Excitonic parameters of InxGa1-xAs-GaAs heterostructures with quantum wells at low temperatures
aa r X i v : . [ c ond - m a t . m t r l - s c i ] M a r N.M. Litovchenko, D.V. Korbutyak, O.M. Strilchuk
N.M. LITOVCHENKO, D.V. KORBUTYAK, O.M. STRILCHUK
V.E. Lashkaryov Institute of Semiconductor Physics, Nat. Acad. of Sci. of Ukraine (41, Prosp. Nauky, Kyiv 03028, Ukraine; e-mail: [email protected])
EXCITONIC PARAMETERS OF In x Ga − x As–GaAsHETEROSTRUCTURES WITH QUANTUM WELLSAT LOW TEMPERATURES
PACS 68.35.Ja, 78.55.Cr,78.67.De
Characteristics of GaAs/In x Ga − x As/GaAs heterostructures with a single quantum well,which were obtained at various growth parameters, are evaluated according to the results ofmeasurements of low-temperature photoluminescence (PL) spectra and their corresponding the-oretical analysis. The experimentally obtained temperature dependences of the energy positionof the PL band maximum, hν max , band half-width, W , and intensity, I , are examined. Thevalues of energy of local phonons, E ph , exciton binding energy, E ex , and the Huang–Rhys fac-tor, N , are determined. A comparison between the values obtained for those quantities andthe growth parameters of considered specimens allowed us to assert that the highest-qualityspecimens are those that are characterized by low N values and one-mode phonon spectra.K e y w o r d s: photoluminescence, quantum well, exciton, phonon
1. Introduction In x Ga − x As–GaAs heterostructures are widely usedin modern optoelectronics as structures that are ca-pable of being adapted for the convenient reception,transmission, and transformation of radiation in var-ious spectral ranges. Special attention is attractedto heterostructures with quantized layers owing totheir enhanced sensitivity and a possibility to ad-ditionally vary the optical spectrum [1–7]. The en-ergy of an emitted quantum in such heterostruc-tures is governed by the distance between the size-quantization levels of electrons and holes, E e - hh ,which, in turn, depend on the quantum well (QW)width d and the composition of a substitutionalsolid solution ( x is the indium content). For in-stance, for the typical values x = 0 . and d == 80 ˚A , the changes of x by 1% and the well widthby the width of a monolayer (approximately 3 ˚A)give rise to the variations by 9 and 4 meV, respec-tively, in the transition energy [4]. Such a highsensitivity to the parameters imposes strict require-ments on both the width and the element composi-tion of QW.Moreover, a shortcoming of those heterostructuresconsists in a considerable mismatch between the lat-tice constants in the epitaxial layer and the substrate, c (cid:13) N.M. LITOVCHENKO, D.V. KORBUTYAK,O.M. STRILCHUK, 2013 which results in the emergence of substantial mechan-ical stresses and the generation of numerous disloca-tions. Buffer layers or the formation of quaternary al-loys with the phosphorus additive usually reduce theinfluence of those undesirable factors, but not com-pletely. Therefore, there arises the requirement in anon-destructive quantitative control over the defor-mation and defect factors.In this report, we pay attention to a possibility ofusing the interaction between phonons and excitedelectrons (the Huang–Rhys factor N ) for the charac-terization of the imperfection degree. This param-eter is determined on the basis of the temperaturebehavior experimentally found for the exciton photo-luminescence band half-widths and subjected to thecorresponding theoretical analysis.
2. Experimental Specimens and Technique
Low-temperature (5–200 K ) photoluminescence (PL)researches are carried out with the use ofheterostructures with a single quantum well,GaAs/In x Ga − x As/GaAs. The specimens weregrown up following the MOCVD technology. Theywere characterized by various contents of indium, var-ious widths of In x Ga − x As quantum wells, and var-ious thicknesses of protective GaAs layers (Table 1).Luminescence was excited by a He–Ne laser (a quan-tum energy of 1.96 eV, and the radiation intensity L = (3 × ÷ ) quantum/(cm · s)). To analyze ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 xcitonic Parameters of In x Ga − x As–GaAs Heterostructures
Table 1
Specimen x In d , ˚A cap, ˚A T = 5 E a , meV E a , meV hν max , eV W , meV I max , rel. unitsNo. 1 0.16 84 220 1.3568 7.4 1093 4.5 52No. 2 0.21 88 230 1.33 9.9 582 2.8 55No. 3-1 0.20 92 600 1.355 7.3 4876 5 70No. 3-2 0.20 92 600 1.3721 10.9 949 2.5 46No. 4-1 0.35 73 600 1.253 15.2 302 2.5 85No. 4-2 0.35 73 600 1.396 13.2 988 2.5 60N o t a t i o n: x is the relative content of indium, d is the quantum well width, cap is the thickness of the protective GaAs la-yer, hν max is the maximum position in the PL spectrum, W is the line half-width, I is the PL intensity, E a and E a are theactivation energies. the PL spectra, we used an MDR-23 monochromatorwith the spectral resolution not worse than 0.2 meV.The signal was registered with the use of a cooledFEP-62 photoelectronic multiplier.
3. Experimental Part
In the photoluminescence spectra of researched spec-imens, we observed the intensive bands, which cor-respond to the exciton recombination e1-hh1 in thequantum well in the interval T = (5 ÷
40) K andto the recombination of free charge carriers in thequantum well in the interval T = (50 ÷ .This fact is confirmed by the dependences of the ra-diation intensity on the excitation one, I ( L ) . Themain growth parameters of studied specimens and thecorresponding photoluminescence bands are quotedin Table 1.In Fig. 1, a , the normalized PL spectra of the spec-imens under investigation obtained at T = 5 K aredepicted. Attention should be paid to some spec-tral features. First of all, it is the spread in the en-ergy positions of PL bands, which stems from dif-ferent values of quantum well widths d and indiumcontents x in the In x Ga − x As quantum well. How-ever, even provided that the corresponding valuesof d and x are identical, the energy positions ofPL bands can differ substantially. For instance, forspecimens 4-1 and 4-2 with the identical x = 0 . and d = 73 ˚A, the energy positions of PL max-ima are different (see Table 1); namely, hν max =1 .
396 eV for specimen 4-2 and 1.253 eV for speci-men 4-1. In our opinion, the origin of such a dis- crepancy consists in fluctuations of the In concen-tration in the QWs of specimens 4-1 and 4-2. Re-ally, if the energy difference between the radiationmaxima, ∆ hν max = 0 .
143 eV , was caused by the dif-ference between the quantum well widths, the latterwould be amount to about
107 ˚A (this value can beobtained with regard for the fact mentioned abovethat a change of the QW width by about 3 ˚A givesrise to a variation of about 4 meV in the transi-tion energy), but such a value is unreal. This rea-soning agrees with the results of work [4], where itwas noticed that a variation in the spectral positionsof exciton peaks for the In x Ga − x As quantum wellis mainly associated with the variations in the Inconcentration x .Different half-widths W (Table 1) and shapes ofexamined PL spectra exhibited in Fig. 1, a composeanother feature of those spectra. The PL band half-width depends on both the degree of exciton lo-calization in the QW and the character of excitonscattering by phonons, defects, inhomogeneities atheterointerfaces, and so forth. The radiation emis-sion spectra of some specimens demonstrate a char-acteristic tail of the PL band in the low-energyinterval, which may be caused by the participa-tion of phonons in the radiative recombination ofexcitons in the QW. As an example, we decom-posed the PL band of specimen 3-2 into two compo-nents: the zero-phonon one and the phonon replica(Fig. 1, b ), with the use of the procedure proposedin work [8]. In so doing, we used an approxima-tion that phonons of only one type participate inPL. This approach enabled us to obtain the value ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 .M. Litovchenko, D.V. Korbutyak, O.M. Strilchuk ab Fig. 1.
PL spectra of the studied GaAs/In x Ga − x As/GAsquantum heterostructures ( a ). Decomposition of PL band 3in panel a in two components ( b ): the zero-phonon one andthe phonon replica. E max = 1 . eV, E ph = 9 . meV, theHuang–Rhys factor N = 0 . E ph = 9 . for the energy of interacting localphonons and N = 0 . for the Huang–Rhys factor,which characterizes the strength of exciton–phononinteraction.As to the half-width of PL bands (Table 1), itchanges from 7.4 meV for specimen 3-1 to 15.2 meVfor specimen 4-1. In our case, the Bohr radius ofan exciton in the QW is comparable with the QWwidth. Therefore, with a high probability, the exci-ton is localized at inhomogeneities of heterointerfaces.The smaller width of the PL band corresponds to alarger localization degree, as it takes place for PL bybound excitons in a bulk semiconductor. The temper- ature dependences of the PL intensity typical of thespecimens under consideration are shown in Fig. 2.At low temperatures ( T = 5 ÷
40 K ), the PL inten-sity varies weakly. As the temperature grows, thePL intensity decreases for specimens 1 and 2 and, forspecimens 3 and 4, first slightly increases and thenfalls down, which is connected with the temperature-induced ejection of charge carriers from the quantumwell into the barrier.In Fig. 3, the temperature dependences of the ra-diation maximum position typical of examined spec-imens are depicted. The dashed curve demonstratesthe results of calculation obtained in the frame-work of the Varshni model. For all specimens, thetemperature dependences of the PL maximum po-sition have an S-like form. At low temperatures,a considerable deviation of the calculated valuesfrom experimental ones is observed: first, the po-sition of the PL maximum shifts toward low en-ergies (red shift); then, up to a certain tempera-ture, the maximum shifts backward toward high en-ergies. At
T > (60 ÷
89) K , the maximum posi-tion shifts toward low energies in accordance with theVarshni model.In Fig. 4, the typical dependences of the PLband half-width on the temperature are shown. Forspecimens 1 and 2, a monotonous increase of thehalf-width with the temperature (the dependence oftype I) is observed. Specimens 4 are characterized bya sharp initial (to a temperature of 40–80 K ) growthof the half-width, then by an insignificant reductionof this parameter followed by its subsequent growth,as the temperature grows further (the dependence oftype II). For specimens 3, the dependences of bothtypes are observed.
4. Discussion of Experimental Results
The temperature dependences of the PL intensity ob-tained for specimens 2 and 4-2 (Fig. 2) were analyzedwith the use of the Arrhenius formula I ( T ) = C/ [1+ a exp( − E a /kT )+ a exp( − E a /kT )] . This enabled us to determine two temperature inter-vals with different slopes: low- and high-temperatureones with the activation energies E a and E a , re-spectively (Table 1). In the low-temperature inter-val, E a = (2 . ÷
5) meV . Such a small value of E a ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 xcitonic Parameters of In x Ga − x As–GaAs Heterostructures testifies that this quantity corresponds to the delocal-ization energy of excitons bound at inhomogeneitiesof heterointerfaces in the QW at low temperatures.It is significant that the higher the delocalization en-ergy (and, accordingly, the deeper is the potentialwell, which is associated with the corrugation of het-erointerfaces), the narrower is the PL band, whichcorresponds to a more localized state of excitons (see,e.g., the PL bands for specimens 1 and 3-1). At tem-peratures
T > K, the activation energy for thetemperature-induced quenching of the PL band owingto the e1-hh1 transitions equals E a = (50 ÷
85) meV ,and, as was indicated above, this is connected withthe temperature-induced ejection of charge carriersinto the barrier.The temperature dependences of the PL maximumdepicted in Fig. 3 and their comparison with theresults of calculations following the Varshni formulaallow the binding energy of excitons in the QW tobe evaluated. As one can see from Fig. 3, theenergy of a quantum emitted at low temperatures( T = (5 ÷
40) K ) is lower than the energy of inter-band transitions calculated by the Varshni formula.The corresponding difference E ex ≈
10 meV is justthe binding energy of excitons in the QW to withinthe accuracy of the energy of exciton localization atheterointerfaces.The theoretical analysis of the temperature depen-dences obtained for the scattering parameter (the PLband half-width W ) is based on the fact that thisquantity comprises the probability of the momentumscattering as a result of several independent processes(by impurities, phonons, and others), W ∼ ~ τ t , τ t ∼ W t ( T ) + W ph . opt ( T ) + W ph . local ( T ) + ... , (1)where τ t is the lifetime of nonequilibrium charge car-riers. The temperature dependences of the scatter-ing probability are different for different mechanisms.Hence, the temperature dependence can be used todistinguish between their contributions. In particu-lar, the Coulomb scattering by local centers dependson T , which is the most pronounced at low enoughtemperatures. At the same time, the role of thephonon mechanism grows with T [9, 10], according Fig. 2.
Temperature dependences of the PL intensity: sym-bols demonstrate experimental results, dashed curves corre-spond to the approximation by the Arrhenius formula
Fig. 3.
Temperature dependences of the photoluminescencemaximum position, hv m : symbols demonstrate the experimen-tal results, dashed curves show the results of calculations bythe Varshni formula to the law W = Σ W oi (cid:18) cth ~ ω ph kT (cid:19) / ,W oi = 2(2 ln 2) / N − / ~ ω phi ∼ N − / , (2)where E ph = hω ph is the energy of a phonon local-ized at a radiative-recombination center, and N ph isthe phonon emission probability at the recombination(the Huang–Rhys factor). In the case N < , the lat-ter is given by the following relation: N ∼
58 ( E ex /E ph ) ( ε /ε ∞ − ∼ ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 .M. Litovchenko, D.V. Korbutyak, O.M. Strilchuk
Fig. 4.
Dependences of the photoluminescence band half-width W on the temperature ∼ e /E ph a B (cid:18) ε ∞ − ε (cid:19) , (3)where E ex is the exciton binding energy, a B the Bohrradius of an exciton, and ε and ε ∞ are the staticand high-frequency dielectric permittivities, respec-tively. From this formula and knowing the phononenergy E ph , it is easy to find the binding energy ofan exciton [11], E ex ≈ N E ph ε ∞ ε − ε ∞ . (4)Hence, the temperature dependence W ( T ) allowsa number of parameters that characterize the het-erostructure state – such as W , E ph , and N [12] – tobe obtained, as well as the Stokes shift, ∆ ω st = 2 N ph ~ ω ph . It also enables one to evaluate the position of thephonon-free line by the formula ~ ω = ~ ω max + n ~ ω ph ,where n is the number of phonon replica. Table 2
Specimen E ph , meV N E ex , meV a B , ˚ANo. 1 8 0.15 9.1 122No. 2 6.5 0.42 20.8 54No. 3-1 11 0.08 6.7 168No. 3-2 8 0.27 16.5 812 0.149 13.6 82No. 4-1 3.2 3.1 78.7 1418 0.13 19.0 58.8No. 4-2 3.5 3.4 95.4 1219 0.22 33.5 33 Special attention should be paid to the quantity W . Its magnitude is reciprocal to the charge carriermobility and is predicted to be much less for a per-fect quantum well than that for the correspondingbulk material. However, mechanical stresses and de-fects can compensate this useful effect. The proposedanalysis allows the contributions of different mecha-nisms to be estimated separately.The features in the temperature dependences ofthe PL intensity, maximum position, and half-widthobtained in this work can be explained by the pres-ence of localized (defect) states in the studied spec-imens [6, 7], which are induced by fluctuations ofQW dimensions, and/or by a variation of the QWcomposition. At low temperatures, photo-inducedcharge carriers (excitons) are captured by the lo-calized potential. As the temperature is elevatedto a value that corresponds to the localization en-ergy maximum, a shift of the PL maximum posi-tion toward lower energies (the red shift) is observed,because excitons obtain a sufficient thermal energyto overcome the potential barrier and become rela-tively free. Some of those excitons relax into lowerstates, which capture them, and recombine there.In this temperature interval, we observe a drasticincrease in the half-width W of the PL band, inaccordance with the growth in the population ofstates owing to the capture of released charge car-riers onto them. As the temperature grows further,the PL maximum shifts into the range of high ener-gies, and the band half-width becomes somewhat nar-rower due to the thermally equilibrium distributionof excitons. This occurs until the temperature cor-responding to the complete delocalization of chargecarriers is attained. At higher temperatures, the e1-hh1 transitions dominate in the PL spectrum, and,according to the Varshni formula, the maximum po-sition changes with the temperature as the energygap width.With the use of Eqs. (2)–(4) and the experimen-tally obtained temperature dependences for the PLband half-width, we determined the parameters E ph , N , E ex , and the Bohr exciton radius a B (see Ta-ble 2). Let us consider this dependence of type I(it is inherent to specimens 1, 2, and 3-1). It hasa monotonous character and can be described wellby Eq. (2), in which the scattering processes withphonons of energies 6 to 11 meV are taken into con-sideration (Fig. 5, a ). ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 xcitonic Parameters of In x Ga − x As–GaAs Heterostructures
For structures 4, the character of the band half-width dependence on the temperature is of the othertype (type II). For those specimens, we determinedtwo values for the energy of local phonons (Fig. 5):(i) in the interval from 5 to 20 K , where a dras-tic increase of the band half-width is observed, theenergy of phonons is 3.5–4 meV;(ii) in the interval from 30 to 200 K , an insignif-icant narrowing of the PL band is observed, whichis followed by the increase of its half-width withthe temperature; here, the energy of phonons equals18–19 meV.Structures 3 revealed the dependences of bothtypes. Specimen 3-1 demonstrated the dependenceof monotonous type I, and the corresponding energyof phonons was 11 meV (Fig. 5, c , curve ). Specimen3-2 was characterized by the dependence of type II:the energy of phonons was 8 meV in the interval 5–60 K and 12 meV in the interval 60–200 K (Fig. 5, c ,curve ).The magnitudes of exciton binding energy ob-tained with the help of Eq. (4) for various speci-mens ( E ex > . ) considerably exceed the cor-responding energy for bulk excitons in In x Ga − x As( E ex ≈ ) [1], which testifies to thequantization of excitons in the In x Ga − x As–GaAsquantum well.Let us compare the values of E ph obtained from thetemperature dependences of the line width with thetheoretical relations (1)–(4) (see Table 2). For ev-ery specimen, it turned out several times less thanthe characteristic values for bulk or surface (con-finement) phonons. An evident reason is the factthat the studied specimens with heterojunctions hadrather a large number of defects, probably local-ized at interfaces. It is known that one of themechanisms of defect emergence in InGaAs struc-tures consists in the segregation of clusters of theIn phase if the optimum epitaxy and temperatureregimes were not followed at the stage of heterostruc-ture formation [3]. Hence, the typical defects haveto include precipitates of the redundant element,i.e. indium.Now let us estimate the energy of local phononsthat correspond to vibrations in vicinities of de-fects at the interfaces between InGaAs and Inprecipitates. It is known that the maximum fre-quency of harmonic vibrations is determined by the abc Fig. 5.
Temperature dependences of the PL band half-width, W ( T . ) for ( a ) specimens 1 and 2, ( b ) specimen 4, and ( c )specimens 3-1 and 3-2. Symbols demonstrate experimental re-sults, and dashed curves correspond to their approximation byformula (2) ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 3 .M. Litovchenko, D.V. Korbutyak, O.M. Strilchuk relation [13] ω ph = 2 πd (cid:18) E m ρ (cid:19) / = 2 d v, (5)where E m is Young’s modulus, v is the thermal ve-locity, ρ = m/V i is the substance density, m isthe atomic (molecular) mass, and V i is the atomic(molecular) volume. In vicinities of defect centers, E m becomes several times smaller, and ρ increasesas the ratio between the densities of defect com-ponents. The lattice constant d increases as theratio between the atomic sizes r of film compo-nents, r ( GaAs) /r ( InGaAs). Hence, according to theestimations made for the InGaAs heterostructure, ( d V /d D ) ∼ / and ρ v /ρ D ∼ m V /m D ∼ (30 / .Whence, ω D ω V = (cid:18) d V d D (cid:19) (cid:18) E D E V S V S D (cid:19) / = 12 (cid:18) · (cid:19) / ∼ . (6)Therefore, we may expect that the energy of localphonons in InGaAs is several times lower than thatin the bulk, i.e. E ph ∼ E ph V ∼ ÷
10 meV .When comparing the values obtained for E ph , E ex ,and N with the growth parameters of specimens,we may assert that the specimens with small val-ues of N have the highest quality, i.e. the specimenswith the highest mobility and the one-mode phononspectrum.
5. Conclusions
Heterostructures GaAs/In x Ga − x As/GaAs that havea single quantum well and are characterized by vari-ous growth parameters were studied with the use ofthe method of low-temperature photoluminescence.The following facts were revealed.(i) The photoluminescence spectra of examinedspecimens demonstrate intense radiation bands.These bands are induced by the recombination ofexcitons in the quantum well in a temperature in-terval of 5–40 K and by the recombination of freecharge carriers in the quantum well in the interval T = 50 ÷
200 K .(ii) For all specimens, the temperature dependenceof the photoluminescence intensity maximum posi-tion has an S-like shape. In the low-temperatureinterval, the values calculated within the Varshni model considerably deviate from the experimen-tal data.(iii) The researched specimens revealed bothmonotonous and nonmonotonous dependences ofthe photoluminescence band half-width on thetemperature.The features observed in the temperature depen-dences of the maximum position and the half-widthof the PL band testify that all examined speci-mens contain defect states, in one quantity or an-other, induced by fluctuations in the QW composi-tion; in particular, the inhomogeneities may occurowing to the segregation of In-phase clusters (in theform of 3D islands). The values of E ph determinedfrom the temperature dependences of the PL bandwidth turned out several times lower than the cor-responding characteristic values for bulk and surfacephonons for all studied specimens. Specimens witha high intensity of radiation emission and a nar-row radiation band were found to be characterizedby a small value of the Huang–Rhys factor and aone-mode phonon spectrum. Local phonons of twotypes – with energies of 3.5–4 and 18–19 meV, re-spectively – take part in the process of exciton scat-tering in specimens with low intensities of radiationand wide radiation bands (i.e. with a worse structuralquality). The authors express their sincere gratitude toCorresponding Member of the NAS of UkraineV.G. Litovchenko for the discussion of the results ofthis work and useful advices.
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Received 12.12.12.Translated from Ukrainian by O.I. Voitenko
Н.М. Литовченко, Д.В. Корбутяк, О.М. Стрiльчук