中国物理B ›› 2002, Vol. 11 ›› Issue (4): 389-392.doi: 10.1088/1009-1963/11/4/314

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On the differentiability of depth distribution function of deposited energy, momentum and ion range

张竹林   

  1. Department of Mathematics and Physics, Huainan Institute of Technology, Huainan, China
  • 收稿日期:2001-09-29 修回日期:2001-12-03 出版日期:2002-04-13 发布日期:2005-06-13
  • 基金资助:
    Project supported in part by the Scientific Research Fund from the Educational Bureau of Anhui Province, China, (Grant No 2001kj226).

On the differentiability of depth distribution function of deposited energy, momentum and ion range - a reply to Dr G. Glazov 

Zhang Zhu-Lin (张竹林)   

  1. Department of Mathematics and Physics, Huainan Institute of Technology, Huainan, China
  • Received:2001-09-29 Revised:2001-12-03 Online:2002-04-13 Published:2005-06-13
  • Supported by:
    Project supported in part by the Scientific Research Fund from the Educational Bureau of Anhui Province, China, (Grant No 2001kj226).

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摘要： Based on the translational invariance of a medium, a new theorem has been proposed and proved rigorously: the depth distributions of the deposited energy, momentum and ion range must be infinitely differentiable functions in amorphous or polycrystalline infinite targets by ion bombardment, if these functions exist. The origin of the "discontinuity", derived by Dr Glazov in 1995 in J. Phys.: Condens. Matter 7 6365, has been analysed in detail. For the power cross section, neglecting electronic stopping, the linear transport equations determining the depth distribution functions of the deposited energy and momentum (by taking the threshold energy into account) have been solved asymptotically. An important formula derived by Dr Glazov has been confirmed and generalized. The results agree with the new theorem.

Abstract: Based on the translational invariance of a medium, a new theorem has been proposed and proved rigorously: the depth distributions of the deposited energy, momentum and ion range must be infinitely differentiable functions in amorphous or polycrystalline infinite targets by ion bombardment, if these functions exist. The origin of the "discontinuity", derived by Dr Glazov in 1995 in J. Phys.: Condens. Matter 7 6365, has been analysed in detail. For the power cross section, neglecting electronic stopping, the linear transport equations determining the depth distribution functions of the deposited energy and momentum (by taking the threshold energy into account) have been solved asymptotically. An important formula derived by Dr Glazov has been confirmed and generalized. The results agree with the new theorem.

Key words: Radiation damage, momentum deposition, ion implantation

中图分类号:  (Ion radiation effects)

  • 61.80.Jh
79.20.Rf (Atomic, molecular, and ion beam impact and interactions with surfaces)