J. Phys. Printed
Chrm. So/id.s in the U.S.A.
Vol.
45. No.
819.
PP.
821870.
1984
OOi?3697/84 Pergamon
REVIEW ARTICLE 6
THE ELECTRONIC STRUCTURE OF SEMICONDUCTOR SURFACES NORMENP. LIESKB Siemens AG, Data Systems Group, Postfach 83 09 52, D8000 Munich 83, Federal Republic of Germany (Receiued 11 March 1983) 1. The semiconductor surfaces 1.1 Atomic structure of the surface region 1.2 Electronic structure of the surface region 1.3 The surface. states 1.4 Theoretical calculations and experimental data 2. Methods for the analysis of surface states 2.1 Theoretical methods 2.1.1 Calculation of the electronic surface states 2.1.2 Calculation ,of the total surface energy 2.2 Low Enerav Electron DiBraction (LEED) ’ 2.2.1 Ge&etrical LEED data . 2.2.2 LEED intensity data Photoelectron Spectroscopy (PES) t: Electron Energy Loss Spectroscopy (ELS) 2.4.1 Interpretation of ELS spectra 2.4.2 Valence and core electron excitation spectra References Review literature BibliographyTabulated and qualified Group IV Semiconductors 3. Silicon 3.1 Si(111) 3.2 Si(100) 3.3 Si(110) 4. Germanium 4.1 Ge(111) 4.2 Ge(100) 4.3 Ge(110) IIIV Semiconductors 5. Gallium Arsenide 5.1 GaAs(ll0) 5.2 GaAs(100) 5.3 GaAs(lll) 6. AlAs, GaP, GaSb, InAs, InP, InSb IIVI Semiconductors 7. Zinc Oxide ZnO 8. CdS, CdSe, CdTe, PbS, PbSe, PbTe, ZnS, ZnSe, ZnTe A. A Typical StudyThe Si( 111) Surface A.1 Structural forms of the Si(ll1) surface A.2 Early results of experimental and theoretical studies A.3 Recent results and present state A.3.1 Si(lll)l x 1 A.3.2 Si(ll1)2 x 1 A.3.3 Si(l1 I)7 x 7 Supplemental References AbstractThe origin and properties of the electronic states on semiconductor surfaces are described with emphasis on the theoretical and experimental methods of analysis. The principles of the most important theoretical methods for the calculation of the electronic surface states and of the surface energy are discussed. Among the experimental techniques of analysis, the surface spectroscopy methods Low Energy Electron Diffraction (LEED), Photo Electron Spectroscopy (PES) and Electron Energy Loss Spectroscopy (ELS) are described. PES and ELS yield information about the occupied and low excited electronic states and are responsible for the chemical and electrical behaviour of the surface. The long range atomic 821
$3.00 Rtss
+ a0
Ltd.
N. P. LIBSKE
822
interactions determine the highly excited electronic states, about which information is gained from LEED. As a typical study the detailed investigations of the Si( 111) surface are described. The Si( I I 1) surface shows three different structural phases, which are characterized by different translational symmetries as visible in LEED patterns: the Si( 11 I)2 X 1 cleavage structure, the room temperature thermally stable Si( 11 I)7 x 7 and the high temperature Si( 1 I I)1 X 1 structure. A review of the experimental and theoretical studies for these surfaces is given. At the present state of knowledge for the Si( 11I)1 X 1 surface, the interpretation of a disordered surface with a short range atomic configuration similar to the Si( 1 I I)7 X 7 surface one is favoured. The experimental results of the Si( 11 I)2 X 1 surface can be fairly well described on the basis of a modified buckled surface model or by the recently proposed IIbonded chain model. For the Si( 1 I I)7 X 7 surface there is still no comprehensive interpretation available.
INTRODUCTION During the last decade experimental methods and the
oretical techniques to study the properties of clean semiconductor surfaces have been developed to a high degree of success. A detailed knowledge about the electronic structure of semiconductor surfaces is necessary to understand their chemical and electrical behaviour, which again is a prerequisite for the further development of semiconductor technology.
A working definition of the surface region can be made by referring to the experimental techniques that are used for the study of its properties. The extent of the surface region then is due to the information depth characteristic of the experiment. This will be discussed in a following chapter. The fundamental properties of the semiconductor surface region are its atomic and electronic structure which again determine the effective surface region potential.
1. THE SEMICONDUCTOR SURFAClZ.S
The region that we will refer to as the semiconductor surface may be defined with the aid of Fig. 1. On both sides of the last plane of atoms at z, (z axis perpendicular to the surface plane) the surface region extends which is limited at z, by the crystal bulk region and at z, by the vacuum region respectively. For a physical definition of the surface region we can use the effective potential seen by the electrons: at z” the potential has no further oscillations parallel to the surface and the potential variation perpendicular to the surface is due to long range Coulomb interaction and is well described by classical electrostatics. At z, the potential oscillations parallel to the surface have become the same as that characteristic for the bulk. Again, there can be a long range potential variation perpendicular to the surface, which is due to a net electrical charge of the surface region. This surface charge is screened via Coulomb interaction within a region, called the space charge layer, whose properties are usually described in terms of bulk energy band bending with the surface region as an electrical boundary [l, 21.
vacuum
surface
1.1 Atomic structure of the surface region Within the region between z0 and z, the geometrical positions of the ion cores may be different from that of the crystal bulk. Generally for semiconductors three types of surface regions are discussed: (i) At the ideal surface the atomic geometry of the bulk is unchanged up to the last plane of atoms. In this case the effective potential in the surface region is mainly characterized by the difference between the average bulk potential and the vacuum level, the so called surface barrier. (ii) At the relaxed surface within the first few atom layers bond lengths and directions between atoms are different from the bulk values, but the periodic&y of the atoms parallel to the surface is unchanged. Surface relaxation arises if long range bonding forces are important for the bulk lattice equilibrium [S]. (iii) At the reconstructed surface there are additional distortions of the atoms parallel to the surface resulting in a change of the translational symmetry parallel to surface.
crystal
region
bulk
I last
plane
of atoms
I
I
abour +
WlSA
+
space charge Layer about some thousands of Angstroms
I
‘b
Fig. 1. Definition of the semiconductor
surface.

823
The electronic structure of semiconductor surfaces 1.2 Electronic structure of the surface region The electronic structure may be defined as the spatial distribution of the valence electron charge density p,,(r) which is derived from the wave functions of the electronic states $,{r) by
P,
[email protected]) = e C JW)12. If a bulk crystal lattice is terminated by a surface, new electronic states arise and their properties are determined by the atomic structure of the surface region. The electronic states can be characterized by a twodimensional wave vector k,l uniquely defined within the surface Brillouin zone, which is given by the translational symmetry of the surface. The bulk band structure can be projected onto the surface Brillouin zone. Then for each k,l there will be continuous energy ranges for which bulk states exist separated by energy gaps for which no bulk states exist. Now the electronic states in the presence of a surface can be divided into two groups [3]: (i) For a given kll and energy E within an allowed bulk energy band one or more electron states exist which deep in the bulk are made up by a superposition of Bloch waves. These states are called scattering or continuum states, their electron charge density is distributed into the bulk. (ii) For a given k,l and E within a forbidden region there are electron states which consist purely of evanescent waves decaying into the bulk. Their electron charge density is confined to the surface region and they are called surface states. The characterization of surface states is usually done with the aid of the electron wave function r(r), the energy momentum dispersion relation E(k,,) and the surface density of states @DOS). The SDOS is derived from .the more general term for the local density of states (LDOS) p(E, r) [l]
all electron states of the total system. The LDOS describes the number of states present in a given spatial region at a certain energy. If the sum over i is done for the continuum or for the surface states, the result will be the bulk or the surface density of states, respectively. Some general features for surface states can be claimed [l5]. For a given surface state (ZC(kl)within a bulk energy gap) several things may happen: the gap and so the surface state can exist over the entire surface Brillouin zone; the gap may close up and therefore the surface state disappears; the surface state can merge into the allowed band at a band edge; the surface state can disappear while the bulk energy gap still persists. For a surface state near the centre of a broad bulk energy gap the charge .&I1 be highly localized within a surface region, whereas for a surface state in a small gap or near the edge of a gap a considerable amount of the charge extends into the decaying tail. A special kind of scattering state is the surface resonance: in this case the wave vector of a scattering state has k,+O and the local density of this state within the surface region is peaked about a special energy. In Fig. 2 the surface, resonance and continuum states are shown schematically. 1.3 The surface states Electronic states localized at the surface of a solid are the direct consequence of the fact that surface atoms have properties different from the normal bulk atoms. A meaningful classification of the surface states can be done according to the ionic&y of the solids [5]: ionic solids include materials with chemical bonds ranging from purely ionic to partially ionic. In this group the electrical properties vary from insulators to moderate gap semiconductors. A second group, the covalent solids include elemental semicon
(2)
ductors and some IIIV semiconductors with chemical bonds of dominantly covalent character. (i) The ionic surface states (Tamm states) arise
where $,(r) and Ei are wave functions and energies of
because surface atoms of ionic solids have an electron affinity different from bulk atoms. Theoretical studies
P(.%r) = C
I
IW)12NE  5)
I
c
I I distance Z Zo Zb ZV Fig. 2. Schematic hehaviour of continuum and surface states; full curve: potential energy; dashed curves: local density of states projected onto the zdirection perpendicular to the surface.
N. P. L‘n?sKE
824
show that the electron orbitals are closely related to nonhybridized atomic orbitals localized on surface ions. If associated with a cation the ionic surface state is an acceptor state energetically located near the bulk valence band edge. If associated with an anion the ionic surface state is a donor state energetically located near the bulk conduction band edge. (ii) The &g&g bond surface states (Shockley states) are due to the rupture of at least one highly directed covalent bond per surface atom resulting in
structure. This procedure is demonstrated by the following flow chart in more detail: (i) Information about the atomic structure is usually obtained from low energy electron diffraction (LEED) experiments. The interpretation of LEED data generally leads to several possible atomic structure models for the analyzed surface. Information about the surface atomic geometry may also be taken from theoretic calculations based upon surface energy minimization [I].
theoretical calculation by surface energy minimization
I
ATOMIC
SURFA4CE
+
STRUCTURE
dangling bonds each occupied by an unpaired electron. These dangling bond electrons represent a high energy configuration which can be lowered by chemical reaction with foreign species or by reconstruction of a clean surface layer. The interpretation of surface states and surface atomic geometries in terms of the ionicity of binary compound semiconductors was worked out in recent years [S, 61. For deviations from the ideal surfaces two further kinds of surface states were found in theoretical and ex~~mental works: on relaxed surfaces back bond surface states exist energetically located within the bulk valence band region [l, 31. Surface reconstruction leads to some overlap of the dangling bond orbitals and the dangling bond bands are split into bonding and antibonding bands separated by energy gaps [7]. The surface states of uncontaminated free surfaces are called intrinsic surfice states. They can be catalogued according to the lattice type, lattice constituents, the surface index and the reconstruction type. Adsorption of atoms or molecules from foreign species or trapping of bulk lattice impurities at the surface leads to surface states termed extrinsic [2]. 1.4 Theoretical calculations and experimental data Information about the surface atomic structure is necessary for a quantitative theory of surface states. The theoretical results have to be proved with data from experiments sensitive to the electronic surface
Il
(ii) With a given atomic structure the surface electronic structure can be calculated. For this purpose different theoretical methods are used. (iii) The main theoretical results, which can be tested by experiments, are the electron charge density p&r), the surface state energy band structure E(k,,) and the surface density of states SDOS. The comparison between experiments and theoretical calculations is done for all atomic surface structures consistent with the LEED results. The ex~~mental methods suitable for the analysis of surface states are widely described in the literature [2, s]. For semiconductor surfaces they can be devided into two groups: the electrical measurements combined with optical techniques yield info~ation about surface states with energy close to the Fermi energy. The mainly applied techniques are work conductivity, measurement, surface function eleetroreflectance, surface photovol~ge and photoconductance, capacityvoltage and conductanceon MetalInsulatorSemivoltage measurement conductor (MIS) systems. These methods are based upon the interaction of the surface states with the surface space charge layer. A second class of experimental techniques are the surface spectroscopies where a beam of primary particles impinging on the solid surface interacts with the surface states, resulting in secondary particles which are emitted from the surface and take the information about the nature of the surface states
The electronic structure of semiconductor Table 1. Spectroscopy
Method
methods
for the analysis of surface states
econdary ‘articles
Primary Particle6
825
surfaces
robed lrfaee
State1
llCO6
Photo Electron SpectroscopyPES
UV, Xrays electrons
occupied
ewe rev.lit.
3lectron Energy Loss Spectroscopy EL.5
electrons
electrons
occupied and unoccupied
see rer.lit. ELS
Soft Xray AppearancePotential Spectroscopy SXAPS
electrons
Xrays
unoccupied
52,
53
Field Emission Microscopy FEH
emission of electrons due to high electric fields
occupied
54,
55
Field Ion
atoms
ions
unoccupied
56,
57
ions
electrons
occupied
58,
59
PES
I
MF:~ro=copy Ion Neutralization SpectroscopyINS
located within a wide energy range from the Fermi level. The surface sensitivity of these techniques is due to the short mean free path of the primary and or secondary particles. In Table 1 the main characteristics of the surface spectroscopy methods, which can be used to probe electronic surface states, am given. The surface spectroscopy experiments have to be performed under ultra high vacuum conditions (residual gas pressure 5 10m9Torr) in order to maintain well defined surface conditions undisturbed by residual gas adsorption. Atomically clean and ordered surfaces are obtained by thermal annealing often combined with inert ion bombardment or by in situ cleavage of the crystal sample, and they are monitored by Auger Electron Spectroscopy (AES) [60,61] and Low Energy Electron Diffraction (LEED) [22, 241. 2.MRTHODSFORTHRANALYSI!3OFSURFACRSTATR.S
2.1 Theoretical methods The aim of doing theoretical calculations to study the electronic structure of semiconductor surfaces is twofold: first, one is interested in the electronic states as far as the occupied and low lying excited states are concerned. This is because these states determine the chemical behaviour of a surface during adsorption, oxidation and the formation of interfaces with metals, insulators or other semiconductors, as well as the interaction with the mobile carriers of space charge regions and inversion layers. Second, one is interested in the total surface energy in order to decide between several possible atomic structure models of the semiconductor surface. 2.1 .l Calculation of the electronic surface states. Only quantum mechanical models give results which are useful for comparison with experiments. Among these the molecular orbital (MO) calculations, where a computer solution of the S&r&linger equation for a limited number of atoms in the surface region is
done, seems to be the most promising approach to the surface problem [5]. The electronic structure at a given surface is determined by the S&r&linger equation V&1+ &i,)ti
= JW
(1)
with IL = $(r, . . . rN, R, . . . RN)
(2)
where ri, Rj are the position vectors of valence electrons and ion cores respectively and N, N’ their total numbers. Equation (1) takes into consideration the full electronelectron and electronion interaction. In a hrst approximation the true many electron Hamiltonian H,, + HcLiionis replaced by an effective one electron Hamiitonian and the N electron wavefunction is constructed in some way by single electron orbitals s,,(r) leading to the new Schriidinger equation [lo] (3) conveniently
the effective
potential
is divided into
vf”,“+ c.
(4)
three parts V,=
v,+
V, represents the total electrostatic potential from the ion cores and the valence electrons, cm the exchange and correlation potential between the core and valence electrons, c the exchange and correlation potential produced by the valence electrons. To get the electronic surface states the surface has to be modeled in a particular way and the Schrodinger equation (3) is solved variationally using special approximations for V, and special base function sets.
826
N. P. LIEXE
(ii) Isolated surface in contact with a semiintnite bulk: the surface region is defined using 35 atomic layers and the entire set of bulk Blochstates augmented by evanescent states is matched to the soluChoice of V, tions of the Schrijdinger equation in the surface (i) In the HartreeFock approximation (HF) [ll] region. This represents the most exact surface model the N electron wave function is constructed as an but complicated numerical procedures are necessary antisymmetrized product of single electron functions. for the calculations [1, 31. This approximation leads to effective electrostatic (iii) In the Green’s fiction method the surface is and exchange potentials, in~~ora~s the spin cortreated as a perturbation of the infinite crystal the relation (via the Pauli principle) but cannot fully surface atom is initially described as a free atom and describe the screening effects resulting from its atomic orbitals are mathematically mixed with the electronelectron correlation due to Coulomb internonlocalized Bloch type orbitals of the bulk elecaction. (ii) In the local tfensity functional approximation tronic states. This calculation is done using a Green’s function formalism (for further details see for exam(LDF) [I, 111the exchange and correlation terms are ple [5, 151). represented by local functions of the electron charge (iv) The crystal surface is simulated by a finite density p,,(r). molecular cluster. As an advantage of this approach (iii) In the pseudopotentialapproach the ion cores ab initio calculations can be done and standard are represented by pseudopotentials, the system conmolecular computational techniques can be used. But taining core plus valence electrons is thereby replaced as a disadvantage a finite number of molecular levels by a system containing valence electrons onfy. Equais obtained which only with increasing duster size tion (3) is changed into the valence electron problem. slowly approaches the surface bandstructure. The calculational techniques based upon this surface model are characterized as quantum chemical methods. They can be divided into the HartFock and calculations (two electrons per molecular orbital) and the generalized valence bond descriptions where only one electron per orbital is allowed and the electronelectron correlation is treated explicitly (see in regions outside the ion cores the energy eigenvalues for example [16, 11). E, and the nodeless pseudopotential wave function 4, Whereas in (i)(iii) the electronic states are should agree with the original values. To achieve this classified by the twodimensional surface wave vector the pseudopotential has to be chosen energy and state K,, a description which is denoted as rigid band model dependent. or ~~structure approach, in method (iv) the elecIn most practical cases semiempirical and purely tron wave functions are constructed by atomic orempirical pseudopotentials are used that fit the thebitals and it is called surface molecule model or oretical and or experimental results for bulk eleclocalized chemical description. These are the two tronic states (for further details see for example [I, 10, dominant models used for the characterization of the 12, 131). electronic behaviour of a surface [S]. Due to this procedure the existing calculation methods can be classified according to:
Model of the surface system (i) In the slab method the surface region is modeled by a finite number of atomic layers. If periodic slabs are used standard bandstructure techniques can be employed, but because this system represents two or an infinite nmber of surfaces, up to 20 atomic layers are to be used for each slab in order to decouple the electronic states of the different surfaces [lo, 12, 141.
Schradinger equation
Serf consistentnot
[email protected] methods In not self consistent calculations an approximate potential, V,*, is constructed in some way and inserted into the Schrodinger equation which is then solved to obtain the wave functions and the energy eigenvalues. The procedure of self consistent calculations may be demonstrated by the following flow chart:
electron wave functions %n(d I
t
1
'construction of a new V,ff
electronic
I
827
The electronic ~truc&reof semiconductor surfaces The iteration process is repeated until it does not
change the wave functions which are then considered as self consistent solutions. Only by this technique can the valence electron ~nt~butions to V, be obtained. In the following two of the most successful calculational techniques are considered in more detail: The method introduced by Appelbaum and Hamann [ 1, 181 is illustrated by this flow chart:
model the surface region by a thin slab and the surface Bloch waves are constructed from atomic orbitals as &, = 2 expW$L)
* d&’ * xA~ RJ
w
where the x,(r  R,,,) are orthogon~~d atomic orbitals about atomic site R,. The basis set is restricted
bulk f atomic experimental data electron
charge
+
starting approxi
valence charge
The ion cores are represented by pse~opotentials determined by fitting bulk bandstructures, the exchange and correlation potential is approximated by a local function of the valence electron charge density @later appro~mation a pCl’p). A starting approximation for pc,is made and the SchrGdinger equation is solved in an iteration process until self consistency for the surface potential Ver and the electronic states is obtained. For the potential and the wave functions Fourier expansions parallel to the surface are used (7) The wave function (b obeys Bloch’s theorem 4(r) = exp(jK~r~)#~~tr)
electro densitiy
to s and p orbitals of each atom and only nearest neighbour interactions are included. The Schriidinger equation is not solved explicitly but the matrix elements of the Hamiltonian, characterized by several parameters due to (lo), are determined by fitting the experimentally and theoretically known bulk energy levels for all valence and the lowest conduction band states. For the ideal surface these bulk Hamiltonian matrix elements are used. This ass~ption can be justified by the excellent agreement of the calculated surface bands with those obtained from selfconsistent pseudopotential calculations. For relaxed and reconstructed surfaces the additions ass~ption is made that the matrix elements MjJ depend exponentially on the change of the bond length d,,,mpbetween nearest neighbours
(8) AMj3. = I%& exp(  &id,,,,).
and
(11)
The
(9) In (7)(9) z is the coordinate normal to the surface, r~ the projection of r on the surface and G, represents the set of two ~rn~~on~ reciprocal lattice vectors which characterize the translational symmetry of the surface under consideration. Using (7)(9) the Schr6dinger equation is integrated numerically with appropriate boundary conditions to the solutions of the bulk (Bloch waves that propagate or decay into the bulk) and of the vacuum region (exponentially decaying plane waves with wave vectors K, + G,,). Quite different from the above selfconsistent pseudopotential calculational technique is the empirical tight binding method introduced for surface state calculations by Pandey and Phillips [14, 19, 201: they
overlap parameter @is determined by fitting to selfconsistent calculations of relaxed surfaces and can then be used for the calculation of large unit cells which often occur on relaxed semiconductor surfaces and where selfconsistent methods are too cumbersome. 2.1.2 Cahlation of the total surface energy. The surface energy of a particular crystal surface can be defined as the energy required to divide the bulk solid along a plane parallel to the surface [l, 211. The total energy of a solid follows the equation E,=E,,V+E;S
02)
where V,S are volume and surface area respectively, EUand Es are energy per unit volume and unit area. The surface energy is given by
828
N. P. Lres~~
Es= &,,A + E, + e,,
(13)
with E,,,~, the kinetic energy of the valence electrons, E, the total electrostatic energy from valencevalence, corecore and corevalence interactions, and E,, the exchange and correlation energy due to valencevalence electron and valencecore electron interactions respectively. E, can be calculated from selfconsistent pseudopotential or tight binding surface band structure results. For the case of relaxed or reconstructed surfaces the total surface energy is lowered due to the distortion of atoms perpendicular or parallel to the surface. 2.2 Low energy electron dzfraction (LEED) Up to date the most powerful technique for determining the atomic structure of ordered solid surfaces is the diffraction of low energy electrons. In a typical LEED experiment primary electrons of a certain energy in the range E = 10500 eV are impinging on a solid surface. The interaction of the incoming electrons with the ion cores and valence electrons of the solid gives rise to elastic and inelastic scattering events. The elastically baclcscattered electrons which are able to leave the solid surface are detected in the experiment and due to their high degree of coherence diffraction occurs. In modem experimental arrangements the diffraction pattern can be directly observed on a fluorescent screen and the intensities of the diffracted beams may be measured using a Faraday cup, by photographic techniques, or in a recently developed fast technique from the video signal of a television camera [1, 22, 231. The main properties of low energy electrons as far as the LEED experiment is concerned are: (i) There is a strong interaction between the electrons and the solid, so the penetration of the incident electrons extends only through several layers and the elastically backscattered electrons contain information of the surface region rather than the bulk. As a disadvantage due to the strong interaction multiple scattering occurs which gives rise to severe problems in the theoretical interpretation of LEED. (ii) The wavelength of the electrons with kinetic energy E in eV is obtained from the de Broglie relation as Iz =h/p ~(150/E)“~A.
(14)
At LEED energies between 10500 eV the wavelength is in the range 1 N OS5 A and therefore diffraction of the electrons by the surface region layers will occur. (iii) The energy spread of the incident beam in a typical LEED system is about 0.5 eV, its angular divergence about OS”, resulting in a coherence width of about 200500 A [22]. Therefore, though the incident beam diameter is about 1 mm, LEED is only sensitive to small surface regions in the order of the coherence width, where periodicity has to be main
tained. Gross surface imperfections are only detected as a background noise. The basic data obtained in a LEED experiment at a given crystal surface are the diffraction angles and the diffraction intensities for specified values of the diffraction parameters which are the electrons energy E and the angles of incidence S, (between incident beam and surface normal) and &, (rotation of the surface about the surface normal). 2.2.1 Geometrical LEED data The LEED diffraction pattern directly reflects the translational symmetry of the surface region. This can easily be deduced from symmetry considerations of the LEED problem. The entire scattering system, vacuum surface region semiinfinite bulk has no translational symmetry in the z direction perpendicular to the surface, but in the x  y direction parallel to the surface it has the translational symmetry of the surface region layers and the bulk layers taken together. In addition to energy conservation the LEED problem therefore is characterized by momentum conservation parallel to the surface. This translational symmetry may be represented by the set of reciprocal net vectors {g} parallel to the surface. The incident electrons are represented in the vacuum region by a plane wave @$ = exp(iK&
(15)
the electrons diffracted backwards into the vacuum can be described by a set of plane waves @=T%exp(iH;r)=C$;.
(16) 8
With amplitudes
a, and wave vectors & given by
IK;r = I&l’
energy conservation (17)
%j = &[I + g
momentum
conservation
resulting in
Equation (18) uniquely defines the possible directions of the backward diffracted beams. For a discussion of LEED results one has to be familiar with the terminology of two dimensional structures and the indexing of LEED diffraction patterns [22, 241. The surface region net with translational vectors parallel to the surface t,=na,+mb,;
(n,m integers)
(1%
is described with respect to the substrate net with translational vectors parallel to the surface t = ua + vb; (u,u integers).
(20)
The electronic structure of semiconductor surfaces
If the surface unit vectors are parallel to the substrate with a, = pa the notation
b, = qb; @,q integers)
(21)
829
(iii) If IGI is an irrational number the superposition of the surface and substrate mesh does not lead to a periodic structure. The LEED diffraction pattern is indexed using the reciprocal vectors (g) of the coincidence net (see 2.17)
is used g=hc*+kd*
c*,d* reciprocal unit vectors.
(26)
(22) where R (h, k, I) stands for the substrate material and its orientation parallel to the surface and D is a symbol of a possible foreign overlayer. Examples are Si{111)7 x 7orA1{111)3 x 3Si. Inthemorecomplicated case with an angle a by which the surface mesh is rotated to the substrate, the notation is used
R{h,k,ljf#.D. a
(23)
In a more general description the surface and substrate nets are related by a 2 x 2 matrix G
(Z)=G(i)
(24)
and a classification according to det G = ICI can be given: (i) If IG/ is an integer or the reciprocal of an integer the translational symmetry is given by the larger unit mesh, usually the surface mesh. (ii) If G is a rational number p/q with p,q integers andp # 1 # q a coincidence net exists which can be constructed by 2 x 2 matrices P,Q
(25)
The specular reffected beam is indexed as 00 beam, the beam associated with g = c* as 10 beam and so on. From the geometry of the LEED diffraction pattern the translational symmetry of the surface region can be deduced. To get detailed information about the surface structure the intensities of the LEED beams have to be analyzed. 2.2.2 LEED intensity data The intensity data are presented for selected beams h,k as a function of one of the diffraction parameters. The most common modes are iFlh(E> or ~~~e~). The dominant features of the diffracted intensity are the primary and secondary Bragg peaks, the monolayer and surface state resonances; the latter being the monolayer resonance of the top most atom layer if different in structure from the substrate layers. A schematic representation of these features from a layer description model [25273 of the LEED problem is given in Fig. 3. Due to the multiple scattering events in LEED a meaningful interpretation of diffracted intensities can only be given based upon a dynamical diffraction theory. Kinematic diffraction only yields the energy positions of Bragg peaks and resonances. This is valuable to roughly distinguish between different surface structure models; but since even in primary
Fig. 3. Schematic representation of the single and double diffraction contributions to the LEEI’Y di&action amplitude in a pseudokinematical layer description model.
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uxnn9aA aq$ u! suowzya am :p %!d bq pavwsnf~! s! poqlaut %ug9~mu pueq au *poqlam 3adeI aql pus %upa)lms aJo no! 30 laponr aQ1 my pawqruo:, s! PoQlam %u!QWUu PuUq aQ1 aJaQM ‘[6Z ‘SZ] &‘uad
kq pmIpo.IJu! leyl SF maiqord uogX?rgp ~e+m?ru(p ayl30 uogdqsap ~3ssmns ~sotu ayl sep 01 dn
%.Q.Xa~~SsShrtXIO!]V)S aQ$ 30
suoyyos
ale
= I$
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aAnFI
sa~u)sua6!a SJADM
SD
mold
Of8
The electronic structure of semiconductor surfaces (ii) The multiple scattering within the atom layers is calculated resulting in transmission and reflexion matrices of the layers. Thereby the approximation concerning the number of scatterers within a layer bas to be made. (iii) The multiple scattering between the atom layers is calculated; due to the assumption of a mu&r tin potential the Bloch waves between the atom layers can be described by a set of plane waves classified by the reciprocal net vectors g. An assumption about the number of g taken into consideration has to be made. The results of this step are the Bloch waves I,&,&,r) with energy E _ h2K2  2m and K = Kj with Kj,, = &II. ti (iv) From the surface matching conditions (2.27) the amplitudes of the Bloch waves Aj and of the diffracted beams s are obtained. The following physical parameters have to be implemented into the calculations: the ion core potential &,,, the mul%n tin potential with real part V, and an imaginary part V, concerning the loss of diffracted electrons due to inelastic and incoherent elastic scattering; with 6, the peaks in the LEED I(V) curves are broadened in energy and reduced in intensity. In addition, lattice vibration effects due to the finite temperature during the LEED experiment have to be regarded. They change the diffracted beam intensities with energy and angle of incidence and are therefore important ingredients in diffraction calculations. A great problem in LEED surface structure analysis arises from the fact that the electronatom scattering factors are not known well enough, especially regarding the screening and exchange effects [30]. Therefore, the first step in a LEED calculation procedure is a sensitivity anafysis, in which the influence of the model force law parameters and of the calculated intensities is examined. Another problem is that LEED structure dete~nations are based on trial and error: for a set of possible surface structures, which are in agreement with the observed geometrical LEED data, the LEED intensities are calculated and compared with the experimental results. The lineshapes, the relative intensities of the various diffracted beams and the reproduction of the prominent observed maxima within 23 eV in energy are examined. To diminish the arbitrariness in such a procedure recently the use of reliability factors has been proposed [31].
2.3 Photoelectron spectroscopy (PES) In PES mon~hromatic photons with energy E =fuu beamed at a sample surface produce electronhole pairs. If the electrons are highly excited, from an occupied energy level to an energy level above the free electron energy, these photoelectrons can leave the surface and their properties are determined in the PES experiment: the energy spectrum of
831
Evat EF
I
_F/ tb
j Ei

I
Fig. 5. Energy diagram for a PES experiment: &1f), initial ftinall state enerav level of the solid state electron; E, Fermi ieve ‘of the sa%ple and of the spectrometer;. I&, free ‘. binding energy of the excited electron energy level; Et,, electron; s(sp), work function of the sample (spectrometer); Ekln, kinetic energy of the emitted photoelectron as detected by the spectrometer.
the photoelectrons is measured and in special cases their angular distribution; as primary variables can serve the photon energy hw, the angle of incidence and the polarization vector A. From PES mainly information about the occupied electron states can be obtained. If the photon energy is chosen in the Xray range PES gives information about the core electron states; the Xray Photoelectron Spectroscopy was introduced by Siegbahn [32]. With photon energies in the UV or soft Xray range the electron states in the valence band region can be analyzed. The Ultraviolet Phot~l~tron Spectroscopy (UPS) has been first developed by Turner [33] and Spicer [34]. The conventional radiation sources for PES have been Xray tubes and UVgasdischarge lamps. In the last decade the use of mon~~omati~ synchrotron radiation sources brought an important improvement [35,36]: the photon energy is continuously tunable in the range 10 eV10 keV and synchrotron radiation is char~te~z~ by a high degree of polarization. With the aid of Fig. 5 the energy relations in PES experiments on solid surfaces can be demonstrated to obey the equation rio=E,E, (28)
where hw is the photon energy, Ei and El are the energies of the initial and final state of the excited electron. ELinis the photoelectron energy as detected by the spectrometer, EC is the binding energy related to the Fermi level of the initiat electron state and 4pslt is the spectrometer work function. The photoemlssion process can be described by two steps 2371:first the incoming photon is absorbed; in this process an oscillator strength between the initial hole and final electron state is involved. In the second step “primary” electrons are emitted which
832
N. P. LIRXE
have undergone only Bragg scattering or phonon scattering, and “secondary” electrons which have lost energy due to creation of electronhole pairs. These two kinds of electrons have to be separated in the PE spectra and interpretations are made regarding the primary electrons. The photoemission current intensity due to primary electrons can be described by [38]

T(&, &)C(l?,  E,  hw)G(&,  Ki)d3K
N (El dN(E)ldE
Jr
(29)
where direct transitions that conserve Kvectors are assumed; the oscillator strength is approximated by electric dipole interaction, and the function T(EJ, K,) describes the probability that the excited electron can escape from the surface as a primary electron. Today PE spectroscopy is treated in several experimental approaches dependent on the kind of analysis for the fInal state electrons [36]. (i) The photon energy ho is kept constant, the final state energy E, is swept by scanning the spectrometer detection energy and the angular distribution of the photoelectrons is not taken into consideration. The resulting photoelectron spectra are called ungle integrated Energy Dbtribution Curves EDCs. The EDCs represent the convolution of the density of occupied states with the density of the unoccupied states modulated by the transition probability ]i>+p}. In some cases the EM= can be assumed to reproduce the density of occupied electron states. (ii) The final state effects in the EDCs can be eliminated with the Constant Final State technique CFS [39]: the photoelectrons are collected at a 6xed energy .?$ and the photon energy hw is swept. The number of primary electrons in CFS directly reproduces the density of occupied states modulated by the transition probabiity. (iii) To study the density of unoccupied states the Constant Initial State technique CIS can be used [39] where Ef and hw are swept synchronously, so that all collected primary electrons originate from the same initial state with energy & = I.$_ ho = const. With CIS only states above the free vacuum level can be studied. (iv) Structural information about the valence electron states can be achieved by photon polarization dependent photoemission experiments. (v) Angie resolved photoemission experiments yield info~ation about the angular dis~bution of photoelectrons. The most important method is the direct twodimensional band structure mapping [40] which is based upon the assumption of momentum wnservation for the transition parallel to the surface, i.e. Ki,, = Q, mod&o a reciprocal lattice vector. The occupied energy bands E&K> can be directly described from the relations
d2N(ElldE2
/II ; St ’ &ED E,: 1I
‘I,E2 I I I 1111 I 9697989900kn02u.3
I
I
E (eV1
Fig. 6. Electron energy distribution N(E), first and second derivative for the quasi elastically scattered primary electron beam with & = 100eV detected at a clean Si(lO0) surface with a cylindrical mirror analyzer; OSeV modulation of analyzer energy, sensitivity in arbitrary units.
E,=E,ho
Km= %I I$& =
(2mE/hy2 sm 8 ws rjJ
KY3= (2mE/ti2)‘/2 sin 0 sin d,
(30)
by varying the angle of detection (polar angle 8, azimuthal angle 4 between Xaxis and Z$,). 2.4 electron Energy Loss Spectroscopy (ELS)
Electrons with a primary energy in the range E,, = 101000 eV are beamed at a surface and the energy distribution of the electrons backscattered from the surface is analyzed. Many of the incoming electrons suffer inelastic interactions with the solid resulting in characteristic energy losses A& of the backscattered electrons. An energy loss spectrum is obtained with peaks at the energy positions E0  AEi which can be distinguished from true secondary electrons or Auger electrons by variation of &. The ELS spectra are usually monitored in the tirst or second derivative mode of electron distribution. This technique results in peak shapes as demonstrated in Fig. 6. In the inelastic scattering of electrons in a solid the following processes are involved: collective excitations of valence electrons (plasmon losses), single electron excitations of core and valence electrons and excitations of phonons. In most ELS studies of surface electron states the phonon excitations are not considered. They play an important role in the study of atomic sites for example due to adsorption processes. An excellent overview of this field was given in the works of Ibach, Froitxheim et al. [41,42]. The structure in the energy loss spectra is tied to the
833
The electronic structure of semiconductor surfaces primary energy and on the other hand the sampling depth is a function of the electron energy. So ELS represents a useful technique of probing both surface and bulk electron states. In order to distinguish between bulk and surface excitations surface treatments and primary energy variations can be used. 2.4.1 Interpretation of ELS spectra. Up to date no fundamental theoretical treatment of the inelastic interaction between low energy electrons and solids is available, but the inherent physical effects can be stated: The inelastic scattering events are preceded or followed by large angle elastic scattering processes including backscattering. The method of measuring ELS spectra in the reflection mode is based upon this fact [43]. At very low primary energies E, 5 100 eV indirect single electron transitions occur with momentum transfer A p = hA K and AK in the range of a reciprocal lattice vector [43,44]. In addition to Coulomb forces quantum mechanical exchange forces are involved [43]. Regarding these facts three models for the interpretation of ELS spectra exist. First the parameters of the ELS experiment have to be defined: with Go, K, and E,, I(, as energy and wave vector of the primary and the backscattered electrons respectively and with SE = ho and Ap = fiAK as energy and momentum transfer due to the interaction under consideration, the energy and momentum conservation at the vacuum solid interface yields E, = E,,  ho KJ.1= Ko.1 AK11+ g
(31)
where g is a reciprocal net vector parallel to the surface. In the experimental set up used most widely for the ELS study of electron surface states the primary energy, the angle of incidence and the angle of detection are held constant and only the detected
4AE) = F ; Fw Wv AK)
s
loss AE = hw is proportional electric loss function
(32) In the special case E0 g ho the momentum transfer is small and the approximation Ak+0 can be made. If in addition the transverse and longitudinal dielectric response are identical, the optical dielectric function (K, 0) can be used in 2.32 leading to
CesSeS.
(i) Dielectric model. The classical dielectric theory for the scattering of electrons at a solid surface was reviewed by Geiger [45]. The scattering of electrons is related to the dielectric response of the system given by the complex dielectric function e(K, o) = cr(K, o) + &(K, o) of the solid. The Coulomb interaction of the incoming electrons creates a space and time dependent polarization field. Its plane wave components are damped in the dielectric medium proportional to
[email protected], 0) resulting in an energy relaxation of the primary electrons. The probability for an energy
1
I 1
W(AE = hw)a  Im 
c(O, w) .
(33)
Now for an interpretation of ELS spectra optical absorption and reflexion data can be used, from which the loss function 2.33 is obtained. The dielectric model was successfully applied in high energy electron loss spectroscopy [46] but the validity of this approximation in the low energy range E0 5 1000 eV has to be proved in each case. (ii) Znterband excitation model. For the inelastic scattering of very low energy electrons 4 5 100 eV three further effects have to be taken into account: momentum transfer AK # 0, diffraction of primary and secondary electrons and quantum mechanical exchange forces. As a consequence of diffraction effects the experimentally detected energy loss structures may be dependent on the primary electron energy and on the spectrometer configuration [4749]. The energy losses of very low energy electrons are mainly due to single electron interband excitations. For this case an interband excitation theory was developed by Bauer [43]. According to this theory for electron transitions from Glled initial states Eh,“&) located in the band v into empty final states &,..,(Kfin) located in the band p (with EC. = Ei” + AE&, = Ki” + A K) the number of electrons suffering an energy loss 6E is given by d2K
IVk[&“.JK + AK) 
energy serves as a variable. In this case only the energy distribution of the characteristic loss events is studied and not the kinematics of the inelastic pro
to the so called di
Ei,..(K)lI,~~,,,~,.~=..
(34)
where FJK, AK) represents the transition probability involving the momentum matrix element and d2K is a surface element in K space on the surface defined by E,,(K + AK)  Eh,,(K) = AE. The integral in 2.32 is a generalization of the joint density of states function for optical (AK+O) interband transitions. Maxima in intensity occur for the so called critical point pairs following the equation ~rJ%,,&) that is for K, AK the ground and the interpretation has to be applied
= V&JKiJ
(35)
pairs for which the energy bands of the excited states are parallel. For of an ELS spectrum condition 2.35 to the explicit energy band structure
N. P. Lmsxs
834 Epr
Epr
AEI=EL
AEI=EL
I E set
EF
I Esec
OeV 13eV
exrltotion
99 ev 25 149evr =
I
zp
enl?rpy
Fig. 7. Principal scheme of valence and core electron excitations detected by ELS, demonstrated for the electron energy level scheme of bulk silicon.
of the solid under consideration. As a result the characteristic energy losses can be attributed to electron transitions between initial and final states in the E(K) band structure. For transitions involving surface states this was first done in the case of ELS on the Si(l1 I)7 x 7 surface [49]. (iii) Density of states (DOS) model. It is an approximation of the above interband excitation model and its subject matter is that transitions are most probable between maxima in the valence band DOS and maxima in the conduction band DOS. These transitions are a subgroup of the transitions given by 2.35. The interpretation of an ELS spectrum with the density of states model is usually done based upon DOS curves obtained from theoretical calculations or from other experiment. For transitions out of a narrow valence band, sufficiently far removed from other interband transitions (typically more than 10 eV) the approximation V&i&K) a 0 is valid and 2.34 can be rewritten as
where p,,‘., is averaged over all available AK and is the conduction band density of states. Apart from a modulation due to F”,:,.(from which no peak structure should be expected) the measured ELS curve is proportional to the conduction band DOS. This was first shown in the case of GaAs(lOO) surface by Ludeke and Esaki [SO]. 2.4.2 Valence and core electron excitation spectra. By ELS valence and core electron excitations can be detected, the former giving energy losses 6E 6 30 eV, the latter resulting in energy losses up to some hundred eV. Both kinds of transitions have the same possible linal states, which is also true for transitions into empty surface states. The principal mechanisms of valence and core electron excitations are demonstrated in Fig. 7. Since the properties of the core electron states are well known, core electron excitation spectra are of great value for the interN,,(AE)
pretation of the valence electron excitation spectra. This was first demonstrated by Ludeke and Koma
1511. The three experimental methods support each other in the following way: the atomic structure information is gained from LEED based upon the
highly excited states of the incoming electrons. The combination of PES and ELS yields information about the occupied and low excited electronic states which are responsible for the chemical and electrical behaviour of a surface. AcknowledgemenrsI am very grateful to W. Heywang, G. Dorda and E. Fuchs for helpful discussions about this article. REFERENCES
1. Appelbaum J. A., Surface Physics of Materials (Edited by J. M. Blakely). Academic Press, New York (1975). 2. Mark P. and Levine J. D., Modern Methodr of Surface Analysis. NorthHolland, Amsterdam (1971). _ _ 3. Atmelbaum J. A. and Hamann D. R.. Reu. Mod. Phvs. &,*479 (1976). 4. Davison S. G. and Levine J. D., SolidState Physics, Vol. 25. Academic Press, New York (1970). 5. Morrison S. R., The Chemical Physics of Surfaces. Plenum Press, New York (1977). 6. Duke C. B., Meyer R. J. and Mark P., J. Vat. Sci. Technof. 17, 971 (1980). 7. Henzler M., Surface Sci. 25, 650 (1971). 8. Harrison W. A., Surface Sci. 55, 1 (1976). 9. Chadi D. J., Phys. Rev. ,+tt. 41, 1062 (1978). 10. Schliiter M., J. Vat. Sci. Technol. 16, 1331 (1979). 11. Slater J. C., The Self Consistent Fieldfor Molecules and Solidr. McGrawHill, New York (1974). 12. Louie S. G., Chelikowsky J. R. and Cohen M. L., J. Vat. Sci. Technol. 13. 790 (1976). 13. Hamann D. R.,.Surfa‘ce S&. 68, 167 (1977). 14. Phillins J. C.. Surface Sci. 53. 474 (19751. 15. Schr&ffer J. R. and Soven P., khys. jbda; 28,24 (1975). 16. Goddard W. A. and McGill T. C., J. Vat. Sci. Technol. 16, 1308 (1979). 17. Laughlin R. B., Joannopoulos J. D. and Chadi D. J., J. Vat. Sci. Technol. 16, 1327 (1979). 18. Appelbaum J. A. and Hamann D. R., Phys. Rev. B 6, 2166 (1972). 19. Pandey K. C. and Phillips J. C., Phys. Reu. Lett. 32,1433 (1974).
The electronic structure of semiconductor 20. Pandey K. C. and Phillips J. C., Phys. Rev. E 13, 750 ( 1976). 21. Appelbaum J. A. and Blount I. J., Phys. Rev. B 8,483 (1973). 22. Estrup P. J. and McRae E. G., Modern Methods of Surface Analysis. NorthHolland, Amsterdam (1971). 23. Heilmann P., Lang E., Heinz K. and Mtiller K., Appl. Phys. 9, 247 (1976). 24. Strozier J. A. Jr., Jepsen D. W. and Jona F., Surface Physics of Materials (Edited by J. W. Blakely). Academic Press, New York (1975). 25. McRae E. G., Surface Sci. 11, 479 (1968). 26. Duke C. B. and Tucker C. W., Surface Sci. 15, 231 (1969). 27. Heinz K., Lieske N. and Miiller K., Z. Nuturforsch. 31a, 1520 (1976). 28. Pendry J.B., J. Phys. C4, 2501 (1971). 29. Pendry J. B., Low Energy Electron Diffraction. Academic Press, New York (1974). 30. Duke C. B., J. Pac. Sci. Technol. 14, 870 (1977). 31. Jona F. and H. D. Shih, J. Pac. Sci. Technol. 16, 1248 (1979). 32. Siegbahn K. et al., ESCA Atomic, Molecular and Solid Structure Studied by Means of Electron Spectroscopy. Almquist & Wikselis, Uppsala (1967). 33. Turner D. W. et al.. Molecular Photoelectron Soectroscopy. WileyInterscience, New York (1970). 1 34. Spicer W. E., Electronic Density of States. NBS Publication 323, Washington (1971). 35. Eastman D. E. and Grobman W. D., Phys. Rev. Lett. 28, 1327 (1972). 36. Margaritondo G. and Rowe J. E., J. Vat. Sci. Technol. 17, 561 (1980). 37. Phillips J. C., Surface Sci. 63, 1 (1977). 38. Fadley C. S., Electron Emission Spectroscopy (Edited by W. Dekeyder et al.). Dordrecht, The Netherlands ( 1973). 39. Lapeyre G. J. et al., Phys. Reu. Lett. 33, 1290 (1974). 40. Smith N. V. and Traum M. M., Phys. Rev. B 11, 2087 (1975). 41. Froitxbeim H. and Ibach H., Z. Physik 269, 17 (1974). 42. Froitzheim H., Ibach H. and Mills D. L., Phys. Rev. B 11, 4980 (1975). 43. Bauer E., Z. Physik 224, 19 (1969). 44. Ludeke R. and Esaki L., Surface Sci. 47, 132 (1975). 45. Geiger J., Elektronen und Festkiirper. Vieweg, Braunschweig (1968). 46. Raether H., Springer Tracts in Modern Physics, Vol. 38, p. 85. SpringerVerlag, Berlin (1965). 47. Sickafus and Steinrisser F., Phys. Rev. B 6, 37 14 (1972). 48. Porteus J. O., Surface Sci. 41, 515 (1974). 49. Lieske N. and Hezel R., Phys. Status Sohdi(b) 92, 159 (1979).
50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61.
surfaces
835
Ludeke R. and Esaki L., Phys. Rev. Lett. 33,653 (1974). LudekeR.andKomaA., Phys.Reu.Lett.34,817(1975). Park R. L., Surface Sci. 48, 80 (1975). Holliday J. E., Surface Sci. 48, 137 (1975). Plummer E. W. and Young R. D., Phys. Rev. B 1,2088 (1970). Gadzuk J. W. and Plummer E. W., Rev. Mod. Phys. 45, 487 (1973). Estrup P. J., Phys. Today 28, 33 (1975). Milller E. W. and Tsong T. T., Field Zon Microscopy. Elsevier, Amsterdam (1969). Hagstrum H. D. and Becker G. E., J. Chem. Phys. 54, 1015 (1971). H. D. Hagstrum, J. Vuc. Sci. Technol. 12, 7 (1975). Chang C. C., Characterization of Solid Surfaces. Plenum Press, New York (1974). Stein D. F., J. Vuc. Sci. Technol. 12, 268 (1975). REVIEW LITERATURE
LEED Reference 22, 24, 29. Haas T. W. et al., Progress in Surface Science (Edited by S. G. Davison), Vol. I, p. 155. Pergamon Press, Oxford (1972). Phillips J. C., J. Vat. Sci. Technol. 13, 178 (1976). Tong S. Y., Comments Solid St. Phys. 9, 1 (1978). PES Reference 32, 33, 36. Feuerbacher B. and Willis R. F., J. Phys. C 9, 169 (I 976). Guichar G. M., Balkanski M. and Sebenne C. A., Surfuce Sci. 86, 874 (1979). Ley L., Cardona M. and Pollak R. A., Photoemission in Solids ZZ.SpringerVerlag, Berlin (1979). ELS Lucas A. A. and Sunjiec M., Progress in Surface Science (Edited by S. G. Davison), Vol. 2, p. 2. Pergamon Press, Oxford (1972). Froitxheim H., Electron Spectroscopy for Surface Analysis (Edited by H. Ibach), Topics Current Physics Vol. 4. SpringerVerlag, Berlin (1977). Theoretical Calculations of Electronic Surface States Reference 3, 8, 13, 14, 17. Harrison W. A., J. Vuc. Sci. Technol. 14, 883 (1977). K. C. Pandey, J. VW. Sci. Technol. 15, 440 (1978). Pantelides S. T. and Pollmann J.. J. Vat. Sci. Technol. 16. 1349 (1979).
836
N. P. LJISKZ BIBLaIOGRAPHYTABULATED AND QUALIFIED
Group IV semiconductors
Table2. Si(ll1) low energyelectron diffraction surface
geometrical intensity model calculations data data
2x7,
+
1X1/7X7
+
7x7
+
7x7
+
7x7
+.
N.J.Taylor, surf.eci.s, 169 (1969)
2x1
+
J.W.T.Ridgewayand D.Hadman surf.sci.l8,441 %(1969)
7x7
+
7x7
+
J.V.Florioand W.D.Robertson, surf.sci.22,459 (1970)
1X1/7X7
+
R.N.Thomasand M.H.Fromcomb Appl.Phys.Lett.,j_'i‘, 80 (197Oj
2X1/7X7
+
J.W.T.Ri.dgeway and D.Halleman Appl.Phys.Lett.u, 130 (197Oj
2X1/7X7
+
F.BXuerle,W.M8nchand M,Hensler, J.Appl.Phys.u, 3917 (1972)
1x1
+
B.A.Joyce, surf.sci.&
2x1/7x7
+
+
+
literature J.J.Landerand J.Morrison, J.Appl.Phys.&, 1403 (1963) R.M.Broudy and H.L.Abbink, Appl.Phys.Lett.11,212 (1968)
G.O.Krause,
phys.stat.sol.2, K 59 (1969)
+
W.Haidingerand S.C.Barnes, surf.sci.&I,313 (1970)
1 (1973)
G.Boskovitzand D.Haneman, surf.sci.&, 253 (1974)
2X1/7X7
M.M.Traum,J.E.Rowe and N.E.Smith, J.Vac.Sci.Technol.12, 298 (1975)
7x7
+
J.D.Levine,P.Mark and S.H.McFarlane, J.Vac.Sci.Technol.l&878 (1977)
7x7
+
W.Mijnch, surf.sci.a, 79 (1977)
+
+
W.M8nch and P.P.Auer, J.Vac.Sci.Technol.3, 1230 (1978)
+
+
\'J.Mcnch, P.P.Auer and R,Fedder, J.Vac.Sci.Technol.%, 1286 (1979)
+
+
D.J.Millerand D.Haneman, J.Vac.Sci.Technol.s, 1270 (1979)
+
+
R.Feddei. W.Mdnch and P.P.Auer, J.Phys.C.12,179 (1979)
1x1/2x1
/7x7
2X1/7X7 7x7 2x1
+
The
electronic structure of serniconductar
surfaces
Table 3. Si(ll1) theoretical calculations of the electronic structure, E(K$ surface energy band structure, SDOS surfacedensity of states surface
method
1x1
LCAO+plane waves
1x1
LCAO+plane waves
literature
E( K,,) SDOS +
J.Alstrup, surf.sci.2, 335 (1970) J.Alstrup phys.stat.sol.(b)&,209 (1971)
+
1X1
F.Indurainand M.Elices, surf.sci.3, 540 (1972)
1X1/2X1
SCF pseudopotential
1Xl /7x7
empirical tight binding
+
J.C.Phillips, surf.sci.a, 474 (1975)
2x1
empirical tight binding
+
K.C.Pandeyand J.C.Phillips, Phys.Rev.Lett.2, 1450 (1975)
lXl/2Xl
bond orbital
S.Ciraci and I.P.Batra Solid State Commun.fi f375 (1975)
1X1/2X1
ie$&al
K.C.Pandeyand J.C.Philllpa, Phy6.Rev.Bu, 750 (1976)
7w
#bEplriCal
M.Schliiter Phys.Rev.B
tight +
et.al., l2, 4200 (1975)
K.C.Pandey, J.Vac.Sci.Technol.& 440 (1978)
tight binding
1X1
tight binding
N.Nishida, J.Phys.C.ll,1217 (1978)
2x1
SCF
C.T.White and K.L.Ngai, J.Vac.Sci.Techno1.u 1237 (1978)
1Xl .&Xl /7x7
P.P.Auer and W.Nlinch,
[email protected], 45 11979)
1x1
+ chemital pseudopotential
F.Casula,
7x7
quantum chemical ab initio
C.C.Snyder,Z.Wassermanand J.W.Moskowitz, j.Vac.Sci.Technol.s, 1266 (1979)
lx1
e:npirical tight binding
+
1x1
tbzkt binding
+
7x7
SCF cluster
K.Nakamua et.al., J.phys.c I& 2165 (1981)
2X1
SCF
F;Easula Pnd A.Selloni, Solid State Comun.g, 405 (1981)
S.Ossicini and A.Selloni, Solid State Commun.2, 309 (1979)
+
I.Ivanov,A.Mazur and J.Pollmann, surf.sci.92,365 (1980) W.K.Malllckand S.T.Chal Phy6.Rer.B& 3471 (196b)
837
N. P. Lrps~e
838 Table 4. Si(
I I I) photoelectron
spectroscopy
angular model resolved calculation spectra
surface
1X1/2X1
literature
H.Ibach and J.E.Rowe, surf.sci.u, 481 (1974)
+
2x1
J.E.Rowe, M.M.Traum and N.V.Smith Phys.Rev.Lett.2, 1333 (1974)
1X1/7X7
J.E.Rowe, H.Ibach and.H.Froitzheim,
[email protected], 44 (1975)
+
2x1/7x7
M.M.Traum, J.E.Rowe and N.V.Smith J.Vac.Sci.Technol.l2, 298 (1975)
2x1
K.C.Pandey and J.C.Phillips, Phys.Rev.Lett.2, 1450 (1975)
1x1
J.E.Rowe, surf.sci.z,
1x1
461 (1975)
J.E.Rowe and S.B.Christman, J.Vac.Sci.Technol.g, 293 (1975)
7x7
+
A.W.Parke, A.MckInley and R.H.Williams, J.Phys.C 11, L 993 (1978)
7x7
+
G.V.Hanson, R.I.G.Urberg and S.A.Flodstram, J.Vac.Sci.Technol.&, 1287 (1979)
2x117x7
D.J.Chadi et.al., Phys.Rev.Lett.&, 799 (1980)
1x1/7x7
D.E.Eastman, F.J.Bimpael Solid State Commun.&
and J.F.Van 345 (1980)
2X1/7X7
+
7x7
+
F.Houaay
2x1/7x7
+
G.M.(lulchar et.al., J.Phys.Soc.Jpn.&
+
G.V.Hanaaon
et.al., aurf.aci.pe,
et.al.,
a~f.aei.~,
13 (1980)
28 (1980)
Table 5. Si( 1 I I) electron energy loss spectroscopy. VES valence electron excitations spectra, CES core electron excitation spectra, HR ELS high resolution energy loss spectra (energy losses IO100 meV) model calculations
literature
surface
experimental spectra
2x1
HR ELS
H.Ibach, etjal,, surf.dci.j& 433 (1973)
1x1
VES
D.R.Arnott and D.Haneman, surf.sci.s, 128 (1974)
2X1/7X7
VES
H.Ibach and J.E.Rowe surf.sci.g, 481 (1974)
2X1/7X7
VES
J.E.Rowe, H.Ibach and H.Froitzheim,
[email protected], 44 (1975)
&1/7x7
VES/CES
A.Koma.and R.Ludeke, surf.sci.2, 735 (1976)
7x7
VES
Y.W.Chang, W.Siekhaus and G.A.Somlrjai, surf.sci.z, 341 (1976)
7x7
VES
7x7
VSS/CES
+
N.Lieske and R.Hezel, phys.stat.601. (b) 92, 159 (1979) N.Lieske and R.Hezel, Inst.Phys.Conf.series z,
206 (1980)
Dar Vaen,
1047
(1980)
839
The electronic structure of semiconductor surfaces Table 6. Si(100) low energy electron diffraction surface 2x1
geometrical data +
literature
intensity model calculations data
R.E.Schlier and H.E.Farnsworth, J.Chem.Phys. s., 472 (1959)
2x1
+
D.Haneman, Phys.Rev.x,
2x1
+
J.J.Lander and J.Morrison, J.Chem.Phys. _ZQ, 729 (1962)
2x1
+
R.Seiwats, surf.eci. 2, 473 (1964)
2x2
+
G.O.Krause, phys.stat.sol.& +
4x4 2x1
1093 (1961)
K 59 (1969)
+
T.A.Clarke, surf.sci.&
+
R.Holtom and P.M.Gundry, surf.sci.Q, 263 (1977)
+
S.J.White and D.P.Woodruff, surf.sci.Q, 254 (1977)
R.Mason and M.Tescari, 553 (1972)
2x1
+
2x1
+
2x1
+
+
F.Jona et.al., J.Phy6.C l0, L 67 (1977)
2x1
+
+
S.Y.Tong, Comments Solid State Phys.2,
S.J.White and D.P.Woodruff, surf.sci.6& 131 (1977)
1 (1978)
2x1
+
+
K.A.R.Mitchell and M.A,Van Hove, surf.sci.z, 1476 (1978)
4x2
+
+
T.D.Poppendieck, T.C.Ngoc and M.B.Webb, surf.sci.2, 287 (1978)
2x1
+
+
S.Y.Tong and A.L.Maldonado, surf.sci.3, 459 (1978)
2x1
+
+
F.Jona et.al., J.Phys.C j& L 455 (1979)
Table 7. Si(100) theoretical calculations of the electronic structure surface
method
E(K,,)
literature
SDOS
ideal
I.Bartos, surf.sci.9,
ideal
I.Bartos and J.Nadrchal, surf.sci.22, 290 (1970)
+
ideal relaxed
SCF pseudopotential
ideal/2xl
SCF pseudopotential
2x1
SCF pseudopotentia;
2x1/4x2
energy minimization
ideal
emprical tight binding
2x1
SCF
paeudopotential
94 (1969)
F.Yndurain and M.Elices, surf.sci.3, 540 (1972)
+
J.A.Appelbaum, G.A.Baraff and D.R.Hamann, Phy6.Rev.B 12, 5749 (1975)
+
G.P.Kerker, S.G.Louie and M.L.Cohen, Phys.Rev.B u, 706 (1978) J.A.Appelbaum and D.R.Hamann, surf.sci.& 21 (1978)
+
+
+
+
+
D.J.Chadi, J.Vac.Sci.Technol.5,
1290 (1979)
I.Ivanow, A.Mazur and J.Polimann, surf.sci.& 365 (1980) J.Iiq L.Cohen and D.J.Cbadl, Phye.Rer.B_ 5, 4592 (1980)
N. P. LZIBKE
840
Table 8. Si(iO0) photoelectronSpectroscoPY surface
model calculation
angular resolved spectra
2x1
+
2x1
+
literature
f
F,J.Hiapeal and D.E. Eastman, J.Vac.Sci.Technol.& 1297 (1979) R.A.Van Roof and M.J.Van Dar YIOI, A~~l.Sf.Scir$ 444 (t 980)
Table 9. Si(100) ek&ron energy loss spectroso~py model calculation
surface
experimental spectra
2x1
VES
R.Holtom and P.M.Gundry, i3urf.eci.~263 (1977)
2x1
VES/CES
N.Lieske and R.Bezel, Inst,Phys.Conf.Series z,
2x1
literature
206 (1980)
J.E.Rowe ted R.Ibach, Phya.Ror.Lett.& 102 (1973)
VFIS
Table 10. Si(110) low energy electrondifiktion surface
:z&c:etrical
literature
mode1 calculationa
innnaity
5x2
+
G.O.Krause, phys.atat.sol.j&
4x5/2x1 /4x1
+
B.Z.Olshanetskyand A.A.Shklyaev, surf.aci.Q, 581 (1977)
K 59 (1969)
Table 11. Si(ll0) theoreticalcalculationsof the eleotronicstructure surface
method
ideal
LCAO
ideal
+
J.Alatrup, phye.stat.601.(b) G,
+
ideal empirical tjght binding
literature
E(K,.) SDOS
+
209 (1971)
F.Yndurain and M.Elices, surf.sci.& 540 (1973) +
I.Ivanov,A.Mazur and Y.Pollmann, 8urf.sci.z 365 (1980)
841
The electronic structure of semiconductor surfaces Table 12. C&$111) low energy electron d&&ion surface
geometrical data
intensity data
literature
model calculations
+
+
J.J.Lander and J.Morrison, J.Appl.Phys.&, 1403 (1963)
2x1
+
+
N.R.Haneen and D.Haneman, surf.sci.2, 566 (1964)
2x1
+
+
P.W.Palmberg and W.T.Peria, surf.sci.6, 57 (1967)
2x1
+
P.W.Palmberg surf.sci.fi,
2%1/2x8
+
M.Henzler, J.AppI.Phys.&,
2x1
;
M.Henzler, .eurf.sci.s,
2x1
153 (1968) 3758 (1969)
159 (1970)
2x1/2x8
+
J.T.Grant and T.W.Haas, J.Vac.Sci.Technol.& 94 (1971)
2x1
+
J.E.Rore, Solid State Commun.g,
673 (1975)
2x1/2x8
+
B.Z.Oluhanetsky, S.M.Repinsky surf.sci.&, 224 (1977)
1X1/2X1
+
A.A.Galaev et.al., Kristallografiya (USSR)2&
and A.A.Shklyaev,
130 (1979)
Table 13. Ge(ll1) theoretical calculations of the electronic structure E(K.,)
SDOS
literature
surface
method
ideal
Greene function
+
M.Elices and F.Yndurain J.Phys.C _5, L 146 (19723
ideal/relaxed
tight binding
+
D.J.Chadi and M.L.Cohen, Solid State Commun.fi, 691 (1975)
ideal
pseudopotential
ideal/relaxed
extendet Htickel
ideal
SCF pseudopotential
ideal
+
E.Louis and M.Elices Phys.Rev. B & 618 f1975) M.Nishida, J.Phy6.C 11, 1217 (1978)
empirical tight binding
J.Ihm, S.G.Louie and M.L.Cohen, Phy6.Rev.B Q, 769 (1978) +
+
I.Ivanov, A.Mazur and J.Pollmann, surf.sci.92, 365 (1980)
Table 14. Ge(1 I I) photoelectronspectroscopy surface 2x1
angular resolved spectra +
literature
model calculations J.E.Rowe, surf.sci.2,
461 (1975)
2x1/2x8
T.Murotani, K.Fujiwara and M.Nishijima, Phys.Rev. B 12, 2424 (1975)
2x1
J.E.Rone, Solid States Commun.x,
1x1/2x8
F.J.Himpael et.al. Pkya.Reo.B 14, 1126 (1981)
673 (1975)
N. P. LIESKR
842
Table 15. Ge(l11) electron energy loss spectroscopy surface
experimental spectra
2xl
VES
literature
model calculations
J.von Wienskowskiand H.Froitzheim, phys.stat.eol.(b)44, 429 (1979)
Table 16. Ge(lOO)/Ge(llO) low energy electron diffraction surface
literature
geometrical intensity model calculations data data
(tool
+
C,R.Baylissand D.L.Kirk, Thin Solid Films 38, 183 (1976)
(110)
+
BZ.Olshanetsky,S.M.Re insky and A.A.Shklyaev, surf.sci.j& 224 (197'7 P +
+
(100)2x1
P.Jona et.al., J.Phys.C 12, L 455 (1979)
Table 17. Ge(lOO)/(llO) theoretical calculations of the electronic structure
, surface
Ef K,,)
method
literature
SDOS
(loo)
I,Bartos, surf.sci.&
(100)
I.Bartos and J.Nadrchal, surf.sci.22,290 (1970)
(IlOfideal tight binding +
(100)ideal emprical (1lO)ideal tight binding
94 (1969)
+
J.D.Joannopoulosand M.L.Cohen, Phys.Rev.Blo, 5075 (1974)
+
I.Ivanov,A.Mazur and J.Pollmann, surf.sci.& 365 (1980)
Table 18. Ge(100) photoelectron spectroscopy surface
angular resolved spectra
model calculations
(100)
literature C.R.Bayltssand D.L.Kirk, Thin Solid Fllme 3, 183 (1976)
Table 19. AlAs photoelectron spectroscopy surface
yu;u
resolved
De
model calculations
literature R.Z.Bachrachet.al. J.Vac.Sci.Technol.lb 797 (1981)
(100)
Table 20. AlAs electron energy loss spectroscopy surface
experimental spectra
(100)
VES
model
calculation8
+
literature R.Ludeke and L.Esaki surf.sci.~* 132 (19fi5)
The electronic structure of semiconductor
843
surfaces
Table 21. GaAs low energy electron diffraction surface
geometrical intensiy model calculation6 data data
+
+
literature
(110)
+
(111)
+
A.U.MacRae, surf.ici.&,247 (1966)
(110)
+
M.Henzler, surf.sci.22,12 (1970)
(110)/(111)
+
J.M.Chen, surf.sci.Q, 305 (1971)
+
A.J.van Bommel and J.E.Crombeen, surf.sci.z, 437 (1976)
(111) (100)
A.I>;acRae and:G.W.Gobelii J.Appl.Phys.2, 1629 (1964)
(110)
C.B.Duke, A.R.Lubinsky,B.W.Lee and P.Nark, J.Vac.Sci.Technol.Q, 761 (1976)
(110)
A.R.Lubinskyet.al., Phys.Rev.Lett.&, 1058 (1976)
(110)
P.Mark. P.Pianetta, I.Lindau and W.E.Spicer, surf.sc>.Q, 735 (1977)
(111)
( 1:10)
+
(110)
+
+
W.Ranke and K.Jacobi, surf.sci.Q, 33 (1977)
+
A.Kahn et.al., J.Vac.Sci.Technol.Q, 1223 (1978) P.Skeath et,al., J.Vac.Sci.Techno1.u 1219 (1978)
+
A.J.van Bommel et.al. 'surf.sci.72,95 (1978)
+
P.Drather, W.Ranke and K.Jacobi, surf.sci.22,L 162 (1978)
+
A.Kahn et.al., surf.sci.& 387 (1978)
+
+
C.B.Duke et.al., J.Vac.Sci.Technol.fi, 1252 (1979)
+
+
R.J.Meyer et.al;, Phy6.Rev.Bs, 5194 (1979)
+
+
J.R.Chelikowskyand M.L.Cohen, Phy8.Rev.Bg, 4150 (1979)
N. P. LIFSKE
844
Table 22. GsAs theoretical calculations ofthe electronic struoture surface
method
(110)
pseudopotential
E(K..) SDOS
literature
(110)
tight binding
+
J.D.Joannopoulos and M.L.Cohen, Phys.Rev.B l0, 5075 (1974)
(111)
tight binaing
+
D.J.Chadi and H.L.Cohen, Solid State C0mmun.s 691 (1975)
(111)
pseudopotential
(110)
tight binding
(110)
empirical tight binding
(100)
SCF pseudopotential
+
(110)
tight binding
+
(110)
tight binding
(lll)/mm
SCF tight binding
G.Ball and D.J.Morgan, phys.stat.sol.(b) s, 199 (1972)
+
E.Louis and M.Elices, Phys.Rev.B 12, 618 (1975) W.A.Harrison, surf.sci.z,
+
(1976)
C.Calandra and G.Santoro, J.Phys.C 2, L 51 (1976) J.A.Appelbaum, G.A.Baraff and D.R.Hamann, J.Vac.Sci.Technol.9, 751 (1976)
+
K.C.Pandey, J.L.Freeouf and D.E. Eastman, J.Vac.Sci.Technol.l& 904 (1977)
+
E.J.Mele and J.D.Joannopoulos, surf.sci.66, 38 (1977) B.DjafariRouhani surf.sci.z, 24'
+
L.Dobrzynski
and M.Lannoo,
11978)
+
W.Schwalm and J.Hermanson, Solid State Commun&, 587 (1978)
tight binding
+
K.C.Pandey, J.Vac.Sci.Technol.s,
440 (1978)
(110)
tight binding
+
D.J.Chadi, J.Vac.Sci.Technol.s,
631 (1978)
(110)
tight binding
D.J.Chadi, J.Vac.Sci.Technol.9,
1244 (1978)
(110)
tight binding
J.A.Knapp et.al., J.Vac.Sci.Technol fi, 1252 (1978)
(110)
SCF pseudopotential
(110)
band orbital
(110)
empirical tight binding
J.R.Chelikowsky and M.'L.Cohen, Phys.Rev.B 20, 4150 (1979)
+
(110)
energy mlaidzation
(110)
SCF pmaudopotontlal
+
(lll,mT
tight binding
+
+
I.Ivanov, A.Mazur and J.Pollmann, surf.sci.92, 365 (1980)
+
Z.KaiMing
and
Y&in&
J.Vac.Sci.Technol.l/,
[email protected],
+
M.Nimhida,
506 (1980)
Phy8.Ror.B 2, J.phy&C
&,
959 (19801 535 (1981)
845
The electronic structure of semiconductor surfaces Table 23. GaAs photoei~n surface
angular resolved spectra
spectroscopy
model calculatioM
(110)
literature H.Froitzhelmand H.Ibach, surf.sCi*~, 713 (1975)
(110)
+
J.C.Phillipsand K.C.Pandey, surf.sci.& 183 (1976).
(110)
+
W.Gudat and D.E.Eastman, J.Vac.Sci.TechnoZ.U, 831 (1976)
+
(100)
J.A.Knapp and G,J.Lapeyre, J.Vac.Sci.Technoll& 757 (1976)
(110)
W.Ranke and K.Jacobi, surf.sci.B, 33 (1977)
(m)
+
(110)
K.C.Pandey,J.L.Fraeouf and D.E.Eastman, J.Vac.Sci.Technol.a,904(1977)
(110)
I.Lindau et.al., =rf.sci&, 45 (1977)
(110)
P.Pianetta e&al., surf,sci.& 298 (1978)
(111) (110)
P.Skeath et.al., J.Vac.Sci.Technol.s, 1219 (1978)
(110)
G.P.Williams,R.J.Smith and G.J.Lapeyre, J.Vac.Sci.Technol.u, 1249 (1978)
(110)
J.A.Knapp et.al., J.Vac.Sci.Technol.,& 1252 (1978)
(110)
D.J.Chadi et.al., J.Vac.Sci.Technol.3, 1244 (1978)
(110)
A.Huijser, J.van Laar and T.L.van Rooy, Phy6.Lett.AG, 337 (1978)
(1.10)
G.B.Duke %t.al., J.Vac.Sci.Technol.5, 1252 (1979) +
(110)
J.Colbert and N.J.Shevchik, J,Vac.Sci.Technol.fi, 1302 (1979)
(100)
P.K.Lars%n,J.H.Neave and B.A,Joyce, J.Phys.C l2, L 869 (19791
ql77
K.Jacobi, C.v.Huschwitzand W.Ranke, surf.sci.82,270 (1979)
Cl101 +
(110)
+
D.E.Eastmac et.al.,
+
P.K.Larasn, J.R.Neave and B.A,Joyee, J.Phye.C 14, 167 (1981)
Phys.Rer.Lett.&&
R.Z.Rachrach pt.al.. J.Vac.Sci.Technol.&
(100)
656 (1980)
797 (1981)
Table 24. GaAs electron energy loss spectroscopy surface
experimental spectra
(110)
VES
H.LUth and G.J.Russell surf.sci.Q, 329 (19743
(110)
VES
H.Froitzheimand H.Ibach, surf.sci.g, 713 (197.5)
(100)
VES
f
R.Ludeke and L.Esaki, surf.sci.u, 132 (1975) ’
~110)/(100~ (111)
VILS
+
R.Ludeke and A.Koma, J.Vac.Sei.Technol.s, 241 (1976)
(110)
VES
+
J.van Laar, A.Huijser and T.L,van Rooy, J.Vac.Sci.Technol&, 894 (1977)
(tlo)
VES
f
R.Xatx aad E&i&h, Phw.Rar.Imtt.&&,_ !500 (19811
model calcualtions
literature
N. P. Lmm
846
Table 25. GaP low energy _. electron diffraction surface
geometrical data
(111)/03l)
+
(111 )/mm
+
intensity data
literature
model calculations
+
+
LGlachant, J.Derrien and M.Bienfait, surf.sci.&O, 683 (?973) J.Derrien, F.Arnand D'Avitaya surf.sci.l&, 162 (1975)
and A.Glachant,
Table 26. GaP theoretical calculation of the electronic structure E(K,.) SDOS
surface
method
(110)
emprical tight binding
+
Cl101
tight binding
+
+
C.M.Bertoni et.al., J.Vac.Sci.Technol.9,
(1llVmn
tight
+
+
M.Nishlda,J.Phy8.C &,
binding
literature
C.Calandra and G.Santoro, J.Phy6.C 2, L 51 (1976) 1256 (1978)
535’(1981)
Table 27. GaP photoelectron spectroscopy surface
literature
angular resolved
model
spectra
calculations K.Jacobi, surf.sci.2,
(ili) +
(110)
29
(1975)
G.k.Guichar, C.A.Sebenne and C.D.Tuault, J.Vac.Sci.TechnOl.16, 1212 (1979)
Table 28. GaP electron energy loss spectroscopy surface
experimental spectra
(110)
VES
(‘iii)
VES
literature
model calculation6
A.C.E;orSan and :/,J&.van Velzen, surf.scz..&G, 360 (1973) K.Jacobi, surf.scf.&
29
(1975)
Table 29. GaSb low energy electron diffraction surface
geometrical data
(110)
+
(111)
+
intensity data
model calculations +
+
literature A.U.?lacRae and G.'N.Gobeli, J.Appl.Phys.j& 1629 (1964) A.U.MacRae, surf.sci.4, 247,(1966)
Table 30. GaSb theoretical calculations of the electronic structure E(K.,) SDOS
surface
method
ill03
Green's.function
+
+
Wl,/mT,
tight btnding
+
+
Literature N.V.Dandekarand A.Madhukar J.Vac.SCi.Technol.16, 1364 fly791 M.Niehida, J.Phye.C 14, 535 (1981)
847
The eiectronic structure of semiconductor surfaces Table 31.GaSb photoelectron spectroscopy
surface
literature
model calculations
angular resolved spectra
(110)
P.E.Viljoen,M.S.Jazzur and T.E.Fischer, surf.sci.JZ,506 (1972)
(110)
I.Lindau et.al., surf.sci.63,45 (1977) +
(110)
D.E.Eaatmanet.al. Wm.Rev.L+tt.& 656 (1980)
Table 32. InAs low energy electron diffraction surface
$;Tytrical
(110)
f
(111)/mi)
+
intensity model data calculations +
+
literature A.U.MacRaeand G.'W.Gobeli, J.Appl.Phys.s, 1629 (1964) J.T.Grant and T.W.Baas surf.sci.26,609 (19715
Table 33. InAs theoretical calculations of the electronic structure
surface
method
(710)
Green's function
E(K,,) SDOS +
literature N.V.Dandakarand A.Madhukar, J.Vac.Sci.Technof.&, 1564 (1979)
Table 34. InP low energy electron affection surface
(110)
g;;ytrical
;;iInsity
literature
model calculations
+
R.H.Williamsand I.T,McGovern, surf.sci51,14 (1975)
Table 35. InP photoelectron spectroscopy surface
angular spat tra
resolved +
(110)
model calculatioris +
literature
A.MckInley,G,P.Srivastavaand R.H.Williams, J.Phys.C 13, 1581 (1980)
Table 36. InP electron energy loss spectroscopy surface
experimental model spectra calculations
(110)
VES
literature R.H.Williamsand I.T.McGovern, surf.sci.z, 14 (1975)
N. P. LIBSKB
848
Table 37. InSb low enemy electron diffraction surface
geometrical data
literature
intensity model data calculations +
+
(110)
+
(111)
+
J.T,Grant and T.W.Haas, J.Vac.Sci.Technol.fi, 94 (1971)
(110)
+
E.W.I'reutz surf:sci.&
A.U.KacRae and G.W.Gobeli, J.Appl.Phys.2, 1629 (1964)
Table 38. InSb theoretical calculations method
(110)
empirical tight binding
+
eqlrical tight bindind
+
(110)
IIVI
of the electronic structure
E(K.,) SDOS
surface.
Z.Rickus and N.Sotnik, 392 (1977)
literature C.Calandra and G.Santoro, J.Phys.C 2, L 51 (1976)
+
J.Poll, swf.wL~,
A.Mazuranil
165 (1980j
KSchmeita,
Semiconductors Table 39. CdS low energy electron diffraction
surface (0001)
geometrical data
intensity data
+
model calculations
B.D.Campbell and H.E.Farnsworth, surf.sci.E, 197 (1968)
+ +
(0001) (0001)/(000i)
+
(1120)/(1010)
+
(1120)
+
literature
L.R.Bedell and H.E.Farnsworth, surf.sci.& 165 (1974) S.C.Chang and P.Mark, J.Vac.Sci.Technol.E, 629 (1975)
+
+
S.C.Chang and P.Mark, J.Vac.Sci.Technol.2, 624 (1975)
+
L.
J.Brillson, surf.sci.Q, 62 (1977)
Table 4O.CdS photoelectronspectroscopy surface
angular resolved spectra
model calculations
(1170_0)
literature L.J.Brillson,
[email protected], 62 (1977)
Table 41. CdSe low energy electron diffraction surface (1120)
geometrical data
i;nsity
+
model calculations +
Table 42. Cd.% photoektron surface (1lZO)
angular resolved spectra
model calculations
literature L.J.Brillson, surf.sci.69, 62 (1977)
spectroscopy literature L.J.Brillson, surf.sci.&, 62 (1977)
The electronic structure of semiconductor
surfaces
849
Table 43. CdSe electron energy loss spectroscopy
surface
experimental spectra
(1120)
VES
literature
model calculations
L.J.Brilleon, J.Vac.Sci.Techno1.U. 325 (1976)
Table 44. CdTe low energy electron diffraction surface
geometrical data +
(110)
literature
intensity model calculations data
L.G.Feinsteinand D.P.Shoemaker, surf.sci.1,294 (1965)
Table 45. CdTe theoretical calculations
surface
method
(110)
tight binding
surface
mngle resolved
of tbe electronic structure
E(K,,) SDOS +
+
Table 46. CdTe photoelectron qactra
literature C.Calandraand G.Santoro, J.Vac.Sci.Technol.s,773 (1976)
SwctroscoRY
mod01
literature
calculation6
+
R.Z.Rachrach et.al. Ruovo Cimento B 2,
704
(1977)
Table 47. CdTe electron energy loss spectroscopy
surface
exaerimental
literature
model
VES
A.Ebina, K.Asano and T.Takahashi, surf.sci.86,803 (1979)
t
Table 48. PbS, Pbse, PbTe low energy electron diffkction surface
geometrical data
cleaned
+
intensity data
model calcultations
Y.Taga, A.Isogai and K.Nakajima, surf.sci.&, 591 (1979
Table 49. PbS, PbSe., PbTe photoelectron surface ...
literature
angular epectra
resolved +
spectroscopy
model calculation
literature A.L.Ragmtrom Appl.Surf.Sci.l,
and A.Fahlman 455 (19785
N. P. LIEWE
850
Table 50. ZnO low enerm electron ciiBiactiou surface
geometrical ininsity data
literature
model calculations
+
G.Heiland and P.Kunstmann, surf.sci.l;i, 72 (1969)
+
K.MiiIler inStructureAnd Chemistry Of Solid Surfaces, Ed. G.A.Somorjai(Wiley,New York,1969)
)~;3/'112"'
f
J.D.Levine,A.Willis, W.R.Bottomeand P.Mark, surf.sci.3, 144 (1972)
(1120)/1010~
+
... (0001)
+
+
S.C.Chang and P.Mark, eurf.sci.&, 721 (1974)
+
(:?20)/(1070~ (000i)/(10T0)
f
(ioio)
+
S.C.Chang and PMark, eurf.sci.Uf 721 (1974) ..0 B.J.Hopkins,R.Leyeen and P.A.Taylor, surf.sci.& 486 (1975) W.Gijpeland G.Neuenfeldt, surf,sci.z, 362 (1976)
(0001 )/(OOOi) (1010)/(1120~
A.R.Lubinskiet.al., J.Vac.Sci.Technol.u, 189 (1976)
(1010)
C.B.Duke et.al., Phys.Rev.B 18, 4225 (1978) V.E.Henrich et.al., 6urf,sci.&, 682 (1978)
Table 51. ZnO theoreticai calculations of the electron structure surface
method
(1010)
SCF
(1010)
tight
binding
+
tight
binding
+
EC&,)
literature
SDOS
C.B.Duke et.al., Phye.Rev.Ba, 4865 (19771 and J.D.Joanopo~~oe, J.Vac.Sol.Technol..l2,987 (1980) J.Ivanor and J.Pollqann, Solid State Commm.36, 361 (1986)
D.&Lee
+
Table 52. ZnO electron energy loss spectroscopy s~face
angular reaolred
weetra
model. calculationa
literature F.Hublet
H.Van Ifovs and A.Neyens, aurf.e=i.&, 178 (1977)
+
Table 53. 2110 ekctron ex%zrgy loss SpectroscoPY surface
experimental spectra
literature
model calculations
R.Dorn and H.Ltith, surf.sci.68, 385 (1977) A.Ebina and T.Tak.ahashi, surf,eci.& 667 (1978)/eurf.eci.a 682 (1978)
Table 54. ZnS low energy dectron &f&action surface (110)
geometrical intensity model calculations data data +
literature Y.Taga, A.Isogai and K.Nakajima, surf.sci.86,591 (19791
The electronic structure of semiconductor surfaces
851
Table 55. ZnS theoretical cakulations of the electronic structure surface
method
(111)
pseudopotential
(110)
tight binding
(110)
tight binding
literature
E(K,,) SDOS
E.Louis and M.Elices, Phy6.Rev.B l2, 618 (1975)
+ +
+
C.Calandra and G.Santoro, J.Vac.Sci.Technol.Q, 773 (1976)
+
S.Tougaard, Phys.Rev.B l8, 3799 (1978)
Table 56. ZnSphotoelectron rrurface
angle resolved euactra
spectroscopy literature
model calculations
+
R.Z.Bachraeh et.al., NOUYOCimento B 2,
704.(1977)
Table 57. ZnSe low energy electron diffraction surface
geometrical data
intensity data
model calculations
(110)
+
+
(110)
+
+
+
(100)
literature C.B.Duke et.al., J.Vac.Sci.Technoll&
294 (1977)
P.Mark et.al., J.Vac.Sci.Technoll&
910 (1977)
K.Asano, A.Ebina and T.Takahashi, Rec.Electr.and Commun.Eng.Conversazione Tohoka Univ. &8, 18 (1979)
Table 58. ZnSe theoretical calculations of the electronic structure
tight
binding
(110)
tight binding
(110
tight binding
l
+
D.J.Chadi and N.L.Cohen, Phy6.Rev.Z 11, 732 (1975)
+
C.Calandra and G.Santoro, J.Vac.Sci.Technol.3, 773 (1976) C.Calandra, F.Manghi and C,M.Bertoni, J.Phy6.C lO, 1911 (1977)
Table 59. ZnSe photoelectron spectroscopy aurfaca
~;fxwolred w
modal calculations
+
literature R.Z.Bachrach et.al. Nouvo Cimento B 2,
704 (1977)
Table 60. ZnSe electron energy loss spectroscopy model calculations
literature
aurfaoe
;xEEgautal D
(110)
VES
C.B.Buke et.al., J.Vac.Sci.Technol.l_&,
(111)
CES
A.Ebina and T.Takahaahi, surf.sci.& 667 (1978) A.Ebina, LAsano and T.Tahahaehi. Surf.SGi.&& 803 (1979)
(111)/(100) (100)
294 (1977)
VES
K.Aaano, A.Ebina and T.Tahahashi, Rec.Electr.and Commun,Bn .Conversazione Tohoka Univ.& 18 (1979 k
N. P. LIESKE
852
Table 61. ZnTe low energy electron diRaction surface
literature
geometrical intensity model +
+
(110)
C.B.Duke et.al., J.Vac.Sci.Technol.16, 647 (1979)
Table 62. ZnTe theoretical calculations of the electronic structure surface
method
(110)
tight binding
E(K.,) SDOS +
+
literature C.Calandra and G.Santoro, J.Vac.Sci.Technol.13, 773 (1976)
Table 63. ZnTe phot~l~tro~ spectroscopy surface
ang?trfeaolved 8ua
literature
model calculationa
+
&Z.Baohrach et.al., Nouro Closnto B B.
704 (1977)
Table 61. ZnTe electron energy loss spectroscopy surface
experimental spectra
model calculations
(ll~)/(il~)/(~OO) VES
APPEND=
Si( 1I 1) surface As a typical example illustrating some of the aforementioned considerations, we consider the silicon (111) surface. This surface is of technological and basic scientific interest as well; therefore its atomic and eiectronic structure has been studied intensively with the techuiques described in the previous section. Note that because of the specialized literature, a supplemental set of references is given at the end of this section. A. A typical studpthe
A. I Stru&tura~.forms of the Si( 1.1I) surface. Silicon cleaves along (111) faces. The clean Si( 111) surface phases: exhibits three different structural Si(lll)l x 1, Si(111)2 x 1 and Si(111)7 x 7. After cleaving at room temperature a thermally metastable, 2 x 1 structure (related to the bulk translational symmetry) can be observed using LEED [I]. Upon thermal annealing to about SOOK an irreversible transformation from this 2 x 1 structure to a 7 X 7 structure is observed 1241, which again reversibly transforms to a 1 X 1 structure at about 1150 K temperature [MS]. The 1 X 1 phase can be stabilized at room temperature by rapid quenching [9, IO], by laser annealing [i 1, 121 or by small amounts (some tenth of a monolayer) of surFace impurities such as Cl [7], Te [lo, 131 or Ni [141.
literature A.sbina, :;.Asano and T.Takahashi, surf.sci.86,803 (1979)
In Fig. 8 the LEED patterns of the 2 x I,1 x 1 and 7 x 7 surfaces are shown [15]. A.2 Early results of exFerime~ta~ and theoretical studies. The first experimental evidence for the existence of surface states was given by the work of Allan and Gobeli [ 161: for cleaved Si(ll1) surfaces they measured the work function and the photoelectric threshold as a function of bulk doping. They found pinning of the surface Fermi energy independent of the bulk Fermi level and concluded that a high density of partially occupied surface states should exist somewhat below the midgap position. This finding was confirmed by the surface conductance measurements of Handler [17j and the field effect rn~s~ernen~ of Henzler and H&and [l&19]. From these works surface states at about 0.25eV below the midgap position with a total surface state density of 2 x 1014/cm2could be deduced. All electrical studies of the silicon surface were reviewed by Davison and Levine [20]. In the bulk silicon the (111) atomic planes have a hexagonal atomic arrangement. If an ideal Si(ll1) surface is formed, from simple considerations it is expected that one bond per surface atom is broken (dangling bond) and three bonds are directed to atoms of the second layer. The principal arrangement of the Si(ll1) surface together with the corresponding Brillouin zone is given in Fig. 9. The first deeper insight was given by the theoretical
853
The electronic structure of semiconductor surfaces
Fig. 8. LEED patterns of Si(ll1) surfaces: (a) 2 x 1 pattern after cleavage, Ep = 60 eV. (b) “1 x 1” pattern after annealing at 350°C for 10 min, E, = 40 eV. (c) 7 x 7 pattern after annealing above 500°C for 10 min, E,,= 35eV. From Ref. [15].
Surface
Top
view
1111) plane 0
first
@
second layer
layer
l
third layer
Fig. 9. Principal atomic arrangement at the ideal (ordered, not reconstructed) silicon (111) surface: top view, side view along the (110) plane and surface Brillouin zone; (a, b) basic vectors of the surface unit mesh, (A, B) corresponding reciprocal unit vectors.
work of Appelbaum and Hamann [21241 who ap plied a self consistent pseudopotential approach in a
semiinfinite model to the relaxed, unreconstructed Si(ll1) surface. They found that relaxation is necessary to obtain selfconsistency. Independent of relaxation they obtained a dangling bond surface state band with the electron charge density highly localized in front of and just behind the surface atoms (see Fig. 1Oa). The dangling bond band lying within the energy gap between the valence and conduction bands is only partially occupied. With an inward relaxation of 0.22 A of the surface atomic layer a Fermi level of EF= 0.3 eV above the valence band maximum is obtained in good agreement with experimental tindings at the Si(ll1)7 x 7 surface. For the first time Appelbaum and Hamann were able to show that inward relaxation gives additional surface states ener
getically located within the bulk valence band region and with the electron charge localized on the bonds between the first and second atomic layer (see Fig. lob). These bands are called back bond surface state bands. These results were confirmed by the empirical tight binding calculations of Pandey and Phillips [25271. For the 0.34A inward relaxed, not reconstructed surface they found one dangling bond and three back bond surface state bands in the r, K, J directions of the surface wave vector (see. Fig. 11). They also reported the density of states for surface and bulk layers (see Fig. 12). For the 2 x 1 reconstructed surface the first the oretical calculations were done by S&titer et al. [29] and Pandey and Phillips [28]. Schlilter et al. used the buckled surface model introduced by Haneman [30],
854
N. P. LIKXE
SILICON
TOP SURFACE STATE
CHARGE DENSITY
la)
VACUUY
SILICON
YIDDLE
SURFACE
STATE
CHARGE DENSITY
W
Fig. 10. Contours of constant charge density for (a} the occupied portion of the dangling bond surface state on the Si(t 11) surface. fb) For the Si( 111)back bond surface state band laying 2 to 3.5 eV below the valence band maximum. Dots locate atom centers, the vacuum is above, and charge density is in a.u. x 10). From J. A. Appelbaum and D. R. Hamann: Proc. 12th Znt. Co& on the Physics of Semiconductors(Edited by M. H. Pilkuhn). Teubner, Stuttgart (1974).
in which alternative rows of atoms in the surface layer are moved inward and outward by 0.11 and 0.18 A respectively and the second layer atoms are shifted laterally to preserve the length of back bonds. With self consistent calculations and using a twelve layer slab model they found that the dangling bond band is split into two bands by the r~nst~ction with an energy gap of about 0.2 eV (see Fig. 13). The energetically lower (higher) band corresponds to electrons mainly located at atoms which have moved outward (inward). Pandey and Phillips using 0.29A and 0.35A for inward and outiard movement respectively and a 0.24A uniform displacement in the second layer found the surface energy band shown in Fig. 14. The splitting of the dangling bond band gives 0.33 eV and 0.65 eV for the indirect and direct energy gap, respectively. Transitions between surface state bands could be detected by the optical absorption experiment of Chiarotti et al. [31], who found a threshold energy of 0.24 eV and a maximum peak at 0.45 eV.
This was confirmed by the high resolution ELS measurement of Rowe et al. 1321 who detected a strong surface state transition at 0.52 eV (see Fig. 15). In normal resolution ELS spectra a number of peaks could be assigned to transitions from surface states, especially back bond states 132351 (see Figs. 15 and 16). Surface states were also detected in photoemission experiments [33, 36401. Dangling and back bond surface states could be observed, both states about 0.5 eV lower in energy on the cleaved 2 x 1 surface compared to the annealed 7 x 7 surface. For the latter a metallic edge near the Fermi level was shown (see Fig. 17). The first angle resolved photoelectron spectra were published by Rowe et al. [41,42]. They found strong polar and azimuthal angular dependence of the photoemission intensity from cleaved Si(ll1)2 x 1 surfaces (see Fig. 18). The in~~~ta~ons of the above mentioned spectroscopical data on the basis of the theoretical calcu
The electronic structure of semiconductor surfaces 2.0
BULK
DANGLING8ONO 15,)
BAN0
____________
_1
les II
ip,
I
VALENCE
BAN0
MAXIMUM
Al
I
0
.V
.
5
u 
5 w 2
5.0 6.0
w i
SURFACE
 9.0 TRUE SURFACE STATE 10.0
/
r /
11 0 
0
/Y
4’ =Y
\
4’ /’ LONGITUDINAL BACK BONO (r6
140’ t
RESOHANCE
(C,1
Dz) 1.2
I
1
K
J
\
\ ‘.
=\
f
hs
Fig. 11. Dangling and backbond surface state bands and resonances for a relaxed Si(111)surface. From Ref. [251.
lations could only be done with a high degree of uncertainty. Miinch et al. studied the correlation of electronic surface properties such as work function, electron affinity and surface potential with the geometrical structure during conversion from the 2 x 1 to the 7 x 7 reconstructed surface [15, 431. Their main results were the interpretation of an apparent intermediate 1 x 1 structure with abrupt changes in electron properties and the observation of an 0.25eV larger electron aflinity at the 2 x 1 compared to the 7 x 7 surface. This was interpreted by MCnch [15] as due to the greater surface roughness of the 2 x 1 surface. A.3 Recent results and present status A.3.1. Si(l1 I)1 X 1. Up to date it is not fully established if the 1 x 1 surface structure is of an ordered or
disordered nature. A 1 x 1 LEED pattern is expected for a truncated ideal bulk structure with a not reconstructed, long range ordered surface as well as for a disordered surface upon ordered substrate atoms. LEED studies for the transition from the thermally stable 7 x 7 to the high temperature 1 x 1 surface were done by Florio and Robertson [6,7] and recently by Webb and Bennet [8]. Both studies clearly revealed that during the transition the loss of scattered amplitude from the superlattice reflection did not appear at the intergral order beam positions but appeared as diffused scattering. This result favours the interpretation of an order to disorder transition. Dynamical LEED calculations were done by Shih et al. for the impurity stabilized Si(lll)l x 1 Te surface [lo] and by Zehner et al. for the laser annealed Si(1 11)l x 1 surface [l 11.The results of both works
856
N. P. LIEBCE
1 
OANGLMJG BOND STATES SADDLE WINT PEAKS IN BACKBONO SURFACE BANOS i
, 2
4
.
1
6
1
I
8
.
I
 to
.
1
12
.
1
VALENCE SAN0 ENEROV IEVI
Fig. 12. Density of states for the Si(1 II) surface atom layer, for the fourth layer and for the bulk. Relaxation of 0.34A is assumed. From Ref. [26].
suggested a truncated bulk layer model with an ordered and relaxed but not reconstructed surface layer, for which an inward shift of about 0.16 A was calculated. Due to the theoretical studies for an ordered 1 x 1 surface [21301 a half lilled surface state band located within the bulk energy gap is expected. This metallic surface behaviour should be clearly detectable with phot~~~ion experiments. PES studies gave rise to interpretations based upon disordered surfaces: Eastman, Himpsel and Van der Veen [ 131 did angle integrated, angle resolved and
0
0.1
0.a
0.1
0.4
0”s
ENERGY (4
Fig. 13. Density of states for the split dangling bond surface state band on the 2 x 1 reconstructed Si(l11) surface. From Ref. [29].
polarization dependent photoemission experiments on TE stabilized 1 x 1 surfaces. They found a back bond surface state 1.8 eV and a dangling bond surface state 0.9 eV below the Fermi level at the 1 x 1 and at the 7 x 7 surface as well. But a metallic band near EF could only be detected on the well annealed 7 x 7 surface (see Fig. 19). These results were contirmed by the PES studies of Chabal et al. 1121on laser annealed and Ni stabilized 1 x 1 surface and of Zehner et al. on laser annealed 1 x 1 surfaces [I I]. ELS studies recently done with a high resolution method by Kobayashi et al. [44] showed that the inelastic contirmum between O650 meV observed on the 7 x 7 surface and due to Drude absorption of electrons in the metallic surface band was not existent on the 1 x 1 surface (see Fig. 20). In summary the spectroscopic experiments clearly suggest that the Si(lll)l x 1 surface is disordered with a short range atomic configuration similar to the Si( 111)7 x 7 one. It was pointed out by Chadi [45] that LEED studies do not rule out a random arrangement of small subunits which normally superpose to a 7 x 7 pattern. A.3.2. Si( ill)2 X 1. Cleaved Si( 111) surfaces exhibit a thermally me&stable 2 x 1 structure which irre
t2 I
91 I
9
_
I I
UYJ JJoi ~01XE
/ ,
,)=s\;i: w
Jo.*
NV313
?‘JJJlac,_OIXS’l
NV313
LS8
858
N. P LWSKE I
I
I
I
+ot
I
CLEAN,
1
(7x73
WEAK ttxt)
tbt +Ta,
Si WI) EDC(ANGLE INTEGRATED) he* 21.0 rV
s,p POLARttAflON
ENERGY
INITIAL INITIAL
ENLRNY W)
(a)
WI
Fig. 19. Angle integrated photoemissiolt spectra for (a) clean Si(llQ7 x 7, (b) Si(l11) + adsorbed Te (trace amount) with a very weak 7 x 7 LEED pattern, (c) Si(lll)l x I Te stabilized with a trace amount of Te. Surface state features am denoted by (i), (ii) and (iii). From Ref. [13].
tensity data (see Fig. 22) for a top layer buckling of 0.3010 and a contraction of 10 and 3.5% of the two topmost interlayer spacings, respectively. In a recent LEED intensity study Auer and Mijnch [51] found that the 2 x 1 surface phase directly transforms to the 7 x 7 one without an intermediate 1 x 1 structure in contrast to their early %nlings 115, 431.
1ooo I
Fig. 18. Angle resolved phot~l~tron energy spectra taken on a clean Si(111)surface: (a) at a sequence of polar angles
2oca
hi7
?
1
1~ 1 Sit1111 (1x1)
with the azimuthal angle kept constant at p = O’, (b) radial plots of the azimuthal dependence of the photoemission intensity with the polar angle kept constant 8 = 30”. From Ref. [42].
13 v
lb c
LEED studies. MGnch and Auer [46] measured the intensity versus energy curves between 30 and 250 eV on single domain Si( 11 I)2 x 1 surfaces and made a theoretical analysis of the double diffraction picture. They confirmed Haneman’s model and found a buckling of 0.47 A for the surface layer and a relaxation of interlayer spacing by loo/, for the l2 and 23 layers respectively. The first dynamical theory analysis of LEED intensity data for the 2 x 1 surface was presented by Feder ef at. f48]. They found strong evidence against the atom pairing model 149, So] and obtained best agreement between theoretical and experimental in
xl00
.i(i L 3, 2
._I
\
> t;
2
E
\
Si(lltI(7x7)
~1~:~~ ENERGY
LOSS (meV)
Fig. 20. Electron energy loss spectra measured in the speo ular mode at the Si( 11I)1 x 1 and 7 x 7 surfaces at 300 K. Primary energy 6.2eV, angle of incidence 60”. From Ref. (441.
The electronic structure of semiconductor
859
surfaces
Surfoce Brillouin
il
\
El B r A
\
Zone K
‘1 J’,)
0
[oil]
first second
t
Ii111
l
third
layer hyer layer
/
Side
view
(110)
mirror
plane
h b2
Fig. 21. Principal atomic arrangement and Brillouin zone of the silicon (111)2 x 1 surface as described by the buckled surface model of Haneman. Arrows t(J) mark outward (inward) displaced surface layer atoms; b,, 6r are the amounts of buckling for the 6rst and second atomic layer; (a. b) and (A, b) are basic vectors of the surface unit mesh and of the Brillouin zone respectively; F, J, J’ and K are characteristic points of the surface Brillouin zone.
PES studies. In the first angle resolved photoemission study on Si(ll1)2 x 1 [41, 421 Traum et al. reported the surface band dispersion E(kt) as shown in Fig. 23, in addition to an aximuthal anisotropy (see Fig. 18b) which is in contrast to the generally expected sp, character of the dangling bond states. Parke et al. [52] measured the surface state band dispersion in the TJ’ direction, found strong positive dispersion and good correlation with the theoretical band structure calculations of Pandey and Phillips [26] (see Fig. 24 and discussion above). Houzay ef al. [53] and Guichar et al. [54] reported angular resolved PES results which favour strong sp, character of surface states and small energy dispersion of 0.1 eV in FJ’ direction. Himpsel et al. [55] cmfirmed the small energy dispersion in the FJ’ direction and, in addition, found two filled dangling bond bands at J energetically 0.15 and 0.7 eV below the valence band maximum. Uhrberg et al. [56] and Hansson et al. [57] also reported small FJ’ dispersion but only one dangling bond band with large positive dispersion in the rJ direction (see Fig. 25). From all photoemission studies the conclusion could be drawn that PES results strongly depend on the surface [58, 591 constitution after cleavage, especially concerning the existence of single domain or multi domain structures. Theoretical studies. The theoretical calculations of surface state baaed upon the buckled surface model revealed serious problems when describing the results of optical, LEED, PES and ELS experiments. For a
buckling intensity
of 0.3 A as determined by dynamical LEED calculations [48] S&Kiter et al. [60] with
selfconsistent pseudopotential calculations found an energy gap of 0.27eV compared to the 0.40.5 eV value of optical and ELS data and in addition obtained a downward dispersion in the FJ’ direction. The optical gap could be reproduced with a 0.47A buckling [45,61] in good agreement with the value of the double diffraction LEED calculations given in [46], but the energy of the dangling bond bands came out 0.5eV too high compared to the PES results. A buckling which would minimize the total surface energy [45,62,63] results in a large optical gap of 2 1 eV and in a downward dispersion along rJ. White and Ngai [64] have demonstrated in a selfconsistent analysis, based upon Harrison’s dehybridization energy mediated reconstruction, that a 2 x 1 surface with a split dangling bond band is thermally unstable towards an 1 x 1 surface with an unsplit dangling bond band. With energy minimization calculations Chadi [62] as well as Pandey [65] could demonstrate that a buckled surface with 2 x 1 reconstruction is unstable compared to the nonbuckled relaxed 1 x 1 surface. The existence of two 6lled dangling bond bands at J as seen in PES by Himpsel et al. [55] initiated the introduction of electron correlation effects for the 2 x 1 surface:
[email protected], lhm and Cohen [66] demonstrated that a nonbuckled surface with a 2 x 1 antiferromagnetic alignment due to spin correlation between dangling bond electrons reveals minimum surface energy.
N. P. Lres~~
o
I
l
O
2
OOSA, 6,  @HA, b,  Q d’x  OA, and 6x,  007 ()16x, b,,  0 (..*)A arc rbown to&cr with expcrimxnul data (j
Energy WI IO spectrum for SitI I lb2 x 1. E.xpcrimental resulta 10 () Pnd Tl (I with 0 = Cp arc shown togctbcr with theoretical data for struclural p8r8mcten xs in tiiurc 2 and 6,, = 007.4 for B = 0 (0.) Md 0 = 3’. 4 = 0” (. . .).
II 011
(1
and
Emrgy WI If spectrum for Siflll)2 x I with 0 = 6O, 4 = 90”. Theoretical results for parxmeters aa in figure 2 (I and &* = ~2 A (. . +, b,  DOS A (..) arc show&
[email protected] with experimental data (j
Fig. 22. Comparison of theoreticaUy calculated and experimental LEED intensities for the silicon (11 I)2 x 1 surface. From Ref. [48].
The electronic structure. of semiconductor
861
surfaces
,
I
?I
/
7
ii
p
3’
I
1 
Fig. 25. Initial state energy dispersion for the dangling bond band along the TJ symmetry line in tbe 2 x 1 Brillouin zone. From Ref. [56]. I
r
Q2 K,,ti“,
0.4
Qb ALONG
M [I
JLD
I”]
Fig. 23. Energy versus parallel wave vector for the experimental surface state peak (tilled circles) and the weaker split off peak (open circle). From Ref. [41].
structure. They argue that the importance of intra atomic correlation and spin ordering is due to the small interaction of dangling bonds because of their large spatial separation. But the most recent photoemission results [56] removed the main experimental basis for the introduction of correlation effects.
Chadi and Del Sole [67] incorporated spin polarization and ordering effects and found minimum surface energy and best agreement with optical and photoemission data for a buckled Si( Ill)2 x 1 surface with a 1 x 2 spin ordering resulting in a 2 x 2 periodicity (see Fig. 26), visible in normal LEED as a 2 x 1 2.0 BUCKLED
Sitlll):
PER’ODlClTY
2X2
I
ATOMS: 2X1 SP,NS: ,X2
I

1 J
SURFACE WAVEVECTOR
Fig. 24. Dispersion of the surface energy bands for vacuum cleaved silicon along N ’ of the surface Brlllouin zone. The full (open) circles represent strong (weak) photoemission features. The Fermi level lies at about 0.30.5 eV. From Ref. [52].
Fig. 26. Calculated electronic band structure for the buckled Si(ll1)2 x 2 surface. The atomic and spin ordering in the unit cell are depicted on top with raised atoms represented by open circles and lowered atoms by dark circles. From Ref. [67J.
862
N.
P. Lrssxs
The most promising surface structure model was proposed by Pandey [65, 68, 691 and worked out by No~h~p and Cohen [70] and Chadi [59]: In the “xbonded chain model” the surface dangling bonds interact via first neighbor instead of second neighbor interactions and they form a onedimensional zigzag chain (see Fig. 27). This results in an appreciable lowering of the surface state energy. This structure is found to be even more stable than the nonbuckled antife~oma~etic surface by 0.15 eV per surface atom. This model provides an excellent description of the highly dispersive surface state band at rJ [56] but cannot as well describe the nearly dispersionless band at TJ’ [S57]. This was realized by Chadi [59] who proposed a molecular type of nbonding (see Fig. 28). With the occurence in varying proportions of both bonding configurations he was able to explain the wellknown cleavage dependent properties of the Si(lll)2 x 1 surface. A.3.3 Si( I 1 I)7 X 7. The 7 X 7 reconstructed phase is the thermally stable structure of the Si(ll1) surface. Its main char~te~sti~ apart from the surface spectroscopical data are: (I) The transition temperature from 2 X 1 to 7 X 7 depends on the surface step density [IS]. (2) From 2 x 1 to 7 x 7 the work function decreases by 0.22 eV and the electron aflinity by 0.27 eV [15]. (3) Compared to 2 x 1 the 7 x 7 surface structure is much more stable against chemisorption and chlorine [71].
(a)
3
1
2
4 3
3 b
e 1 2
4
3
3
(b) 5
7
7 8
6
8
m 4
2 1
3
3
(cl 7 8
7
5 6
8
~ Fig. 28. Top and side views of the nbonded molecular structure are shown in (a) and (b) respectively; side view of the ideal 1 x 1 surface in (c). From Ref. 1591.
of hydrogen
W
2
4
3
4
Fig. 27. Top and side views of the xbonded chain structure are shown in (a) and (h) respectively. The side view of the ideal I x 1 surface is shown in (c). The numbering on the atoms is to facilitate a comparison of the atomic positions in the ideal and reconstructed structures. From Ref. [SS].
(4) In contrast to the 7 x 7 surface the 2 x 1 structure shows optical transitions between filled and empty dangling bond states [31]. The surface models which have been proposed up to now can be divided into rough and smooth types [72]. The smooth models which are treated below assume atomically complete surfaces with small periodic displacements of surface atoms. The rough models mainly suggested due to the chemical resistance of the 7 x 7 surface assume a distinct distribution of vacancies or excess atoms at the surface. Lander and Morrison [5, 731 proposed a structure with 13 vacancies within each unit mesh of the iirst layer (see Fig. 29). Harrison’s adatom model 1631 contains 13 adsorbed atoms per unit mesh at the same atomic sites as in the Lander vacancy model. These rough models mainly referred to the facts of the high 2 x 1 to 7 x 7 transition temperature, to the great difference in work function and to the chemical resistance of the 7 x 7 surface. LEEll studies. Levine, Mark and McFarlane 174, 751made a kinematical analysis of the fractional order LEED pattern symmetries. They ruled out vacancy and adatom models and proposed a new surface model characterized by a small rippling of the first two double layers (see Fig. 30). Miller and Haneman [76] applied an improved kinematic single scattering analysis to the fractional order beam intensities and to the integral order beam intensity vs energy curves.
The electronic structure of semiconductor surfaces
863
They tested the Lander vacancy, Harrison
Fig. 29 (a) The Lander vacancy model for the 7 x 7 reconstruction of the Si( Ill) surface. (b) The Lander vacancy 2 X 2 unit mesh for the Si( I I 1) surface. From Ref. [87].
(4
adatom, LevineMcFarlane.Mark distortion model and suggested a new hexagon based distortion model (see Figs. 3133). Their results clearly favored the distortion models over the vacancy or adatom models. Up to now no dynamical LEED calculation has been performed because of the large and complicated unit mesh of the 7 x 7 reconstructed surface. ELS studies. Several experimental findings pointed to the similarity of the 7 x 7 and 1 x 1 silicon (111) surfaces as, for example, concerning the LEED intensities of the integral order beams, the work function and electron affinity, and the spectroscopical data of PES and ELS. This suggests that Si( 111)l x 1 and 7 x 7 surfaces differ only by small displacements of atoms resulting in small energy differences of surface states [2123, 461. The short range atomic configurations are expected to be very similar; differences mainly concern the long range atomic configuration. Therefore, it seems reasonable to describe at least the energetically lower, filled electronic surface states of the 7 x 7 surface based upon the electronic states of the 1 x 1 surface. Lieske and Hezel [77] measured angle integrated ELS spectra of the Si(lll)7 x 7 surface and detected additional characteristic energy losses as compared to earlier ELS results. This fact could be explained as due to the importance of diffraction events in ELS at low electron energies (see Fig. 34). An interband excitation model for surface to surface state and for surface to bulk state transitions, respectively, was developed. Based upon this model the experimentally detected characteristic energy losses could be interpreted as due to interband transitions within the energy band structure calculated for the Si(1 1l)l x 1 surface by Pandey and Phillips [25281 (see Fig. 35). Backes and Ibach [78] using high resolution ELS detected an intensive inelastic Drude type absorption which indicates metallic dangling bond surface states (see Fig. 36). This finding was confirmed by the measurements of Kobayashi et al. [44] (see Fig. 20). The angle resolved ELS spectra of Ohkawa, Yamada and Kawamura [79] again revealed the diffraction nature of ELS spectra at Si(lll)7 x 7.
(4
Id)
I_
7 ATOM PERIOD 2
Fig. 30. schematic of atoms in the Si(ll1) surface region and an illustration of how the 7 x 7 ripple deformation is generated: (a) The ideally terminated lattice with unstable dangling bonds. (b) Ma&ion of the surface atoms to form a nearly graphitelike layer. (c) Relaxation of the subsurface atoms. (d) Periodic ripple found by the small amount of residual compressive stress in the surface layers. The ripple amplitudes are shown greatly exaggerated for clarity. From Ref. [74].
PES studies. With angle resolved photoemission Hannson, Uhrberg and Flodstrom [80] detected surface states at 2 and 0.8 eV below the Fermi level and a strong metallic edge near EF (see Fig. 37). These results were contlrmed by the measurements of Eastman et al. [81]. Houzay et al. [82] using a synchroton radiation source analyzed energy dependence, angle and polarization dependence of Si( 111)7 x 7 photoemission (see Fig. 38). They verified the surface states at minus 1.8 eV and minus 0.8 eV but found only a low density of states near the Fermi level. This was con6rmed by recent measurements of Hansson et al. [83]. The earlier results may have been influenced by extrinsic effects [82]. The dangling bond states at minus 0.8 eV for pand near EF show greatest intensity polarization, for primary energies near 50 eV and at
N. P. Ltsstrs
864
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Fig. 3 1. (a) The arrangement of the 13 surface vacancies in the Lander vacancy model. (b) The contours of vertical displacement of the first layer atoms in the Levine, McParlane and Mark model. (c) Contours of d~~la~~t
of the first layer atoms in the hexagon model. From Ref. [76l.
emission in normal direction. These findings strongly support smooth surface models. In view of these results Chadi [45,84,851 proposed a new model based on ringlike arrangements of raised and Iowered atoms (see Fig. 39). From energy minimization calculations it was derived that the short range atomic aviations are very similar to the 2 x 1 ordered surface and that it has a 0.02 eV lower surface energy than the 2 x 1 surface. Theoretical studies. The first &ore&I calculation for the 7 x 7 reconstructed surface was done by Pandey [86]. Using the semiempirical tightbinding approach for the Lander vacancy model he obtained a
fairly good description of the photoelectron spectra published before. Snyder, Wasserman and Moskowitz [87] did quantum chemical ub initio cakxlations for the mo1ecuIar chemistry of the Si( 111)7 x 7 surface. They found the Lander vacancy model to be strongly endothermic with respect to the ~~~~t~ surface. They proposed a milk stool model which consists of three membered rings of atoms bonded to three dangling bonds of the top surface layer. The stability of the miik stool is due to the increased coupling of its dangling bonds which are nearest neighbors in contrast to the dangling bond of the unr~onst~cted surface.
The electronic structure of semiconductor surfaces
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Fig. 32. (a) Experimental diffraction screen at normal incidence and 75eV. (b) Computed diffraction screen from the Lander vacancy model. The area of the spots is proportional to the calculated kinematic intensity averaged between 95 and 140 eV. (c) Calculated diffraction screen for the Levine, McFarlane and Mark model. (d) Calculated diffraction screen for the hexagon model. From Ref. [76].
Phillips proposed a bilayer atomic microdomain model [88]. The microdomains result from the large epitaxial strain misfit energy which is present even on pure silicon surfaces. This model gives a reasonable explanation for the chemical stability of the Si( I 11)7 X 7 surface.
Nakamura et il. [89] did first principal DVXa cluster calculations for the buckled and the vacancy model, respectively. They obtained the density of surface states and compared them to photoemission spectra. From their results they favour a low density vacancy model with about 6% vacancies per unit cell which was introduced by Ino [90].
Recently Pandey [69,91] and Chadi [59] proposed xbonded structures for the silicon (111)7 x 7 surface with the main argument of surface energy reduction compared to other models. In a very recent work Binnig et al. observed the Si(ll1)7 x 7 surface in real space with scanning tunneling microscopy. Their results favour the milk stool model [87] or a modified adatom model with I2 adatoms per unit cell. This experimental technique seems very promising but should be improved to give quantitative relations between brightness and atomic altitude. In summary there is still no interpretation for the Si( 111)7 x 7 surface structure which is able to explain
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The etectronic structure of semiconductor
surfaces
867
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EWffiY
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Fig. 36. Eiectmn energy loss spectra of a clean Sif 1 I I)7 X 7 surface and after exposure to atomic hydrogen. The eiectron impact energy was 7.3 eV. The small hump on the spectrum of the clean surface around 900 cm’ is caused by a small carbon contamination. From Ref. [78].
868
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Fig. 37. Photoemission spectra of the Si( 11I)7 x 7 snrface. (a) Energy ~s~bution curve for electrons emitted in the surface normal direction: A, 8 bulk state photoelectrons (their energetical position is primary energy dependent), C, D, E surface state photoelectrons. (b) Angle resolved photoemission for different polar angles in a plane 22” from the (112) direction. From Ref. [So].
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Fig. 38. (a) Normal photoemission spectra of Si(l11)7 x 7 for s and ppolarized light (hw = 52 eV). (b) Normal photoemission spectra of Si(l I I)7 X 7 for ppoiarized light of different energies. (c) Angie resolved photoemission spectra of Si( 111) for ppolarized li&t (hw = 52 eV) and different polar angles in the (2 11) plane. From Ref. [82].
The electronic structure of semiconductor (a)
Fig. 39. (a) Chadi model for the 7 x 7 surface of Si( 111). @) The hexagonal symmetry of the surface atoms around the comer atom of the unit cell. Raised and lowered surface atoms are represented by open and tilled circles respectively. From Ref. [45’J.
all the experimental findings. Dynamical LEED intensity calculations, self consistent band structure calculations and an improvement of the scanning tunneling microscopy technique should be done to clear the situation.
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