Summary Paper at Paris Conference on Iv-vi Compounds, July 1968

A review is given of the present status of several of the main areas of investigation of the IV-VI compounds, with the emphasis placed on problems that still have to be solved. It would be presumptuous of me to give a critique of all of the diverse things that have been discussed at this conference, since we have covered quite a lot of ground. I shall simply try to point out some things that I regard as new progress or residual problems, obviously biassing my remarks towards those parts of the subject with which I feel most at ease. Crystal Structure and Perfection. First, let me make a few remarks about crystal structure and perfection. Much of the crystal structure is very well established. However, it is to be noted that, when one is evaluating measurements on epitaxial thin films, one has to be careful about the degree of strain and the mechanism of strain release. We have had some experience in my laboratory of taking a thin PbS film deposited on a backing a very good epitaxial layer and subjecting it to a cycle of high hydrostatic pressure, when it was established quite unambiguously that we were producing first considerable uniaxial elastic strain and eventually plastic flow in the film as a result of the difference in compressibility between film and substrate. This is consistent with the expectation that epitaxial films deposited at high temperatures and then cooled may be considerably strained because of the difference in thermal expansion coefficient between film and substrate. Dr. Zemel referred to this possibility and to the deduction that in his work there was found to be zero strain in his films at room temperature. Of course this does not mean that no strain is present at other temperatures, so that a mild warning about the possibility of strained films and about uncritical comparisons of film and bulk data would seem to be appropriate. A remaining problem in this category would seem to be the establishment of the phase diagram between SnTe and GeTe. The original work suggested a phase transition, cubic to rhombohedral, in the SnTe near 0 OK. However, this deduction emerged from extrapolations from work on GeTe-SnTe alloys, and careful reexamination suggests rather that the phase transition could occur anywhere between 0 OK and 80 O K . I think it is quite important for the proper interpretation of all of the low temperature data that the question of distortions away from cubic structure be resolved. In fact it is important for the interpretation of the band structure calculations that we have accurate data on lattice constants and on distortions in all of the parent materials and their alloys. One final remark in this category. It might be interesting for those engaged in the deposition of epitaxial films to try to deposite GeTe in the cubic phase by using a cubic substrate, or alternatively to attempt to put down SnTe in the rhombohedral phase by using, say, the rhombohedral GeTe as substrate. Measurements of the reflectivity of the cubic GeTe could then be compared with those on the normal rhombohedral variety to provide evidence on the differences in electronic band structure produced by the slight distortion from the cubic symmetry. Band Structure. First, a trivial point. In some of the early papers those of Pratt and his collaborators at M. I. T., and those of Kleinman and his collaborators there was a difference in the symmetry of the lowest conduction band state in PbTe. Specifically, Kleinman and Lin found that the conduction band of PbTe was derived from the L,, state in the single group notation, whereas the conduction bands of PbS and PbSe were derived from a L,. state. Actually, it appears that these states are so mixed by spin-orbit interaction that this is somewhat of an Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968427 C 4 172 WILLIAM PAUL academic question, and the conduction band state is L i jn all three crystals. Nevertheless, it is probably worth remarking that this ambiguity about the parentage of the Li conduction band does exist in the literature. Now let me make a few remarks about relativistic corrections. I think, after the attention which has been paid to such terms in the Hamiltonian over the last two or three years, that everyone accepts that a calculation not taking account of them will very likely give incorrect results. There is some question, however, about the emphasis we should place on these terms in the Hamiltonian when we are extrapolating to new band structures or interpolating band structures for alloys. It seems to me that in recent publications undue emphasis has been placed on this part of the Hamiltonian relative to other parts and I propose to illustrate this thesis with an example. SubsEnergy Gap Lattice A(L$(u) L;(c)) tance (LZ LC) Constat~t A0 vol PbTe 0.2 eV 6.42 SnTe 0.3 eV 6.31 -0.15 eV GeTe -0.2 eV 5.99 -0.6 eV In table I, I have set down for PbTe, SnTe and GeTe their lattice constants, and the change in the energetic separation of ~ s f ( v ) and L ~ ( c ) caused by the change in volume alone, using the PbTe value as starting point. I have used approximate values for the difference in deformation potential of these states culled from the experimental work of Dr. Prakash in my laboratory on the three lead salts. These are the changes in band gap you would get by ignoring any change in the constituent atoms, and so in the electrostatic potential or in the relativistic corrections, and simply took account of the change in volume. In the case of SnTe, the volume correction has nearly closed the gap to zero by itself, while in GeTe, whose actual band gap is about 0.2 eV, a compensating correction to the volume one is required. I am not suggesting that the volume corrections are the most important ones ; I do suggest that the identification of the relativistic shift as the cause of inversion may overemphasize its importance. When there are several contributing physical mechanisms it may make sense from an historical point of view to say that the inclusion of such and such an overlooked term corrected the situation ; it does not make sense to emphasize it to the exclusion of other contributions when extrapolations to other substances or alloys are made. Thus the extrapolation PbTe -+ SnTe -t GeTe has to be carefully done including all changes in the Hamiltonian. Another case which has come up at the Conference is that of PbTe-CdTe alloys, where the band gap increases even though a cation giving a smaller relativistic correction to the energy of the valence band maximum is being added. While I am on the subject of band structure, I should like to remark on what I consider reasonably well established and what may not be established in these compounds. The L-symmetry of the conduction and valence band extrema in the lead compounds is pretty well established. The temperature coefficients of their fundamental energy gaps are positive, while those of the fundamental gaps of SnTe and GeTe are negative. Dr. Howard (*) has suggested that the matrix elements of the momentum between the conduction and valence band extremum states of SnTe and GeTe are equal, and he has suggested also that there is a lighter mass second valence band in SnTe and a heavier mass second valence band in GeTe. Dr. Andreev, on the contrary, wants to see heavier second valence bands in both SnTe and GeTe. I think we would all probably agree that the L6+ state is very sensitive to pressure, temperature, or anything else we do to it. It is the valence band maximum state in the lead compounds and its behaviour is largely responsible for the sign of the temperature coefficient of the fundamental gap. From the opposite sign of the gap temperature coefficient in SnTe and GeTe we guess that the L G ~ state is probably not the valence band maximum state in either SnTe or GeTe. That however does not force it to be the conduction band minimum state in these compounds, as it has been postulated to be. Let me act the devil's advocate for the moment. You can take the sf state out of the situation by sending it deeper into the valence band instead of turning it into a conduction band. For the moment, we forget about relativistic corrections to the energy of S-like states, and simply demand that the L: state no longer be the maximum of the valence band. Then we have a situation where we might be able to fit the temperature dependence of the gaps in SnTe and GeTe from the displacements of states other than the 15:. Of course I know there are arguments suggesting that the conduction band in SnTe and GeTe has L: symmetry ; I have described a very different possibility to emphasize that, whereas the identification of the L: state as the valence band (*) The substance of Dr Howard's remarks, which will not form part of the Conference Proceedings, is to be found in an article by Tsu, Howard and Esaki, Phys. Rev., 172, 779 (1968). SUMMARY PAPER AT PARIS CONFERENCE ON IV-VI COMPOUNDS C 4 173 maximum in the lead compounds is soundly based on Knight shift measurements, we do not have an equally credible identification of the postulated ~ 6 + conduction band in the tin compounds. (No n-type SnTe !) It might be a good idea if we could figure out some experiments giving information on the symmetry of the states in the tin and germanium compounds, and especially the symmetry of the SnTe conduction band. Temperature Coefficients of Gaps and Masses. Now I'd like to make some comments on the temperature dependence of energy gaps. You will recall that the opposite sign of coefficient between PbTe and SnTe is quoted as one argument for the inversion of the band structure between these compounds. It seems worthwhile reviewing qualitatively the several reasons for temperature coefficients. The first usually quoted is a change in volume caused by the thermal expansion. From the results of pressure experiments we recognize that this contribution may be positive or negative. The second reason offered is a change in the electron-phonon interaction. The theory for this, first given by Fan and by Radkowsky, leads to a displacement of the absolute extremum of a band into the forbidden gap and an increase in the effective mass. It is conceivable, but somewhat unlikely, that interaction with other bands could alter this qualitative result. Band edges which are not absolute extrema may shift either way with temperature, since some interactions perturb their energy to greater values, and some to lesser. Thus, this second contribution, the explicit electron-phonon interaction, is expected to lead to a decrease in the fundamental energy gap. I shall describe the experimental situation in a little more detail than is usual. Table I1 shows experimental results for PbS, PbSe and PbTe, obtained by Dr. Prakash in my laboratory. The experimental T-coefficients of the gaps for PbS, PbSe and PbTe are + 5 x lo-' eV/OK, + 4.1 x eV/OK and + 4.5 x lo-' eV/OK. These are average values taken from the displacement