Inelastic energy-loss estimate for the Biersack-Ziegler interatomic potential

Volume 106A, number 5,6

PHYSICS LETTERS

10 December 1984

INELASTIC ENERGY-LOSS ESTIMATE FOR THE BIERSACK-ZIEGLER INTERATOMIC POTENTIAL D.S. KARPUZOV and K.I. YORDANOVA

Institute of Electronics, Bulgarian Academy of Sciences, Sofia 1184, Bulgaria Received 5 September 1984

The impact parameter dependence of inelastic energy loss, based on a revised Firsov model, is calculated for collisions ot" Cu, Ne, Ar, Kr and Xe projectile ions with Cu atoms by assuming a Biersack-Ziegler interatomic potential. The results compare favourably with similar estimates for a Moliere potential and an exponential decrease of which the closest approach distance may be a fair approximation.

In most problems of the interaction o f energetic ions with solids the inelastic energy lost by the incident beam plays an important role. Estimates o f ion penetration or backscattering, especially for slowingdown in crystalline targets, need accurate evaluation of the electronic stopping power (Se) in different materials. In recent years a number o f attempts were made to link the Lindhard [1] and Firsov [2] models of inelastic loss evaluation and to measure the electronic stopping power for various ions in solids (see refs. [3,4] for instance). In ref. [5] we have shown that more accurate estimates of quantities involved in the original Firsov model, especially those cases where Moliere [6] or eroded r - 2 potentials were used, result in Se-values close to that found through the semiempirical formula suggested by Oen and Robinson [7]. Recently these values were found to be quite close to the data measured for keV helium ions backscattered from silicon [8]. It has been known for some time, however, that the screening length used in the Moliere potential should be shorter than the values suggested by both Firsov and Lindhard, and a reduction o f 15 to 25% was considered reasonable [9,10]. It seems that in the energy interval o f interest such a reduction results in an interaction close to that "universal" potential suggested recently by Biersack and Ziegler [11]. For this BZ potential we have recalculated here the elec246

tronic stopping power, Se, by using the procedure outlined in ref. [5]. The influence of the potential chosen is discussed. Within the Firsov model the inelastic energy loss in a collision determined by an impact parameter p and a primary energy E 0 = miv2/2 is given by

Te(P, E O) = 2gvoY e , where

Y e = Z 2 Y e l +Z2Ye2 ,

g=h/22/3aB,

aB=0.529A.

Here Yek is dependent on the interatomic potential chosen [5]. Fig. 1 illustrates the Ye-values as function of the closest approach distance r 0 for 2 and 10 keV ions of Ar and Cu incident on Cu. As in the case o f a Moliere potential [5], the inelastic energy loss based on the BZ potential seems to be nearly an exponential function o f r0, except for a small region corresponding to very close collisions. Furthermore, Ye = 100 e x p ( - 0 . 3 5 / 0 . 1 3 2 ) is again a fair approximation for energies E 0 = 10 keV, where r 0 and Ye are measured in A. For the case of E 0 = 2 keV a small reduction o f the preexponential factor might be recommended. A comparison of electronic stopping cross sections estimated by using three different potentials is given in fig. 2. The TF-potential as tabulated b y Gombas 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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0.5

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1.0 t5 2.0 C[0sest approach distance, ro[~]

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Fig. 1. The dependence of the Ye-function on the closest approach distance of the collision, r o. e~

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