, and ellipsometrymethods to obtain the dispersion of n for a series ofBexZn1−xTe alloys. Initially, we used the prism-coupler technique to find discrete values of n as wellas the thickness of the semiconductor film. Theseparameters were then used to decipher the spectraobtained from reflection spectroscopy and to obtainthe dispersion of n below the fundamental energygap for the BexZn1−xTe alloys. Because the ellipso-metric spectra have to be carefully analyzed usingseveral parameters to infer n, the prior knowledge ofthe thickness and the dispersion of n (below the fun-damental gap) obtained from the prism-coupler andreflectivity methods facilitate this analysis. Hence,the results obtained, from both the prism couplerand the reflection spectroscopy, were used to guidethe analysis of the ellipsometric spectra. By usingthese three experimental methods in unison, one isable to determine the dispersion of the n forBexZn1−xTe alloys very accurately.

MOLECULAR-BEAM EPITAXY GROWTHAND STRUCTURAL CHARACTERIZATION

All of the thin BexZn1−xTe films were grown bymolecular-beam epitaxy (MBE) on semi-insulating,epi-ready (001) InP substrates using a Riber 2300MBE system. Before depositing the BexZn1−xTefilms, the substrates were deoxidized at 500°Cunder As flux, and a ∼100-nm-thick, lattice-matchedInGaAs-buffer layer was grown on the InP sub-strate. The growth temperature for the BexZn1−xTeTe layer was maintained around 270°C. The growthrate was approximately 0.5 �m/h, and BexZn1−xTelayers were 0.5–1.5 �m thick. No cap layer was nec-essary, as no surface degradation of this materialhas been observed even over extended periods oftime. We have used five samples of BexZn1−xTe al-loys for this study, with Be concentrations (x) rang-ing from x = 0 to x = 0.378.

The composition of the films was determined byusing �-2� x-ray diffraction experiments, assuming alinear dependence of the lattice constant with respectto the alloy concentration. In all of the x-ray diffrac-tion spectra, the (004) reflection for BexZn1−xTe is in-dicated by a single peak. Furthermore, a full-widthat half-maximum in the range of 70–90 arcsec wasobserved for the epilayers closely lattice matched toInP. The photoluminescence experiments performedat 6 K for these samples are dominated by narrowband-edge emission lines that indicate the high crys-talline quality of the BexZn1−xTe specimens.8

PRISM-COUPLER MEASUREMENTS

In the prism-coupler technique, a laser beam is cou-pled via a prism to the semiconductor layer for whichn is of interest. The evanescent coupling between theprism and the semiconductor layer excites guided-wave modes in the layer, which depend on both nand on the thickness of the layer.9 Hence, both these

The Indices of Refraction of Molecular-BeamEpitaxy–Grown BexZn1−xTe Ternary Alloys 743

quantities can be determined if the semiconductorlayer is sufficiently thick (i.e., if it can accommodateat least two guided modes within the layer). Using theprism-coupler technique, one can determine n with aprecision of at least 0.1% and obtain the film thick-ness with an uncertainty of less than 0.5%.

The instrument was operated at two differentwavelengths, and the measurements were made intransverse electric (TE) polarization mode. A He-Nelaser operating at 632.8 nm was used in conjunctionwith a rutile prism for one of the measurements, whilea semiconductor-diode laser operating at 1300 nmwas used with a Si prism for the other measure-ment. The experimental details concerning the prism-coupler method are discussed in Ref. 6. In Fig. 1, weshow a rotation spectra obtained for one of the sam-ples (Zn0.831Be0.169Te) at two different wavelengths.The dips in the reflected spectra shown in Fig. 1 corre-spond to the excitations of specific modes in the film.Both n and the thickness are calculated from theangular positions at which these dips occur in the re-flected spectra. The n values obtained at the two dis-crete wavelengths as well as the thickness obtainedfor the film will be later used as input parameters toanalyze the reflectivity and ellipsometric data.

It has to be mentioned that the n of the prism usedin the experimental setup dictates the range of the nof the films that can be measured using the prism-coupler technique. For this reason, it is advantageousto use a prism that has an n that exceeds the n of thefilm. However, even in the absence of such prisms,the prism coupler is capable of determining the n andthe thickness of films. Because the n of the BexZn1−xTealloys are greater than the value for n of rutileat 632.8 nm, as shown in Fig. 1b, the first few wave-guide modes are absent from the spectra.10 Alterna-tively, as shown in Fig. 1a, because the n of the Siprism is greater than the n of the BexZn1−xTe alloys,the spectra show the initial waveguide modes. Whendetermining the n and the thickness from spectra

Fig. 1. A prism-coupler reflection spectrum obtained forZn0.831Be0.169Te at (a) � = 1,300 nm and (b) � = 632.8 nm. The dips inthe spectra correspond to the excitations of specific modes in the film.

a

b

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744 Peiris, Buckley, Maksimov, Munoz, and Tamargo

rays that are reflected from the air/film and from thefilm/substrate interfaces. As mentioned before, byusing the two n values (i.e., at 632.8 nm and 1300 nm)as well as the thicknesses obtained from the prism-coupler technique, one can determine the n valuescorresponding to each of the extrema in the reflec-tion spectrum. Figure 3 displays the dispersion of nobtained for BexZn1−xTe using both the prism-cou-pler data (full squares) and the reflectivity data(open squares). The solid line displayed in the figurecorresponds to a Sellmeier-type dispersion fit ob-tained for the experimental data.12 As can be seen inFig. 3, the increase of n as the wavelength decreasesreflects the dispersion expected as the photon energyof light approaches the fundamental energy gap ofthe BexZn1−xTe alloy.

ELLIPSOMETRIC RESULTS

Spectroscopic ellipsometry is a nondestructiveoptical-characterization technique that gives in-formation on dielectric functions, band-structurecritical points, thickness, interfaces, as well as thesemiconductor-alloy composition. Compared to theprism coupler and the reflectivity technique de-scribed previously, it has the distinct advantage ofobtaining n both below and above the fundamentalabsorption edge of the semiconductor system. How-ever, the ellipsometric measurement is an indirectmethod to obtain the dielectric response of a multi-layer structure, whereby one has to simulate a lay-ered model (with a varying thickness and a dielectricfunction for each layer in the model) until a propertheoretical fit is obtained that accurately describesthe experimental spectra.7 It is, therefore, advanta-geous to know some of the parameters of the struc-ture a priori in order to increase the reliability of thevalues obtained for the dielectric function of thesemiconductor layer by such modeling. In this work,

such as Fig. 1b, one has to calculate these parameterstogether with their standard deviation, assumingthat a specific number of modes are absent from thespectra. Following this procedure, the number ofabsent modes is found when the standard deviationfor both n and the thickness are at their lowestvalues.

REFLECTION SPECTROSCOPY

The reflectivity technique is a complementarymethod suitable for determining the dispersion of nby carefully analyzing the Fabry–Perot oscillationsin the reflection spectrum. However, to accuratelydetermine the values for n from reflectivity mea-surements, one requires prior knowledge of thethickness of the film. This can usually be accom-plished by another measurement, such as scanningelectron microscopy. Because the prism-couplermethod determines the thickness of semiconductorfilms with much higher accuracy than scanning elec-tron microscopy, reflectivity data can be analyzedmore accurately if they are combined with theprism-coupler data. Additionally, to correctly deci-pher the reflectivity spectra, one needs to determinethe optical thickness corresponding to each of the ex-trema in the spectrum. Here again, one can use thediscrete values of n determined by the prism-couplermethod to obtain the optical thickness at the corre-sponding points in the reflectivity spectra.11 Withthis input from the prism-coupler data, the reflectiv-ity can produce a nearly continuous spectrum of n(usually, but not necessarily, obtained from positionsof the Fabry–Perot maxima and minima).

The reflectivity measurements were carried out atnormal incidence, and the data were calibratedusing a Si-reference sample of known reflectivity. Atypical spectrum is shown in Fig. 2 for the samesample as that used to illustrate the prism-couplerspectrum in Fig. 1. The Fabry–Perot oscillationsseen in the spectrum arise from interference between

Fig. 2. A room-temperature reflectivity spectrum obtained forZn0.831Be0.169Te.

Fig. 3. The dispersion of the index of refraction of Zn0.831Be0.169Te ob-tained by the prism-coupler (full squares) and the room-temperaturereflectivity (open squares) techniques. The solid line corresponds to aSellmeier-type dispersion fit obtained for the experimental data.

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The Indices of Refraction of Molecular-BeamEpitaxy–Grown BexZn1−xTe Ternary Alloys 745

known.13 Hence, the parameters that need to be var-ied in the model are the thicknesses of each layerand the dielectric constant of the Zn1−xBexTe layer.However, because we already know the thickness ofthe Zn1−xBexTe layer as well as its dispersion of nbelow the energy gap from our previous prism-cou-pler and reflectivity measurements, the ellipsomet-ric analysis will be further simplified.

The n determined from this procedure is plotted inFig. 5 for the same Zn1−xBexTe sample as in Figs. 1and 2. In Fig. 5, both the prism-coupler and the re-flectivity data are also plotted as filled squares andopen squares, respectively. We see in this case thatthe prism-coupler and the reflectivity data stand toguide the ellipsometric data. The excellent agree-ment in the data obtained below the fundamentalgap from all three experimental methods gives cre-dence to the above-bandgap dispersion of n deter-mined by ellipsometry. In observing the ellipsomet-ric spectra obtained for the different Zn1−xBexTesamples, we immediately notice that the incorpora-tion of Be into the lattice blue shifts the energy gapin the Zn1−xBexTe-alloy system. In addition, we alsoobserve the presence of distinct excitonic peaks inthe dielectric spectra of samples with higher Be con-centration, which also indicates the high crystallinestructure of the Zn1−xBexTe alloy used for this study.

In measuring � and � of the Zn1−xBexTe alloysamples, we did not use chemical-etching proceduresto eliminate Zn1−xBexTe-surface oxide that could in-fluence the ellipsometric results.14 However, byadding a surface-oxide layer to our semiconductormodel, we were able to circumvent the need for suchsurface treatments.15 Additionally, it must also bementioned that the thin films used in this study wererelaxed as their thicknesses exceeded the criticalthickness for strain relaxation.16 Hence, we expectthat the dispersion of n calculated for our thin films ofZn1−xBexTe to be essentially that of bulk Zn1−xBexTe.

the prism coupler and the reflectivity results ob-tained prior to performing the ellipsometric methodwill serve this function.

The spectroscopic analysis was performed usingan ellipsometer, capable of taking ellipsometric datawith photon energies of 0.7–6.5 eV. For each sample,we obtained room-temperature ellipsometric dataat angles of incidence of 65°, 70°, and 75°. The twoparameters, � and �, measured by ellipsometry ateach wavelength are related to the ratio of reflectioncoefficients by

� = Rp/Rs = tan(�)ei�

where Rp is the complex-reflection coefficient forlight polarized parallel to the plane of incidence, andRs is the coefficient for light polarized perpendicularto the plane of incidence. Here, both � and � are pre-sented in terms of two angles that are a function ofboth wavelength and the angle of incidence. In Fig. 4,we show the � and � spectra for the Zn0.831Be0.169Tealloy sample obtained from the ellipsometer. In the� spectrum (Fig. 4a), the observed oscillations at thehigher wavelength range are due to Fabry–Perot in-terference within the Zn1−xBexTe film. The film isboth transparent and below its energy gap in thespectral range where these oscillations occur. As oneobserves in Fig. 4a, the disappearance of the oscilla-tions around 480 nm signals the transition from thetransparent region to the absorption region in thesemiconductor.

For a given specimen, the � and � obtained fromthe ellipsometric measurement depend on the opti-cal properties of the entire structure. For the alloysused in this study, a four-layer model (i.e., InP sub-strate, InGaAs buffer, Zn1−xBexTe layer, and surface-oxide layer) was constructed for each sample. Theoptical constants of the modeled oxide layer were anaverage between that of air and the Zn1−xBexTelayer beneath. It must be mentioned that the opticalproperties of the substrate and the buffer are already

Fig. 4. The (a) � and (b) � spectra of Zn0.831Be0.169Te measured byspectroscopic ellipsometry for an angle of incidence of 75°.

Fig. 5. The dispersion of the index of refraction of Zn0.831Be0.169Tedetermined by ellipsometry (solid line), reflectivity (open squares),and prism-coupler (filled squares) techniques.

a

b

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746 Peiris, Buckley, Maksimov, Munoz, and Tamargo

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CONCLUSIONS

In summary, we have used a combination of prismcoupler, reflectivity, and spectroscopic ellipsometry tomeasure the index of refraction of a series of MBE-grown Zn1−xBexTe alloys. The discrete values of n aswell as the film thickness obtained from the prismcoupler are used to analyze the reflectivity spectraand to obtain n as a function of wavelength. Thesetwo experimental methods allow one to find the dis-persion of n for a film below its fundamental energygap. By using the data obtained from these twomethods as input parameters in analyzing the ellip-sometric spectra, one can obtain the dispersion of nfor the Zn1−xBexTe-alloy system at wavelengthsabove its fundamental energy gap. Hence, by combin-ing the techniques of prism coupler, reflection spec-troscopy, and ellipsometry, one is able to accuratelydetermine the dispersion of n for a semiconductorthin film both below and above its fundamentalenergy gap.

ACKNOWLEDGEMENTS

The authors thank Professor J.K. Furdyna forallowing the use of the prism coupler in his lab.Acknowledgement is also made to the donors of theAmerican Chemical Society Petroleum ResearchFund (ACS PRF No. 38069) for support of thisresearch.

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TITLE: The Indices of Refraction of Molecular-BeamEpitaxy-Grown BexZn1-xTe Ternary Alloys

SOURCE: J Electron Materns Part A 32 no710 Jl 20032000

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