Electronic structure of semiconductor-metal-semiconductor heterostructures

Electronic structure of semiconductor-metal-semiconductor heterostructures

Applied Surface Science56-58119921363-369 North-Holland "L al~d surface science Electronic structure of semiconductor-metal-semiconductor heterostru...

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Applied Surface Science56-58119921363-369 North-Holland

"L al~d surface science

Electronic structure of semiconductor-metal-semiconductor heterostructures Pierre M a s r i Lahoratoire d'Et.de~ des Surfaces, hlterfaces e l C~mposauts IZA, u. CNRS D07870. Unicer~it~;de Mantpellier II Tethulques du Languedoc, Ca~e 08~. Place Et~gt~neIJalaillon, 34005 Manlpellicr Cedex 05, France


Scie/ttes et

Received 7 May 1991;acceple I for publicalion 31) May 1991

For tile first time. we pr:~nt in this arlicle a microscopic self-consistent Iheol3:of tile electronic structure of ~elniconducmrracial-semiconductor (SMSl heterostruclures. This is done within the framework of a tlght-binding approximation, We use a one-florid model and a siml~lifiedtwo-band model 1o describe metal and semiconductor bulk bands, respeelively. Resultsare given for a material-symmelrical and inlerface-asymmetrical SMS structure: this involves the same semicnndactors, but different interface polarities (anion- and callou-like interfaces), Tbese results include metal-like slateg (built-in metal band) and metal-induced semiconductor-like staLes.The relewmce I)f the charge neutrality condition to Ibis feature and to the determination of the p~sitinn nf the SMS Fermi levd is discussed. We also emphasize the confining role of interfaces, with respect to semiconducl(ir-like states, ',~ilhin the semiconductor gap.

1. Introduction The increasing interest in semiconductormetal-semiconductor (SMS) structures is mainly due to their possible efficient utilization as transistors: three terminal devices as common metalbase transistor (MBT) or permeable-base transistor [1-4] (PBT) for integrated circuit (IC) technology. Progress in this field is now possible due to the development of crystal growth techniques as molecular beam epitaxy (MBE). The most studied structures involve Si and metal-silicide layers like $ i / N i S i 2 / S i and S i / C o S i J S L In this article, we present a self-consistent theory of the electronic structure of $ M 5 heterostructures by using the Green function method within the framework of tight-binding approximation. The system we consider is formed out of a metal layer, of thickness L. sandwiched between two identical semiconductors. However, a kind of asymmetry is introduced by considering that the interface atoms of the first semiconductor are anion-like while the interface atoms of the sec-

ond semiconductor arc cation-like. This different ionic character may be simulated by assuming that the two semi-infinite semiconductors are terminated in polar surfaces, respectively constituted of anions and cations. A relevant issue of this work is the discovery of an interesting feature related to Fermi level position.

2. Interaction model A detailed discussion of the model will be given elsewhere [5], 2.1. B u l k

(i) A one-band model is used to simulate the bulk electronic properties of the metal. When a nearest-neighbor interaction approximation is used (hopping integral y.), the electron dispersion relation is given by the following relationship [6] ( E n is the energy of the band center, k is the wave vector, of components kx, k r and k : , and a

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is the lattice parameter): E2(k)


E ~ - 2 ~ [ c o s ( a k , ) + cos(ak~ )



(ill A two-band model is used to simulate the bulk electrorlie properties of semiennduetors. Tile bulk bands are then given by the following expression 171: & = ( e. + E,,)/2 _+

l( t:,,

- r:.,

y'/4 l/z






j ( = 1 or 3) is the semiconductor index; E~i and E~ represent orbital self-energies, respectively associated with anion and cation; yj is the bulk hopping integral.

with the whole SMS system. This quantity is obtained within the t'o~Iowing scheme: (i) Build a three-block matrix of Green's function GI~ with Green's functions of isolated bulk materials. The euergy spectrum of this reference quantity provides the bulk electronic bands of deeoupled metal and semiconductor materia'.s. (ii) Create the SMS heterostructure in two steps: I l l extract a metallic film (thickness L) and two semi-infinite semiconductors, respectively, from their bulk lattices. (2) Insert the metal slab between the lwo previous semiconductors and let these materials interact by means of two hopping integrals and allow charge flow to achieve self-consisteucy. The resulting perturbations may be summarized within the same perturbation matrix Vp [5]. (iii) Calculate the matrix:

2.2, b~tert'oee

0 = I - VpG..

Two semiconductor-metal interfaces are introduced in the SMS structure, where anionqike and cation-like semiconductor atoms are, respectively, in direct interaction with metal atoms (two hopping integrals ~ and ~,). The creation of these interfaces produces a charge flow between metal and semiconductor atoms. In order not to overestimate the charge transfer, one must introduce two Coulomb potentials U~ and U~. This is equivalmlt to a Hartree-Fock approximation on the Coulomb interaction site. We limit the charge oscillations, at each interface, to one plauc on either interface sides. We then obtain, for each interface, a model with two charged (SQ and -,,$Q) intcrfacial layers. In order to fulfill the charge rmutrality cor,dition, the Fermi level and the self-consistent potcntials must satisfy the Friedcl sum rule:

The entire SMS electronic structure is then obtained b~.,solving the following equation:

-a,V(E F, U~, U_,)



3. Formalism

The quantity required to calculate the electronic s[rllcture is the Green's function associated






4. Results It is worth noting that our method allows us to calculate lhe dispersima relations of all SMS electronic structures, created by interaction betweeu metal and semiconductor materials. As we will see, our study reveals four types of SMS electronic structures. These include: (i) interface states localized within the semiconductor gap outside the metal band; (it) metal-like states falling within the bulk-metal band. These represent a quasi-continuum of metallic states which converge towards the bulk band for very thick metal layers (built-in metal band); (iii) interfacerelated states, showing a semiconductor-like character, and whose energies are situated within the metal band outside the semiconductor bands. These stak.s show a fight relation to metal-like states; (iv) states falling within the semiconductor

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bands sllowJng a strong correlation to tile laller slates and to the true interface states. Because of their extension into the metal, metal-like states are, as we will see, insensitive to interface perturbations. The main relevant SMS electronic features result fror~ the interaction of these states with semiconductor bulk electronic bands. Let us notice that the interface planes in the SMS structure are ({)l)i) planes. The dispersion relations are represented along the [100] direction of the first bi-dimensional Brillouin zone adapted to tile symmetry of the system. This symmetry consists in a translational periodicity along interface planes. In what follows, the results correspond to a symmetrical SMS structure in that the same material is used on both sides of the metal layer. However. an interracial asymmetry is introduced into the system by considering semiconductor polar surfaces interacting with metal layers. This enables us to ctmsider different polarities for semiconductors 1 and 3. We then end up with two interfaces constituted respectively of anionand cation-like aloms interacting with metal atoms. We may anticipate that this asymmetry will generate specific electronic feato|-es. The energies of metal- and semiconductor-like states are represented in fig. 1, in function of metal thickness L, for a wave vector k~ = 0.63~r/a. These levels are picked up from the dispersion relation curves of SMS states. One can notice that the separation in energ'j between the two components of each doublet decreases as the thickness L of the metal layer increases. In fig. 2, we represent the dispersion relations of SMS electron states, along the [100] direction. tbr L = 7. Partial overlapping occurs between metal and semiconductor bands (valence or conduction) at different wave vectors. We obtain sevcil two-state structures (seven doublets), whose energies are confined within the semiconductor gap and the bulk metal band. The central structure is referred to as the doublet (1, 2). One of these two-states (curve 2) shows a strong, intrinsic metal-like character. At the short wavelength tlmits, where features are revealed on an atomic scale, the corresponding dispersion relation (curve 2) reaches the metal-characteristic level E0.








Fig. I. Energies of two-slat,: eleclronic s~ructures as a funcli[)n c~fmetal Ihickness L. tot an asylr,,melricinterracial SMS heleroslructure. Dashed lines ( • --I represent the limitsnf the mela! bulk band. while s'.Jlid lines shoe, Ihe valence (lower) and c~nduction (upper) semlconducUlr bands. The zero a [ energy s taken at Ihe middle o[ Ihc sc~iTonducEor gap. The chosen example correspnnds Io E~ = - E = - ) 5 eV: YI = 1 eV: E~ = 0.2 eV; },, = 0.25 eV: ~1 = f-, = 11.25eV: E r = - 0 . l eV; k ~ O . 6 3 ~ r / a : t.ll= 0154 e'¢; U_~=fi.f199 eV. The second state (e.g., curve 1) corresponds to electronic structures, induced by the metal layer, strongly coupled to the metal-associated state belonging to me same doublet. T!lese structures emerge from the top of valence bands and may extend into true interface states or may interact with them. They may also exist as doublet structures, resonant with semiconductor bands and extending into gap states at valence band limits. Because of these reasons, we will refer to these states as metal-induced semiconductor-like states, although they may reveal an interfacial contribution. especially enhanced in the neighborhood of the semiconductor gap. The 6ispersion relation represented by curve 3. indeed, emerges from the top of the metal band and transforms into a true interface state near the Brillouin zone center.

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kx(~,.) Fig. 2. This figure shows ;he dcClrOn dispersion relations, in an asymmetric inlerfaeial SMS slructure, along file II00] dip:e~i'-'~ ,2t ~he in!erfacial BrilIouir~ znne. Th~'~e slrtnclUres illustrate the ¢lectamic signature of the melullic layer as t~-state syslems (e.g., curves I and 2k We also sho~ the Fermi level (E r) .in,ing at the energy co[lesp:lnding Ill the intersection pllinl of Ihe t~o comp~nt:J.ts (curves I and 2) of the central w.o-slate structure, al k~ ~ a.63~/a. The central metal-like state (cu,~e2) reaches t~e m~:al atomic level at the zone boundal~,,. Evm, E w e Ec,~ a~d ECM represcnl, re~peclively, the limits ~ff semiconductor valence and conductinn bands, and d~shed lines ( - - . - - I show the metal bulk band limits. Curve 4 gives the dispersion relation of a true imerlace stale induced by an anion-like interface. Curve 3 is associated with a racial-induced semicanductor-l;ke stale which extends into a t ~ e intertace stale, near the z:me center (Iong-wv,velenglh limiO, It a non-self-consiste.l calculation is carried out. metal-like states le.g., t~rve 2) remain ,inch,need. while semiconductor-like and interface states are shifted (cu~es I ~ 1' and 3 ~ 3'1. The metal layer i~ seven monolayer thick. The rein,icing parameters are the ~;~meas in fig. 1.

T h e r e , this state s h o w s a s t r o n g sensitivity to self-eensistency as a n o n - s e l f - c o n s i s t e n t calculat i o n shifts c u r v e 3 t o w a r d s c u r v e 3'. H o w e v e r , this sensitivity d e c r e a s e s f o r states s i l u a t e d in t h e i n n e r p a r t o f t h e m e t a l b a n d . as a s m a l l shift is o b s e r x e d (e.g., c u r v e i ~ 1'). T h i s shift is e v e n s m a l l e r f o r states r e s o n a n t w i t h t h e v a l e n c e b a n d

b e c a u s e o f t h e e x t e n s i o n o f t h e s e states d e e p in b o t h m e t a l a n d setnicoaduL:toi a~alefials (see fig. 2. d a s h e d curves associated w i t h o n e r e s o n a n t doublet), L e t us n o w c o m p a r e o u r results w i t h t h o s e o f L o w y et al. [8]. T h e system w e have to c o n s i d e r is formed of a semi-infinite metal adsorbed on a s e m i - i n f i n i t e s e m i c o n d u c t o r . I n o u r m o d e l this system c a n b e s i m u l a t e d by s w i t c h i n g o f f t h e resonance integral between the metal and semic o n d u c t o r 3 a n d by t a k i n g t h e limit L ~ o~ in eq. (4). By u s i n g t h e s a m e p a r a m e t e r s as t h o s e c o r r e s p o n d i n g to fig. 2 o f L o w y el al. [8], w e have c h e c k e d t h a t o u r curves 3 a n d 4 (fig. 2) p r o v i d e t h e s a m e result s h o w n in fig. 2 (rcf. [8], c u r v e s b). C u r v e 4 c o r r e s p o n d s to a t r u e i n t e r f a c e s t a t e w h i c h exists o n l y at s h o r t w a v e l e n g t h limits. F o r this r e a s o n , t h e associated e l e c t r o n w a v e s a r e s~rongly localized a r o u n d t h e i n t e r f a c e atoms. C o n s e q u e n t l y , this s t a t e v a n i s h e s w h e n self-consistency is n o t t a k e n i n t o a c c o u n t , c o n t r a r y to t h e l o n g - w a v e l e n g t h state ( c a r v e 3 ' ) . T h e lowest reson a n t e l e c t r o n i c s t r u c t u r e is r e l a t e d to t h e s t a t e (4) b e c a u s e it is t h e closest o n e to t h e g a p w h e r e t h e slate ( 4 ) exists. L e t us n o w e m p h a s i z e a n i m p o r t a n t f e a t u r e w h i c h e s t a b l i s h e s t h e basic role o f t h e two-state c h a r a c t e r o f t h e S M S e l e c t r o n i c s p e c t r u m , in t h e determination of fundamental electronic properties o f this s t r u c t u r e . T h i s f e a t u r e is r e l a t e d t o t h e inv,'rseetion o f t h e d i s p e r s i o n r e l a t i o n s , associa t e d w i t h e a c h d o u b l e t , at a c e r t a i n v a l u e k~ o f t h e b i - d i m e n s i o n a l w a v e v e c t o r (see fig. 2). T h i s will r e v e r s e I h e relative position o f m e t a l - a n d s e m i c o n d u c t o r - l i k e states. A m o n g all t w o - s t a t e s t r u c t u r e s (seven), t h e d o u b l e t (1, 2) r e p r e s e n t e d in fig. 2, w h i c h c o r r e s p o n d s to a m e t a l - l i k e state (curve 2 ) c o n v e r ~ i n g t o w a r d s t h e i n t r i n s i c m e t a l l i c level E a, s h o w s a clever f e a t u r e , T h i s is t h a t t h e e n e r g y level, at t h e p o i n t o f i n t e r s e c t i o n ( k ~ = 0 . 6 3 ~ / a ) is a l i g n e d w i t h t h e F e r m i level E F = - 0 . 1 e V a s s o c i a t e d w i t h t h e S M S system. T h i s f e a t u r e also a p p e a r s in fig. 1. W e h a v e c h e c k e d t h a t this f e a t u r e is n o t specific to t h e c h o i c e o f p a r a m e t e r s w e h a v e m a d e , as d i f f e r e n t sets o f p a r a m e t e r s give t h e s a m e b e h a v i o r . L e t us n o w e m p h a s i z e t h e role o f a s y m m e t r y in t h e S M S system u n d e r study. W e recall t h a t this

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asymmetD' is created because of different polarities of semiconductor surfaces on both sides of the metal layer. This configuration will generate two interfaces, constituted, respectively, of anionand cation-like semiconductor surfaces between which the metal layer is buried. The metal-induced semiconductor-like states, described in this section, are strongly related to semiconductor valence bands from which they emerge into the sere!conductor gap within the hulk metal band. This location inhibits the associated electron waves from extending into the scmicondttctor materials because only conduction states may do so. As the corresponding dispersion relations approach the semiconductor conduct ion bands, the question of their evolution, after interaction with this band, will arise. Are they going to stay confined within the metal layer or be transfm'med into resonant states falling within the conduction band and then extended into the semiconductor materials? One way to deal with this problem is to consider it when one interface exists, as in metal-semiconductor (MS) structures, and to understand thL' effects when a second asymmetrical interface is added, as in the S M S heterostructure. The former case (MS) is illustrated in fig. 3 for a semiconductor terminated by anion-like surface atoms in interaction with a metal layer of thickness L cqual to three mouolaycrs. ~n this case, we do not obtain interface states originating from the conduct ion band. One can notice that the upper two-state structure (doublet l, 2) transforms, in the neighborhood of the conduction band, into a doublet (3, 4) resonant with this latter band and emerges from the top of this band, Thurc is a strong correlation between the two components of the doublet as their dispersion relations stay very close. However, a basically different process occurs in SMS systems, Let us first recall that due to the second cation-like interface we may obtain an interface state confined within the metal layer. If we consider thicker metal layers, additional two-state electronic structures will be created (see figs. 4 and 5), respectively, for an L = 3 and 5 monolaycr thick metal. The semiconductor-like state of the upper twostate structure (fig. 4 cu,'~,e 3) extends into a true interface state, at the long-wavelength limit (curve


ttlt'l(tl-.Tcmiiwtldltctor hct£'r(157rllctllrcs





// / /'



0,5 k x (~r/a)


t t


Fig. 3 Eh'ctron dispersion relations~ in a racial semlconducIor helertlstructur¢, along the [nla] symmet,3/ direction. The

semiconductor sulfate is terminated in anion-like atoms. Curves I and 2 shtlw the tipper two-state structure which extends inlOthe scm[c~mductor conduction band teu,x,cs 3, 4). Curve 5 represent~ the dispersion relation of a true interface slalc induced hy anion-like interface. "rile smt~)lheningof Ihe sk)pe of cum~e 6 reveals Ihe attractive imcracUon bel~een Ih¢ true interface sl~ltc~,d the metal-induced semiconductor-like stale. The racial thickness is equal m three monolayers. 'l'he remaining parameters are the same as in fig. 3. Y]. In principle, both anion- (valence character) and cation-like (conduction character) interfaces contribute to this localized state. ~,ceause of its metal-induced origin, it is, in the case of fig. 4, closer to the valence band, as the top of the bulk metal band is situated within the lower part of the semiconductor gap. Let us now follow the evolution of the doublet (3, 4), to which state (3') belongs, along the [100] direction of the bi-dimensional Brillouin zone. By approaching the short-wavelength limit, electronic waves are more sensitive to the microscopic nature of interfaces. At this limit, state (3), having a valence-like character and consequently associated with an anion-like interface, experiences a weight-enhanced interaction with the




P Ma~n i [+.'k,ctro~Jk' slnuwtre of~t.#,it.,M+,~ tot mct


;." 3


3, curve 5) and the lowest semiconductor-like state (curve 6). In a non self-consistent calculation of the SMS -h:ctronic structure (fig. 4, curve 3 " ) the semiconductor-like state {3") tends towards the bottom of the conduction band. As a consequence of the mechanism described above, the upper metal-like state (fig. 4, curve 4), freed of its interaction with state (3), extends into the conduction band (curve 4') where it progressively approaches tile bulk metal band. The effect of the cation-like interface on metal-induced semiconductor-like states, as shown in fig. 4, corresponds to a situation where no intermediate (between semiconductor- and interface cation-like






k x t "r/al Fig. 4. This figure show:, thu effecl of a cation-like interface. in SMS heterostrueturt:s on u semiconductor-gke slate (curve 3~3"k This ~lat¢ Ilansfornls inlo a Iru¢ interface slate (curve 3'). The upper-+nelal-gke ~tale (curve 4) extend~ into a resonant slate tcurve 4'}. A non-self-consislem calculation shifts curve 3 t~ward~ curve 3 " Curv¢~ I. 2 represent the

,// N


dispersion relations of the central t~Olstale structure. The metal layer is three monola~ers thick. The remaining parame+


i¢i~ are the same ;is in fig. 3.

cation-like interface. There, this interaction prod u c e s a smoothness of tile slope of curve 3 which

becomes negative at k , = 0.91w/a, in the neighborhood (below) of the bottom of the conduction band where cation-like interface states would like to exist. Beyond k.~, state (3) transforms into state (3") which shows a dispersion relation which closely resembles a cation-interface-like state. The mechanism which leads to this feature is definitely induced by a cation-like interface, rather than resulting from the direct interaction (repulsive) of state (3) with conduction bands. This is. indeed, demonstrated by the absence of this effect in a metal-semiconductor system (fig. 3) where one :qlilm-like interface wag asgumed. In this latter ease, an attractive interaction was observed between the anion-interface-like state (fig.


_o.~[e+./ / o

/// o.s kx~'r

g ' *-

/2' k



Fig. 5. Same as fig. 4. bul whh L = 5 rectal monolaye~. Cu~es 7 and 9 represent tile dlsperslon rclaUons a ~ i a t e d

with cation- and aniomllke inl=rfaccs, respectively. Curve 8 corresponds to a r~:manl slru,:ture related to the caUon-like interface stale. The change in the slope of the dispersion

rc!atinn associated with the met;d-induced semiconductor-llke state (cn~e 6) at the zone boundaly ( k , = 0 o5z-/a) is due to the interaction between slate 6 and tile ealion-like interface. Curves i and 2 give the dispersion relations assoClaled wilh

the central doublet. We also show the pinning of Fermi level E F at the point of intersection of these two states.

I~ Masri / Electronic street.re of semicondt,ct~r mctd-~emi.~ond.clor hetero~tp.ctute~

states) metal-like state exists. Another alternative is presented in fig. 5 where such an intermediate screening state exists (curve 5). This will have the effect of inhihlting the fusion of cation-llke interface states (curve 7) and semiconductor-like states (curve 6). However, a repulsive interaction still remains, leading to the previously observed sign change of the slope of curve 6 at k~ = 0.95~r/a. Figs. 4 and 5 show the pinning of E~: at the energy level correspondin[~ to lhe point of intersection of curves l lnd 2 (central two-state structure).

5. Cunelusion We give new qualitative results ¢~n the elecironic structure Gf interface-asymmetric SMS heterostructures within the framework of a self-consistent microscopic model. Our results are relevant to Fermi level position determination and


illustrate the effect of the nature (anion- or cation-like) of the metal-semiconductor interface. We hope that all these new results will stimulate further investigations on electronic properties of SM$ heterostructures.

References Jl] E. Rt~encher, S. Deluge. Y. Camplddli and F Arnaud d'Avilaya, Eleclr.m. LetL 21l0984) 762. 12] J.C. tlensel. A,I~J. Levi. R.T. Tung and J.M, Gibslln, AppL Phys. Len. 47 {1985) 15[. [3] E. RiJsencher. G. Glastr¢. G. Vincent, A. Vareille and F. Amaud d'Avltaya. Electron. I~ll. 22 (1986)699. J4] F. Arnaud d'Avitaya, LA. Chroboczek. C. d'Anterrodles, G. Glastrc, Y. Campid¢lli and E. Rusencher, J. Cryst. Growth 81 {Iq871463. [51 P. Masri,to he published. [6l G. Allan. Ann. Phys. (Paris) 5 (1970) 169. [7l W. |1o. S.L. Cun,linaham. W.H. Weinherg and L. Dobrzynski. Phys. Rt:v. B 12 (1975) 31127, laj D.N.l.xl~vy and A. Madhukar. Phys. Rev. B 17 (1978) 3832.