I had calculated transport length of ions in PMMA using ions' Monte-Carlo trajectories modeled by TRIM with option 'Detailed calculations with full damage cascades'. I used the coordinates of large angle atomic collisions from file generated by SRIM in order to calculate mean free-flight distance L and mean cosine of scattering angle . Then I calculated transport length L_transp as L_transp =L/(1 - ) ..
I have seen the transport length increase with ions' atomic number.
But in the article [Firsov O.B., Scattering of ions by atoms, Sov. Phys. JETP 34/7, 308 (1958)] the expression for transport cross section was evaluated, according to that transport length should decrease with atomic number.
What do you think about this contradiction?
Could you advise me some other articles about transport length of ions calculation?
Please find attached a short explanation of my calculations and mentioned Firsov's article.
Many thanks in advance,
May be the cause for the contradiction that Firsov in his work and TRIM use different interaction potential?
I'm not sure if the definition you use for transport length is meaningful for heavy ions traveling through matter because the most important interaction that stops the ions is an energy transfer to electrons in the resident atoms (ionization). This is usually not modeled as a set of discrete collisions. Instead it is modeled as a continuous slowing down of the incident ion which eventually stops the ion with very little change in trajectory direction. The definition you are using for transport length would predict an infinite length in the limiting case of no change in trajectory direction when, in fact, the range is finite.
Ion interaction with matter can be approximated as a sum of two parts, elastic and inelastic (ionization). The contribution of these parts depends on the ion energy, atomic numbers of both ion and target atom. Both Firsov (who consider elastic scattering in this article only) and TRIM (if I remember it right in TRIM you can have contribution of both elastic and inelastic interactions) are correct. Your transport length prediction is wrong, use projected range from TRIM if you want to find the depth of penetration, and full ion range in TRIM if you want to evaluate the length of the whole trajectory. In photoresists like PMMA most important is the deposited energy rather than ion trajectories. There are many books and papers on these, we published a review in Progress of Surface Science recently. I'll send you a reference if you can't find it.
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