Range profiles of 10 to 390 keV ions (29 ≦ Z1 ≦ 83) implanted into amorphous silicon

481

Nuclear Instruments and Methods in Physics Research B28 (1987) 481-487 North-Holland, Amsterdam

RANGE PROFILES OF 10TO 390 keV IONS (29 5 2,~ INTO AMORPHOUS SILICON P.F.P. FICHTNER,

M. BEHAR,

CA. OLIVIERI,

R.P. LIVI, J.P. DE SOUZA and F.C. ZAWISLAK

Institute de Fisica, Uniuersidade Federal do Rio Grande do Sul90049

J.P. BIERSACK Hahn - Meitner-Institut

83) IMPLANTED

Port0 Alegre, RS, Brazil

and D. FINK Berlin, Germany

Received 10 April 1987 and in revised form 13 July 1987

Our recent range profile measurements for a series of elements (29 5 Z, s 83) implanted from 10 to 390 keV in amorphous silicon are compared with the Biersack-Ziegler (BZ) calculations. While the theoretical predictions are in good agreement with the experimental ranges at implantation energies larger than 70 keV, the results for several elements at lower energies are strongly underestimated by the calculations. These differences are ascribed to the Zi-range oscillation effect. In the present work we perform range calculations simulating a decrease of the elastic interaction at low energies. This approach is phenomenologicallyrelated to

modifications of the charge distribution during the collisions. The results obtained show a better agreement between the calculations and the great majority of the existing low energy experimentalranges in silicon substrates.

1. Introduction In all studies of the interaction of energetic particles with solids the interatomic potential plays an important role, as for example in events that lead to backscattering, radiation damage and in the spatial distribution of the implanted ions. Statistical models for interatomic interactions [l-3] have been widely employed in the calculation of the nuclear stopping power and consequently in the range predictions of the implanted ions. However in the past few years more refined theoretical and experimental studies [4-91 have shown that none of the statistical interatomic models could be applied with satisfactory accuracy. In order to improve the theoretical situation Biersack and Ziegler have recently developed a new “universal potential” obtained as a least square fit to more than 500 individually calculated binary potentials [lO,ll]. It turns out that using this universal potential and also an improved electronic stopping power based on the theory of Brandt and Kitagawa [12], the calculated projected ranges (R,) and range stragglings (A RP) are in overah good agreement with most of the previously published data, for a wide implantation energy

* Work supported in part by FINEP, CNPq and CAPES.

0168-583X/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

range, and for a large set of ion-target combinations. However, for several ions implanted into silicon at energies below 50 keV [6-81 significant discrepancies still exist. The work described here was undertaken to gain more insight into the reason for this disagreement. We measured range profiles for several elements (29 5 2, $ 83) implanted into amorphous silicon in a wide energy range (lo-390 keV) and analyzed the corresponding depth profiles with the Rutherford backscattering technique. Our data show that in most cases the theory reproduces the experimental results quite well (within &lo%). However, for Au, Eu and Yb we have found (see ref. [13] and [14]), significant disagreements at low implantation energies. (E < 70 keV). In the case of Au, the measured range at e.g. 20 keV was found to be nearly 50% larger than the predicted one. In the present paper we analyze our experimental data in terms of semiempirical modifications of the Biersack-Ziegler potential (Vsz). This approach was undertaken in order to test the sensitivity of the projected range R, predictions to slight variations of the potential in the region corresponding to low energy interactions. This procedure resulted in a phenomenological approach giving reasonable agreement not only to our own experimental results, but also with the great majority of other experimental low energy range data in Si.

482

P. F. P. Fichtner et al. / Range profiles for 10 - 390 keV, 29 5 Z, 1; 83 ions in Si

2. Experimental procedure and data analysis The targets were prepared from polished (100) oriented silicon single crystal wafers. After the chemical cleaning processes the thin silicon dioxide surface layer was removed by HF etching. The samples were amorphized by Ar+ bombardment using different energies and fluences in order to obtain an amorphized layer extending from the surface to a depth larger than 2000 A. The total argon fluences were always smaller than 10” cmw2 [15]. Small pieces of the wafers (= 1 cm2) were then implanted with fluences and energies ranging from 8 x 1Or4 atoms cmd2 at 10 keV to 4 x 1015 atoms cm-2 at 390 keV. For those fluences, using the experimental sputtering yields reported in ref. [16], the expected shifts of the ion profiles towards the surface are small (< 5%) as compared with the ranges. All implantations were made with the 400 kV HVEE ion implanter of the Institute of Physics, Porto Alegre, and performed at room temperature. The beam current densities were P 0.1 PA cm -2 in order to avoid excessive heating of the samples. Depth profiles were obtained by Rutherford backscattering analysis using 760 keV alpha particles (4He21) from the same implanter. Each sample was measured at least two times, with the beam impinging perpendicular onto the sample’s surface and under angles of 60° to 70° with the samples’s normal. The tilted geometry improves the depth resolution of the measurement. Backscattered alpha particles were registered by a silicon surface barrier detector placed at 160° with respect to the beam direction. The detection system resolution is defined as the fwhm of the edge of a gold film used for the energy calibration of the system, and was 13 keV. Some measurements were additionally made with sample and detector placed at - 70 o and - 160 o respectively. This geometry provides a test of a possible misalignment of the system. Data analysis was performed in two steps. The centroids and fwhm of the ion distributions and the width and position of the silicon edge were determined by fitting the spectra via Gaussian and error function distributions respectively. In a second step, the centroids and fwhm of the same particle distributions were obtained by direct numerical computation and, in all cases, showed an excellent agreement with the values obtained via the Gaussian fit. The position and the width of the silicon edge provides a check of the system resolution and stability. The electron stability was additionally checked by observing the position of an externally generated pulse. Projected ranges were then determined using the surface approximation [17], with the alpha particle stopping power taken from the HESTOP subroutines reported in ref. [ll]. Range stragglings have been evaluated after performing the deconvolution process under the assumption that the estimated energy

straggling of the 4He ions in Si and the system resolution function are Gaussian [17,18]. The other contributions to the system resolution (finite acceptance angle and the angular multiple scattering of the alpha particle) can be neglected for the geometry used in the present work. The errors in the profile measurements, estimated from the stability of the Si edge and the pulse generator peak position, resulted to be better than 0.4 channel corresponding to less than 1 keV ( f 1.4 nm).

3. Results The main objective of this work is to compare accurately measured range data with the predictions based on the Va, potential. Table 1 displays our experimental data, including previously published results [13,14,19, 201. Preliminary results of the present experimental data have been reported elsewhere [21]. For illustration, we show in figs. 1 and 2 the experimental and theoretical R, and AR, results for Rb and Eu implanted into Si. The predicted R, values for Rb are in good agreement with the experimental points. For Eu, however, the measured projected ranges R, at low energies are not fitted by the theoretical curve obtained from the universal stopping power, With increasing energy the discrepancies diminish, and good agreement is attained above 100 keV. In order to give an overall view of the present experimental data as compared to theory, fig. 3 displays the data from table 1 in reduced p-r coordinates, defined as pr,= 4aa2NR,MlM2/(Ml E = aEMJZ,Z,e*

+ M,),

( Ml + M,) .

In these relations N is the target density, e the electronic charge, Mi and Zj correspond to mass and atomic number of the projectile (i = 1) and target (i = 2), E is the energy, R, the projected range and a is the new screening length defined by Biersack and Ziegler [ll] as a (A)

= 0.4863/( ZF.23 + Zt.23).

The data points show regular behaviour at reduced energies e > 0.06, what is well reproduced by the theoretical predictions (see figs. 3a and b). However at low energies, the experimental data cluster in individual branches (particularly for Au, Yb, Eu and Cs), which are not predicted by the theoretical calculation. This behaviour may be better seen in fig. 3c where the experimental to theoretical reduced projected range ratio pP/peOr is plotted as a function of the reduced energy. From fig. 3 it can be seen that (i) for Bi, Sn, Pd, Rb, Ga and Cu, the theoretical results agree within *lo% with the experimental data; (ii) for Au, Yb and

483

P.F. P. Fichtner et al. / Range profiles for IO- 390 keV, 29 ( Z, 5 83 ions in Si Table 1 Measured parameters R, and AR, (given in parentheses) of 29 $ Zt $83 in A and the errors are 5 + 14 A (see text)

ions in amorphous silicon. The values of R and AR,

are

Energy (keV)

Ions

10

15

20

30

40

70

100

150

63cu

168

170

225

276

356

560

793

1235

(57) 115

(63) 160

(95) 194

(127) 267

(152)

69Ga

(237) 531

(294) 705

(487) 1033

(57)

79Br

(45) 120

(71) 183

(98) 251

:iO) 355

(190) 445

(260) 600

1122

85Rb

(40) 108

(65) 172

(85) 256

(130) 325

(165) 502

(255) 650

1310

io6Pd

(37) 115

(54) 181

(74) 240

(118) 332

(170) 435

(230) 550

(425) 1020

(31) 105

(46) 150

(68) 210

(108) 285

(140)

(185) 525

(315) 945

85

(60) 188

(85) 270

(155)

*=cs

(47) 137

(267) 785

i53Eu

144

(50) 194

(67) 247

286

(84) 318

395

;:0, 496

(230) 855

1180

174Yb

158

(29) 200

(46) 235

(63) 270

(68) 310

(91) 380

(115) 468

(202) 796

(296) 1110

(43) 250

(51)

(64)

(84) 375

(92) 428

(126) 484

(220) 782 a1

(280) 1100 b,

1366

(103)

(130) 425

570 c,

(198)

(290)

(335)

(115)

(150)

120s n

(30) 19’Au 209~i

110

140 (46)

177 (23)

210 (50)

(42)

315 (110)

50

(54) 160

198

245

(84) 270

(50)

(60)

(69)

(75)

200

300

350

380

390

1373

1725 (500)

1725 (550) 1485 (415) 1420 (350)

1245 (310)

a) Energy = 190 keV. b, Energy = 290 keV. ‘) Energy = 145 keV.

t

ION

85Rb37

,102; E -s

-

. PRESENT EXf? RESULT o DATA FROM REF: 7

E h 10’ y

10' ENERGY

102 CkeV)

Fig. 1. Comparison of experimental and calculated projected range R, and range straggling AR,, for *‘Rb implanted in silicon at energies from 10 to 350 keV. The full lines correspond to calculations using the Vsz universal potential and the points represents the experimental data from table 1. The dashed line represents the prediction using the Vri potential (see the text).

Fig. 2. Comparison of experimental and calculated projected range R, and range straggling AR, for 153Eu implanted in silicon at energies from 10 to 380 keV. The full lines correspond to calculations using the V,, universal potential and the dashed Iine is a result based on the ei potential approach (see the text).

484

P.F.P. Fichtner el at. / R~ngepr~~iie~~~r IO-390 keV, 29 5 Z, 5 83 ions iB Si

further examination of this potential. It is known that for a given reduced energy the reduced nuclear stopping power

(a)

S,,(E) = luhrna; sin2(8/2)

4

100

8 6

4

P pexp’ Ptheor

Id PI

0.7

/ 6

8 jo-2

c 2

/

~rll//lllll

4 6 810-l

/ 2

I

4

/Ill/i 6

8 100

REDUCED ENERGY Fig. 3. a) The experimental projected ranges from table 1 plotted in terms of the reduced range-energy variables defined in the text. b) The responding theoretical predictions obtained by means of the PRAL code algorithm [ll] using the universal BZ stopping. c) Experimental to theoretical reduced range ratios (p”p/~*~“‘).

Eu ions, the measured ranges exceed the calculated ones at low energies, but in all the three cases the pexP/$h”’ decreases rapidly with increasing energy, approaching 1 at higher energies; (iii) the Cs data show an average deviation of about -15%, which depends weakly on energy, except for the lowest energy point.

4. Discussion The present work shows that the universal potential approach gives an overall good description of the experimental R p results. However, the observed discrepancies at law energy point out to the need of

2b db

(1)

depends only on a limited part of the atomic interaction potential. In this equation i? is the scattering angle in the center-of-mass system and b =p/a the reduced impact parameter. Therefore as a first step we will find how the reduced transfer energy density (which is the integrand of (1)) depends on the reduced distance of closest approach R ,,/a. In order to calculate d&(e) = E sin*(0/2)2b db for each reduced energy the orbit integral was solved numeri~~y using the I’& potential, with the integration performed in terms of the variable u = (1 Ro/R)“2, where R is the interatomic separation. The results of these calculations for each reduced energy are presented as full lines in fig. 4. The set of d5’, values which gives a significant contribution to the S,(e) integral, also characterizes the region of the interatomic potential which is significant for collisions with the given reduced energy E. For a better illustration of these regions the universal screening function +sz {dashed line) is also plotted in fig. 4 as a function of the reduced distance x = R/a. Therefore fig. 4 gives for each reduced energy value the reduced distance from which V,, has to be modified. The modification is performed by cutting off the Vsz potential at a given distance the decrease in X max_ This means that for x > x,, interaction energy is represented by a potential Y(x) = 0. This form of potential is further referred to as I$?. Hence for incident particles with kinetic energies smaller than Vsz(xmax) the projectile-target interaction will be given by hard sphere collision. Our experimental data (see fig. 3) show that large disagreements with the theory occur at implantation energies in the 0.01 < e < 0.06 range. It was shown [22], that the last phase of the slowing down of the implanted ions (up to E = 0.001) still gives a si~fic~t contribution to the total R,, whereas lower energy collisions may be negIected. This corresponds to the potential function region of x d 18 (see fig. 4). Therefore we defined a new nuclear stopping power with a potential cutoff at x,, = 18. In a next step we calculate new R, values via the PRAL algorithm [ll] using the new nuclear stopping power and the improved electronic stopping derived from the Brandt-Kitagawa theory [12] as input. A comparison between the new and the old results, calculated by using respectively the Vu, and the I$$’ potentials did not show any noticeable improvement. By decreasing further the upper limit x,, of the reduced distance in the Vgg potential we were able to reproduce the experimentally observed R, values nicely.

P.F.P. Fichtner et al. / Range profiles for lo- 390 key

10-3

I 10-l

IO0

10’ X

Fig. 4. Reduced energy transfer density distribution for elastic binary collision events with reduced energies c from low4 to 10’ (full lines). The Biersack-Ziegler screening function is given by the dashed line. The x axis corresponds to reduced distances (see the text).

For example, the ranges represented by the dashed lines in fig. 2 were calculated for x,, = 12, and as is observed a much better agreement with the experimental data of Eu implanted in Si is achieved. Following the same kind of procedure we arrived at similarly good agreements also for Yb and Au implanted in Si, where especially large deviations have been observed. It turns out that the sensitive x,, values for each of the above case are well correlated to the interatomic distances given by the sum of the colliding partners ionic radii. This fact provides the basis for a generalization of the Vi$L approach by using the sum of the ionic radii as an empirical parameter. The method described above has been applied to calculate ranges for all the experimental data quoted in table 1. The x_ used in the present calculations was obtained from the ionic radii quoted in ref. [23], taking the larger valence state up to + 4 for the implanted ions and + 4 valence for silicon. In the case of Br, since the only tabulated ionic radii correspond to the + 5 and + 7 valences, we have used the +5 value. Therefore the quoted ionic radii correspond to the +1 valence state for the alkaline metals and to the +2 or + 3 state for the other implanted ions. These choices are empirical, based only on the best agreement between experiment and theory.

29 s Z, 5 83 ions in Si

485

The limitation in range of the interatomic potential provides smaller calculated stopping powers and consequently larger projected ranges. This means that the ei approach provides a better agreement between experiment and theory only when the experimental values are underestimated by the calculations. Fig. 5 presents the general results of the above calculations. A comparison with fig. 3c clearly shows an improved pr, agreement for the low energy Au, Yb and Eu data while the other pt, values are left nearly unchanged. This means that the VF; approach is consistent with all the experimental data. In the “Rb case (fig. l), for example, the results of the Vgt approach, given by the dashed line, did not change the good agreement already existing between the experimental values and the calculation via the Vaz standard universal potential. Furthermore 9 the Vgg approach was extended to the series of ranges reported in refs. [6] and [7]. Since, in some cases, the tabulated ionic radii are given for more than one valence state close to the + 4 valence, e.g. + 2, + 4, and + 6, the quoted results correspond to the mean of the R, values calculated considering all valences up to +6. Fig. 6 presents the results obtained, where the full circles correspond to the experimental data for e = 0.015 and the open ones for e = 0.004. The curves in fig. 6 represent the R, values obtained using the V$ potential (dashed lines) and V,, standard potential (full lines). It is evident that the calculations with Vs’$ reproduce much better the experimental results. In all the cases the T,’ approach provides R, correction in the right direction. In some few cases (Br and I) the corrections are slightly overestimated. In others like Kr, Xe and alkaline metals, the vi predictions are equal to the V,, ones, anyway good agreement between theory and experiment is found.

REDUCED

Fig.

ENERGY

5. Experimental to theoretical reduced range ratios using the VP&’ approach and the data from table 1,

pP/pbheor

plotted as a function of the reduced energy C.

486

_200-

P.F.P. Fichtner et al. / Rangeprofiles for IO-390 keT/;29 ( 2, s 83 ions in Si

. EXPERIMENT (~=0.015) o EXPERIMENT (E = 0.004) UNIVERSAL STOPPING -

LN,,,,,,,,,

l_-

30

,,I

40

,,,,,,,,.

((,,,),,

50

,,,,,,

-7

60

_

,,,,,,,,

70

_

,,,,

80

_,,,I

Ll

Fig. 6. Experimentalprojected range data from refs. [6] and [7] for various elements 20 5 2 $83 implanted in silicon at energies corresponding to E= 0.015 (full circles) and F = 0.004 (open circles). The full curves represent the theoretical predictions based on the VnZ potential and the dashed lines express the predictionsbased on the VBg potential (see text).

The results summarized in figs. 5 and 6 show an overall improvement in the agreement between theory and experiment. This fact means that by using the VP; potential in some way we take into account the general features of the low energy atomic collisions. What we have shown is that the deviation between the experimental and the calculated R, values can be consistently described simulating a decreasing in the Vu, interatomic potential at interatomic distances corresponding to the sum of the ionic radii of the colliding partners. At these distances the interaction energy comes mainly from the increase of the kinetic energy due to the colliding atoms valence electrons overlap. One of the basic approximations used in the V,, interatomic potential calculation [ll] is to assume that no rearrangement or distortion of the atomic charge distributions takes place when the atoms are brought together. Therefore the complex modification of the outer electron distributions occurring during the atomic collisions in solid targets should be phenomenologically related with the above described deviations between experimental and theoretical projected ranges.

5. Conclusions It was shown that, for large energies corresponding to r > 0.06, the present experimental data of R, and AR, for various ions implanted in amorphous silicon are in good agreement with predictions based on the V BZ universal potential. For low energies (E < 0.06) some of the experimental points are not fitted by the calculation using the V,, potential.

Since the experimental data suggest that the Vn, potential should be lowered, we first identified the regions of the potential responsible for the deviations, and then the potential was modified by introducing the Vg approach. This potential is the original one ( VBz), with a cutoff at x,, values given by the sum of the ionic radii of the colliding atoms. It is important to point out that the lowering of the elastic interatomic potential should be phenomenologically related to the modification of the outer electron distribution. In this sense, the present approach can provide an explanation for the empirical correlations observed between ranges or stopping powers with the atomic volume [7,24] and the solid state atomic density [25]. Although the present approach has improved noticeable the agreement between the calculations and the great majority of the experimental R, data, an inspection of figs. 5 and 6 shows that cases with disagreements of up to 25% still exist. We hope that our results will stimulate the search for an appropriate theoretical a priori description of low energy atomic collisions. The authors thank Agostinho A. Bulla, Clodomiro F. Caste110 and Ivo Bello for technical assistance. The support of the DAAD-CNP, German-Brazilian exchange program is also acknowledged.

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P.F.P. Fichtner et al. / Range profiles for IO- 390 keV, 29 s Z, 5 83 ions [15] G. Miter and S. Kalbitzer, Philos. Mag. B41 (1980) 307. [16] H.H. Andersen and H.L. Bay, J. Appl. Phys. 46 (1975) 1919. [17] W. Chu, J.W. Mayer and M.A. Nicolet (eds), Backscattering Spectrometry (Academic Press, New York 1978). [18] J.W. Mayer and E. Rimini, Ion Beam Handbook for Material Analysis, (Academic Press, New York, 1977). [19] M. Behar, P.F.P. Fichtner, C.A. Olivieri, J.P. de Souza, F.C. Zawislak, J.P. Biersack, F. Fink and M. Stadele, Radiat. Eff. 90 (1985) 103. [20] M. Behar, J.P. Biersack, P.F.P. Fichtner, D. Fink, C.V. de B. Leite F&o, C.A. Olivieri, B.K. Patnaik, J.P. de Souza and F.C. Zawislak, Radiat. Eff. Lett. 85 (1984) 117.

in Si

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[21] P.F.P. Fichtner, M. Behar, C.A. Olivieri, R.P. Livi, J.P. de Souza, F.C. Zawislak, D. Fink and J.P. Biersack, Nucl. Instr. and Meth. B15 (1986) 58. [22] P.F.P. Fichtner and J.P. Biersack, private communication. [23] R.C. Weast (ed.), Handbook of Chemistry and Physics, 56th ed. (CRC Press, Cleveland, 1975). [24] E. Geyer, D. Reschke and K. Freitag, Nucl. Instr. and Meth. B15 (1986) 81. [25] S.K. Gupta and P.K. Bhattacharya, Phys. Rev. B29 (1984) 2449.