Neutron depth profiling by large angle coincidence spectrometry

Nuclear Instruments and Methods in Physics Research B73 (1993) 523-530 North-Holland

k!lOMl B

Beam Interactions with Materials 8 Atoms

Neutron depth profiling by large angle coincidence spectrometry V. Havrhek,

V. Hnatowicz, J. Kvitek, J. Vacik and J. Hoffmann

Institute of Nuclear Physics of Czech Academy of Sciences, 250 68 ke?, Czech Republic

D. Fink Hahn - Meitner Institute, P.O. Box 390128, D-1000 Berlin, Germany

Received 10 July 1992 and in revised form 3 November 1992

A measuring device for large angle coincidence neutron depth profiling was installed behind a 5.6 m long neutron guide. Two large area PIN diodes placed at a distance of 2 mm from the sample serve for the detection of particles emitted at different angles. Coincidence event registration and sorting was accomplished using a PC AT computer. A simple but effective technique for two-dimensional data evaluation is proposed. The feasibility of the method was tested on various standards. The detection limits and the depth resolution are determined and possible refinements of the technique are discussed.

1. Introduction

Neutron depth profiling (NDP) is one of the most powerful nondestructive techniques for the depth profiling of some light elements in solids [l-4]. A list of useful nuclear reactions induced by thermal neutrons has been given in refs. [5,6]. Two of the most important reactions, 6Li(n,,, 4He)3H and “B(n,,, 4He)7Li having thermal neutron capture cross-sections of 940 and 3837 b respectively, are commonly employed for the determination of lithium and boron. In the standard experimental arrangement, the sample examined is irradiated by the thermal neutron beam, and the charged reaction products are registered by a surface barrier detector placed at a considerable distance from the sample. The solid angle subtended by the detector is typically of the order of lo-’ sr. Under these experimental conditions the practical detection limit for lithium and boron is 10m6 and a depth resolution of about 10 nm can be achieved using glancing angle measuring geometry [3,5]. The detection limits may generally be improved by increasing counting statistics and by eliminating spectral background. Despite the relatively large cross-sections of some nuclear reactions induced by thermal neutrons, obtaining good measuring statistics in NDP analyses is time-consuming because of the low neutron

Correspondence to: Dr. V. Hnatowicz,WInstitute of Nuclear Physics of Czech Academy of Sciences, Rei CS-250 68, Czech Republic. 0168-583X/93/$06.00

fluxes available at standard research reactors. The counting statistics may be improved by using large area detectors and by placing them in the proximity of the target. Bringing the detector closer to the target and accordingly to the neutron beam generally leads to an increase of the background noise and to the deterioration of the depth resolution because the emission angle of the detected particle is no longer well defined, The background may greatly be reduced by measuring the energies of both charged reaction products emitted in opposite directions simultaneously. A great disadvantage of this technique is that the samples examined have to be thin enough so that both particles can reach the detectors. Nevertheless, it seems that the coincidence method could be applied in many instances mainly due to its excellent sensitivity. The coincidence technique has been applied in NDP analysis [7], demonstrating an improvement in lithium and boron detection limits by 5-6 orders of magnitude. Later, a similar technique was employed for the determination of the depth profile of implanted Li atoms [8]. The idea of NDP analyses using the coincidence technique has been further pursued by Chu [9], who suggested the use of large area detectors in close geometry and two-dimensional data handling. In such an experimental arrangement, detector solid angles close to 27~ sr seem to be accesible, registering simultaneously particles emitted at different angles. The measured energies of coinciding particles can be transformed to depth vs. emission angles and the depth distribution is obtained by properly sorting the measured two-dimensional data.

0 1993 - Elsevier Science Publishers B.V. All rights reserved

524

V. Haurhnek et al. / Neutron depth profiling

In this study, the idea suggested in ref. [9] is realized. The coincidence device described comprises two large area PIN detectors arranged in close geometry and two-dimensional data handling. A simple algorithm for two-dimensional data evaluation is proposed and the feasibility of the system for NDP analysis is demonstrated for depth profiling of boron and lithium in some standards.

2. Experimental The present experiment was performed using a thermal neutron beam from a 5.6 m long neutron guide installed at the LWR-15 nuclear research reactor of the Nuclear Research Institute at Rei (CR). The guide radius is 825 m and its full internal cross-section is 4 x 150 mm2. At 6 MW reactor power, the thermal neutron flux was 7 X lo6 cmm2 s-l and the measured cadmium ratio was R,, = 9 X 104. The neutron beam enters a target chamber installed just behind the neutron guide end and evacuated to a presssure of 10v2 Torr. The sample investigated together with associated particle detectors was placed in the chamber centre. The sample-detector arrangement is shown schematically in the upper part of fig. 1 together with the associated electronics. Two PIN photodiode detectors Dl, D2 (for details, see below) were

Fig. 1. Schematic of the experimental arrangement. Details are given in the text. The detector-sample (Dl, D2, S) arrangement is not drawn to scale, namely the sample thickness is enlarged in order to show a typical coincidence event and to illustrate the meaning of basic quantities used in the data evaluation. The sample tilt with respect to the neutron beam axis, discussed in the text, is also not shown.

placed at a distance of 2 mm from the sample. In this close measuring geometry, the coinciding particles (~1, p2) emitted from the sample midpoint in angular range 0 = O-70” can be registered. The solid angle subtended by each detector with respect to the sample centre was about 0.3 x 2~ sr. By additional shielding, the neutron beam was collimated to a cross-section of 1.0 X 50 mm2 at the sample position. Thorough beam collimation prevents neutrons from directly hitting the particle detectors situated in close geometry and reduces detector load substantially. The samples, usually in the form of self-supporting films or foils, were fastened by two opposite edges to sample holder arms situated along the neutron beam. All holder components were placed outside the neutron beam, so that additional neutron absorption and scattering were avoided. The holder construction and the sample fastening procedure ensure a perfectly flat sample surface and its precise positioning with respect to the detectors. The absolute depth scale and the reproducibility of the depth profiling depend critically on how precisely the sample-detector arrangement is defined and fixed. The mechanical construction of the detector frame and the sample holder, which in fact constitute one block, enable the detector front faces and the sample surface to be set parallel to each other. Precise orientation of the sample-detector block with respect to the neutron beam is not easy. In the present experimental setup, the sample was tilted by about 3” with respect to the neutron beam axis defined by the slits in the neutron shielding. In this way, unwanted neutron absorption and scattering in extended samples was greatly reduced. A separate experiment was performed in which the sample was tilted in a small angular range around the working position with respect to the neutron beam and the dependence of the count rate vs. angle was followed. Within counting statistics no variation in the total count rate was observed. For the present experiment, large area particle detectors with thin dead layer and good energy resolution are needed. Modern PIN photodiodes meet these requirements. The use of PINS as alternative particle detectors has been reported in refs. [lO,ll], and their excellent energy resolution has been experimentally demonstrated, see ref. [X2]. In the present experiment, 10 X 10 X 0.5 mm3 PIN photodiodes (type Hamamatsu S 3590-06 windowless) working at 50 V bias (HV) were employed. The pulses from the detectors are processed by two identical electronic chains comprising Canberra model CI 2003T charge preamplifiers (PA), CI 2020 spectroscopy amplifiers (A) and Nuclear data type ND 575 ADCs (ADC). The timing signals obtained from the preamplifiers were processed in a logical system comprising timing preamplifiers (TA), single channel analysers (SCA) and coincidence circuit (Cl, all proposed and manufactured at NPI. The 1 ps time resolu-

V. Havrrinek et al. / Neutron depth profiling

tion of the coincidence circuit is adequate in view of the relatively low counting rates. A coincidence event gives rise to gating signals for both ADCs. The output codes from the ADCs are forwarded to an interface (I-also manufactured at NPI) and after a 128 l.~sdelay, ensuring that both codes are properly received, the combined codes of coinciding pulses are stored in a buffer memory of personal computer. Occasionally, the buffer content is transferred to a floppy disc. The measuring process is managed by a simple computer program written for this purpose. Using the same program the data can be depicted in two-dimensional form during the measurement. As a result of the measurement one obtains all aquired events as data files on floppy discs. The properties of PIN detectors were thoroughly examined in separate experiments using proton and a-particle beams from the 2.5 MeV NPI electrostatic accelerator. In the energy spectra of monoenergetic particles obtained with unshielded detectors, the principal peak was accompanied by a smaller one shifted to lower energy. The intensity of the spurious peak was a few percent of the principal one. It was demonstrated experimentally that the occurrence of the spurious peak is caused by an about 0.5 mm wide strip along the detector frame where the incoming particles probably meet a slightly thicker dead layer. After this marginal region of the detector was shielded by a suitable mask, the spurious peaks disappeared. With the above-mentioned detector shielding, an energy resolution (FWHM) of 12.2 keV for 2055 keV o-particles and 6.2 keV for 2727 keV tritons was achieved in the initial phase of detector operation using a Canberra model CI 2024 spectroscopy amplifier with 1 ps shaping time. These values compare well with those reported earlier [12] for smaller PIN detector. In long-term measurements at the neutron beam, however, the actual FWHMs for 2055 keV a-particles and 2727 keV tritons from the 6Li(n,h, orj3H nuclear reaction were I7 and 12 keV, respectively. This resolution deterioration is explained by an unfavourable noise situation in the reactor hall. For the determination of the dead layer thickness, the PIN detector was irradiated with a collimated beam of mono-energetic u-particles at different angles of incidence with respect to the detector front surface. From the angular dependence of the measured particle energy, the dead layer thicknesses were determined to be 240 and 120 nm of Si for detector biases of 20 and 50 V, respectively.

525

[91. In ref. [81, the basic equations relating the measured particle energies to the emission angle and the event depth have been given in approximation assuming energy-independent stopping powers. Here, a slightly different approach was chosen, based on the residual particle range concept. In this formalism, no approximations are made and final formulae transforming the particle energies into the emission angle and the event depth and vice versa are obtained in a simple concise form. In the following, samples in the form of thin uniform sheets comprising one or several major elements are considered. The analyzed element (B, Li, etc.) is assumed to be present in minute concentration, so that it does not affect significantly the material stopping power. The detector-sample geometry is shown schematically in the upper part of fig. 1, together with a typical coincidence event. Let us consider the event taking place at a depth x under the sample surface. In the nuclear reaction induced by thermal neutrons, both charged reaction products (pl, p2) are emitted isotropically in opposite directions. Therefore, each coincidence event is determined only by the depth x at which the reaction takes place, and by the angle 0 (referring to the sample surface normal) at which the reaction products are emitted. In a typical event, as depicted in fig. 1, the particles pl and p2 reach the detectors Dl and D2 so that the event is registered in the coincidence matrix at the position (E,(x, O), E,(x, O)), with E, and E, being the energies registered by the first and the second detectors. The particle energies E, and E, are related to the depth x and the emission angle 0 by following simple equations

5

=RdW

t-x cos

=WE*d -WJ%)

-NEA

’

where t is the total sample thickness, 0 is the angle to the surface normal at which both particles are emitted, and R, and R, are the corresponding ranges of the first and the second particle, respectively, in the sample material, expressed as a function of the particle instantaneous energy. In the following, for the sake of simplicity, the variable y = cos 0 is used instead of emission angle 0. The particle range is related to its stopping power S(E) by the well known definition: R,(E,)

= /ik&(E)-’

dE,

i = 1, 2.

3. Data evaluation The principles of the method and the evaluation

two-dimensional

of NDP data have been reported in ref.

The initial particle energies, E,, and E,,, are determined by the energy yield of the particular nuclear reaction used in the NDP analysis. For very thin sam-

526

V. Havrrinek et al. / Neutron depth profiling to,01

(Eto,O)

El

XOZO

E2

Fig. 2. Two complementary mappings of the coincidence matrix. On the horizontal and vertical axes, the particle energies measured by two detectors are outlined. The maximum energies, ,Q, and E,,, correspond to the particles emitted from the sample surfaces. The coincidence matrix can be adequately described in terms of depth, x, and the particle emission angle, 0. In the surface approximation, the curves of equal depth (x, < x1 < . etc.) are straight lines originating from the point (&,, E,). The events corresponding to the same emission angle are situated on the straight lines denoted by Oi with Oi < Bi+ 1 and i = 1,2, etc.

ples and low emission angles, the surface approximation can be used neglecting the energy dependence of the particle stopping power. In this approximation (which has also been used in ref. [8]), the right sides of eqs. (1) become a linear function of the final particle energies. In thicker samples, however, where the particle energy losses are appreciable, the exact energy dependence of the particle stopping power should be considered. Using eqs. (l), the measured particle energies E, and E, can be easily transformed into variables x and y = cos 0 and vice versa. One obtains

‘=

-R,(W)

(R,(&)

-WE,)

+Rd-W

’ = (R,(E,,)

-R,(E,)

:R,(E,) -&(Ed)

(3a) ’ (3b)

’

Hence the coincidence matrix can alternatively be mapped in (x, y) space as is shown schematically in fig. 2. In the above-mentioned surface approximation, the lines of equal depth x are straight lines passing through the point (E,,, E,,), with slopes inversely proportional to the depth x. The common slope of the lines of equal emission angle 0 is given by the ratio of the stopping powers of both coinciding particles in the sample material.

The data evaluation is performed off-line on an AT PC by means of the computer code TWODIM allowing comfortable data handling and manipulation. The program is written in Pascal 6.0 and occupies only 50 kB of computer memory. The TWODIM program ensures reading of the measured data from floppy disks, visual operator inspection of the whole data, selection of a relevant data region and depth profile calculation of the element examined. The TWODIM program makes use of geometrical factors and the R(E) vs. E dependence calculated by separate PC programs (see below). First, all acquired events (E,, EJ are read and depicted as points in a two-dimensional plot on the monitor. Then, using graphical software, an operator can directly set the limits on the plot to reduce the amount of data and at the same time to specify the two-dimensional region of interest. An example of the procedure can be seen in fig. 5, where a particular region of interest was indicated by a rectangle whose borders were set by the operator. In the next step, only data events within the stated limits are collected. The energies E, and E, are transformed into variables x and y by eqs. (3) and a coincidence matrix is obtained with elements N(x, y) being the number of events per pixel (dx, dy). The count numbers N(x, y) are related to the depth-dependent concentration of the analyzed element C(x) by a simple equation N(x,

y)dxdy

= C(x)uQE(y)dn

dy,

(4)

where u is the reaction cross-section and Q the neutron fluence. The geometrical factor E(Y) describing the deviation of the actual measuring geometry from the ideal 47~ one was calculated for the present experimental setup using a separate Monte Carlo simulation program written for the PC AT. In fact, E(Y) gives a solid angle for particles emitted under angle 0 (y = cos O), averaged over the sample surface. The E(Y) vs. y dependence can also be determined from two-dimensional coincidence measurement of a suitable sample. In fig. 3, the E(Y) vs. y dependence calculated for the present measuring geometry is compared with that determined experimentally from the measurement of a Li standard (see below). The calculated curve was convoluted with the instrumental response function. One can see quite reasonable agreement between calculated and experimental dependencies. The total effective solid angle for the present experimental setup with a spatially extended sample, calculated as an integral of E(Y), was 0.26 X 47~ sr. From eq. (41, the depth concentration profile C(x) of the analyzed element can be determined providing all factors entering the right side of eq. (4) are known. The size of the elementary pixel dx dy is chosen by the operator. The particle ranges R, and R, as a function of the

K Havninek et al. / Neutron depth profiling

527

particle energies, which are necessary for the conversion of particle energies into x, y variables, were obtained by numerical integration of pertinent stopping powers. The latter were taken from the subroutine RSTOP of the TRIM program [13] (version 1991) which is based on the Ziegler-Biersack-Littmark theory [ 141. The calculated R(E) vs. E dependencies were stored as a table for subsequent usage in the TWODIM program. The depth resolution Ax (FWHM) can be estimated in the standard manner by differentiating eq. (3a) and summing up quadratically the contributions from both detectors. After some manipulation one obtains Ax= (2.36~[(t-x)~ +x2 A E$,(

AE:S,(E,)’ El)‘] “‘>

where S&E,) and S,(E,) are the corresponding stopping powers of both particles in the sample taken at measured particle energies, and A E, and A E, are the energy uncertainties in both spectrometric chains. The latter quantities combine the contributions of detector energy resolution, particle straggling and multiple scattering in the sample and the detector dead layer as well. One can see from eq. (5) that the surface depth resolution on opposite sides of the sample (x = 0 and x = t) is inversely proportional to the stopping power of the particle which is registered by the adjoining detector. The angular dependence of the depth resolution in this limiting case is the same as in the standard detector measuring setup.

‘.O1 4

I

0.0

0.2

0.4

0.8 0.6 cos(0)

1.0

Fig. 4. The dependence of the depth resolution on the particle emission angle 8 for different depths, as calculated from eq. (5) for the 6Li(n, aj3H reaction in a 3.6 p,rn thick mylar sample (for details, see text). The numbers on the curves of equal depth resolution are Ax [nm].

The uncertainties A E, and A E, as funetions of the emission angle 0 and the depth x at which the nuclear reaction occurs, were calculated using the simple formalism proposed earlier in ref. [15]. The depth resolution Ax as derived from eq. (5) for the 6Li(n, a)‘H nuclear reaction in a 3.8 pm thick mylar foil is shown in fig. 4 as a function of the emission angle 0 and the depth x (measured from the front of the sample). It was assumed that a-particles are registered by the detector facing the back of the sample, so that the best depth resolution less than 50 nm is achieved for large depths in this case. One can see that for fiied depth and within the angular range 0 = O-70” accessible in the present case, the depth resolution changes only slightly. For fiied emission angle 0, the depth resolution increases only two times when moving from the sample back to the sample front face. For samples thin enough, complementary parts of the coincidence matrix can be employed and whole depth profile may be extracted with uniformly low depth resolution.

1.2

Fig. 3. Geometrical factor &OS 8) of eq. (41, as calculated by a Monte Carlo simulation for the present experimental arrangement (the detector collimated to 8x8 mnIz area and placed at a distance of 2 mm from the sample). Full line, MC simulation (lo4 events) convoluted with spectrometer response function (this convolution is responsible for cos 8 exceeding unity). Circles, experimental data.

4. Results The performance of the present device was checked by several measurements of different standards with known composition and structure. Thin standards were prepared by evaporating minute amounts of boron and lithium onto 1.9 km thick mylar foils. More intricate

V. Havrrinek et al. / Neutron depth profiling

Lithium

500

0 channels

1oou (

Dl

)

Fig. 5. Two-dimensional plot of coincidence data measured on the sample comprising two thin Li/B layers at depths of 1.8 and 3.6 urn in the mylar. The Li events of two layers are well separated from each other and from the B events arising only from deeper layers. The total measuring time was 1.1 X lo4 s. Only each second event of 4~ lo4 total count number is depicted.

samples

were prepared

by packing

two foils together.

The samples were thoroughly stretched on a frame placed between the detectors. In fig. 5, the raw coincidence data from the sample comprising two Li/B layers are depicted. The measuring time was 3 h. Both spectrometric chains work in the same manner registering all incoming particles, so that the same depth information can be extracted from two complementary regions of the two-dimensional coincidence data. Enclosed in the rectangle are the coincidence events from the 6Li(n, CX)~Hreaction when the triton was registered in the first detector (Dl) and the o-particle in the second (D2). The two distinct traces correspond to the reaction events taking place in two thin Li layers at depths x = 1.8 and 3.6 pm with corresponding area1 densities 3.3 x 1015 and 5.0 X 1014 6Li at. crnm2, Low-energy tails correspond to the particles emitted at progressively increasing emission angles (with respect to the sample surface normal). The same data are enlarged and depicted as a three-dimensional plot in fig. 6 with the number of events per 2 x 2 channel pixel on the log vertical axis. Using eqs. (3) and (4), the depth profile of 6Li atoms in the sample can be determined from the measured coincidence data. The depth profile extracted from the data of fig. 6 is shown in fig. 7. Only the events in the angular interval A0 = O-25” were summed. The widths of the two distinct distributions are close to the theoretical depth resolutions as calculated above. As expected, the depth resolution increases for larger depths (see fig. 4). One can see from fig. 6 that the overall background due to accidental coincidences is negligible. The Li

Fig. 6. Three-dimensional plot of the C,rcraence oata enclosed in the rectangle in fig. 5. The number of registered events (vertical log axis) as a function of channel number (or particle energies) of detectors Dl and D2 is depicted.

detection limit for a thermal neutron flux of 7 X lo6 cme2 s-l and 3 h measuring time is estimated to be about 10” 6Li at. cme2. For boron, the situation is less favourable due to a higher background level (see also fig. 5). Another sample investigated was a 10 p,rn thick Al foil homogenously doped with about 3 at.% Li. The relevant part of the coincidence spectrum measured with rather low statistics is shown in fig. 8. The well

1 .o

2.0 depth

3.0

4.0

[w-n]

Fig. 7. The 6Li depth profile determined from the coincidence data of fig. 6 by means of a standard procedure described in the text. Only events corresponding to emission angles 0 < 8 < 25” were summed.

VI Havrhnek et al. / Neutron depth profding

529

7

Fig. 10. The particular coincidence data obtained from an 8 urn thick Al foil doped with Li. The sample was subjected to thermal annealing, resulting in a highly nonuniform Li distribution. For details, see text. Fig. 8. The relevant coincidence data for a 10 urn thick Al foil homogenously doped with Li. The total measuring time was 1.1 x lo4 s. For other details. see text.

pronounced high energy edges correspond to the events arising at front and back sample surfaces when a-particles or tritons are registered by adjacent detectors with their respective maximum energies E,, and E,. The coincidence matrix decomposes into three regions defined by the maximum particle energies. For the determination of the Li depth profile only those events can be used in which the tritons are registered in the detector with energies above E,,. In the coincidence matrix, these events are situated in the strips parallel to the high energy edges with the energy span between E, and E,,. The events in which both particles are registered with energies below E,, cannot be recog-

Fig. 9. The Li depth profile determined from 8. Two complementary curves corresponding surfaces were obtained from different parts of matrix, with the alpha particles registered by tors. Fgr details, see text.

the data of fig. to two sample the coincidence adjacent detec-

nized unambiguously, so that they are rendered irrelevant for the depth profile determination. The ‘Li depth profile determined by the standard procedure is shown in fig. 9. Two complementary curves were determined from two different parts of the coincidence matrix corresponding to a-particle registration by front or back side detectors. The Li depth profile throughout the entire sample is thus obtained by combining both curves. The last example deals with a similar Al foil about 8 km thick, doped with Li. The sample was subjected to thermal annealing resulting in sample surface oxidation, and Li diffusion and segregation. For details of the physical process of the oxidation of such Al/Li alloys, see ref. [16]. The relevant part of the coincidence spectrum is shown in fig. 10. The Li distribution

depth

(pm)

Fig. 11. The Li depth profile determined from the coincidence data of fig. 10. The profile is composed of two branches, each obtained from different parts of the coincidence matrix.

530

K Havrrinek et al. / Neutron depth profiling

is highly nonuniform, with pronounced concentration maxima at the sample surfaces. The calculated Li depth profile is shown in fig. 11. The entire profile determined with high depth resolution was composed of two parts as described above.

The computer programs used for data collection and evaluation exist only in working versions and they are presently not available. The listing of the TWODIM code can be sent on request.

Acknowledgements 5. Conclusion An experimental device was built for NDP analyses of light elements, which is based on the simultaneous detection of both reaction products emitted at a broad angular range. The samples in the form of thin selfsupporting foils are irradiated with thermal neutrons from the neutron guide, and the reaction products are detected with large area PIN diodes situated in close vicinity to the sample. Standard electronics were used for the signal processing and data storage. The technique for two-dimensional data handling and evaluation was proposed and the corresponding computer programs were written. Several measurements performed on thin standards confirmed the feasibility of the method and enable assessment of its inherent limits. The depth resolution depends on the analyzed depth and particle emission angle, but varies only slightly throughout the accessible angular range from 0 to 70” for greater depths. The surface depth resolution, however, improves by a factor of 2 at glancing emission angle. For thin samples the entire depth profile can be determined with uniform depth resolution by combining complementary parts of the coincidence matrix. The surface depth resolution obtained in the present setup is close to that achievable by conventional NDP measurements. The detection limit for a fixed measuring geometry is restricted mainly by the low accessible neutron flwc. Here, the use of a neutron lens recently reported in ref. [17] could be very beneficial for further sensitivity enhancement. The neutron lens can focus the neutron beam down to some 30 km diameter, with corresponding flux enhancement by several orders of magnitude. Apart from this, the present detection efficiency could be further increased by bringing the detectors closer to the sample. Utilization of very large emission angles is presently still impossible, due to relatively thick dead layers of the used PIN detectors. The use of detectors with thinner dead layer (e.g., PIPS detectors) is therefore desirable.

The authors would like to thank Dr. J. eervena, Dr. I. Tomandl and Mr. A. Dvoiak for their assistance in the experiment and data evaluation.

References [l] J.F. Ziegler, G.W. Cole and J.E.E. Baglin, J. Appl. Phys. 43 (1972) 3809. [2] D. Fink, Thesis, Free University Berlin (1974), Bibl. no. HO?, 0833. [3] J. Cervena, V. Hnatowicz, J. Hoffmann, Z. Kosina, J. Kvitek and P. Onheiser, Nucl. Instr. and Meth. 188 (1981) 185. [4] R.C. Downing, J.T. Maki and R.F. Fleming, J. Radioanal. Nucl. Chem. 112 (1987) 33. [5] J.P. Biersack, D. Fink, R. Henkelmann and K. Mueller, Nucl. Instr. and Meth. 149 (1978) 93. [6] R.G. Downing, R.F. Fleming, J.K. Langland and D.H. Vincent, Nucl. Instr. and Meth. 218 (1983) 47. [7] D. Fink, J.P. Biersack, Chr. Strumpff and S. Schlosser, Nucl. Instr. and Meth. B15 (1986) 740. [8] N.R. Parikh, E.C. Frey, H.C. Hofsass, M.L. Swanson, R.G. Downing, T.Z. Hossain and W.K. Chu, Nucl. Instr. and Meth. B45 (1990) 70. [9] W.K. Chu, Radiat. Eff. Def. in Sol. 108 (1989) 125. [lo] D. Kollewe, Nucl. Instr. and Meth. A254 (1987) 637. [ll] P.H. Gooda and W.B. Gilboy, Nucl. Instr. and Meth. A255 (1987) 222. [12] N. Markewich, I. Gertner and J. Felsteiner, Nucl. Instr. and Meth. A269 (1988) 599. [13] J.P. Biersack and L.G. Haggmark, Nucl. Instr. and Meth. 174 (1980) 93. [14] J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Ranges of Ions in Matter, vol. 1 (Pergamon, New York, 1985). [15] J.P. Biersack, D. Fink and R. Henkelmann, Nucl. Instr. and Meth. 149 (1978) 93. [16] D. Fink, V. Hnatowicz, J. Kvitek, V. Havranek and J.T. Zhou, Surf. Coat. Technol. 51 (1992) 57. [17] M.A. Khumakov, personal communication; M.A. Khumakov, V.A. Sharov and V.V. Kardakov, Report IAE-5412/14, I.V. Kurchatov Institute of Atomic Energy, Moscow (1991), Nature 3.52 (1992) 390.