- Email: [email protected]
Luminescence and spectroscopy
Journal of Luminescence 100 (2002) 57–64
Luminescence and spectroscopy Emmanuel I. Rashbaa,b,* a
Department of Physics, The State University of New York at Buffalo, Buffalo, NY 14260, USA b Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract The connection between luminescence and different chapters of spectroscopy is discussed. Modern theoretical concepts and experimental techniques wiped away the boundaries that traditionally existed between them. Nevertheless, the basic notions of luminescence remain valid. Being focused on the dynamics and kinetics of electronically excited states, luminescence serves as an effective tool in solving numerous problems in contemporary solid-state physics. Electron–phonon interaction, excitons in disordered systems, the emission spectroscopy of the fractional quantum Hall effect and spin injection are discussed as specific examples. r 2002 Elsevier Science B.V. All rights reserved. PACS: 71.35; 71.38; 71.70.E; 72.25; 73.43; 78.60 Keywords: Solid-state spectroscopy; Excitons; Electron–phonon interaction; Self-trapping; Polarons; Fractional quantum Hall effect; Spintronics
1. Introduction In this brief paper, I speculate about the interconnection between luminescence and spectroscopy mostly as applied to condensed matter physics. What unifies luminescence and absorption spectroscopy and what makes them different? Is the community studying them and converting their studies into new technologies a single community or do these people constitute two different communities? The Conference that brings these people together is currently named the International Conference on Luminescence and Optical Spectro*Corresponding author. Department of Physics, The State University of New York at Buffalo, Buffalo, NY 14260, USA. E-mail address: [email protected] (E.I. Rashba).
scopy of Condensed Matter; however, it emerged from the luminescence conferences and this birthmark still manifests itself in its logo ICL. If these fields have drawn nearer, in fact partly merged, do there still exist scientific problems that are specific for luminescence? The subtitle of the Journal of Luminescence, ‘‘research on excited state processes in condensed matter’’, added when Michael Sturge took over the editorship of the journal, answers most of those questions. I argue that fundamental studies in luminescence have the following main goals: first, investigating the kinetics of electronically excited states for finding the evolution of nonequilibrium populations; second, observing optical transitions that for different reasons cannot be seen in absorption. Taking some successful studies
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performed in the space of about 40 years as examples, I show that the luminescence technique was indispensable for them. Both luminescence and absorption spectroscopy have important applications that drive the research and are very diversified. The applications specific for both fields and the related experimental methods and technologies are also critical for establishing the connections and differences between them.
2. Why the two fields diverged? Every science has its own prehistory. However, it is a remarkable fact that the contemporary history of absorption and emission spectroscopy began simultaneously, from the same discoveries by Bunsen and Kirchhoff made in the middle of the 19th century. They observed atomic emission and absorption lines whose wavelengths exactly coincided. This discovery was applied by Stokes and Kirchhoff for the explanation of the Fraunhofer spectra. Nearly at the same time (1852), exactly 150 years ago, Stokes explained the conversion of absorbed ultraviolet light into the emitted blue light and introduced the term fluorescence. Apparently, the discovery of the Stokes shift marked the birth of luminescence as a science. The classical physics had no potential for describing optical spectra and, in particular, it established no common ground for the comparative study of the emission and absorption spectra. As a result, these spectroscopies ‘‘separated’’, and the people working in these fields formed different communities. In some places even bureaucratic barriers developed between them. 2.1. Two communities in the FSU In this section I will describe how these communities developed in the Former Soviet Union (FSU) because I know their history and belonged to them since the mid-1950s. However, the existence of separate journals and conferences in the West signifies that this division was not a local phenomenon.
In the l920–1930s, optical research in Moscow was led by two remarkable physicists, Leonid Mandelstam and Sergei Vavilov. Mandelstam and his collaborators focused on nonlinear vibrations. The research included radio engineering, optics, and even nonlinear differential equations. Despite the isolation from the West, this group achieved outstanding prominence. In 1928, Landsberg and Mandelstam discovered the inelastic light scattering nearly at the same time as Raman and Krishnan. Following the term they originally proposed, Raman scattering is traditionally called combination scattering in Russia. This strong tradition in nonlinear phenomena culminated in the Nobel Prize awarded to Basov and Prokhorov for the discovery of quantum generators (they shared it with Townes). Vavilov and his collaborators focused on luminescence and its practical applications. Their greatest scientific achievement was the discovery of $ the Cerenkov effect which, remarkably, has $ nothing to do with luminescence. Cerenkov (or Cherenkov, in modern spelling) and Vavilov shared the National Prize with Tamm and Frank who developed the theory. Three of them shared the Nobel Prize (1958) after Vavilov’s death in 1951. In the FSU, the Academy of Sciences was the body in charge of coordinating the development of science around the country. For this purpose, the Councils on different problems were established. According to those regulations, each of these two groups had its own Council, on spectroscopy and luminescence, respectively. Organizing all-union conferences became the main activity of these councils. Therefore, there were separate conferences on spectroscopy and on luminescence. Some people used to attend both conferences (and sometimes presented the same talks there) while other people attended only one of them. Gradually scientific arguments started to outweigh the bureaucratic ones. Atomic and molecular spectroscopy became the main subject of the spectroscopic conferences while the condensed matter community grouped around the luminescence conferences. Beginning from late 1950s when participation in international conferences became possible (but still
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horribly difficult for most of us) these councils became powerful bodies because they selected the groups that were sent by the Academy abroad to different conferences. Here the scientific differences between the spectroscopy and luminescence played absolutely no role. I was lucky to go to Western Europe for the first time in my life thanks to the Council on Spectroscopy that included me into a group sent to the conference on molecular spectroscopy in Liege (Belgium, 1969). The journal Optics and Spectroscopy, founded in 1956, covered from the very beginning a wide scope of problems including luminescence. It became very popular among chemists. The difference in materials became a watershed: papers on the spectroscopy of semiconductors were published mostly in Solid State Physics and Semiconductors. I complete this section with a note about the personal fate of both men who initiated the research in the spectroscopy and luminescence in the FSU. Nikolai Vavilov, the elder brother of S. Vavilov, was a renowned biologist and a founder and long time President of the Academy of Agriculture. However, in the late 1930s when the anti-genetic campaign led by pseudo-scientist Lysenko, which used practical gardener Michurin as its icon, gathered force, Vavilov lost his position. Finally, he was arrested and perished in prison in 1943. Two years later, in 1945, the same Government that destroyed Nikolai Vavilov nominated Sergei Vavilov for the President of the Academy of Sciences; election by Academicians was only a formality. Some people considered this nomination as one of Stalin’s sardonic jokes: ‘‘How will he behave after receiving such a good lesson?’’ Nevertheless, Vavilov’s behavior was courageous and honest. He invested a lot of efforts in saving physics from a pogrom after genetics was destroyed in 1948 and supported individuals who were in danger. Mandelstam died in time, as people used to say, in 1944. In accordance with the Academy’s regulations, his selected works were published. The 5th volume of the collection included his lectures on relativity and quantum mechanics. It appeared at a time when our philosophers (and
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some of the physicists who followed them) ‘‘criticized’’ these chapters of modern physics; hence, it was no surprise that ‘‘idealism’’ and similar heresies were found in the volume. A shameful posthumous inquisition trial over the 5th volume was staged. However, Mandelstam was already out of their reach.
3. Quantum unification Quantum mechanics established an intimate connection between the absorption and emission spectra. Squares of the matrix elements, jM j2 ; entering into the golden rule are equal for the direct and inverse processes because of the unitarity of the quantum mechanics. At a more phenomenological level, this connection manifests itself in the Einstein relation between the absorption and emission coefficients. This relation also clarifies the phenomena of spontaneous and induced optical transitions. If one disregards the photon population numbers, the transition probabilities are proportional to the products fi jMfi j2 ð1 ff Þ where fi and ff are the electron populations in the initial and the final states, respectively. Because M 2 ¼ jMfi j2 ; quantum mechanics unifies both if fields to the extent that, for the same transition, absorption and emission are described by equivalent formulae. Under these conditions, a comparative study of these spectra can provide information about the populations fi and ff and their dynamics. However, it is not unusual that either fi is too close to zero or ff is too close to unity; hence, the transition can be seen only in absorption or only in emission. Then both techniques provide complementary information.
4. Quasi-equilibrium luminescence In the early studies of luminescence from solids and molecules, it was usually assumed that phonon quasi-equilibrium is established during the electron excitation lifetime. Under these conditions, a theory of the multiphonon optical
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spectra of impurity centers has been developed in great detail (for a review, see Ref. [1]). It is important to note that when the electron–phonon coupling is strong, and, therefore, the Stokes shift is large, the transitions that can be seen in absorption and in emission usually correspond to different pairs of electron–phonon quantum levels. Indeed, multiphonon transitions dominate the spectra, so that at moderate temperature the number of phonons involved exceeds the Planck phonon population numbers. As a result, under conditions of quasi-equilibrium, where the overlap of the absorption and emission is relatively small, the data taken in the absorption and emission are mostly independent, and their comparison provides quite different information about the centers. Therefore, this basic model system provides a simple example of the complementarity between the information coming from the absorption and emission spectra.
5. Nonequilibrium luminescence Quasi-equilibrium in the electronically excited state is not universal. It can be established only if trel =trad 51where trel and trad are the relaxation time and radiative time, respectively. E.g., trel can be very long when excitations are trapped by spatially separated centers. Luminescent dating based on thermostimulated and optically stimulated luminescence makes possible the detection of accumulated radiation damage at the scale of 100,000 years. It became recently an effective method in archaeology [2]. However, even much more modest trel can provide a clue to the physical origin of the initial states. After the narrow lines at the edge of the fundamental absorption of Cu2O had been discovered and assigned to excitons [3,4], many lines observed in different semiconductors were ascribed to excitons despite the inconsistencies in their intensities, reproducibility, etc. A similar problem existed in the spectra of molecular crystals where exciton lines were discovered previously [5] and discussed in terms of Davydov multiplets [6]. In both cases the total number of
‘‘exciton’’ lines exceeded any reasonable theoretical expectations, and identification of the specific lines as intrinsic (free exciton) or extrinsic (caused by impurities and defects) was problematic. The solution of the problem came from low-T luminescence [7]. There is good reason to believe the populations of different free exciton states to be in quasi-equilibrium, while bound excitons trapped by spatially separated defects are expected to show much longer times trel : Therefore, emission bands having comparable intensities and separated by energies exceeding kB T should be treated as extrinsic, i.e., they should be assigned to bound excitons. Application of this simple criterion dramatically reduced the list of candidates for free exciton assignment. More powerful methods for distinguishing free and bound exciton lines for both Wannier–Mott [8,9] and molecular excitons [10] came later. The intensity of the bound exciton lines in absorption is proportional to the concentration of defects. Therefore, it was surprising that the absorption in these lines could be strong enough to compete with the intrinsic exciton absorption and confuse the line assignments. The giant oscillator strengths inherent in bound excitons were the origin of this seeming paradox [11]. The oscillator strength for bound exciton per single defect is a factor ðEB =Ebind Þ3=2 larger than the oscillator strength of a free exciton per unit cell, where EB is the exciton band width and Ebind is the binding energy of an exciton to the defect. For shallow levels, this factor is typically as large as 102 for molecular excitons and 104 for semiconductors. This factor caused confusion in line assignments and results in fast radiative decay of bound excitons, increasing their quantum yield. More recently, the strong dependence of trel on exciton energy has made it possible to prove the applicability of modern concepts of localization phenomena to excitons. The spectral dependence of the excitation spectrum of the exciton luminescence, the energy dependence of the homogeneous linewidth found from resonant Rayleigh scattering, and the exciton diffusivity measured by the transient grating technique resulted in discovering the Mott–Anderson localization of excitons and investigating its basic features, including the
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existence of the mobility edge and hopping spectral diffusion [12].
6. Self-trapping of excitons and related phenomena Luminescence makes it possible to follow the decay of different metastable states. One of the interesting systems of this kind are free excitons against the background of self-trapped (ST) excitons that are discussed in more detail below in this section. When the exciton–phonon interaction is strong enough, the energy of ST states is lower than the bottom of the free exciton band. Nevertheless, free states are protected by the potential barrier originating from lattice deformation and, therefore, coexist with the ST states [13,14]. In alkali halides and rare gas solids, the metastable free states are seen in absorption but only the ST states are usually seen in emission because of the fast scattering of free excitons by different defects into the ST states. It took about 20 years after the theoretical prediction of the coexistence of free and ST states when crystals of such a high quality were grown that the emission from the free states could be observed. More recently, the peak-to-peak ratio of the emission of free and ST excitons in Xe as large as 50 has been achieved [15]. This ratio for the free/ST emission is controlled not only by the decay rate of thermalized free excitons but also by branching in the relaxation of hot free excitons. Indeed, the hot excitons produced by light can either thermalize (and be self-trapped from the thermalized states) or relax directly into ST states [16]. This nontrivial relaxation of hot excitons bypassing the thermalization has been observed in pyrene [17]. In this problem the careful comparison of the absorption and emission spectra allowed one to assign the narrow and broad bands in these spectra and to discover the free and ST excitons. Recent active interest in polarons in high-Tc superconductors [18] and in colossal magnetoresistance materials, and also developing new powerful computational techniques (for comparison of the results found by different numerical methods, see Ref. [19]), resulted in drawing together the theoretical research on the self-trapping of charge
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carriers and excitons. The traditional theoretical work on the self-trapping phenomena, based on analytical techniques, provided the basic concepts and elucidated many related phenomena. New computational techniques permit one to formulate some problems more rigorously, to find interesting details that are out of reach of the analytical methods, and to establish the accuracy of these methods. Therefore, it is instructive to compare some of the results derived by these two different techniques, and the comparison shows that the results are in a quite satisfactory agreement. The dependence of the polaron ground state on the coupling constant a in systems of different dimensionality is the first example [13,20]. When the electron–phonon interaction is of a short-range type, then in three dimensions (3D) all adiabatic continuum theories predict a sharp changeover from the free particle to the ST particle ground state when a reaches some critical value ac (this is just the value of a when the ST barrier first emerges). The ground state energy E0 ðaÞ shows a cusp and the polaron effective mass mn ðaÞ changes abruptly at a ¼ ac ; but only if the decay of the metastable state is neglected. On the other hand, in 1D a similar theory results in a smooth dependence of the ground state on a: Quite inaccurately, the changeover in 3D is sometimes termed a ‘‘phase transition’’ despite the fact that there cannot be any phase transition in a single quasi-particle (polaron or exciton) system, hence, this term is confusing. A numerical theory of a polaron on a discrete lattice (Holstein model) results in a smooth dependence of m on a in 1D and in a steep increase in m near a ¼ ac in 3D [21], in agreement with the expectations based on the adiabatic theory. There are no singularities at a ¼ ac in E0 ðaÞ or in mn ðaÞ because the interaction of free and ST states near a ¼ ac is automatically included into the computational procedure. Another problem is concerned with excited polaron states. For a 3D strong coupling Pekar– . Frohlich polaron (long-range electron–phonon interaction) there exist a sequence of electronically excited states with excitation energies on the scale of the polaron binding energy [22]. These states that can be observed in the absorption spectra of
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polarons, should form wide resonances because of their multiphonon decay into the polaron ground state. Stable excited states should have their excitation energy less than _o0 ; _o0 being the phonon energy, and such states exist for both large 3D and 1D polarons [13,23]. For nondispersive phonons, in the strong coupling limit there exist an infinite number of such states that are traditionally considered as local phonon modes or the bound states of a polaron and a phonon (for a review, see Ref. [24]). Polarization of the electron cloud of the polaron by dynamic lattice deformation is the physical mechanism underlying the polaron– phonon coupling. Analytical theories cannot find the critical values of a when these polaron– phonon bound states disappear, these values being the branching points of the polaron spectrum. For a 1D Holstein polaron, the critical value of a for the lowest bound state was found numerically [25]. There is one more problem related to the ST barrier. Landau who initiated the concepts of ST and the ST barrier discussed them as applied to electrons in the ionic crystals like NaCl [26]. However, Pekar proved that in the course of the self-trapping of free electrons in ionic crystals the total energy decreases monotonically, i.e., the ST barrier does not exist for them [22]. Similar arguments are applicable to any particle in 1D. The existence of a ST barrier is typical of 3D systems with a short-range electron–phonon coupling, i.e., for electrons in nonpolar crystals and for excitons in crystals of any type [13]. Criteria of the analytical theory of the ST barrier are rather stringent because they should ensure both the applicability of the semiclassical description of phonons and the sufficient height W of the ST barrier, W b_o0 [16]. Therefore, it is remarkable that a detailed numerical study of the ST barrier for a Wannier–Mott exciton indicates that free states survive even when the ST barrier is as low as W ¼ 2_o0 ; they are no longer seen for W ¼ ð1=2Þ_o0 [27]. This study has also shown a considerable softening of local modes when the energies of free and ST excitons nearly coincide, a result that seems quite understandable because of the high polarizability of the system near the free to the ST exciton transition.
Interests of the communities working on polarons in unconventional materials and on excitons may converge also in the study of self-trapping from degenerate bands where the most interesting phenomenon is the spontaneous symmetry breaking of the ST states [28]. In the luminescence of excitons the symmetry breaking manifests itself in the emission from quasi-molecular ST states sideby-side with the emission from the quasi-atomic ST states [29].
7. Fractional quantum Hall effect At low temperatures, a 2D electron gas subject to a strong perpendicular magnetic field B passes as a function of B through a multitude of phases, the distinctive feature of which is the quantized Hall resistance. In these phases the 2D electrons are in incompressible states, gaps open in the electron energy spectrum, and the current is carried by Laughlin particles, quasi-electrons and quasi-holes, possessing fractional charges like en ¼ 7e=3; where e is the elementary charge. These quasi-particles obey fractional statistics and therefore are called ‘‘anyons’’. Magnetoresistance and the Hall effect have provided the basic information about these phases. However, optical studies also turned to be highly effective. One of the techniques is based on radiative recombination of the electrons from the 2D phase with photo-holes trapped on acceptors residing outside it [30]. Because the acceptors are neutral in the initial state, they do not perturb the 2D phase and serve as the probes. When the 2D gas passes through an incompressible state, the position of the emission band vs. the field B shows a cusp, and the cusp strength allows one to measure the gap [31]. Because the matrix element of the optical transition is controlled by the electron tunneling, it is small and the transition can be observed only in luminescence. If a 2D hole moves freely in a different 2D layer, and the ffiseparation between the layers d\2lB ; lB ¼ pffiffiffiffiffiffiffiffiffiffiffiffi c_=eB being the magnetic length, ‘‘anyon’’ excitons form. These are four-particle entities consisting of a hole bound to three quasi-electrons [32]. Their energy spectrum and optical properties
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differ strongly from the properties of usual 2D magnetoexcitons. Different ions of that type can also exist. Experiments with controlled layer separation d have been already initiated [33] but the observation of exciton-like entities including fractional charges is still elusive and remains a challenging problem. These experiments can be performed only in emission because of the small tunnel matrix element.
8. Spin-polarized electrons Many of the problems of the emerging field of spintronics [34], including development of the spin transistor [35] based on electron spin precession controlled by the external electric field via spin– orbit interaction [36], are based on the efficient spin injection into semiconductor microstructures. Control of spin polarization and alignment of free carriers and excitons through polarized luminescence has been developed in the experiments with optical pumping [37,38]. Similar techniques were recently applied to detection of spin injection into semiconductors through resistive spin-selective contacts [39–41]. Contemporary optical techniques based on femtosecond instrumentation for controlling the spin coherence were discussed in Ref. [42].
9. Conclusions From the theoretical point of view, the spectroscopy including absorption, luminescence, light scattering, nonlinear responses, etc., is a single indivisible field. Contemporary experimental techniques based on resonance excitation also wipe away the traditional differences between absorption, Raman scattering, and luminescence. Therefore, the term ‘‘secondary emission’’ is widely used for phenomena at the boundary of light scattering and luminescence. This unification of the spectroscopy is most evident for excitons because in the polariton picture [43,44] the absorption and fluorescence are described by the same process of polariton scattering. From this standpoint, lumi-
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nescence is a part of spectroscopy, just as spectroscopy is a part of physics. Nevertheless, with all these general concepts in mind, many problems can be significantly simplified by reducing them to more traditional terms. I have tried to show in this paper that the traditional concepts of luminescence are still highly productive as applied to a growing range of problems of the modern solid-state physics. At the level of the experiment, and especially as applied to the material science and technical applications, the eroding interfaces between different subfields of the spectroscopy are still visible enough to keep the notion of luminescence well defined.
Acknowledgements Support from DARPA/SPINS by the Office of Naval Research Grant N000140010819 is gratefully acknowledged.
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[16] A.S. Ioselevich, E.I. Rashba, in: Yu. Kagan, A.J. Leggett (Eds.), Quantum Tunneling, Elsevier, Amsterdam, 1992, p. 347. [17] M. Furukawa, K. Mizuno, A. Matsui, N. Tamai, I. Yamazaki, Chem. Phys. 138 (1989) 423. [18] A.S. Alexandrov, N.F. Mott, Rep. Prog. Phys. 57 (1994) 1197. [19] A.W. Romero, D.W. Brown, K. Lindenberg, J. Chem. Phys. 109 (1998) 6540. [20] E.I. Rashba, in: E.I. Rashba, M.D. Sturge (Eds.), Excitons, North-Holland, Amsterdam, 1982, p. 543. [21] L.-C. Ku, S.A. Trugman, J. Bon&ca, Phys. Rev. B 65 (2002) 174306. [22] S.I. Pekar, Research in the Electron Theory of Crystals, Gostekhizdat, Moscow, Leningrad, 1951 [English Translation: AEG, Division of Technical Information, Washington, DC, transl. series No. AEC-tr-5575 Physics]. [23] T. Holstein, Adv. Phys. 8 (1959) 325. [24] E.I. Rashba, Inst. Phys. Conf. Ser. 43 (1979) 1325; I.B. Levinson, E.I. Rashba, Sov. Phys.—Uspekhi 16 (1974) 892. [25] J. Bon&ca, S.A. Trugman, I. Batisti!c, Phys. Rev. B 60 (1999) 1633. [26] L.D. Landau, Phys. Zs. Sowjet. 3 (1933) 664. [27] A.S. Mishchenko, N. Nagaosa, N.V. Prokof’ev, A. Sakamoto, B.V. Svistunov, Phys. Rev. B 66 (2002) 020301. [28] F.V. Kusmartsev, E.I. Rashba, Sov. Phys.—JETP Lett. 33 (1981) 155. [29] I.Ya. Fugol’, Adv. Phys. 27 (1978) 1. [30] I.V. Kukushkin, V.B. Timifeev, Adv. Phys. 45 (1996) 147.
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Luminescence and spectroscopy Emmanuel I. Rashbaa,b,* a
Department of Physics, The State University of New York at Buffalo, Buffalo, NY 14260, USA b Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract The connection between luminescence and different chapters of spectroscopy is discussed. Modern theoretical concepts and experimental techniques wiped away the boundaries that traditionally existed between them. Nevertheless, the basic notions of luminescence remain valid. Being focused on the dynamics and kinetics of electronically excited states, luminescence serves as an effective tool in solving numerous problems in contemporary solid-state physics. Electron–phonon interaction, excitons in disordered systems, the emission spectroscopy of the fractional quantum Hall effect and spin injection are discussed as specific examples. r 2002 Elsevier Science B.V. All rights reserved. PACS: 71.35; 71.38; 71.70.E; 72.25; 73.43; 78.60 Keywords: Solid-state spectroscopy; Excitons; Electron–phonon interaction; Self-trapping; Polarons; Fractional quantum Hall effect; Spintronics
1. Introduction In this brief paper, I speculate about the interconnection between luminescence and spectroscopy mostly as applied to condensed matter physics. What unifies luminescence and absorption spectroscopy and what makes them different? Is the community studying them and converting their studies into new technologies a single community or do these people constitute two different communities? The Conference that brings these people together is currently named the International Conference on Luminescence and Optical Spectro*Corresponding author. Department of Physics, The State University of New York at Buffalo, Buffalo, NY 14260, USA. E-mail address: [email protected] (E.I. Rashba).
scopy of Condensed Matter; however, it emerged from the luminescence conferences and this birthmark still manifests itself in its logo ICL. If these fields have drawn nearer, in fact partly merged, do there still exist scientific problems that are specific for luminescence? The subtitle of the Journal of Luminescence, ‘‘research on excited state processes in condensed matter’’, added when Michael Sturge took over the editorship of the journal, answers most of those questions. I argue that fundamental studies in luminescence have the following main goals: first, investigating the kinetics of electronically excited states for finding the evolution of nonequilibrium populations; second, observing optical transitions that for different reasons cannot be seen in absorption. Taking some successful studies
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performed in the space of about 40 years as examples, I show that the luminescence technique was indispensable for them. Both luminescence and absorption spectroscopy have important applications that drive the research and are very diversified. The applications specific for both fields and the related experimental methods and technologies are also critical for establishing the connections and differences between them.
2. Why the two fields diverged? Every science has its own prehistory. However, it is a remarkable fact that the contemporary history of absorption and emission spectroscopy began simultaneously, from the same discoveries by Bunsen and Kirchhoff made in the middle of the 19th century. They observed atomic emission and absorption lines whose wavelengths exactly coincided. This discovery was applied by Stokes and Kirchhoff for the explanation of the Fraunhofer spectra. Nearly at the same time (1852), exactly 150 years ago, Stokes explained the conversion of absorbed ultraviolet light into the emitted blue light and introduced the term fluorescence. Apparently, the discovery of the Stokes shift marked the birth of luminescence as a science. The classical physics had no potential for describing optical spectra and, in particular, it established no common ground for the comparative study of the emission and absorption spectra. As a result, these spectroscopies ‘‘separated’’, and the people working in these fields formed different communities. In some places even bureaucratic barriers developed between them. 2.1. Two communities in the FSU In this section I will describe how these communities developed in the Former Soviet Union (FSU) because I know their history and belonged to them since the mid-1950s. However, the existence of separate journals and conferences in the West signifies that this division was not a local phenomenon.
In the l920–1930s, optical research in Moscow was led by two remarkable physicists, Leonid Mandelstam and Sergei Vavilov. Mandelstam and his collaborators focused on nonlinear vibrations. The research included radio engineering, optics, and even nonlinear differential equations. Despite the isolation from the West, this group achieved outstanding prominence. In 1928, Landsberg and Mandelstam discovered the inelastic light scattering nearly at the same time as Raman and Krishnan. Following the term they originally proposed, Raman scattering is traditionally called combination scattering in Russia. This strong tradition in nonlinear phenomena culminated in the Nobel Prize awarded to Basov and Prokhorov for the discovery of quantum generators (they shared it with Townes). Vavilov and his collaborators focused on luminescence and its practical applications. Their greatest scientific achievement was the discovery of $ the Cerenkov effect which, remarkably, has $ nothing to do with luminescence. Cerenkov (or Cherenkov, in modern spelling) and Vavilov shared the National Prize with Tamm and Frank who developed the theory. Three of them shared the Nobel Prize (1958) after Vavilov’s death in 1951. In the FSU, the Academy of Sciences was the body in charge of coordinating the development of science around the country. For this purpose, the Councils on different problems were established. According to those regulations, each of these two groups had its own Council, on spectroscopy and luminescence, respectively. Organizing all-union conferences became the main activity of these councils. Therefore, there were separate conferences on spectroscopy and on luminescence. Some people used to attend both conferences (and sometimes presented the same talks there) while other people attended only one of them. Gradually scientific arguments started to outweigh the bureaucratic ones. Atomic and molecular spectroscopy became the main subject of the spectroscopic conferences while the condensed matter community grouped around the luminescence conferences. Beginning from late 1950s when participation in international conferences became possible (but still
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horribly difficult for most of us) these councils became powerful bodies because they selected the groups that were sent by the Academy abroad to different conferences. Here the scientific differences between the spectroscopy and luminescence played absolutely no role. I was lucky to go to Western Europe for the first time in my life thanks to the Council on Spectroscopy that included me into a group sent to the conference on molecular spectroscopy in Liege (Belgium, 1969). The journal Optics and Spectroscopy, founded in 1956, covered from the very beginning a wide scope of problems including luminescence. It became very popular among chemists. The difference in materials became a watershed: papers on the spectroscopy of semiconductors were published mostly in Solid State Physics and Semiconductors. I complete this section with a note about the personal fate of both men who initiated the research in the spectroscopy and luminescence in the FSU. Nikolai Vavilov, the elder brother of S. Vavilov, was a renowned biologist and a founder and long time President of the Academy of Agriculture. However, in the late 1930s when the anti-genetic campaign led by pseudo-scientist Lysenko, which used practical gardener Michurin as its icon, gathered force, Vavilov lost his position. Finally, he was arrested and perished in prison in 1943. Two years later, in 1945, the same Government that destroyed Nikolai Vavilov nominated Sergei Vavilov for the President of the Academy of Sciences; election by Academicians was only a formality. Some people considered this nomination as one of Stalin’s sardonic jokes: ‘‘How will he behave after receiving such a good lesson?’’ Nevertheless, Vavilov’s behavior was courageous and honest. He invested a lot of efforts in saving physics from a pogrom after genetics was destroyed in 1948 and supported individuals who were in danger. Mandelstam died in time, as people used to say, in 1944. In accordance with the Academy’s regulations, his selected works were published. The 5th volume of the collection included his lectures on relativity and quantum mechanics. It appeared at a time when our philosophers (and
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some of the physicists who followed them) ‘‘criticized’’ these chapters of modern physics; hence, it was no surprise that ‘‘idealism’’ and similar heresies were found in the volume. A shameful posthumous inquisition trial over the 5th volume was staged. However, Mandelstam was already out of their reach.
3. Quantum unification Quantum mechanics established an intimate connection between the absorption and emission spectra. Squares of the matrix elements, jM j2 ; entering into the golden rule are equal for the direct and inverse processes because of the unitarity of the quantum mechanics. At a more phenomenological level, this connection manifests itself in the Einstein relation between the absorption and emission coefficients. This relation also clarifies the phenomena of spontaneous and induced optical transitions. If one disregards the photon population numbers, the transition probabilities are proportional to the products fi jMfi j2 ð1 ff Þ where fi and ff are the electron populations in the initial and the final states, respectively. Because M 2 ¼ jMfi j2 ; quantum mechanics unifies both if fields to the extent that, for the same transition, absorption and emission are described by equivalent formulae. Under these conditions, a comparative study of these spectra can provide information about the populations fi and ff and their dynamics. However, it is not unusual that either fi is too close to zero or ff is too close to unity; hence, the transition can be seen only in absorption or only in emission. Then both techniques provide complementary information.
4. Quasi-equilibrium luminescence In the early studies of luminescence from solids and molecules, it was usually assumed that phonon quasi-equilibrium is established during the electron excitation lifetime. Under these conditions, a theory of the multiphonon optical
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spectra of impurity centers has been developed in great detail (for a review, see Ref. [1]). It is important to note that when the electron–phonon coupling is strong, and, therefore, the Stokes shift is large, the transitions that can be seen in absorption and in emission usually correspond to different pairs of electron–phonon quantum levels. Indeed, multiphonon transitions dominate the spectra, so that at moderate temperature the number of phonons involved exceeds the Planck phonon population numbers. As a result, under conditions of quasi-equilibrium, where the overlap of the absorption and emission is relatively small, the data taken in the absorption and emission are mostly independent, and their comparison provides quite different information about the centers. Therefore, this basic model system provides a simple example of the complementarity between the information coming from the absorption and emission spectra.
5. Nonequilibrium luminescence Quasi-equilibrium in the electronically excited state is not universal. It can be established only if trel =trad 51where trel and trad are the relaxation time and radiative time, respectively. E.g., trel can be very long when excitations are trapped by spatially separated centers. Luminescent dating based on thermostimulated and optically stimulated luminescence makes possible the detection of accumulated radiation damage at the scale of 100,000 years. It became recently an effective method in archaeology [2]. However, even much more modest trel can provide a clue to the physical origin of the initial states. After the narrow lines at the edge of the fundamental absorption of Cu2O had been discovered and assigned to excitons [3,4], many lines observed in different semiconductors were ascribed to excitons despite the inconsistencies in their intensities, reproducibility, etc. A similar problem existed in the spectra of molecular crystals where exciton lines were discovered previously [5] and discussed in terms of Davydov multiplets [6]. In both cases the total number of
‘‘exciton’’ lines exceeded any reasonable theoretical expectations, and identification of the specific lines as intrinsic (free exciton) or extrinsic (caused by impurities and defects) was problematic. The solution of the problem came from low-T luminescence [7]. There is good reason to believe the populations of different free exciton states to be in quasi-equilibrium, while bound excitons trapped by spatially separated defects are expected to show much longer times trel : Therefore, emission bands having comparable intensities and separated by energies exceeding kB T should be treated as extrinsic, i.e., they should be assigned to bound excitons. Application of this simple criterion dramatically reduced the list of candidates for free exciton assignment. More powerful methods for distinguishing free and bound exciton lines for both Wannier–Mott [8,9] and molecular excitons [10] came later. The intensity of the bound exciton lines in absorption is proportional to the concentration of defects. Therefore, it was surprising that the absorption in these lines could be strong enough to compete with the intrinsic exciton absorption and confuse the line assignments. The giant oscillator strengths inherent in bound excitons were the origin of this seeming paradox [11]. The oscillator strength for bound exciton per single defect is a factor ðEB =Ebind Þ3=2 larger than the oscillator strength of a free exciton per unit cell, where EB is the exciton band width and Ebind is the binding energy of an exciton to the defect. For shallow levels, this factor is typically as large as 102 for molecular excitons and 104 for semiconductors. This factor caused confusion in line assignments and results in fast radiative decay of bound excitons, increasing their quantum yield. More recently, the strong dependence of trel on exciton energy has made it possible to prove the applicability of modern concepts of localization phenomena to excitons. The spectral dependence of the excitation spectrum of the exciton luminescence, the energy dependence of the homogeneous linewidth found from resonant Rayleigh scattering, and the exciton diffusivity measured by the transient grating technique resulted in discovering the Mott–Anderson localization of excitons and investigating its basic features, including the
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existence of the mobility edge and hopping spectral diffusion [12].
6. Self-trapping of excitons and related phenomena Luminescence makes it possible to follow the decay of different metastable states. One of the interesting systems of this kind are free excitons against the background of self-trapped (ST) excitons that are discussed in more detail below in this section. When the exciton–phonon interaction is strong enough, the energy of ST states is lower than the bottom of the free exciton band. Nevertheless, free states are protected by the potential barrier originating from lattice deformation and, therefore, coexist with the ST states [13,14]. In alkali halides and rare gas solids, the metastable free states are seen in absorption but only the ST states are usually seen in emission because of the fast scattering of free excitons by different defects into the ST states. It took about 20 years after the theoretical prediction of the coexistence of free and ST states when crystals of such a high quality were grown that the emission from the free states could be observed. More recently, the peak-to-peak ratio of the emission of free and ST excitons in Xe as large as 50 has been achieved [15]. This ratio for the free/ST emission is controlled not only by the decay rate of thermalized free excitons but also by branching in the relaxation of hot free excitons. Indeed, the hot excitons produced by light can either thermalize (and be self-trapped from the thermalized states) or relax directly into ST states [16]. This nontrivial relaxation of hot excitons bypassing the thermalization has been observed in pyrene [17]. In this problem the careful comparison of the absorption and emission spectra allowed one to assign the narrow and broad bands in these spectra and to discover the free and ST excitons. Recent active interest in polarons in high-Tc superconductors [18] and in colossal magnetoresistance materials, and also developing new powerful computational techniques (for comparison of the results found by different numerical methods, see Ref. [19]), resulted in drawing together the theoretical research on the self-trapping of charge
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carriers and excitons. The traditional theoretical work on the self-trapping phenomena, based on analytical techniques, provided the basic concepts and elucidated many related phenomena. New computational techniques permit one to formulate some problems more rigorously, to find interesting details that are out of reach of the analytical methods, and to establish the accuracy of these methods. Therefore, it is instructive to compare some of the results derived by these two different techniques, and the comparison shows that the results are in a quite satisfactory agreement. The dependence of the polaron ground state on the coupling constant a in systems of different dimensionality is the first example [13,20]. When the electron–phonon interaction is of a short-range type, then in three dimensions (3D) all adiabatic continuum theories predict a sharp changeover from the free particle to the ST particle ground state when a reaches some critical value ac (this is just the value of a when the ST barrier first emerges). The ground state energy E0 ðaÞ shows a cusp and the polaron effective mass mn ðaÞ changes abruptly at a ¼ ac ; but only if the decay of the metastable state is neglected. On the other hand, in 1D a similar theory results in a smooth dependence of the ground state on a: Quite inaccurately, the changeover in 3D is sometimes termed a ‘‘phase transition’’ despite the fact that there cannot be any phase transition in a single quasi-particle (polaron or exciton) system, hence, this term is confusing. A numerical theory of a polaron on a discrete lattice (Holstein model) results in a smooth dependence of m on a in 1D and in a steep increase in m near a ¼ ac in 3D [21], in agreement with the expectations based on the adiabatic theory. There are no singularities at a ¼ ac in E0 ðaÞ or in mn ðaÞ because the interaction of free and ST states near a ¼ ac is automatically included into the computational procedure. Another problem is concerned with excited polaron states. For a 3D strong coupling Pekar– . Frohlich polaron (long-range electron–phonon interaction) there exist a sequence of electronically excited states with excitation energies on the scale of the polaron binding energy [22]. These states that can be observed in the absorption spectra of
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polarons, should form wide resonances because of their multiphonon decay into the polaron ground state. Stable excited states should have their excitation energy less than _o0 ; _o0 being the phonon energy, and such states exist for both large 3D and 1D polarons [13,23]. For nondispersive phonons, in the strong coupling limit there exist an infinite number of such states that are traditionally considered as local phonon modes or the bound states of a polaron and a phonon (for a review, see Ref. [24]). Polarization of the electron cloud of the polaron by dynamic lattice deformation is the physical mechanism underlying the polaron– phonon coupling. Analytical theories cannot find the critical values of a when these polaron– phonon bound states disappear, these values being the branching points of the polaron spectrum. For a 1D Holstein polaron, the critical value of a for the lowest bound state was found numerically [25]. There is one more problem related to the ST barrier. Landau who initiated the concepts of ST and the ST barrier discussed them as applied to electrons in the ionic crystals like NaCl [26]. However, Pekar proved that in the course of the self-trapping of free electrons in ionic crystals the total energy decreases monotonically, i.e., the ST barrier does not exist for them [22]. Similar arguments are applicable to any particle in 1D. The existence of a ST barrier is typical of 3D systems with a short-range electron–phonon coupling, i.e., for electrons in nonpolar crystals and for excitons in crystals of any type [13]. Criteria of the analytical theory of the ST barrier are rather stringent because they should ensure both the applicability of the semiclassical description of phonons and the sufficient height W of the ST barrier, W b_o0 [16]. Therefore, it is remarkable that a detailed numerical study of the ST barrier for a Wannier–Mott exciton indicates that free states survive even when the ST barrier is as low as W ¼ 2_o0 ; they are no longer seen for W ¼ ð1=2Þ_o0 [27]. This study has also shown a considerable softening of local modes when the energies of free and ST excitons nearly coincide, a result that seems quite understandable because of the high polarizability of the system near the free to the ST exciton transition.
Interests of the communities working on polarons in unconventional materials and on excitons may converge also in the study of self-trapping from degenerate bands where the most interesting phenomenon is the spontaneous symmetry breaking of the ST states [28]. In the luminescence of excitons the symmetry breaking manifests itself in the emission from quasi-molecular ST states sideby-side with the emission from the quasi-atomic ST states [29].
7. Fractional quantum Hall effect At low temperatures, a 2D electron gas subject to a strong perpendicular magnetic field B passes as a function of B through a multitude of phases, the distinctive feature of which is the quantized Hall resistance. In these phases the 2D electrons are in incompressible states, gaps open in the electron energy spectrum, and the current is carried by Laughlin particles, quasi-electrons and quasi-holes, possessing fractional charges like en ¼ 7e=3; where e is the elementary charge. These quasi-particles obey fractional statistics and therefore are called ‘‘anyons’’. Magnetoresistance and the Hall effect have provided the basic information about these phases. However, optical studies also turned to be highly effective. One of the techniques is based on radiative recombination of the electrons from the 2D phase with photo-holes trapped on acceptors residing outside it [30]. Because the acceptors are neutral in the initial state, they do not perturb the 2D phase and serve as the probes. When the 2D gas passes through an incompressible state, the position of the emission band vs. the field B shows a cusp, and the cusp strength allows one to measure the gap [31]. Because the matrix element of the optical transition is controlled by the electron tunneling, it is small and the transition can be observed only in luminescence. If a 2D hole moves freely in a different 2D layer, and the ffiseparation between the layers d\2lB ; lB ¼ pffiffiffiffiffiffiffiffiffiffiffiffi c_=eB being the magnetic length, ‘‘anyon’’ excitons form. These are four-particle entities consisting of a hole bound to three quasi-electrons [32]. Their energy spectrum and optical properties
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differ strongly from the properties of usual 2D magnetoexcitons. Different ions of that type can also exist. Experiments with controlled layer separation d have been already initiated [33] but the observation of exciton-like entities including fractional charges is still elusive and remains a challenging problem. These experiments can be performed only in emission because of the small tunnel matrix element.
8. Spin-polarized electrons Many of the problems of the emerging field of spintronics [34], including development of the spin transistor [35] based on electron spin precession controlled by the external electric field via spin– orbit interaction [36], are based on the efficient spin injection into semiconductor microstructures. Control of spin polarization and alignment of free carriers and excitons through polarized luminescence has been developed in the experiments with optical pumping [37,38]. Similar techniques were recently applied to detection of spin injection into semiconductors through resistive spin-selective contacts [39–41]. Contemporary optical techniques based on femtosecond instrumentation for controlling the spin coherence were discussed in Ref. [42].
9. Conclusions From the theoretical point of view, the spectroscopy including absorption, luminescence, light scattering, nonlinear responses, etc., is a single indivisible field. Contemporary experimental techniques based on resonance excitation also wipe away the traditional differences between absorption, Raman scattering, and luminescence. Therefore, the term ‘‘secondary emission’’ is widely used for phenomena at the boundary of light scattering and luminescence. This unification of the spectroscopy is most evident for excitons because in the polariton picture [43,44] the absorption and fluorescence are described by the same process of polariton scattering. From this standpoint, lumi-
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nescence is a part of spectroscopy, just as spectroscopy is a part of physics. Nevertheless, with all these general concepts in mind, many problems can be significantly simplified by reducing them to more traditional terms. I have tried to show in this paper that the traditional concepts of luminescence are still highly productive as applied to a growing range of problems of the modern solid-state physics. At the level of the experiment, and especially as applied to the material science and technical applications, the eroding interfaces between different subfields of the spectroscopy are still visible enough to keep the notion of luminescence well defined.
Acknowledgements Support from DARPA/SPINS by the Office of Naval Research Grant N000140010819 is gratefully acknowledged.
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