- Email: [email protected]
The electronic structure of wurtzite CdS studied using angle-resolved U.V. photoelectron spectroscopy
Solid State Communications, Printed in Great Britain.
Vol. 55, No. 7, pp. 643-647,
THE ELECTRONIC
0038-1098185 $3.00 + .OO Pergamon Press Ltd.
1985.
STRUCTURE OF WURTZITE CdS STUDIED USING ANGLE-RESOLVED U.V. PHOTOELECTRON SPECTROSCOPY K.O. Magnusson and S.A. Flodstrom
Max-lab, Lund University, P. Martensson, Dept. of Physics and Measurement
Technology,
Box 117, S-22 1 00 Lund, Sweden
J.M. Nicholls and U.O. Karlsson Linkoping
Institute
of Technology,
S-581 83 Linkoping,
Sweden
R. Engelhardt II. Institut
fur Experimentalphysik
der Universitat
Hamburg, West Germany
and E.E. Koch Hamburger Synchrotronstralungslabor.
Hasylab, Deutsches Elektronen-Synchrotron West Germany
Desy, 2000 Hamburg 52,
(Received 27 March 1985 by L. Hedin)
The bulk and surface electronic structure of the (1 12 0) surface of wurtzite CdS has been studied in the I’MLA-plane and along the F-X’ line respectively, with angle-resolved U.V. photoelectron spectroscopy using synchrotron radiation. Utilizing polarization selection rules for bulk states of odd or even parity with respect to the lTl4L.4 mirror plane, direct bulk transitions from the upper valence band can be resolved and their dispersions studied. An additional structure appearing close below the projected valence band edge cannot be described as a direct bulk transition. We argue that this structure is due to emission from a surface state of dangling-bond character.
ANGLE-RESOLVED U.V. photoelectron spectroscopy (ARUPS) has been found to be a powerful technique in the investigation of bulk and surface electronic especially when synchrotron structure of matter, radiation is used as the source of excitation. Among the various systems examined, semiconductors have been of particular interest and much effort has been put into trying to understand the properties of these materials. The bulk and surface electronic structure of the homopolar semiconductors Si and Ge has been subject to extensive studies and much understanding of these covalently bonded solids has been gained. When we leave the column IV semiconductors and approach the heteropolar compounds, i.e. the III-V and the II-VI semiconductors, the bonding is still tetrahedrally coordinated, but from being strictly covalent in the homopolar case the bonds are now described as covalent bonds having considerable ionic character. This is due to charge transfer between nearest-neighbors and we can picture this as the sp3-hybrid derived u-bonds having shifted their center of electron density towards the more electronegative ion. In the case of the II-VI semiconductors, work on understanding in what way this 643
affects the bulk and surface electronic structure has not involved ARUPS as a test for the theoretical predictions, except in a few recent cases [ 1,2] . We believe that with the knowledge previously gained on the elemental semiconductors Si and Ge and the III-V compound d.o. as a basis, the investigation of the electronic structure of the II-VI compound semiconductors will give vital information on how the chemical bond, being somewhere between the covalent and ionic extremes, should be treated. The work on CdS presented in this article has been done in this spirit. The measurements were carried out at the synchrotron radiation laboratory, Hasylab. at Desy in Hamburg, West Germany, using a modified VG ADES 400 u.h.v. spectrometer equipped with an electron energy analyzer rotatable in two planes inclined at 90” [3]. The base pressure during the experiment was < 5 - lo-” torr. A CdS (1 1 2 0) single crystal bar of low resistivity @ = 1Oacm) and dimensions 5 x 5 x 20 [mm] was held in a sample holder with three degrees of freedom and cleaved in situ under u.h.v. conditions. The Fermi level of the sample was measured by recording a photoemission spectrum from the sputter-cleaned stainless
644
ELECTRONIC STRUCTURE
OF WURTZITE
CdS
Vol. 55, No. 7
steel sample holder, which was in electrical contact with the sample. The total energy resolution (monochromator + analyzer) was in all spectra better than 0.3 eV. CdS crystallizes in two phases, one cubic (zincblende) structure and one hexagonal (wurtzite) structure. Technologically more important is the wurtzite phase, which is the one studied here. This can be described as a h.c.p. structure with a basis consisting of two atoms, one of type 1 (e.g. Cd) at (0, 0, 0) and one of type 2 (e.g. S) at (0, 0, u), where u is close to 0.375, in units of the hexagonal lattice vectors {a, b, c}. From this it is obvious that all crystal planes containing the c-axis are non-polar and thus candidates for cleavage planes. The two non-polar crystal planes with lowest indices (and largest plane-spacings) are called (1 010) and (1 1 20). These are used as “natural” cleavage planes in wurtzite crystals. However, there is disagreement about the correct way of assigning Miller-like indices to lattice planes in hexagonal structures. By using the conventional set of base vectors in the direction lattice {a, b, b’, c}, where b’ = - (a + b), and constructing the reciprocal lattice r X base vectors {A, B, B’, C}, we define the Miller-like indices as the components of the shortest reciprocal lattice vector in the normal direction of the direct lattice plane being considered. Figure l(a), shows the surface geometric structure and the first surface Brillouin zone (SBZ) of the cleavage face of wurtzite CdS examined in this paper, which will be referred to as the (1 12 0) surface. Note that the plane containing the normal to the (1 12 0) surface and the c-axis is a mirror plane of the whole crystal and also of the unreconstructed [4] (1 1 Z 0) surface. As Dietz ef al. [S] have pointed out, within a direct-transition model of photoemission, this can be exploited to make initial bulk states of definite parity with respect to the mirror plane become either symmetry-allowed or -forbidden by using an exciting r M A L source with a high degree of plane polarization parallel to the mirror plane or perpendicular to it. From the Fig._l. (a) The surface geometric structure of CdS first surface Brillouin photoemission transition matrix element (Gil p *Al$f), (1 1 2 0) and the corresponding zone. (b) Calculated bulk band structure [6_1 along the it is seen that light polarized parallel to the mirror plane symmetry lines for the (1 12 0) surface (A 11 c)canonly excite initial states of even parity while important of CdS together with the hexagonal first Brillouin zone. initial states of odd parity are only excited when the polarization is perpendicular to the mirror plane. labelled the valence states from the calculation (local To utilize this in an ARUPS experiment we have density approximation) by Chang ef al. [6] in this used synchrotron radiation, which is highly polarized manner and show them together with the hexagonal in the plane of the storage ring, and moved the analyzer BZ in Fig. l(b). in the mirror plane of the (1 13 0) surface, thus probing bulk states in the I’MLA plane of the first Brillouin The recorded electron distribution curves (EDC’s) zone (BZ) of wurtzite CdS. Stoffel [l] assigned parities from CdS (1 130) for various angles of emission, Be, in the mirror plane using synchrotron radiation with a with respect to the mirror plane to the bulk valence photon energy of 20eV and a polarization vector, E, states on the F-M and the A-L lines and we have
Vol. 55, No. 7
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Fig. 2. Electron distribution curves for various angles of emission, 8,, in the mirror plane of the CdS (1 12 0) surface, recorded at a photon energy of 20 eV and with the polarization vector perpendicular (a) and parallel (b) to the c-axis of the crystal. perpendicular and parallel to the c-axis are presented in Figs. 2(a) and (b), respectively. As indicated in Fig. 2(a), the EDC’s have four distinct features, A, B, 2 and Si. Peaks A and Sr have a downward dispersion while peak B disperses upwards in energy, going from I? towards X’ in the SBZ. The point X’, upon which the A-L line in the bulk BZ is projected, is reached at 19~= 17.5’ for A and B and at 13~= 15” for structure Si. The peak indicated 2 shows no dispersion and is also very broad and featureless, being centered around Ei z-- 6.6eV relative to the Fermi energy of the crystal. With the electric field vector, E, parallel to the c-axis a quite different series of spectra is revealed [see Fig. 2(b)] . Here three reasonably sharp structures C, D and F are identified, while a weak peak E is observed in only a few spectra. In addition to these, there is a dispersing shoulder, S2, the exact position of which is rather difficult to determine in most of the EDC’s. A
broad, non-dispersive peak at Ei LX-- 6.5eV, is also present in this series, but structure F is located in the same region and this complicates the resolution of the two structures. This labelling of the structures appearing in the EDC’s also applies when similar series of spectra are recorded at other photon energies. In Figs. 3(a) and (b), the peak energy-positions Ei relative to the Fermi energy are plotted as a function of kl, , the electron wave vector parallel to the surface. With E 1 c, EDC’s were recorded at photon-energies of 17, 20 and 28eV, while with E 11c the photon energies used were 20 and 28 eV. Using the calculated bulk band structure of Chang et al. [6] we can give an interpretation of the origin of the observed structures. In Fig. l(b), the bands are shown on the F-M line (which we probe in normal emission, k/l = 0), on the A-L line (corresponding to emission with /cl, = 0.47 [A-‘]) and on the F-A line.
ELECTRONIC
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STRUCTURE
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Vol. 55, No. 7
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Fig. 3. (a, b) Initial energy positions of the peaks relative to the Fermi energy plotted vs k,l, the wave vector parallel to the surface. The photon energies used were 17 eV (M), 20eV (0) and 28eV (+) and the polarization vector was perpendicular b) and parallel (b) to the mirror plane of CdS (1 12 0). (c) The initial energy position of the structure S1 plotted relative to the projected bulk valence band edge, as derived from the calculation of Chang er al. [6]. The position of the valence band maximum relative to the Fermi energy was found using the experimental position of the Cd 4d levels and the results from Stoffel [l] .
bulk transitions from the two valence bands of odd parity, 2i and 22 [see Fig. l(b)]. Structure Z is not shown in the plot since its energy position is independent of both k,, and kl and therefore cannot be due to direct bulk transitions. On the other hand, structure Si shows a 0.4eV wide downward dispersion Ei (kll) without any dependence on the wave vector perpendicular to the surface, kl. Continuing with this line of reasoning we expect direct bulk transitions from even parity valence states, labelled li, when E 11c. Here transitions from bands 12 and 1 a should be degenerate on the A-L line with emission at an energy close to that from the odd bands 2i and 22 at each photon energy. Structures C and D can thus be interpreted as direct bulk transitions from the even parity valence bands I2 and la. Furthermore, the observed structure F is identified as emission from the lowest of the upper valence bands, la. Whether structure E is due to direct bulk transitions from the band 11 cannot be determined. StructureZ is also present in this case but has been left out for the same reason as above. Structure Sz is worth a comment. In the spectra where it can be observed, i.e., when the peak (or shoulder) is not too disturbed by the stronger emission C, the dispersion Ei(kll) closely resembles that previously observed for structure Sr , at the two photonenergies used.
Vol. 55, No. 7
ELECTRONIC
STRUCTURE
We interpret this as indicating that the structures Sr and S2 are both due to emission from the same state. Further, this structure cannot be due to emission from a direct bulk transition, since it shows no initial energy dispersion with the wavevector perpendicular to the surface, k,, as is the case with the structures A to F. The hypothesis we wish to put forward here is that structure Sr is due to emission from a surface state of dangling-bond character. Since, to our knowledge, no calculation of the surface band structure of CdS exists, we can only make our hypothesis probable by comparing the results from our experiment with the theoretical predictions for other materials with properties similar to CdS. From the bulk band calculation by Chang et al. [6], the shape of the projected bulk valence band edge can be derived by assuming that this is determined by the valence band edge along the F-A line. Comparing this with the observed dispersion of structure Sr , considerable similarities in both shape and width are found. In their work on ZnO, Lee and Joannopoulos [7] explained this as arising from the ionicity of the danglingbonds created by the cleavage. If, due to the ionic character of the bonds, the creation of the surface (by breaking these bonds) is not a very strong perturbation of the electron density associated with the bonds, then we expect the surface states to be closely related to the equivalent bulk states. Reasoning in this way, we can conclude that the interaction between the electronic dangling-bond states on the CdS (1 1 20) surface, which are mainly of S 3p character, should closely resemble the interaction between the corresponding bulk states, in a (1 1 20) plane. Thus the dispersion of the surface states found close to the projected valence band edge, measured in the FMLA plane of the BZ, should be related to the top valence bulk band on the F-A line (being S 3p derived), since this corresponds to a wavevector in a (1 1 2 0) bulk crystal plane. In Fig. 3(c) the projected bulk valence band edge is shown in the part of the SBZ of interest, together with the experimentally observed dispersion of the structure Sr. Since the position of the valence band maximum could not be determined directly from the experiment, we have used the positions of the Cd 4~’ levels determined in this experiment and the results from Stoffel [ 1] to derive the energy of the valence band maximum, relative to the Fermi energy. The difference between measured initial energy in our experiment and the results from Stoffel [l] is the difference between the two reference levels, i.e., between the Fermi energy and the valence band maximum. Using
OF WURTZITE
CdS
647
this procedure we find that the observed dispersion lies approximately 0.25 eV below the projected valence band edge. Theoretical work on wurtzite ZnO by Lee and Joannopoulos [7] shows that in this material a danglingbond surface state with a downward dispersion resembling the projected valence band edge in shape and width exists on the (1 1 20) surface. Ivanov and Pollman [8] report a calculation of the surface band structure of ZnO where a similar surface state is found on this surface along f-X’. Other work on ZnSe [9] and GaAs [lo], both of zincblende structure, show surface state dispersions along analogous directions in the SBZ with essentially the same properties as the dispersion we observe on CdS (1 1 20). In conclusion, our hypothesis that the observed structure Sr is due to a dangling-bond surface state on the cleaved CdS (1 120) surface is supported by two arguments. First, the experimental results which exclude the possibility of it being a direct bulk transition and make it a good candidate for a dangling-bond surface state, and second, the surface band calculations of the related compound semiconductors ZnO [7, 81, ZnSe [9] and GaAs [lo] , in which we can notice a common trend, into which we believe the results on CdS will Ldso fit. Acknowledgement - This work was supported by the Swedish Natural Science Research Council. We thank the staff at HASYLAB for excellent technical assistance.
REFERENCES :: 3. 4. 5. 6. 7. 8. 9. 10.
N.G. Stoffel, Phys. Rev. B28,3306 (1983). A. Ebina, T. Unno, Y. Suda, H. Koinuma & T. Takahashi,J. Vat. Sci. Technol. 19,301(1981). C.A. Feldman, R. Engelhardt, T. Permien, E.E. Koch & V. Saile, Nucl. Instrum. Methods 208, 785 (1983). S-C. Chang & P. Mark, J. Vat. Sci. Technol. 12 624 (1975). E. Dietz, H. Becker & U. Gerhardt, Phys. Rev. Lett. 36,1397;37,115 (1976). K.J. Chang, S. Froyen & M.L. Cohen, Phys. Rev. B28,4736 (1983). D.H. Lee & J.D. Joamropoulos, J. Vat. S&. Technol. 17, 987 (1980); Phys. Rev. B24, 6899 (1981). I. Ivanov & J. Pollman, Phys. Rev. B24, 7275 (1981). C. Calandra, F. Manghi & C.M. Bertoni, J. Phys. ClO, 1911 (1977). K.C. Pandey , J.L. Freeouf & D.E. Eastmann, J. Vat. Sci. Technol. 14,904 (1977).
Vol. 55, No. 7, pp. 643-647,
THE ELECTRONIC
0038-1098185 $3.00 + .OO Pergamon Press Ltd.
1985.
STRUCTURE OF WURTZITE CdS STUDIED USING ANGLE-RESOLVED U.V. PHOTOELECTRON SPECTROSCOPY K.O. Magnusson and S.A. Flodstrom
Max-lab, Lund University, P. Martensson, Dept. of Physics and Measurement
Technology,
Box 117, S-22 1 00 Lund, Sweden
J.M. Nicholls and U.O. Karlsson Linkoping
Institute
of Technology,
S-581 83 Linkoping,
Sweden
R. Engelhardt II. Institut
fur Experimentalphysik
der Universitat
Hamburg, West Germany
and E.E. Koch Hamburger Synchrotronstralungslabor.
Hasylab, Deutsches Elektronen-Synchrotron West Germany
Desy, 2000 Hamburg 52,
(Received 27 March 1985 by L. Hedin)
The bulk and surface electronic structure of the (1 12 0) surface of wurtzite CdS has been studied in the I’MLA-plane and along the F-X’ line respectively, with angle-resolved U.V. photoelectron spectroscopy using synchrotron radiation. Utilizing polarization selection rules for bulk states of odd or even parity with respect to the lTl4L.4 mirror plane, direct bulk transitions from the upper valence band can be resolved and their dispersions studied. An additional structure appearing close below the projected valence band edge cannot be described as a direct bulk transition. We argue that this structure is due to emission from a surface state of dangling-bond character.
ANGLE-RESOLVED U.V. photoelectron spectroscopy (ARUPS) has been found to be a powerful technique in the investigation of bulk and surface electronic especially when synchrotron structure of matter, radiation is used as the source of excitation. Among the various systems examined, semiconductors have been of particular interest and much effort has been put into trying to understand the properties of these materials. The bulk and surface electronic structure of the homopolar semiconductors Si and Ge has been subject to extensive studies and much understanding of these covalently bonded solids has been gained. When we leave the column IV semiconductors and approach the heteropolar compounds, i.e. the III-V and the II-VI semiconductors, the bonding is still tetrahedrally coordinated, but from being strictly covalent in the homopolar case the bonds are now described as covalent bonds having considerable ionic character. This is due to charge transfer between nearest-neighbors and we can picture this as the sp3-hybrid derived u-bonds having shifted their center of electron density towards the more electronegative ion. In the case of the II-VI semiconductors, work on understanding in what way this 643
affects the bulk and surface electronic structure has not involved ARUPS as a test for the theoretical predictions, except in a few recent cases [ 1,2] . We believe that with the knowledge previously gained on the elemental semiconductors Si and Ge and the III-V compound d.o. as a basis, the investigation of the electronic structure of the II-VI compound semiconductors will give vital information on how the chemical bond, being somewhere between the covalent and ionic extremes, should be treated. The work on CdS presented in this article has been done in this spirit. The measurements were carried out at the synchrotron radiation laboratory, Hasylab. at Desy in Hamburg, West Germany, using a modified VG ADES 400 u.h.v. spectrometer equipped with an electron energy analyzer rotatable in two planes inclined at 90” [3]. The base pressure during the experiment was < 5 - lo-” torr. A CdS (1 1 2 0) single crystal bar of low resistivity @ = 1Oacm) and dimensions 5 x 5 x 20 [mm] was held in a sample holder with three degrees of freedom and cleaved in situ under u.h.v. conditions. The Fermi level of the sample was measured by recording a photoemission spectrum from the sputter-cleaned stainless
644
ELECTRONIC STRUCTURE
OF WURTZITE
CdS
Vol. 55, No. 7
steel sample holder, which was in electrical contact with the sample. The total energy resolution (monochromator + analyzer) was in all spectra better than 0.3 eV. CdS crystallizes in two phases, one cubic (zincblende) structure and one hexagonal (wurtzite) structure. Technologically more important is the wurtzite phase, which is the one studied here. This can be described as a h.c.p. structure with a basis consisting of two atoms, one of type 1 (e.g. Cd) at (0, 0, 0) and one of type 2 (e.g. S) at (0, 0, u), where u is close to 0.375, in units of the hexagonal lattice vectors {a, b, c}. From this it is obvious that all crystal planes containing the c-axis are non-polar and thus candidates for cleavage planes. The two non-polar crystal planes with lowest indices (and largest plane-spacings) are called (1 010) and (1 1 20). These are used as “natural” cleavage planes in wurtzite crystals. However, there is disagreement about the correct way of assigning Miller-like indices to lattice planes in hexagonal structures. By using the conventional set of base vectors in the direction lattice {a, b, b’, c}, where b’ = - (a + b), and constructing the reciprocal lattice r X base vectors {A, B, B’, C}, we define the Miller-like indices as the components of the shortest reciprocal lattice vector in the normal direction of the direct lattice plane being considered. Figure l(a), shows the surface geometric structure and the first surface Brillouin zone (SBZ) of the cleavage face of wurtzite CdS examined in this paper, which will be referred to as the (1 12 0) surface. Note that the plane containing the normal to the (1 12 0) surface and the c-axis is a mirror plane of the whole crystal and also of the unreconstructed [4] (1 1 Z 0) surface. As Dietz ef al. [S] have pointed out, within a direct-transition model of photoemission, this can be exploited to make initial bulk states of definite parity with respect to the mirror plane become either symmetry-allowed or -forbidden by using an exciting r M A L source with a high degree of plane polarization parallel to the mirror plane or perpendicular to it. From the Fig._l. (a) The surface geometric structure of CdS first surface Brillouin photoemission transition matrix element (Gil p *Al$f), (1 1 2 0) and the corresponding zone. (b) Calculated bulk band structure [6_1 along the it is seen that light polarized parallel to the mirror plane symmetry lines for the (1 12 0) surface (A 11 c)canonly excite initial states of even parity while important of CdS together with the hexagonal first Brillouin zone. initial states of odd parity are only excited when the polarization is perpendicular to the mirror plane. labelled the valence states from the calculation (local To utilize this in an ARUPS experiment we have density approximation) by Chang ef al. [6] in this used synchrotron radiation, which is highly polarized manner and show them together with the hexagonal in the plane of the storage ring, and moved the analyzer BZ in Fig. l(b). in the mirror plane of the (1 13 0) surface, thus probing bulk states in the I’MLA plane of the first Brillouin The recorded electron distribution curves (EDC’s) zone (BZ) of wurtzite CdS. Stoffel [l] assigned parities from CdS (1 130) for various angles of emission, Be, in the mirror plane using synchrotron radiation with a with respect to the mirror plane to the bulk valence photon energy of 20eV and a polarization vector, E, states on the F-M and the A-L lines and we have
Vol. 55, No. 7
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Fig. 2. Electron distribution curves for various angles of emission, 8,, in the mirror plane of the CdS (1 12 0) surface, recorded at a photon energy of 20 eV and with the polarization vector perpendicular (a) and parallel (b) to the c-axis of the crystal. perpendicular and parallel to the c-axis are presented in Figs. 2(a) and (b), respectively. As indicated in Fig. 2(a), the EDC’s have four distinct features, A, B, 2 and Si. Peaks A and Sr have a downward dispersion while peak B disperses upwards in energy, going from I? towards X’ in the SBZ. The point X’, upon which the A-L line in the bulk BZ is projected, is reached at 19~= 17.5’ for A and B and at 13~= 15” for structure Si. The peak indicated 2 shows no dispersion and is also very broad and featureless, being centered around Ei z-- 6.6eV relative to the Fermi energy of the crystal. With the electric field vector, E, parallel to the c-axis a quite different series of spectra is revealed [see Fig. 2(b)] . Here three reasonably sharp structures C, D and F are identified, while a weak peak E is observed in only a few spectra. In addition to these, there is a dispersing shoulder, S2, the exact position of which is rather difficult to determine in most of the EDC’s. A
broad, non-dispersive peak at Ei LX-- 6.5eV, is also present in this series, but structure F is located in the same region and this complicates the resolution of the two structures. This labelling of the structures appearing in the EDC’s also applies when similar series of spectra are recorded at other photon energies. In Figs. 3(a) and (b), the peak energy-positions Ei relative to the Fermi energy are plotted as a function of kl, , the electron wave vector parallel to the surface. With E 1 c, EDC’s were recorded at photon-energies of 17, 20 and 28eV, while with E 11c the photon energies used were 20 and 28 eV. Using the calculated bulk band structure of Chang et al. [6] we can give an interpretation of the origin of the observed structures. In Fig. l(b), the bands are shown on the F-M line (which we probe in normal emission, k/l = 0), on the A-L line (corresponding to emission with /cl, = 0.47 [A-‘]) and on the F-A line.
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STRUCTURE
OF WURTZITE CdS
Vol. 55, No. 7
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Fig. 3(b). Unfortunately, calculations for the remainder of the IX&4 plane have not been available to us. With E 1 c we expect to observe only direct bulk transitions from initial states of odd parity, i.e. from the two valence states labelled 2i. These are characterized by a band separation of the r--M line of 0.7 eV, and, further, by the fact that the upper state disperses downwards and the lower upwards so that they are degenerate on the A-L line. This behavior closely resembles the observed dispersions of structures A and B. When, in addition, these dispersions shift in initial energy with the change in photon energy, thus indicating an energy dependence on /cl as well as on k,l, we feel confident in interpreting structures A and B as arising from direct
Fig. 3. (a, b) Initial energy positions of the peaks relative to the Fermi energy plotted vs k,l, the wave vector parallel to the surface. The photon energies used were 17 eV (M), 20eV (0) and 28eV (+) and the polarization vector was perpendicular b) and parallel (b) to the mirror plane of CdS (1 12 0). (c) The initial energy position of the structure S1 plotted relative to the projected bulk valence band edge, as derived from the calculation of Chang er al. [6]. The position of the valence band maximum relative to the Fermi energy was found using the experimental position of the Cd 4d levels and the results from Stoffel [l] .
bulk transitions from the two valence bands of odd parity, 2i and 22 [see Fig. l(b)]. Structure Z is not shown in the plot since its energy position is independent of both k,, and kl and therefore cannot be due to direct bulk transitions. On the other hand, structure Si shows a 0.4eV wide downward dispersion Ei (kll) without any dependence on the wave vector perpendicular to the surface, kl. Continuing with this line of reasoning we expect direct bulk transitions from even parity valence states, labelled li, when E 11c. Here transitions from bands 12 and 1 a should be degenerate on the A-L line with emission at an energy close to that from the odd bands 2i and 22 at each photon energy. Structures C and D can thus be interpreted as direct bulk transitions from the even parity valence bands I2 and la. Furthermore, the observed structure F is identified as emission from the lowest of the upper valence bands, la. Whether structure E is due to direct bulk transitions from the band 11 cannot be determined. StructureZ is also present in this case but has been left out for the same reason as above. Structure Sz is worth a comment. In the spectra where it can be observed, i.e., when the peak (or shoulder) is not too disturbed by the stronger emission C, the dispersion Ei(kll) closely resembles that previously observed for structure Sr , at the two photonenergies used.
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We interpret this as indicating that the structures Sr and S2 are both due to emission from the same state. Further, this structure cannot be due to emission from a direct bulk transition, since it shows no initial energy dispersion with the wavevector perpendicular to the surface, k,, as is the case with the structures A to F. The hypothesis we wish to put forward here is that structure Sr is due to emission from a surface state of dangling-bond character. Since, to our knowledge, no calculation of the surface band structure of CdS exists, we can only make our hypothesis probable by comparing the results from our experiment with the theoretical predictions for other materials with properties similar to CdS. From the bulk band calculation by Chang et al. [6], the shape of the projected bulk valence band edge can be derived by assuming that this is determined by the valence band edge along the F-A line. Comparing this with the observed dispersion of structure Sr , considerable similarities in both shape and width are found. In their work on ZnO, Lee and Joannopoulos [7] explained this as arising from the ionicity of the danglingbonds created by the cleavage. If, due to the ionic character of the bonds, the creation of the surface (by breaking these bonds) is not a very strong perturbation of the electron density associated with the bonds, then we expect the surface states to be closely related to the equivalent bulk states. Reasoning in this way, we can conclude that the interaction between the electronic dangling-bond states on the CdS (1 1 20) surface, which are mainly of S 3p character, should closely resemble the interaction between the corresponding bulk states, in a (1 1 20) plane. Thus the dispersion of the surface states found close to the projected valence band edge, measured in the FMLA plane of the BZ, should be related to the top valence bulk band on the F-A line (being S 3p derived), since this corresponds to a wavevector in a (1 1 2 0) bulk crystal plane. In Fig. 3(c) the projected bulk valence band edge is shown in the part of the SBZ of interest, together with the experimentally observed dispersion of the structure Sr. Since the position of the valence band maximum could not be determined directly from the experiment, we have used the positions of the Cd 4~’ levels determined in this experiment and the results from Stoffel [ 1] to derive the energy of the valence band maximum, relative to the Fermi energy. The difference between measured initial energy in our experiment and the results from Stoffel [l] is the difference between the two reference levels, i.e., between the Fermi energy and the valence band maximum. Using
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this procedure we find that the observed dispersion lies approximately 0.25 eV below the projected valence band edge. Theoretical work on wurtzite ZnO by Lee and Joannopoulos [7] shows that in this material a danglingbond surface state with a downward dispersion resembling the projected valence band edge in shape and width exists on the (1 1 20) surface. Ivanov and Pollman [8] report a calculation of the surface band structure of ZnO where a similar surface state is found on this surface along f-X’. Other work on ZnSe [9] and GaAs [lo], both of zincblende structure, show surface state dispersions along analogous directions in the SBZ with essentially the same properties as the dispersion we observe on CdS (1 1 20). In conclusion, our hypothesis that the observed structure Sr is due to a dangling-bond surface state on the cleaved CdS (1 120) surface is supported by two arguments. First, the experimental results which exclude the possibility of it being a direct bulk transition and make it a good candidate for a dangling-bond surface state, and second, the surface band calculations of the related compound semiconductors ZnO [7, 81, ZnSe [9] and GaAs [lo] , in which we can notice a common trend, into which we believe the results on CdS will Ldso fit. Acknowledgement - This work was supported by the Swedish Natural Science Research Council. We thank the staff at HASYLAB for excellent technical assistance.
REFERENCES :: 3. 4. 5. 6. 7. 8. 9. 10.
N.G. Stoffel, Phys. Rev. B28,3306 (1983). A. Ebina, T. Unno, Y. Suda, H. Koinuma & T. Takahashi,J. Vat. Sci. Technol. 19,301(1981). C.A. Feldman, R. Engelhardt, T. Permien, E.E. Koch & V. Saile, Nucl. Instrum. Methods 208, 785 (1983). S-C. Chang & P. Mark, J. Vat. Sci. Technol. 12 624 (1975). E. Dietz, H. Becker & U. Gerhardt, Phys. Rev. Lett. 36,1397;37,115 (1976). K.J. Chang, S. Froyen & M.L. Cohen, Phys. Rev. B28,4736 (1983). D.H. Lee & J.D. Joamropoulos, J. Vat. S&. Technol. 17, 987 (1980); Phys. Rev. B24, 6899 (1981). I. Ivanov & J. Pollman, Phys. Rev. B24, 7275 (1981). C. Calandra, F. Manghi & C.M. Bertoni, J. Phys. ClO, 1911 (1977). K.C. Pandey , J.L. Freeouf & D.E. Eastmann, J. Vat. Sci. Technol. 14,904 (1977).