Applied Surface Science 167 Ž2000. 12–17
www.elsevier.nlrlocaterapsusc
Work function change caused by alkali ion sputtering of
a sample surface
Yuriy Kudriavtsev ) , Rene Asomoza
Dep. Ingenieria Electrica-SEES, Centro de InÕestigacion y Estudios AÕanzados del IPN, AÕ. IPN a2508, Apdo Postal 14-740,
Mexico 14 D.F. 07300, Mexico
Received 20 January 2000; accepted 7 May 2000
Abstract
The steady state ion sputtering of a solid surface was studied. Based on a simple model, the surface concentration of ions
implanted during sputtering was calculated in the case of cesium ion sputtering of silicon. The corresponding work function
shift was calculated using the model developed. q 2000 Published by Elsevier Science B.V.
Keywords: Ion sputtering; Ion implantation; Work function
1. Introduction
During ion sputtering, a part of the primary ions
may be implanted into a near surface layer of the
bombarded target. In the case of alkali ion sputtering, such implantation leads to a change of the work
function of the target surface. A decrease of the work
function leads to an increase of negative ion emission. This effect is used in SIMS as a standard
method for the measurement of electronegative elements. According to a current theoretical model the
ionization probability of sputtered particles depends
on the work function F as follows
PyA exp y Ž F y A . r´n ,
Ž 1.
in the case of positive secondary ions. Here, IP is the
ionization potential, A is the electron affinity, ´ n
and ´ p are parameters which depend on the normal
component of the ion emission velocity w1x. So, for
interpretation of SIMS data, it is important to know
the real value of the work function.
It was experimentally demonstrated that the shift
of the work function is proportional to the surface
concentration of alkali atoms w2–4x. It is, however, a
difficult task to measure the real surface concentration of alkali atoms during alkali ion sputtering of
samples. This paper is devoted to a simple method
for calculation of the surface concentration of ions
implanted during sputtering as well as the corresponding change of the work function.
in the case of negative, and
PqA exp y Ž IP y F . r´ p ,
)
Ž 2.
2. Surface concentration of ions implanted into
target during sputtering
Corresponding author. Fax: q52-5747-7114.
E-mail address: [email protected] ŽY. Kudriavtsev..
The first step of our study was the calculation of
the surface concentration of the implanted projec-
0169-4332r00r$ - see front matter q 2000 Published by Elsevier Science B.V.
PII: S 0 1 6 9 - 4 3 3 2 Ž 0 0 . 0 0 3 8 1 - 0
Y. KudriaÕtseÕ, R. Asomozar Applied Surface Science 167 (2000) 12–17
tiles. Below, we present shortly the simple model
developed in Ref. w5x.
Two assumptions form this model.
Ž1. It is well known that the number of implanted
Žduring sputtering. ions may reach values around
10% Žrelative concentration. and it looks reasonable
to consider the near surface layer as a binary system
consisting of target atoms with a concentration of Ct
and implanted ions with a concentration of Ci . Hence,
it follows that we can describe the sputtering of this
layer as the sputtering of two component targets. The
total sputtering yield, in this case, is given by
Ytot s Yi q Yt ,
Ž 3.
where Yi and Yt are the partial sputtering yield of
implanted particles and target atoms, respectively.
The thickness of this layer is the result of a competition between ion implantation and ion sputtering.
Ž2. Under the steady state sputtering regime, the
number of primary ions irradiating the surface Ž jo .
becomes equal to the secondary flux of the same
particles due to scattering-jo R and resputtering-jo Yi
jo s jo R q jo Yi ,
Ž 4.
here R is the reflection coefficient.
For steady state sputtering, Patterson and Shirn w6x
developed the following equation
Yi
s
Yt
Civ
Ctv
,
Ž 5.
where C stands for concentration and the superscription v means AvolumeB Žsee below.. A combination
of the Eqs. Ž4. and Ž5. with the evident relation
Civ q Ctv s 1 leads to the equation for the relative
concentration of implanted particles
Civ f
b
Yt q b
,
Ž 6.
where b is the coefficient of accommodation: b s 1
y R.
It is well known that the sputtering of binary
systems is usually accompanied by the preferential
sputtering of one of the elements. As a result, the
binary layer, which we study, may be separated into
two AsublayersB with different compositions: the
AsurfaceB layer, which consist of approximately two
monolayers on top, and an undersurface layer. The
concentration of implanted projectiles in the under-
13
surface layer may be calculated using Eq. Ž6.
ŽAvolumeB concentration.. The AsurfaceB composition we calculated using well-known Andersen–
Sigmund equation w7x
Yi
s
Yt
Cis Mt
2m
Cts Mi
Ut
1y2 m
,
Ui
Ž 7.
here Uj and M j are the surface binding energy and
mass of the components, respectively; m is a parameter laying in the range from 0 to 1, whose value
depends on the primary ion energy. Combining Eqs.
Ž7. and Ž4., and taking into account that Cis q Cts s 1,
we can obtain the formula for the relative AsurfaceB
concentration of implanted projectiles
Cis f
b
Yt w MtrMi x
2m
w UtrUi x 1y2 m q b
.
Ž 8.
Note that we did not take into account the AsecondaryB effects like diffusion and segregation accompanying the sputtering. Now, concerning b , for
Mi ) Mt its value is close to 1 w5x.
We have used Eq. Ž8. for the calculation of the Cs
concentration at the silicon surface, during Cs ion
sputtering. Eq. Ž8. contains the sputtering yield of
the target atoms Yt . So, the next step of our approach
was the study of the energy dependence of the
sputter yield Yt .
We used the semi-empirical model of Yudin w8x.
According to this model, the sputtering yield is
inversely proportional to the mean path length of an
ion in the substrate between displacement collisions.
Yudin suggested an empirical formula for the stopping power as follows
Sn f
c'e
Ž 9.
dqe
where e is the reduced energy: e s EF, E is the
incident energy, c s 0.45 and d s 0.3 are empirical
constants and the ratio F is obtained by the following equation
F s 6.92 P 10 6 a tf
Mt
Zi Zt Ž Mi q Mt .
,
Ž 10 .
where Z j and M j are the atomic number and mass
of primary ions and target atoms, respectively; a tf
is the Thomas–Fermi screening length: a tf s
Y. KudriaÕtseÕ, R. Asomozar Applied Surface Science 167 (2000) 12–17
14
0.8853 A brŽ Zi2r3 q Zt2r3 .1r2 Žhere A b s 5.29 =
10y9 cm is the Born radius..
For normal ion incidence, Yudin derived the following formula for the sputtering yield
Yt s 2Ymax
(ErE
max
1 q ErEmax
,
Ž 11 .
where Emax s 0.3rF is the energy of the primary
ions at which the sputtering yield reaches its maximum value
Ymax s L Ž Zi ,Zt . Nps 2r Ž FUo . ,
Ž 12 .
here, N is the atomic concentration of the target,
s s p a 2tf is the screening cross-section, Uo is the
surface binding energy of the target. The coefficient
LŽ Zi ,Zt . has the following empirical dependence
Fig. 2. The surface and undersurface ŽAvolumeB . concentration of
cesium implanted in silicon as a function of the energy of primary
ions ŽCsq ..
L Ž Zi ,Zt . s L Ž Zt . y 4.65 P 10y1 2 Ž Zi y 18 . , Ž 13a .
considered normal incident of the projectiles. In the
case of other angles of incidence for our consideration Ž Mi 4 Mt ., the empirical formula derived in
Ref. w9x may be used
where
L Ž Zt . s 1.3 P 10y1 0 Zt0.5
ž
= 1 q 0.25sin 2p
Zt q Z
Zo
q pr2
/
Yt Ž u .
.
Ž 13b.
For Zt - 18, Zo s 8 and Z s 0; and for Zt ) 18,
Zo s 18 and Z s 2.
Fig. 1 shows the energy dependence of the sputter
yield of silicon under Csq ion bombardment. We
Fig. 1. The sputtering yield of silicon as a function of the primary
Csq ion energy, calculated using Yudin’s model for two angle of
incidence of the primary ions: 08 and 428 off to the normal
incidence.
Yt Ž 0 .
1
f
cos Ž u .
,
Ž 14 .
where u is the angle of incidence of primary ions
Žsee the second curve in Fig. 1..
The calculated energy dependence of the sputtering yield allows us to analyze the dependence of the
surface and undersurface concentration of implanted
projectiles on the primary ion energy. Fig. 2 demonstrates the energy dependence of the surface and
undersurface concentrations of Cs in the case of the
steady state sputtering of silicon by Csq ions. Following a common practice we used in our calculations ŽEq. Ž8.. the sublimation energy of element as
its surface binding energy. The surface concentration
of Cs is approximately two times less than undersurface concentration. The reason for this effect is a
very low surface binding energy of Cs Ž0.812 eV. in
comparison with Si Ž4.74 eV. w8x.
3. Change of work function due to ion implantation
The change of the work function of different
materials upon adsorption of alkali metals has been
Y. KudriaÕtseÕ, R. Asomozar Applied Surface Science 167 (2000) 12–17
Fig. 3. Schematic illustration of cesium atoms deposed on Ža., and
implanted into Žb. silicon target.
studied for a long period. A depolarization model of
Tooping w10x developed in 1927, based upon a depolarization field formed by the dipole moment of
adparticles, has frequently been used. According to
this model, the work function change DF depends
on the number of adparticles per unit surface area
Nad as follows w11x
DF s "
eNad po
´o Ž 1 q a 9Nad3r2 .
,
Ž 15 .
where e is the elementary charge, ´o is the permittivity of vacuum, po is the dipole moment of an
isolated adparticle, and a is the polarizability of the
adparticle. It was demonstrated in Ref. w12x that the
polarizability of the adparticles is a function of the
density of adatoms Nad : for low coverage, the polarizability is constant and is approximately equal to the
polarizability of the ion up to about 0.25 ML. Then
the polarizability increases with coverage and reaches
a maximum at 0.7 % 1.0 ML of coverage. The maximum value of a is between 50% and 75% of the gas
15
phase value. The dipole moment is extracted from
the slope of the work function Žexperimental. as a
function of coverage in the limit of zero coverage.
Taking this into account, it is difficult to use Eq. Ž15.
for any estimation.
However, a more important question is the possibility to use the described model Ž15. in the case of
ion bombardment. Indeed, the position of the implanted alkali particles differs radically from the
position of adsorbed particles Žsee Fig. 3.. The ionization energy of Cs atom Ž3.89 eV. is lower than the
work function of silicon Ž4.85 eV. Žas well as than
the work function of other semiconductors and metals.. Thus, the cesium should be absorbed as a
positive ion or, more exactly, as a strongly polarized
atom ŽFig. 3a.. In this case, the layer of the adparticles produces an electrical field, which reduces the
work function of the target. The obvious illustration
for specific character of this effect was done in Ref.
w13x: the Na deposition on metallic Cs leads to
decrease of the work function of Cs. The work
function change achieves y0.06 eV for small coverage of Na. Another world, the charge transfer occurs
from Na to the more electropositive Cs Žthe work
functions of Cs and Na are presented in Table 1..
In the case of ion bombardment, the alkali particles are incorporated into the lattice ŽFig. 3b.. The
implanted particles are in close association with
neighbor atoms and previously described effect
caused by deposed dipoles is absent. Generally, the
molecular bond between implanted Cs atoms and
target atoms ŽSi. is partly ionic in contrast with the
bond between Si atoms in pure silicon. So we can
suggest that the change of the work function is
caused by Cs implantation. Additionally, the work
function can be modified due to amorphization of the
near surface layer caused by ion bombardment. It
was experimentally obtained w14x that the work function of samples covered by monolayers of alkali
metal atoms is close to the work function of the
Table 1
Work function of some elements w16x
Element
F ŽeV.
Element
F ŽeV.
Si
4.85
4.91 Ž100.
4.60 Ž111.
Ga
Na
Cs
4.2
2.5
2.14
Y. KudriaÕtseÕ, R. Asomozar Applied Surface Science 167 (2000) 12–17
16
Fig. 4. The shift of the work function of silicon as a function of
the surface concentration of cesium implanted during sputtering.
corresponding alkali metal. Some differences are
associated with the crystalline structure of the target.
There is a great difference in the surface states
distribution, it depends on the crystalline orientation
of the surface and on the target temperature w14,15x.
The adsorption of alkali metals can result to the bond
bending effect, which also modifies the work function w15x. It is clear that all AcrystallineB effects are
insignificant in the case of amorphous target. So we
can skip these effects in our future consideration of
Cs sputtered surfaces.
Everything discussed above allows us to suggest
that the work function change of the sample under
ion bombardment strongly correlates with the surface
composition change. And we wrote the work function Fq
of an ion irradiated target as AweightedB
t
average of the work functions of components Žtarget
atoms and implanted atoms in this case.
1
Cis
Cts
f
q
,
Ž 16 .
Fq
Fi
Ft
t
where F j is the work function of pure target Žt. and
the pure material used as the bombarding ions Ži.,
and C js is the surface concentration of the components. A simple transformation of Eq. Ž16., taking
into account the evident relation: Fq
t s F t y DF
Žwhere DF is the change of work function due to the
ion implantation., leads to an equation that correlates
the change of the work function with the surface
concentration of implanted ions
Fi
DF f F t 1 y s
.
Ž 17 .
Ci Ž F t y F i . q F i
ž
/
The work function varies between the limits of
the work function of the pure matrix F t Žbefore ion
sputtering. and the work function of ion pure material F i , in the case when the concentration of these
ions on the sample surface achieves 100% Žthe physical limit..
The change of the work function of silicon as a
function of cesium surface concentration calculated
using Eq. Ž17. is presented in Fig. 4. In our calculations, we used the experimentally obtained work
functions of pure materials w16x ŽTable 1.. Note that
we have used the work function of polycrystalline
silicon to take into account the amorphization of a
near surface layer due to ion bombardment.
For comparison, we present in Fig. 4 the curve
calculated using Tooping’s model, Eq. Ž15.. We
˚ 3 w12x Žaphave used for cesium a equals to 38 A
proximately 64% of gas phase value.. The dipole
moment po was calculated from the AboundaryB
conditions: DF is equal to the difference between
the work function of pure silicon and silicon covered
with 1 ML of Cs.
Additionally, we calculated the change of the
work function in the different regimes of sputtering
of Cameca ims-4f% 6f ion microprobes Žsee Table
2.. The analytical parameters: the primary ion energy
Ž E . and the angle of incidence Ž u ., as well as the
sputtering yield Ž Yt ., the surface and undersurface
concentration of Cs, calculated using ŽEqs. Ž6., Ž8.,
Ž11. and Ž14. are presented in the Table 2. It is seen
that the work function decreases with decrease of the
primary ion energy. According to Eq. Ž1., this leads
Table 2
s .
v .
Sputtering yield Yt , surface Ž CCs
and undersurface Ž CCs
concentration of Cs, and corresponding change of the work function
Ž DF ., calculated using Eqs. Ž6., Ž8., Ž11., Ž14. and Ž17.. Typical
regimes of Cameca ims-4f%6f instruments were studied in the
case of Csq ion sputtering of silicon
No.
E
ŽkeV.
u
Ž8.
Yt Žatomsr
ion.
v
CCs
Ž%.
s
CCs
Ž%.
DF
ŽeV.
1
2
3
4
5
6
7
1
1.6
2
3
5.5
10
14.5
60
17.8
52.2
54.7
42
24.7
24
3.15
2.08
3.61
4.66
4.85
5.22
6.11
24.1
32.4
21.7
17.7
17.1
16.1
14.1
7.1
10.3
6.2
4.9
4.7
4.4
3.8
y0.398
y0.560
y0.353
y0.282
y0.272
y0.255
y0.220
Y. KudriaÕtseÕ, R. Asomozar Applied Surface Science 167 (2000) 12–17
to an increase in the ionization probability of the
secondary negative ions. But simultaneously, the
decrease of the primary ion energy causes a decrease
in the sputtering yield. So the monitored SIMS signal
of analyzed elements will be a result of a competition of two noted effects.
We must note a lack of experimental results,
which correlates the work function change with the
concentration of implanted alkali atoms. A comparison of the calculated work function change and the
measured one reported in Refs. w4,17x is difficult
because of a conflicting character of the experimental data. In both cases, authors studied the Cs implanted silicon. The authors of Refs. w4,17x obtained
the same shift of the work function of 0.55 eV. Note
that authors of these works used different sputtering
regimes: in Ref. w4x, the sputtering was performed by
Gaq ions and in Ref. w17x, by Csq ions. However,
the Cs concentration in the case of Ref. w17x was
30.5% and in Ref. w4x, it was equal to 3.3% Žthe bulk
concentration in both cases.. Moreover, the authors
of both works did not take into account the possible
preferential sputtering of Cs and the change of the
surface concentration of Cs in comparison with its
bulk concentration during their measurements. Taking this into account, we recalculated the surface
concentration of Cs for both studies, Refs. w4,17x,
using Eq. Ž7.. The obtained surface concentration
was equal to 9.5% and 0.86% for experiments of
Refs. w17,4x, respectively. These data are presented in
Fig. 4. Note that obtained difference can be partly
explained by difference in primary ions used for
sputtering. We can note that the data of Ref. w17x
showed a good agreement with calculations based on
the proposed model, Eq. Ž17.. The data of Ref. w4x
are close to the prediction of Tooping’s model.
Another result was reported in Ref. w18x. Its author measured the work function change for initial
stage of cesium incorporation on the Csq irradiated
silicon surface. The work function change of y1.3
eV was obtained for the steady state sputtering with
energy of 5.5 keV and the angle of incidence of 428.
Corresponding cesium concentration at the surface
layer was calculated Žusing T-DYN code. as 12%.
The result is presented in Fig. 4 and lies between two
AtheoreticalB curves.
In such manner, the experimental data are rather
conflicting. In order to find a ArightB model, it is
17
necessary to obtain experimentally the work function
change as a function of the surface cesium concentration. As a next step in our study, we are going to
perform such experiments.
4. Conclusions
A simple technique for calculating of the work
function of targets, which are being under ion bombardment, was presented. Based on this model, the
shift of the work function of silicon due to cesium
ion sputtering was calculated for a number of experimental regimes.
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