Schottky barrier formation. II. Etched metal-semiconductor junctions

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1 Home Search Collections Journals About Contact us My IOPscience Schottky barrier formation. II. Etched metal-semiconductor junctions This content has been downloaded from IOPscience. Please scroll down to see the full text J. Phys. C: Solid State Phys ( View the table of contents for this issue, or go to the journal homepage for more Download details: This content was downloaded by: jsdehesa IP Address: This content was downloaded on 13/10/2013 at 17:44 Please note that terms and conditions apply.

2 J. Phys. C: Solid State Phys., 17 (1984) Printed in Great Britain Schottky barrier formation: 11. Etched metalsemiconductor junctions J Sanchez-Dehesa, F Flores and F Guinea Departamento de Fisica del Estado Sdlido, Universidad Autdnoma, Cantoblanco, Madrid 34, Spain Received 17 May 1983, in final form 14 October 1983 Abstract. By means of a self-consistent tight-binding method, a realistic calculation of a Si-H-Ag junction is made. More general cases for different interlayer atoms are analysed by changing the parameters of the interface. Our results show that the barrier height of the junction may have slightly changed values (by up to 0.2 ev) for different atom electronegativities. For atoms of low (high) electronegativity, we find larger (smaller) barrier heights. 1. Introduction This is the second part of a work aimed at elucidating the mechanism of Schottky barrier formation for those cases in which interdiffusion and reactivity between the metal and the semiconductor can be ignored (Andrews and Phillips 1975, Brillson et a1 1981, McKinley er a1 1979). In I (Guinea er a1 1983) we analysed clean interfaces, for which there is a well defined separation between the metal and the semiconductor structures. In this paper we analyse etched interfaces, for which a reactant (H, 0, C1,...) is left between the two crystals. As was stressed in I, there is no systematic theoretical analysis available even for the abrupt junctions considered in this work; we think that such an analysis would not only give a better understanding of the abrupt interfaces, but would also throw light on the specific effects associated with interdiffusion and reactivity. In this paper we follow the procedure given in I and present a self-consistent tightbinding calculation of the interface properties of etched covalent junctions. Where necessary we shall give information complementary to that in I, but many of the arguments and steps given in I will only be very briefly commented on here. In 2 we discuss the model proposed to analyse the etched junction, while in 3 we present our results and discussion. 2. Themodel The semiconductor and the metal are described by adequate tight-binding parameters: for the covalent semiconductor we use sp3 hybrids and introduce interaction parameters up to second neighbours; for the metal we use two orbitals in each atom to simulate an s and a d band (see I) /84/ $ The Institute of Physics 2039

2040 J Sdnchez-Dehesa, F Flores and F Guinea For an etched junction we introduce an interlayer of H between the metal and the semiconductor with one atom in the semiconductor surface unit cell.

3 2040 J Sdnchez-Dehesa, F Flores and F Guinea For an etched junction we introduce an interlayer of H between the metal and the semiconductor with one atom in the semiconductor surface unit cell. Moreover, we assume the H to sit on top of an atom of the last covalent layer; this is the appropriate position for H (Pandey 1976). For this atom we use an s orbital and build up the junction by introducing definite interactions with the last layers of the metal and the semiconductor (see below). The dependence of the interface properties on the electronegativity of the atom forming the interlayer (say Cs or C1 instead of H) has been analysed using a proper modification of the atomic parameters, although in all the cases we have assumed the atom to sit on top of the last semiconductor layer. This point will be discussed further later. As regards the metal structure, we have chosen a (111) FCC structure matching to the (111) covalent face (see I). This implies that there are three metal atoms in the semiconductor surface unit cell. Furthermore we assume that one of these three metal atoms is aligned with an atom of the interlayer and one of the last semiconductor layer. Let us now discuss how to get self-consistency at the junction once the interface is built up by switching on the metal interlayer and the semiconductor interlayer interactions. (Note that the bulk metal and semiconductor interactions are assumed to be unaffected by the surface and to extend up to the same interface.) Let us start by discussing briefly the metal-semiconductor junction Metal-semiconductor self-consistency In I we showed that metal-semiconductor self-consistency can be obtained by imposing the following three conditions. (i) There must be charge neutrality in the first semiconductor sublayer: 8n@ = 0. This condition arises from the strong coupling between the interface and the semiconductor sublayer. (Hereafter, 6n means n minus the neutral value no.) (ii) There must be charge neutrality of the whole system: an@ + = 0. (2) This equation expresses the complete charge neutrality of the semiconductor and metal surface layers. Note that we assume that there is automatic charge neutrality in the first metal sublayer and in any other metal or semiconductor layers. (iii) Finally, there must appear an induced dipole, D, between the metal and the semiconductor defined in terms of the transfer of charge, dn@ = - between the metal and the semiconductor, and the distance, d, between the last two layers of both crystals : D = rudsn@. Here CY = 4n/A, A being the area per surface semiconductor atom. Equations (l),(2) and (3) give the three conditions needed to determine the three parameters V@, Vfi) (the diagonal perturbations at the two surface layers) and D Metal-interlayer-semiconductor self-consistency Let us now discuss how to get self-consistency at the metal-interlayer-semiconductor (1) (3)

Schottky barrier formation: II 2041 junctions. Compared with the metal-semiconductor interface we have a new freedom at the junction: that associated with the interlayer.

4 Schottky barrier formation: II 2041 junctions. Compared with the metal-semiconductor interface we have a new freedom at the junction: that associated with the interlayer. Thus, we have to determine selfconsistently the charge of H, nh, and its mean electronic level, EH. Accordingly, we have four parameters to be determined self-consistently at this interface: the two diagonal perturbations at the last layers of the metal and the semiconductor, Vu) and Vi& the induced dipole, D, between the two crystals; and the mean atomic level for the interlayer, EH. The conditions determining these parameters are given below. (i) As at the metal-semiconductor junction, we impose charge neutrality at the first semiconductor sublayer. This gives equation (1) as our first condition. (ii) The condition of charge neutrality of the whole system yields the following equation: dn@ + 6nH + dnfi) = 0. (4) (iii) On the other hand, the induced dipole between the semiconductor and the metal, D, is determined by anh and &@,according to the equation D = a(ddn@ + d 6nH) (5 1 where d (d ) is the distance between the semiconductor surface layer (interlayer) and the metal surface layer (compare (5) and (3)). (iv) Finally, we need a self-consistent equation for the mean atomic level of the interlayer, EH. This can be obtained by using a Hartree scheme; within this approximation the mean atomic level depends on the electrostatic potential induced at the interlayer and on the electrostatic repulsion between electrons of different spins inside the atom. Thus EH = Eg) + cu(d - d ) an@ + a U6nH. (6) In this equation, E#) is the mean atomic level for the isolated atom, a(d - d )bn&! is the electrostatic potential induced at the interlayer as measured from the semiconductor, and Udn~ = USnd gives the intra-atomic repulsion. (From now on, all the levels will be referred to the semiconductor bands. In particular we shall analyse the Schottky barrier formation by discussing how the metal Fermi level is located with respect to the semiconductor gap.) Equations (l), (4), (5) and (6) give the four conditions determining the four parameters V#, Vis, D and EH. Note that (5) can be substituted for, approximately, by ddn@ + d 6nH = 0 (7) since otherwise the induced dipole, D, would be very high (see I). In contrast with the results of I, where this kind of approximation had to be improved in a further step, equation (7) now turns out to be quite satisfactory for making calculations for the metal-interlayer-semiconductor junction. Thus (l),(4), (6) and (7) can be used to get self-consistency at the interface studied here. A few words clarifying the meaning of the approximated equation (7) should be given. The main point to be stressed is that (7) is a reasonable approximation for the interface problem, but it does not imply that the induced dipole, D, between the metal and the semiconductor must be zero. In other words, with conditions (l),(4), (6) and (7) we obtain the result that the metal Fermi level is located at a given energy in the Cll-N

5 2042 J Sanchez-Dehesa, F Flores and F Guinea semiconductor gap, and this can only be achieved with a finite dipole, D. Note, however, that D is less than 1 ev and thus D/ad = dn@ + (d'/d)dn, turns out to be around a hundredth of a unit charge. The physical meaning of the approximated equation (7) is that the induced dipole, D, can be sustained by the transfer of a negligible charge between the metal and the semiconductor (a case reminiscent of the so-called Bardeen limit for the junction). 3. Results and discussion In this paper we present detailed calculations for the Si-H-Ag junction and discuss general properties of the interface using an appropriate change of the atomic parameters. Table 1. Interaction parameters used in the calculation of the Si band structure (in ev). y2, y3, y4, ys and y6 define the first-neighbour interactions in the Chadi and Cohen (1975) notation; (ppu)2 and (pp42 define the second-neighbour interactions For Si we use the Pandey and Phillips (1976) parameters given in table 1. In I, we commented on the problems associated with using these parameters, since the Fermi level at the free semiconductor surface almost coincides with the valence band edge; as the junction is formed, the Fermi level may enter the valence band and the procedure followed in this work does not allow us to achieve complete self-consistency in the inner semiconductor layers. However, we solved the problem for the junction by looking for self-consistency only in the last two semiconductor layers, and neglecting the lack of neutrality, which then appears in the inner layers. When we proceeded on this way, we found that all the main results related to changes in the Fermi level due to the barrier formation obtained with the Pandey-Phillips parameters gave a good agreement with the results obtained using other parameters giving a better description of the surfacestate positions (but a worse description of the valence band). For Ag we use the following parameters introduced in I: ~ k g - ~ = g ev VApAg = ev V&--"g = ev &d - E, = ev. For H we need parameters defining the coupling between this atom and the orbitals of the last layers of the metal and the semiconductor. We have followed Pandey (1976) and used the following parameters for the Si-H interaction: e-" = ev V:;iH = ev (8) where V,, and Vspo give the interactions between H and the s and p orbitals of Si, respectively. For the Ag-H coupling, we need the interactions between the adatom and the s orbitals (V$-H) or d orbitals (Vi""); these parameters have been obtained by averaging the Si-H interactions with the Ag-Ag interactions, V$-*g and V,&Ag, given above. This yields: VkpH = -2.3 ev VieH = -1.0 ev. (9)

6 Schottky barrier formation: II 2043 E lev) Figure 1. Density of states in the H monolayer for the Si-H system. Ec = conduction band edge. E" = valence band edge. E levi Figure 2. Density of states in the semiconductor surface layer for the Si-H system. Ec = conduction band edge. E" = valence band edge. On the other hand, ER, the mean atomic level for the isolated atom, has been adjusted to give an appropriate solution for the case of a H monolayer adsorbed on a clean 111 Si surface (Pandey 1976). In figures 1 and 2 we give the density of states in the adsorbed monolayer and in the last semiconductor layer as obtained for ER = -5.4 ev (10) by means of a self-consistent calculation. This density of states shows a good agreement with other calculations (Pandey 1976) and it corresponds to a solution for which there is a small transfer of charge, around 0.01 electrons/atom, from the monolayer to the semiconductor surface layer; this is in agreement with the experimental evidence (Ibach and Rowe 1974). Note that for the monolayer case we get self-consistency by means of

7 2044 J Sanchez-Dehesa, F Flores and F Guinea an equation similar to (6); in this equation, U has been taken equal to 8 ev, following many other chemisorption analyses for H (Baldo et a1 1983, Newns 1969). One more comment must be made to complete the model. In order to apply (7) we need the distances d and d. For H we have assumed that the atom is located on top of the outermost Si atom (Schliiter and Cohen 1978), and the distances d and d can thus be obtained approximately by adding the covalent atomic radii. All these parameters, taken together, determine the junction. In figures 3 and 4 we present the density of states in the interlayer and the last semiconductor layer for the self-consistent Si-H-Ag junction. EleVl Figure 3. Density of states in the H monolayer for the Si-H-Ag junction. EF = Fermi level. Ec = conduction band edge. EV = valence band edge. b + n!i L L 0 YI + U 0 C. YI L ii. C. v) E lev1 Figure 4. Density of states in the semiconductor surface layer for the Si-H-Ag junction. EF = Fermi level. EC = conduction band edge. EV = valence band edge.

Schottky barrier formation: II 2045 It is of interest to comment that, in this junction, we have found almost no transfer of charge from the interlayer to the metal or the semiconductor.

8 Schottky barrier formation: II 2045 It is of interest to comment that, in this junction, we have found almost no transfer of charge from the interlayer to the metal or the semiconductor. This is similar to the result found for the Si-H surface and it is related to the H electronegativity, which is similar to the Si and Ag electronegativities. On the other hand, our calculation shows that the Fermi level for the junction is around ev below the Fermi level for the free surface. It is worth remarking that this level almost coincides with the one obtained in I for the clean Ag-Si junction: &(Si-H-Ag) = EF(Si-Ag) * 0.05 ev. We conclude that for H, and for any other atom having similar electronegativity (see below), the interface Fermi level for the etched Si-H-Ag junction is very close to that appearing at the clean Si-Ag interface. We now turn our attention to more general junctions and analyse the barrier formation for interlayers formed with atoms having more or less electronegativity. In our calculation we have changed the parameters from the values used for H in order to simulate Cs and C1, two extreme cases. For the Cs interlayer we have determined the parameters defining the interface in the following way. Firstly, we obtained the effective Vgs-cs interaction by means of a procedure given by Harrison (1980). Then we obtained the different Si-Cs and Ag-Cs interaction parameters by averaging the effective interaction, V:*", with the Si-Si and Ag-Ag interaction parameters. This procedure yields On the other hand, Eg) has been taken equal to the average of the affinity and the ionisation levels for the free atom: ~g) = -2.0 e ~. (12) Finally, for Cs, the intra-atomic interaction, U, has been taken equal to 1.5 ev, close to the difference between the affinity and the ionisation levels. In order to analyse the effect of C1 on the junction properties we have used the previous model, keeping only an s atomic orbital but introducing stronger interactions with the metal and the semiconductor. To this end, we have practically scaled the H-Si and H-Ag interactions with the Cl-Si and C1-Ag ones, by means of the bond energies for H and C1 with Si and Ag (Pauling 1972). This yields Moreover, following the criterion given above for Cs, we have selected the parameters E;) = -8.3 ev U = 7 ev (14) which completely determine our interface model Hamiltonian. One more comment must be made about the values of d and d' used in these calculations. For C1 we can assume that the atom is located on top of the outermost Si atom (Pandey 1976, Schluter and Cohen 1978) in such a way that d and d' can be obtained, as for H, by adding the covalent atomic radii. However, for Cs a more appropriate position for the atom would be sitting above the centre of three Si atoms. Then the distance between the interlayer and the last semiconductor layer, (d' - d),

2046 J Sanchez-Dehesa, F Flores and F Guinea would be substantially reduced. This fact can have a considerable effect in the final self-consistency ; we shall discuss its implications later.

9 2046 J Sanchez-Dehesa, F Flores and F Guinea would be substantially reduced. This fact can have a considerable effect in the final self-consistency ; we shall discuss its implications later. (Despite this comment, for the sake of simplicity we shall make calculations for the case with a Cs interlayer with a model Hamiltonian having parameters appropriate for an atom adsorbed in the top position; the effect of the adsorption site will only be simulated by changing the distance (d'- d).) Our calculations for Cs and C1 were performed in two steps. Firstly, the interface Fermi level was obtained by assuming no transfer of charge from the atom to the semiconductor or the metal; note that this implies adjustment of the interlayer level (EH in (6)) to satisfy this condition. In a second step, we determined the interface Fermi level by allowing the charge to transfer from (or to) the interlayer to (or from) the metal or the semiconductor. Note that this second step gives the effect on the Fermi surface level due to the transfer of charge associated with the high (or low) adatom electronegativity. For Cs, we find an important transfer of charge from the adatom to the semiconductor. The first step mentioned above gives a surface Fermi level located 0.07? 0.05 ev below the free-surface Fermi level. Also, the Fermi level shifts to lower energies due to the transfer of charge from the atom to the semiconductor and the metal; this effect can be understood as being due to the repulsion between the interlayer and the metal levels: the atomic level of Cs pushes the metal Fermi level towards the semiconductor valence band. Our calculation shows that this shift ~ Eis F related to the transfer of charge, Ants, by the equation 6EF = 0.4 AnCs (15) with 6EF given in ev and AnCs in units of electronic charge per atom. Now, it is important to note that Ancs is strongly dependent on (d- d'), the distance between the interlayer and the last semiconductor layer. For a position on top of the Si atom we have estimated AnCS to be around 0.16 units of electronic charge. However, for a site above the midpoint of three Si atoms we have estimated that AnCS must be around 0.5 units of electronic charge. For the two cases, the charge neutrality level shifts towards lower energies by 0.08 and 0.25 ev, respectively. Considering the second case to be the most likely, we obtain a Fermi level for Si-Cs-Ag located ev below the Fermi level for the free surface and 0.21? 0.05 ev below the Fermi level for the clean Si-Ag interface. For C1 we find an important transfer of charge to the adatom. With the first step (no transfer of charge), the charge neutrality level is located at 0.17? 0.05 ev below the Fermi level for the free surface. In the second step, we find that the charge neutrality level shifts to higher energies; ~ Eis F related to Ancl by the equation ~ E= F 0.6 Ancl (16) with Ancl measured in units of electronic charge per atom. With the on the top position for C1, we have estimated that Ancl = 0.14 and ~ E= F 0.08 ev. Accordingly, we obtain a Fermi level for the Si-C1-Ag junction located around 0.09? 0.05 ev below the Fermi levelfor the freesurface and0.02 f 0.05 evabove thefermilevelforthesi-ag junction, Putting together these results with the H-case, note that the Fermi level for the Si-Cs-Ag, Si-H-Ag and Si-C1-Ag junctions have been obtained at energies: -0.21? 0.05 ev, ev and ev, respectively, referred to the Fermi level for the Si-Ag function. The main changes in the Fermi level (and the corresponding changes in the barrier height) are induced by atoms of very low electronegativity. This is mainly due to the fact

10 Schottky barrier formation: II 2047 that Cs has been supposed to sit on the mid of three Si atoms. In other words, had we assumed C1 to sit at the same position, we would have obtained a greater shift in the Fermi level, around 0.2 ev, but towards higher energies. In other words, atoms of low (high) electronegativity shift the Fermi level towards lower (higher) energies. These changes are small, however, and in no case greater than 0.2 ev. This conclusion seems to be in agreement with the experimental evidence presented by Mottram et af (1975) and Archer and Attala (1963). These authors found that the effect of a monolayer of 0 between Si and Cu was to lower the barrier height by approximately 0.15 ev. We have, finally, analysed the effect of the metal density of states at the Fermi level on the interface Fermi level position. To this end, we have repeated the previous calculations by assuming that the metal Fermi level was located at the d-band. Our results show no significant change from previous calculations. Thus, the barrier height for the interlayer junctions seems to be practically independent of the metal density of states at the Fermi level. This suggests that the barrier height for etched junctions is mainly determined by the interaction between the adatom and the last semiconductor and metal layers. In conclusion, the crucial physical quantities determining the barrier formation for the metal-interlayer-si junction seem to be the electronegativity and the adsorption site of the atomic interlayer. The barrier height is practically determined by the coupling between this interlayer and the last semiconductor and metal layers. Moreover, atoms of high (low) electronegativity tend to decrease (increase) the barrier height. Acknowledgments We thank Dr C Tejedor and Professor R H Williams for many helpful discussions and acknowledge the partial contractual support from the US Army via its European Research Office (contract DAJA C-0118). References Andrews J M and Phillips J C 1975 Phys. Rev. Lett Archer R J and Attala M M 1963 Ann. NY Acad. Sci Baldo M, Flores F, Martin-Rodero A, Piccito G and Pucci R 1983 Surf. Sci Brillson L J, Brucker C F, Staffel N G, Katuani A D and Margaritondo G 1981 Phys. Rev. Lett Chadi D J and Cohen M L 1975 Phys. Sturur Solidi b Guinea F, SBnchez-Dehesa J and Flores F 1983 J. Phys. C: Solid State Phys Harrison W A 1980 Electronic Structure and the Properties of Solids (San Francisco: Freeman) p 49 and table of p. 550 Ibach H and Rowe J E 1974 Surf. Sci McKinley A, Williams R H and Parke A W 1979 J. Phys. C: Solid State Phys Mottram J D, Northrop D C, Reed C M and Thanailakis A 1979 J. Phys. D: Appl. Phys Newns D M 1969 Phys. Rev Pandey K C 1976 Phys. Rev. B Pandey K C and Phillips J C 1976 Phys. Reu. B Pauling L 1972 The Narure ofthe Chemical Bond 3rd edn (Ithaca, New York: Cornel1 University Press) Schliiter M and Cohen M L 1978 Phys. Rev. B

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Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. Electron States at Semiconductor Interfaces: The Intrinsic and Extrinsic Charge Neutrality Levels Author(s): F. Flores, R. Perez, R. Rincon, R. Saiz-Pardo Source: Philosophical Transactions: Physical Sciences