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Langmuir 1993,9, 177-185
Influences of NH3 Adsorption on the Electronic Structure of CdS(OOO1) and - ( l l Z O ) Surfaces Albert B. Rives Department of Chemistry, University of North Carolina at Greensboro, Greensboro, North Carolinu 27412 Received July 6,1992. In Final Form: September 14, 1992 Fenske-Hall molecular orbital calculations on thin slabs of CdS have been wed to explore- the origins of the band bending and the formation of the space charge region at the CdS(0001) and 41120) surfaces with and without adsorbed NH3. Results of the calculations indicate that the polar nature of the CdS(0001) surface is such that electronic energy levels at the surface are stabilized enough relative to the bulk to let a fraction of the lowest conduction band orbitale at the surface become occupied. This imparta a small negative charge to the CdS units in the surface layer which in turn gives rise to a wide space charge region. NH3 adsorption on the (0001) surface pushes a small fraction of that negative charge on the surfcce back toward the bulk and thereby reduces the width of the space charge region. On the nonpolar (1120) surface, there is virtually no build-up of charge in the surface layer with or without adsorbed NHS;hence the space charge region and any adsorption-induced changes in its width are predicted to be ineignificant. The calculations on CdS(0001) do reasonably well at explaining the experimental photoluminescence results in the context of a simQle model which relates photoluminescence to the width of the space charge region. The results on CdS(ll2O),however, suggestthat adsorption-inducedchangea in photoluminescence are not entirely determined by changes in the width of the space charge region.
Introduction The bending of semiconductor's conduction and valence bands in response to an electric field near its surface is central to the interesting electronic, photophysical, and photochemical properties displayed by semiconductors. In moet applications,one can view the electric field at the surface as arising from the small transfer of electrons between the semiconductorsurface and the surrounding medium to equalize the Fermi levels of the two materials when the interfaceis formed. For a p-type Semiconductor, this typically meane that electrons move from the surrounding medium into the mobile charge carriers,or holes, in the semiconductor's valence band; and for an n-type semiconductor mobile electrons in the semiconductor's conduction band move into the surround medium. In either case, charge is built-up in both the semiconductor and the Surrounding medium. However, in the semiconductor that charge is not concentrated at the surface near the countercharge in the surround medium but is spread over a volume known as the %pace charge region-. This region is characterized by a depletion of mobile charge carriers, and it may extend several thousand angstroms into the bulk of the semiconductor. Since the charge in the surrounding medium is countered by charge spread throughoutthe spacecharge region, a nonzero electric field exieta in the space charge region, and it is this field that givee rise to the band bending. The above scenario is fine for explaining the origins of the band bending when the semiconductor is in contact with some medium that can receive or relinquishelectrons; but bands can also bend when the semiconductor is in contact with a vacuum or some kinetically stable gas. In order to describe the origins of the band bending in these situations,one might argue that residual ionsleftover from sample preparation or impurities in the surrounding atmosphere could generate the electric field. However in those ~8888,one would expect widely varying properties depending on preparation and handlingtechniquesas well as the identity of the residual ions. It would also call into question what ia meant by a clean surface. The object of the work reported in this paper was to computationally explore th0 electronicstructure of a clean semiconductor
surface with approximate molecular orbital calculations to see what they might contribute to the understanding of the origins of the band bending at these semiconductor/ vacuum or semiconductor/stable-gasinterfaces. The motivation for this work came from reporta of the photoluminescence experiments done by Ellis and coworker~.'~In that work the change in a semiconductor's photoluminescence when a given gas is adsorbed on it is used to deduce the correspondingchange in the width of the space charge region.5 The equation used to express the relationship between photoluminescence intensities and the change in the width of the space charge region is given in eq 1 PL,/PL, = exp(-a A W )
(1)
where PL1 is the photoluminescent intensity in the presence of an inert gas or vacuum, PL2 is the photoluminescent intensity in the presence of an adsorbate, a ie the s u m of the absorbtivities of the semiconductor at the particular exciting and emitting wavelengths, and A W is the change in width of the space charge region. The derivationof this equationcomes from the assertion that electron hole pairs that are photogenerated in the space charge region are separated by the electric field and are unable to radiatively recombine. Hence, the photo(1) (a) VanRyewyk, H.; Ellis,A. B. J. Am. Chem. SOC. 1986,108,24642455. (b) Lieensky, G.C.; Meyer, G.J.; Ellis, A. B. A d . Chem. 1988, 60,2531-2534. (c) Meyer, G.J.; Luebker, E.R. M.; Lieensty, G. C.; Ellis, A. B. InStudiesinSurfaceScienceandCatalysis, V o l . 4 ~ P h t o c h e ~ t r y on Solid Surfaces; Anpo, M., Matauura, T., Eda.; Elmvier: Amsterdam, 1989; p 388. (d) Murphy, C. J.; Lieensky, G.C.; bun&,L. K.; Kowach, G. R.; Ellis,A. B. J. Am. Chem. Soc. 1990,112,8344-8348. (2) Meyer, G.J.; Lieensky, G.C.; Ellis, A. B. J. Am. Chem. SOC. 1988, 110,4914-4918. (3) Leung, L. K.; Meyer, G. J.; Lisensky, G. C.; E W ,A. B. J. Phys. Chem. 1990,94,1214-1216. (4) Meyer, G. J.; Leung,L. K.; Jim, C. Y.;Lieensky, G.C.; Ellis, A. B. J. Am. Chem. SOC.1989,111,6146-6148. (5) In discussing photoluminescence experimenta it is more common to discuss the 'dead layer" rather than the 'space c region".m The two are not strictly identical,but they are c l w l y rela ,and they reflect band bending in the name way. To mini" confusion and to more clearly establish the broad applicability of them nwults, only the term 'space charge region"is used in this report. Consideringthe accuracy of calculations 8uch 88 theee, nothing is lost by lumping these two similar concepts together.
0743-7463/93/2409-0177%04.00/0 Q 1993 American Chemical Society
3
178 Langmuir, Vol. 9,No.1, 1993
Rive8
Intensity Photoluminescence LOW
CB
VB
High Intensity Photoluminescence
I
CB VB Figure 1. Schematic representation of the space charge region and ita relation to photoluminescence intensity. luminescence intensity is reduced as the size of the space charge region is widened. This is shown schematically in Figure 1. The width of the space charge region depends on the dielectricconatant of the semiconductor, the charge carrier concentration, and the electrostatic potential difference between the surface and the bulk4
W = [2e,e,V/(n,e)1~/~
(2)
where W is the width of the space charge layer, e, is the permitivity of free space, e, is the dielectric constant of thematerial(aesumedtobeco~tantfr0msurf~to bulk), Vis the electrostaticpotential difference between surface and bulk, neis the charge carrier concentration in the bulk semiconductor, and e is the electronic charge. The charge per unit surface area, q, that generates the electric field that gives rise to the space charge region is just the charge that would have been in the space charge region had it not been depleted of chargewhen the interface was formeds q = Wnee
(3)
Hence, if one can know the charge that builds up on the surface and the charge carrier concentration, then one can determine the width of the space charge region. The work of Meyer et with n-type CdSe and amines showed that the photoluminescence is increased when amines are adsorbed on eithjr the (OOO1) face or the "cleaved" face (presumably (1010)or (11%)).These resulta are taken to indicate that negative charge is built-up at the CdSe surface, and the amine pushes electron density offthe surface back toward the bulk, thereby reducing the width of the space charge region and increasing the photoluminescence. This is reminiscent of the situation depicted in Figure 1. Similar observations are made on both the (OOO1) and cleaved surfaces? i.e. amine adsorption increases photoluminmnce, but there are fundamentaldifferences,some of which suggest that the concepta that led to eq 1do not d d b e the photoluminescent behavior of the cleaved surfaces. The most apparent difference between the two types of surfaces is that the photoluminescent intensity is much higher on the cleaved surfaces.2 More impor~~
(6) COX,P. A. The Electronic S t m t u r e and Chemistry of Solids; Oxford Univemity: New York, 1987; pp 236-237.
tantly, however, the AWs predicted using eq 1for a given adsorbing amine on a cleaved surface are not the same at different exciting wavelengths.2 Additionally, the time constant for photoluminescence changes with adsorption on the cleaved surfaces but not on the (OOO1) surface.3 Consequently, while the changes in photoluminescence that accompany adsorption on the (OOO1) surface can be explained well by changes in the width of the space charge region, it is not clear how much of the changes that accompany adsorption on the cleaved surfaces are related to the width of the space charge region.2 In the work reported here, electronic structure calculations have been performed to explore the origins of any charge build-up at CdS surfaces with and without adsorbates like NH3. In addition,the computationally predicted difference in the width of the space charge region when NH3 is adsorbed is analyzed and compared with the experimentalresult. The experimentsreported by Meyer et al.lce2 were done with both CdS and CdSe, but the best quantification was reported for CdSe.2 Fortunately, the resulta for CdS and CdSe are very similar$ and in cases where direct comparisons can be made, they predict changes in the width of the space charge region that differ by lees than a factor of 2 (CdS showing the greater change). Consequently, it is reasonable to expect a semiquantitative comparison of the resulta of these calculations on CdS with the experimenta on CdSe. Exploratory calculations such as these involving solid surfaces with adsorbates are not reasonably carried out with the rather rigorous techniques like ab initio HartreeFock or even the local density hctional m e t h a the size of the problem would make them very expensive, and the uncertain nature of the results increasesthe likelihood of having to carry out many calculations. Clearly,. an approximatemethod iepreferred, but not all are well suuted to treat the systems of interest here. Extended Hiickel, for instance, does not allow the orbital energies to respond to an electric field. The zero differential overlap methods could possibly be used, but the reliability of their parameterizations in such an application is uncertain. I have elected to use the Fenske-Hall (FH)approximate molecular orbital technique.' It has some key aspecta in common with INDO but does not rely on empirical interaction parameters and does not neglect atomicorbital overlaps in normalizing the molecular orbitals. Beyond the choice of technique, one must also choose the sort of system on which to do the calculations. Calculationson small cluaters cannot adequately describe the electricfield in binary (partiaUyionic) semiconductors, such as CdS, with suitable uniformity across a given face of the cluster. To avoid this problem the systems used in these calculations are slabs that extend infinitely in two dimensions. The FH technique has not been u88d in this manner before, so it f i t needed to be adapted for use on systems with translational symmetry. D e w of the adaptation of the conventional FH method to systems with translational symmetry are given in the Appendix. Despite being able to better d d b e the electric field generated by the ions, theae slabs are still not ideal. The thickness of the slab is computationally limited to several tens of angstroms; and the explicit inclusion of dopant ions is precluded by both theneed to have relatively small repeating unite and the inabilityto include enough dopant atoms in such narrow slabs. Nonetheless, thin crystdine slabs can be used to learn about the forces that tend to push electrons toward or away from the surface. Electron density pulled to the surface from several layers away (7)Hall, M.B.;Femke, R. F. Znorg. Chem. 1972, 22,768-775.
Langmuir, Vol. 9, No.1, 1999 179
NHs Adsorption on CdS Surfaces Table I. Basis 8et Summary atom core Cd ls-4da
s
1s-2p' 3sd
C
valence
atom core valence Se,Sp(exp= 1.8Ib N lec 2e,2pd 3pd H 1s (exp 5 1.O)b
a Single-zeta orbitals from ref 8. * Single-zeta orbitalsw ith orbital exponent indicated. Single-zeta orbitals from ref 9. Contraction of double-zeta orbitals from ref 10.
reflects a tendency for the surface to receive electron density from the bulk. Additionally, the contributions from dopant ions can be treated by allowing the Cd and S ions to have nonintegral nuclear charges and corresponding nonintegral numbers of electrons. This effectively spreads the effects of the dopant ions uniformly over the system and provides extra electrons in the conduction band or holes in the valence band. Such a treatment is of value if the conduction band is suitably stabilized at the surface and draws electron density to the surface. However, if the stabilization is so great as to take the conduction band below part of the valence band, the extra electrons would only serve to fd the holes left in the top of the valence band and would not have a particularly important influence on the overall calculation. As will be shown, the two surfacea studied here have their conduction bands stabilized either too little or too much at the surface to warrant the somewhat arbitrary inclusion of the extra electrons. Hence, the simple extension of conventional molecular orbitaltechniques applied to thin slabswithout inclusion of dopant ion effects should be suitable for exploringthe important aspecta of the electronicstructure of these surfaces. The bulk of the space charge region need not be explicitly described with such techniques. It is more efficiently described as a response to the surface charges using eqs 2 and 3 rather than a molecular orbital calculation.
Computational Details A version of the FH program adapted for systems with translational symmetry was used for all the calculations reported here. The calculations on both bulk CdS and CdS surfaces included interactions among atoms in first, second, and third nearest-neighbor unit cells. For the bulk calculations64 k vectors in the three-dimensional Brillouin zone were used, while the calculations on the (OOO1) and the (1120) surfaces involved 48 and 8 k vectors in their respective two-dimensional Brillouin zones. A minimal basis set was used in these calculations. The atomic orbitals were taken primarily from the single zeta basis seta and contractions of the double zeta basis seta of Clementi and co-workers.8-10 The atomic orbitals were partitioned into "corew and "valence" seta. The core orbitals were taken to be doubly occupied and were not permitted to m u with the valence orbitale. An outline of the basis set is given in Table I. The S 3s orbital was put into core because including it among the valence orbitals gives a band gap about 10times too large. This stems from the S 3s orbital's significant overlap with the surrounding Cd 5s orbitals. Since the S 3s bands are energeticallywell isolated about 10 eV below the 5 3p valence bands, and since the 3s bands show very little dispersion,ll putting the S 3s orbitals in core is (8) Clem", E.; Raimondi, D. L.; Rainhardt, W. P. J. Chem. Phys. 1987,47,130&1907. (9) Clementi, E.; Raimondi, D. L. J. Chem. Phys. 1968,38,2686-2689. (10) Ftoetti, C.; Cbmenti, E. J. Chem. Phys. 1974,60,4125-4729. (11) C ,K. J.; hoyen, 8.; Cohen, M. L. Phys. Rev. B l983,28, 47756-4749.
W
000 1
J 1120
oi i o
Figure 2. (a, top) CdS (wurtzite) bulk geometry. Open circles are Cd atom and fiied circles are S abm. (b, bottom) Representation of the f i t Brillouin zone of the hexagonal CdS lattice with designated symmetry points.
physically reasonable. However, the need to include the S 3s orbitals in core seems to indicate that the value of approximate calculations such as these lies in their ability to describe the orbitals near the Fermi level, and they should not be called on to describe core levels or high lying unoccupied orbitals. Calculations were carried out on bulk CdS, CdS(0001) with and without adsorbed NH3, and CdS(ll20) with and without adsorbed T h e surface calculationswere done using slabs approximately 20 A thick. The structurea of the CdS portion of these systems were taken from the experimentally determined bulk structure of CdS,l*Figwe 2a. Surface calculations simply used a truncated bulk CdS structure and did not allow for any relaxation. This is not a severe approximation sincethe relaxation is known to be very small on these surfaces.13 The relaxation on the S-rich (OOOI) face is not small,19but this is of no concern here since we are not interested in that face; in the study of the (OOO1) surface, the S-rich face serves only as a link to the bulk. The adsorbed NH3 was placed with the nitrogen coordinated to each surface Cd so as to maintain tetrahedral coordination around both the Cd and N and with a Cd-N distance of 2.0 A,a commonmetal to nitrogen distance for second-row transition metals." The N-H distances were fixed at 1.01 A.
m.
(12) Wyckoff, R W. 0. Crystal Structures, 2nd d.;John Wiley and Sone: New York, 1966; Vol. 1, pp 111-112. (13)(a) Chang, S.-C.; Mark,P. J. Vac. Sci. Technol. 1976,12,SzaeSr. (b) Chang, S.4.; I+k, P. J. Vac. sei. Technol. 1976,12,6u-628.
(14) Chatt, J.; Ddworth, J. R.; hchardr, R. L. Chem. Rev. 1978, 78, 589-626.
Rives
180 Langmuir, Vot. 9, No.1, 1993 1n .- I
I
I
I 1
CdS (0001)
n
-5
Figure 3. Electronic band structure for CdS based on FH calculations. Refer to Figure 2b for the symmetry designations. The zero of energy was arbitrarily assigned to the top of the valence band.
All calculations were done on UNCGs VAXclustev using primarily a VAX 8700 and a VAX 6000-610. Results and Discussion Bulk CdS. In order to demonstrate the general applicabilityof the FH method to crystallinesystems,the initial calculations were done on bulk CdS. Figure 2 shows the CdS unit cell (wurtzite structure) and the Brillouin zone for the hexagonal lattice. Figure 3 shows the calculated band structure. The gross features of the calculation are in line with experimental results16 and more rigorous calculations.ll The calculation shows CdS to be a direct band gap semiconductor with a band gap of about 2.6 eV; this compares well with the experimentallydetermined direct band gap of 2.42 eV.16 The valence band is essentiallyall S 3p in character, and the bottom two levels of the conduction band are primarily Cd 5s in character, one the symmetric combination of the two Cd 5s orbitals in the unit cell and the other the antisymmetdc combmtion-the Cd Spderived levels are several electronvolts above the top of the Cd 5s-derived levels. The large dispersion of the conduction band indicates that any electron density in the conduction band will occupy states close to the I? point. Someof the quantitativeaspects of the calculationshow only modest agreement with experimentand more rigorous calculations. The dispersion at the top of the valence band as determined by the difference between the I? and M points is calculated here to be 1.0 eV as compared to the experimentalvalue of 0.7 eV;'s the dispersion of the bottom of the conductionband as again measured between the I? and M points is calculated here to be 4.6 eV as compared to 2.5 eV calculated with a more rigorous local density functionalcalculation,11and the width of the valence band at the r point is calculatedhere to be 2.7 eV, as compared to the experimental result of 4.5 eV.15 Overall the FH calculationgives good semiquantitative correspondence to the experimental resulta on bulk CdS. Better correspondence with selected experimental properties could be obtained by changing the basis set, but different properties require different basis set changes. The basis set chosen for these calculations represents a good middle-ground. (16) (a) Stoffel,N.0.Phys. Reo. B: Condem. Matter 1983,28,33063319. (b) Magnuson, K. 0.;Flhtrom, S.A.;Martensson, P.;Nicholb, J. M.; K a r b n , U.0.;Englehnrdt, R.;Koch, E. E. Solid State Commun. 1986. _ _ _MI. ._ . 643-647. ,. ~ ._
(16)Handbook of Chembtry and Physics, 71et ed.; Lide, D.R.,Ed.;
CRC Boca Raton, FL,ISSO;p 12-69.
Figure4. Surfacegeometricstructureof CdS(0001)viewed from along the [00011direction. The open circles are Cd atoms. and the filled circles are S atoms. CdS(OO01). Calculationsweredoneonslabs6 CdSunita thick (18A). One side is the Cd-rich (0001) surface and the other side is the S-rich (0001). Figure 4 shows a view of the (0001) face and Figure 5 shows a cross sectionof the slab. It should be re-emphasized that these slabs are much thinner than a common spacecharge region. Nonetheless, as discussed in the Introduction, these calculations can still fulfii their ultimate objective of casting light on the origins of the band bending in these materials by showing to what extent electron density is pushed from the surface layers to the bulklike layers of the slab. The different amounts of charge build-up in the surface layers with and without adsorbates can be used in eqs 1and 2 to deduce A W. Only a few layers are required to describe the initial charge build-up, assuming that one portion of the slab can be treated as a bulklike source or sink for electrons. Because of the electrostaticpropertiesof the polar (OOO1) surface,the results of these calculationsare not as simple as the bulk calculationsor the calculationson the (1120) surface discussed below. If one pictures the slab being formed by removing portions of the bulk, the most important aspect of that process is the removal of the negatively-charged layer of S ions from the Cd-rich (OOO1) surface and removal of the positively-charged layer of Cd ions from the (0001) face. The consequence of thisis that a slab made of equal but oppositelycharged Cd and S ions will have an electrostatic potential extending across it resembling the electrostatic potential inside a capacitor with the positive plate located at the Cd-rich (OOO1) surface and the negatively charged plate located at the S-rich (0001) surface. This electrostatic potential shifts the atomic orbital energies and causes those toward the Cdrich side to be lower in energy than the corresponding energies toward the S-rich side. Such a potential will be important in pushing electron density toward the Cd-rich surface. In order to estimate the electrostatic potential at points inside the slab, one can treat the layers of Cd and S ions parallel to the surface as uniformly charged platee and calculate the potential using the equation V = 2rup(lz/p), where V is the potential, z is the distance from the plate, u is the charge per unit area on the plate, and p is the radius of the plate (much larger than z). Assuming that the magnitude of the charge on each ion is 0.5e, as determined in the bulk calculation,and that the geometry is as discussed in the Computational Details section,then by adding the potentials from all the plates in the slab one comes up with a potential difference of 5.2 eV between neighboring CdS layers parallel to the (0001) surface. In other words, if one assumes a band gap of 3 eV in each
Langmuir, Vol. 9, No. 1, 1993 181
NHs Adeorption on CdS Surfaces
layer of the slab, the bottom of the conduction band on a given layer will be 2.2 eV below the top of the valence band on the next layer away from the (0001) surface. Consequently, the potential gradient strongly pushes electrons from the valence band on the S-rich face into the conduction band on the Cd-rich face. On the other hand, the potential gradient is sensitive to the charges in the various layers, and the tendency of electronsto be pulled from the valence band on the S-rich side of the slab to the conductionband on the Cd-rich side is a strong function of how much electron density has already been transferred. Such factors indicate why the large potential gradient will not exist in the actual surface, and it also indicates why there is a major convergence problem in the self-consistentfield portion of the calculation, with pairs of orbitals on opposite faces of the slab repeatedly relinquishing and accepting electrons from each other as the iterations proceed. The convergence problem is worse when the orbitals exchanging electronsare further apart, and with the 20-A slab was impossible. While the potential gradient will clearly be important in determining the distribution of charge in the slab, the fact that it continues across the slab does not match the expectation that on the side of the slab representing the bulk one would expect it to disappear. To eliminate the potential gradient near the S-rich surface and make it more bulklike without affecting the potential gradient on the Cd-rich (0001) surface, and to minimize convergence difficulties by minimizing the distances between the orbitals accepting and relinquishing electrons,the calculation was modified by adding two oppositely charged plates to the slab. Specifically, a plane of negatively charged centers was put between the third and fourth layers of CdS's (counting from the Cd-rich face), and a plane of positively charged centers-was put just beyond the sixth layer of CdS's at the (0001) face. These planes of oppositely charged centers will be referred to as the "capacitor". Since no basis functions were put on any of these centers,their only effect was to essentiallyeliminate the electric field in the part of the slab away from the (0001) face. This allows the strong field associated with the polar surface to extend only through the top layers of the surface, and essentiallyeliminates it on the S-richside of the slab where one expects to find bulklike electronic properties. Appropriate charges for the centers making up the capacitorwere empirically found to be 0.36 to 0.36e, with one center per capacitor plate per unit cell. While the CdS units adjacent to these extra charged centers were electronically perturbed by their presence, the other layers of CdS units showed the desired responseto the capacitor. Figure 6 shows a cross section of the CdS(0001) slab with the imbedded capacitor as well as an idealized plot of the electrostatic potential extending through the slab. The key results of the calculationon the CdS(0001) slab with the imbedded capacitor are summarized in Figure 6 and Table II. Figure 6 shows the energies of the orbitals at the bottom of the conduction band and the top of the valence band in the two-dimensional Brillouin zones for the two layers closest to the surface and one in the center of the bulklike region. The one-electron wave functions for the slab are not strictly localized on one layer, but one can easily use the percent characters to unambiguously decide which layer dominates a given orbital. One sees that the electric field associated with the polar surface stabilized the energy levels in the surface layers so that a significant fraction (about 1576 ) of the Brillouin zone for the lowest conductionband orbital in the surfaceplane is below the top of the system valence band and is
(00011
(OOOT)
Figure 5. Cross section of the CdS(0001) slab including the imbedded capacitor (top) along with an idealized plot of the electrostaticpotential (bottom). The open circles are Cd atoms and the fiied circles are S atoms. The small circles representthe charged centers making-up the imbedded capacitor.
h
> Q,
Y
h
m L
al C
W
Figure 6. Two-dimensionalband structures including only the highest valence band level and the lowest conduction band level for layers parallel to the CdS(0001) surface. Table 11. Atomic Charges from FH Calculationr on CdS Surfaces with and without Adsorbed NHa* atomic charges (OOO1) NHd(0001) (11%) NHs/(ll%) Cd ( f i i t layer) 0.461 0.372 0.698 0.853 S (fiist layer) -0ma -0.644 -0.691 -0.772 CdS (fiist layer) -0.047 -0.172 0.007 -0.119 Cd (second layer) 0.523 0,641 0.582 0.585 S (second layer) -0.567 -0.576 -0.590 -0.607 CdS (second layer) -0.044 -0.035 -0.008 -0.022 Cd (center) 0.595 0.589 0.590 0.692 S (center) -0.560 -0.560 -0.589 -0.591 CdS (center) 0.035 0.029 0.001 0.001 NHs 0.124 0.141 a All charges have units of the magnitude of the electronic charge, e.
consequentlyoccupied. As a result of this situation each Cd on the (0001) surface gets about 0.3 electron it would not have in the bulk. The atomic charges resulting from the calculations on the CdS(0001) surface are given in Table 11. The 0.3 electron in the conduction band at the surface does not make the Cd's in the outermost layer fully 0.3e more negative than the other Cd's for two reasons: (1)there ie some rearrangementof charge in the other orbitale to partly negate the negativecharge build-up on the Cd's and, moat importantly, (2) in forming the surface,the Cd atoms have
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182 Langmuir, VoZ. 9, No.1, 1993
lost the shared electron density from the heterolyticey broken Cd-S bonds. Based on the results from the (1120) surface to be discussed below, this shared electron density is about O.lle per Cd. The net charges on the layers of CdS units are also given in Table 11. One sees that the partial occupation of the conduction band at the surface gives rise to a small charge of -0.047e for the first CdS layer, and -0.044e for the next layer. This is the charge that comes from the bulklike region of the slab to the surface under the influence of the field created by the polar surface, and this is the charge build-up we were looking for to explain the origins of the band bending. It should be emphasized that in order for the negative charge on the outermost layers to cause band bending in the real material, it must not be fully countered by holes in the valence band of the nearby layers. If it were, there would not be any band bending, only a shift in the work function since only a surface dipole would have been established. In thin slab calculationssuch as these in which charge neutrality is maintained and dopants are not accounted for, the negatively charged surface layers will necessarily be countered by holes in the valence band of layers on the other side of the slab. In the real material the electrons from the dopants or lattice defects would fill such holes in the valence band, and the net effect would be that electrons came from the bulk to occupy the stabilized portion of the conduction band at the surface. Hence, in the real material the countercharge to the negative surface layers comes from the dopant ions and lattice defects which are not very mobile and are not concentratednear the surface. They do not readily negate the electric field associated with the negatively charged surface, and band bending extends over a substantial distance. The part of the calculation that is predicted to correspond to the real surface is the build-up of electron density in the conductionband at the surface. The valence band holes needed in the calculation to counter the negative charge at the surface are not predicted to exist on the real surface; on the real surface their function is fulfilled by the positively charged dopant centers and lattice defects extending much further into the bulk. Another interesting feature of the (0001) surface is the nature of the surface states. Figure 6 shows no special states arising from the top of the valence band or the bottom of the conduction band at the surface. No levels show up in what would be referred to as the surface band gap. One might have expected that the CdS antibonding levels in the conduction band would be stabilized into the band gap when the Cd-S bonds are broken to form the surface. Examinationof some of the higher energy regions of the conduction band shows that there is an antibonding level that becomes stabilized when the surface is formed, but since the Cd portion of that level is primarily Cd 5p in nature and since the Cd 5p orbitals lie high above the band gap, the stabilization of the antibonding level does not necessarily bring the level all the way into the band gap. Indeed, a surface state which is primarily Cd 5p in nature is between the lowest conduction band levels for the first two layers, but never gets below the lowest Cd 5s-derived level. Hence, the calculationspredict that no surface state should be seen in the band gap, and, indeed, there is no high density of surface states experimentally detected in the band gap.17 NH3/CdS(OOOl). Calculations on NH3 adsorbed on CdS(0001)were carried out using the same unrelaxed slab (17) Lagowski, J.; Balestra, C. L.; Gatos, H. C. Surf. Sci. 1972, 29, 213-229.
a
NH3/CdS
(000:)
LJ
w w
f
db
Figure7. Surface geometric stryctureof NH3 adsorbed on CdS(OOO1) viewed from along the [03311direction. The open circles are Cd atoms; the filled circles ar S atoms; the stripped and cross-hatched circles are N and H atoms, respectively.
and capacitor used for the bare slab calculations. The NH3 adsorption geometry is as discussed in the Computational Details section and is shown in Figure 7. The results listed in Table I1 show that the NH3 puts about 0.124 electron into the surface, but almost all of that stays in the first two layers of CdS's. Only 0.008 electron moves into the bulklike region where the capacitor eliminates the electric field. Using eq 3 with a typical ne of 10 ppm, one finds that a change in charge of 0.008e should lead to a change in the width of the space charge region of 2700 A; the observed change, derived from the photoluminescence experiments2 was about 750 A on CdSe.l* Sinceexperimental results using butenes showed that CdS has almost 2 times greater change in the width of the space charge region than CdSe, one might expect that the calculated value of 2700 A ought to be compared with an experimental value of about 1500A. Considering the level of the calculation, it is gratifying that the order of magnitude appears to be correct. In addition to the displacement of electron density toward the bulk, NH3 adsorption polarizes the lower conduction band orbitals away from the surface, but not very far. In the bare slab the contribution from the first Cd layer to the lowest conduction band orbital at the r point is 97 % Cd 5s,but with adsorbed NH3 it is only 7396 Cd 5s, the remainder being Cd 5p polarizing the orbital away from the NH3. It may seem surprising that the NH3 adsorption did not suitably destabilize the bottom of the conduction band, but since the bottom levels of the conduction band are primarily Cd 5s in character and since the NH3 interacts most strongly with the Cd 5p orbitals perpendicular to the surface, only the levels which were predominantly Cd 5p were greatly destabilized and the lower lying Cd 5s levels were unaffected energetically, but were polarized away from the adsorbed NH3. Little can be concluded from these calculations about non-radiative surface recombination. If any goes on involving electrons in the conduction band at the surface, these calculations suggest that NH3 adsorption does not influence it by destabilizingthat band. One would predict a change in surface recombination with NH3 adsorption only if it were sensitive to the polarization of the orbitals making up the bottom of the conduction band. CdS(ll20). Calculations were also done on the (1120) surface for comparison with the results from the (0001) surface. The surfaceis shownin Figure 8. Sincethe (1120) surface has equal numbers of Cd and S atoms, it is not polar, and the convergence problems associated with the (18) In doing this calculation the resulta from Table I of ref 2 were modified to pertain to a full monolayer. Based on Figure 6 of ref 2, the conditions used in Table I gave surface coverages of about 76%.
Langmuir, Vol. 9, No. 1, 1993 183
NH3 Adsorption on CdS Surfaces
NH3/CdS
,
.
(19) Wiklund, S.;Magnwon, K.0.; Flodatrom, S.A. Surf. Sci. 1990, 238,187-191.
w
g
Fig-ure 9. Surface geometric strusture of NH3 adsorbed on CdS(1120) viewed from along the [1123] direction. The open circles are Cd atoms; the filled circles are S atoms; the striped and crosshatched circles are N and H atoms, respectively.
Figure 8. Syface geometric structure of CdS(ll20) viewed from along the [1123] direction. The open circles are Cd atoms, and the filled circles are S atoms.
(0oO1) surface were not encountered. However, since the convergenceproblemswith the (0001)surfacewere caused by the physical situation (a polar surface) that wound-up leading to the band bending at that surface, the lack of convergenceproblems with (1120)suggeststhat any band bending or photoluminescent changes accompanying adsorption occurs for different reasons than on the (0oO1) surface. The results show that the calculated band structure is basically an extension of the bulk band structure. However, since there is no strong electric field associated with forming the surface, none of the resulting orbitals are concentrated on particular layers of atoms parallel to the surface. Indeed, the conduction band orbitals are spread across the slab and resemble particle-in-a-box wave functions perpendicular to the surface. The calculated atomic charges are listed in Table 11. The surface Cd’s are much more positive than the bulk, and the surface S’s are much more negative than the bulk. This is simply because the electron density shared in a Cd-S bond goes to the sulfur when the Cd-S bond is broken to form the surface. Part of that extra electron density is shared with the neighboring Cd in the second layer. Consequently the net charge on the first surface layer is slightly positive and the charge on the next layer down is slightly negative, but they are about equal in magnitude, so the calculations predict no charge build-up on the CdS(1120) surface. This prediction of the greater charge on the surface atoms is in line with recent observations of the shifts in the XPS peaks for surface atoms CdS(1120),19 but, as reported with the experimental results, this effect is small, and the change in the Madelung potential from bulk to surface is the primary cause of the shift in XPS peaks. This lack of charge build-up on the CdS(ll20) surface is in line with the fact that photoluminescence is at least an order of magnitude higher on the nonpolar cleaved face.2 Without the charge build-up no electric field is generated to bend the bands and create a space charge region, and without much of a space charge region the photoluminescence intensity is high. The calculations also predict that inclusion of electron density in the conduction band would not lead to surface charge build-up. The fact that the conduction band orbitals resemble particle-in-a-box wave functions perpendicular to the surface indicates that any electron density in the conduction band would be concentrated away from the surface like the particle-in-a-boxfunctions. NHdCdS (1120). Calculationsinvolving NH3 adsorbed on CdS (1120) were done using the same slab used in the
(1120)-
TI 0
.-C L 9)
10-
: CdS
u
81
0
6-
E 0 Y
t
i
4-
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.
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a
2-
I
A.-
1
2
3 4 Layer
5
L
J
6
Fig-ure 10. Contribution of Cd atoms in each layer of the CdS(1120) slab to the bottom of the conduction band at the I’point with and without adsorbed NH3. Open circles refer to the bare slab, and filled circles refer to the slab with NH3 adsorbed on the first layer.
bare slab calculations discussed above. The adsorption geometry is as discussed in the Computational Details section and is shown in Figure 9. The resulting atomic charges are listed in Table 11. Unlike the (OOO1) surface, on the (1190) surface all of the electron density donated to the CdS by the NH3 remains in the first two layers of CdS units. Consequently, one would not expect any change in any space charge layer; adsorption of NH3 simply creates a dipole at the surface and does not move any charge to or from the bulk. While NH3 adsorption does not influencethe charge distribution in a manner that would be predicted to affect the width of the space charge region, it does have one noteworthy effect on the electronic structure; it pushes the crystal orbitals at the bottom of the conduction band away from the surface toward the bulk. Figure 10 shows the atomic character (defined as the sum of the Mulliken percent characters of the atomic orbitals on a Cd atom in a given layer) of the lowest lying conduction band orbital in the slab as a function of distance from the surface layer with and without adsorbed NH3. The NH3 effectively cuts the surface contribution to the conduction band in half, and the effect is felt across the entire slab. Consequently, if, for reasons unaccounted for in these calculations, any electron density builds up in the conduction band at the bare surface, it will be pushed back toward the bulk when NH3 is adsorbed. This would enhance the photoluminescence when the NH3 is adsorbed, but not in a manner easily quantifiable with calculations like these which do not explicitly include electron density in the conduction band and which do not predict a build-up of electron density in the conduction band at these surfaces.
184 Longmuir, Vol. 9,No. 1, 1993
Conclusions These calculations have shown that the electrostatic potential generated by the formation of the (OOO1) surface stabilizesthe Bottom of the conduction band at the surface enough to drop below the top of the bulk valence band and consequently becomes partially occupied. Assuming that the field aerbciated with the polar surface is not felt more than a few layers from the surface, then it is the charge build-up in the stabilized conduction band at the surface that gives rise to the space charge region. NH3 adsorption pushes a small fraction of the built-up electron density back toward the bulk, and this small amount is more than enough to account for the change in the width of the space charge region deduced from the photoluminescence experiments.2 Even though these calculations have dealt only with NHs adsorption, the general conclusions can be extended to the many other adsorbates that have been experimentally examined on such surfaces.14~20The key feature uncovered with these calculations is that the conduction band is partially occupied at the (OOO1) surface due to the polarity of that surface. The Lewis base adsorbates would be predicted to push that surface electron density to the bulklike region in a manner similar to NH3, thereby reducing band bending, and Lewis acid adsorbates, like SOz,lCwould be predicted to pull additional electron density from the bulklike region, thereby increasing band bending. On the (1120) surface the absence of an electric field associated with the creation of the surfaceleads to virtually no charge build-up at the surface and, consequently, no significant space charge region. It is found that NH3 adsorption pushes the lowest conduction band orbital toward the bulk, but this would only affect the width of the space charge region if there was electron density builtup in this orbital near the surface before adsorption, and these calculations show no motivation for this happening. The best correlation with experiment for the calculations on the (1130) surface is that the prediction of essentially zero width for the space charge region is in line with the large photoluminescence intensity.2 The model of photoluminescence enhancement with NHs adsorption that depends on the change in the width of the spacecharge layer is well established experimentally as far as the (OOO1) Surfaceis concerned,and it is gratifying that our computational results show a good correlation with the model. Our computational results do not show a good correlation with this model as applied to the (1120) surface, but that is not necessarily bad since the experimental results on the cleaved surfaces do not showa good correlation with the model either. The poor match to model predictions2 and the time dependence of the photoluminescent decay on NH3 adsorption3suggest that the photoluminescenceis being enhanced, at least partly, by some other mechanism on the cleaved surfaces. Overall the calculations show the strong influence of the electrostaticfield generated by the ions on the behavior of the important electronic energy levels near a binary semiconductor surface. The field is dependent on the charges on the ions, and if these charges have been overestimated in the calculation, some of the quantitative conclusionsreached in this paper may need to be modified. (20) (a) Lmn~ky, G. C.;Penn, R. L.Murphy, C. J.; Ellis,A. B. Science 1990,248,840-843. (b)Murphy, C. J.; Ellie, A. B. Polyhedron 1990,9, 1913-1918. (21) Weat. A. R. Solid State ChemMtry and it8 Applications; John W h y and SOM:Chicheater, U.K., 1987; pp 292-296. (22) Holliigsworth, R. E.; Sites,J. R. J. Appl. Phys. 1982,63,53575358.
Rives The principal concluBions, however, are not sensitive to the method's ability to predict the atomic charges. Even if the charges are as small a 0.176, as the Sanderson electronegativity scheme*lwould predict, the conduction band edge at the (OOO1) surface would still be stabilized relative to the corresponding levels in the bulk, and there would be a build-upof negative charge as the mobile charge carriers partially fill the conduction band at the surface. It is not essential that the electric field be so strong as to bring the conduction band at the (OOO1) surface below the bulk valence band; either way charge will be built-up at the surface and lead to band bending. On the (1120) surface smaller atomic charges would not change the predictions of this paper; the surface would still be nonpolar, no significant charge would be built-up at the surface,and there would still be no significantspace charge region. Acknowledgment. I am grateful to Professors A. B, Ellis and A. J. Bard for helpful discussions. This work was supported by the UNCG m a r c h Council and the UNCG Division of Instructionaland Research Computing. Appendix Like other adaptations of molecular orbital techniques to problems involving translational symmetry, the tightbinding approximation is utilized for the FH technique. The resultant crystal orbitals, $k, are expressed as linear combinations of crystal orbital basis functions, $a, which are themeelves linear combinations of a particular type of atomic orbital, e,, in each unit cell a
Here the wave vector k refers to a point in the Brillouin zone and serves essentially the same function as an index identifyingthe symmetrytype in a conventionalmolecular orbital calculation; j refers to a unit cell at lattice point, rj; a refers to a particular atomic orbital in a unit cell;the c values are the coefficients which are solutions to the Hartree-Fock equation for a particular k;and the 1 values are normalization coefficients. Once the form of the orbitals is defined, one can solve the conventionalRoothaan's equationswhere the matrices are defined with respect to the crystal orbital basis functions FkCk
shc$k
where Fk is the matrix of the Fock operator for a given k vector, c k is the coefficients matrix, Sh is the overlap matrix, and & is the vector of crystal orbital energies. Similar to any other self-consistent field problem, an approximate density €unction or density matrix ia used to evaluatethe standard one-electron Fock matricesfor some predetermined set of k's spread over the f i t Brillouin zone. Solving Roothaan's equations gives a set of eigenvectors or crystal orbitals from which can be constructed a new electron density. The process is repeated until selfconsistency is attained. Sincethe crystal orbital basis functionsare simplysums of atomicorbitals modulated by the exponentiala involving the wave vectors, the Fock matrix elements can be expressed as modulated sums of conventional integrala over atomic orbitals
Langmuir, Vol. 9, No. 1, 1983 186 Table 111. Results of FH Calculationi on Bulk CdS Using Different Numbers of Unit Cells*b dispersion band valence conduction charge/ unit cells bandd gap bandc atom (e)
But since the sum for any one lattice point j is the same as for any other, eqs A1 can be simplified as follows Fm,,,(k)= l k m l k f l
c I
exP(ik*(rj- ro))( ~ m o I F I ~ n j ) (A21
where N is the number of lattice points in the crystal, and the lattice point r, identifies a reference unit cell. Since N will cancel out in the Roothaan equations, its value is not important, but the value will define what is meant by a normalized crystal orbital. For simplicity,N is set equal to unity in this program. The adaptation of the FH method or any other molecular orbital technique to problems involving translational symmetry is simply a matter of expressing the necessary integrals over the atomic orbitals in eqs A2 in terms of the method‘s established approximations. For the FH technique these approximations are given in ref 7. Two decisions need to be made for the practical implementation of this technique: (1) when to truncate the remaining summation in eqs A2 and (2) how many of the potentially infiiite number of k vectors to treat explicitly. Truncating the summation in eq A2 is simply a matter of deciding how far apart unit cells can get before the interactions between their atomic orbitals can be neglected. This can alternatively be viewed as deciding how small the overlap integrals can get before simply neglecting them. With a minimal basis set this can involve as little as one layer of unit cells around the reference unit cell,but if diffuseatomic orbitals are used, more unit cells are needed. If too few cells are chosen, the overlapmatrix of crystal orbital basis functions may be so poorly defined that it has negative eigenvaluesand the calculationcannot proceed. In addition to the short-range overlap-related interactions, the Coulombic influence of atoms much further away will also affect the orbital energies and must be accounted for. As typically run, the adapted FH program includes orbital interactions up to about 10 A and includes Coulombic interactions up to about 60 A. The choice of k’s to use in the calculationinfluences the calculated electron density. Population analysis on the results of calculations at different k’s can have widely differentresults. In bulk CdS, for example,the calculation at the r point results in a Cd charge of +0.934e, while at the M point the Cd charge is +0.474e. The actual charges and orbital occupations used in evaluating the various matrix elements are determined by averaging over the k’s. Consequently, one sees that in order to get a good average of the electron density, one needs to have a good selection of k’s.
9 15 27 33 45 69 101 131
0.514 0.516 0.516 0.516 0.516 0.515 0.515 0.515
2.85 2.82 2.61 2.60 2.62 2.63 2.63 2.63
1.02 1.07 1.00 1.01 1.00 1.00 1.00 1.00
4.85 4.76 4.62 4.61 4.57 4.56 4.56 4.56
*
a All energiea have units of eV. All calculations used 84 k vectors throughout the first Brillouin zone. Difference in energy between the r and M pointe at the top of the valence band. d Difference in energy between the r and M pointa at the bottom of the conduction band.
Table IV. Results of FH Calculations on Bulk CdS Using Different Numbers of P Vectors*b diswrsion k charge/ band valence conduction vectors atom(& gap bandC bandd 8 64 192
0.549 0.516 0.513
2.51 2.62 2.63
0.97 1.00 1.00
4.65 4.57 4.57
All energiee have units of eV. b All calculationsused 33 interacting unit cells. Difference in energy between the I’ and M points at the top of the valence band. Difference in energy between the l’ and M points at the bottom of the conduction band.
Tables I11 and IV respectively show the dependence of the bulk CdS results on the number of unit cells and number of k’s used in the calculation. One sees that only 27 unit cells are needed to obtain an essentiallyconverged result. This represents the collection of nearest neighbors and next nearest neighbors around a given lattice point. Similarly, using 64 k vectors closely approximates the limiting result which would be obtained with a large number of k vectors. Even with smaller numbers of unit cells and k vectors the results are not dramaticallydifferent from the converged limit; consequently, the method is rather forgiving in parameter selection. Further changes have been made to the FH program to make it more suitablefor solid-statecalculations. It allows for noninteger nuclear charges and noninteger numbers of electronsin a unit cell; this is designed to let one account for the mobile charge carriers in a semiconductorwithout having to use unit cells large enough to includethe dopant atom or lattice defect that gives rise to the mobile charge carriers. Also, the ability to include plane waves in the basis set for systemswith three-dimensional translational symmetry has been added. Neither of these two changes to the FH program has been found to be particularly valuable in the CdS calculations reported in this paper, so they are not discussed further.
