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Spin-flip Raman scattering studies of II–VI heterostructures
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Spin-#ip Raman scattering studies of II}VI heterostructures J.J. Davies*, D. Wolverson, O.Z. Karimov, I.J. Gri$n Department of Physics, University of Bath, Bath BA2 7AY, UK
Abstract Spin-#ip Raman (SFR) scattering is now an established technique for the investigation of semiconductor heterostructures. Because the scattering is resonantly enhanced when the laser is adjusted to coincide with the appropriate excitonic transition, the technique has high sensitivity. It is also highly selective, since the resonance enhancement occurs at di!erent wavelengths for scattering by carriers con"ned under di!erent circumstances. For electrons, the SFR spectra enable the g-factor to be determined, thus providing tests of band structure theories. The g-factor is sensitive also to quantum con"nement, when it may become anisotropic. In the case of holes, the higher angular momentum (J") makes the SFR spectra highly dependent on the state of strain of the material. Spin-#ip signals from localised excitons can also be detected. Such signals enable the electron}hole exchange interactions to be determined and are thus a sensitive probe of the localisation properties of the exciton, for example in quantum dots of di!ering sizes. Recent developments will be reviewed to illustrate how the technique can be used to investigate the physics and materials issues associated with II}VI structures. 2000 Elsevier Science B.V. All rights reserved. PACS: 71.55.Gs; 78.30.Fs; 78.55.Et; 78.66.Hf Keywords: Spin-#ip; II}VI; Raman; g-Values; Exciton localisation
1. Introduction In its most usual form, Raman spectroscopy is associated with the creation or destruction of vibrational excitations when a laser beam is inelastically scattered by the medium under study. As such, the technique is very commonly used for the investigation of molecular structures and, in the context of semiconductor science, for studies of phonon behaviour. In general, however, Raman scattering can be caused by several other types of excitation, most
* Corresponding author. Tel.: #44-1225-323-324; fax: #441225-826-110. E-mail address: [email protected] (J.J. Davies).
notably those which involve changes in the energy states of charge carriers. Amongst such scattering processes, those which take place in the presence of a magnetic "eld have recently become the subject of increasing attention. Since such scattering results in a change in the spin orientation of the electron or hole, it has become known as spin-#ip Raman (SFR) scattering. The purpose of this paper is to demonstrate that SFR spectroscopy is a very powerful technique for the investigation of semiconductors in general and for epitaxial II}VI materials in particular. We shall show that the information provided is very similar to and complements that obtained from magnetic resonance studies. However, the sensitivity is much higher, which makes the approach particularly suitable for
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investigations of specimens in which the region of interest is very small, for example, thin epitaxial layers and quantum wells. Although SFR is a somewhat specialised technique, the discussion will be directed towards those which are concerned with the properties of II}VI semiconductors in general. We shall restrict attention to non-magnetic II}VI materials since the application of the technique to dilute magnetic semiconductors based on II}VI and related compounds has been discussed thoroughly elsewhere ([1]; see also Ref. [2]).
2. Basic concepts SFR is not a new technique: such experiments were carried out for InSb in 1967 [3] whilst, for II}VI compounds, a series of elegant experiments on CdS was reported by Thomas and Hop"eld in 1968 [4]. The basic concept is indicated in Fig. 1,
Fig. 1. Energy level scheme to illustrate SFR scattering by an electron bound at a neutral donor. The small arrows indicate the magnetic moments of the electron and the separation between the two spin states is given by g k B. The excited level X corresponds to one of the spin states of an exciton bound at the neutral donor. If the incoming photon energy corresponds to the transition shown, the scattering intensity is dramatically enhanced.
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which shows the two energy levels (one for each spin direction) in the presence of a magnetic "eld B for the case of an electron bound at a neutral donor. Before the incident photon is scattered, the electron is imagined to be in the lower state. After scattering, the electron is left in the upper state, that is, its spin has been reversed. Clearly, in this simple case, the change in photon energy is given by the Zeeman splitting g k B, where g is the gyromag netic ratio of the electron and k is the Bohr magneton. The process considered, in which the photon has lost energy, is called Stokes (S) scattering; if an electron is already in the upper spin state and, after scattering, is then in the lower state, the photon gains energy and the process is called anti-Stokes (AS) scattering. An SFR spectrum thus appears as in Fig. 2, the ratio of the S and AS lines being determined in part by the occupancy of the spin states and therefore by the temperature. A point of crucial importance is that the crosssection for scattering is a very strong function of the
Fig. 2. SFR spectrum from a fractional monolayer of CdSe in ZnSe (grown by MBE by S.V. Ivanov of the Io!e Institute). The Stokes and anti-Stokes spin-#ip Raman lines lie respectively at negative and positive energy shifts relative to the original laser light (2.7367 eV). The lines marked electron correspond to SFR scattering by electrons (see Section 2) whilst those marked exciton are caused by the so-called dark excitons (Section 5 [41,42]). The Raman shifts depend on the magnetic "eld as shown later in Fig. 6. The broad background is due to photoluminescence.
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Fig. 3. Schematic arrangement for resonance SFR experiments. Observation of the scattering may be with the "eld along the growth axis (Faraday con"guration) or perpendicular to it (Voigt con"guration). To reduce problems caused by stray light, the re#ected (elastic) component of the laser beam is directed back out of the cryostat.
resonance with the correct spin state of the exciton (as a result, the resonance wavelengths for Stokes and anti-Stokes signals di!er, so that the ratio of the S and AS intensities di!ers from that predicted from the temperature alone). It should be noted that the requirement that the incoming photon be in resonance also results in the outgoing photon being in resonance, so that SFR scattering is a doubly resonant process: it is for this reason that the scattering can be very strong. In the following sections, the essential features of the experimental arrangement will be described. SFR experiments on electrons will then be discussed in greater detail. SFR spectroscopy can also be applied to the study of hole states. Because holes have an angular momentum of , their magnetic behaviour is more complicated than that of electrons: in particular, the SFR spectra can be strongly anisotropic with respect to the direction of the magnetic "eld and this anisotropy can be used to investigate strains in the material, for example, the strains that commonly exist in heterostructures. Such experiments will be described separately, followed by examples of a phonon-assisted scattering process that makes it possible to study excitonic states. Finally, we shall compare the results obtained from SFR spectroscopy with those obtained by other magneto-optical techniques.
3. Experimental requirements photon energy. The scattering intensity is hugely increased, sometimes by several orders of magnitude, when the incoming photon energy coincides with the energy required to create an exciton bound to the centre under study. Such &resonance' behaviour has been discussed by Yafet [5] and plays a vital part in SFR studies. Thus, for the case of electrons bound at neutral donors, the laser should be in resonance with the donor-bound exciton transition (sometimes called D X or I ). In the cases of bulk CdS [4] and bulk ZnSe [6], lines from an argon ion laser are fortuitously suitable, but in general a tunable laser is needed, since, for optimum enhancement, the laser photon energy has often to be adjusted to within 1 meV. The requirement is stringent, since certain selection rules must be obeyed (see later) and the laser has to be in
The basic experimental arrangement is shown in Fig. 3. Epitaxial specimens are studied in the backscattering geometry, as indicated, most experiments being carried out at low temperatures (for example, to prevent the centres under study from being ionised). In comparison with phonon Raman scattering, the Raman shifts in spin-#ip experiments are small, often being less than 1 meV, so that a specialised spectrometer with good stray light rejection close to the laser line is required. In our laboratory we use a triple spectrometer with a 1 m "nal dispersing stage, with either a charge-coupled detector (CCD) array or a photon counting system. Clearly, the magnetic "eld should be as strong as possible since in most cases this maximises the Raman shift.
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Of crucial importance is the ability to tune the laser wavelength, since maximisation of the resonance enhancement often requires an accuracy of better than 1 meV: for this purpose dye or Ti}sapphire lasers are convenient, since they readily provide the necessary powers (tens of mW). In a spin-#ip scattering experiment the electrons undergo a change in spin of one, leading to the selection rule that the incident and scattered light be p and n polarised respectively (or vice versa). For holes, with their greater angular momentum and the possibility of mixing between heavy- and lighthole states, the selection rules are more complicated [7]. These rules dictate whether the direction of observation should be along the direction of the magnetic "eld (Faraday geometry) or perpendicular to it (Voigt geometry). Since the Raman shifts often depend on the direction of the magnetic "eld relative to the crystal axes, mechanisms for adjusting the specimen orientation are essential.
4. Electron SFR in epitaxial II}VI materials It will be clear that SFR experiments enable direct measurement of the g-value of electrons. For electrons bound in conduction band related states, the signi"cance of this is that g (which can di!er even in sign from the free-electron value) is a very sensitive to the forms of the conduction band and valence bands, in ways that are very similar to those of e!ective masses. Determinations of g can therefore be used to test band structure theories. The g-value is also strongly a!ected by quantum con"nement and its determination can thus lead to improved understanding of quantum wells and quantum dots. Further, if the electron is trapped at deep centres, the g-value departs from the conduction band value, providing tests of theories for localised centres. Excellent accounts of electron SFR in bulk specimens of CdS, ZnSe and ZnTe can be found in Refs. [4,6,7]. For II}VI materials in epitaxial form, the research is much more recent and has concentrated mainly on ZnSe [8,9] and its alloys and on CdTe [10] and related materials. In simple epitaxial layers, the g-values for electrons bound at shallow donors are essentially those that are observed for
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bulk material [11,12] and are found not to be sensitive to strain. The k . p theories that describe these g-values are now well developed and produce good agreement with observation [13}16]. An important aspect of SFR experiments is that they work very well not only in binary materials but also in ternary and quaternary systems such as ZnSSe, ZnCdSe, ZnMgSe and ZnMgSSe [17,18], since the SFR linewidths remain narrow despite the alloying. Analysis of g-value behaviour in such alloys has recently been published [17,18]. Such information also forms an essential precursor to studies of systems in which quantum con"nement becomes important, since in such structures one or more of the component materials is often a ternary or quaternary alloy. It has been noted already that when the depth of the centre that traps the electron becomes large, the g-value is expected to depart from the conduction band value (1.12 for ZnSe [11,12]). A striking example of this is found in p-type ZnSe doped with nitrogen, for which it is now well known that for nitrogen concentrations in excess of about 10 cm\ a compensation process sets in, due at least in part to the formation of deep donor centres [19}22]. These deep (50 meV) donors were found in optically detected magnetic resonance (ODMR) experiments [23] to have a g-value of 1.38, a value later con"rmed by SFR [9]. Later experiments [24, 25] have shown that this g-value remains constant when ZnSe is alloyed with up to at least 10% of ZnS, in contrast to the g-value of electrons trapped at shallow donors, which increases by 0.11 over this range. SFR can also be used to investigate the relative concentration of shallow donors, deep donors and acceptors (see Section 5) as functions of post-growth sample treatment [26]. All these experiments are consistent with the popular model [20, 27] for this centre of a substitutional nitrogen atom paired with a selenium vacancy, particularly since the insensitivity of the g-value to the sulphur/selenium ratio suggests strongly that the electron wave function is well localised. However, there still remains the problem of accounting for the large shift (0.62) of the g-factor from the spin-only value, since for a strongly localised centre the orbital contribution should be quenched [25]. The modelling of the g-value of the deep donor centre and
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in ZnMgSSe barriers [28]. In both cases the results con"rm the validity of the k . p theories used to describe electron g-values in these semiconductors. An example of the dependence of the electron gvalue on well width is shown in Fig. 4. A similar study for the III}V system GaAs/AlAs is given in Ref. [29].
5. Hole SFR in epitaxial II}VI materials
Fig. 4. Behaviour of the average g-value for electrons as a function of well width for a ZnSe quantum well with ZnMgSSe barriers (produced by MBE at the University of Bremen). As the well width decreases and the penetration of the wave function into the barrier increases, the g-value changes from the ZnSe value of 1.12 to the barrier value. The g-tensor also becomes anisotropic (see text).
the unambiguous identi"cation of the centre's structure therefore present a continuing theoretical challenge. The sensitivity of resonance SFR is also su$ciently great for electrons to be studied under conditions of quantum con"nement. In quantum wells, the g-value of the con"ned carriers changes because the wave functions extend beyond the well into the barrier material and also because the e!ective band gap is changed, so that the interband mixing that produces the g-shifts is altered. In addition, the strain- and con"nement-induced splitting between the light-hole and heavy-hole states produces a measurable anisotropy in the electron g-value, so that the SFR shifts *E are given by an equation of the form *E"(g cos h#g sin h ) k B, (1) , , where h is the angle between the magnetic "eld and the normal to the plane of the well. Such behaviour has been studied for CdTe quantum wells in CdMgTe barriers by Sirenko et al. [10], and has recently also been studied for ZnSe quantum wells
When the laser is adjusted to be in resonance with excitons bound at neutral acceptors, the SFR signals observed are those due to holes bound at the acceptors. For bulk II}VI materials, hole SFR has been reported for ZnTe, which is easily obtained in p-type form. In contrast, it is only comparatively recently that it has been possible to obtain p-type ZnSe and the epitaxial form of the specimens has inevitably led to the spectra being strongly a!ected by strain. For thick layers of ZnSe grown on GaAs, the ZnSe is relaxed: however, because of the di!erence in the thermal expansivities of the epitaxial layer and the substrate, the ZnSe is under biaxial tensile strain at low temperatures and it is the light-hole states that are occupied. For thin, pseudomorphic layers, the strain is of the opposite sign because of the di!erence in lattice constants and it is then the heavy-hole states that are occupied. The SFR processes for the two cases are shown in Fig. 5. As a result of the strain e!ects, the SFR shifts for holes have a more complicated behaviour than those for electrons. To a "rst approximation, the shifts for heavy holes are of the form of Eq. (1) with g "3g and g "0 (leading to *E" , , 3g k B cos h). For light holes, Eq. (1) also applies, but with g "g and g "2g . SFR lines from , , heavy holes thus lie at 3g k B when the "eld is along the growth axis and move towards zero as the "eld direction approaches the layer plane; in contrast light-hole signals start at g k B and move to the greater value of 2g k B. The two types of hole signal can therefore readily be distinguished (see e.g. Fig. 3 of Ref. [30]). Examples of SFR spectra for holes bound at nitrogen acceptors in ZnSe layers of di!erent thicknesses and thus of di!erent states of strain (both
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6. Spin-6ip signals involving changes in excitonic spin states
Fig. 5. Energy level scheme to illustrate SFR scattering by a hole bound at a neutral acceptor in an epitaxial layer for a magnetic "eld directed along the growth axis. Two cases are shown, corresponding to compressive and tensile biaxial strains, leading to scattering by heavy and light holes, respectively. When the magnetic "eld is in the layer plane, the heavy-hole splitting becomes very small, whilst the light-hole splitting doubles (see text). In this diagram, the excited level now corresponds to one of the spin states of an exciton bound at the neutral acceptor. The resonance enhancement thus occurs at a laser energy that is di!erent from that in Fig. 1, so that scattering by holes can be studied separately from that due to electrons.
compressive and tensile) have been described in detail [30}32], together with cases in which the strain is very small and the heavy- and light-hole states are mixed by the magnetic "eld [33]. As discussed in Ref. [33], the SFR shifts are very sensitive to strain splittings that are comparable with the Zeeman energies. SFR is therefore a very useful method of studying such splittings in a range which lies much below that which is measurable by other techniques. In practice, there also exist higher-order terms in the spin Hamiltonian (for example linear in "eld but cubic in the angular momentum operator J) which must also be taken into account [33]. The calculation of these terms and of the hole g-values themselves present strong challenges for band structure theories.
In SFR experiments involving electrons bound at neutral donors or holes bound at neutral acceptors, the Raman process is straightforward to envisage. In the Stokes process, the energy lost by the photon on scattering is gained by the electron or hole that undergoes the change in spin. Such processes are described in terms of diagrams such as Figs. 1 and 4 and the spin-#ip energy is simply that of the carrier concerned. The scattering intensity is enhanced when the laser is in resonance with the exciton bound at the neutral donor or neutral acceptor. In contrast, it has been known for some time that it is possible to obtain strong SFR scattering when the laser is in resonance with the transition energies of free excitons or of excitons localised not at dopants but at potential #uctuations caused, for example, by alloy disorder. In such cases, the spin #ip occurs in the optically excited state (i.e. in the excitonic state): the incoming photon creates the exciton, which undergoes a change in angular momentum through the intervention of an acoustic phonon, followed by emission of a photon of lower energy [34,35]. Through such processes it is possible to observe spin-#ip signals for excitonic states (see also Ref. [36], where signals from &dark excitons' localised in a ZnSe/ZnCdSe quantum-well system are reported). The interest in such signals arises from the fact that in the excitonic state there exists an exchange interaction between the electron and the hole. The SFR experiments now enable this exchange interaction to be measured. In III}V systems, SFR has been used to study quantum dots formed by Stranski}Krastanov growth in InAs/GaAs [37] and InP/InGaP [38] and, for II}VI compounds, in the CdS/glass system [39]. In II}VI systems, the exchange parameter is typically of order 0.1}1 meV but can be greatly enhanced under conditions of quantum con"nement [40] or when the excitons are localised. A particularly intriguing example (Figs. 2 and 6) of such measurements is encountered in the study of CdSe fractional monolayers in ZnSe matrix [41,42]. Here, small ZnCdSe &islands' of
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7. Contrast with other experimental methods It is useful to compare the sensitivity and spectral resolution obtained by resonance SFR with that of other magnetic and magneto-optical techniques. 7.1. Electron spin resonance (ESR)
Fig. 6. Dependence on magnetic "eld of the signals shown in Fig. 2. The electron SFR shift is proportional to the "eld, as expected from Section 2 and does not depend on the direction of the "eld. The exciton signal varies non-linearly as a consequence of the electron}hole spin exchange interaction, which determines the intercept at zero "eld. Two examples of exciton signals are shown, for two di!erent laser energies. Altering the laser energy brings into resonance excitons that are localised in di!erent environments, so that the exchange interaction changes, as shown.
We have seen that SFR provides information on the magnetic parameters of electrons and holes bound at donors and acceptors. This information is similar to that which, in principle, could be provided by ESR experiments, in which the spectral resolution would be very much better. However, the sensitivities of ESR spectrometers are typically of the order of 10}10 spins for a linewidth of 1 mT. For example, for a specimen of area 0.1 cm and thickness 10\ cm, ESR would be expected to be able under favourable circumstances to detect magnetic centres present at a concentration of 10}10 cm\. In contrast, resonance SFR can detect 10 cm\ (and in specimens of area 10\ cm or less). Resonance SFR has also the advantage of selectivity, since the resonance enhancement for scattering by electrons or holes occurs at wavelengths that are speci"c to the location and state of binding of the carrier concerned. 7.2. Optically detected magnetic resonance
various sizes and composition are believed to be formed. When the monolayer fraction is less than 0.5, the lateral dimensions of these quantum islands and the separation between them are smaller than the exciton radius. The exciton thus experiences an average potential, but with #uctuations that lead to localisation. The recombination emission energy depends on the state of localisation and, by tuning the laser to di!erent energies, the exchange energy can be correlated with the localisation energy. In this particular case, the exchange splitting is found to depend linearly on the localisation energy, changing from 0.7 to 1.15 meV as the localisation energy increases from 5 to 25 meV [42]. In the case of excitons con"ned within quantum dots, the exchange splitting is expected to increase as the dot size is reduced, an e!ect discussed in Ref. [40] for CdSe dots in a glass matrix.
In both II}VI and III}V compounds, ODMR has been used with great success to investigate many centres that participate in electron}hole recombination emission [43}46]. Since such photoluminescence is subject to spin selection rules, the changes in the electron or hole spin distributions that are induced by the magnetic resonance lead to changes in the intensity or polarisation of the emitted light. It is these changes that are monitored to provide the ODMR spectrum, in which the resolution can approach that of conventional ESR. The technique provides information about donors and acceptors that are involved in recombination processes but is limited to recombination processes in which the lifetimes are longer than about 10\}10\ s [43,44]. It is well suited to studies of centres involved in donor}acceptor pair recombination but cannot usually be used to study
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excitonic states in II}VI materials, since such states have much shorter lifetimes. Since such states can be investigated by SFR, the two techniques are in a sense complementary. 7.3. Zeeman spectroscopy In principle, the splittings in excitonic transitions induced by application of magnetic "elds can be measured directly by means of high-resolution photoluminescence and a large number of such studies has been reported. However, the splittings are small and comparable with the linewidths, so that the di!erent transitions are often only poorly resolved, if at all. As pointed out earlier, the linewidthgs in SFR are often limited not by the specimen but by the laser linewidth and the resolution is consequently much higher. Moreover, in ternary and quaternary specimens, the PL transitions are broadened by compositional #uctuations and in such cases Zeeman studies are not possible: in contrast, the linewidths in the SFR spectra remain narrow. In SFR scattering by electrons at shallow donors or by holes at shallow acceptors, the information from the SFR experiments usually relates to the ground state (i.e. to the properties of the bound electron or hole) whereas that obtained from Zeeman studies concerns both the ground state and the excited (excitonic) state. Again, the two techniques are complementary.
8. Summary SFR spectroscopy is now a well-developed technique both for the study of the fundamental properties of electrons, holes and excitons in semiconductor structures and also for the investigation of the materials issues involved with growth and doping. The data provide important challenges for band structure theories for the magnetic behaviour of carriers, for example as functions of material composition or of quantum con"nement, and the combination of resonance selectivity and high spectral resolution enables di!erent types of scattering centres to be monitored as functions of specimen preparation. The technique is well suited to the
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study of epitaxial layers and promises to continue to be of great value in this context. Further, the sensitivity is such that spin-#ip scattering by carriers con"ned in a wide variety of quantum structures can be observed and it is here that much exciting work remains to be done.
Acknowledgements We have bene"ted considerably from excellent II}VI specimens from Heriot Watt University (Edinburgh), from the North East Wales Institute (Wrexham), from the Universities of Bremen, Kyoto, Lecce, WuK rzburg, from the Sony Research Laboratory (Yokohama), from Matsushita Electrical Laboratories (Kyoto), from JRCAT (Tsukuba) and from the Io!e Institute (St Petersburg). We thank the Max Planck Institut, Stuttgart (Dr. T. Ruf) for making available high magnetic "elds for some of the studies. The work has been supported by the Engineering and Physical Sciences Research Council (grants GR/L62283 and M55077), the British Council and the MURST (Italy).
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[30] C.L. Orange, W. Heimbrodt, D. Wolverson, J.J. Davies, J. Crystal Growth 184/185 (1998) 510. [31] C.M. Townsley, B. Schlichtherle, D. Wolverson, J.J. Davies, K. Ogata, Sg. Fujita, Solid State Comm. 96 (1995) 437. [32] C.L. Orange, B. Schlichtherle, D. Wolverson, J.J. Davies, T. Ruf, K. Ogata, Sg. Fujita, Phys. Rev. B55 (1997) 1607. [33] W. Heimbrodt, C.L. Orange, D. Wolverson, J.J. Davies, K. Kimura, T. Yao, Phys. Rev. B56 (1997) 6889. [34] V.F. Sapega, M. Cardona, K. Ploog, E.L. Ivchenko, D.N. Mirlin, Phys. Rev. B 45 (1992) 4320. [35] V.F. Sapega, T. Ruf, M. Cardona, K. Ploog, E.L. Ivchenko, D.N. Mirlin, Phys. Rev. B 50 (1994) 2510. [36] J. Puls, F. Henneberger, Phys. Status Solidi A 164 (1997) 499. [37] A.A. Sirenko, T. Ruf, N.N. Ledentsov, A.Yu. Egorov, P.S. Kop'ev, J.M. Ustinov, A.E. Zhukov, Solid State Comm. 97 (1998) 169. [38] A.A. Sirenko, in: M. Sche%er, R. Zimmermann (Eds.), The Physics of Semiconductors, World Scienti"c, Singapore, 1996, p. 1385. [39] A.A. Sirenko, V.I. Belitsky, T. Ruf, M. Cardona, A.L. Ekimov, C. Trallero-Giner, Phys. Rev. B 58 (1998) 2077. [40] U. Woggon, F. Gindele, W. Langbein, M. Hetterich, Phys. Status Solidi A 164 (1997) 505. [41] O.Z. Karimov, D. Wolverson, J.J. Davies, T. Ruf, L. Tenishev, Phys. Status Solidi B 215 (1999) 373. [42] T. Ruf, O.Z. Karimov, D. Wolverson, J.J. Davies, A.N. Reznitsky, A.A. Klochkhkin, S.Yu. Verbin L.Tenishev, S.A.Permogorov, S.V Ivanov, Physica B 273/274 (1999) 911. [43] J.J. Davies, J. Crystal Growth 72 (1985) 317. [44] J.J. Davies, J. Crystal Growth 86 (1988) 599 and references therein. [45] B.C. Cavenett, Adv. in Physics 30 (1981) 475 and references therein. [46] K.H. Chow, G.D. Watkins, Phys. Rev. Lett. 81 (1998) 2084 and references therein.
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Spin-#ip Raman scattering studies of II}VI heterostructures J.J. Davies*, D. Wolverson, O.Z. Karimov, I.J. Gri$n Department of Physics, University of Bath, Bath BA2 7AY, UK
Abstract Spin-#ip Raman (SFR) scattering is now an established technique for the investigation of semiconductor heterostructures. Because the scattering is resonantly enhanced when the laser is adjusted to coincide with the appropriate excitonic transition, the technique has high sensitivity. It is also highly selective, since the resonance enhancement occurs at di!erent wavelengths for scattering by carriers con"ned under di!erent circumstances. For electrons, the SFR spectra enable the g-factor to be determined, thus providing tests of band structure theories. The g-factor is sensitive also to quantum con"nement, when it may become anisotropic. In the case of holes, the higher angular momentum (J") makes the SFR spectra highly dependent on the state of strain of the material. Spin-#ip signals from localised excitons can also be detected. Such signals enable the electron}hole exchange interactions to be determined and are thus a sensitive probe of the localisation properties of the exciton, for example in quantum dots of di!ering sizes. Recent developments will be reviewed to illustrate how the technique can be used to investigate the physics and materials issues associated with II}VI structures. 2000 Elsevier Science B.V. All rights reserved. PACS: 71.55.Gs; 78.30.Fs; 78.55.Et; 78.66.Hf Keywords: Spin-#ip; II}VI; Raman; g-Values; Exciton localisation
1. Introduction In its most usual form, Raman spectroscopy is associated with the creation or destruction of vibrational excitations when a laser beam is inelastically scattered by the medium under study. As such, the technique is very commonly used for the investigation of molecular structures and, in the context of semiconductor science, for studies of phonon behaviour. In general, however, Raman scattering can be caused by several other types of excitation, most
* Corresponding author. Tel.: #44-1225-323-324; fax: #441225-826-110. E-mail address: [email protected] (J.J. Davies).
notably those which involve changes in the energy states of charge carriers. Amongst such scattering processes, those which take place in the presence of a magnetic "eld have recently become the subject of increasing attention. Since such scattering results in a change in the spin orientation of the electron or hole, it has become known as spin-#ip Raman (SFR) scattering. The purpose of this paper is to demonstrate that SFR spectroscopy is a very powerful technique for the investigation of semiconductors in general and for epitaxial II}VI materials in particular. We shall show that the information provided is very similar to and complements that obtained from magnetic resonance studies. However, the sensitivity is much higher, which makes the approach particularly suitable for
0022-0248/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 1 6 5 - 2
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investigations of specimens in which the region of interest is very small, for example, thin epitaxial layers and quantum wells. Although SFR is a somewhat specialised technique, the discussion will be directed towards those which are concerned with the properties of II}VI semiconductors in general. We shall restrict attention to non-magnetic II}VI materials since the application of the technique to dilute magnetic semiconductors based on II}VI and related compounds has been discussed thoroughly elsewhere ([1]; see also Ref. [2]).
2. Basic concepts SFR is not a new technique: such experiments were carried out for InSb in 1967 [3] whilst, for II}VI compounds, a series of elegant experiments on CdS was reported by Thomas and Hop"eld in 1968 [4]. The basic concept is indicated in Fig. 1,
Fig. 1. Energy level scheme to illustrate SFR scattering by an electron bound at a neutral donor. The small arrows indicate the magnetic moments of the electron and the separation between the two spin states is given by g k B. The excited level X corresponds to one of the spin states of an exciton bound at the neutral donor. If the incoming photon energy corresponds to the transition shown, the scattering intensity is dramatically enhanced.
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which shows the two energy levels (one for each spin direction) in the presence of a magnetic "eld B for the case of an electron bound at a neutral donor. Before the incident photon is scattered, the electron is imagined to be in the lower state. After scattering, the electron is left in the upper state, that is, its spin has been reversed. Clearly, in this simple case, the change in photon energy is given by the Zeeman splitting g k B, where g is the gyromag netic ratio of the electron and k is the Bohr magneton. The process considered, in which the photon has lost energy, is called Stokes (S) scattering; if an electron is already in the upper spin state and, after scattering, is then in the lower state, the photon gains energy and the process is called anti-Stokes (AS) scattering. An SFR spectrum thus appears as in Fig. 2, the ratio of the S and AS lines being determined in part by the occupancy of the spin states and therefore by the temperature. A point of crucial importance is that the crosssection for scattering is a very strong function of the
Fig. 2. SFR spectrum from a fractional monolayer of CdSe in ZnSe (grown by MBE by S.V. Ivanov of the Io!e Institute). The Stokes and anti-Stokes spin-#ip Raman lines lie respectively at negative and positive energy shifts relative to the original laser light (2.7367 eV). The lines marked electron correspond to SFR scattering by electrons (see Section 2) whilst those marked exciton are caused by the so-called dark excitons (Section 5 [41,42]). The Raman shifts depend on the magnetic "eld as shown later in Fig. 6. The broad background is due to photoluminescence.
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Fig. 3. Schematic arrangement for resonance SFR experiments. Observation of the scattering may be with the "eld along the growth axis (Faraday con"guration) or perpendicular to it (Voigt con"guration). To reduce problems caused by stray light, the re#ected (elastic) component of the laser beam is directed back out of the cryostat.
resonance with the correct spin state of the exciton (as a result, the resonance wavelengths for Stokes and anti-Stokes signals di!er, so that the ratio of the S and AS intensities di!ers from that predicted from the temperature alone). It should be noted that the requirement that the incoming photon be in resonance also results in the outgoing photon being in resonance, so that SFR scattering is a doubly resonant process: it is for this reason that the scattering can be very strong. In the following sections, the essential features of the experimental arrangement will be described. SFR experiments on electrons will then be discussed in greater detail. SFR spectroscopy can also be applied to the study of hole states. Because holes have an angular momentum of , their magnetic behaviour is more complicated than that of electrons: in particular, the SFR spectra can be strongly anisotropic with respect to the direction of the magnetic "eld and this anisotropy can be used to investigate strains in the material, for example, the strains that commonly exist in heterostructures. Such experiments will be described separately, followed by examples of a phonon-assisted scattering process that makes it possible to study excitonic states. Finally, we shall compare the results obtained from SFR spectroscopy with those obtained by other magneto-optical techniques.
3. Experimental requirements photon energy. The scattering intensity is hugely increased, sometimes by several orders of magnitude, when the incoming photon energy coincides with the energy required to create an exciton bound to the centre under study. Such &resonance' behaviour has been discussed by Yafet [5] and plays a vital part in SFR studies. Thus, for the case of electrons bound at neutral donors, the laser should be in resonance with the donor-bound exciton transition (sometimes called D X or I ). In the cases of bulk CdS [4] and bulk ZnSe [6], lines from an argon ion laser are fortuitously suitable, but in general a tunable laser is needed, since, for optimum enhancement, the laser photon energy has often to be adjusted to within 1 meV. The requirement is stringent, since certain selection rules must be obeyed (see later) and the laser has to be in
The basic experimental arrangement is shown in Fig. 3. Epitaxial specimens are studied in the backscattering geometry, as indicated, most experiments being carried out at low temperatures (for example, to prevent the centres under study from being ionised). In comparison with phonon Raman scattering, the Raman shifts in spin-#ip experiments are small, often being less than 1 meV, so that a specialised spectrometer with good stray light rejection close to the laser line is required. In our laboratory we use a triple spectrometer with a 1 m "nal dispersing stage, with either a charge-coupled detector (CCD) array or a photon counting system. Clearly, the magnetic "eld should be as strong as possible since in most cases this maximises the Raman shift.
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Of crucial importance is the ability to tune the laser wavelength, since maximisation of the resonance enhancement often requires an accuracy of better than 1 meV: for this purpose dye or Ti}sapphire lasers are convenient, since they readily provide the necessary powers (tens of mW). In a spin-#ip scattering experiment the electrons undergo a change in spin of one, leading to the selection rule that the incident and scattered light be p and n polarised respectively (or vice versa). For holes, with their greater angular momentum and the possibility of mixing between heavy- and lighthole states, the selection rules are more complicated [7]. These rules dictate whether the direction of observation should be along the direction of the magnetic "eld (Faraday geometry) or perpendicular to it (Voigt geometry). Since the Raman shifts often depend on the direction of the magnetic "eld relative to the crystal axes, mechanisms for adjusting the specimen orientation are essential.
4. Electron SFR in epitaxial II}VI materials It will be clear that SFR experiments enable direct measurement of the g-value of electrons. For electrons bound in conduction band related states, the signi"cance of this is that g (which can di!er even in sign from the free-electron value) is a very sensitive to the forms of the conduction band and valence bands, in ways that are very similar to those of e!ective masses. Determinations of g can therefore be used to test band structure theories. The g-value is also strongly a!ected by quantum con"nement and its determination can thus lead to improved understanding of quantum wells and quantum dots. Further, if the electron is trapped at deep centres, the g-value departs from the conduction band value, providing tests of theories for localised centres. Excellent accounts of electron SFR in bulk specimens of CdS, ZnSe and ZnTe can be found in Refs. [4,6,7]. For II}VI materials in epitaxial form, the research is much more recent and has concentrated mainly on ZnSe [8,9] and its alloys and on CdTe [10] and related materials. In simple epitaxial layers, the g-values for electrons bound at shallow donors are essentially those that are observed for
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bulk material [11,12] and are found not to be sensitive to strain. The k . p theories that describe these g-values are now well developed and produce good agreement with observation [13}16]. An important aspect of SFR experiments is that they work very well not only in binary materials but also in ternary and quaternary systems such as ZnSSe, ZnCdSe, ZnMgSe and ZnMgSSe [17,18], since the SFR linewidths remain narrow despite the alloying. Analysis of g-value behaviour in such alloys has recently been published [17,18]. Such information also forms an essential precursor to studies of systems in which quantum con"nement becomes important, since in such structures one or more of the component materials is often a ternary or quaternary alloy. It has been noted already that when the depth of the centre that traps the electron becomes large, the g-value is expected to depart from the conduction band value (1.12 for ZnSe [11,12]). A striking example of this is found in p-type ZnSe doped with nitrogen, for which it is now well known that for nitrogen concentrations in excess of about 10 cm\ a compensation process sets in, due at least in part to the formation of deep donor centres [19}22]. These deep (50 meV) donors were found in optically detected magnetic resonance (ODMR) experiments [23] to have a g-value of 1.38, a value later con"rmed by SFR [9]. Later experiments [24, 25] have shown that this g-value remains constant when ZnSe is alloyed with up to at least 10% of ZnS, in contrast to the g-value of electrons trapped at shallow donors, which increases by 0.11 over this range. SFR can also be used to investigate the relative concentration of shallow donors, deep donors and acceptors (see Section 5) as functions of post-growth sample treatment [26]. All these experiments are consistent with the popular model [20, 27] for this centre of a substitutional nitrogen atom paired with a selenium vacancy, particularly since the insensitivity of the g-value to the sulphur/selenium ratio suggests strongly that the electron wave function is well localised. However, there still remains the problem of accounting for the large shift (0.62) of the g-factor from the spin-only value, since for a strongly localised centre the orbital contribution should be quenched [25]. The modelling of the g-value of the deep donor centre and
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in ZnMgSSe barriers [28]. In both cases the results con"rm the validity of the k . p theories used to describe electron g-values in these semiconductors. An example of the dependence of the electron gvalue on well width is shown in Fig. 4. A similar study for the III}V system GaAs/AlAs is given in Ref. [29].
5. Hole SFR in epitaxial II}VI materials
Fig. 4. Behaviour of the average g-value for electrons as a function of well width for a ZnSe quantum well with ZnMgSSe barriers (produced by MBE at the University of Bremen). As the well width decreases and the penetration of the wave function into the barrier increases, the g-value changes from the ZnSe value of 1.12 to the barrier value. The g-tensor also becomes anisotropic (see text).
the unambiguous identi"cation of the centre's structure therefore present a continuing theoretical challenge. The sensitivity of resonance SFR is also su$ciently great for electrons to be studied under conditions of quantum con"nement. In quantum wells, the g-value of the con"ned carriers changes because the wave functions extend beyond the well into the barrier material and also because the e!ective band gap is changed, so that the interband mixing that produces the g-shifts is altered. In addition, the strain- and con"nement-induced splitting between the light-hole and heavy-hole states produces a measurable anisotropy in the electron g-value, so that the SFR shifts *E are given by an equation of the form *E"(g cos h#g sin h ) k B, (1) , , where h is the angle between the magnetic "eld and the normal to the plane of the well. Such behaviour has been studied for CdTe quantum wells in CdMgTe barriers by Sirenko et al. [10], and has recently also been studied for ZnSe quantum wells
When the laser is adjusted to be in resonance with excitons bound at neutral acceptors, the SFR signals observed are those due to holes bound at the acceptors. For bulk II}VI materials, hole SFR has been reported for ZnTe, which is easily obtained in p-type form. In contrast, it is only comparatively recently that it has been possible to obtain p-type ZnSe and the epitaxial form of the specimens has inevitably led to the spectra being strongly a!ected by strain. For thick layers of ZnSe grown on GaAs, the ZnSe is relaxed: however, because of the di!erence in the thermal expansivities of the epitaxial layer and the substrate, the ZnSe is under biaxial tensile strain at low temperatures and it is the light-hole states that are occupied. For thin, pseudomorphic layers, the strain is of the opposite sign because of the di!erence in lattice constants and it is then the heavy-hole states that are occupied. The SFR processes for the two cases are shown in Fig. 5. As a result of the strain e!ects, the SFR shifts for holes have a more complicated behaviour than those for electrons. To a "rst approximation, the shifts for heavy holes are of the form of Eq. (1) with g "3g and g "0 (leading to *E" , , 3g k B cos h). For light holes, Eq. (1) also applies, but with g "g and g "2g . SFR lines from , , heavy holes thus lie at 3g k B when the "eld is along the growth axis and move towards zero as the "eld direction approaches the layer plane; in contrast light-hole signals start at g k B and move to the greater value of 2g k B. The two types of hole signal can therefore readily be distinguished (see e.g. Fig. 3 of Ref. [30]). Examples of SFR spectra for holes bound at nitrogen acceptors in ZnSe layers of di!erent thicknesses and thus of di!erent states of strain (both
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6. Spin-6ip signals involving changes in excitonic spin states
Fig. 5. Energy level scheme to illustrate SFR scattering by a hole bound at a neutral acceptor in an epitaxial layer for a magnetic "eld directed along the growth axis. Two cases are shown, corresponding to compressive and tensile biaxial strains, leading to scattering by heavy and light holes, respectively. When the magnetic "eld is in the layer plane, the heavy-hole splitting becomes very small, whilst the light-hole splitting doubles (see text). In this diagram, the excited level now corresponds to one of the spin states of an exciton bound at the neutral acceptor. The resonance enhancement thus occurs at a laser energy that is di!erent from that in Fig. 1, so that scattering by holes can be studied separately from that due to electrons.
compressive and tensile) have been described in detail [30}32], together with cases in which the strain is very small and the heavy- and light-hole states are mixed by the magnetic "eld [33]. As discussed in Ref. [33], the SFR shifts are very sensitive to strain splittings that are comparable with the Zeeman energies. SFR is therefore a very useful method of studying such splittings in a range which lies much below that which is measurable by other techniques. In practice, there also exist higher-order terms in the spin Hamiltonian (for example linear in "eld but cubic in the angular momentum operator J) which must also be taken into account [33]. The calculation of these terms and of the hole g-values themselves present strong challenges for band structure theories.
In SFR experiments involving electrons bound at neutral donors or holes bound at neutral acceptors, the Raman process is straightforward to envisage. In the Stokes process, the energy lost by the photon on scattering is gained by the electron or hole that undergoes the change in spin. Such processes are described in terms of diagrams such as Figs. 1 and 4 and the spin-#ip energy is simply that of the carrier concerned. The scattering intensity is enhanced when the laser is in resonance with the exciton bound at the neutral donor or neutral acceptor. In contrast, it has been known for some time that it is possible to obtain strong SFR scattering when the laser is in resonance with the transition energies of free excitons or of excitons localised not at dopants but at potential #uctuations caused, for example, by alloy disorder. In such cases, the spin #ip occurs in the optically excited state (i.e. in the excitonic state): the incoming photon creates the exciton, which undergoes a change in angular momentum through the intervention of an acoustic phonon, followed by emission of a photon of lower energy [34,35]. Through such processes it is possible to observe spin-#ip signals for excitonic states (see also Ref. [36], where signals from &dark excitons' localised in a ZnSe/ZnCdSe quantum-well system are reported). The interest in such signals arises from the fact that in the excitonic state there exists an exchange interaction between the electron and the hole. The SFR experiments now enable this exchange interaction to be measured. In III}V systems, SFR has been used to study quantum dots formed by Stranski}Krastanov growth in InAs/GaAs [37] and InP/InGaP [38] and, for II}VI compounds, in the CdS/glass system [39]. In II}VI systems, the exchange parameter is typically of order 0.1}1 meV but can be greatly enhanced under conditions of quantum con"nement [40] or when the excitons are localised. A particularly intriguing example (Figs. 2 and 6) of such measurements is encountered in the study of CdSe fractional monolayers in ZnSe matrix [41,42]. Here, small ZnCdSe &islands' of
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7. Contrast with other experimental methods It is useful to compare the sensitivity and spectral resolution obtained by resonance SFR with that of other magnetic and magneto-optical techniques. 7.1. Electron spin resonance (ESR)
Fig. 6. Dependence on magnetic "eld of the signals shown in Fig. 2. The electron SFR shift is proportional to the "eld, as expected from Section 2 and does not depend on the direction of the "eld. The exciton signal varies non-linearly as a consequence of the electron}hole spin exchange interaction, which determines the intercept at zero "eld. Two examples of exciton signals are shown, for two di!erent laser energies. Altering the laser energy brings into resonance excitons that are localised in di!erent environments, so that the exchange interaction changes, as shown.
We have seen that SFR provides information on the magnetic parameters of electrons and holes bound at donors and acceptors. This information is similar to that which, in principle, could be provided by ESR experiments, in which the spectral resolution would be very much better. However, the sensitivities of ESR spectrometers are typically of the order of 10}10 spins for a linewidth of 1 mT. For example, for a specimen of area 0.1 cm and thickness 10\ cm, ESR would be expected to be able under favourable circumstances to detect magnetic centres present at a concentration of 10}10 cm\. In contrast, resonance SFR can detect 10 cm\ (and in specimens of area 10\ cm or less). Resonance SFR has also the advantage of selectivity, since the resonance enhancement for scattering by electrons or holes occurs at wavelengths that are speci"c to the location and state of binding of the carrier concerned. 7.2. Optically detected magnetic resonance
various sizes and composition are believed to be formed. When the monolayer fraction is less than 0.5, the lateral dimensions of these quantum islands and the separation between them are smaller than the exciton radius. The exciton thus experiences an average potential, but with #uctuations that lead to localisation. The recombination emission energy depends on the state of localisation and, by tuning the laser to di!erent energies, the exchange energy can be correlated with the localisation energy. In this particular case, the exchange splitting is found to depend linearly on the localisation energy, changing from 0.7 to 1.15 meV as the localisation energy increases from 5 to 25 meV [42]. In the case of excitons con"ned within quantum dots, the exchange splitting is expected to increase as the dot size is reduced, an e!ect discussed in Ref. [40] for CdSe dots in a glass matrix.
In both II}VI and III}V compounds, ODMR has been used with great success to investigate many centres that participate in electron}hole recombination emission [43}46]. Since such photoluminescence is subject to spin selection rules, the changes in the electron or hole spin distributions that are induced by the magnetic resonance lead to changes in the intensity or polarisation of the emitted light. It is these changes that are monitored to provide the ODMR spectrum, in which the resolution can approach that of conventional ESR. The technique provides information about donors and acceptors that are involved in recombination processes but is limited to recombination processes in which the lifetimes are longer than about 10\}10\ s [43,44]. It is well suited to studies of centres involved in donor}acceptor pair recombination but cannot usually be used to study
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excitonic states in II}VI materials, since such states have much shorter lifetimes. Since such states can be investigated by SFR, the two techniques are in a sense complementary. 7.3. Zeeman spectroscopy In principle, the splittings in excitonic transitions induced by application of magnetic "elds can be measured directly by means of high-resolution photoluminescence and a large number of such studies has been reported. However, the splittings are small and comparable with the linewidths, so that the di!erent transitions are often only poorly resolved, if at all. As pointed out earlier, the linewidthgs in SFR are often limited not by the specimen but by the laser linewidth and the resolution is consequently much higher. Moreover, in ternary and quaternary specimens, the PL transitions are broadened by compositional #uctuations and in such cases Zeeman studies are not possible: in contrast, the linewidths in the SFR spectra remain narrow. In SFR scattering by electrons at shallow donors or by holes at shallow acceptors, the information from the SFR experiments usually relates to the ground state (i.e. to the properties of the bound electron or hole) whereas that obtained from Zeeman studies concerns both the ground state and the excited (excitonic) state. Again, the two techniques are complementary.
8. Summary SFR spectroscopy is now a well-developed technique both for the study of the fundamental properties of electrons, holes and excitons in semiconductor structures and also for the investigation of the materials issues involved with growth and doping. The data provide important challenges for band structure theories for the magnetic behaviour of carriers, for example as functions of material composition or of quantum con"nement, and the combination of resonance selectivity and high spectral resolution enables di!erent types of scattering centres to be monitored as functions of specimen preparation. The technique is well suited to the
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study of epitaxial layers and promises to continue to be of great value in this context. Further, the sensitivity is such that spin-#ip scattering by carriers con"ned in a wide variety of quantum structures can be observed and it is here that much exciting work remains to be done.
Acknowledgements We have bene"ted considerably from excellent II}VI specimens from Heriot Watt University (Edinburgh), from the North East Wales Institute (Wrexham), from the Universities of Bremen, Kyoto, Lecce, WuK rzburg, from the Sony Research Laboratory (Yokohama), from Matsushita Electrical Laboratories (Kyoto), from JRCAT (Tsukuba) and from the Io!e Institute (St Petersburg). We thank the Max Planck Institut, Stuttgart (Dr. T. Ruf) for making available high magnetic "elds for some of the studies. The work has been supported by the Engineering and Physical Sciences Research Council (grants GR/L62283 and M55077), the British Council and the MURST (Italy).
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