- Email: [email protected]
Closing address
SURFACE
SCIENCE 37 (1973) 1002-1010 Q North-Holland
CLOSING
Publishing Co.
ADDRESS
B. 0. SERAPHIN Optical
Sciences
Center.
University
of Arizor!a,
Tucson, Arizona 85721, U.S.A.
Most of you have probably been to one or several of the International Semiconductor Conferences. The closing speaker at these conferences is supposed to address himself to the question: “Is semiconductor physics still sufficiently alive to warrant continuation of this type of conference?” He then assures the audience that this is indeed still the case and that everybody can confidently look forward to the next conference two years later. Fortunately, there is not yet a need for this ritual in modulation spectroscopy. This may very well be the first and the last conference at the same time. I will come back to this question at the end of my address. But if no second conference on modulation spectroscopy follows, it will not mean that the field is stagnating. Using the average number of discussion remarks per paper as a quantitative yardstick, you must have noticed that the results were more vigorously discussed than at comparable conferences. Those who have been in the field from the beginning were surprised how much it has expanded and has shown strong tendencies of a divergence into many different directions. It is exactly this surprising divergence that makes it so difficult to sum up the result of these four days. Any evaluation must necessarily be biased and one-sided. If much first-rate work is simply not mentioned, it is for the reason that it continues along lines that had been established before. Let us go back two years and choose as a baseline for evaluation the Semiconductor Conference in Boston, the first international conference at which modulation spectroscopy was represented on a sufficiently large scale. It was apparent at that time that an initial period had been completed in which much attention was focused on effects, on novel modulation techniques and applications, and on asomewhat superficial investigation of new materials. As shown clearly by this conference, the past two years have moved the field firmly into a second-generation phase in which the novelty has worn off, in which problems are probed in depth, and in which modulation methods are used in a study of the physics rather than in an occupation with the new tool itself. 1002
CLOSING
ADDRESS
1003
We have definitely overcome an initial period of disenchantment in which the problems of lineshape interpretation seemed to limit the usefulness of the new spectroscopy. We know, at least in the outlines, in what respect the theoretical tools were incomplete and in what respect the initial experiments were poor. The present position of modulation spectroscopy is one of cautious optimism. We have definitely passed the minimum, and confidence and initial enthusiasm are being restored. Greatly expanded theoretical concepts have made us aware of the factors that enter the lineshape. Experimental techniques have reached a degree of sophistication that permits the recording of spectra that can be interpreted with more confidence than before. Many of the widely spread applications reported here in the past four days are based on modulation mechanisms such as piezo-, thermo-, and wavelength or polarization modulation that are simpler and yield more easily to interpretation. If electroreflectance was left behind owing to the complexity of the lineshape, this is a temporary state of affairs. The papers at this conference have demonstrated how some of the previous discrepancies can be explained and how we arrive at a conceptual grasp of the basic mechanisms of electromodulation. The work of Aspnes and coworkers in particular provided the internal connection between the various mechanisms on the basis of their character as first- and third-derivative modulation. By dealing with the electrooptical effect in the framework of perturbation theory and nonlinear optics, a low-field version of the theory was developed that is rich in conceptual content and simplifies its application to band structure spectroscopy. We now realize that the same basic electro-optical effect manifests itself in lineshapes drastically different for the low-field, the intermediate, and the high-field case, respectively. We realize that the same field can generate different cases for different materials, for different experimental conditions, and for different spectral regions in the same material. We understand the sharpness of electroreflectance spectra and their emphasis on critical points. We understand how the various modulation mechanisms are related to each other and to the unperturbed state of the crystal and its nonlinear properties. Although of nontensorial character in its general form, we know now the conditions under which we can use a tensorial simplification of the theory, interpreting the low-field spectra on the familiar basis of piezo-optical analysis. This pioneering work is of great conceptual and practical consequence. If handled properly, the results will provide the basis for a solid-state analogy to the spectroscopy of atoms and molecules. The interpretation of low-field electroreflectance spectra of GaAs in terms of a set of band structure parameters indicates how closely we have already approached the goal of highresolution solid-state spectroscopy. However, a couple of comments are in order before overconfidence in
1004
B.O.SERAPHIN
quantitative lineshape interpretation runs the field into another crisis. We must first realize that the simplified interpretation is strictly tied to the conditions of the low-field case. Unless we are certain that these conditions prevail, which in most cases will require additional measurements and not just conclusions of circumstantial character, we cannot use the simplifications that the theory offers. Such abuse of the low-field theory could lead to a renewed rush into quantitative lineshape interpretations that resemble the old controversy of Franz-Keldysh theory versus exciton effects, We must second remind ourselves of the role of adjustable parameters in the interpretation. We are now aware of a whole set of interactions that affect the lineshape, and that we can account for them by adjusting their prefactors accordingly. If this curve fitting leads subsequently to a determination of band structure parameters by proper choice of these parameters, the result is probably irreievant. This is true in particular with respect to Coulomb interactions, as pointed out in the extended and penetrating discourses between Aspnes and Dow at the end of their respective reviews. We can proceed more safely if we separate the variables that determine the lineshape and search for invariants. The three-point adjustment of Aspnes and Rowe is a remarkable success in this search for invariants and leads to signi~cant results as shown by the study of the ~ontpeIlier group on mixed crystals. Symmetry analysis could be the final way out of all the difficulties encountered in lineshape interpretation. In its early, naive form it did not live up to the expectations and to the impressive examples set by magneto-optics, for instance. We begin to learn why this is so, however, and Rehn has shown in his review how to further improve naive symmetry analysis. It was a step in the right direction to recognize that in noncentrosymmetric crystals such as the III-V’s, a large first-order electroreflectance response is encountered with polarization anisotropies unrelated to critical point symmetries, which are coupled into the regular second-order electrorefiectance signature by inhomogeneous fields, strains, crystal imperfections, etc. Difficulties in an interpretation of transverse electroreflectance disappear, once these effects are properly considered. Here again, the discussion following Rehn’s review elaborates on the aspects in which the original naive symmetry analysis was oversimplified, and which must be improved in order to bring out its full potential. While this is a step in the right direction, we still have a long way to go. Looking at the papers presented here, it is noticeable how most interpretations still rely substantially on existing band structure calculations rather than providing an ah initio test on these models based on symmetry experiments. Polarization dependences are increasingly being used, but even in anisotropic systems such as the ternary chalcopyrites, controversies are eventually settled on the basis of non-symmetry-related arguments and on reliance on
CLOSING
ADDRESS
1005
band models. One is almost grateful for studies such as that by Shay and coworkers on materials like the I-III-VI’s compounds where band structure calculations have not yet caught up with experiment. It should by now be fairly obvious that this speaker is most impressed by the bandstructure-analytical potential of modulation spectroscopy. Of course, the field has developed tremendously beyond this first sprout, and the surprising spread became apparent by assembling everybody in one place. Let me at least superficially mention the most important of these new additions. The modulation spectroscopy of light scattering joins two fields that have the fundamental excitation process in common and also much of the theoretical concepts describing the influence of external perturbations on the scattering cross section. An electric field in particular affects the Raman scattering by an atomic displacement mechanism and a Franz-Keldysh mechanism. Because the interference of field-induced and allowed terms in the transition susceptibility leads to a modulated Raman scattering intensity proportional to the electric field, information can be obtained on surface conditions in a manner similar to that for surface barrier electroreflectance. It is gratifying, indeed, to have so many reports on the theoretical as well as the experimental aspects of this new combination presented here at the conference. In connection with impurity-induced Raman scattering, this may be the place to mention the modulation spectroscopy of localized excitations correlated with impurities and defects, as reviewed by Ltity. Interesting and stimulating reports came from the Finnish group on radiation damage introduced into GaAs, on impurity-state electroabsorption in oxygen-doped GaAs from Jonth and Bube, and on the modulation spectra involving localized and itinerant states in transition-metal oxides reported by the Santa Barbara group. There are a number of new modulation mechanisms, and the review by Cardona demonstrated how diversified the fringe areas of modulation spectroscopy can be. As new entries we can list studies of the response of properties other than reflectance and absorptance to a modulation of the fundamental absorption process. The interesting study of gold by modulated photoemission and the reports on modulated photoconductance can serve as examples. One can go one step further and investigate the effect of a modulation of the band structure on processes other than those involving the fundamental optical process. As examples we have heard reports on strain-modulated electron tunneling and on modulated beam-foil spectroscopy. Polarization modulation of magneto-optical spectra has provided a bridge that links up the advantages of both magneto-optical and modulation spectroscopy. It must be appreciated that electric-field effects in wavelength modulation spectroscopy begin to attract attention. Since the fist experimental investiga-
1006
B. 0. SERAPHIN
tions of the electroreflectance effect, it has been recognized that surface electric fields in a semiconductor or insulator could influence the values of optical “constants,” determined either directly by means of normal- or nonnormalincidence techniques or indirectly by means of first-derivative techniques. Yet in most such experimental measurements, electric field effects either have been ignored altogether or their neglect has been justified by extrapolating null results obtained in a limited spectral range on one material to a series of spectra on different materials. While field effects are negligible in many optical measurements, this is by no means always the case, the exact conditions being pointed out earlier this fall by Aspnes in cooperation with this speakerl). The study of the effects of carrier concentrations on the reflectivity spectrum reported here by the Berkeley group is at variance with our predictions but actually has little bearing on the effect of surface fields on wavelength modulation spectra. Samples of varying impurity concentrations result in variations of the surface field only if the Fermi level at the surface is locked by a high density of surface states - a condition that is fulfilled in Ge by very special preparation only. In general, in qualitatively different materials such as pure Ge and highly doped Ge, large differences in the bulk dielectric function will mask surface effects. These objections, together with an oversimplified analysis that uses 300 K parameters for 5 K experiments, make it appear that electric-field effects in wavelength modulation spectroscopy are experimentally still an open question. Optical and first-derivative modulation spectra ideally should be run on semiconductor samples in which the surface field is zero, or the surface field can be varied in a controlled manner. If this is not possible, then the surface field should be determined by some independent measurement such as field-effect conductance, photovoltaic response, or surface capacitance. The results of such a carefully surface-controlled experiment may assist in interpretations of dielectric function and first-derivative modulation spectra to the extent that these spectra will be even more informative than they are at present. While these effects recommend caution in the interpretation, the work by Wemple reminds us that there is in principle nothing in a wavelength modulation spectrum that cannot be retrieved from a carefully recorded static spectrum - a fact that tends to be hidden by the rich profile and the imaginative interpretation of some derivative spectra. Wemple’s result is as illuminating as that of Hoffmann who showed in 1968 on ZnO that electroreflectance is really nothing else but the difference between the reflectance with and without the electric surface field. One of the most significant additions to the field is the use of optical modulation techniques in investigations of solid-state phase transitions and the influence of these transitions on the electronic structure. Their abrupt or
CLOSING
continuous
nature
in paraelectric,
1007
ADDRESS
ferroelectric,
and ferromagnetic
materials
and the coexistence of different phases is elucidated through the high resolution of modulation spectroscopy. The influence of magnetic short-range order in the vicinity of the magnetic ordering temperature is the main subject of studies in which the polarization modulation has been successful. High resolution and anisotropic response to different directions of polarization permits the decomposition of rich sets of structure into their origin according to different types of optical transitions. Undoubtedly, the modulation spectroscopy of phase transitions reported here for the first time on a large scale is only the beginning of a field that has great promise and that will expand accordingly. After years of struggling, modulated surface spectroscopy has come to adulthood as demonstrated by the large number of papers at this conference. A refinement of the methods, as reviewed in Heiland’s talk, now permits a detailed diagnosis of surface layers with respect to their composition, prevalent orientation of adsorbants, concentration, and the parameters of the reaction kinetics. One arrives at a quantitative understanding of surface reactions such as passivation and corrosion processes. In view of the large technological significance of these processes, it can be expected that modulated surface spectroscopy will further expand together with such studies as the ones on doping inhomogeneities reported by Sittig or field inhomogeneities reported by members of the Frova group. A great effort by various laboratories, in particular by McIntyre at Bell and by the groups in Cleveland and in Nice, has brought us closer to an interpretation of the electroreflectance spectra of metals and of processes at the metal-electrolyte interface. The observed spectra, for years a rather controversial issue, can be interpreted in terms of free-carrier effects that hide the interband transition. It will be a challenge to the experimentalist to suppress one in favor of the other. In spite of an impressive spread of optical modulation techniques into a variety of different fields, there is one glaring omission in the program that needs pointing out strongly: modulation spectroscopy of disordered solids is largely a white spot on our map that invites exploration. We are fortunate to have with Fritzsche, Paul, and Taut (Stuke had to cancel for health reasons) the main contributors to the physics of disordered solids present here at our conference; we hope that they will initiate some bridge-building at their end of the gap. Let us try to evaluate the situation and characterize where we stand on the subject of a modulation spectroscopy of disordered solids. The optical properties of a solid reflect essentially the density of states, if reasonable assumptions about the transition probability between these states can be made. Much of what is known about the electronic structure of crystals was derived from the interpretation of optical measurements.
1008
8.0.
SERAPHIN
Modulation spectroscopy has added considerably to this diagnostic potential by correlating more clearly the structure in modulated spectra to discontinuities in the electronic structure. Static optical spectroscopy has been extended to disordered solids with similar success to confirm the persisting importance of the density-of-states function. Observation of sharp absorption edges and related phenomena in amorphous semiconductors has stimulated much recent theoretical effort, to give just one example2). While the persistence of the concept of a density-of-state function in the disordered phase is generally accepted, it is not immediately obvious that the discontinuities of this function should also persist. If we now tie modulation spectroscopy closely to these discontinuities, we obtain exactly the psychological barrier that has stopped the modulation spectroscopy of disordered solids from getting a start. The premise needs correction on both counts. True, the Van Hove singularities are tied to the periodicity of the crystalline system. Structure in the optical spectra of crystals is determined by singularities in the joint densityof-state function, whereas spectra of disordered systems reflect convolutions of single band densities-of-state. However, this does not imply the disappearance of discontinuities in the single-band profile. The fact that band edges are sharp, for instance, is emerging more and more clearly from the data3), whether this be a result of a mobility edge or reflecting the sharpness of the actual density-of-state profile. Turning to the second premise, it must be pointed out that recent developments in modulation spectroscopy have expanded its initial interpretation exclusively in terms of critical points. In particular the recent work of Aspnes and coworkers has classified modulation effects with respect to their firstderivative and third-derivative nature and has established correlations between the various effects. The critical-point nature of the band structure region in which the response originates takes second place in this interpretation. Modulation of first-derivative nature such as observed in piezo- and thermoreflectance depends on deformation-potential features rather than on the singular character of the interband density-of-state function, for instance. Experimental results on a variety of disordered solids support this theoretical viewpoint. Most prominent is the large volume of mainly electroreflectante work on mixed-crystal systems 5, that in this context figure as disordered alloys with long-range structural order - a model that serves as a vehicle for most theoretical work on the subject”). In the disordered state of fractional composition, the modulated spectra are still sharp and only slightly broadened compared with the spectra of the pure crystalline phase on either end of the compositional range. Because these spectra are considerably sharper than the
CLOSING
structure
in static reflectance,
ADDRESS
they serve as experimental
1009
input for models that
deal with a random occupation of the atomic sites. According to a theory of Van Vechten and Bergstresser7), the influence of disorder can be read out from the “bowing parameter” quantitatively with the result that disorder must be taken into account for an interpretation of the data*). The conclusion is apparent: While we cannot interpret compositional shifts and spectral location of structure without admitting disorder, the disorder is on the other hand not able to broaden this structure to any significant extent. The loss of long-range order as given by the random occupation of the sites is not equivalent to disappearance of the modulated spectrum. Electroreflectance work on systems of positional disorder such as the elemental semiconductors Ge and Se gives further support g). Early work on Ge films evaporated on substrates of different temperature shows electroreflectance response to persist into the amorphous phase in the spectral region of the fundamental response of the crystalline phase, whereas all response in the spectral regions of higher interband transitions disappears at the crystalline-amorphous phase transition. Because at that time the effect of the substrate temperature on the density of the film was not yet known, the mass-monitored deposition resulted in films of different thickness. As a consequence, it has been speculated’ O) that the observed response is due to interference effects based on photogenerated free carriers. However, this speculation misses the mark for at least two reasons. Interference effects have carefully been monitored in the original work with the result that the electroreflectance response does not depend upon the presence or the spectral position of interference fringes. If, on the other hand, photoexcited free carriers are held responsible for the electro-optical modulation observed, one arrives at either densities or optical cross sections for these carriers that are not supported by any experimental results. Later and more refined work has essentially confirmed the conclusions drawn from the early study and will be published shortly by Piller and coworkersl’). It most be concluded that the electroreflectance response of amorphous Ge films between 0.6 and 1.O eV is not an artifact but reflects the response to the electric-field perturbation of a band edge that is reasonably discontinuous due to the bond-antibond character of the fundamental gap. Electroreflectance spectra observed on amorphous Se by Stuke and Weiser12) are in line with the findings on Ge. The response persists into the amorphous state for the spectral region of the fundamental edge but disappears for higher interband transitions. This result was much more readily accepted than the identical observation in amorphous Ge, proving the influence of periodicity-conditioned theoretical models. For Se, it was easier to shake off the critical-point concept and find an explanation based on
1010
B. 0. SERAPHIN
excitons coupled to the suspected ring structure of the amorphous phase of Se. In summing up the experimental situation, it is apparent that the existing results of modulated spectroscopy of disordered systems lack volume and depth. This may in part be due to a material preparation that only recently has developed reliable criteria for characterization and reproducibility. However, theoretical concepts must take greater blame by not providing the basis for a modulation spectroscopy that was understood essentially as a critical-point phenomenon. Recent developments changed the premise, and we can expect modulation spectroscopy to be as helpful in the diagnosis of the electronic structure of disordered solids as it has started to be in that of crystals. I am at the end of my closing address. The prognosis for modulation spectroscopy must be considered very good. It is firmly entrenched among the major experimental methods of solid-state physics. Contributions were made to a variety of topics that could not have been made by any other method. Recalling the review by Phillips that led off this conference, we can expect major contributions in particular to material science, to the chemistry of optical processes in solids, and their response to the variations and perturbations that are characteristic for modulation spectroscopy. To the new sophisticated and elaborate theoretical concepts that correlate chemical trends with phase transitions and optical constants, modulation spectroscopy will give much of the experimental verification by providing spectroscopic inputs of high quality. While all the various modulation methods are safe from extinction and oblivion, we must ask the question : Is there enough of a common ground to keep them together as the various branches of “modulation spectroscopy?” Is the internal bond strong enough to counteract the diverging tendencies, the spread into widely separated directions that the program of this conference reflects? The question is difficult to answer at this time. The field is spreading so vigorously, however, that the answer will come all by itself and within the next two to three years. By the time the next conference comes around (there are plans to hold it in Italy in 1975) we will know whether it is worthwhile to emphasize the ancestry that modulated band structure spectroscopy, modulated surface spectroscopy, modulated Raman spectroscopy, modulated spectroscopy of phase transitions, etc. have in common. Thank you very much for coming to Tucson and making these last four days so exciting, profitable, and pleasant. I hope you also had a good time. Have a good trip home! References 1) B. 0. Seraphin and D. E. Aspnes, Phys. Rev. B 6 (1972) 3158. 2) D. Adler, in: Critical Reviews in Solid State Sciences, Vol. 2 (1971) p. 317; H. Ehrenreich, National Materials Advisory Board, Report 284 (1971);
CLOSING
3) 4) 5) 6)
7) 8) 9) 10) 11) 12)
ADDRESS
1011
W. Paul, in: Proc. Eleventh Intern. Conf. Pysics of Semiconductors, Warsaw, 1972 (to be published); H. Fritzsche, in: Electronic Properties of Amorphous Semiconductors, Ed. J. Taut (Plenum, New York, 1972). T. M. Donovan and W. E. Spicer, Phys. Rev. Letters 21(1968) 1572. D. E. Aspnes and J. E. Rowe, Phys. Rev. Letters 27 (1971) 188. S. S. Vishnubhatla, B. Eyglunent and J. C. Wooley, Can. J. Phys. 47 (1969) 1661. E. N. Economou, S. Kirkpatrick, M. H. Cohen and T. P. Eggarter, Phys. Rev. Letters 25 (1970) 520; E. N. Economou and M. H. Cohen, Phys. Rev. Letters 25 (1970) 1445. J. A. Van Vechten and T. K. Bergstresser, Phys. Rev. B 1 (1970) 3351. C. Alibert and G. Bordure, A. Laugier and J. Chevalher, Phys. Rev. B 6 (1972) 1301. H. Piller, B. 0. Seraphin, K. Markel and J. E. Fischer, Phys. Rev. Letters 23 (1969) 775. J. E. Fischer, Phys. Rev. Letters 27 (1971) 1131. H. Piller and R. Whited, Solid State Commun. (in print). G. Weiser and J. Stuke, Phys. Status Solidi 35 (1969) 747.
SCIENCE 37 (1973) 1002-1010 Q North-Holland
CLOSING
Publishing Co.
ADDRESS
B. 0. SERAPHIN Optical
Sciences
Center.
University
of Arizor!a,
Tucson, Arizona 85721, U.S.A.
Most of you have probably been to one or several of the International Semiconductor Conferences. The closing speaker at these conferences is supposed to address himself to the question: “Is semiconductor physics still sufficiently alive to warrant continuation of this type of conference?” He then assures the audience that this is indeed still the case and that everybody can confidently look forward to the next conference two years later. Fortunately, there is not yet a need for this ritual in modulation spectroscopy. This may very well be the first and the last conference at the same time. I will come back to this question at the end of my address. But if no second conference on modulation spectroscopy follows, it will not mean that the field is stagnating. Using the average number of discussion remarks per paper as a quantitative yardstick, you must have noticed that the results were more vigorously discussed than at comparable conferences. Those who have been in the field from the beginning were surprised how much it has expanded and has shown strong tendencies of a divergence into many different directions. It is exactly this surprising divergence that makes it so difficult to sum up the result of these four days. Any evaluation must necessarily be biased and one-sided. If much first-rate work is simply not mentioned, it is for the reason that it continues along lines that had been established before. Let us go back two years and choose as a baseline for evaluation the Semiconductor Conference in Boston, the first international conference at which modulation spectroscopy was represented on a sufficiently large scale. It was apparent at that time that an initial period had been completed in which much attention was focused on effects, on novel modulation techniques and applications, and on asomewhat superficial investigation of new materials. As shown clearly by this conference, the past two years have moved the field firmly into a second-generation phase in which the novelty has worn off, in which problems are probed in depth, and in which modulation methods are used in a study of the physics rather than in an occupation with the new tool itself. 1002
CLOSING
ADDRESS
1003
We have definitely overcome an initial period of disenchantment in which the problems of lineshape interpretation seemed to limit the usefulness of the new spectroscopy. We know, at least in the outlines, in what respect the theoretical tools were incomplete and in what respect the initial experiments were poor. The present position of modulation spectroscopy is one of cautious optimism. We have definitely passed the minimum, and confidence and initial enthusiasm are being restored. Greatly expanded theoretical concepts have made us aware of the factors that enter the lineshape. Experimental techniques have reached a degree of sophistication that permits the recording of spectra that can be interpreted with more confidence than before. Many of the widely spread applications reported here in the past four days are based on modulation mechanisms such as piezo-, thermo-, and wavelength or polarization modulation that are simpler and yield more easily to interpretation. If electroreflectance was left behind owing to the complexity of the lineshape, this is a temporary state of affairs. The papers at this conference have demonstrated how some of the previous discrepancies can be explained and how we arrive at a conceptual grasp of the basic mechanisms of electromodulation. The work of Aspnes and coworkers in particular provided the internal connection between the various mechanisms on the basis of their character as first- and third-derivative modulation. By dealing with the electrooptical effect in the framework of perturbation theory and nonlinear optics, a low-field version of the theory was developed that is rich in conceptual content and simplifies its application to band structure spectroscopy. We now realize that the same basic electro-optical effect manifests itself in lineshapes drastically different for the low-field, the intermediate, and the high-field case, respectively. We realize that the same field can generate different cases for different materials, for different experimental conditions, and for different spectral regions in the same material. We understand the sharpness of electroreflectance spectra and their emphasis on critical points. We understand how the various modulation mechanisms are related to each other and to the unperturbed state of the crystal and its nonlinear properties. Although of nontensorial character in its general form, we know now the conditions under which we can use a tensorial simplification of the theory, interpreting the low-field spectra on the familiar basis of piezo-optical analysis. This pioneering work is of great conceptual and practical consequence. If handled properly, the results will provide the basis for a solid-state analogy to the spectroscopy of atoms and molecules. The interpretation of low-field electroreflectance spectra of GaAs in terms of a set of band structure parameters indicates how closely we have already approached the goal of highresolution solid-state spectroscopy. However, a couple of comments are in order before overconfidence in
1004
B.O.SERAPHIN
quantitative lineshape interpretation runs the field into another crisis. We must first realize that the simplified interpretation is strictly tied to the conditions of the low-field case. Unless we are certain that these conditions prevail, which in most cases will require additional measurements and not just conclusions of circumstantial character, we cannot use the simplifications that the theory offers. Such abuse of the low-field theory could lead to a renewed rush into quantitative lineshape interpretations that resemble the old controversy of Franz-Keldysh theory versus exciton effects, We must second remind ourselves of the role of adjustable parameters in the interpretation. We are now aware of a whole set of interactions that affect the lineshape, and that we can account for them by adjusting their prefactors accordingly. If this curve fitting leads subsequently to a determination of band structure parameters by proper choice of these parameters, the result is probably irreievant. This is true in particular with respect to Coulomb interactions, as pointed out in the extended and penetrating discourses between Aspnes and Dow at the end of their respective reviews. We can proceed more safely if we separate the variables that determine the lineshape and search for invariants. The three-point adjustment of Aspnes and Rowe is a remarkable success in this search for invariants and leads to signi~cant results as shown by the study of the ~ontpeIlier group on mixed crystals. Symmetry analysis could be the final way out of all the difficulties encountered in lineshape interpretation. In its early, naive form it did not live up to the expectations and to the impressive examples set by magneto-optics, for instance. We begin to learn why this is so, however, and Rehn has shown in his review how to further improve naive symmetry analysis. It was a step in the right direction to recognize that in noncentrosymmetric crystals such as the III-V’s, a large first-order electroreflectance response is encountered with polarization anisotropies unrelated to critical point symmetries, which are coupled into the regular second-order electrorefiectance signature by inhomogeneous fields, strains, crystal imperfections, etc. Difficulties in an interpretation of transverse electroreflectance disappear, once these effects are properly considered. Here again, the discussion following Rehn’s review elaborates on the aspects in which the original naive symmetry analysis was oversimplified, and which must be improved in order to bring out its full potential. While this is a step in the right direction, we still have a long way to go. Looking at the papers presented here, it is noticeable how most interpretations still rely substantially on existing band structure calculations rather than providing an ah initio test on these models based on symmetry experiments. Polarization dependences are increasingly being used, but even in anisotropic systems such as the ternary chalcopyrites, controversies are eventually settled on the basis of non-symmetry-related arguments and on reliance on
CLOSING
ADDRESS
1005
band models. One is almost grateful for studies such as that by Shay and coworkers on materials like the I-III-VI’s compounds where band structure calculations have not yet caught up with experiment. It should by now be fairly obvious that this speaker is most impressed by the bandstructure-analytical potential of modulation spectroscopy. Of course, the field has developed tremendously beyond this first sprout, and the surprising spread became apparent by assembling everybody in one place. Let me at least superficially mention the most important of these new additions. The modulation spectroscopy of light scattering joins two fields that have the fundamental excitation process in common and also much of the theoretical concepts describing the influence of external perturbations on the scattering cross section. An electric field in particular affects the Raman scattering by an atomic displacement mechanism and a Franz-Keldysh mechanism. Because the interference of field-induced and allowed terms in the transition susceptibility leads to a modulated Raman scattering intensity proportional to the electric field, information can be obtained on surface conditions in a manner similar to that for surface barrier electroreflectance. It is gratifying, indeed, to have so many reports on the theoretical as well as the experimental aspects of this new combination presented here at the conference. In connection with impurity-induced Raman scattering, this may be the place to mention the modulation spectroscopy of localized excitations correlated with impurities and defects, as reviewed by Ltity. Interesting and stimulating reports came from the Finnish group on radiation damage introduced into GaAs, on impurity-state electroabsorption in oxygen-doped GaAs from Jonth and Bube, and on the modulation spectra involving localized and itinerant states in transition-metal oxides reported by the Santa Barbara group. There are a number of new modulation mechanisms, and the review by Cardona demonstrated how diversified the fringe areas of modulation spectroscopy can be. As new entries we can list studies of the response of properties other than reflectance and absorptance to a modulation of the fundamental absorption process. The interesting study of gold by modulated photoemission and the reports on modulated photoconductance can serve as examples. One can go one step further and investigate the effect of a modulation of the band structure on processes other than those involving the fundamental optical process. As examples we have heard reports on strain-modulated electron tunneling and on modulated beam-foil spectroscopy. Polarization modulation of magneto-optical spectra has provided a bridge that links up the advantages of both magneto-optical and modulation spectroscopy. It must be appreciated that electric-field effects in wavelength modulation spectroscopy begin to attract attention. Since the fist experimental investiga-
1006
B. 0. SERAPHIN
tions of the electroreflectance effect, it has been recognized that surface electric fields in a semiconductor or insulator could influence the values of optical “constants,” determined either directly by means of normal- or nonnormalincidence techniques or indirectly by means of first-derivative techniques. Yet in most such experimental measurements, electric field effects either have been ignored altogether or their neglect has been justified by extrapolating null results obtained in a limited spectral range on one material to a series of spectra on different materials. While field effects are negligible in many optical measurements, this is by no means always the case, the exact conditions being pointed out earlier this fall by Aspnes in cooperation with this speakerl). The study of the effects of carrier concentrations on the reflectivity spectrum reported here by the Berkeley group is at variance with our predictions but actually has little bearing on the effect of surface fields on wavelength modulation spectra. Samples of varying impurity concentrations result in variations of the surface field only if the Fermi level at the surface is locked by a high density of surface states - a condition that is fulfilled in Ge by very special preparation only. In general, in qualitatively different materials such as pure Ge and highly doped Ge, large differences in the bulk dielectric function will mask surface effects. These objections, together with an oversimplified analysis that uses 300 K parameters for 5 K experiments, make it appear that electric-field effects in wavelength modulation spectroscopy are experimentally still an open question. Optical and first-derivative modulation spectra ideally should be run on semiconductor samples in which the surface field is zero, or the surface field can be varied in a controlled manner. If this is not possible, then the surface field should be determined by some independent measurement such as field-effect conductance, photovoltaic response, or surface capacitance. The results of such a carefully surface-controlled experiment may assist in interpretations of dielectric function and first-derivative modulation spectra to the extent that these spectra will be even more informative than they are at present. While these effects recommend caution in the interpretation, the work by Wemple reminds us that there is in principle nothing in a wavelength modulation spectrum that cannot be retrieved from a carefully recorded static spectrum - a fact that tends to be hidden by the rich profile and the imaginative interpretation of some derivative spectra. Wemple’s result is as illuminating as that of Hoffmann who showed in 1968 on ZnO that electroreflectance is really nothing else but the difference between the reflectance with and without the electric surface field. One of the most significant additions to the field is the use of optical modulation techniques in investigations of solid-state phase transitions and the influence of these transitions on the electronic structure. Their abrupt or
CLOSING
continuous
nature
in paraelectric,
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ADDRESS
ferroelectric,
and ferromagnetic
materials
and the coexistence of different phases is elucidated through the high resolution of modulation spectroscopy. The influence of magnetic short-range order in the vicinity of the magnetic ordering temperature is the main subject of studies in which the polarization modulation has been successful. High resolution and anisotropic response to different directions of polarization permits the decomposition of rich sets of structure into their origin according to different types of optical transitions. Undoubtedly, the modulation spectroscopy of phase transitions reported here for the first time on a large scale is only the beginning of a field that has great promise and that will expand accordingly. After years of struggling, modulated surface spectroscopy has come to adulthood as demonstrated by the large number of papers at this conference. A refinement of the methods, as reviewed in Heiland’s talk, now permits a detailed diagnosis of surface layers with respect to their composition, prevalent orientation of adsorbants, concentration, and the parameters of the reaction kinetics. One arrives at a quantitative understanding of surface reactions such as passivation and corrosion processes. In view of the large technological significance of these processes, it can be expected that modulated surface spectroscopy will further expand together with such studies as the ones on doping inhomogeneities reported by Sittig or field inhomogeneities reported by members of the Frova group. A great effort by various laboratories, in particular by McIntyre at Bell and by the groups in Cleveland and in Nice, has brought us closer to an interpretation of the electroreflectance spectra of metals and of processes at the metal-electrolyte interface. The observed spectra, for years a rather controversial issue, can be interpreted in terms of free-carrier effects that hide the interband transition. It will be a challenge to the experimentalist to suppress one in favor of the other. In spite of an impressive spread of optical modulation techniques into a variety of different fields, there is one glaring omission in the program that needs pointing out strongly: modulation spectroscopy of disordered solids is largely a white spot on our map that invites exploration. We are fortunate to have with Fritzsche, Paul, and Taut (Stuke had to cancel for health reasons) the main contributors to the physics of disordered solids present here at our conference; we hope that they will initiate some bridge-building at their end of the gap. Let us try to evaluate the situation and characterize where we stand on the subject of a modulation spectroscopy of disordered solids. The optical properties of a solid reflect essentially the density of states, if reasonable assumptions about the transition probability between these states can be made. Much of what is known about the electronic structure of crystals was derived from the interpretation of optical measurements.
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8.0.
SERAPHIN
Modulation spectroscopy has added considerably to this diagnostic potential by correlating more clearly the structure in modulated spectra to discontinuities in the electronic structure. Static optical spectroscopy has been extended to disordered solids with similar success to confirm the persisting importance of the density-of-states function. Observation of sharp absorption edges and related phenomena in amorphous semiconductors has stimulated much recent theoretical effort, to give just one example2). While the persistence of the concept of a density-of-state function in the disordered phase is generally accepted, it is not immediately obvious that the discontinuities of this function should also persist. If we now tie modulation spectroscopy closely to these discontinuities, we obtain exactly the psychological barrier that has stopped the modulation spectroscopy of disordered solids from getting a start. The premise needs correction on both counts. True, the Van Hove singularities are tied to the periodicity of the crystalline system. Structure in the optical spectra of crystals is determined by singularities in the joint densityof-state function, whereas spectra of disordered systems reflect convolutions of single band densities-of-state. However, this does not imply the disappearance of discontinuities in the single-band profile. The fact that band edges are sharp, for instance, is emerging more and more clearly from the data3), whether this be a result of a mobility edge or reflecting the sharpness of the actual density-of-state profile. Turning to the second premise, it must be pointed out that recent developments in modulation spectroscopy have expanded its initial interpretation exclusively in terms of critical points. In particular the recent work of Aspnes and coworkers has classified modulation effects with respect to their firstderivative and third-derivative nature and has established correlations between the various effects. The critical-point nature of the band structure region in which the response originates takes second place in this interpretation. Modulation of first-derivative nature such as observed in piezo- and thermoreflectance depends on deformation-potential features rather than on the singular character of the interband density-of-state function, for instance. Experimental results on a variety of disordered solids support this theoretical viewpoint. Most prominent is the large volume of mainly electroreflectante work on mixed-crystal systems 5, that in this context figure as disordered alloys with long-range structural order - a model that serves as a vehicle for most theoretical work on the subject”). In the disordered state of fractional composition, the modulated spectra are still sharp and only slightly broadened compared with the spectra of the pure crystalline phase on either end of the compositional range. Because these spectra are considerably sharper than the
CLOSING
structure
in static reflectance,
ADDRESS
they serve as experimental
1009
input for models that
deal with a random occupation of the atomic sites. According to a theory of Van Vechten and Bergstresser7), the influence of disorder can be read out from the “bowing parameter” quantitatively with the result that disorder must be taken into account for an interpretation of the data*). The conclusion is apparent: While we cannot interpret compositional shifts and spectral location of structure without admitting disorder, the disorder is on the other hand not able to broaden this structure to any significant extent. The loss of long-range order as given by the random occupation of the sites is not equivalent to disappearance of the modulated spectrum. Electroreflectance work on systems of positional disorder such as the elemental semiconductors Ge and Se gives further support g). Early work on Ge films evaporated on substrates of different temperature shows electroreflectance response to persist into the amorphous phase in the spectral region of the fundamental response of the crystalline phase, whereas all response in the spectral regions of higher interband transitions disappears at the crystalline-amorphous phase transition. Because at that time the effect of the substrate temperature on the density of the film was not yet known, the mass-monitored deposition resulted in films of different thickness. As a consequence, it has been speculated’ O) that the observed response is due to interference effects based on photogenerated free carriers. However, this speculation misses the mark for at least two reasons. Interference effects have carefully been monitored in the original work with the result that the electroreflectance response does not depend upon the presence or the spectral position of interference fringes. If, on the other hand, photoexcited free carriers are held responsible for the electro-optical modulation observed, one arrives at either densities or optical cross sections for these carriers that are not supported by any experimental results. Later and more refined work has essentially confirmed the conclusions drawn from the early study and will be published shortly by Piller and coworkersl’). It most be concluded that the electroreflectance response of amorphous Ge films between 0.6 and 1.O eV is not an artifact but reflects the response to the electric-field perturbation of a band edge that is reasonably discontinuous due to the bond-antibond character of the fundamental gap. Electroreflectance spectra observed on amorphous Se by Stuke and Weiser12) are in line with the findings on Ge. The response persists into the amorphous state for the spectral region of the fundamental edge but disappears for higher interband transitions. This result was much more readily accepted than the identical observation in amorphous Ge, proving the influence of periodicity-conditioned theoretical models. For Se, it was easier to shake off the critical-point concept and find an explanation based on
1010
B. 0. SERAPHIN
excitons coupled to the suspected ring structure of the amorphous phase of Se. In summing up the experimental situation, it is apparent that the existing results of modulated spectroscopy of disordered systems lack volume and depth. This may in part be due to a material preparation that only recently has developed reliable criteria for characterization and reproducibility. However, theoretical concepts must take greater blame by not providing the basis for a modulation spectroscopy that was understood essentially as a critical-point phenomenon. Recent developments changed the premise, and we can expect modulation spectroscopy to be as helpful in the diagnosis of the electronic structure of disordered solids as it has started to be in that of crystals. I am at the end of my closing address. The prognosis for modulation spectroscopy must be considered very good. It is firmly entrenched among the major experimental methods of solid-state physics. Contributions were made to a variety of topics that could not have been made by any other method. Recalling the review by Phillips that led off this conference, we can expect major contributions in particular to material science, to the chemistry of optical processes in solids, and their response to the variations and perturbations that are characteristic for modulation spectroscopy. To the new sophisticated and elaborate theoretical concepts that correlate chemical trends with phase transitions and optical constants, modulation spectroscopy will give much of the experimental verification by providing spectroscopic inputs of high quality. While all the various modulation methods are safe from extinction and oblivion, we must ask the question : Is there enough of a common ground to keep them together as the various branches of “modulation spectroscopy?” Is the internal bond strong enough to counteract the diverging tendencies, the spread into widely separated directions that the program of this conference reflects? The question is difficult to answer at this time. The field is spreading so vigorously, however, that the answer will come all by itself and within the next two to three years. By the time the next conference comes around (there are plans to hold it in Italy in 1975) we will know whether it is worthwhile to emphasize the ancestry that modulated band structure spectroscopy, modulated surface spectroscopy, modulated Raman spectroscopy, modulated spectroscopy of phase transitions, etc. have in common. Thank you very much for coming to Tucson and making these last four days so exciting, profitable, and pleasant. I hope you also had a good time. Have a good trip home! References 1) B. 0. Seraphin and D. E. Aspnes, Phys. Rev. B 6 (1972) 3158. 2) D. Adler, in: Critical Reviews in Solid State Sciences, Vol. 2 (1971) p. 317; H. Ehrenreich, National Materials Advisory Board, Report 284 (1971);
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3) 4) 5) 6)
7) 8) 9) 10) 11) 12)
ADDRESS
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W. Paul, in: Proc. Eleventh Intern. Conf. Pysics of Semiconductors, Warsaw, 1972 (to be published); H. Fritzsche, in: Electronic Properties of Amorphous Semiconductors, Ed. J. Taut (Plenum, New York, 1972). T. M. Donovan and W. E. Spicer, Phys. Rev. Letters 21(1968) 1572. D. E. Aspnes and J. E. Rowe, Phys. Rev. Letters 27 (1971) 188. S. S. Vishnubhatla, B. Eyglunent and J. C. Wooley, Can. J. Phys. 47 (1969) 1661. E. N. Economou, S. Kirkpatrick, M. H. Cohen and T. P. Eggarter, Phys. Rev. Letters 25 (1970) 520; E. N. Economou and M. H. Cohen, Phys. Rev. Letters 25 (1970) 1445. J. A. Van Vechten and T. K. Bergstresser, Phys. Rev. B 1 (1970) 3351. C. Alibert and G. Bordure, A. Laugier and J. Chevalher, Phys. Rev. B 6 (1972) 1301. H. Piller, B. 0. Seraphin, K. Markel and J. E. Fischer, Phys. Rev. Letters 23 (1969) 775. J. E. Fischer, Phys. Rev. Letters 27 (1971) 1131. H. Piller and R. Whited, Solid State Commun. (in print). G. Weiser and J. Stuke, Phys. Status Solidi 35 (1969) 747.