Recent experiments have shown that the cation core excitons

on the (110) surface of many III-V semiconductors have very

large binding energies.(^1) They are sometimes reported to be bound by as much as ≳0.8 eV, tightly bound compared to

bulk binding energies of ≾0.1 eV. To explore this phenomenon, we have calculated the binding energies and oscillator strengths of core excitons on the (110) surface of GaAs, GaSb, GaP, and InP

Daw, M. S.

McGill, T. C.

Smith, D. L.

English

Caltech Authors - Main

Summary Abstract: Surface core excitons in 111-V 
semiconductors 
M. S. Daw, D. L. Smith, and T. C. McGill 
California Institute of Technology, Pasadena, California 91125 
(Received 18 March 1981; accepted 18 June 1981) 
PACS numbers: 71.35. + z, 73.20.Cw, 72.80.Ey 
Recent experiments have shown that the cation core excitons 
on the (llO) surface of many III-V semiconductors have very 
large binding energies. 1 They are sometimes reported to be 
bound by as much as ~0.8 eV, tightly bound compared to 
bulk binding energies of ;:50.1 eV. To explore this phenome-
non, we have calculated the binding energies and oscillator 
strengths of core excitons on the (llO) surface of GaAs, GaSh, 
GaP, and InP. 
At last year's PCSI conference, Wang and Joannopolous2 
presented their tight-binding calculation of Ga core excitons 
on the unrelaxed (llO) GaAs surface. This treatment used an 
unrealistic exciton potential and did not allow for surface 
relaxation which is known to push empty Ga derived surface 
states from the band gap into the band.3 With an inherently 
surface related excitation, it is important that one include 
surface relaxation so that the final state for the electron is 
described accurately. 
We present here a theoretical picture of anion and cation 
core excitons for III-V surfaces, using relaxed surface 
geometries. A qualitative picture serves to summarize our 
concept of surface core excitons. On the (llO) surface of Ill-
Y's there are two species of dangling bonds: the cation dan-
gling bond, which because of surface relaxation is mostly p 
(3% s) and is completely empty, and the anion dangling bond 
which is mostly sp3-hybrid and fully occupied. A dipole 
transition out of a cation d- or s-core level, for example, goes 
easily to the empty, p-type dangling bond on that atom. The 
electron in this final state is localized near the hole and the 
Coulombic attraction produces strong binding. The d- or s-
core excitation would have different transition energies, but 
closely similar binding energies because the potential due to 
a s-core hole is hardly different from that due to a d-core hole, 
as viewed by the excited electron. 
An excitation out of a surface cation p-core level would 
have the same binding energy as s- or d-core excitons, but this 
transition couples to the smalls-component of the dangling 
bond, reducing the oscillator strength by a factor of about 30 
from the cation d-core level transition. 
In the case of excitation out of the anion core, the on-site 
dangling bond is fully occupied and the electron must go to 
other unoccupied states, any of which are less localized. One 
would therefore expect less binding for surface anion core 
excitons than for the cation excitation. We thus find a sharp 
contrast between anion and cation surface core excitations. 
The presence of the dangling bonds causes surface core 
excitons to be markedly different from bulk4 or interface5 core 
excitons. The dangling bond state allows the localization of 
the electron not possible in bulk, producing the deeper 
binding. 
The quantitative calculations were based on a realistic 
tight-binding Hamiltonian for relaxed surface geometries. 
We employed a Koster-Slater approach, very similar to our 
previous surface vacancy calculations.3 The effective on-site 
potential is viewed as a shift in the atomic state energies of the 
excited surface atom, which is estimated from atomic calcu-
lations. Specifically, in the case of a Ga core excitation, for 
example, the potential is described by shifting the atomic 
levels on the Ga atom to the energy levels of a Ge atom. This 
reasonably assumes that the core hole resembles a positive 
charge added to the nucleus of the excited atom. The potential 
can be considered as effectively localized to one atom because 
in this region the potential goes as -e2/r, whereas for larger 
distances the screening by the rest of the solid dampens the 
potential to -e2 / fr, where f = 12 for GaAs, for example. In 
the bulk, the long-range part of the potential is important. For 
surface excitations, the binding energy is strongly determined 
by the short-range part. 6 
In Table I we present our results for binding energies and 
oscillator strengths. The cation p and d core excitations on 
GaAs, GaP, and InP are seen to be strongly bound. The Ga 
core excitations on GaSh are weakly bound with respect to the 
conduction band minimum. We find no binding for any of 
the anion core excitations; we find that these states occur in 
the conduction band. We also present the oscillator strengths 
relative to the d-core exciton for deeply bound excitons. In 
GaAs, GaP, and InP, we see that the cation p-core transition 
is more than an order of magnitude weaker than the cation 
d-core, though they have the same binding. This difference 
in magnitude reflects the small s-character of the cation 
dangling bond. 
Experimental values for the binding energies of the exci-
tations in the table are somewhat scattered. The values for Ga 
(3d) binding on GaSh vary by about 0.6 eV, for example.7 For 
this reason, we defer a detailed discussion and comparison 
with experiment to a longer publication. 6 In general, though, 
the calculated binding energies are in agreement with much 
of the reported data. 
Also, experimentally, the cation p-core excitons have not 
appeared, while the cation d-core excitons have been the ones 
to be reported; this is consistent with our evaluation of oscil-
lator strengths. 
Anion core excitons have not been reported except for a 
rather incomplete description by Bauer of an observed As(3p) 
exciton on GaAs with binding on the order of the band gap. 
388 J. Vac. Sci. Techno!., 19(3), Sept./Oct. 1981 0022-5355/81/030388-02$01.00 © 1981 American Vacuum Society 388 
389 Daw, Smith and McGill: Summary Abstract: Surface core excltons 389 
TABLE I. 
Material 
GaAs 
GaP 
GaSb 
InP 
Core 
level 
Ga(3p) 
Ga(3d) 
As (3p) 
As( 3d) 
Ga(3p) 
Ga(3d) 
P(2p) 
P(2d) 
Ga(3p) 
Ga(3d) 
Sb(4p) 
Sb(4d) 
ln(4p) 
In(4d) 
P(2p) 
P(2d) 
Binding 
energy 
(eV) 
0.9 
0.9 
2:::0.0 
2:::0.0 
0.8 
0.8 
::50.0 
::50.0 
::50.0 
::50.0 
::50.0 
::50.0 
0.6 
0.6 
::50.0 
::50.0 
Theory 
Relative 
oscillator 
strength 
(d = 100%) 
3% 
100% 
3% 
100% 
3% 
100% 
This observation contradicts our picture of surface core ex-
citons. For a surface As(3p) electron to be promoted to a 
dangling bond, it must wind up principally on the neighboring 
surface Ga dangling bonds, and the resulting separation be-
tween hole and electron is larger than in the case of a Ga core 
exciton where the electron can reside on the same atom as the 
hole. The resulting larger separation for the As excitation 
lowers the Coulombic interaction and, one would expect, also 
the binding energy. One would believe that the As exciton 
would have less binding, not more, than the Ga exciton. Also, 
J. Vac. Sci. Techno!., Vol. 19, No.3, Sept./Oct. 1981 
the selection rules valid for the cation excitation would not 
hold for the anion case because the latter transition involves 
states centered on separate sites. The reported As(3p) exciton 
is clearly in contradiction with this theory. Preliminary results 
from other experiments do not confirm Bauer's observa-
tion.8 
Our calculations are confirmed somewhat by calculations 
by Swarts et al. 9 in this volume. They calculate for clusters 
of surface atoms the transition energies of various core exci-
tations and the nature of the electron's final state. The anion 
excitation is less bound, in particular, than the cation exciton, 
in agreement with our results. 
We have presented a theoretical picture of anion and cation 
surface core excitons for III-V semiconductors. Cation d-core 
excitons are seen to generally have large binding with the 
cation p-core excitons having the same binding but lower 
oscillator strength. Anion core excitations are not seen to be 
bound. 
1R. S. Bauer, R. Z. Bachrach, S. A. Flodstrom, and J. C. McMenamin, J. Vac. 
Sci. Techno!. 14,378 (1977). J. van Laar, A. Huijser, and T. L. van Rooy, 
J. Vac. Sci. Technol. 14,894 (1977). W. Gudat and D. E. Eastman, J. Vac. 
Sci. Techno!. 13,831 (1976). D. E. Eastman, T. C. Chiang, P. Heimann, 
and F. J. Himpsel, Phys. Rev. Lett. 45, 656 (1980). 
2Y. Wang and J.D. Joannopoulos, J. Vac. Sci. Technol. 17,997 (1980). 
3M. S. Daw and D. L. Smith, Phys. Rev. B 20, 5150 (1979). 
4S. M. Kelso, D. E. Aspnes, C. G. Olson, D. W. Lynch, and D. Finn, Phys. Rev. 
Lett. 45, 1032 (1980). 
5H. P. Hjalmarson, R. E. Allen, H. Buttner, and J. D. Dow, J. Vac. Sci. 
Technol. 17,993 (1980). 
6M. S. Daw, D. L. Smith, and T. C. McGill (to be published). 
7The last three papers of Ref. I list Ga(3d) binding energies on (110) GaSh 
as 0.1 eV, R>0.1 eV, and ;::o.7 eV, respectively. 
BC. A. Swarts, W. A. Goddard, III and T. C. McGill, these proceedings. 
9P. Zurcher (private communication). 


Surface core excitons in III-V semiconductors

https://authors.library.caltech.edu/32549/1/DAWjvst81b.pdf

Surface core excitons in III-V semiconductors

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main

Caltech Authors - Main