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Schottky barrier formation: Al deposition on GaAs(110)
ii!ii¸¸~i¸~i£!i!!~!iii~i~:~ ! ~i~i~iii!~!iii~iiil ~i~ applied
Applied Surface Scimlcefd)/hl (1992)73fi-741 North-Holland
surface science
Schottky barrier formation: AI deposition on GaAs(1
1 0/1 ~
L Ortega, R. Rinc6n, R. Pdrez. FJ. Garcla-Vidal and F. Flares l,~'llarl, ltnt'lm~ tit' I'i~ica tit' la Materhl Ctutth,nxada C-,¥IL Fat'tdlad tlt' ('leilcias, UnR e~hlad Alltdnonul, E-28Od9 ,~htdrltL ,$)~lbl
Received 211November 19t)l;accepted bit publication h Jnnuals, It)Y2
The Scholtky barrier furmation for AI on GaAr4IIdl has been analysed as a funclion af the metal c(~'erage. Fnr different AI coverages ~e have calculated Ih¢ most stahle geomelriesusing a consistent tree-parameter LCAO method. Our resuhs show that for an AI manolayer, no densily of slatvs appears near the semiconductor charge neulrallty level. "File Fermi level is. however, pinned, and ihe Sehonky harrier completely formed, for a ¢~werageof twt~metal nn)lltlklyers. For Ihis limil wc recover Ihe intrinsic metal sta|e~ model and find goad agreement with the Schottky harrier height ftlr thick metal hlyers.
l . lntroduetlun One of the main experimental facts, recently obtained in the field of Scbottky barrier formation. is the evolution of Schottky barrier height as a function of the metal coverage deposited on a ;emiconductor [I-3]. Typically. for H I - V semiconduczors, the free surface shows no Fermi level pinning; the metal deposition introduces a quick evolution on the interface f, ermi energy that is eventually pinned by a high density of states induced in the semiconductor gap by 1 or 2 metal mona[dyers. Those results have supplied important information as regards tile mechanisms controlling Schottky barrier formation. These results have also stimulated theoretical work [4-6] for understanding the chemisorption processes associated with the metal deposition on the semiconductor, and their relation to the mechanism of the metal-semiconductor interface formation. Much work [3.6,7] has been recently perforr.~ed on the deposition of alkali metal.~ on G:lAs(ll0); this is a case that presents some particular advantages, because the metal atoms are very large and do not seem to diffuse into the semiconductor. The Scbottky barrier formation appears to be controlled in that case by a competition betv~een the formation of a conventional conduction band that induces a strong density of
states m the semiconductor energy gap, and typical electron correlation effects that tend to open a gap inside the metal conduction band (for low metal coverage), reduchtg the density of states induced by the metal in the semiconductor gap. The aim of the present communication is to analyze the deposition of Al on GaAs(110) in the submonolayer and the overlayer regimes. Chentisorption properties, Fermi energies and barrier heights are analyzed as a function of the metal coverage. Our analysis tries to elucidate how the Sehottky barrier depends on the AI coverage, comparing with the results for the aikali metals case. We will discuss the main differences and similarities between both cases. Let us mention that the deposition of AI on GaAs is compticeted by an exchange reaction whereby AI replaces G a in the last semiconductor layers. This reaction appears at room temperalure, but it is inhibited at very low temperature. Our theoretical work assumes we at," ~n tb;, !nw temperature limit, and only considers how AI chemisorbes when it is deposited on the semiconductor. Even with this assumption, the problem is far from being a simple task; we will analyse different adsorption sites and look for the geometry having the lowest energy. The rest o[ the paper is organized as follows: in section 2 we present a summary of our method
016q-4332/qZ/S[6.f10t) ]q92 - ElsevierScience Publishers B.V.All rlghts reserved
,t
Ortega et al. / Schottky barrier fonhation bl At-deposition GaAsl] lot
737
of calculation, in section 3 we discuss our main results, and ill section 4 we prc~ent our main conclusions.
where U,Im and j~a are the intrasite and intersite bare Coulomb interactions, respectively, and ][~u is an effective [9] interslte Coulomb interaction given by:
2. Model and method of calculation
J,']'} = J[)"(l +S~)_j~
The electronic structure of GaAs is described using an LCAO model with sp3s * hybrids and interactions discussed by Vogl et al. [8]. The interaction between the AI atoms and between Al and the substrate is analyzed by means of an LCAO method [9] that gives a orescription to calculate the hopping elements between the different orbitals as well as the one-body and the mapy-body contributions to the total energy of the ehemisorption system. A full discussion oi this free-parameter method is presented else. where [91: here, we only quote its main characteristics. First of all, let us mention that the hopping integrals, Ti,, between two orbitais 6; and 6"j (taken as the atornic orbitals of two atoms) are related to the Bardcen tunneling current. T~+ by
T,~ = r~p,
<1)
h 'E~ - ff~b.~*, i. = ~Zm ) k t ~ - 6 ~I 0 tl]Ji ds •
(2)
~E,= - ESijT,] + ~ ZS~(Ei-E,), j.i j,~i
(3)
where E, and Ej are the mean levels of the ith and jth orbitats. Many-body contributions are introduced by means of the following terms in the total HamiltoniaT.:
,q°'~ = E v , a % , ' L , + ~ E J,')",+,,vL~ i
; =j,.r
+½ E ZT'&/',,,, i *j.+r
t),".,~" = E U , ' " ' ¢ , , , 0 % ) i
(4)
+ 32 # ? ' & , 0 % ) ~*i.a
+ E Y,~",*~..<~j,,>+ E-v~.,,,,~ .... j+r.~r
i+r
(6)
plus some constant terms cancelling the double counting in the electron-eleclron interaction. V,.+~ is related to the exchange pair distribution function g,,(i, j) given by 15... =
where ~/ is typically around 1.3-1.5, a parameter that can be caleu!ated exactly [9]. The overlap between difl~rent orbitals, S u = (6i145), introduces a contribution to the total energy that is found to be well described by the following correction to the diagonal level, ~E,, of a given orbital ~b/:
(5)
xhere j~c.~j +s the exchangu integral between the ith and jth orbitals, The terms given by eq. (4) are treated using a many-t:.ody approximation equivalent to the one given by $1ater for a free-electron gas. This means using a mean-field approximation suplemented by a Slater-fike potential, V,,,,. Thus, we replace the Hamiltonian (4; by the following mean-field Hamiltonian:
El]]')g,.(i./),
(7)
where g,,(i, j) is defined by (c~,,e~,,) (c]~,e;,,) = (fii,,)g,,(i, j ) .
(8)
In eq. (6), c~ is taken to be 7: this is shown [9] to include interatomic correlation effects. This implies neglecting bztra-atomic correlation effects which could be, however, included by using a perturbative approach [10]. In our actual calculation we have solved the LCAO mean-field Hamiltonian using conventional Green-function techniques [ll]. Moreover, selfconslstency in the charges is achieved by relating the induced potential (as given by the manybody Hamihonian) to the charges induced in each atom. Let us finally comment that, in general, the semiconductor surface is not allowed to relax. Different theoretical calculations have shown [12,13] that A1 tendn to eliminate very efficiently the surface relaxation appearing at a free semi-
,L Ortega et aL / Schou£3" borrk,r [ormadon itl Al.deporifiou GaAs¢ l loJ
738
conductor surface. Thus. in all o a r results, the ehemisorption energy of different over ayers is referred to the semiconductor unrelaxed sm'faee.
the AI layer and the last semiconductor layer. T h e minimum of the interaction potential yields the following chemisorption energies per adsorbed atom: Ed,~m(As bonded) = - !.8 cV.
3. Results
Ecn,~lbridge ) = - 2 . 1 eV. We have analyzed the geontctries associated with different AI eove:,~ges. We have considered three different cases: ha!f a monolayer, a munolayer, and t',vo monolayecs. (Here. one ML is defined as two AI atoms per semiconductor surface cell). For each case, we t:ave looked for the most stable geometry. 3. !. H a l f a ~vonolayer
Fig. 1 shows the two most ex+ergetie geometries. In ~me case, the AI atoms are bonded to As, while in the second case, A1 is bonded simultaneously to As and Ga, occupying the mid-poiot of the largest bridge distance between the eatiun and the anion. Although the bridge 9osition seems to be the most energetic geometry, we only find small differences with the As-bonded tree. Fig. 1 also shows the chemisorption energy for each case, a.s a function of the distance between
We should also mention that for AI bonded to Ga we find the following ehemi~orption energy: E,,ho.,(Ga bonded) = - 1.0 cV. 3 . 2 T h e m o n o l a y e r case
Ill Ibis ease we have two AI atoms per surface unit cell. We have explored different geometries and have found that the most favourable geometries correspond to the following eases: (a) the A| atom bonded to As and Ga f~ee fig. 2); (b) the Al atom bonded to Ga, and tile other atom located on top of As. Th¢se cases yield the following ehemisorption energies: (a) Eehem = - 5 . 3 eV, ( b ) E~,~,~, = - 4 . 3 e V .
It is interesting to mention that the total ehemisorption energy we find for the most stable
"12 [b
I
I
,\
;o +
7[
g, -
\
.~ ,,o -
,/
",~,
}
I
"
jJ
1 t~ 22 ~9 21 23 25 c ~ =. ce (~,) dista'~ce (A) Fig. 1. ChemNorption energy for half a mono}ayer of AI on GaAs as a funclion of the metal distance to the last semiconductor layer ,c
!=
(in A): (a) bridge posilion. (b) As-position. The in~Is show the corresponding geometries+
Z Ortegt* et al. / Schottky barrierformation inAI-deposition GuAs(i 10)
~
1
~______)_~
Fig. 2. Local density of states (LDO$) oil the metal atoms blinded hi Ga and As, and iin the cation and the anion of the last serni~mducmr layer, for Ihe monolayer case shown in the inscl. This case corresponds Io Ihe most stable AI monolayer gcomctr~'. E = 0 is Ihe lop of the semiconductor valence band.
geometry of the monolayer, is larger than the sum of the chemisorption energies calculated independently for the cases of half a monolayer of AI bonded to either As or Ga. This yields 2.8 eV, showing that the AI atoms atract each other tending io lorm clusters on the G a A s ( l t 0 ) surface. Even the most stable monolayer case yields a more favourable geometrical configuration than having two AI atoms chemisorbed on the bridge positions. Fig. 2 shows the geometry of ease (a), and the local density of states projected on the two AI atoms and the As and Ga atoms of the last semiconductor layer. Let us comment these resuits, in the perspective of other theoretical approaches [12] and ~ m e experimental evidence [14]. First of all, let us mentim~ that the results that we alreedy have presented fi~r the geometries of half and one monolayers are in good agreement with other results [12] obtained using an LDA method. In particular, the LDA calculation has also obtained the long-bridge position
739
and the G a and As dan~ling bonds positions as the most favourable geometries for half a monolayer and one monolayer, respectively. This good agreement between the two different theoretical approaches is very satisfactory, because recently some experimental S T M results 114] have suggested that AI adsorbed on GaAs should be located on top of Ga. This conclusion is drawn from the different spots that S T M images show for positive and negative biases: basically, these image~ show that for both biases, brighter spots appear on Go. In order to see whether these results are compatible with the most stable geometry calculated by the theoretical results, we have shown the different local density of states of an AI monolayer in fig. 2. The important results one can draw from this figure are the following: (a) T h e unoccupied states located just above the energy gap have mainly a Ga character; in particular the AI bonded to Ga presents also a larger weight in this part of the electronic spectrum. (b) The occupied states located below the energy gap have as much weight n~ Ga as on As, if not a little more. This implies that the local states distributed around the energy gap present a strong G a character; thus, these theoretical data seem to explain the S T M results, resolving the apparent contradiction between the most stable AI monolayer as calculated here and in ref. [12], and the S T M results of ref. [14]. It is also of interest to mention that the density of states shown in fig. 2 presents an energy gap of around 1.2 eV, in good agreement with the value of 1.0 e V obtained by Suzuki and Fukuda [14] using the scanning tunneling microscope. 3.3. T h e t w o - m o n o l a y e r case
F r o m the point of view of the Schottky barrier formation, one is interested in knowing how the Fermi level is pinned by the electron density of states created in the semiconductor gap. For the monolayer case, we have found that the induced density of states presents an energy gap, around 1.2 eV wide. The crucial point is to know how this gap is closed with further deposition of the metal. This has prom~ted us to analyze the two-
z flrh?,w el ill. f S{'hottky barrier ]broul~km hi Ai.dt'l~oslth~ GaAMIIO)
/
.~ ,.:'.
Fig. 3. Lc~caldensity of slates (LDOS) un the P.~ometld layers lind the: IIIM~emicl~ilductt)rlayer I'nr iwo AI nlOlll)layers de.no~iled on GaAstlln}. The seo~nd AI monolayer is 2.4 A aho~e the fizst reeled monola~er,
monolayer case. Fig. 3 shows the geometry of the AI overlayer we have considered; distances between the second AI layer and the o~her atoms have been calculated by maximizing the chemisorption energy. We should comment that this geometry has not been minimized, however, with respect to many other geometrical configurations of the second AI layer. T h e symmetry of the first layer suggests to use the geometry drmvn in fig. 3, since in this case the new AI atoms are directly bonded to a high number of AI atoms located in the first layer. Fig. 3 also shows the local density of states we have calculated for the two-monolayer case, projected onto the different metal layers and the last semiconductor layer. "lhe important point to notice is that the new interaction introduced by the second AI monolayer has closed the gap appearing tor the monol~yer case. At the same time. we find that the Fermi energy is pinned at 0.6 eV above thc semi~,onductor valence band top. All these results show a good agreement w i t h the b e h a v i o u r o f t h e O a A s ( l l 0 ~ / A I interface for low metal coverage [2]. For a free semiconductor surface initially the Fermi level is not pinned by an~ electron density
of states; ~t very low metal coverage, we expect to have a t~w islands with a monolayer height, and then we shoold find the electron density of states shown in fig. 2. Thus the n- and p-doped semiconductor Fermi levels at the interface would approach each other, but still differing significantly. Then, for a further coverage, AI clusters start to grow and a~';soon as a second layer of the cluster is formed, the local Fermi energy is going to he pinned by a high density of states. A macroscopic region will present Fermi level pinning if the whole surface is covered by AI; this is related, however, to how the At atoms grow on the GaAs surface. What is important to realize ts that the Fermi energy given by our calculation for two monolayers, should practically coincide with the thick metal overlayer since the barrier height depends only very slightly on the metal coverage [15], once we have created an important density of states in the semiconductor gap. Now, c~mparing our calculated Fermi level with the experimental one [2], we find quite a good agreement, giving further support to tile results presented in this paper.
4. Concluding remarks The aim of this paper has been to understand the Sehottky barrier formation in the case of AI deposition on GaAs(l lO). It has been established that this barrier formation depends crucially on the interaction between the semiconductor and the first metal layers deposited on the surface [15,16]. These facts have prompted us to analyze the chemisorption energy of the first metal layers deposited on the semiconductor and determining the most favourable geometries. O u r results present good agreement with other theoretical resuits and have been showk~ to be iil agzeemeot with the available experimental evidence. Using the most favourable geometries we have analyzed the Schottky barrier evolution as a function of the coverage. T h e main conclusion of our analysis is that for an AI monolayer there appears an energ) gap around the Fermi energy in the density of states induced by the deposited metal. This explains that for very low AI coverage the Fermi
K Ortega el aL / Sclltlttky hamerfnr,n,tir, n in AI.depositt~n GrlAx(I]OI
level c a n n o t b e p i n n e d by t h e intrinsic states t h a t t h e I D I S m o d e l [!6,17] w o u l d p r e d i c t to a p p e a r a r o u n d t h e s e m i c o n d u c t o r c h a r g e n e u t r a l i t y level. O u r results also s h o w t h a t I o r a l a r g e r d e p o s i t i o n , as s o o n am a s e c o n d AI layer is f o r m e d (pr<>bahly. by t h e f o r m a t i o n o f AI clusters at t h e starface), a n i m p o r t a n t d e n s i t y of states in i n d u c e d by t h e metal around lhc semiec.nductor charge neutrality level. T h e n , t h e I D I S m o d e l starts to b e o p e r ative a n d t h e i n t e r f a c e F e r m i level s h o u l d be l o c a t e d close tu t h a t c h a r g e n e u t r a l i t y level. "['his basically implies t h a t t h e o a t r i m is c o m p l e t e l y formed, and that no turther evohttion of the S c h o t t k y b a r r i e r a n d t h e F e r m i level w o u l d a p p e a r for f i l r t h e r m e t a l d e p o s i t i o n . It s h o u l d b e e m p h a s i z e d t h a t this S c h o t t k y b a r r i e r e v o l u t i o n is in c o n t r a s t w i t h w h a t h a s b e e n f o u n d for t h c alkali a t o m s [6,7,18]. I n this case, t h e a t o m s h a v e a l a r g e size a n d ~br t h e first m o n o l a y e r d e p o s i t i o n , only o n c a t o m is d e p o s i t e d o n t h e s e m i c o n d u c t o r p e r u n i t cell. T h e m o n o l a y e r case p r e s e n t s a typical m e t a l d e n s i t y of states a r o u n d t h e s e m i c o n d u c t o r c h a r g e n e u t r a l i t y level: it h a s b e e n a r g u e d , h o w e v e r , t h a t m e t a l c o r r e l a t i o n effects w o u l d il~hibi~ t h e d e v e l o p m e n t o f t h a t d e n s i t y o f slates u n t i l a f u r t h e r d e p o s i t i o n w o u l d c r e a t e t h e typical m e t a I - i n d u c c d states [7,18]. F o r AI, we find a d i f f e r e n t case: t w o m e t a l ~ t o m s p e r u n i t cell a r c d e p o s i t e d o n t h e s e m i c o n d u c t o r f o r t h e fir';t m o n o l a y e r . T h i s implier; a n e v e n n u m b e r o f electrons, and a kind of surface semiconductor e l e c t r o n s t r u c t u r e for t h e first d e p o s i t e d m o n o layer. T h e 5 c h o t t k y b a r r i e r f o r m a t i o n is, t h e n , r e l a t e d t o t h e c l o s i n g o f this g a p d u e to t h e f u r t h e r d e p o s i t i o n of t h e m e t a i o n t h e s e m i c o n ductor.
Acknowledgements T h i s w o r k h a s b e e n partially f u n d c d by t h e Comisidn lnterministerial de Cieneia y Tecnologia
741
( 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 M A T 88-0544, a n d t h e C E E u n d e i c o n t r a c t S C 1 - C T 91-069t.
References [ll K. Stiles A, Kahn, D,G. Kiltlay and G, MargariIimdo, J. Vac, gel, Technoh n 5 (19871 987; K, Slil¢~ and A. Kahn. Phys, Rev. Lea. 60 (!(188) 44lh 121 T. Kendelewicz, P. Soukiassian. M.II. lIahshk Z, [lurych. I, Lindau and W.E. Spicer. Phys. Rev. B 3[4 (lY881 7568: W.E, Spicer, Appl. Surf. SCL 41/42 (19891 I. [3] M. Prie~tdl. M Danke. C. Laubschat and G, Kaindl. Phys. Rev. L..)II.hi) ( 19~81 436; M. Prie~lch, M. Danke, C. Laubschat, T, Mandel, C. Xue and G, Kaindl, Z. Phys. ~ 74 (IriSh)) 21. 141 W. MSoch. Europhys. tell. 63 (19881 275 [5] 1 Lefebvre, M. l_anoo and G, Allan, Phy~, Rev, Len, 63 (1~891 25(10, 161 J. Ortega and F. Flores. Phys. Rev. tell. 63 (19891 250D; J. Ortega, R. Pgrez and F. Flore~. Surf, Sci, 251/252 (lt191) 442. [7] T. Maeda Won8, NJ. DiNardt), D. Hesken and E,W, Phlmmer, Phys. nev. B 41 119YIU1~372: N.J, DiNardo, T, Maeda Wong and E.W. Phlmmer, Phys. Rev. Leu. g5 (IgY0)2177. [g] P. Vogl. P. Hjalmarson and J.D. Do~. J. Phys, Chem. St.lids 44 119831 365. [ol E,C. Goldberg. A. Martln-Rodero, R, M(mreal and F. Flores. Phys. Rev, B 59 (19891 5684; F.J. Garc[a-Vidal. A. Martin-Rndero. F. FIoles. J. Ortega and R. Pgrez, Phys. Ruv. B 44 (199II 11412. [l[)l F. Flores and L Orlega. Europhys. ten. 17 t 1992) 619. [ 1II F. Guinea. C. Tcjcdor. F. FIt)rcs and E. Louis. Phys, RLw, B 28 ( 19831 4397. [[2] J. Ihm and D. Joannopoulos. Phys. RLw. B 26 (19821 4429. J13] S.B. Zhang, M,L. Cohen and S.G. LaJuie, Phys. Rev, B 34 ( 1986176s, [14] M. Suzuki and T. Fukuda, Phys. Rev. n ~4 (19gl) 3is?. [15] J. Ortega. J, Sanchez-D¢ilesa and F. Flores. Phys. Rev. B 37 ~tt)881 8516. [16} F. Flores and C. Tejedor, L Phys. C 20 (19871 145. [17] C, Tejedor. F. Ftores and E. Louis. J. Phys. C In (1977) 2163: J. ~cr~off. Phys. Rev. Lelt. 3(1 (i()84) 4874. [18l J. Ortega, R. Pgrez, F,J. Garc~a-Vidal and F, Flt)rc~, Appl. Surf, Sci. 56-58 ( 19tJ21264.
Applied Surface Scimlcefd)/hl (1992)73fi-741 North-Holland
surface science
Schottky barrier formation: AI deposition on GaAs(1
1 0/1 ~
L Ortega, R. Rinc6n, R. Pdrez. FJ. Garcla-Vidal and F. Flares l,~'llarl, ltnt'lm~ tit' I'i~ica tit' la Materhl Ctutth,nxada C-,¥IL Fat'tdlad tlt' ('leilcias, UnR e~hlad Alltdnonul, E-28Od9 ,~htdrltL ,$)~lbl
Received 211November 19t)l;accepted bit publication h Jnnuals, It)Y2
The Scholtky barrier furmation for AI on GaAr4IIdl has been analysed as a funclion af the metal c(~'erage. Fnr different AI coverages ~e have calculated Ih¢ most stahle geomelriesusing a consistent tree-parameter LCAO method. Our resuhs show that for an AI manolayer, no densily of slatvs appears near the semiconductor charge neulrallty level. "File Fermi level is. however, pinned, and ihe Sehonky harrier completely formed, for a ¢~werageof twt~metal nn)lltlklyers. For Ihis limil wc recover Ihe intrinsic metal sta|e~ model and find goad agreement with the Schottky harrier height ftlr thick metal hlyers.
l . lntroduetlun One of the main experimental facts, recently obtained in the field of Scbottky barrier formation. is the evolution of Schottky barrier height as a function of the metal coverage deposited on a ;emiconductor [I-3]. Typically. for H I - V semiconduczors, the free surface shows no Fermi level pinning; the metal deposition introduces a quick evolution on the interface f, ermi energy that is eventually pinned by a high density of states induced in the semiconductor gap by 1 or 2 metal mona[dyers. Those results have supplied important information as regards tile mechanisms controlling Schottky barrier formation. These results have also stimulated theoretical work [4-6] for understanding the chemisorption processes associated with the metal deposition on the semiconductor, and their relation to the mechanism of the metal-semiconductor interface formation. Much work [3.6,7] has been recently perforr.~ed on the deposition of alkali metal.~ on G:lAs(ll0); this is a case that presents some particular advantages, because the metal atoms are very large and do not seem to diffuse into the semiconductor. The Scbottky barrier formation appears to be controlled in that case by a competition betv~een the formation of a conventional conduction band that induces a strong density of
states m the semiconductor energy gap, and typical electron correlation effects that tend to open a gap inside the metal conduction band (for low metal coverage), reduchtg the density of states induced by the metal in the semiconductor gap. The aim of the present communication is to analyze the deposition of Al on GaAs(110) in the submonolayer and the overlayer regimes. Chentisorption properties, Fermi energies and barrier heights are analyzed as a function of the metal coverage. Our analysis tries to elucidate how the Sehottky barrier depends on the AI coverage, comparing with the results for the aikali metals case. We will discuss the main differences and similarities between both cases. Let us mention that the deposition of AI on GaAs is compticeted by an exchange reaction whereby AI replaces G a in the last semiconductor layers. This reaction appears at room temperalure, but it is inhibited at very low temperature. Our theoretical work assumes we at," ~n tb;, !nw temperature limit, and only considers how AI chemisorbes when it is deposited on the semiconductor. Even with this assumption, the problem is far from being a simple task; we will analyse different adsorption sites and look for the geometry having the lowest energy. The rest o[ the paper is organized as follows: in section 2 we present a summary of our method
016q-4332/qZ/S[6.f10t) ]q92 - ElsevierScience Publishers B.V.All rlghts reserved
,t
Ortega et al. / Schottky barrier fonhation bl At-deposition GaAsl] lot
737
of calculation, in section 3 we discuss our main results, and ill section 4 we prc~ent our main conclusions.
where U,Im and j~a are the intrasite and intersite bare Coulomb interactions, respectively, and ][~u is an effective [9] interslte Coulomb interaction given by:
2. Model and method of calculation
J,']'} = J[)"(l +S~)_j~
The electronic structure of GaAs is described using an LCAO model with sp3s * hybrids and interactions discussed by Vogl et al. [8]. The interaction between the AI atoms and between Al and the substrate is analyzed by means of an LCAO method [9] that gives a orescription to calculate the hopping elements between the different orbitals as well as the one-body and the mapy-body contributions to the total energy of the ehemisorption system. A full discussion oi this free-parameter method is presented else. where [91: here, we only quote its main characteristics. First of all, let us mention that the hopping integrals, Ti,, between two orbitais 6; and 6"j (taken as the atornic orbitals of two atoms) are related to the Bardcen tunneling current. T~+ by
T,~ = r~p,
<1)
h 'E~ - ff~b.~*, i. = ~Zm ) k t ~ - 6 ~I 0 tl]Ji ds •
(2)
~E,= - ESijT,] + ~ ZS~(Ei-E,), j.i j,~i
(3)
where E, and Ej are the mean levels of the ith and jth orbitats. Many-body contributions are introduced by means of the following terms in the total HamiltoniaT.:
,q°'~ = E v , a % , ' L , + ~ E J,')",+,,vL~ i
; =j,.r
+½ E ZT'&/',,,, i *j.+r
t),".,~" = E U , ' " ' ¢ , , , 0 % ) i
(4)
+ 32 # ? ' & , 0 % ) ~*i.a
+ E Y,~",*~..<~j,,>+ E-v~.,,,,~ .... j+r.~r
i+r
(6)
plus some constant terms cancelling the double counting in the electron-eleclron interaction. V,.+~ is related to the exchange pair distribution function g,,(i, j) given by 15... =
where ~/ is typically around 1.3-1.5, a parameter that can be caleu!ated exactly [9]. The overlap between difl~rent orbitals, S u = (6i145), introduces a contribution to the total energy that is found to be well described by the following correction to the diagonal level, ~E,, of a given orbital ~b/:
(5)
xhere j~c.~j +s the exchangu integral between the ith and jth orbitals, The terms given by eq. (4) are treated using a many-t:.ody approximation equivalent to the one given by $1ater for a free-electron gas. This means using a mean-field approximation suplemented by a Slater-fike potential, V,,,,. Thus, we replace the Hamiltonian (4; by the following mean-field Hamiltonian:
El]]')g,.(i./),
(7)
where g,,(i, j) is defined by (c~,,e~,,) (c]~,e;,,) = (fii,,)g,,(i, j ) .
(8)
In eq. (6), c~ is taken to be 7: this is shown [9] to include interatomic correlation effects. This implies neglecting bztra-atomic correlation effects which could be, however, included by using a perturbative approach [10]. In our actual calculation we have solved the LCAO mean-field Hamiltonian using conventional Green-function techniques [ll]. Moreover, selfconslstency in the charges is achieved by relating the induced potential (as given by the manybody Hamihonian) to the charges induced in each atom. Let us finally comment that, in general, the semiconductor surface is not allowed to relax. Different theoretical calculations have shown [12,13] that A1 tendn to eliminate very efficiently the surface relaxation appearing at a free semi-
,L Ortega et aL / Schou£3" borrk,r [ormadon itl Al.deporifiou GaAs¢ l loJ
738
conductor surface. Thus. in all o a r results, the ehemisorption energy of different over ayers is referred to the semiconductor unrelaxed sm'faee.
the AI layer and the last semiconductor layer. T h e minimum of the interaction potential yields the following chemisorption energies per adsorbed atom: Ed,~m(As bonded) = - !.8 cV.
3. Results
Ecn,~lbridge ) = - 2 . 1 eV. We have analyzed the geontctries associated with different AI eove:,~ges. We have considered three different cases: ha!f a monolayer, a munolayer, and t',vo monolayecs. (Here. one ML is defined as two AI atoms per semiconductor surface cell). For each case, we t:ave looked for the most stable geometry. 3. !. H a l f a ~vonolayer
Fig. 1 shows the two most ex+ergetie geometries. In ~me case, the AI atoms are bonded to As, while in the second case, A1 is bonded simultaneously to As and Ga, occupying the mid-poiot of the largest bridge distance between the eatiun and the anion. Although the bridge 9osition seems to be the most energetic geometry, we only find small differences with the As-bonded tree. Fig. 1 also shows the chemisorption energy for each case, a.s a function of the distance between
We should also mention that for AI bonded to Ga we find the following ehemi~orption energy: E,,ho.,(Ga bonded) = - 1.0 cV. 3 . 2 T h e m o n o l a y e r case
Ill Ibis ease we have two AI atoms per surface unit cell. We have explored different geometries and have found that the most favourable geometries correspond to the following eases: (a) the A| atom bonded to As and Ga f~ee fig. 2); (b) the Al atom bonded to Ga, and tile other atom located on top of As. Th¢se cases yield the following ehemisorption energies: (a) Eehem = - 5 . 3 eV, ( b ) E~,~,~, = - 4 . 3 e V .
It is interesting to mention that the total ehemisorption energy we find for the most stable
"12 [b
I
I
,\
;o +
7[
g, -
\
.~ ,,o -
,/
",~,
}
I
"
jJ
1 t~ 22 ~9 21 23 25 c ~ =. ce (~,) dista'~ce (A) Fig. 1. ChemNorption energy for half a mono}ayer of AI on GaAs as a funclion of the metal distance to the last semiconductor layer ,c
!=
(in A): (a) bridge posilion. (b) As-position. The in~Is show the corresponding geometries+
Z Ortegt* et al. / Schottky barrierformation inAI-deposition GuAs(i 10)
~
1
~______)_~
Fig. 2. Local density of states (LDO$) oil the metal atoms blinded hi Ga and As, and iin the cation and the anion of the last serni~mducmr layer, for Ihe monolayer case shown in the inscl. This case corresponds Io Ihe most stable AI monolayer gcomctr~'. E = 0 is Ihe lop of the semiconductor valence band.
geometry of the monolayer, is larger than the sum of the chemisorption energies calculated independently for the cases of half a monolayer of AI bonded to either As or Ga. This yields 2.8 eV, showing that the AI atoms atract each other tending io lorm clusters on the G a A s ( l t 0 ) surface. Even the most stable monolayer case yields a more favourable geometrical configuration than having two AI atoms chemisorbed on the bridge positions. Fig. 2 shows the geometry of ease (a), and the local density of states projected on the two AI atoms and the As and Ga atoms of the last semiconductor layer. Let us comment these resuits, in the perspective of other theoretical approaches [12] and ~ m e experimental evidence [14]. First of all, let us mentim~ that the results that we alreedy have presented fi~r the geometries of half and one monolayers are in good agreement with other results [12] obtained using an LDA method. In particular, the LDA calculation has also obtained the long-bridge position
739
and the G a and As dan~ling bonds positions as the most favourable geometries for half a monolayer and one monolayer, respectively. This good agreement between the two different theoretical approaches is very satisfactory, because recently some experimental S T M results 114] have suggested that AI adsorbed on GaAs should be located on top of Ga. This conclusion is drawn from the different spots that S T M images show for positive and negative biases: basically, these image~ show that for both biases, brighter spots appear on Go. In order to see whether these results are compatible with the most stable geometry calculated by the theoretical results, we have shown the different local density of states of an AI monolayer in fig. 2. The important results one can draw from this figure are the following: (a) T h e unoccupied states located just above the energy gap have mainly a Ga character; in particular the AI bonded to Ga presents also a larger weight in this part of the electronic spectrum. (b) The occupied states located below the energy gap have as much weight n~ Ga as on As, if not a little more. This implies that the local states distributed around the energy gap present a strong G a character; thus, these theoretical data seem to explain the S T M results, resolving the apparent contradiction between the most stable AI monolayer as calculated here and in ref. [12], and the S T M results of ref. [14]. It is also of interest to mention that the density of states shown in fig. 2 presents an energy gap of around 1.2 eV, in good agreement with the value of 1.0 e V obtained by Suzuki and Fukuda [14] using the scanning tunneling microscope. 3.3. T h e t w o - m o n o l a y e r case
F r o m the point of view of the Schottky barrier formation, one is interested in knowing how the Fermi level is pinned by the electron density of states created in the semiconductor gap. For the monolayer case, we have found that the induced density of states presents an energy gap, around 1.2 eV wide. The crucial point is to know how this gap is closed with further deposition of the metal. This has prom~ted us to analyze the two-
z flrh?,w el ill. f S{'hottky barrier ]broul~km hi Ai.dt'l~oslth~ GaAMIIO)
/
.~ ,.:'.
Fig. 3. Lc~caldensity of slates (LDOS) un the P.~ometld layers lind the: IIIM~emicl~ilductt)rlayer I'nr iwo AI nlOlll)layers de.no~iled on GaAstlln}. The seo~nd AI monolayer is 2.4 A aho~e the fizst reeled monola~er,
monolayer case. Fig. 3 shows the geometry of the AI overlayer we have considered; distances between the second AI layer and the o~her atoms have been calculated by maximizing the chemisorption energy. We should comment that this geometry has not been minimized, however, with respect to many other geometrical configurations of the second AI layer. T h e symmetry of the first layer suggests to use the geometry drmvn in fig. 3, since in this case the new AI atoms are directly bonded to a high number of AI atoms located in the first layer. Fig. 3 also shows the local density of states we have calculated for the two-monolayer case, projected onto the different metal layers and the last semiconductor layer. "lhe important point to notice is that the new interaction introduced by the second AI monolayer has closed the gap appearing tor the monol~yer case. At the same time. we find that the Fermi energy is pinned at 0.6 eV above thc semi~,onductor valence band top. All these results show a good agreement w i t h the b e h a v i o u r o f t h e O a A s ( l l 0 ~ / A I interface for low metal coverage [2]. For a free semiconductor surface initially the Fermi level is not pinned by an~ electron density
of states; ~t very low metal coverage, we expect to have a t~w islands with a monolayer height, and then we shoold find the electron density of states shown in fig. 2. Thus the n- and p-doped semiconductor Fermi levels at the interface would approach each other, but still differing significantly. Then, for a further coverage, AI clusters start to grow and a~';soon as a second layer of the cluster is formed, the local Fermi energy is going to he pinned by a high density of states. A macroscopic region will present Fermi level pinning if the whole surface is covered by AI; this is related, however, to how the At atoms grow on the GaAs surface. What is important to realize ts that the Fermi energy given by our calculation for two monolayers, should practically coincide with the thick metal overlayer since the barrier height depends only very slightly on the metal coverage [15], once we have created an important density of states in the semiconductor gap. Now, c~mparing our calculated Fermi level with the experimental one [2], we find quite a good agreement, giving further support to tile results presented in this paper.
4. Concluding remarks The aim of this paper has been to understand the Sehottky barrier formation in the case of AI deposition on GaAs(l lO). It has been established that this barrier formation depends crucially on the interaction between the semiconductor and the first metal layers deposited on the surface [15,16]. These facts have prompted us to analyze the chemisorption energy of the first metal layers deposited on the semiconductor and determining the most favourable geometries. O u r results present good agreement with other theoretical resuits and have been showk~ to be iil agzeemeot with the available experimental evidence. Using the most favourable geometries we have analyzed the Schottky barrier evolution as a function of the coverage. T h e main conclusion of our analysis is that for an AI monolayer there appears an energ) gap around the Fermi energy in the density of states induced by the deposited metal. This explains that for very low AI coverage the Fermi
K Ortega el aL / Sclltlttky hamerfnr,n,tir, n in AI.depositt~n GrlAx(I]OI
level c a n n o t b e p i n n e d by t h e intrinsic states t h a t t h e I D I S m o d e l [!6,17] w o u l d p r e d i c t to a p p e a r a r o u n d t h e s e m i c o n d u c t o r c h a r g e n e u t r a l i t y level. O u r results also s h o w t h a t I o r a l a r g e r d e p o s i t i o n , as s o o n am a s e c o n d AI layer is f o r m e d (pr<>bahly. by t h e f o r m a t i o n o f AI clusters at t h e starface), a n i m p o r t a n t d e n s i t y of states in i n d u c e d by t h e metal around lhc semiec.nductor charge neutrality level. T h e n , t h e I D I S m o d e l starts to b e o p e r ative a n d t h e i n t e r f a c e F e r m i level s h o u l d be l o c a t e d close tu t h a t c h a r g e n e u t r a l i t y level. "['his basically implies t h a t t h e o a t r i m is c o m p l e t e l y formed, and that no turther evohttion of the S c h o t t k y b a r r i e r a n d t h e F e r m i level w o u l d a p p e a r for f i l r t h e r m e t a l d e p o s i t i o n . It s h o u l d b e e m p h a s i z e d t h a t this S c h o t t k y b a r r i e r e v o l u t i o n is in c o n t r a s t w i t h w h a t h a s b e e n f o u n d for t h c alkali a t o m s [6,7,18]. I n this case, t h e a t o m s h a v e a l a r g e size a n d ~br t h e first m o n o l a y e r d e p o s i t i o n , only o n c a t o m is d e p o s i t e d o n t h e s e m i c o n d u c t o r p e r u n i t cell. T h e m o n o l a y e r case p r e s e n t s a typical m e t a l d e n s i t y of states a r o u n d t h e s e m i c o n d u c t o r c h a r g e n e u t r a l i t y level: it h a s b e e n a r g u e d , h o w e v e r , t h a t m e t a l c o r r e l a t i o n effects w o u l d il~hibi~ t h e d e v e l o p m e n t o f t h a t d e n s i t y o f slates u n t i l a f u r t h e r d e p o s i t i o n w o u l d c r e a t e t h e typical m e t a I - i n d u c c d states [7,18]. F o r AI, we find a d i f f e r e n t case: t w o m e t a l ~ t o m s p e r u n i t cell a r c d e p o s i t e d o n t h e s e m i c o n d u c t o r f o r t h e fir';t m o n o l a y e r . T h i s implier; a n e v e n n u m b e r o f electrons, and a kind of surface semiconductor e l e c t r o n s t r u c t u r e for t h e first d e p o s i t e d m o n o layer. T h e 5 c h o t t k y b a r r i e r f o r m a t i o n is, t h e n , r e l a t e d t o t h e c l o s i n g o f this g a p d u e to t h e f u r t h e r d e p o s i t i o n of t h e m e t a i o n t h e s e m i c o n ductor.
Acknowledgements T h i s w o r k h a s b e e n partially f u n d c d by t h e Comisidn lnterministerial de Cieneia y Tecnologia
741
( 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 M A T 88-0544, a n d t h e C E E u n d e i c o n t r a c t S C 1 - C T 91-069t.
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