Nuclear Instruments and Methods in Physics Research B59/60 (1991) 643-646 North-Holland

643

Analysis of RBS spectra from samples implanted to high dose

Ken Jensen and G.C. Farlow Wright State University, Dayton, OH 45435, USA

A procedure for extracting the local stoichiometry and atomic fraction of constituents from RBS spectra of a sample implanted to high dose is described The procedure is applied to SiOz and when combined with an assumption about oxygen concentration is used

to deduce the volume concentration of Si vs depth in the sample.

1. Introduction

A recent study of SiOz implanted to high dose with Si [l] brought to our attention the need to be able to analyze RBS spectra which are compositionally nonuni- form in depth. Fig. 1 compares the RBS yield vs chan- nel number of unimplanted SiO, (circles) with SiOz

implanted with 8 x 10” a/cm* at 135 keV (squares). The excess Si yield between channels 400 and 550, and the deficiency of oxygen yield between channels 220 and 330 reflects the altered stoichiometry of the sample in the depth range to which these channels correspond.

There are two items of information that one would

like to extract from such a spectrum: (1) the amount of excess Si in the sample and (2) its distribution in depth. Part of the excess Si is not obvious in the spectrum. The excess number of atoms in any given physical layer increases the energy loss per unit length so that the energy width of the layer is expanded. Thus, for a fixed

3000

1

2000

9

F

1000

. i

c

.

9 00

Fig. 1. 2 MeV Rutherford backscattering spectra for unim- planted SiO, (circles) and SiO, implanted with 2$i (135 keV,

8 x 10”/cm2) (squares).

energy width/channel the backscattering from the physical layer is spread over more channels than if the excess number of atoms were not present. This accounts for the diminished yield from the oxygen; but it also means that part of the yield in fig. 1 which is below the “normal” level of Si yield (circles), as well as all of the yield above the “normal” level, is due to excess Si atoms. Thus, one cannot simply subtract the yield from unimplanted SiO, from the implanted SiO, to get the number of implanted Si atoms. That layers of equal thickness in a sample are spread over different energy intervals depending on the number of “excess” Si atoms present means that the depth scale is nonuniform. This would not be a problem except that the relation of an energy interval to physical thickness is determined by the atomic density which is unknown due to alteration by the implantation. Thus, one cannot even assign varying values of thickness to energy levels without some a priori notion of the local atomic density.

The suggested ways to treat such spectra involve either iterative [2] or simulation [3] procedures. We have found an alternative procedure for extracting the local stoichiometry and atomic fraction directly from spectra such as those shown in fig. 1. With the addition of some physically based assumptions about the atomic density of oxygen, values for the volume concentration and/or depth distribution of the excess Si can be inferred.

2. Theory

We start with a sample consisting of two elements, labeled “a” and “b” which has been divided into layers indexed consecutively from the surface. The yield due to backscattering from element “a” in a layer of index i is given by the well known expression [4]

Aai= m, (1)

0168-583X/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland) VI. HIGH-E/-DOSE IMPLANTATION

644 K. Jensen, G.C. FatIow / RBS spectra from samples implanted to high dose

where is the Rutherford scattering cross section for scattering from element “a”,

$2 is the solid angle subtended by the detector,

Q is the number of particles incident on the sample,

0, is the angle between the sample normal and the backscattered trajectory,

A&, is the energy interval ~~esponding to particles backscattered from element “a” in layer i,

f,; is the atomic fraction of element “a” in layer i, [r$‘ll is the stopping cross-section factor for an ion

passing through a mixture of elements “a” and “b” which scatters from element “a” in layer i.

In the surface energy approximation [ci’] is [2]

where 8, and 0, are the angles between the sample surface normal and the incoming and outgoing trajecto- ries of the ions, respectively, K, is the kinematic factor for scattering from element “a”, and cab(&) and cab( K,E,,) are the stopping cross sections for a mixture of elements “a” and “b” at energies E, and K,E,,

respectively. Bragg’s rule for stopping cross sections provides that the stopping cross sections for these mix- tures are found by

eab(&)i=faiea(Ec) +fbiCb(&b

and

(3)

c”( K,%>i =faic”( Ka&) ‘fbicb( KaEO), (4)

where ea and eb are elemental cross sections for ele- ment “a” and “b”, respectively, evaluated at the en- ergies indicated. The subscript i has been added to the combined stopping cross section to reflect the possibil- ity that the atomic fraction of elements “a” or “b” can vary from layer to layer. Eqs. (2)-(4) can be combined to give

[cZ”l p =fai [ &“jE,) + &“.(K~EClfj

+fbi 1

&pb(h) + &JYK,Eo) I

(5)

(6)

where [E:] and [et] are defined by the terms in brackets above and maybe interpreted as the stopping cross-sec- tion factors for elements “a” and “ b”, respectively, provided scattering took place with an atom of element “a”. These factors depend only on the geometry and the elemental stopping cross sections of the elements in- volved. In the surface energy approximation, they are independent of the depth at which the scattering event occurs. Further, the variation in the local stopping power due to variation in composition between layers is

explicitly displayed via the atomic fractions fai and fbi of eq. (6).

Using eq. (6) for [eP] in eq. (11, the expression for yield becomes

(7)

where S, is the ratio f,,/f,,, the stoichiometry of the layer i. All the parameters in this expression are availa- ble from the geometry of the backscattering or from the RBS spectrum itself except for S,. Thus eq. (7) can be used to calculated 5’;. (Note that division by fai can give strange artifacts if fai approaches 0.) From eq. (7) the stoichiometry in each layer may be found, and from the stoichiometry the atomic fractions of elements “a” and “b” can be found.

Using the atomic fractions, the stopping cross-sec- tion factor for each layer can be calculated from eq. (6). The stopping cross-section factors can then be used with the energy width of the layer, obtained from the spectrum, to calculate Nsi, the total number of atoms/cm’ in each layer, according to

AE,, = [et”] iNs,. (8)

If one can make some reasonable assumptions about the concentration of one of the constituents, the con- centration of the other can be inferred from the local stoichiometry. The thickness of each layer can then be inferred since Nsi = NViti, where NVi is the volume con- centration in layer i and t, is the layer thickness. If reasonable assumptions about the concentration cannot be made, the RBS spectrum can be broken up into energy intervals having the same number of atoms/cm* in each interval. These intervals are by no means certain to have the same physical thickness; however, given that the atoms in most materials are rather nearIy close packed, these intervals are likely to be within a factor of 2 of the same physical thickness. For instance, the thickness/channel deduced below for the implanted samples was found to be only about 40% less than that found for routine analysis of stoic~ome~c SiO,. One or the other of these approaches should give some idea of the depth distribution of a region whose composition has been altered by implantation.

3. Analysis of results

The yield from each channel in the spectrum in fig. 1 was compared with the yield in the same channel in a spectrum taken from an unimplanted portion of the same sample. Examination of eq. (6) shows that 0, Q, and cos 8, are the same for spectra of both implanted and unimplanted samples. Since the energy calibrations are the same, AEai is the same for both spectra. We also assume that all particles detected at energy E had

K. Jensen, G. C. Farlow / RBS spectra from samples implanted to high dose 645

,. . . . . . . . . . , 400 450 500 550 600

CHANNEL NUMBER

Fig. 2. The oxygen/Si stoichiometry vs channel number of SiO, implanted with 28Si (135 keV, 8XlO”/cm*) deduced from the backscattered yield from Si atoms. The sample surface

is located at channel 550.

the same energy E’ immediately before scattering so that a, is the same for both spectra. The ratio of yields is

A, _ 14 + si* [ 4 A:--’ (9)

where the asterisk denotes a value taken from the unim- planted sample. Only S, from the implanted sample is unknown and can be calculated from the ratio. The result is shown in fig 2 in which the local stoichiometry is plotted vs channel number. The atomic fractions of Si and oxygen in the implanted sample are plotted vs channel number in fig. 3. The circles denote the atomic fraction of Si and the squares denote the atomic frac- tion of oxygen. The values between channels 550 and 600 are artificially inserted to designate the samples’

1.0

I 0.6

t

$ ’ l . 6 0.6 -

m=m’..._m .e.** . . 0.0

k? .

. . l .: a.*

. ..* 0. . .

0.. .: ;..

. .‘..

n =. . .

==... . . .

. .

0.2

t

t 0. ?3’ I

50 400 450 500 550 600

CHANNEL NUMBER

Fig. 3. The atomic fraction8 of Si (circles) and oxygen (squares) in SiO, implanted with *% (135 keV, 8XlO”/cm*) deduced from the backscattered yield from Si atoms. The sample surface

is located at channel 550.

12 r t ‘.. _. . . * . . *. . .

. . .* . .

. . . . .

00 I 50 100 I ’ 5 200 oDEml 5

(“m’o 50

O 3s

O 400

Fig. 4. The volume concentration of Si vs depth in SiO, implanted with *$i (135 keV, 8 x lO”/cm*) deduced from the backscattered yield from Si atoms and the volume concentra-

tion for oxygen in Si02, 3.6 x 102’/cm3.

surface boundary. Note that these characteristics agree with those of bulk SiO, in regions to which the Si ions did not penetrate.

Fig. 4 is a plot of volume concentration of Si vs depth. It is obtained by assuming that the concentration of oxygen is not markedly changed during ion implanta- tion. The oxygen concentration and the local stoichiom- etry from fig. 2 is then used to find the local concentra- tion of Si. The atomic fractions in fig. 3 are used to find the local stopping cross sections from eq. (6). Eq. (8) then gives Nsi the local number of atoms/cm’. iVsi is then divided by the sum of the local oxygen and Si concentrations to get the thickness associated with the channel. Depth is obtained by summing the thickness of each channel from channel 550 to the channel whose depth is desired. Note that the concentration ap- proaches that of bulk SiO, at depth regions to which the Si ions did not penetrate. The peak concentration occurs at approximately 140 nm which is just less than the 160 run predicted by the program used to choose the energy of implantation. (The program ARANGE is an unpublished analytical procedure for approximating mean ranges and straggling. It is available at the Surface Modification and Characterization Facility at Oak Ridge National Laboratory.) The peak concentration is how- ever twice what is expected from the ratio of the fluence to the expected straggling. This suggests the assumption of unperturbed oxygen concentration is not adequately true and the implantation has resulted in a diminished oxygen concentration as well as a diminished oxygen atomic fraction.

4. Conclusions

A procedure for finding the stoichiometry and atomic fractions of elements in a sample implanted to high

VI. HIGH-E/-DOSE IMPLANTATION

646 K. Jensen, G.C. Farlow / RBS spectra from samples implanted to high dose

dose by comparison of RBS spectra from implanted and unimplanted regions has been described which is con- sistent with usual methods of analysis of RBS spectra for samples implanted to low doses. This procedure has been applied to samples of SiOz implanted with Si to doses of 8 X 101J/cm2. With the addition of a plausible assumption about the oxygen concentration in the sam- ple it was possible to deduce the concentration of Si as a function of depth which is consistent with known concentration in regions unaffected by the implanta- tion, with the expected depth distribution of the im- planted Si, but with higher than expected peak con- centration. With greater experience with the assump- tions made in using the procedure, it shows some prom-

ise of utility in analyzing directly the RBS spectra of samples implanted to high dose.

References

[l] H.E. Jackson, U. Ramabadran and G.C. Farlow, Appl. Phys. Lett. 55 (1989) 1199.

[2] W.-K. Chu, J.W. Mayer and M.-A. Nicolet, Backscattering Spectroscopy (Academic Press, New York, 1978) pp. 129- 130,134-137.

[3] E.g. the RUMP program; L. Doolittle, Nucl. Instr. and Meth. B15 (1986) 227.

[4] See ref. [2], p. 71. [5] See ref. [2], p. 63.