On the Description of the Coadsorption of Cesium and Selenium Atoms on the Silicon Surface

ISSN 063-7834, Physics of the Solid State, 009, Vol. 5, No. 4, pp. 849 853. Pleiades Publishing, Ltd., 009. Original Russian Text S.Yu. Davydov, 009, published in Fizika Tverdogo Tela, 009, Vol. 5, No. 4, pp. 803 807. LOW-DIMENSIONAL SYSTEMS AND SURFACE PHYSICS On the Description of the Coadsorption of Cesium and Selenium Atoms on the Silicon Surface S. Yu. Davydov Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 6, St. Petersburg, 940 Russia e-mail: sergei_davydov@mail.ru Received July 5, 008 Abstract Adsorption of cesium and selenium atoms on silicon surface has been considered in terms of the Anderson Newns Mooskat model with allowance for the dipole dipole repulsion. The results obtained have been applied to the problem of coadsorption of Cs and Se atoms. It has been shown that even a small addition of cesium adatoms to a submonolayer selenium adatom film on silicon strongly increases the charge of selenium adatoms. This effect is initiated by the mutual enhancement of the dipole fields of the Cs and Se adatom sublattices. All the results obtained agree well with experimental observations. PACS numbers: 73.0.Hb, 73.43.Cd DOI: 0.34/S063783409040374. INTRODUCTION At present, adsorption of alkali metals on silicon can be considered fairly well understood, both experimentally and from the theoretical standpoint (see, e.g., [] and references therein). It has been reliably established that electrons transfer from the adatoms to the substrate, which makes their charge positive and reduces the work function of the system. On the other hand, adsorption of Group VI atoms (S, Se, Te) on silicon has not been explored as thoroughly [ 4]. A theoretical analysis [5] has revealed, however, that in this case electrons transfer from the substrate to adatoms, which acquire a negative charge, thus raising the work function of the adsorption system. Papageorgopoulos and Kamaratos [4] experimentally studied a more complex case, namely, coadsorption of cesium and selenium on the Si()-7 7 surface. This study revealed intriguing effects (see below) which are going to be clarified theoretically in the present publication. Sections and 3 consider separately the Cs/Si()-7 7 and Se/Si()-7 7 systems, and in Section 4 we shall establish the pattern of Cs and Se adatom interaction. In all cases, we are going to treat the adsorption process within the Anderson Newns Mooskat model, which has been found to apply nicely to a broad range of adsorption systems (see, e.g., [, 5 7]).. ADSORPTION OF CESIUM ON SILICON We start with characteristics of the silicon substrate. Silicon has an electron affinity χ = 3.99 ev and a band gap E g =. ev [8]. We accept for the work function of the () face ϕ() = 4.60 ev [9]. Whence it follows that the Fermi level (chemical potential) lies below the band gap of silicon, making it a hole semiconductor. Adsorption of cesium atoms involves electron transfer from the cesium 6s state to the dangling, singly filled sp 3 substrate orbital. Alternately, these can be dehybridized s p 3 or sp orbitals. Considered from the standpoint of model description, this fact is rather inessential, because the interaction of the atom being adsorbed by the substrate is described by a single matrix element V. The model of Anderson Newns Mooskat proposes the following relations for the adatom charge Z and the change in the work function φ caused by adsorption [, 5 7]: Z( Θ) Ω ξθ 3/ Z( Θ) = -- arctan------------------------------------, π Γ ξ = e λ N 3/ ML A, φ( Θ) = ΦΘZ, Φ = 4πe N ML λ. () () Here, the coverage Θ = N/N ML, where N is the concentration of adatoms on the surface and N ML is that in a monolayer (0 Θ ); λ is the adsorption bond length, For some obscure and poorly understood reasons, authors of experimental publications dealing with adsorption systems do not feel fit to identify the original work function of the clean substrate ϕ. Furthermore, one not always communicates to the Reader even its type of conduction. For instance, only the second of the studies [4, 0] with which we are going to compare the results of our calculations mentions that the substrate was boron doped and, hence, is a hole semiconductor. 849

850 DAVYDOV Parameters of the problem and results of the calculation (λ in Å; Ω, Γ, ξ, and Φ in ev; Z 0 Z(0)) System λ Ω Γ ξ Φ Z 0 Z ML Cs/Si().5.77.8 7.83 9.4 0.630 0.6 Se/Si().5 0.63 8.98 4.0.30 0.045 0.0 Note: By the charge Z ML for the Cs/Si() system we understand here the charge Z 0.5 Z(0.5). the position of the quasi-level of a single adatom relative to the substrate Fermi level is Ω = φ I + e /4λ, (3) where I = 3.89 ev is the ionization energy of the cesium atom and e /4λ is the Coulomb shift; Γ = πρ s V is the quasi-level halfwidth (ρ s is the energy density of states of the substrate); and A ~ 0 is a dimensionless coefficient which is an analog of the Madelung constant and depends only weakly on the structure of the adatom lattice, We note that Eq. () is written accounting for the dipole dipole interaction of adatoms which is characterized by the constant ξ. Let us turn now to determination of the characteristics of the Cs/Si adsorption system starting with the length of the arm of the surface dipole λ, which is equal to the thickness of the double electric layer formed by the charged adatoms and their images in the substrate. While being fairly conventional, it is an extremely important characteristic (see Eqs. () and ()) valid for an ideal (specular) surface. The cesium- φ, ev 0 3 Cs/Si() 7 7 3 4 0 0. 0. 0.3 0.4 0.5 Fig.. () Theoretical values and (, 3) experimental data taken from () [4] and (3) [0] for changes in the work function φ(θ) of the Cs/Si()-7 7 adsorption system. coated Si()-7 7 face is by far not so perfect. We shall have therefore to choose the values of λ such that the calculated curve φ(θ) will fit the experimental relation, the only essential point to be followed in this procedure being that the value of λ lie within the 0.5 3-Å interval. This procedure yielded the value λ =.5 Å. Next, we set the density of silicon atoms on the () face equal to N ML() (Si) = 7.83 0 4 cm [4]. We shall assume that for one monolayer coverage (ML Θ Si = ), Cs atoms are at a distance d = 5.35 Å from one another, which fits the nearest neighbor separation in bulk cesium crystals []. Significantly, this value of d practically coincides with the value of r a, where r a =.6 Å is the atomic radius of cesium [9]. For Θ Cs =, we obtain now for the density of cesium atoms N ML (Cs) = d = 3.65 0 4 cm ; this means that the value Θ Cs = corresponds to Θ Si() = N ML (Cs)/N ML() (Si) = 0.47. It is Θ Si() that we are going to understand by coverage Θ subsequently in this Section. The other parameters of the problem are determined by the scheme described in detail in our preceding publications (see [, 5 7] and references therein). The parameters of the problem and the results of the charge calculations are presented in the table and displayed graphically in Fig.. Examining Fig., we see that the calculations fit well with experimental data. Figure plots the Z(Θ) relation showing that the charge decreases with increasing Θ. This result is of a general nature; indeed, all interaction channels of adatoms bring about their depolarization, i.e., a decrease of their charge []. This effect is particularly easy to interpret in the case of dipole dipole repulsion, the only process we are considering here. We note first of all that the dipoles considered here are induced rather than rigid, p = eλz. An external electric field is known to affect the dipole moment p of such dipoles. Imagine a lattice of identically oriented dipoles. The fields of all dipoles acting on the dipole of interest suppress its field, thus reducing its dipole moment. It appears then only natural that as the lattice period corresponding to an increase of the coverage Θ decreases, the resultant field suppressing the given dipole moment increases. This is what underpins the mechanism of dipole dipole depolarization. Translat- Experimentalists have been recently following the convention of presenting measurements of work function variation vs. the exposure time (adatom deposition time on the substrate surface) t, without even making an attempt at assigning a specific value of Θ to the measured value of φ. This entails certain difficulties for theory, because it forces the theoretician to accept an exposure time t as t ML corresponding to monolayer coverage. As a rule, one accepts for a monolayer the value of t at which the relation φ(θ) reaches saturation. PHYSICS OF THE SOLID STATE Vol. 5 No. 4 009

ON THE DESCRIPTION OF THE COADSORPTION OF CESIUM AND SELENIUM ATOMS 85 0.7 0.6 Cs/Si() 7 7 0.5 0.4 Se/Si() 7 7 Ζ 0.5 0.4 φ, ev 0.3 0. 0.3 0. 0. 0 0. 0. 0.3 0.4 0.5 Fig.. Charge Z of cesium adatoms vs. coverage of the Si()-7 7 surface. 0 0. 0. 0.3 0.4 0.5 Fig. 3. () Theoretical and () experimental [4] values of changes in the work function φ(θ) for the Se/Si()- 7 7 adsorption system. ing this to terms of energy, we can say that an increase of Θ corresponds to a shift of the quasi-level Ω ( θ) = Ω ξθ 3/ Z( Θ) (4) down, i.e., toward the Fermi level. In these conditions, the originally nearly empty adatom quasi-level starts becoming filled by electrons of the substrate, thus lowering its charge Z. Another point is worth mentioning here. Figure reveals the existence of three characteristic regions of charge variation, namely, those of low coverage (0 Θ 0.), intermediate coverage (0. Θ 0.3) and high coverage (0.3 Θ 0.5). This behavior of the Z(Θ) function can be traced to a displacement of the adatom density of states (the Lorentzian contour) ρ a ( ω) Γ = -- ------------------------------. π( ω Ω ) + Γ (5) At low coverages, only the lowest tail of the Lorentzian distribution overlapping with the Fermi level operates, as a result of which the shift of the quasi-level affects only weakly its filling. At intermediate coverages, where the center of the quasi-level Ω begins to approach the Fermi level, the part of the contour closest to the maximum becomes operative, after which the charge will decrease faster with increasing Θ. Finally, at high coverages only the upper tail of the contour falls close to the Fermi level, which slows down again the charge variation. 3. ADSORPTION OF SELENIUM ON SILICON The model we are going to use here in studying adsorption of selenium will be the one proposed in [5]. Experiment shows [4] that adsorption of selenium on the Si()-7 7 surface increases the work function ( φ > 0); this evidences electron transfer from the substrate to the adatom, a process in which the electron hops from the dangling silicon sp 3 orbital to the vacant p orbital of selenium. 3 The electron affinity of the selenium atom is A =.0 ev [9] (with the energy reckoned from the vacuum level down). We thus obtain the following relation for the quasi-level energy of a free adatom relative to the Fermi level e Ω = A φ + -----. (6) 4λ This expression is an analog of Eq. (3). In the case of Eq. (3) describing electropositive adsorption the electron transfers to the substrate from an upward shifted level I' = I e /4λ, whereas Eq. (6) relates to the substrate electron transferring to the downshifted vacant level A' = A + e /4λ. In [5], one accepted for the λ parameter the atomic radius r a =.6 Å of the selenium atom [9]. We choose here λ =.5 Å, i.e., the value for the cesium adatom, which permits us to cut by one the number of parameters of the problem. The starting parameters and results of the calculation for the selenium adatom charge are listed in the table. In experimental data treatment, we took for the selenium mono- 3 As before, we assume that only one electron is involved in the charge transfer. PHYSICS OF THE SOLID STATE Vol. 5 No. 4 009

85 0.45 0.40 Se/Se() 7 7 DAVYDOV.4.0 Se Cs/Si() 7 7 0 Z 0.35 0.30 α.6 0.5. 0.0 0 0. 0.4 0.6 0.8.0 Fig. 4. Charge Z of selenium adatoms vs. coverage of the Si()-7 7 surface. 0.8 0 0.05 0.0 0.5 0.0 0.5 Θ Cs, ML Fig. 5. () Ratio α defined by formula (8) vs. coverage of the Si()-7 7 surface by cesium. () Experimental values of the ratio taken from [4]. layer the value corresponding to 0 exposures (see footnote ). The results of the calculation of the φ(θ) relation are shown graphically in Fig. 3. The agreement of calculated with experimental data can be considered satisfactory, although it should be added that choosing the atomic radius r a =.6 Å for the length of the adsorption bond [5] resulted in a better correspondence. Figure 4 plots the absolute value of the charge of selenium adatoms vs. their concentration. We again see a clear manifestation of adatom depolarization. Note that in this particular case the Z(Θ) relation within the intermediate and high coverage region is close to linear. At low coverages, only the lower tail of the Lorentzian contour is seen. We note with interest also the extremely small value of the selenium charge compared with the charge of cesium. In this case, adatom depolarization is of the same origin as in the case of cesium adsorption. The only difference is that in these particular conditions the dipole moments p are oriented in the opposite direction (compared with those of cesium). 4. EFFECT OF SMALL CESIUM EXPOSURE DOSES ON SELENIUM ADATOM CHARGE IN THE CS SE/SI()7 7 STRUCTURE It was demonstrated [4] that already small additions of cesium reduce drastically the work function of the Se/Si()-7 7 system. This effect manifests itself in an increase of the original (corresponding to the zero coverage limit) charge of selenium adatoms Z 0 (Se) initiated by adding small amounts of cesium (see Fig..7 in [4]). To fine a proper interpretation of this effect, one should, generally speaking, solve a system of two selfconsistent equations of the type of Eq. (), where in place of one dipole term in the numerator, however, one would have to put three terms with different dipole interaction constants ξ Cs Cs, ξ Se Se and ξ Cs Se, which correspond, accordingly, to cesium cesium and selenium selenium repulsion and cesium selenium attraction. We shall choose a simpler way and calculate the initial values of selenium charge Z 0 (Se) from the formula Z 0 ( Se) Ω ξ -- Cs Cs Θ 3/ Cs Z Cs ( Θ Cs ) = arctan-------------------------------------------------------, π Γ (7) where the parameters Ω and Γ relate to selenium adatoms. Figure 5 plots the ratio Z 0 0 α Z 0 ( Se) = ----------------, Z 0 0 ( Se) (8) where (Se) is the selenium charge in the absence of cesium, vs. cesium coverage of the Si()-7 7 surface. The calculated data are seen to fit well with experiment. The physical factors accounting for the increase of selenium adatom charge initiated by insertion of cesium charge were first revealed in [3] and are as follows. Imagine a lattice of alternating, oppositely oriented dipoles. In this case, the field generated by the sublattice, say, of identical cesium dipoles tends to increase the dipole moments of adatoms in the selenium sublattice. And conversely, the field of the selenium sublattice amplifies that of the cesium sublattice. PHYSICS OF THE SOLID STATE Vol. 5 No. 4 009

ON THE DESCRIPTION OF THE COADSORPTION OF CESIUM AND SELENIUM ATOMS 853 When the lattice constant decreases, a case corresponding to the increase of Θ, the dipole sublattice interaction becomes enhanced. Thus, we have here additional polarization rather than depolarization of adatoms as in the two preceding cases. Thus, using apparently the simplest adsorption model of Anderson Newns Mooskat, with only the dipole dipole interaction added, we have succeeded in adequately describing the variation of the Si()-7 7 surface work function stimulated by both separate and codeposition of layers of electropositive cesium and electronegative selenium. Thus, this model has once more substantiated its validity. ACKNOWLEDGMENTS This study was performed within the program Development of the Scientific Potential of the Higher School of the Russian Federation (project no. RNP..76 K). REFERENCES. S. Yu. Davydov and A. V. Pavlyk, Zh. Tekh. Fiz. 74 (8), 96 (004) [Tech. Phys. 49 (8), 050 (004)].. A. C. Papageorgopoulos and M. Kamaratos, Surf. Sci. 35 354, 364 (996). 3. A. C. Papageorgopoulos and M. Kamaratos, Surf. Sci. 466, 73 (000). 4. A. C. Papageorgopoulos and M. Kamaratos, J. Phys.: Condens. Matter 4 (), 555 (00). 5. S. Yu. Davydov, Fiz. Tverd. Tela (St. Petersburg) 47 (9), 7 (005) [Phys. Solid State 47 (9), 779 (005)]. 6. S. Yu. Davydov and S. V. Troshin, Fiz. Tverd. Tela (St. Petersburg) 50 (7), 06 (008) [Phys. Solid State 50 (7), 56 (008)]. 7. D. G. An chkov, S. Yu. Davydov, and S. V. Troshin, Pis ma Zh. Tekh. Fiz. 34 (8), 54 (008) [Tech. Phys. Lett. 34 (9), 795 (008)]. 8. F. Bechstedt and R. Enderlein, Semiconductor Surfaces and Interfaces (Akademie, Berlin, 988; Mir, Moscow, 990). 9. Handbook of Physical Quantities, Ed. by I. S. Grigoriev and E. Z. Meilikhov (Énergoatomizdat, Moscow, 99; CRC Press, Boca Raton, FL, United States, 996). 0. T. Kan, K. Mitsukawa, T. Ueyama, M. Takada, T. Yasue, and T. Koshikawa, Surf. Sci. 460, 34 (000).. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 953; Nauka, Moscow, 978).. O. M. Braun and V. K. Medvedev, Usp. Fiz. Nauk 57 (4), 63 (989) [Sov. Phys. Usp. 3 (4), 38 (989)]. 3. S. Yu. Davydov, Appl. Surf. Sci. 40 (), 58 (999). Translated by G. Skrebtsov SPELL:. ML - italic or plain? PHYSICS OF THE SOLID STATE Vol. 5 No. 4 009