Low coverage deposition of alkali metals on GaAs(110)

Applied Surface Science 56-58 (1992) 264-270 North-Holland

appNeo

surface science

Low coverage deposition of alkali metals on GaAs(ll0) J. O r t e g a , R . P6rez, F.J. Garc~a-Vidal a n d F. F l o r e s Departamento de Fi~icu de la Materia Condensada C-Xll, Faeuftad de Ciencias~ Unb e~idad Autdnoma, E-2a049 Madrid, Spai~

Received 6 May 1991; accepted for publication 30 May 1091

An ab-initio LCAO method is used to calculate the electronic properties of different overlayers of Li, Na and K deposited on GaAs(llO). Results for a monolayer, half a monolayer and the isolated alkali metal atom are presented. Cnemisorption energies and the most favourable adsorption sites are calculated for each case. The interface Fermi cnerg2t and the Schonky harrier formation are discussed as a function of the metal coverage. An important conclusion is that for alkali atoms, the induced density of interface states model is operative for coverages larger than a half monolayer.

1. Introduction

The main work in the last few years in the field of Schottky barriers has been addressed to understanding the electronic properties and the barrier height evolution in the limit of low metal coverages deposited on semiconductors [1-3]. The aim of this work is to understand the mechanism controlling the barrier formation. Two main models have been proposed in this regards: (i) T h e induced density of interface states (IDIS) model [4-6] proposes that the barrier formation is due to the intrinsic density of interface states created by the metal deposited on the semiconductor; (if) in the defect model [7-10], the Fermi level is assumed to be pinned by the defects created in the semiconductor by the metal deposition. The work done in the low-metal-coverage limit on semiconductors has given a deep insight on how the interface Fermi level evolves with the metal deposition. Different metals [1-3] have been analysed by depositing them on GaAs(110). An important case corresponds to the alkali atoms [1,2] thai present very little interdiffusion into the semiconductors due to their large size. This fact reduces the number of defects created by their deposition on the semiconductors, and makes them the best candidates for studying the Schottky-barrier low-coverage evolution.

In this paper, we analyse theoretically the K, Na and Li-GaAs(110) interfaces in the submonolayer regime. We present results for a monolayer (ML) [11,12], half a ML and an atom deposited on the semiconductor. We follow a free parameter consistent molecular orbital method and calculate chemisorption energies, Fermi levels and adsorption sites. O u r analysis yields a clear picture for the process of the Schottky-barrier formation. For a single atom deposited on the semiconductor we find a donor level at the semiconductor gap; for half a monolayer a metal band starts to be developed but correlation effects reduce substantially the local density of states at the Fermi level [14,15]; finally, for a monolayer we still find important correlation effects in the metal density of states', in this limit we already find that the Fermi energy is the same as for a thick layer.

2. The method of calculation

T h e method we follow to analyse the problem is discussed in full detail elsewhere [13]. Let us only mention here the main points used to calculate the interface electronic properties. In our approach we use a L C A O method with a prescription to calculate the hopping elements

0169-4332/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All right~ rese~,ed

Z Ormga el aL / Low coverage deposition o[alkali metals on GaAs(llO) between different orbitals and the one body and marly-body contributions to the total energy. The hopping integrals, Tq. are basically related to the Bardeen tunneling currents [16], Tff between the corresponding orbitals, O~ and S r Thus: TU - T ~ p , h

( 1)

(2)

y is greater than 1 (typically around 1.3-1.5) and ean be calculated exactly. The overlap between different orbitals, Sij (@i]@;), introduces a contribution to the total energy that is found to be well described by the following correction to the diagonal level. ~SE~,of a given orbital: ~ e , = - E s , , r , , + ~ El s , A e2:, - e j ) . (3) j*i j÷l where E, and E / a r e the mean levels of the i and j orbita!s. Many-body contributions are introduced by means of the following terms in the total Hamiltonian: i

i *j.~

+ ½ E J,~a'n,~n,¢, ~¢j.u

(4)

where U,(")and j/tilt are the intrasite and intersite bare Coulomb interactions, respectively, and ]~o~ an effective [13] intersite Coulomb interaction given by: -~o)

Vx.,~= - E ~ g . ( i .

j),

to)

(7)

j+i where g¢(i, j ) is defined by: (c~i~ci¢)(c~oct¢) -- (Fl,~)g~(i, j ) .

T,p= ~ m f(~iV4J,-¢,V4Jl)n ds;

265

V,,i,r is related to the exchange pair distribution function g¢(i. j) given by the fcqlowing equation:

(8)

In eq, (6), a is taken to be ~: this is shown to include interatomic correlation effects [13], It should be commented that in order to obtain eq. (6) the intra-atomic correlation interaction associated with the term U~tO~n~tn~t has been neglected, It is important to realize this point as regards the discussion we shall present below for correlation effects in the alkali atoms layer. In our actual calculation we have solved the LCAO mean-field Hamiltonian using eooventional Green-funcfion techniques. Moreover, self-consistency !a the charges is achieved by rel a d l e the induced potential (as given by the many-body Hamiltonian) to the charges induced in each atom. We should also comment that. in general, the semiconductor surface is not allowed to relax except where stated otherwise. The chemisorption energy is calculated for different metal overlayers that are allowed to relax in the direction perpendicular to the semiconductor surface.

3. Results and discussion

3.1. Mean-field solutions

where J ~ is the exchange integral between the i and j orbitals. The terms given by eq. (4) are treated using a many-body approximation equivalent to the one given by Slater for a free electron gas [13], This means using a mean-field approximation supplemented by a Slater-like potential, V~.i,. Thus, we replace Hami!tnnian (4) by the following meanfield Hamiltonian:

t?~, ~ = E~'°~,.<~,,.> + E C",L,.<~j~) i

j~-i.¢

+ E J,~t))hw(aW) + EotVx.io~t,¢ • 1..~i.¢ i¢

(6)

In a first step we have analysed the mean-field solutions for the deposition of a ML and half a ML of Li, Na and K on GaAs(110), moving the adatoms along four different chemisorption sites (fig. la). In fig. lb, we also show the geomet~,we have considered for the half ML case. Fig. 2 shows the chemisorption energy per alkali atom as calculated by moving simultaneously all the alkali atoms in the direction perpendicular ':0 the surface (in cases I and I! the atoms are moved along the Ga or As dangling bonds). Cases (a), (b) and (c) refer to Li, Na and K, respectively. In each figure we show the results

266

J. Ortega el al. / Low coremge depositiot~ of alkali metals ol1 Ga4s(l lO)

calculated for the most favourable position (on Ga for all the eases, site I in fig. la ) and for both a M L and half a M L (small differences with the results of ref. [11] for a monolaycr are due to a better treatinent in the actual work of correlation effects). A few comments are worthwhile: (i) at the equilibrium position for 0 = 1 the G a - a d a t o m distance is 0A-6.2 A smaller than the sum of the covalent radii of Ga and the alkali atom; this is due to the transfer of charge from tbe alkali atoms to GaAs. For 0 = ½ the alkali atom is closer to Ga: this .;s due to the increase in the transfer of charge between the adatom and the semiconductor that has been calculated to be 0.3e- per alkali atom for 0 = 1 and ~ 0.5efor 0 = ½ (this implies that the metal-semiconductor bonding is more ionic [12] for 0 = ½}. Ebr half a ML the transfer of charge allows the alkali atom to approach closer to the semiconductor. (ii) In all the cases, the chemisorption energy is larger for 0 = n. This is basically due to the smaller overlap between alkali atoms for this case: the adatoms tend to repel each other and the results of fig. 2 yield a measure of this repulsive potential. For K this effect is much more important: this is due to the larger overlap between K nearest neighbours for 0 = 1. (rid For {a}

0 = ½, the chcmisorption energies per alkali atoms at the equilibrium distances are the following: EeL(Z(Li) = 1.07 eV, Ecl(Z(Na)= 1.18 e V and E~(2(K) = 1.25 eV, their values increasing with the metal electropositJvity. (iv) W e have also calculated the Fermi energy referred to the semiconductor valence band top. O u r values at the equilibrium distances of the most favourable positions are the following: E~I'(Li) = 0.60 eV,

E~t~(Na) = 0.66 e V ,

E ~ ( K ) = 0.70 eV, E~/2(Li) ~ 0.90 eV,

E~/Z(Na) = 0.94 eV,

E ~ / Z ( K ) = 1.00 eV.

For a ML, the Fermi energy is found close to the intrinsic charge neutrality level [17] of GaAs, while for half a ML the Fermi level is found typically 0.3 eV higher in energy. On the other hand, it is of interest to realize that the Fermi energy for 0 = l increases slightly with the metal electropositivity. In fig. 3 we also show the total density of states in the metal and the semiconductor layers for K / G a A s ( I I 0 ) . Fig. 3a shows the ML case, 0 = 1, and fig. 3b. the case 8 = t.,. These figures show (b)

• ° "6" ° "6" °" I

.......

"6" °'6" °'6"

I I

"o,6,o,6,o,

II - -

I I I

I

I

O @ a:S.SSA

S= ½

0

Ga As

Allali.tom

Fig. I, {al Shows the four dlfferent chemlsnrption sitesanalysed in this paper. In cases ] and ]I the alkaliadatoms are moved along

the Ga or As dangling bonds, while in the other two cases they are moved in the direction perpendicular to the semiconductor surface. (b) Showsthe 2D geometry wc have considered for the half monolayer case.

J. Orte~t~el aL / Low cot'erage deposition ~Jfalkali metals on CaAs( l lO)

how t h e interface Fermi energy is pinned by an intrinsic band induced in t h e middle of the gap by the metal deposition. In fig. 3c we also show the case 0 = ½, but assuming that the G a a t o m s not bonded to an alkali atom keep the relaxation of t h e free G a A s surface. This last case has been calculated to show that the density of states app e a r i n g in fig. 3b in t h e middle o f t h e gap is yielded by the overlap of two different surface bands, one associated with the G a a t o m s bonded to K, t h e o t h e r with the G a dangling bond levels not yet s a t u r a t e d by an alkali atom. T h e effect o f relaxing these last G a atoms is to shift the dangling bond states to l h e semiconductor conduc-

(a).~°

,E'

/

(b) 9

E, t

la

-o.5

~'~ . . . . . . .

1 ~ 90

K

~,40

6.'9. . . . . . .

~ ~. . . . . . . .

:k'9'

ENERGY(ev)

o 5 ~ 15.

~ ~. . . . .

Fig. 3. Local density of states (LDOS) for the cases of (a) 0=1. (b) 0=0.5 (ideal surface) and (c) 0=0.5 (relaxed surface) for til¢ K-OaAs(110) interface. The solid Iin~s represent the LDOS at the K atones, while dashed lines show Ihe LDOS at different Ga atoms. The zero of the energy axis corresponds to Ihe valence band top. 1

....

2.90

DIST~,NCE tA) Fig. 2. The chcmisorption energy per alkali atom as a function

of the dislance of the alkali layer to the last GaAs layer, for 0 = 1 and O= 0.5. In both cases the alkali aloms are placed on position I of fig. In. Chemisorption energies are given in eV and the perpendicular distance is glvcn in A.

tion band, but still keeping an intrinsic metal-induced surface b a n d in the middle o f t h e semiconductor gap. Although we cannot e~elude that some relaxation, like the one discussed above, exists for 0 = i .~, we concentrate in this p a p e r on analyzing the unrelaxed semiconductor case. A s figs. 3b and 3e show, both cases yield similar barrier heights. 3.2. M a n y - b o d y effects

Previous results have been obtained neglecting the intrasite C o u l o m b correlation effects. T h e s e effects can be important in the low-coverage

.~ Ortega el aL / Low coverage deposition of alkali metals on GaAs(110)

268

regime we are considering here. Regarding this point, it is important to consider the total density of states as calculated in our previous section and shown in fig. 3. The important point to realize now is the narrow surface band induced by the adsorbed metal, and located around the middle of the semiconductor gap; this bandwidth is smaller than the effective Hubbard interaction associated with the surface band (see the discussion below) and one can expect the intrasite correlation effects, neglected in the mean field solution, to be important. One can analyse these effects by considering the following two-dimensional Hamlfionian:

/~= ~'~Etlhi,+ + ~tJ,~ith i

~ t..(c* e i + c* c . .

(9)

In this Hamiltonian, each site is associated with the i-Wannier function of the metal-induced surface band appearing in the solution discussed above; tij is assumed to be operating only between nearest neighbours, and U~ is an intrasite Coulomb interaction that takes into account correlation effects in our two-dimensional model. For the sake of simplicity, tij is fitted to the results of section 3.1. U~ is calculated by considering the Wannier wavefunction, ~bi(r) , and the screened interaction of $~(r) with itself, symbolically: l (/s= f t b ? ( r ) ~ ¢ p T ( r ' )

d r d r '.

(lO)

For the Wannier xvavefunetlons calculated for Li, Na and K and 0 - ½ we have found that, approximately, U~ = 1.5 eV (Li),

~ = 1.4 eV ( N a ) ,

and b'~ = 1.2 eV ( K ) . (Details will be given elsewhere.) For these values, the narrow surface band induced by the metal should show important correlation effects. We have argued elsewhere [14], that these effects introduce new structures in the local density of states associated with the surface band: one finds a Konde4ike peak at the Fermi

energy pin~'.ing the Fermi level and two other peaks located at the energies E F + U 0 / 2 related to the affinity and ionization levels of the Wannier wavefonction associated with the surface band. The Kondo-like resonance mean energy is given by the Fermi level calculated in section 3.1: this means that the Fermi energies given above for 0 = ½ and # = l, and for different alkali atoms, should be compared directly with the experimental Fermi levels. Correlation effects explain however that the actual density of states at the Fermi level must be small and in many cases below the level of experimental detection [15]. These correlation effects should modify more strongly other properties like the chemisorption energies found above within the mean4ield approximation. The main point to notice is that strong correlation effects tend to reduce strongly the probability that two electrons have of being found at the same place. Without any further calculation, one can argue that the mean field ehemisorption energy found above should be increased approximately by / / , / 4 per surface atom, this quantity being the energy associated with the repulsive term U.~(nlt)(ni~) since ( n i , ) ~ (n~ ~) = ½. Taking into account this contribution, we should modify the values shown in fig. 2 to the following figures: 0= I O= ½

Li

Na

K

1.12 eV 1.45 eV

i.18 eV 1.53 eV

1.11 eV 1.55 eV

We turn our attention to the case of a single alkali atom adsorbed on GaAs(ll0). Instead of attempting a complete calculation, we shall use the results obtained for O = ½, to extrapolate approximate figures lbr the properties of the chemisorbed atom. First of all, we should mention that for O = ½, the distances between nearest-neighbour alkali atoms are far enough for their direct interaction to be negligible. From this point of view, the energies given above for 0 = ½ might be considered as the diluted limit. This argument neglects, however, the dipolc-dlpolc interaction between adsorbed atoms due to the transfer of charge to the semiconductor. By correcting for the dipole-

269

d. Ortega et al. / Low coveragedeposition of alkali metals on GaAMI I01

dipole interaction that cannot operate in the diluted limit, we find the following ehcmisorption energies (for 0 ~ 0):

E~h~m

Li

Na

K

1.71 eV

1.80 eV

1.92 eV

Comparing these figures with those obtained above for the monolayer case, we see that, roughly speaking, the ehemisorption energy of alkali atoms on G a A s ( l l 0 ) changes from 2 eV (for 0 ~ 0 ) to 1 eV (for 0 ~ 1) in good agreement with the experimental evidence [18]. Another important quantity is the donor level [19,20] associated with a single atom adsorbed on GaAs. This level can also be approximately calculated using the solution for a half ML if we notice that this energy coincides with the ionization level of the Wannier function associated with the adatom. As in the case just discussed, we go from the half ML case, (O = ½), to (0 --, 0) by correcting for the dipole-dipole interaction. This yields the following donor levels (Ed ):

Ed

Li

Na

K

0.90 eV

1.04 eV

1.24 eV

(above the semiconductor valence band top). Fig. 4 shows the evolution of the donor level (or the ionization of the metal-induced surface band Wannier function) as a function of the alkali atom coverage.

4. Final comments and concluding remarks

The results obtained in this paper show a clear picture of the metal-semicunductor interface formation as a function of the metal deposition, in good agreement with the experimental evidence [1,2]. First of all, we mention that our values for the chemisorption energies show that all the alkali atoms considered tend to be adsorbed on the Ga sites [21]. Initially, the donor level (a kind of defect level) tends tu pin the Fermi energy for p-doped semiconductors [1,2], but for half or a full monolayer our results show that the electrostatic interface dipole is large enough to pin the Fermi level, within a metal-induced interface

1,S

K

oa

-o.2 ao

0.5

Fig. 4. E~olution of the dont~r level for the different alkali a l o m s (Li, N a a n d K) as a function of the alkali m e t a l coverage.

band. The transition from the isolated atom case to the IDIS model limit seems to appear for 0 _< ~; then the interface dipole is found to have evolved to values such that the metal induced band states are already pinning the Fermi energy. Our calculations have allowed us to obtain also the chemisorption energies for deposited alkali atoms as a function of coverage; in particular, we mention that these chemisorption energies increase with the metal electropositivity. Also very satisfactory is the good agreement found between our calculated interface Fermi levels and the experimental results. The evolution of this Fermi energy with the metal coverage follows very closely the experimental data [1,2]. We should mention, however, that our calculated donor levels seem to be a little too high in energy, but not more than 0.2 eV [1]. In conclusion, our theoretical results seem to confirm the validity of the IDIS model for alkali metal coverages larger than ½. For very low metal coverages, however, the alkali metal donor level seems to control the interface Fermi energy, the donor energy playing the role of a defect level. These results, calculated using a consistent LCAO

1o

270

Z Ortega et aL / Low cot er#g¢ deposition o f ulkali metals on GaAs (l It))

m e t h o d , confirm, in t h e limit of low coverages, t h e validity o f previous s i m p l e r a p p r o a c h e s p r e s e n t e d by o t h e r r e s e a r c h e s [19,20] to a n a l y z e t h e m e t a l d o n o r levels on G a A s .

Acknowledgements T h i s work h a s b e e n partially f u n d e d by t h e Comisibn A s e s o r a d e Investigaci6n Cientifiea y T e c n o l b g i c a ( S p a i n ) u n d e r c o n t r a c t s PB-89-0165 a n d MAT-88-0544.

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