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Partial charge injection from surface and adsorbate states into semiconductor space charge layers
Surface Science 95 (1980) 431-446 0 North-Holland Publishing Company
PARTIAL CHARGE INJECTION FROM SURFACE AND ADSORBATE INTO SEMICONDUCTOR SPACE CHARGE LAYERS
STATES
W. LORENZ and C. ENGLER Sektion Chemie, Karl-Marx-hive&&,
Leipzig, GDR
Received 7 December 1979; accepted for publication 28 January 1980
Chemisorption processes on semiconductor interfaces are generally coupled with partial charge injection into a space charge layer. A computational approach of this phenomenon is closely related to the problem of discriminating surface and space charges on semiconductors. We report on the present state of model computations of partial charge injection, based on a local density of states treatment of semiconductor surfaces and on a superposition approximation of local chemical states and macroscopic band bending. Relation to macroscopic dynamic theory of interface reactions is indicated. As examples, ideal and (1 x 1) reconstructed GaAs(ll0) surfaces and chemisorption of a Li atom are discussed in some detail.
1. Introduction The quantummechanical appearance of partial charges on atoms or molecules has, in spite of their approximate definition, essential influence on the macroscopic formulation of chemical species and chemical reactions in condensed systems and on interfaces considered
[l].
Partial
charge
in electrochemical
transfer, kinetics
in its macroscopic of metal
electrodes
consequences,
at first
with the beginning
six-
In electrochemical kinetics, potentially all reactions over adsorbed intermediates and most of the related measuring methods are concerned; experimental data are up to now available mostly on mercury electrodes. On semiconductor interfaces, partial charge transfer has recently been taken into consideration for electrochemical processes as well as for surface photoeffects [2]. A further topic being concerned is chemisorption from gas phase and semiconductor catalysis of gas reactions. The very point in all these cases is that specific types of partial charge transfer enter into measurable macroscopic charge balance expressions and therewith into macroscopic behaviour. A survey of the different types of partial charge transfer coefficients (I, h, m) appearing in the theory of interfacial processes has been given in ref. [ 11. In order to define chemical species in condensed systems on the quantummechanical level, “local” potential surfaces of molecular subsystems interacting with their environment can be introduced under the condition of electron delocalities, can occur
on several
types
of chemical
431
elementary
processes.
432
W. Lorenz, C, EnglerfPartial charge injection
zation over the entire system [3]. We consider here especially “electronic open” molecular subsystems on a semiconductor surface. Local densities of states have proved to be most favourable for expressing local charges. A process generally coupled with chemisorption on semiconductor surfaces is partial charge injection into a space charge layer. In what follows we use this term in a somewhat generalized sense for all processes for which partial charges can be separately attributed to a surface subsystem, e.g. a molecular chemisorption complex, and an environmental space charge layer subjected to one-electron statistics. The present paper deals with a more detailed exploration of partial charge injection phenomena.
2. Approximate separation of semiconductor surface and space charges Separation of semiconductor surface and space charges can be achieved approximately by supposing the following conditions * : (a) Local densities of states of a semiconductor host lattice are supposed to be not substantially influenced by doping. Doping can then be simulated by fixing the Fermi energy EF within the bulk band gap of the semiconductor host lattice. (b) The Fermi energy at the surface is determined by the band bending fpSCin the semiconductor space charge layer. pSCis related to the space charge QsC. (c) Owing the electroneutrality, QSCis complementary to the surface charge qSS. Requiring superposition of the local chemical state and macroscopic band bending in the space charge layer **, qSS can simply be obtained by integrating local densities of states at surface sites of the semiconductor host lattice up to EF.
3. Computation of ideal and (1 X 1) reconstructed GaAs( 110) surfaces
For the following computations, we have adopted a bond orbital (BO) model including bonding and antibonding orbitals (valence and conduction band) for IV and III-V semiconductors, in connection with a local expansion (recursion) method [6] for determination of the Green matrix and local densities of states at bulk, surface and adsorbate sites. Local densities n(E ,c) are derived from n(E, c) = --rr-l Im G,(E) , with G, = (c IG ]c) = diagonal elements of a Green matrix G(E) = (E1 -H)-’
(1)
in
* These conditions are implicit also in corresponding considerations of recent photoemission studies [4]. The problem of surface and space charge separation derives from early semiconductor surface concepts [S]. ** This corresponds to the usual decomposition of the electrochemical potential into a chemical and an electrical part.
W. Lorenz, C. Engler/Partial charge injection
433
bond orbital representation; c = bonding or antibonding BO. The computational approach has been outlined in ref. [7a] and extensively proved on Si and GaAs bulk, (111) and (110) surfaces and some small adsorbates [7b]. The follo~ng data refer to GaAs(1 lo), with inclusion of (1 X 1) reconstruction and chemisorption of a Li atom. G(E) and n(E, c) have been calculated within a cluster of 11000 interacting orbitals. The parametrization of the Green matrix has been performed by adjustment of bulk BO matrix elements to empirical pseudopotential band structure, with subsequent determ~ation of the surface BO and dangling bond (hybrid) matrix elements of the substrate. Determination of adsorbate parameters follows orbital-theoretical methods. Matrix elements of one bond, the first, and the second neighbour interactions are denoted by (Y,0, y. All computations of this paper have been carried through with a somewhat improved parameter set obtained by optimized adjustment of 5 bulk bonding and 5 bulk antibon~ng matrix elements to respectively 5 points of bulk valence band structure and 8 points of conduction band structure, from pseudopotential calculations after ref. [S]. (BO interband matrix elements have been neglected in the following calculations. For a proof of the influence of these elements on Si, cf. ref. [7b] ,) Valence band structure has been expressed in terms of BO parameters, e.g., in refs. [9,10]; inclusion of the conduction band is str~~tfo~ard. In order to arrive at BO matrix elements for the GaAs(llO) surface, bulk elements CY, 0, y have been decomposed into hybrid matrix elements. For Q!elements this decomposition is unique if the polarity (ionicity) of the anion-cation bond is given. Because the remaining 8 bonding and antibonding elements p, y are to be replaced by 14 hybrid elements (denoted S), the resulting indeterminateness has been removed by supposing the hybrid interactions at the same atom to be constants, and the other hybrid interactions to be proportional to hybrid overlap S and the mean value of the involved hybrid 01integrals
(2) with 6 different const~ts K for 6 types of interactions. Overlap integrals have been computed with Slater AO’s. Thus the 8 bulk elements 0, y are straightforwardly expressed by hybrid terms. Subsequently, the BO parameters for an ideal surface have been determined. Interaction elements between BO’s and dangling bond hybrids have been constructed by using bulk hybrid parameters, the constituting equations assumed to be the same as in the analogous bulk case. For (1 X 1) reconstructed (relaxed) GaAs(ll0) surface we have applied structural data from ref. [l la]. (After ref. [ll], on (1 X 1) reconstructed GaAs(llO), the As atoms are displaced about 0.1-0.25 A outward, and the Ga atoms about 0.55-0.45 A inward from their ideal positions.) The change of the angular arrangement of surface atoms yields a change of the s and p character of the hybrids and
434
W. Lorenz, C. EngIer/Partial charge injection
the hybrid (Yintegrals have correspondingly been recalculated. Ideal sp3 hybridization has been set up already for the second layer of atoms (the resulting misfit of hybrid directions of the first and second atomic layer is small), With eq. (2) one obtains 6reconstr --6,Ideal
_ S reconstr
sideal
%wmtr zide&
-
5.4 *
5.4
(3)
(The energy zero point for all a! elements is the valence band edge. The terms -5.4 eV in eqs. (3) and (4) allow for the difference of the valence band edge and the vacuum level for GaAs.) The procedure so far described is denoted by (I). In a second procedure (II), not being based on overlap proportionalities, the mentioned indeterminateness of bulk 6 elements has been removed by some simplifications. For reconstructed surface, the S have then been set proportional to i/d”, with d = bond length [ 121. Instead of (3) one now gets s reconstr --m
_
dieal
= ijireccmk
-
5.4
(4) 5.4 ’ Values of the main BO matrix elements thus obtained are summarized in table 1. Herewith somewhat different ionicities of the GaAs bond have been set up. Band structure data aIlow indeed some variation of ionicity because (a) the choice of ionicity is less definite than the adjustment of BO’s to band structure, and (b) pseudopotential charge density maps do not fully correspond to hybrid charge densities constructed with Slater orbitals. Two values of the spectroscopic ionicity after refs. [13,14] have been put up: fi = 0.34 and 0.21; this corresponds to a polarity after refs. [9,10] of or, = 0.50 and 0.38 (the BO polarity parameter X used in ref. [7a] is related to or,; the last value of 01~corresponds to TB data from ref. [ 151). We note that the larger fi or oP, the more positive (negative) comes out the hybrid CY integral of the cation (anion). 6
ideal
d&onstr
Olideal -
4. LocaI densities of states and surface charge on ideal and (1 X 1) ~~onst~cted GaAs( 110)
Figs. l-5 show local densities of states computed with BO parameters after table 1. The largest contributions to GaAs surface charge result from dangling bond hy brid densities on the anion and cation which cancel each other to a great part, however, whereas the back bond and parallel bond densities contribute each only a small amount (
W. Lorenz, C. Engler/Partial charge injection
435
Table 1 Parameters for GaAs Bulk parameters ab
(independent
7b,trans ‘ya
Ya,trans Parametrization Ionicity olD
of ionicity)
-4.98 0.31 6.18 -0.51
Ph(As)
-1.83
7b.cis
-0.05
PatAs) Ya,cis
-0.89 0.28
procedure
Pb(Ga)
-1.09
fla(Ga)
-0.80
(1) 0.50
(11) 0.50
(1) 0.38
ah&)
-2.19
%@a) Pbh(Ga) Ybh,trans(As) Ybh,cis(As) ‘Ybh,trans(Ga) Ybh,cis(Ga) Yhh,cis Pah(As) Pah(Ga)
3.39 -1.73 -0.51 0.36 -0.18 0.78 -0.44 -0.56 -0.88 0.67
-2.19 3.39 -2.03 -1.29 0.38 -0.09 0.81 -0.30 -0.40 -1.21 1.12
-1.52 2.12 -1.65 -0.71 0.39 -0.19 4.66 -0.36 -0.51 -0.70 0.73
SaE$r;trg) Yih’trans(Ga) Tab :cis(Ga)
-0.88 0.54 0.54 -0.36
-0.91 0.41 0.55 -0.29
-0.77 0.48 0.55 -0.40
q&As)
4.94
-5.53
q,(Ga)
4.11 -2.04 5.04 -6.05 6.11 -4.01 5.90
4.71 -1.99 5.31 -8.42 1.45 -3.76 5.92
-4.01 3.51 -2.12 4.96 -6.43 6.30 4.17 5.80
Ideal (I 10) surface
flbh(As)
(I XI) reconstmcted
Back bond on As Back bond on Ga Parallel bond
(110) surface
“b Ola “b &a Qb aa
Additionally, there occur 25 p and 7 integrals between BO’s and dangling bonds, and 38 ints grals between BO’s of the reconstructed surface For signification of (Y,p and 7, see text. Indices a, b and h: bonding BO, antibonding BO and dangling bond hybrid, respectively. (As) and (Ga) denote the localization of interacting BO’s or of dangling bond hybrids. AU values are given in eV.
where a is the area of a GaAs surface site. The sum is to be extended over orbitals which contribute noticeably to surface charge. For n-type semiconductors EF=%-e~,,, where Et
psck 0, is the Fermi level at the surface in absence of band bending.
(6) The space
W. Lorenz, C. EnglerfPartialcharge injection
436
-v.
-9
-6
0
-3
+9
Fig. 1. Local densities of states at (1 X 1) reconstructed GaAs(l10). Parameter set (I),orp = 0.50. For designations, see table below. Ordinate: local density (states eV_‘); abscissa: energy (eV>. (a) Dangling bond on As (b) Dangling bond on Ga (e) Back bond on Ga (d) Back bond on As Band gap ranges from E = 0 to E = 1.4 eV.
(c) Parallel bond (f) Bulk bond orbital
Curve
Surface
Parameter set
&P
1 2 3 4
Ideal Ideal (1 x 1) reconstructed (1 x 1) reconstructed
(I) (I) (I) (I)
0.50 0.38 0.50 0.38
charge
for the common
Schottky
case of depletion
formula
Q,, = k%e(ND
- NA) Cpscl 112
and weak inversion
is given by the Mott-
431
W. Lorenz, C. Engler/Partialcharge injection 2
405
(a)
cb)
v
Fig. 2. Local densities of states at GaAs(ll0)
i
:
in the band gap range (enlarged scale). For designa-
tions, see table below fig. 1. Ordinate: local density (states eV-‘); abscissa: energy (eV). Fig. 3. Local densities of states at GaAs(ll0) in the band gap range (enlarged scale). For designations, see table below fig. 1. Ordinate: local density (states eV-‘); abscissa: energy (eV).
(positive for n-type semiconductor;ND, NA = donor or acceptor density). The relation of qss and Qsc has already been considered in ref. [S]. What has been changed now is the basic formulation of surface charge in terms of local partial charges. Using data from table 1, surface and space charges in dependence of band bending are shown in fig. 6. Electroneutrality requires Qsc = +ss, being fulfilled at the crossing points of curves 1 and 2 of fig. 6.
I
I
-l,o
0;5
0
+0,5
+(O
+$5
+&a
E
Fig. 4. Local densities of states at GaAs(ll0)
-{cl
-0,s
0
+0,5 ‘f,O E
in the band gap range (enlarged scale).
+/5
For de&a-
tions, see table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (eV). Fig. 5. Local densities of states at GaAs(ll0) in the band gap range (enlarged scale). For designations, see table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (eV).
l+2,0
W. Lorenz, C. Engler/Partial charge injection
438
I +
0,lO ..
4a
I.
‘**
+4@-,
4b -/c ----
+0,06..
fd _.._ ,e -.-
+O,W--
‘F -
/v
+0,02-,
/
0 -y2
:
.5’,.‘;...*-;‘_:_
o/y 0,s ,J’
: ,/ .‘.,‘O$’ .,. ,/”
_..
,
/
I,0
E
$4
$2
I’
Fig. 6. Surface and space charges on GaAs(ll0). Curves 1: -qssa/e
after eq. (5)
Curve
Surface
Parameter set
la lb lc Id le If
Ideal Ideal Ideal (1 x 1) reconstructed (1 X 1) reconstructed (1 X 1) reconstructed
(I) (II) (I) (I) (II) (I)
Curves 2: Q,ca/e
after eq. (7)
Curve
ND - NA ( cmv3)
Supposed Ef (eV)
2a 2b
101’ 10’9
1.36 1.43
0.50 0.50 0.38 0.50 0.50 0.38
W. Lorenz,
C. EnglerJPartial charge injection
439
5. Discussion Figs. l-5 give an account of the influence of details of parametrization, of surface reconstruction, and of ionicity on computed local densities of states. For our problems as shortly outlined in the introduction, the local densities at surface sites are important. Fig. 1 gives an overview of relevant densities. Variations of local charges with Fermi energy are determined by local densities in the band gap range which are shown for the main local orbitals in figs. 2-5 on an enlarged scale. We can at first state that the optimized parametrization described in section 3 delivers much smaller densities of states in the band gap range than a non-optimized parametrization applied in ref. [7b] ; this holds already for ideal GaAs(ll0). Comparison of the curves 1.4 of figs. 2-5 shows that the densities at ideal and at (1 X 1) reconstructed surface differ, but not dramatically. On reconstructed surfaces, very low densities of states in accordance with experimental tindings have already been stated in recent calculations: cf. refs. [12,16], and references given therein. Inspection of figs. 2-5 shows indeed that the curves 3 are mostly the lowest ones, in agreement with the above statements. At this place we should point out that the remaining density of states in the band gap range in all cases shown is very small, corresponding to some 1012 up to 1013 states per cm2: this purely theoretical result based essentially on band structure adjustment is not too far from upper limits derived from experimental data, e.g., ref. [ 181. Another point to be mentioned is the ionicify of the Ga-As bond: its variation as considered in figs. 2-5 has a rather moderate influence on local densities. With increasing ionicity the resulting hybrid densities of states are slightly shifted upwards and downwards from the band gap. Although not yet all points are settled it seems that even for very low ionicity similar densities are obtainable [ 161. Comparison of curves 1 to 2 and 3 to 4 of figs. 2-5 shows that the mentioned ionicity shift of local densities is somewhat greater for ideal than for reconstructed surface, but in all cases quite small. The lower the densities of states at surface sites in the band gap range, the flatter become the curves 1 of fig. 6. Thus, the influence of space charge curves 2 on the surface Fermi level increases, at least at high doping. In curves 1 of fig. 6, likewise a comparison of parametrization procedures (I) and (II) of section 3 is included. We have mostly preferred procedure (I), developed in section 3, which is based on overlap proportionalities after eq. (2) in order to determine interaction matrix elements 0, y at surfaces from bulk matrix elements. Procedure (II) has been applied also in literature, e.g. ref. [12]. From fig. 6 we get an estimate of the influence of these parametrization procedures. Another point to be deduced from fig. 6 is the variatiod of the surface Fermi level EF with semiconductor doping. It should again be remembered that the curves 1 have been determined theoretically by adjustment to band structure. Clamping of EF by surface charge is increasingly removed, the larger the doping level ND or (ND -NA). (One should notice that the bulk electron density of an n-type semiconductor is considerably smaller at high doping than ND, and
440
W. Lorenz, C. EnglerjPartial charge injection
that the No values used in fig. 6 are far below the upper possible doping limit. Eq. (7) supposes complete ionization, especially of the donors in the depletion layer; incomplete ionization will be allowed for at a later stage of development.) The results discussed so far give a sufficiently sound basis for the subsequent calculations of single atom chemisorption on semiconductor surfaces.
6. Local densities of states: Li atom adsorbed on GaAs(ll0) Now, we pass on to the main part of the present paper in which chemisorption of one Li atom attached to As on GaAs(ll0) will be treated. In order to obtain directly the local charges on Li and on the bonding hybrid on As, both orbitals have been set up separately (alternatively a bond orbital can be combined). The cuintegral of Ii 2s has been set equal to the ionization potential, a.02 eV. The Li-As bond length has been estimated to be 2.9 A. Calculation of interaction integrals with the adsorbate has been performed by applying procedure (I), eq. (2), with the same K values for different interaction types as before. This is in a first approxima-
Fig. 7. Local densities of states: chemisorbed Li atom attached to As on (1 X 1) reconstructed GaAs(ll0). Parameter set (I), ap = 0.50. (a) Adsorbate orbital; (b) bonding hybrid on As; (c) parallel bond; (d) back bond next to the adsorbate. Ordinate: local density (states eV_‘); abscissa: energy (eV).
441
W. Lorenz, C. EnglerlPartial charge injection
tion justified by orbital-theoretical arguments. Further refinement would require adjustment of adsorption energy which is not available so far. Parametrization of molecular adsorbates and local potential surfaces in the Green function formalism has been treated in ref. [ 171, and is applied in subsuquent calculations. The following Li atom-substrate interactions have been allowed for: the 0 integral of the adorbital with the bonding hybrid on As; the yCiSintegral with the neighbouring dang ling bond on Ga (all subsequent matrix elements both bonding (b) and antibonding (a)): two different fl integrals with the first neighbour parallel bond and with the first neighbour back bond on As; two rds integrals with the second neighbour parallel bond in the surface and in the second atomic layer; two Ttrans integrals with the second neighbour back bond on Ga of the first atomic layer and on Ga of the second atomic layer. Results on local densities of the adsorbed Li atom, of the bonding hybrid on As,
4
o;lo
408
?
rb,
I I
2 :
3
i ::: I
Fig. 8. Local densities of states: chemisorbed Li atom attached to As on ideal and reconstructed GaAs(ll0). Band gap range, enlarged scale. (a) Adsorbate orbital, (b) bonding hybrid on As. Designation of curves 14 as in table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (ev).
442
W. Lorenz, C. Engler/Partial charge injection
of the neighbouring parallel bond and back bond on As are shown in fig, 7, and the first two densities once more in the band gap range on an enlarged scale and including different parametrizations in fig. 8. Computations have been performed for both the ideal and (1 X 1) reconstructed surface, using ionicities of the Ga-As bond as in section 3. Comparison of curves (b, c, d) of fig. 7 with the corresponding curves (a, c, d) of fig. 1 shows how the density curves are influenced by the chemisorption process. From fig. 8. analogous to figs. 2-5, effects of parametrization can again be deduced in greater detail. Local densities of the neighbouring parallel bond and back bond on As (fig. 7) are in~uenced by the adsorbate but the resulting local charges at these sites remain nearly the same as before (cf. table 3); the differences are somewhat greater on the reconstructed surface. Local densities of the dangling bond and back bond on Ga next to the adsorbate are not significantly changed.
7. Chemisorption-induced
partial charge injection
At low coverage with adsorbate atoms, the total surface charge per cm2 is not noticeably changed by chemisorption. Thus, the Fermi level EF on the surface remains near the crossing points of fig. 6. Assuming this EF also for the adsorbate, the change of local charges on all surface sites induced by chemisorption is obtainable. The complement of this non-integral charge is injected into the space charge layer. We have therewith gained a model approach of the partial charge injection coefficient m which enters into macroscopic charge balance expressions of semiconductor surface processes [l-3]. The local charge on a GaAs surface site with an attached Li atom has been calculated in table 2 in the low-coverage limit. Q(S) signifies the sum of charges over the mentioned sites which contribute to surface charge, relative to the charge per GaAs surface site without adsorbate. Q(,Sz) signifies the local charge on the adsorbed Li atom alone. Referring to ref. 1, the present example belongs to a negative partial charge injecticn into a depletion layer, and a coefficient m may be defmed as m = Q@s)
63)
In table 3, the components of Q(S) are separately given for two parameter sets. One recognizes that the main contribution to Q(S) comes from the diminishment of the negative charge of the bonding hybrid on As to which the Li atom is attached. The change of the Fermi energy at higher coverage and its reaction on the coefficient m can str~~tfo~ardly be obtained_ In fig. 9, a typical dependence of the surface Fermi level EF and of the coefficient m is plotted over adsorption density, under the supposition that the adsorbates can be considered to be ‘“isolated” up to medium coverage: this is supported by the very small lateral interactions of the adsorbates established in ref. [7b] and the present example also. The above computations give not yet full account of the conditions of Li+ ion
W. Lorenz, C. Engler/Partial charge injection
443
Table 2 Computed charges Q(fl and Q(&) for low coverage of Li, attached to As on GaAs(ll0) Surface
QQb
f?cs2>
0.81 0.54 0.85 0.71
0.5 0.76 0.81 0.82
0.11 0.215 0.135 0.145
0.52 0.20 0.52 0.21
0.88 0.90 0.89 0.92
0.325 0.34 0.21 0.27
EF~ (eV)
Ideal
0.5 0.38
(1 X 1) reconstructed
0.5 0.38
a The values given for EF correspond to a doping level ND of about lo1 ’ and 10’ ‘, respectively. b The reference for Q(s) is the surface charge without adsorbate per GaAs site, which amounts in the given range ofND and EP to about -0.030 to -0.002.
adsorption
from
solution
on a GaAs electrode,
the electrode
case, the quantities
which
enter
m = 1 - QQ
and h = 1 - Q(s,),
cf. refs.
because
of neglect
into macroscopic
of solvation. charge
[ 1,3]. Corresponding
balance
For are
data are in prepara-
tion. With view to the next section,
Table 3 Local charge components
we notice
shortly
the effect
of a shift of
EF at
of Q(5)
Surface
Ideal
(1 X 1) reconstructed
Ionicity ep
0.50
0.50
Surface Fermi energy EF (eV)
0.87
0.52
With adsorbate Li 2s Bonding hybrid on As Neighbouring bond orbitals Parallel bond a Back bond on As Dangling bond on Ga Back bond on Ga Total
Without adsorbate
0.109 -0.366
0 -0.794
-0.015 0.034 0.837 -0.034 0.550
-0.024 0.028 0.834 -0.040 -0.020
a There are two parallel bonds per GaAs(ll0)
surface site.
With adsorbate 0.325 -0.435 0.022 0.070 0.839 0.008 0.851
Without adsorbate 0 -0.890 -0.028 0.076 0.840 0.002 -0.028
the
W. Lorenz, C. EnglerjPartial charge injection
444
G
i
48 46
B-t
Fig, 9. Dependence of surface Fermi level ,!?F (eV) and of Q(S) = m on Li adsorption density I’ (mol cmw2); c+, = 0.50, ND - NA = 10’ 9; (a) ideal, (b) reconstructed surface.
adsorbate. @(&)/=F From
The corresponding = 24%
82)
chargeshift on the adsorbate
is
-
fig. 7, its value can be estimated
to be of the order of magnitude
0.05-l
eV-‘_
8. Charge-dependentparametrization and influence of a Helmholtz potential drop We add yet some general remarks on possible influences of a charge-dependence of Hamiltonian diagonal elements, and of a microscopic counterpart of the Helmholtz potential drop at the interface. Charge-dependent parametrization has been considered already [7b,17] but without definitive results so far in the present context. We note however that it leads generally to an interaction of the local chemical state at surface sites and macroscopic band bending. There is no difficulty of principle to include a charge dependence into the plots of fig. 6 which may now be attainable by iteration.
W. Lorenz, C. Engler/Partialcharge injection
445
The other question regards the m&roscopic expression of what is formulated in macroscopic dynamical models the potential drop over a Helmholtz plane. In microscopic models, any surface double layer structure contributes to the local Hamiltonian. This raises involved questions and one is forced to introduce approximations. A very simple one is to include a surface potential step into diagonal elements of the local Hamiltonian, or just more simply: to neglect any double layer contribution to the Hamiltonian and to introduce a step of the Fermi level at the surface which could be adjusted semiempirically. The effect on local charges at adsorbates may qualitative be the same as with charge-dependent Hamiltonian. On free semiconductor/vacuum (or gas) surfaces, hints to surface dipolar layers from photoemission data [4,18] are so far rather uncertain. On metal/solution (electrode) interfaces, on the lines of the above approximations, a possible dependence on electrode potential of the partial charge transfer coefficients X has been estimated to be mostly small. Semiconductor/solvated adsorbate studies are forthcoming and the points made in this section will be further proved.
9. Summary The aim of this paper was a further investigation of the possibilities for quanturnmechanical computation of partial charge transfer coefficients which appear in the macroscopic dynamical theory of semiconductor surface processes. We have chosen at first GaAs for that purpose because of the availability of band structure and surface reconstruction data, and of its similarity to GaP which provides well suited semiconductor electrodes for experimental work. The following main results have been gathered: (a) The orbital approach of large semiconductor/adsorbate systems in local density of states representation, with optimized adjustment to empirical pseudopotential band structure, offers possibilities for theoretical determination of partial charge transfer coefficients m and h. (b) For unsolvated Li atom adsorption attached to As on ideal or (1 X 1) reconstructed GaAs(1 lo), the presented computations point to a negative partial charge injection into a depletion layer, with first data on m = Q(S) given in section 7. Several extensions of this work are in progress.
References [l] W. Lorenz, Z. Chem. 18 (1978) 288; Electrochim, Acta 2$ (1980), in press. Chem. 259 (1978) 1173; Electiochim. Acta 25 (1980), in press. [3] W. Lorenz, Z. Physik. Chem. 260 (1979) 241. [4] W. Eberhardt, G. Kalkofen, C. Kunz, D. Aspnes and M. Cardona, Phys. Status Solidi (b) 88 (1978) 135.
[ 21 W. Lorenz and M. Handschuh, Z. Physk
446
W. Lorenz, C. Engler/Partial charge injection
[S] J. Bardeen, Phys. Rev. 71 (1947) 717; J. Bardeen and S.R. Morrison, Physica 20 (1954) 873. [6] R. Haydock, V. Heine and I&J. Kelly, J. Phys. C8 (1975) 2591. [‘7] (a) C. Engler and W. Lorenz, 2, Pbysik. Chem. 261 (1980) 122. (b) C. Engler and W. Lorenz, Z. Physik. Chem. 261 (X980) 92. [8] J. Chelikowsky and M.L. Cohen, Phys. Rev. B14 (1976) 556. [9] W.A. Harrison, Phys. Rev. B8 (1973) 4483; W.A. Harrison and S. Ciraci, Phys. Rev. BlO (1974) 1516. [lo] ST. Pantelides and W.A. Harrison, Phys. Rev. Bll (1975) 3006. [ ll] (a) A. Kahn, G. Cisneros, M. Bonn, P. Mark and C.B. Duke, Surface Sci. 71 (1978) 387. (b) M.A. Van Hove, Surface Sci. 81 (19’79) 1. [ 121 D.J. Chadi, Phys. Rev. B18 (1978) 1800. [ 131 J.C. Phillips and J.A. Van Vechten, Phys. Rev. Letters 22 (1969) 705. [14] J.C. PhiBips, Rev. Mod. Phys. 42 (1970) 317. [15] D.J. Chadi and M.L. Cohen, Phys. Rev. Bll(1975) 732. [16} E.J. Mele and J.D. Joannopoulos, Phys. Rev. B17 (1978) 1816. [ 171 W. Lorenz, C. Engler and M. Kretschmer, Z. Physik. Chem. 260 (1979) 881. 1183 A. Huijser and J. van Laar, Surface Sci. 52 (1975) 202; R.H. Williams, R.D. Varma and A. McKinley, 3. Phys. Cl0 (1977) 454.5.
PARTIAL CHARGE INJECTION FROM SURFACE AND ADSORBATE INTO SEMICONDUCTOR SPACE CHARGE LAYERS
STATES
W. LORENZ and C. ENGLER Sektion Chemie, Karl-Marx-hive&&,
Leipzig, GDR
Received 7 December 1979; accepted for publication 28 January 1980
Chemisorption processes on semiconductor interfaces are generally coupled with partial charge injection into a space charge layer. A computational approach of this phenomenon is closely related to the problem of discriminating surface and space charges on semiconductors. We report on the present state of model computations of partial charge injection, based on a local density of states treatment of semiconductor surfaces and on a superposition approximation of local chemical states and macroscopic band bending. Relation to macroscopic dynamic theory of interface reactions is indicated. As examples, ideal and (1 x 1) reconstructed GaAs(ll0) surfaces and chemisorption of a Li atom are discussed in some detail.
1. Introduction The quantummechanical appearance of partial charges on atoms or molecules has, in spite of their approximate definition, essential influence on the macroscopic formulation of chemical species and chemical reactions in condensed systems and on interfaces considered
[l].
Partial
charge
in electrochemical
transfer, kinetics
in its macroscopic of metal
electrodes
consequences,
at first
with the beginning
six-
In electrochemical kinetics, potentially all reactions over adsorbed intermediates and most of the related measuring methods are concerned; experimental data are up to now available mostly on mercury electrodes. On semiconductor interfaces, partial charge transfer has recently been taken into consideration for electrochemical processes as well as for surface photoeffects [2]. A further topic being concerned is chemisorption from gas phase and semiconductor catalysis of gas reactions. The very point in all these cases is that specific types of partial charge transfer enter into measurable macroscopic charge balance expressions and therewith into macroscopic behaviour. A survey of the different types of partial charge transfer coefficients (I, h, m) appearing in the theory of interfacial processes has been given in ref. [ 11. In order to define chemical species in condensed systems on the quantummechanical level, “local” potential surfaces of molecular subsystems interacting with their environment can be introduced under the condition of electron delocalities, can occur
on several
types
of chemical
431
elementary
processes.
432
W. Lorenz, C, EnglerfPartial charge injection
zation over the entire system [3]. We consider here especially “electronic open” molecular subsystems on a semiconductor surface. Local densities of states have proved to be most favourable for expressing local charges. A process generally coupled with chemisorption on semiconductor surfaces is partial charge injection into a space charge layer. In what follows we use this term in a somewhat generalized sense for all processes for which partial charges can be separately attributed to a surface subsystem, e.g. a molecular chemisorption complex, and an environmental space charge layer subjected to one-electron statistics. The present paper deals with a more detailed exploration of partial charge injection phenomena.
2. Approximate separation of semiconductor surface and space charges Separation of semiconductor surface and space charges can be achieved approximately by supposing the following conditions * : (a) Local densities of states of a semiconductor host lattice are supposed to be not substantially influenced by doping. Doping can then be simulated by fixing the Fermi energy EF within the bulk band gap of the semiconductor host lattice. (b) The Fermi energy at the surface is determined by the band bending fpSCin the semiconductor space charge layer. pSCis related to the space charge QsC. (c) Owing the electroneutrality, QSCis complementary to the surface charge qSS. Requiring superposition of the local chemical state and macroscopic band bending in the space charge layer **, qSS can simply be obtained by integrating local densities of states at surface sites of the semiconductor host lattice up to EF.
3. Computation of ideal and (1 X 1) reconstructed GaAs( 110) surfaces
For the following computations, we have adopted a bond orbital (BO) model including bonding and antibonding orbitals (valence and conduction band) for IV and III-V semiconductors, in connection with a local expansion (recursion) method [6] for determination of the Green matrix and local densities of states at bulk, surface and adsorbate sites. Local densities n(E ,c) are derived from n(E, c) = --rr-l Im G,(E) , with G, = (c IG ]c) = diagonal elements of a Green matrix G(E) = (E1 -H)-’
(1)
in
* These conditions are implicit also in corresponding considerations of recent photoemission studies [4]. The problem of surface and space charge separation derives from early semiconductor surface concepts [S]. ** This corresponds to the usual decomposition of the electrochemical potential into a chemical and an electrical part.
W. Lorenz, C. Engler/Partial charge injection
433
bond orbital representation; c = bonding or antibonding BO. The computational approach has been outlined in ref. [7a] and extensively proved on Si and GaAs bulk, (111) and (110) surfaces and some small adsorbates [7b]. The follo~ng data refer to GaAs(1 lo), with inclusion of (1 X 1) reconstruction and chemisorption of a Li atom. G(E) and n(E, c) have been calculated within a cluster of 11000 interacting orbitals. The parametrization of the Green matrix has been performed by adjustment of bulk BO matrix elements to empirical pseudopotential band structure, with subsequent determ~ation of the surface BO and dangling bond (hybrid) matrix elements of the substrate. Determination of adsorbate parameters follows orbital-theoretical methods. Matrix elements of one bond, the first, and the second neighbour interactions are denoted by (Y,0, y. All computations of this paper have been carried through with a somewhat improved parameter set obtained by optimized adjustment of 5 bulk bonding and 5 bulk antibon~ng matrix elements to respectively 5 points of bulk valence band structure and 8 points of conduction band structure, from pseudopotential calculations after ref. [S]. (BO interband matrix elements have been neglected in the following calculations. For a proof of the influence of these elements on Si, cf. ref. [7b] ,) Valence band structure has been expressed in terms of BO parameters, e.g., in refs. [9,10]; inclusion of the conduction band is str~~tfo~ard. In order to arrive at BO matrix elements for the GaAs(llO) surface, bulk elements CY, 0, y have been decomposed into hybrid matrix elements. For Q!elements this decomposition is unique if the polarity (ionicity) of the anion-cation bond is given. Because the remaining 8 bonding and antibonding elements p, y are to be replaced by 14 hybrid elements (denoted S), the resulting indeterminateness has been removed by supposing the hybrid interactions at the same atom to be constants, and the other hybrid interactions to be proportional to hybrid overlap S and the mean value of the involved hybrid 01integrals
(2) with 6 different const~ts K for 6 types of interactions. Overlap integrals have been computed with Slater AO’s. Thus the 8 bulk elements 0, y are straightforwardly expressed by hybrid terms. Subsequently, the BO parameters for an ideal surface have been determined. Interaction elements between BO’s and dangling bond hybrids have been constructed by using bulk hybrid parameters, the constituting equations assumed to be the same as in the analogous bulk case. For (1 X 1) reconstructed (relaxed) GaAs(ll0) surface we have applied structural data from ref. [l la]. (After ref. [ll], on (1 X 1) reconstructed GaAs(llO), the As atoms are displaced about 0.1-0.25 A outward, and the Ga atoms about 0.55-0.45 A inward from their ideal positions.) The change of the angular arrangement of surface atoms yields a change of the s and p character of the hybrids and
434
W. Lorenz, C. EngIer/Partial charge injection
the hybrid (Yintegrals have correspondingly been recalculated. Ideal sp3 hybridization has been set up already for the second layer of atoms (the resulting misfit of hybrid directions of the first and second atomic layer is small), With eq. (2) one obtains 6reconstr --6,Ideal
_ S reconstr
sideal
%wmtr zide&
-
5.4 *
5.4
(3)
(The energy zero point for all a! elements is the valence band edge. The terms -5.4 eV in eqs. (3) and (4) allow for the difference of the valence band edge and the vacuum level for GaAs.) The procedure so far described is denoted by (I). In a second procedure (II), not being based on overlap proportionalities, the mentioned indeterminateness of bulk 6 elements has been removed by some simplifications. For reconstructed surface, the S have then been set proportional to i/d”, with d = bond length [ 121. Instead of (3) one now gets s reconstr --m
_
dieal
= ijireccmk
-
5.4
(4) 5.4 ’ Values of the main BO matrix elements thus obtained are summarized in table 1. Herewith somewhat different ionicities of the GaAs bond have been set up. Band structure data aIlow indeed some variation of ionicity because (a) the choice of ionicity is less definite than the adjustment of BO’s to band structure, and (b) pseudopotential charge density maps do not fully correspond to hybrid charge densities constructed with Slater orbitals. Two values of the spectroscopic ionicity after refs. [13,14] have been put up: fi = 0.34 and 0.21; this corresponds to a polarity after refs. [9,10] of or, = 0.50 and 0.38 (the BO polarity parameter X used in ref. [7a] is related to or,; the last value of 01~corresponds to TB data from ref. [ 151). We note that the larger fi or oP, the more positive (negative) comes out the hybrid CY integral of the cation (anion). 6
ideal
d&onstr
Olideal -
4. LocaI densities of states and surface charge on ideal and (1 X 1) ~~onst~cted GaAs( 110)
Figs. l-5 show local densities of states computed with BO parameters after table 1. The largest contributions to GaAs surface charge result from dangling bond hy brid densities on the anion and cation which cancel each other to a great part, however, whereas the back bond and parallel bond densities contribute each only a small amount (
W. Lorenz, C. Engler/Partial charge injection
435
Table 1 Parameters for GaAs Bulk parameters ab
(independent
7b,trans ‘ya
Ya,trans Parametrization Ionicity olD
of ionicity)
-4.98 0.31 6.18 -0.51
Ph(As)
-1.83
7b.cis
-0.05
PatAs) Ya,cis
-0.89 0.28
procedure
Pb(Ga)
-1.09
fla(Ga)
-0.80
(1) 0.50
(11) 0.50
(1) 0.38
ah&)
-2.19
%@a) Pbh(Ga) Ybh,trans(As) Ybh,cis(As) ‘Ybh,trans(Ga) Ybh,cis(Ga) Yhh,cis Pah(As) Pah(Ga)
3.39 -1.73 -0.51 0.36 -0.18 0.78 -0.44 -0.56 -0.88 0.67
-2.19 3.39 -2.03 -1.29 0.38 -0.09 0.81 -0.30 -0.40 -1.21 1.12
-1.52 2.12 -1.65 -0.71 0.39 -0.19 4.66 -0.36 -0.51 -0.70 0.73
SaE$r;trg) Yih’trans(Ga) Tab :cis(Ga)
-0.88 0.54 0.54 -0.36
-0.91 0.41 0.55 -0.29
-0.77 0.48 0.55 -0.40
q&As)
4.94
-5.53
q,(Ga)
4.11 -2.04 5.04 -6.05 6.11 -4.01 5.90
4.71 -1.99 5.31 -8.42 1.45 -3.76 5.92
-4.01 3.51 -2.12 4.96 -6.43 6.30 4.17 5.80
Ideal (I 10) surface
flbh(As)
(I XI) reconstmcted
Back bond on As Back bond on Ga Parallel bond
(110) surface
“b Ola “b &a Qb aa
Additionally, there occur 25 p and 7 integrals between BO’s and dangling bonds, and 38 ints grals between BO’s of the reconstructed surface For signification of (Y,p and 7, see text. Indices a, b and h: bonding BO, antibonding BO and dangling bond hybrid, respectively. (As) and (Ga) denote the localization of interacting BO’s or of dangling bond hybrids. AU values are given in eV.
where a is the area of a GaAs surface site. The sum is to be extended over orbitals which contribute noticeably to surface charge. For n-type semiconductors EF=%-e~,,, where Et
psck 0, is the Fermi level at the surface in absence of band bending.
(6) The space
W. Lorenz, C. EnglerfPartialcharge injection
436
-v.
-9
-6
0
-3
+9
Fig. 1. Local densities of states at (1 X 1) reconstructed GaAs(l10). Parameter set (I),orp = 0.50. For designations, see table below. Ordinate: local density (states eV_‘); abscissa: energy (eV>. (a) Dangling bond on As (b) Dangling bond on Ga (e) Back bond on Ga (d) Back bond on As Band gap ranges from E = 0 to E = 1.4 eV.
(c) Parallel bond (f) Bulk bond orbital
Curve
Surface
Parameter set
&P
1 2 3 4
Ideal Ideal (1 x 1) reconstructed (1 x 1) reconstructed
(I) (I) (I) (I)
0.50 0.38 0.50 0.38
charge
for the common
Schottky
case of depletion
formula
Q,, = k%e(ND
- NA) Cpscl 112
and weak inversion
is given by the Mott-
431
W. Lorenz, C. Engler/Partialcharge injection 2
405
(a)
cb)
v
Fig. 2. Local densities of states at GaAs(ll0)
i
:
in the band gap range (enlarged scale). For designa-
tions, see table below fig. 1. Ordinate: local density (states eV-‘); abscissa: energy (eV). Fig. 3. Local densities of states at GaAs(ll0) in the band gap range (enlarged scale). For designations, see table below fig. 1. Ordinate: local density (states eV-‘); abscissa: energy (eV).
(positive for n-type semiconductor;ND, NA = donor or acceptor density). The relation of qss and Qsc has already been considered in ref. [S]. What has been changed now is the basic formulation of surface charge in terms of local partial charges. Using data from table 1, surface and space charges in dependence of band bending are shown in fig. 6. Electroneutrality requires Qsc = +ss, being fulfilled at the crossing points of curves 1 and 2 of fig. 6.
I
I
-l,o
0;5
0
+0,5
+(O
+$5
+&a
E
Fig. 4. Local densities of states at GaAs(ll0)
-{cl
-0,s
0
+0,5 ‘f,O E
in the band gap range (enlarged scale).
+/5
For de&a-
tions, see table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (eV). Fig. 5. Local densities of states at GaAs(ll0) in the band gap range (enlarged scale). For designations, see table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (eV).
l+2,0
W. Lorenz, C. Engler/Partial charge injection
438
I +
0,lO ..
4a
I.
‘**
+4@-,
4b -/c ----
+0,06..
fd _.._ ,e -.-
+O,W--
‘F -
/v
+0,02-,
/
0 -y2
:
.5’,.‘;...*-;‘_:_
o/y 0,s ,J’
: ,/ .‘.,‘O$’ .,. ,/”
_..
,
/
I,0
E
$4
$2
I’
Fig. 6. Surface and space charges on GaAs(ll0). Curves 1: -qssa/e
after eq. (5)
Curve
Surface
Parameter set
la lb lc Id le If
Ideal Ideal Ideal (1 x 1) reconstructed (1 X 1) reconstructed (1 X 1) reconstructed
(I) (II) (I) (I) (II) (I)
Curves 2: Q,ca/e
after eq. (7)
Curve
ND - NA ( cmv3)
Supposed Ef (eV)
2a 2b
101’ 10’9
1.36 1.43
0.50 0.50 0.38 0.50 0.50 0.38
W. Lorenz,
C. EnglerJPartial charge injection
439
5. Discussion Figs. l-5 give an account of the influence of details of parametrization, of surface reconstruction, and of ionicity on computed local densities of states. For our problems as shortly outlined in the introduction, the local densities at surface sites are important. Fig. 1 gives an overview of relevant densities. Variations of local charges with Fermi energy are determined by local densities in the band gap range which are shown for the main local orbitals in figs. 2-5 on an enlarged scale. We can at first state that the optimized parametrization described in section 3 delivers much smaller densities of states in the band gap range than a non-optimized parametrization applied in ref. [7b] ; this holds already for ideal GaAs(ll0). Comparison of the curves 1.4 of figs. 2-5 shows that the densities at ideal and at (1 X 1) reconstructed surface differ, but not dramatically. On reconstructed surfaces, very low densities of states in accordance with experimental tindings have already been stated in recent calculations: cf. refs. [12,16], and references given therein. Inspection of figs. 2-5 shows indeed that the curves 3 are mostly the lowest ones, in agreement with the above statements. At this place we should point out that the remaining density of states in the band gap range in all cases shown is very small, corresponding to some 1012 up to 1013 states per cm2: this purely theoretical result based essentially on band structure adjustment is not too far from upper limits derived from experimental data, e.g., ref. [ 181. Another point to be mentioned is the ionicify of the Ga-As bond: its variation as considered in figs. 2-5 has a rather moderate influence on local densities. With increasing ionicity the resulting hybrid densities of states are slightly shifted upwards and downwards from the band gap. Although not yet all points are settled it seems that even for very low ionicity similar densities are obtainable [ 161. Comparison of curves 1 to 2 and 3 to 4 of figs. 2-5 shows that the mentioned ionicity shift of local densities is somewhat greater for ideal than for reconstructed surface, but in all cases quite small. The lower the densities of states at surface sites in the band gap range, the flatter become the curves 1 of fig. 6. Thus, the influence of space charge curves 2 on the surface Fermi level increases, at least at high doping. In curves 1 of fig. 6, likewise a comparison of parametrization procedures (I) and (II) of section 3 is included. We have mostly preferred procedure (I), developed in section 3, which is based on overlap proportionalities after eq. (2) in order to determine interaction matrix elements 0, y at surfaces from bulk matrix elements. Procedure (II) has been applied also in literature, e.g. ref. [12]. From fig. 6 we get an estimate of the influence of these parametrization procedures. Another point to be deduced from fig. 6 is the variatiod of the surface Fermi level EF with semiconductor doping. It should again be remembered that the curves 1 have been determined theoretically by adjustment to band structure. Clamping of EF by surface charge is increasingly removed, the larger the doping level ND or (ND -NA). (One should notice that the bulk electron density of an n-type semiconductor is considerably smaller at high doping than ND, and
440
W. Lorenz, C. EnglerjPartial charge injection
that the No values used in fig. 6 are far below the upper possible doping limit. Eq. (7) supposes complete ionization, especially of the donors in the depletion layer; incomplete ionization will be allowed for at a later stage of development.) The results discussed so far give a sufficiently sound basis for the subsequent calculations of single atom chemisorption on semiconductor surfaces.
6. Local densities of states: Li atom adsorbed on GaAs(ll0) Now, we pass on to the main part of the present paper in which chemisorption of one Li atom attached to As on GaAs(ll0) will be treated. In order to obtain directly the local charges on Li and on the bonding hybrid on As, both orbitals have been set up separately (alternatively a bond orbital can be combined). The cuintegral of Ii 2s has been set equal to the ionization potential, a.02 eV. The Li-As bond length has been estimated to be 2.9 A. Calculation of interaction integrals with the adsorbate has been performed by applying procedure (I), eq. (2), with the same K values for different interaction types as before. This is in a first approxima-
Fig. 7. Local densities of states: chemisorbed Li atom attached to As on (1 X 1) reconstructed GaAs(ll0). Parameter set (I), ap = 0.50. (a) Adsorbate orbital; (b) bonding hybrid on As; (c) parallel bond; (d) back bond next to the adsorbate. Ordinate: local density (states eV_‘); abscissa: energy (eV).
441
W. Lorenz, C. EnglerlPartial charge injection
tion justified by orbital-theoretical arguments. Further refinement would require adjustment of adsorption energy which is not available so far. Parametrization of molecular adsorbates and local potential surfaces in the Green function formalism has been treated in ref. [ 171, and is applied in subsuquent calculations. The following Li atom-substrate interactions have been allowed for: the 0 integral of the adorbital with the bonding hybrid on As; the yCiSintegral with the neighbouring dang ling bond on Ga (all subsequent matrix elements both bonding (b) and antibonding (a)): two different fl integrals with the first neighbour parallel bond and with the first neighbour back bond on As; two rds integrals with the second neighbour parallel bond in the surface and in the second atomic layer; two Ttrans integrals with the second neighbour back bond on Ga of the first atomic layer and on Ga of the second atomic layer. Results on local densities of the adsorbed Li atom, of the bonding hybrid on As,
4
o;lo
408
?
rb,
I I
2 :
3
i ::: I
Fig. 8. Local densities of states: chemisorbed Li atom attached to As on ideal and reconstructed GaAs(ll0). Band gap range, enlarged scale. (a) Adsorbate orbital, (b) bonding hybrid on As. Designation of curves 14 as in table below fig. 1. Ordinate: local density (states eV_‘); abscissa: energy (ev).
442
W. Lorenz, C. Engler/Partial charge injection
of the neighbouring parallel bond and back bond on As are shown in fig, 7, and the first two densities once more in the band gap range on an enlarged scale and including different parametrizations in fig. 8. Computations have been performed for both the ideal and (1 X 1) reconstructed surface, using ionicities of the Ga-As bond as in section 3. Comparison of curves (b, c, d) of fig. 7 with the corresponding curves (a, c, d) of fig. 1 shows how the density curves are influenced by the chemisorption process. From fig. 8. analogous to figs. 2-5, effects of parametrization can again be deduced in greater detail. Local densities of the neighbouring parallel bond and back bond on As (fig. 7) are in~uenced by the adsorbate but the resulting local charges at these sites remain nearly the same as before (cf. table 3); the differences are somewhat greater on the reconstructed surface. Local densities of the dangling bond and back bond on Ga next to the adsorbate are not significantly changed.
7. Chemisorption-induced
partial charge injection
At low coverage with adsorbate atoms, the total surface charge per cm2 is not noticeably changed by chemisorption. Thus, the Fermi level EF on the surface remains near the crossing points of fig. 6. Assuming this EF also for the adsorbate, the change of local charges on all surface sites induced by chemisorption is obtainable. The complement of this non-integral charge is injected into the space charge layer. We have therewith gained a model approach of the partial charge injection coefficient m which enters into macroscopic charge balance expressions of semiconductor surface processes [l-3]. The local charge on a GaAs surface site with an attached Li atom has been calculated in table 2 in the low-coverage limit. Q(S) signifies the sum of charges over the mentioned sites which contribute to surface charge, relative to the charge per GaAs surface site without adsorbate. Q(,Sz) signifies the local charge on the adsorbed Li atom alone. Referring to ref. 1, the present example belongs to a negative partial charge injecticn into a depletion layer, and a coefficient m may be defmed as m = Q@s)
63)
In table 3, the components of Q(S) are separately given for two parameter sets. One recognizes that the main contribution to Q(S) comes from the diminishment of the negative charge of the bonding hybrid on As to which the Li atom is attached. The change of the Fermi energy at higher coverage and its reaction on the coefficient m can str~~tfo~ardly be obtained_ In fig. 9, a typical dependence of the surface Fermi level EF and of the coefficient m is plotted over adsorption density, under the supposition that the adsorbates can be considered to be ‘“isolated” up to medium coverage: this is supported by the very small lateral interactions of the adsorbates established in ref. [7b] and the present example also. The above computations give not yet full account of the conditions of Li+ ion
W. Lorenz, C. Engler/Partial charge injection
443
Table 2 Computed charges Q(fl and Q(&) for low coverage of Li, attached to As on GaAs(ll0) Surface
QQb
f?cs2>
0.81 0.54 0.85 0.71
0.5 0.76 0.81 0.82
0.11 0.215 0.135 0.145
0.52 0.20 0.52 0.21
0.88 0.90 0.89 0.92
0.325 0.34 0.21 0.27
EF~ (eV)
Ideal
0.5 0.38
(1 X 1) reconstructed
0.5 0.38
a The values given for EF correspond to a doping level ND of about lo1 ’ and 10’ ‘, respectively. b The reference for Q(s) is the surface charge without adsorbate per GaAs site, which amounts in the given range ofND and EP to about -0.030 to -0.002.
adsorption
from
solution
on a GaAs electrode,
the electrode
case, the quantities
which
enter
m = 1 - QQ
and h = 1 - Q(s,),
cf. refs.
because
of neglect
into macroscopic
of solvation. charge
[ 1,3]. Corresponding
balance
For are
data are in prepara-
tion. With view to the next section,
Table 3 Local charge components
we notice
shortly
the effect
of a shift of
EF at
of Q(5)
Surface
Ideal
(1 X 1) reconstructed
Ionicity ep
0.50
0.50
Surface Fermi energy EF (eV)
0.87
0.52
With adsorbate Li 2s Bonding hybrid on As Neighbouring bond orbitals Parallel bond a Back bond on As Dangling bond on Ga Back bond on Ga Total
Without adsorbate
0.109 -0.366
0 -0.794
-0.015 0.034 0.837 -0.034 0.550
-0.024 0.028 0.834 -0.040 -0.020
a There are two parallel bonds per GaAs(ll0)
surface site.
With adsorbate 0.325 -0.435 0.022 0.070 0.839 0.008 0.851
Without adsorbate 0 -0.890 -0.028 0.076 0.840 0.002 -0.028
the
W. Lorenz, C. EnglerjPartial charge injection
444
G
i
48 46
B-t
Fig, 9. Dependence of surface Fermi level ,!?F (eV) and of Q(S) = m on Li adsorption density I’ (mol cmw2); c+, = 0.50, ND - NA = 10’ 9; (a) ideal, (b) reconstructed surface.
adsorbate. @(&)/=F From
The corresponding = 24%
82)
chargeshift on the adsorbate
is
-
fig. 7, its value can be estimated
to be of the order of magnitude
0.05-l
eV-‘_
8. Charge-dependentparametrization and influence of a Helmholtz potential drop We add yet some general remarks on possible influences of a charge-dependence of Hamiltonian diagonal elements, and of a microscopic counterpart of the Helmholtz potential drop at the interface. Charge-dependent parametrization has been considered already [7b,17] but without definitive results so far in the present context. We note however that it leads generally to an interaction of the local chemical state at surface sites and macroscopic band bending. There is no difficulty of principle to include a charge dependence into the plots of fig. 6 which may now be attainable by iteration.
W. Lorenz, C. Engler/Partialcharge injection
445
The other question regards the m&roscopic expression of what is formulated in macroscopic dynamical models the potential drop over a Helmholtz plane. In microscopic models, any surface double layer structure contributes to the local Hamiltonian. This raises involved questions and one is forced to introduce approximations. A very simple one is to include a surface potential step into diagonal elements of the local Hamiltonian, or just more simply: to neglect any double layer contribution to the Hamiltonian and to introduce a step of the Fermi level at the surface which could be adjusted semiempirically. The effect on local charges at adsorbates may qualitative be the same as with charge-dependent Hamiltonian. On free semiconductor/vacuum (or gas) surfaces, hints to surface dipolar layers from photoemission data [4,18] are so far rather uncertain. On metal/solution (electrode) interfaces, on the lines of the above approximations, a possible dependence on electrode potential of the partial charge transfer coefficients X has been estimated to be mostly small. Semiconductor/solvated adsorbate studies are forthcoming and the points made in this section will be further proved.
9. Summary The aim of this paper was a further investigation of the possibilities for quanturnmechanical computation of partial charge transfer coefficients which appear in the macroscopic dynamical theory of semiconductor surface processes. We have chosen at first GaAs for that purpose because of the availability of band structure and surface reconstruction data, and of its similarity to GaP which provides well suited semiconductor electrodes for experimental work. The following main results have been gathered: (a) The orbital approach of large semiconductor/adsorbate systems in local density of states representation, with optimized adjustment to empirical pseudopotential band structure, offers possibilities for theoretical determination of partial charge transfer coefficients m and h. (b) For unsolvated Li atom adsorption attached to As on ideal or (1 X 1) reconstructed GaAs(1 lo), the presented computations point to a negative partial charge injection into a depletion layer, with first data on m = Q(S) given in section 7. Several extensions of this work are in progress.
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[ 21 W. Lorenz and M. Handschuh, Z. Physk
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