Temperature Dependence of the Band-Edge Transitions of ZnCdBeSeChang-Hsun HSIEH, Ying-Sheng HUANGÃ, Ching-Hwa HO1, Kwong-K...
of the (004) rocking curves of the ZnCdSe sample is ratherbroad, indicating that the sample is partially strained. Theasym...
(Zn0:38Cd0:62)1ÀxBexSe. To identify the physical origin of thedoublets, we make a spectral comparison of the CER andPzR me...
for InGaAs films grown on GaAs substrate.20)The physicalorigin of this residual strain is not clear and moreinvestigative w...
contributions from both thermal expansion and electron(exciton)–phonon coupling effects. To obtain the parametersdirectly r...
eliminated. The dashed lines shown in Figs. 4(a)–4(c) are theleast-squares fits of the relevant energy terms to eq. (5a) or...
À3:9 Â 10À4eV/K for sample A, À3:3 Â 10À4eV/K forsample B and À3:1 Â 10À4eV/K for sample C. By takinghigh temperature limi...
light-hole (lh) and heavy-hole (hh) excitonic transitions ofthe ZnCdBeSe samples. The enhanced lh feature with lowerenergy...
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Temperature Dependence of the Band-Edge Transitions of ZnCdBeSe


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Japanese Journal of Applied Physics
Vol. 43, No. 2, 2004, pp. 459–466

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Temperature Dependence of the Band-Edge Transitions of ZnCdBeSe

  1. 1. Temperature Dependence of the Band-Edge Transitions of ZnCdBeSeChang-Hsun HSIEH, Ying-Sheng HUANGÃ, Ching-Hwa HO1, Kwong-Kau TIONG2, Martin MUN˜ OZ3,Oleg MAKSIMOV3and Maria C. TAMARGO3Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, Republic of China1Department of Materials Science and Engineering, National Dong Hwa University, Shoufeng, Hualien 974, Taiwan, Republic of China2Department of Electrical Engineering, National Taiwan Ocean Univesity, Keelung 202, Taiwan, Republic of China3Center for Advanced Technology (CAT) on Photonic Materials and Applications, Center for Analysis of Structures and Interfaces (CASI),Department of Chemistry, City College-CUNY, New York, NY 10031, USA(Received May 13, 2003; accepted October 29, 2003; published February 10, 2004)We have characterized the temperature dependence of band-edge transitions of three (Zn0:38Cd0:62)1ÀxBexSe II–VI films withdifferent Be concentrations x by using contactless electroreflectance (CER) and piezoreflectance (PzR) in the temperaturerange of 15 to 450 K. By a careful comparison of the relative intensity of PzR and CER spectra, the identification of light-hole(lh) and heavy-hole (hh) character of the excitonic transitions of the samples has been accomplished. The temperaturedependence analysis yields information on the parameters that describe the temperature variations of the energy (includingthermal expansion effects) and broadening parameter of the band edge transitions of ZnCdBeSe. The study shows that Beincorporation can effectively reduce the rate of temperature variation of the energy gap. [DOI: 10.1143/JJAP.43.459]KEYWORDS: ZnCdBeSe, electroreflectance, piezoreflectance, temperature dependent band gap, broadening parameter1. IntroductionRecently the growth of II–VI wide-band-gap semicon-ductor heterostructures has attracted considerable attentiondue to their novel physical properties and a wide range ofapplications in optoelectronic devices. The applicationsinclude the use of II–VI compound based materials as lightsources, in full color displays and for increasing theinformation density in optical recording. Thin films ofZnCdBeSe II–VI compounds grown on III–V compoundsubstrates are of particular interest in the device applicationsof light emitting diodes (LEDs) and laser diodes (LDs) ofvisible and UV spectral region due to their good operationstability in terms of temperature variation and lifetime.1–3)According to theoretical prediction and subsequent exper-imental verification, the beryllium containing II–VI com-pounds had been found to possess an enhanced ability tosignificantly reduce the defects propagation due to a moreprevalence of strong covalent bonding and lattice hardeningin the materials.4,5)The strong covalent bonding in beryl-lium-based II–VI compounds achieves a considerable latticehardening which avoids multiplication of defects during theoperation of II–VI semiconductor laser devices.6,7)Up-to-date, in spite of the anticipated advantages of the Be-basedII–VI compounds, very little work has been done on thetemperature dependence of the near band edge transitions ofthese materials. The temperature dependence of the energyand broadening of interband electronic transitions can yieldimportant information concerning the physical properties ofthe materials such as electron (exciton)–phonon interactions,excitonic effects, etc. The practical aspect of this inves-tigation is related to the control of the operating temperatureof the laser structure itself. An increase in temperature leadsto a red shift of band gaps as well as an increase in thelinewidth.In this article, we report a detailed study of the temper-ature dependence of the energy and broadening parameter ofthe near band edge interband transitions of three(Zn0:38Cd0:62)1ÀxBexSe films, grown on InP substrates, usingcontactless electroreflectance (CER) and piezoreflectance(PzR) measurements in the temperature range of 15 to450 K. The identification of the light-hole (lh) and heavy-hole (hh) character of the excitonic transitions of(Zn0:38Cd0:62)1ÀxBexSe samples has been accomplished bycomparing the relative intensity of the PzR and CER spectra.Transition energies for the band-to-band excitonic transi-tions of (Zn0:38Cd0:62)1ÀxBexSe are determined by fitting theexperimental spectra to a Lorentzian line-shape function.Two factors, namely, the thermal expansion and electron(exciton)–phonon coupling effects contribute to the temper-ature shift of the transition energy of (Zn0:38Cd0:62)1ÀxBexSecompounds. Thermal expansion effect8,9)can be accountedfor and the parameters that describe the temperaturevariation of energy and broadening function of lh and hhtransitions for ZnCdBeSe are evaluated and discussed. Ourstudy shows evidence of reduced temperature variation ofthe energy gap upon adding beryllium to the ZnCdSesystem.2. ExperimentalThe schematic of (Zn0:38Cd0:62)1ÀxBexSe epilayers grownon InP substrate by molecular beam epitaxy is shown inFig. 1. Prior to the growth, the InP substrate was deoxidizedat 480C and an InGaAs buffer layer was grown at 450C for5 min. in III–V chamber. Then, the sample was transferred inultra high vacuum to the II–VI chamber. Keeping thesubstrate temperature at 170C, a Zn irradiation wasperformed for 20 s and a ZnCdSe buffer layer was grownfor 1 min. After the growth of ZnCdSe buffer layer, thesubstrate temperature was increased to 250C and theZnCdBeSe film was grown for 1 h. The thickness of thefilm was about 1.0 mm. Three samples (A, B and C) withdifferent Be concentrations were prepared. In order to obtaina reasonable estimate of the Be content of the quarternaryZnCdBeSe system, a test ternary ZnCdSe alloy (sample A)was also grown together with the quaternary system usingthe same Zn/Cd flux ratio. The composition of the ZnCdSewas then determined from the lattice constant measured bysingle and double-crystal X-ray diffraction (XRD) using theCu K1 radiation. The full width at half maximum (HWHM)ÃCorresponding author. E-mail address: ysh@et.ntust.edu.twJapanese Journal of Applied PhysicsVol. 43, No. 2, 2004, pp. 459–466#2004 The Japan Society of Applied Physics459
  2. 2. of the (004) rocking curves of the ZnCdSe sample is ratherbroad, indicating that the sample is partially strained. Theasymmetrical reflection double-crystal X-ray rocking curve(DCXRC) was used to obtain the perpendicular and parallellattice constants: a? and ak. The bulk lattice constant, a0,can then be calculated from the equation10)a0 ¼ a? 1 À2#1 þ #a? À aka? ð1Þwhere # is Poisson’s ratio and a value of # ¼ 0:2810)wasused for the present calculation. Then, assuming thatVegard’s law is valid for ZnCdSe, the composition of Znfor the sample was calculated. We have used the followingvalues of the lattice constants: aZnSe ¼ 5:6676 #A11)andaCdSe ¼ 6:052 #A11)in the calculation. The composition of theZnCdSe film was also examined by electron probe micro-analysis (EPMA). The deviation in the Zn compositionbetween XRD and EPMA is less than 2%. For the as grownquarternary system, we assumed that Be incorporation didnot affect the sticking coefficients of Zn and Cd. A similarestimation of the lattice constant parallel to the ternarysystem was performed. The difference in the lattice constantof ZnCdSe and ZnCdBeSe was then utilized to estimate theBe content. The results are as following: Sample A isZn0:38Cd0:62Se whose lattice constant is 5.907 #A, and thelattice mismatch to InP is À0:65%, while sample B is(Zn0:38Cd0:62)0:93Be0:07Se with a lattice constant 5.842 #A andlattice mismatch of 0.45%. Sample C is (Zn0:38Cd0:62)0:89Be0:11Se. The lattice constant of sample C is 5.83 #A and thelattice mismatched is 0.63%. It is known that the ratio of akto a? can give the strain information directly. The values ofak=a? of the samples have been checked. The number forsample A is slightly smaller than one (ak=a? ¼ 0:996) whilethe values for samples B and C are determined to be 1.006and 1.009 respectively. This might imply a compressive typestress in sample A and the existence of tensile-type stress insamples B and C. These results are further confirmed withthe CER and PzR measurements as described in thefollowing section.The implementation of the CER experiment utilizes acondenser-like system consisting of a front wire gridelectrode with a second electrode separated from the firstelectrode by insulating spacers, which are $0:1 mm largerthan the sample thickness. The sample is placed in betweentwo capacitor plates such that no direct contact with the frontsurface of the sample would be made. The probe beam isincident through the front wire grid. Electric field modu-lation is achieved by applying an ac voltage ($1 kV peak topeak at 200 Hz) across the electrodes. A 150 W xenon arclamp filtered by a 0.35 m monochromator provided themonochromatic light. The reflected light was detected by aUV-enhanced silicon photodiode and the dc output of siliconphotodiode was maintained constant by a servo mechanismof variable neutral density filter (VNDF). A dual-phase lock-in amplifier was used to measure the detected signals. Fortemperature dependent measurements, a closed-cycle cryo-genic refrigerator equipped with a digital thermometercontroller was used for the low-temperature measurements.For the high-temperature experiments, each sample wasmounted on one side of a copper finger of an electricalheater, which enabled one to control and stabilize the sampletemperature. The temperature dependent measurements weremade between 15 and 450 K with a temperature stability of0.5 K or better. PzR measurements were achieved bysticking each sample with glue on a 0.15 cm thick lead-zirconate-titanate (PZT) piezoelectric transducer driven by a200 Vrms sinusoidal wave at 200 Hz. The alternating ex-pansion and contraction of the transducer subjects thesample to an alternating strain with a typical rms Ál=l valueof $10À5.3. Results and DiscussionFigures 2(a) and 2(b) illustrate the CER and PzR spectraof three (Zn0:38Cd0:62)1ÀxBexSe samples at 15 K and 300 K,respectively. The experimental data for CER and PzR areshown, respectively, as square and circle curves in Figs. 2(a)and 2(b). These spectra exhibit doublet features near theband edge of (Zn0:38Cd0:62)1ÀxBexSe. These features arequite similar to those of the excitonic transitions in ZnTe/SLSs/GaAs examined by Tu et al.12,13)The appearance ofthe doublets has been shown to be an indication of theheavy-hole (hh) and light-hole (lh) related excitonic tran-sitions.12,13)The transition features for beryllium containingsamples B and C present an energy blue-shift behavior and abroadened line-shape character with respect to the beryl-lium-free sample A. The broader line-shape for the samplesB and C can be attributed in part, to the alloy scatteringeffects and most likely, in a larger proportion due to thepoorer crystalline quality in the beryllium-incorporatedsamples. The experimental spectra in Fig. 2 was fitted tofirst derivative Lorentzian line shape (FDLL) function of theform14–16)ÁRR¼ ReX2j¼1AjeiÈjðE À Ej þ iÀjÞÀnð2Þwhere Aj and Èj are the amplitude and phase of the lineshape, Ej and Àj are the energy and broadening parameter ofthe transitions, and the value of n depends on the origin ofthe transitions. For the first derivative functional form, n ¼ 2is appropriate for the bound states such as excitons.15)TheFDLL fits for both CER and PzR spectra clearly show twostructures (indicate with arrows) near the band edge ofZnCdSe 5 nm(ZnCd)1-xBexSe 1 µmZnCdSe 10 nmBuffer LayerInGaAs Buffer LayerInP Substrate}}Fig. 1. Schematic for the epitaxial structure of ZnCdBeSe samples.460 Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al.
  3. 3. (Zn0:38Cd0:62)1ÀxBexSe. To identify the physical origin of thedoublets, we make a spectral comparison of the CER andPzR measurements.For the PzR measurement under [001]-symmetry coplanarstress, the ratio between the light-hole to electron and heavy-hole to electron transitions under the coplanar piezomodu-lation has been shown to obey the relation16,17)KPzR ¼ðdElh=dSÞðdEhh=dSÞ¼að2 À !Þ þ bð1 þ !Það2 À !Þ À bð1 þ !Þ; ð3ÞThe variable S refers to the modulating stress applied to thesample. The parameters a and b represent the hydrostatic andthe shear deformation potentials, respectively and ! ¼À2S12=ðS11 þ S12Þ, where Sij, i; j ¼ 1 or 2, is the elasticcompliance constant. For Zn0:38Cd0:62Se, the numericalvalues S11 ¼ 2:33  10À3kbarÀ1, S12 ¼ À0:884  10À3kbarÀ1, a ¼ À4:19 eV and b ¼ À0:95 eV, are deduced.11,18)These values are assumed for the present Be-incorporatedsamples as the concentration of Be is small. The ratio ofKPzR is then evaluated to be about 4.6 from eq. (3). Thisresult indicates that the transition of light hole is moresensitive than that of heavy hole under the [001]-symmetrycoplanar piezomodulation. The CER spectrum of the samesample, in which the relative intensity of the lh and hhtransitions is insensitive to strain, has been used as areference. The ratio ðdElh=dSÞ=ðdEhh=dSÞ is relative toðIlh=IhhÞPzR in the PzR spectra and ðIlh=IhhÞCER in the CERspectra. In the strain-insensitive CER spectra the modulationcoefficient is the same for all transitions, so that the ratioðIlh=IhhÞPzR=ðIlh=IhhÞCER gives that ratio of the piezomodula-tion coefficients of the lh and hh transitions. From the PzRmeasurements for the beryllium free sample A, the enlargedlh feature appeared at the higher energy side with respect tothe hh feature indicating the presence of a compressive-typestress in the sample. The KPzR is determined to be 1.5 and2.6 at 15 and 300 K, respectively. However, in samples Band C, the enlarged lh feature appeared at the lower energyside, the KPzR is determined to be 1.8 (2.1) and 1.2 (1.5),respectively, for samples B and C at 15 K (300 K). The lowerenergy value of the lh transition for ZnCdBeSe sampleprovides an evidence that tensile-type stress exists in theZnCdBeSe epitaxial layers of samples B and C. Theidentified transition features are denoted as Elh and Ehhand indicated with arrows in Fig. 2. The difference betweenthe experimentally deduced values of KPzR and that of thetheoretical calculation might be attributed to the partialrelaxation of the samples. Further evident points to thepartial relaxation of the samples can be derived form theevaluation of the strain induced splitting of the heavy holeand light hole transitions defined as ÁE Ehh À Elh. Acalculation for the fully strained sample led to ÁE ¼À28 meV, 20 meV and 29 meV, respectively, for samples A,B and C at 300 K. Our experimental values for ÁE at 300 Kwere determined to be À17 Æ 4 meV, 16 Æ 4 meV and20 Æ 4 meV respectively, for the three samples. The smallermeasured ÁE values is an indication of partial relaxation ofthe strained layers. Further evidence of partial relaxationalso showed up in the low temperature measurement at 15 K,which yielded ÁE ¼ À15 Æ 2 meV, 18 Æ 2 meV and 22 Æ2 meV respectively for samples A, B and C. The similarityof ÁE at 300 K and 15 K is contrary to what one generallyexpects for a strained layer. The thermal expansioncoefficients at room temperature for InP,18)ZnSe,11)wurtziteCdSe19)and BeSe19)are found to be 4:75  10À6KÀ1, 7:7 Â10À6KÀ1, 7:3  10À6KÀ1, 8:7  10À6KÀ1, respectively.The thermal expansion coefficients for Zn0:38Cd0:62Se,(Zn0:38Cd0:62)0:93Be0:07Se and (Zn0:38Cd0:62)0:89Be0:11Se aredetermined to be 7:45  10À6KÀ1, 7:54  10À6KÀ1and7:59  10À6KÀ1, respectively, by linear interpolation ofvalues of the end-point materials. At 15 K, since we can notfind any data of expansion coefficient for CdSe and BeSe,we tentatively take the ZnSe value of this parameter for theZnCdBeSe samples. The values of the expansion coefficientsfor InP18)and ZnSe11)at 15 K are À0:1  10À6KÀ1andÀ0:3  10À6KÀ1, respectively. In view of the differences inthe linear expansion coefficients at 300 K and 15 K, weshould expect to observe some variations of ÁE at the twotemperatures due to the additional induced strain. The factthat no appreciable difference in the measured ÁE can beobserved may indicate the state of partial relaxation of thestrained layer. We have also estimated the critical thick-nesses of the samples from the elastic constants. Theestimated critical thicknesses are about an order smaller thanthe sample thickness of $1:0 mm. This means that thesamples should relax completely. However, our experimen-tal results seem to indicate the existence of residual straineven for sample thickness much larger than the criticalthickness. Similar existence of residual stain is also found2.0 2.1 2.2 2.3 2.4hhElhElhEhhElhE hhE2(a)Sample C (x = 11%)Sample B (x = 7%)Sample A (x = 0%)PzRCERFit15K(Zn0.38Cd0.62)1-xBexSe∆R/R(arb.units)Photon Energy (eV)1.8 1.9 2.0 2.1 2.2 2.3 2.4lhElhEhhEhhElhE hhESample A (x = 0%)Sample C (x = 11%)Sample B (x = 7%)2(b)PzRCERFit300K(Zn0.38Cd0.62)1-xBexSe∆R/R(arb.units)Photon Energy (eV)Fig. 2. CER and PzR spectra for three different compositions ofZnCdBeSe samples in spectral range between 1.9 and 2.4 eV at (a)15 K and (b) 300 K.Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al. 461
  4. 4. for InGaAs films grown on GaAs substrate.20)The physicalorigin of this residual strain is not clear and moreinvestigative works should be performed to clarify thispoint. In addition, a broad feature located at the lower energyside of the low-temperature spectra of samples B and C wasobserved. This feature is most probably related to somestructural defects at the II–VI/III–V interface in samples Band C.Displayed by dashed curves in Figs. 3(a), 3(b) and 3(c)are, respectively, the experimental CER spectra of samplesA, B and C at several temperatures between 15 and 450 K.The solid lines are the fitted spectral data to eq. (2) withn ¼ 2, which yield transition energies indicated by arrows.As the general property of most semiconductors, when thetemperature is increased, the lh and hh transitions in theCER spectra exhibit an energy red-shift and lineshapebroadening characteristics. The broader lineshapes of thetransition features are due to the increase of lattice-phononscattering effects.Plotted by the open circles and open squares in Figs. 4(a),4(b) and 4(c) are the temperature variations of theexperimental values of Elh and Ehh, respectively with therepresentative error bars for ZnCdBeSe samples A, B and C.The temperature shift of the transition energies contains1.7 1.8 1.9 2.0 2.1 2.2 2.3hhEhhElhElhE3(a)Expt.Fit450K300K200K77K15KSample AZn0.38Cd0.62SeCER∆R/R(arb.units)Photon Energy (eV)1.8 1.9 2.0 2.1 2.2 2.3 2.4hhElhElhE hhE3(b)450K300K200K77K15KExpt.FitSampleB(Zn0.38Cd0.62)0.93Be0.07SeCER∆R/R(arb.units)Photon Energy (eV)1.9 2.0 2.1 2.2 2.3 2.4hhEhhElhElhE450K300K200K77K15K3(c)Expt.FitSample C(Zn0.38Cd0.62)0.89Be0.11SeCER∆R/R(arb.units)Photon Energy (eV)Fig. 3. Experimental CER spectra of (a) Zn0:38Cd0:62Se (Sample A), (b)(Zn0:38Cd0:62)0:93Be0:07Se (Sample B), and (c) (Zn0:38Cd0:62)0:89Be0:11Se(Sample C) at several temperatures between 15 and 450 K. The dashedlines are the experimental curves and the solid lines are least-squares fitsto eq. (2).0 100 200 300 400 5001.962.∆EthExpt.-∆EthVarshni FitBose-Einstein FitSampleAZn0.38Cd0.62SeCEREnergy(eV)Temperature (K)0 100 200 300 400 5002. Expt.Expt.Expt.-∆EthExpt.-∆EthVarshni FitBose-Einstein Fit4(b)Sample B(Zn0.38Cd0.62)0.93Be0.07SeCEREnergy(eV)Temperature (K)0 100 200 300 400 5002. Expt.Expt.Expt.-∆EthExpt.-∆EthVarshni FitBose-Einstein Fit4(c)Sample C(Zn0.38Cd0.62)0.89Be0.11SeCEREnergy(eV)Temperature (K)Fig. 4. The temperature variations of light-hole (lh) and heavy-hole (hh)transition energies of (a) Zn0:38Cd0:62Se (Sample A), (b) (Zn0:38-Cd0:62)0:93Be0:07Se (Sample B), and (c) (Zn0:38Cd0:62)0:89Be0:11Se (Sam-ple C) with representative error bars. The solid curves are least-squaresfits to the Varshni-type semiempirical relationship and the dashed linesare fitted to the Bose–Einstein-type expression.462 Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al.
  5. 5. contributions from both thermal expansion and electron(exciton)–phonon coupling effects. To obtain the parametersdirectly related to the latter contribution, it is necessary toeliminate the contribution of the former. The energy shiftÁEthðTÞ due to thermal expansion can be written as8,9)ÁEthðTÞ ¼ 3aZ T0ðT0ÞdT0ð4Þwhere a is the interband hydrostatic deformation potentialand ðTÞ is the temperature-dependent linear-expansioncoefficient. For the ZnSe binary compound, the value of a isÀ5:4 eV and ðTÞ can be deduced from Ref. 11. ForZn0:38Cd0:62Se, a value of a ¼ À4:2 eV can be obtained froma linear interpolation between the hydrostatic pressurecoefficient of ZnSe and the lowest-lying exciton (A exciton)of wurzite CdSe.11)Since we found no data for ðTÞ forCdSe and BeSe, we tentatively take the ZnSe value of thisparameter for this II–VI ZnCdBeSe alloy system. Theenergy terms, which are relevant to the electron (exciton)–phonon scattering influence can be expressed as Elh ÀÁEthðTÞ and Ehh À ÁEthðTÞ, and illustrated in Figs. 4(a),4(b) and 4(c) as solid circles and squares, respectively. Thetransitions energies contain contributions from the thermalexpansion and electron–phonon interaction, and can be fittedto the Varshni semiempirical relationship21)EjðTÞ ¼ Ejð0Þ ÀjT2ðj þ TÞð5aÞHere, Ejð0Þ is the energy at 0 K; j and j are constants, and jrefers to lh or hh. The constant j is related to the electron(exciton)–phonon interaction and j is closely related to theDebye temperature.21)If we remove the thermal expansioncontribution from EjgðTÞ, the Varshni-type relation can bewritten as8,9)EjgðTÞ À ÁEthðTÞ ¼ Ejgð0Þ À0jT2ð0j þ TÞð5bÞwhere the primed parameters are defined similarly to theunprimed counterparts in eq. (5a). The temperature depend-ent energy values of Ehh À ÁEthðTÞ and Elh À ÁEthðTÞ areleast-square fits to the eq. (5b) and indicated as solid curvesin Fig. 4. The values obtained for Ejð0Þ, j, 0j, j and 0j arelisted in Table I together with the fitted parameters for thedirect gaps of ZnSe,9)Zn0:56Cd0:44Se,9)CdSe,,22)GaAs,23)InP,24)and In0:06Ga0:94As8)given for comparison purpose.The nearly equal value of 0j and that of 0j for samples A, B,and C, respectively, in Table I indicates that the transitionsof lh and hh have almost identical temperature dependenceas illustrated in the Fig. 4.The temperature dependence of excitonic transitions ofthe ZnCdBeSe II–VI compounds can also be analyzed by aBose–Einstein type expression of the form8,9)EjðTÞ ¼ Ejð0Þ À2ajBexpÂjBT À 1 ; ð6aÞEjðTÞ À ÁEthðTÞ ¼ Ejð0Þ À2a0jBexpÂ0jBT!À 1 # ð6bÞwhere Ejð0Þ is the energy value at 0 K, ajB represents thestrength of average electron–phonon interaction, and ÂjBcorresponds to the average phonon temperature and theindex j refers to lh or hh interaction. The primed parametersin eq. (6b) are defined similarly to the unprimed terms in eq.(6a) with the contribution from thermal expansion effectTable I. Values of the Varshni-type fitting parameters, which describe the temperature dependence of transition energies ofZn0:38Cd0:62Se, (Zn0:38Cd0:62)0:93Be0:07Se, and (Zn0:38Cd0:62)0:89Be0:11Se obtained from the CER experiments. The parameters forZnSe, Zn0:56Cd0:44Se, CdSe, GaAs, InP, and In0:06Ga0:94As are included for comparison.Ejg(0) j j 0j 0jMaterial(eV) (10À4eV/K) (K) (10À4eV/K) (K)Zn0:38Cd0:62SeaÞEhh 2:138 Æ 0:002 5:6 Æ 0:2 195 Æ 20 4:5 Æ 0:2 150 Æ 20Elh 2:153 Æ 0:002 5:7 Æ 0:2 210 Æ 20 4:5 Æ 0:2 160 Æ 20(Zn0:38Cd0:62)0:93Be0:07SeaÞElh 2:203 Æ 0:002 4:9 Æ 0:2 180 Æ 35 3:9 Æ 0:2 140 Æ 35Ehh 2:221 Æ 0:002 5:1 Æ 0:2 190 Æ 35 3:9 Æ 0:2 130 Æ 35(Zn0:38Cd0:62)0:89Be0:11SeaÞElh 2:242 Æ 0:002 4:8 Æ 0:2 175 Æ 35 3:7 Æ 0:2 125 Æ 35Ehh 2:264 Æ 0:002 4:8 Æ 0:2 160 Æ 35 3:7 Æ 0:2 115 Æ 35ZnSebÞ2:800 Æ 0:005 7:3 Æ 0:4 295 Æ 35 5:0 Æ 4 206 Æ 35Zn0:56Cd0:44SebÞ2:272 Æ 0:004 6:1 Æ 0:5 206 Æ 35 4:5 Æ 0:5 153 Æ 45CdSecÞ1.834 (3) 4.24 (20) 118 (40)GaAsdÞ1:512 Æ 0:005 5:1 Æ 0:5 190 Æ 82InPeÞ1:432 Æ 0:007 4:1 Æ 0:3 136 Æ 60In0:06Ga0:94AsfÞ1:420 Æ 0:005 4:8 Æ 0:4 200 Æ 50 2:5 Æ 0:4 140 Æ 40a) Present work.b) ref. 9.c) ref. 22. The numbers in parentheses are error margins in units of the last significant digit.d) ref. 23.e) ref. 24.f) ref. 8.Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al. 463
  6. 6. eliminated. The dashed lines shown in Figs. 4(a)–4(c) are theleast-squares fits of the relevant energy terms to eq. (5a) or(5b). The obtained values of the fitting parameters are listedin Table II. For comparison, the parameters for the directgaps of ZnSe,9)Zn0:56Cd0:44Se,9)CdSe,22)GaAs,25)InP,24)and In0:06Ga0:94As8)are also included. The temperaturevariations of the excitonic transition energies are dominatedby lattice constant variations and the interactions withrelevant acoustic and optical phonons. The parameters a0jBand Â0jB in eq. (6b) are related to 0j of eq. (5b) by taking thehigh temperature limit of both expressions. This yieldsrelationship of 0j % 2a0jB=Â0jB. Comparison of Table I and IIshows that within error limits this relationship is satisfied.The experimental values of the temperature dependenceof the linewidth ÀjðTÞ [half width at half maximum(HWHM)] of the excitonic features for the three ZnCdBeSeSamples, as obtained from the line-shape fits, are displayedin Figs. 5(a), 5(b) and 5(c), respectively. The open and solidcircles are the data points of lh and hh transitions and thesolid lines are least-square fits to an expression responsiblefor the temperature dependence of the linewidth of the directgap for zinc-blende-type semiconductors of the form26)ÀjðTÞ ¼ Àjð0Þ þ jACT þÀjLOexpÂjLOT!À 1 # ð7ÞIn eq. (7), the index j refers to either lh or hh interactions.The first term of eq. (7) is due to intrinsic effects (electron-electron interaction, impurity, dislocation, and alloy scatter-ing) at T ¼ 0 K, while the second term corresponds tolifetime broadening due to the electron (exciton)–acousticalphonon interaction, where jAC is the acoustical phononcoupling constant. The third term is caused by the electron(exciton)–LO phonon (Fro¨hlich) interaction. The quantityÀjLO represents the strength of the electron (exciton)–LOphonon coupling while ÂjLO is the LO phonon temperature.As shown in Figs. 5(a)–5(c), as the temperature is raised, thelinewidth first increases from its zero-temperature valuebecause of acoustical phonon scattering. Above about 50 Kthe LO phonon contribution becomes important and even-tually dominates the linewidth broadening. In this article, wetreat the four terms Àjð0Þ, jAC, ÀjLO and ÂjLO as fittingparameters. Least-squares fits to eq. (6) yields the solid linesas illustrated in Figs. 5(a)–5(c) and the obtained values ofÀjð0Þ and ÀjLO as well as the numbers for jAC and ÂjLO arelisted in Table III. For comparison, the values of ÀLO (interms of HWHM) for ZnSe,9,26,27)Zn0:56Cd0:44Se,9)CdSe (Aexciton),22)GaAs,28)In0:06Ga0:94As,8)InP,29)and GaN30,31)from other works are also included in Table III. The valuesof Àjð0Þ for the beryllium containing samples are muchlarger than those of beryllium free sample due mainly to thepoorer crystalline quality of the Be-incorporated samples. Infact it is not easy to grow high-quality Be-related II–VIquaternaries.In general, temperature variations of the energy gap aredue to both lattice constant variations and interactions withrelevant acoustic and optical phonons. According withexisting theory25,32–34)this leads to a value of ÂjBðÂ0jBÞsignificantly small than ÂjLO. From Tables I and II, it can beseen that our observations agree well with this theoreticalconsideration. Figures 4(a), 4(b), and 4(c) show linearizingof the energy gap as the temperature is raised above $200 K.Least-square fits by a straight line in this region yieldstemperature coefficient of the energy shift for either lh or hhinteractions (with thermal expansion eliminated) to beTable II. Values of the Bose–Einstein-type fitting parameters, which describe the temperature dependence of the transition energies ofZn0:38Cd0:62Se, (Zn0:38Cd0:62)0:93Be0:07Se, and (Zn0:38Cd0:62)0:89Be0:11Se obtained from CER experiments. The parameters for ZnSe,Zn0:56Cd0:44Se, CdSe, GaAs, InP, and In0:06Ga0:94As are included for comparison.Material Ejð0Þ ajB ÂjB a0jB Â0jB(eV) (meV) (K) (meV) (K)Zn0:38Cd0:62SeaÞEhh 2:138 Æ 0:002 48 Æ 4 195 Æ 20 36 Æ 4 175 Æ 20Elh 2:153 Æ 0:002 50 Æ 4 205 Æ 20 38 Æ 4 185 Æ 20(Zn0:38Cd0:62)0:93Be0:07SeaÞElh 2:203 Æ 0:002 46 Æ 4 205 Æ 30 34 Æ 4 185 Æ 30Ehh 2:221 Æ 0:002 45 Æ 4 200 Æ 30 33 Æ 4 175 Æ 30(Zn0:38Cd0:62)0:89Be0:11SeaÞElh 2:242 Æ 0:002 45 Æ 4 205 Æ 30 33 Æ 4 185 Æ 30Ehh 2:264 Æ 0:002 44 Æ 4 200 Æ 30 32 Æ 4 175 Æ 30ZnSebÞ2:800 Æ 0:005 73 Æ 4 260 Æ 10 47 Æ 4 220 Æ 10Zn0:56Cd0:44SebÞ2:267 Æ 0:004 62 Æ 4 236 Æ 10 43 Æ 4 201 Æ 10CdSecÞ1.830(5) 36(5) 179(40)GaAsdÞ1:512 Æ 0:005 57 Æ 29 240 Æ 102InPeÞ1:423 Æ 0:01 51 Æ 2 259 Æ 10In0:06Ga0:94AsfÞ1:420 Æ 0:005 44 Æ 9 203 Æ 45 33 Æ 7 280 Æ 45a) Present work.b) ref. 9.c) ref. 22. The numbers in parentheses are error margins in units of the last significant digit.d) ref. 25.e) ref. 24.f) ref. 8.464 Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al.
  7. 7. À3:9 Â 10À4eV/K for sample A, À3:3 Â 10À4eV/K forsample B and À3:1 Â 10À4eV/K for sample C. By takinghigh temperature limits of either eqs. (5b) or (6b), we cancorrelate these values to that of 0j or 0jB as given in Tables Iand II, respectively. These numbers also indicate that theaddition of Be reduces the rate of change of the energy gapwith temperature for the Be-containing ZnCdSe compounds.This is a desirable feature for the device applications of thesecompounds. Our fitted values for ÀLO are comparable to thatof ZnSe,9,26,27)CdSe22)and most of the III–V semiconduc-tors8,28,29)with the exception of GaN.30,31)It has been showntheoretically that Fro¨hlich interaction is stronger in the moreionic crystals of II–VI semiconductors than the III–Vsemiconductors.26)Our results show no clear trend to thateffect and seem to indicate that other factor may contributeto the electron (exciton)–LO phonon coupling constant, ÀLO.In the case of GaN, it may be possible that a largerdeformation potential interaction may contribute a signifi-cant proportion to ÀLO in addition to the Fro¨hlich inter-action.30,31)The ionicity dependence of Fro¨hlich interactionrequires further consideration and more work needs to bedone in this area.4. SummaryIn summary, the temperature dependence of band-edgetransitions of ZnCdBeSe II–VI compounds with different Beconcentration was studied using contactless electroreflec-tance (CER) in the temperature range of 15 to 450 K. Theexperimental results of CER spectra for beryllium contain-ing samples demonstrate an energy blue-shift behavior and abroadened lineshape character with respect to the ZnCdSespecimen. Strain modulated piezoreflectance (PzR) meas-urements were utilized to facilitate the identification of theFig. 5. Experimental variation of the broadening parameter (HWHM) forthe direct excitonic transitions of (a) Zn0:38Cd0:62Se (Sample A), (b)(Zn0:38Cd0:62)0:93Be0:07Se (Sample B), and (c) (Zn0:38Cd0:62)0:89Be0:11Se(Sample C) with representative error bars. The open and solid circles arerespectively the experimental values of lh and hh transitions, respectively,and the solid lines are least-square fits to eq. (7).Table III. Values of the parameters that describe the temperature depend-ence of À (HWHM) for the energy gaps of Zn0:38Cd0:62Se,(Zn0:38Cd0:62)0:93Be0:07Se, and (Zn0:38Cd0:62)0:89Be0:11Se obtained fromthe CER experiments. The relevant parameters for ZnSe, Zn0:56Cd0:44Se,CdSe, GaAs, InP, In0:06Ga0:94As and GaN are also included forcomparison.Material Àjð0Þ ÀLO ÂLO AC(meV) (meV) (K) (meV/K)Zn0:38Cd0:62SeaÞEhh 3 Æ 2 33 Æ 8 320 Æ 100 2 Æ 1Elh 4 Æ 2 35 Æ 8 310 Æ 100 2 Æ 1(Zn0:38Cd0:62)0:93Be0:07SeaÞElh 17 Æ 2 25 Æ 8 330 Æ 100 2 Æ 1Ehh 18 Æ 2 32 Æ 8 335 Æ 100 2 Æ 1(Zn0:38Cd0:62)0:89Be0:11SeaÞElh 19 Æ 2 26 Æ 8 345 Æ 100 2 Æ 1Ehh 20 Æ 2 31 Æ 8 350 Æ 100 2 Æ 1ZnSe 6:5 Æ 2:5bÞ24 Æ 8bÞ360b),c)2.0bÞ;cÞ30 Æ 7dÞ30eÞZn0:56Cd0:44SebÞ6:0 Æ 2:0 17 Æ 6 334cÞ1.1cÞCdSefÞ2.3(3) 23(1) 300cÞGaAsgÞ23 Æ 1:5 417cÞIn0:06Ga0:94AshÞ7:5 Æ 0:5 23 Æ 6 370 Æ 122InPiÞ1:5 Æ 0:5 31 Æ 3:0 496cÞGaN 10jÞ375jÞ1065cÞ152.4kÞ390kÞ1065cÞ16a) Present work.b) ref. 9.c) Parameter fixed.d) ref. 26.e) ref. 27.f) ref. 22. The numbers in parentheses are error margins in units of lastsignificant digit.g) ref. 28.h) ref. 8.i) ref. 29. Excitonic transition.j) ref. 30.k) ref. 31.Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al. 465
  8. 8. light-hole (lh) and heavy-hole (hh) excitonic transitions ofthe ZnCdBeSe samples. The enhanced lh feature with lowerenergy in the PzR spectrum provides conclusive evidencethat tensile-type stress existed in the ZnCdBeSe epilaxiallayers. The temperature variations of transition energies areanalyzed by both the Varshni- and Bose–Einstein-typeexpressions, which take into consideration the contributionof thermal expansion. The parameters extracted from bothexpressions are found to agree reasonably well by extendinginto the high temperature regime. In addition, our analysisshows evidence of a reduced energy shift due to temperaturevariations by incorporating beryllium into the ZnCdSecompound.AcknowledgementsThe authors C. H. Hsieh and Y. S. Huang acknowledgethe support of the National Science Council of the Republicof China under Project No. NSC91-2215-E-011-002.Authors C. H. Ho and K. K. Tiong acknowledge thesupports of National Science Council under ProjectNos. NSC91-2215-E-259-004 and NSC91-2112-M-019-003. M. Mun˜oz, O. Maksimov, and M. C. Tamargoacknowledge the partial support from the NSF IGERT grantnumber DGE9972892.1) F. Fisher, G. Landwehr, Th. Litz, H. J. Lugauer, U. Zehnder, Th.Gerhard, W. Ossau and A. Waag: J. Cryst. Growth 175/176 (1997)532.2) T. B. Ng, C. C. Chu, J. Han, G. C. Hua, R. L. Gunshor, E. Ho, E. L.Warlick, L. A. Kolodziejski and A. V. Nurmikko: J. Cryst. Growth175/176 (1997) 552.3) F. Vigue´, E. Tournie´ and J. P. Faurie: Appl. Phys. Lett. 76 (2000) 242.4) A. Waag, F. Fischer, K. Schu¨ll, T. Baron, H. J. Lugauer, Th. Litz, U.Zehnder, W. Ossau, T. Gerhard, M. Keim, G. Reuscher and G.Landwehr: Appl. Phys. Lett. 70 (1997) 280.5) J. Y. Zhang, D. Z. Shen, X. W. Fan, B. J. Yang and Z. H. Zheng: J.Cryst. Growth 214/215 (2000) 100.6) A. Mun˜oz, P. Rodrı´guez-Herna´ndez and A. Mujica: Phys. Status SolidiB 198 (1996) 439.7) A. Waag, F. Fischer, H. J. Lugauer, Th. Litz, J. Laubender, U. Lunz,U. Zehnder, W. Ossau, T. Gerhardt, M. Mo¨ller and G. Landwehr: J.Appl. Phys. 80 (1996) 792.8) Z. Hang, D. Yan, F. H. Pollak, G. D. Pettit and J. M. Woodall: Phys.Rev. B 44 (1991) 10546.9) L. Malikova, W. Krystek, F. H. Pollak, N. Dai, A. Cavus and M. C.Tamargo: Phys. Rev. B 54 (1996) 1819.10) S. P. Guo, Y. Luo, W. Lin, O. Maksimov, M. C. Tamargo, I.Kuskovsky, V. Tian and G. Neumark: J. Cryst. Growth 208 (2000)205.11) Semiconductors, Physics of II–VI and I–VII Compounds, Semimag-netic Semiconductors, eds. O. Madelung, Landolt-Bo¨rnstein (Springer,New York, 1982) New Series, Group III: Crystal and Solid StatePhysics, Vol. 17, Subvol. b.12) R. C. Tu, Y. K. Su, H. J. Chen, Y. S. Huang and S. T. Chou: Appl.Phys. Lett. 72 (1998) 3184.13) R. C. Tu, Y. K. Su, H. J. Chen, Y. S. Huang, S. T. Chou, W. H. Lanand S. L. Tu: J. Appl. Phys. 84 (1998) 2866.14) D. E. Aspnes: Handbook on Semiconductors, ed. by T. S. Moss(North-Holland, New York, 1980) Vol. 2, p. 109.15) F. H. Pollak and H. Shen: Mater. Sci. Eng. R10 (1993) 275.16) F. H. Pollak: Semiconductor and Semimetals, ed. T. P. Pearsall(Academic, New York, 1990) Vol. 32, p. 17.17) H. Mathieu, J. Alle´gre and B. Gil: Phys. Rev. B 43 (1991) 2218.18) Semiconductors, Physics of Group IV Elements and III–V Compounds,eds. O. Madelung, Landolt-Bo¨rnstein (Springer, New York, 1982)New Series, Group III: Crystal and Solid State Physics, Vol. 17,Subvol. a.19) V. Kumar and B. S. R. Sastry: Cryst. Res. Technol. 36 (2001) 565.20) J. H. Chen, W. S. Chi, Y. S. Huang, Y. Yin, F. H. Pollak, G. D. Pettitand J. M. Woodall: Semicond. Sci. Technol. 8 (1993) 1420.21) Y. P. Varshni: Physica (Amsterdam) 34 (1967) 149.22) S. Logothetidis, M. Cardona, P. Lautenschlager and M. Garriga: Phys.Rev. B 34 (1986) 2458.23) H. Shen, S. H. Pan, Z. Hang, J. Leng, F. H. Pollak, J. M. Woodall andR. N. Sacks: Appl. Phys. Lett. 53 (1988) 1080.24) Z. Hang, H. Shen and F. H. Pollak: Solid State Commun. 73 (1990) 15.25) P. Lautenschlager, M. Garriga, S. Logothetidis and M. Cardona: Phys.Rev. B 35 (1987) 9174.26) S. Rudin, T. L. Reinecke and B. Segall: Phys. Rev. B 42 (1990) 11218.27) N. T. Pelekanos, J. Ding, M. Hagerott, A. V. Nurmikko, H. Luo, N.Samarth and J. K. Furdyna: Phys. Rev. B 45 (1992) 6037.28) H. Qiang, F. H. Pollak, C. M. Sotomayor Torres, W. Leitch, A. H.Kean, M. Stroscio, G. J. Iafrate and K. W. Kim: Appl. Phys. Lett. 61(1992) 1411.29) S. Y. Chung, D. Y. Lin, Y. S. Huang and K. K. Tiong: Semicond. Sci.Technol. 11 (1996) 1850.30) A. J. Fischer, W. Shan, J. J. Song, Y. C. Chang, R. Horning and B.Goldenberg: Appl. Phys. Lett. 71 (1997) 1981.31) A. J. Fischer, W. Shan, G. H. Park, J. J. Song, D. S. Kim, D. S. Yee, R.Horning and B. Goldenberg: Phys. Rev. B 56 (1997) 1077.32) C. K. Kim, P. Lautenschlager and M. Cardona: Solid State Commun.59 (1986) 797.33) S. Zollner, S. Gopalan and M. Cardona: Solid State Commun. 77(1991) 485.34) P. Lautenschlager, M. Garriga, L. Vin˜a and M. Cardona: Phys. Rev. B36 (1987) 4821.466 Jpn. J. Appl. Phys., Vol. 43, No. 2 (2004) C.-H. HSIEH et al.