Studies of Positron-Surface Interactions in Semiconductors
Using Positron Annihilation Induced Auger Electron
Spectroscopy
a,b
N. G. Fazleev,
a
J. L. Fry, and A. H. Weiss
a
a
Department of Physics, Box 19059, University of Texas at Arlington,
Arlington, Texas 76019-0059, USA
b
Department of Physics, Kazan State University, Kazan 420008, Russian Federation
Abstract. A surface sensitive technique, Positron-Annihilation-Induced Auger-Electron Spectroscopy (PAES), is
becoming a powerful tool available for studies of positron surface phenomena and characterization of semiconductor
surfaces. In this paper the results of studies of Si(111) and GaAs(100) surfaces using PAES are analyzed by
performing quantum mechanical calculations of positron surface states and annihilation characteristics for the
reconstructed Si(111)-(7×7) surface and for both As- and Ga-rich (100) surfaces of GaAs with c(2×8), (2×4), and
c(4×4) reconstructions. Estimates of the positron binding energy, work function, and annihilation characteristics
reveal their sensitivity to surface reconstruction and chemical composition of the topmost layers of semiconductors.
Calculations show that the positron is getting trapped at the corner hole sites of the reconstructed Si(111)-(7×7)
surface. It is shown that comparison of theoretical positron annihilation probabilities computed for different
reconstructed GaAs(100) surfaces with experimental ones estimated from the measured Auger peak intensities
permits identification of the chemical composition of the topmost layers of the GaAs(100) surface.
quantum mechanical calculations including discretelattice effects of the positron surface states, work
functions, and annihilation characteristics. These
calculations are performed for both As- and Ga-rich
non-reconstructed and reconstructed GaAs(100)
surfaces with c(2×8), (2×4), c(4×4) reconstructions,
and for the non-reconstructed and reconstructed
Si(111)-(7×7) surfaces. Theoretical annihilation
probabilities of the surface trapped positrons with
relevant core electrons computed for the GaAs(100)
and Si(111) surfaces are compared with the ones
estimated from experimental Auger peak intensities.
Previous calculations of the positron surface and bulk
states and annihilation characteristics were performed
for the non-reconstructed Si and GaAs surfaces [3,4].
INTRODUCTION
Recently the GaAs(100) and Si(111) surfaces
have become the subject of experimental studies using
positron annihilation induced Auger electron
spectroscopy (PAES) [1]. In PAES experiments, most
of the low-energy positrons implanted into the sample
under study diffuse back to the vacuum-solid interface
and are trapped in an image-correlation potential well
at the surface [1,2]. A certain fraction of the surface
trapped positrons annihilate with neighboring core
electrons, creating core-hole excitations and initiating
Auger processes. The measured high-resolution PAES
spectrum from GaAs(100) displays six As and three
Ga Auger peaks corresponding to M4,5VV, M2M4V,
M2,3M4,5M4,5 Auger transitions for As and
M2,3M4,5M4,5 Auger transition for Ga. The highresolution PAES spectrum from Si(111) displays the
Si Auger peak corresponding to the L2,3VV Auger
transition. The Auger peak intensities were used to
obtain experimental annihilation probabilities for each
core level. We analyze PAES data by performing
EXPERIMENTAL DETAILS
The PAES measurements were made on the
high resolution PAES spectrometer at the University
of Texas at Arlington. Details of the high resolution
PAES system have been reported elsewhere [5]. The
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
509
GaAs(100) sample (n-type, Si doping level ~ 1×1018
cm−3) and the Si(111) sample were etched in a 50%
solution of hydrofluoric acid (HF) and de-ionized
water before mounting in the sample chamber. Both
samples were sputtered with 3 keV argon ions. The
GaAs(100) and Si(111) samples were annealed
respectively to 450°C and 550°C before each data
collection cycle. The samples were maintained at a
pressure of 2×10-10 – 4×10-10 Torr during data
collection. Their cleanliness was monitored using
EAES that showed no measurable carbon or oxygen
contamination of the surface over the period of time
required for data acquisition in each cycle. By
controlling the sputtering time and annealing
temperature, the surface structure and composition
were kept consistent for each data collection cycle.
EAES was also used to monitor the As M45VV / Ga
M23M45M45 peak-to-peak ratio to determine the
stoichiometry of the first few layers of atoms of the
GaAs(100) sample. A 20-minute sputtering and 10minute annealing cycle was found to result in an
As/Ga EAES peak to peak ratio of 1.6 + 0.2, which
remained consistent over the total period of PAES
data collection.
0.8
(E) As M23M45V
(A) As M45VV
arbitrary units
0.6
(B) As M23M45M45
(D) Ga M23M45V
(C) Ga M23M45M45
0.4
0.2
As Ga
As
As
0
0
10
20
30
40
50
60
70
80
90 100 110
Electron Energy (eV)
FIGURE 1. PAES spectrum from the GaAs(100) surface
with the dark count, gamma-ray induced, and low energy
tail backgrounds removed. The secondary electron cutoff is
at Ek = 10 eV, the positron beam energy. The sample bias
was +1.5 V.
0.03
RESULTS AND DISCUSSION
Experiment. The background of the PAES
data (due to detector dark counts and gamma ray
induced counts) was measured and subtracted from
the raw data. Backgrounds due to Auger electrons that
have lost energy as they exit the surface have also
been subtracted. The Auger spectra were obtained
with the 10 eV positron beam with a sample bias of Vs
= 1.5 V and are shown in Figs. 1 and 2. The
GaAs(100) Auger spectrum displays six As peaks and
three Ga peaks below 110eV corresponding to
M4,5VV, M2M4V, M2,3M45M45 Auger transitions for
As and M2,3M4,5M4,5 Auger transition for Ga. Several
Auger peaks from each element of GaAs result from
annihilation of the same core level. The primary
Si(111) Auger peak at 90 eV corresponds to the Si
L2,3VV Auger transition. The measured peak
intensities of Auger transitions are used to calculate
experimental annihilation probabilities of relevant
core electrons, pn,l, by considering the ratio of the
integrated intensities of the peaks resulting from
Auger transitions involving the selected core level to
the secondary electron yield obtained on the same
apparatus at the same time.
counts / second
0.02
0.01
0
-0.01
0
10 20 30 40 50 60 70 80 90 100 110 120
Electron Energy (eV)
FIGURE 2. PAES spectrum from the Si(111) surface with
the dark count, gamma-ray induced, and low energy tail
backgrounds removed.. The secondary electron cutoff is at
Ek = 10 eV, the positron beam energy. The sample bias was
+1.5 V.
The integrated intensities were obtained by summing
the counts under each peak in the background
subtracted data and dividing by the average energy of
the peak to take into account the energy dependence
of the cylindrical mirror analyzer (CMA). Also
considered in the calculations are the relative solid
510
angle of acceptance and transmission efficiency of the
spectrometer and the positronium fraction, i. e., the
number of trapped positrons that form positronium
and are thus unavailable to annihilate with core
electrons [6]. Estimates of the experimental pn,l for
the As 3d, 3p, and Ga 3p core level electrons are
given in Tables I and II. Estimates of the sum of
experimental pn,l for the Si 2s and 2p core level
electrons give 0.80 %.
Theory. Positron surface states and
annihilation characteristics for GaAs(100) were
calculated for the ideally terminated nonreconstructed (100) surface consisting of a single
element in the topmost layer, As and Ga, respectively,
and for both As- and Ga-rich c(2×8), (2×4), and
c(4×4) surface reconstructions of the GaAs(100)
surface. Calculations for the Si(111) surface were
performed for the non-reconstructed surface and the
7×7 reconstruction. Discrete-lattice effects were taken
into account within a modified superimposed-atom
method [7]. Atomic calculations were performed self
consistently
within
the
local-spin-density
approximation [8] using the exchange-correlation
functional from Ceperley and Alder [9]. To account
for effects of the charge redistribution at the surface,
we used the method of Weinert and Watson [10].
Following this method we placed Ga, As, and Si
atoms in a "compensating" potential well of 0.27, –
0.27, and –0.15 Ry, respectively, extending from the
atom center out to one Wigner-Seitz radius and then
linearly ramping to a value of 0.00 Ry at twice the
Wigner-Seitz radius and beyond. Atomic wave
functions then provided the overlapping electron
densities and corresponding electron-positron
potential at the semiconductor surface via Poisson's
equation. Electron-positron correlation was included
by using a corrugated image potential in the vacuum
and a local density approximation inside the surface
[4,7]. With these approximations it is possible to treat
both perfect and reconstructed surfaces. Positron
surface states were obtained by solving Schrödinger’s
equation numerically with the boundary condition that
the positron wave function vanishes sufficiently far
into the bulk or the vacuum. The positron work
function, Φp, was calculated for the GaAs(100)
surfaces with the positron potential used in surface
state calculations by imposing periodic boundary
conditions deep inside the surface and assuming k=0
to be the lowest Bloch state. The computed binding
energies for a positron trapped at the As- and Ga-rich
GaAs(100) surfaces, Eb, and positron work functions,
Φp, are given in Tables I and II, respectively.
TABLE I. Theoretical positron binding energy, Eb, positron work function, Φp, and annihilation probability
of the surface trapped positron with core electrons for the As-rich GaAs(100) surface.
System
Eb (eV)
(theory)
Φp (eV)
(theory)
GaAs(100) non-reconstructed
GaAs(100)-c(2×8) reconstructed
GaAs(100)-(2×4) reconstructed
GaAs(100)-c(4×4) reconstructed
GaAs(100)-Experiment
2.63
2.55
2.58
2.59
-0.69
-1.17
-0.95
-0.68
-0.603
Annihilation probability (%)
Core level
As 3p
As 3d
Ga 3p
0.50
1.63
0.08
0.43
1.30
0.18
0.36
1.15
0.16
0.66
2.06
0.04
0.51
0.92
0.33
Ga 3d
0.37
0.76
0.71
0.16
TABLE II. Theoretical positron binding energy, Eb, positron work function, Φp, and annihilation probability
of the surface-trapped positron with core electrons for the Ga-rich GaAs(100) surface.
System
Eb (eV)
(theory)
Φp (eV)
(theory)
GaAs(100) non-reconstructed
GaAs(100)-c(2×8) reconstructed
GaAs(100)-(2×4) reconstructed
GaAs(100)-c(4×4) reconstructed
GaAs(100)-Experiment
1.76
1.76
1.80
1.39
-0.69
-0.66
-0.17
-0.74
-0.603
511
Annihilation probability (%)
Core level
As 3p
As 3d
Ga 3p
0.06
0.18
0.53
0.39
1.18
0.15
0.33
1.06
0.14
0.02
0.07
0.50
0.51
0.92
0.33
Ga 3d
2.27
0.62
0.61
2.22
TABLE III. Theoretical and experimental positron binding energies, Eb, and positron surface-state and
bulk lifetimes, τ .
System
Eb (eV)
(theory)
Eb (eV)
(experiment)
Si(111) non-reconstructed
Si(111)-(7×7) reconstructed
Cu(111)
2.54
2.70
2.797
2.69(7)2
2.69(7)2
2.80(5)7
τ (ps)
surface-state
(theory)
650
486
5027
τ (ps)
bulk-state
(theory)
219
219
1097
TABLE IV. Theoretical and experimental positron annihilation probabilities with relevant Si core electrons, pn,l
at the non-reconstructed and reconstructed Si(111) -(7×7) surfaces.
System
Level
non-reconstructed Si(111)
reconstructed Si(111)-(7×7)
Si 2s
0.55
0.15
pn,l (%)
(theory with γLDA)
Si 2p
1.62
0.45
These values are comparable to Eb computed
for the (100) surfaces of Si and Ge [4,11]. As it
follows from Tables I and II the computed values of
the binding energy Eb of the surface-trapped positrons
show sensitivity to the surface structure and chemical
composition of the topmost layers of the reconstructed
GaAs(100) surface.
pn,l (%)
(experiment)
Si 2s+2p
0.80
0.80
Si 2s+2p
2.17
0.60
surfaces. As it follows from Fig. 4 the (7×7)
reconstruction of the Si(111) surface changes
significantly the behavior of the positron at the
surface: the positron is found to be localized in the
XY plane in the corner holes of the reconstructed
Si(111)-(7×7) surface.
-21.70
-17.47
-9.98
-13.23
-5.14
-9.00
-0.30
-4.76
-0.53
4.54
3.70
9.38
7.94
14.21
12.17
16.41
20.64
Z (a.u.)
FIGURE 3. Contour plot of the calculated positron surface
state wave function at the non-reconstructed Si(111) surface
in the X-Z plane for Y=0. Vacuum is at the left. Contours
are separated by 0.002 atomic units.
24.88
Z(a.u.)
FIGURE 4. Contour plot of the positron surface state wave
function at the reconstructed Si(111)-(7×7) surface in the XZ plane for Y=0. Vacuum is at the left. Contours are
separated by 0.004 atomic units.
It follows from Fig. 3 that for the nonreconstructed Si(111) surface the computed positron
surface state wave function extends in the XY plane
of the semiconductor surface and is localized in the Z
direction mostly on the vacuum side of the topmost
layer of Si atoms, as in the case of transition metal
The computed binding energies Eb for a positron
trapped at Si(111) surfaces are given in Table III.
512
These values are comparable to Eb computed for the
surfaces of Cu [7].
Probability of annihilation of surface trapped
positrons with an electron in a specific core level pn,l
characterized by the quantum numbers n and l, is
obtained by dividing the positron annihilation rate
λn,l, by the total positron annihilation rate λ
calculated using the Local Density Approximation
(LDA): pn,l=λn,l/λ [4]. Theoretical pn,l are given in
Tables I, II, and IV. As it follows from Tables I and
II, the computed annihilation probabilities of the As
3d, 3p and Ga 3d, 3p core electrons are found to be
sensitive to reconstruction and chemical composition
of the top layers of the GaAs(100) surface.
Experimental Φp and pn,l for the As 3d, 3p, and Ga
3p core electrons estimated from the labeled peak
intensities in Fig. 1 are equal to -0.60 eV, 0.51%,
0.92%, and 0.33%, respectively. It follows from
Tables I and II that the experimental results agree best
with Φp and pn,l for the As 3d, 3p, and Ga 3p core
electrons computed for the Ga-rich reconstructed
GaAs(100)-c(2×8) surface: -0.66 eV, 0.39%, 1.18%,
and 0.15%, respectively. A comparison of theoretical
and experimental values for pn,l from Table IV
suggests that theoretical pn,l are also quite sensitive to
the reconstruction of the Si(111) surface due to the
different behavior of the positron surface state wave
function. It also follows from Table IV that the sum of
theoretical pn,l for the Si 2s and 2p core electrons
calculated with the enhancement factor γ within LDA,
0.60%, agrees with the sum of annihilation
probabilities for the Si 2s and 2p core electrons,
0.80%, estimated from the PAES intensity.
positron surface states and annihilation characteristics
have been presented and compared to experimental
results. The computed binding energy of the surfacetrapped positron, positron work function, and positron
annihilation probabilities with the As 3d and 3p and
Ga 3d and 3p core electrons have been found to be
sensitive to the reconstruction and composition of the
topmost layers of GaAs(100). Thus, a comparison of
annihilation probabilities of surface-trapped positrons
with relevant core electrons computed for different
reconstructed As- and Ga-rich surfaces with the ones
estimated from the labeled peak intensities of Auger
transitions helps to identify the chemical composition
of the top layers of the GaAs(100) surface.
The computed binding energy of the surface
trapped positrons and annihilation probabilities of the
Si 2s and 2p core electrons have been also found to be
sensitive to the reconstruction of the Si(111) surface,
reflecting differences in the localization and extent of
the positron surface state wave function at
semiconductor surfaces with different structure of the
topmost layers. Theoretical annihilation probabilities
of the Si 2s and 2p core electrons calculated for the
reconstructed Si(111)-(7×7) surface have been found
to agree with the estimates of probabilities obtained
from the experimental PAES spectrum.
ACKNOWLEDGMENTS
This work was supported in part by The
National Science Foundation and The Robert A.
Welch Foundation.
REFERENCES
1.
2.
CONCLUSIONS
3.
The high-resolution PAES spectrum from a
compound semiconductor, GaAs(100) displays six As
and three Ga Auger peaks below 110eV. The Auger
spectrum from the Si(111) surface displays an Auger
signal corresponding to the LVV Auger transition for
Si. Annihilation probabilities have been estimated for
the As 3d, 3p, Ga 3p, and Si 2s and 2p core electrons
from the measured Auger peak intensities. PAES data
have been analyzed by performing first-principles
calculations of positron surface states and annihilation
characteristics for the non-reconstructed and
reconstructed Si(111)-(7×7) surface and for both Asand Ga-rich non-reconstructed and reconstructed
(100) surfaces of GaAs with c(2×8), (2×4), and c(4×4)
reconstructions. The results of quantum mechanical
calculations including discrete lattice effects of the
4.
5.
6.
7.
8.
9.
10.
11.
513
Weiss, A. H., Materials Sci. Forum 105-110, 511-520 (1992).
Schultz, Peter J., and Lynn, K. G., Rev. Mod. Phys.60,
701-779 (1988).
Fazleev N. G., Starnes S., Weiss A. H., Fry J. L., Radiation
Physics and Chemistry 58, 667-673 (2000).
Fazleev, N. G., Kuttler, K. H., Fry, J. L., and Weiss,
A. H., Appl. Surf. Sci. 116, 304-310 (1996).
Yang, S., Zhou, H. Q, Jung, E., Citrin, P. H., and Weiss,
A. H., Rev. Sci. Instrum. 68, 3893-3897, (1997).
Weiss, A. H., Yang, S., Zhou, H., Jung, E., and Wheeler, S.,
J. Electron Spectrosc. Relat. Phenom. 72, 305-309 (1995).
Fazleev, N. G., Fry, J. L., Kuttler, K., Koymen, A. R.,
and Weiss, A.H., Phys. Rev. B 52, 5351-5363 (1995).
Gunnarsson, O., and Lundqvist, B. I., Phys. Rev. B 13,
4276-4298 (1976).
Ceperley, D. M., and Alder, B. J., Phys. Rev. Lett. 45,
566-569 (1980).
Weinert, M., and Watson, R. E., Phys. Rev. B 29,
3001-3008 (1984).
Fazleev, N. G., Fry, J. L., and Weiss, A. H.,
Materials Sci. Forum 255-257, 145-149 (1997).