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U. Müller-Jahreis, P. Thiele, M. Bouafia, A. Seghir
To cite this version:
U. Müller-Jahreis, P. Thiele, M. Bouafia, A. Seghir. Determination of Low-Energy Ion Implantation Damage Parameters by an Ellipsometric Method. Journal de Physique III, EDP Sciences, 1995, 5 (5), pp.575-584. �10.1051/jp3:1995147�. �jpa-00249332�
J- Phys. III £Fance 5 (1995) 575-584 MAY1995, PAGE 575
Classification Physics Abstracts
61.70T 78.90
Determination of Low-Energy Ion Implantation Damage
Parameters by an Ellipsometric Method
U. Miiller-Jahreis(~), P. Thiele(~), M. Bouafia(~) and A. Seghir(~)
(~) Humboldt~Universitit zu Berlin, Institut fur Physik, Unter den Linden 6, D-10099 Berlin, Germany
(~) Ferhat-Abbas Universit4 de S4tif, 1-O-M-P-, DZ-19000 S4tif, Algeria
(Received 26 September 1994, revised 20 January 1995, accepted 15 February 1995)
R4sumk. L'implantation ionique des semi-conducteurs avec des ions I basse 4nergie provoque dans des regions superficielles des d4fauts, qui peuvent Atre detect4s sensiblement par la m6thode
411ipsom4trique. En appliquant l'411ipsom4trie seulement I une longueur d'onde, it est possible
de d4terminer les parambtres d'implantation : la deviation standard de la distribution des dd- fauts et leur concentration critique menant h l'4tat amorphe, si l'on utilise un modble analytique simple. Cela sera demontr4 dans le cas d'implantation de l'argon (500-2500 eV) dans le silicium.
Abstract. Low-energy ion implantations in semiconductor materials cause defects in near surface regions, which can sensitively be detected by ellipsometry. By means of a simple analytic model, implantation parameters as ion damage straggling and amorphization threshold can be
obtained by using only one-wavelength ellipsometry. This will be demonstrated for the
case of
argon implantations (500 2500 eV) in silicon.
l~ Introduction
Ion implantation of solids by heavy ions with low energies (~- 1000 eV) is connected with ion penetration depths of only a few nanometers. In this case the investigation of implantation parameters (ranges, straggling, damage distributions) requires methods with a depth resolution in the order of monolayers. Ellipsometry is such a method, even suited to enlighten details of the collision processes, because ion implantation often causes changes in the optical state of the target (especially in the case of semiconductors).
It is well known that ion beam damage in silicon single crystals is connected with marked
changes of the silicon dielectric function (for low-energy Ar ion bombardment see [1-7]). In the low-energy range, the damage is localized to a thin surface layer and the optical properties
are sensitive to the ion species and energy and to the dose implanted [7]. This can be detected by ellipsometric measurements. To show this, a section of an argon ion beam profile was
recorded by scanning ellipsometry of a 20 x 40 mm~ silicon target that had been exposed
© Les Editions de Physique 1995
j
S d~
j~
i~
I
4~
~z o
'V~
W~
Fig. 1. Section of an Ar+ ion beam profile recorded by scanning ellipsometry of an ion beam
exposed silicon target (ion energy 1500 eV, dose 2 x 10~~cm~~).
to a 1500 eV-ion beam with a dose of 2 x 10~~ cm~~ (Fig- I). In this special case, the shape of the peak (ellipsometric angle ill) corresponds approximately to the ion beam profile, because the generated damage depends on the local ion dose. This is a convenient way to take
"photographs" of low-energy and low-intensity ion bearn profiles.
For a more detailed analysis of ion-target interactions, it is necessary to develop a suitable optical layer model that can be fitted to the ellipsometric data. Such a procedure allows to
restore a depth resolution, which is normally not an intrinsic feature of ellipsometry.
If spectroscopic ellipsometry is used, it is possible to obtain the dielectric function for an extended wavelength range and to fit a layer model to the experimental data. In this way, complex layers consisting of amorphous and crystalline material including voids can be treated
[3-5,8-1Ii.
Further, multiple-angle-of-incidence ellipsometry at only one wavelength in connection with different optical layer models has been applied [12,13]. Combinations of ellipsometry with
layer-by-layer removal of the damaged silicon using anodic oxidation have been reported in
references [12], [14] and [15]. An iterative numerical method to derive damage profiles from ellipsometric data has been suggested in reference [16].
In the following it will be shown, that one-wavelength ellipsometry combined with a simple analytic model permits to determine some important parameters of the ion implantation and of the damage process. The restriction to the one-wavelength ellipsometry enables fast mea-
surements, which are interesting for in-situ applications. The method will be demonstrated here for the case of low-energy argon implantation in silicon.
N°5 DAMAGE PARAMETERS 577
A
~ ~~'
i ->
Q D ~
~ 2
~/
5 nm
i
I low ion doses
2 hi§h ion doses
3 Si
~ on Sl (calculated)
3 15
i'
Fig- 2. Experimental ill A curve for the 500 eV Ar implantations in silicon. The arrows mark the
increasing ion dose. 1) low ion doses. The solid line is the best fit according to the model (see Sect.
3), 2) high ion doses, 3) calculated ill-A values due to a thin Si02 layer of variable thickness.
2~ Experimental
Silicon wafers (n«type, 2 fl cm, < III > orientation) with oxide layer thicknesses of about 2 nm were implanted with argon ions from a Kaufman-type ion source at a dose range from 6 x 10~~ to 4 x 10~~ ions/cm~ with energies from 500 eV to 2500 eV. The implantations were
carried out at the temperature of 300 K + 3il. During the ion implantation at constant ion current density of 3 pA/cm~ a damaged silicon layer will be formed in or nearby the interface oxide /silicon. The actual value of the ion dose determines the kind of this layer (low damaged, amorphous, amorphous with Ar voids) and its extent in depth.
Contrary to the damaged silicon, whose optical constants are strongly influenced by the ion
implantation, the optical state of the oxide surface layer remains unchanged. This was proved by additional implantations in thicker oxide layers.
The ellipsometric measurements were carried out using an automatic rotating analyzer ellip-
someter (5E400, Sentech Instruments) with a HeNe laser (632.8 nm). The angle of incidence
of the laser beam was variable between 40° and 70°. Here, a fixed angle of 70° was chosen. At this angle the laser spot is elliptical with an area of about 6 mm~.
As usual, the measuring results are available in the form of the ellipsometric angles lY and /h that are correlated with the amplitude and the phase of the complex reflectance ratio
p =
~~
= tan flfe~~,
rs
where rp and r~ are the reflection coefficients of the p- and the s-polarized components.
ill and /h values were measured for 5 energies in dependence on the ion dose. Results are shown in Figure 2 for the ion energy 500 eV. The arrows indicate the increasing ion dose from I x 10~~ to 4 x 10~~ cm~~. Before a detailed analysis will be performed, two parts in
the curve can be clearly distinguished: part ii) is characterized by growing ill and /h values
if
~~
" (nD
' voids ->
2 '
C O
fi 2N
« D (
~~
E
°
low damage
i)~,,
io 12 io 13 io io '~ io '~
Jose (ions cm ~)
Fig. 3. Measured ill values for the 1500 eV implantations in dependence on the Ar ion dose.
The good approximation of the experimental values by simple mathematical functions in the low and medium dose range suggests the model described in Section 3.
and will be interpreted as a result of the increasing thickness of the amorphous layer (see below). Here, the solid line is the best fit to the experimental values in this region according
to the model described below. From the intersection point with the (calculated) oxide curve
an oxide layer thickness of about 2 nm can be derived, corresponding to the natural oxide on silicon. In part (2) with decreasing /h values, the formation of voids in the amorphous silicon is expected [3, 4,7-9]
In Figure 3 the dependence of the ill values on the ion dose is shown for an ion energy of 1500 eV. In the low dose range the ill values exhibit a linear dependence on the ion dose (note
the logarithmic dose scale), which will be discussed in the following due to low damage below
an amorphization threshold. In the medium dose range the dose dependence of ill becomes
approximately logarithmic, due to the formation of an amorphous layer and its extent in the
depth. The higher dose range will be explained by the formation of voids in the amorphous
silicon. There is no simple mathematical approximation of the dose dependence.
From the lY, /h values in the medium dose range both the complex refractive index fi
= n ik
and the thickness of the respective amorphous zone can be derived by fitting model calculations to the measured values. For as-implanted silicon samples the value fi
= 4A io.9 was an
acceptable fit for all energies investigated here. This complex refractive index is characterized by comparatively high n and (k( values compared with crystalline silicon ii m 3.86 -10.02),
which are typical of amorphous silicon created by ion damage [2,Iii or deposition [18].
3~ Data 3lreatment and Discussion
The model used here concerns the lower and medium dose range, I-e-, doses below the threshold of Ar void formation. In the model, it will be assumed that the maximum of the damage depth
distribution is located not far from the interface oxide/silicon and that the distribution can be
N°5 DAMAGE PARAMETERS 579
surface interface
S102 Si
n
o
ZlI damage profile
~i
I n,(x)
~ ~2jX
o ,,
° amorphous ' no
o d x
d thickness of the amorfhous layer
d~ effective thickness of he
transition layer d,n = d + d,
Fig. 4. Schematic diagram of the damage distribution, designating the different regions of damage.
approximated by a Gaussian (Fig. 4). The first condition is well satisfied in the chosen energy range for thin oxide layer thicknesses. The approximation of the damage distribution by a
Gaussian is quite good, because only the part in the silicon must be considered, attributed to the missing optical influence of ion bombardment in the oxide. Sputtering can be neglected
for the low doses applied here in this low-energy range.
Two regions can be distinguished: ii) the region of highly damaged silicon above the amor-
phization threshold, which results in an optical homogeneous layer with the refractive index fi = n ik for amorphous silicon, even though the argon ions and the displacement events are not homogeneously distributed, and iii) the region that is influenced by the tail of the argon
depth distribution. Since no complete amorphization is reached in this region, fi will change depending on the depth [19].
The thickness of the amorphous layer d is given by the parameters of the damage distribu~
tion. If the maximum of the assumed Gaussian damage distribution is exactly located in the
oxide/substrate interface, d~ is simply given by
d2
= 2b2 in ~jj~ = 2b2 in
)
ii)while b is the standard deviation of the damage depth distribution, n~~~ the'maximum con- centration of the defects, n~ the threshold defect concentration of (optical) amorphization, D the ion dose, and D~ the amorphization dose leading to n~a~ = n~.
The amorphous layer is followed by the less damaged zone, which will be treated in the model in a rough approximation as an additional amorphous layer of the thickness df, here defined by
oo ~2
~~ ~ ~~
/
~~'~~~~~~
2b2 ~~~ ~~~
That means, the residual damage distribution with a concentration per unit area given by the
integral will be replaced by an equivalent amorphous zone with the same concentration per unit area na x df.
_~
6=3nm
« ,
~ /
,
c /
+~ /
/
"~J 40 ,'
/ , ,
C /
j ,
d.,/ ,1' ,~ ~~~'
20 d~
/"
,
"~
/ ,
/ / / /
, ,
, ,
, ,
, ,
o
~'~ ~~
D/Da
Fig. 5. Calculated d(~ and d~ curves for two 6 values.
So, both layers are treated as one homogeneous amorphous layer with a thickness dea
= d+ df:
For low ion doses with D/Da < I the thickness of the amorphous layer is zero and therefore deR = di. For these doses the approximation is expected to be rather poor. Above the
amorphization threshold, an increasing ion dose yields an increasing d and a decreasing df (cf. the dashed curve n2(x) in Fig. 4). Therefore, the quality of the approximation improves
rapidly with the growing ion dose.
In Figure 5 the dependence of d(~ and d~ on the ion dose is shown in a semi-logarithmic plot,
which is an adequate representation of equation (I). The two curve pairs are related to two different values of b. In this plot the d~ curves are straight lines beginning in D /Da
= I and with
a slope of 2b~. At D/Da
= I the corresponding d(~ curves show a typical discontinuity in the
slope. This point indicates precisely the appearance of the amorphous zone and, in principle, Da could be directly derived from the experimental values. But such a determination of the
amorphization dose Da is usually not favourable because of its relatively poor precision.
A more convenient way is to fit a best d~a curve to the experimental values and to determine from the corresponding d~ curve both the slope (2b~) and the intersection point with the
abscissa (Da).
The fitting procedure has to favour the experimental values at higher doses because of the
rough approximation of the lower dose range in the model.
So far, the maximum of the damage distribution has been assumed to be located in the interface oxide / substrate. Normally, this cannot be expected in the implantation procedure
because the position of the damage distribution depends on the chosen ion energy. Since there
occurs a shift s of the damage distribution towards the silicon substrate, s must be added to
d (or subtracted in the case of a shift in direction of the surface). If the shift s is unknown, it
N°5 DAMAGE PARAMETERS 581
30
' ~~
d~f
m( . experimental values
7J
thickness values
~derived from model
Da
~
lo " lo lo '~
dose D (ions cm~~)
Fig. 6. Experimental values for 1500 eV, fitted by a calculated curve pair.
can also be determined through the fitting process. The Da values are generally not affected
by a shift s, but a shift towards the surface reduces the accuracy of the fitting process.
The application of the model is shown in Figure 6 for an implantation energy of150o eV.
To compare the experimental values with model curves, the lY-/h values must be converted into d~a values or ~ice ~ersa. This can be realized by means of the standard software of each
ellipsometer usual in the trade. In this paper, curves like (I) in Figure 2 were fitted to the
experimental data. If each point of such a curve corresponds to a certain deR value, these d~R values can be assigned to the experimental values (here ~ia identical lY values) and to the
corresponding ion dose. Figure 6 reveals a change in the slope of the experimental values near the dose of10~~ ions/cm~, which indicates the beginning of a transition from the low damaged
to the amorphous state at a certain depth.
In Figure 6, the calculated d(~ curve with b
= 2.35 nm has been the best fit with a shift of the damage distribution of s
= 0A nm towards the oxide. Then, from the corresponding d~
curve an amorphization dose Da = 1.0 x 10~~ ions/cm~ will be derived.
Because of the satisfactory approximation of the experimental values in the model curve, an accuracy of10i~ should be attainable with the help of this method.
More realistic approximations of the low damaged zone concerning its optical qualities have been suggested (see [13,20]), but in the case considered here such improvements have only a
slight influence on the accuracy.
The results are summarized in Figure 7. The b values increase as expected with the argon ion energy. The values are compared with theoretical values of the vacancy straggling derived from the TRIM program [21]. Since the b values depend on the thickness of the passed oxide layer, two curves related to nm and 3 nm are shown. Note that the 3 nm curve can be derived
only for ion energies E > 1500 eV with sufficient accuracy. The experimental values confirm the theoretical dependency to a great extent.
In Figure 7 the D~ values are included too. As can be seen, they increase with ion energy.
Because the shift between the distributions of nuclear stopping power and defect concentration
t
~ m
o m
I
Id0~~
"
4
3nm Sio~
~i 3
c ,
'
~~ ,5
$ ,
2 6
, nm SiO~ f~
~E
,
(
Da ~
~
° ~,,
~° ~
E(kev) ~
Fig. 7. Energy dependence of 6, Da and nd,a. The solid lines designated by 1 nm and 3 nm Si02
are calculated curves (see text); the other solid lines are only guides for the eye.
cannot be neglected in the here investigated low-energy range, a concept of determining critical densities of the nuclear deposited energy necessary for amorphization fails. Therefore, here the critical density of defects has been estimated by forming the product of the D~ values with the respective number of vacancies per ion and unit of length [21] in the maximum of the vacancy distribution (nd,a values in Fig. 7). Under the implantation conditions applied here
(comparatively high ion dose rate at room temperature), the values are evidently not constant.
Their increase with implantation energy indicates in~situ annealing during the ion implantation.
In Figure 8 the D~ values are plotted together with data obtained by Dennis and Hale [22]
for higher energies and for the temperature of 80 K. The value for 20 kev is completed by a value from the same authors corresponding to 300 K to demonstrate the dependence on the temperature. To estimate the energy dependence in the whole energy range, a Da value for 1000 eV and 150 K [23] was added. Supposing this value is enhanced compared with a value
measured at 80 K, the real dependency on the energy should be somewhat more pronounced than the here suggested one. The low-energy Da values for 300 K indicate such a dependence
for these energies too, possibly less distinct for the lowest energies.
Recently, Bock et al. [24] reported Da values in the energy range from 100 eV to 3000 eV derived from LEED measurements. They found increasing values below 1000 eV in agreement with their own model calculations and also increasing experimental values in the energy range from 1000 eV to 2500 eV, comparable with the here in Figure 7 reported results.
4. Conclusions
Data of ion beam damage in the low-energy range (around 1000 eV) are rare. It was the intention of this paper to present a method consisting of ellipsometric measurements combined with a model that is easy to handle and that allows to determine ion implantation damage
parameters at low ion energies.
N°5 DAMAGE PARAMETERS 583
0 ~~
~s
'~ 9 300K
Io
C' 300K
_--- BOK
10 "
_~_,~,-,~~"~'
~~OK
~ -this pa er
b O-
ef.[22(
o Ref. 23
~~
l lo loo
E(kev)
Fig. 8. Comparison of the Da values with data from the literature.
In contrast to methods that use spectroscopic ellipsometry, here the one~wavelength ellip-
sometry has proved to be sufficient.
Although the method was tested only with argon ions implanted in silicon, its application to other ion-target combinations seems to be promising. Statements to ion damage distributions and amorphization thresholds are possible in principle. The method should also be applied to low temperature implantations were in-situ annealing processes are less important.
Acknowledgments
Two of the authors (M. Bouafia and A. Seghir) gratefully acknowledge the financial support given by the DAAD, Germany.
References
[1] Ibrahim M-M- and Bashara N-M-, Ellipsometric study of 400 eV ion damage in silicon, Surf.
Sci. 30 (1972) 632-640.
[2] Martens J-W-D-, van den Bogert W-F- and van Silfhout A., The influence of argon ion bombard- ment on the electrical and optical properties of clean silicon surfaces, Surf. Sm. 105 (1981) 275-288.
[3] Burns T-M-, Chongsawangvirod S., Andrews J-W-, Irene E-A-, Mc.Guire G. and Chevacharoeukul S., A comparison of the measurement of ion damage in silicon surfaces using differential reflectance
and spectroscopic ellipsometry, J. Vac. Sci. Technol. 89 (1991) 41-49.
[4] Hu Y.Z., Andrews J-W-, Li M. and Irene E-A-, in situ spectroscopic ellipsometric investigation of argon ion bombardment of single-crystal silicon and silicon dio~ide films, Nucl. Instrum. Methods Phys. Res. 859/60 (1991) 76-79.
