#### Access Type

Open Access Dissertation

#### Date of Award

1-1-2010

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Physics and Astronomy

#### First Advisor

Karur R. Padmanabhan

#### Abstract

ABSTRACT

HARMONIC SPUTTERING THEORY

By

ZHU LIN ZHANG

February 2010

Advisor: Dr. Karur R. Padmanabhan

Major: Physics

Degree: Doctor of Philosophy

Based on the standard Botzmann equation in Classical Statistics Mechanics, we have derived a variety of Linear Transport Equations appeared in Sputtering Theory for a random, infinite multi-components medium. The pertinent relations among these Linear Transport Equations have been studied in detail. We have introduced exact classical scattering cross-sections of power potential interaction collision into these Transport Equations and solved them asymptotically by using Laplace Transformation for both isotropic term and anisotropic term. A pool of analytical asymptotic solutions has been given for both Lindhard power cross-section and our exact cross-section, such as slowing-down, recoil, scattering and collision densities, etc. The accuracy of these analytical solutions is demonstrated by comparison with Monte Carlo simulations in some cases. For the sputtered atom ejection process, based on the intrinsic relation between recoil density and sputtering calculations, we have proved that the Falcone "mean free path" theory directly contradicts the transport theory, and confirmed that the Falcone-Sigmund "slow down straight" theory is tenable for mono-atomic medium. We have showed that, if let the sputtering yield calculated by using our exact scattering cross-section equal to the corresponding one in Sigmund's theory, the depth of origin of sputtered atoms must be shorter about one half due to the hard sphere collision is dominant in the low energy cascade. Therefore, the entire Sigmund sputtering theory has been rebuilt and the problem on the depth origin of sputtered atoms has been solved. In addition, we have found that a theory proposed by Urbassek et al. (1993) could generate a non-physics negative sputtered particle flux in some cases simulated by themselves. We also have given the Glazov's paradox (1994,1995) an exact explanation.

We have derived an expression for the anisotropic sputtered particle flux at first time for multi-components target. Taking the momentum deposition into account, a new modified Sigmund Sputtering Theory has been developed to describe anisotropic sputtering phenomena induced by low energy and heavy ion bombardment, including sputtering yield energy and angular distributions as well as isotopic effect. The momentum deposition usually ignored in literetures, but could play an important role in the atom collisions in solid, such as the anisotropic transport in the ion mixing. We have clearly demonstrated the intrinsic relation between the ion energy dependence of total sputtering yields and the angular distribution of sputtered atoms induced by low-energy heavy ion bombardment. The sputtering yield energy and angular distributions have calculated based on the ion energy dependence of total sputtering yields for many ion-target combinations. Our new theory has been shown to fit the corresponding experimental results of sputtering yield energy distributions well except the cases where the larger ion incident angle and larger sputtering emission angles were considered.

Our new anisotropic sputtering theory predicted that the ratio of the asymmetric term and the isotropic term must be negative, and proportional to in magnitude for a normal incidence. This is the intrinsic reason why isotopic mixtures are characterized by higher erosion rates for lower isotopic masses and vice versa for a low energy ion bombardment. In particular, the asymmetric term could be comparable with the isotropic term in magnitude for the near threshold energy ion incidence. The former may cancel the most part of the latter. Thus, this effect could be magnified and become even more pronounced in some ratios. Therefore, the present theory successfully solved the isotope puzzle in low energy sputtering.

More recently, according to the experiment measurements published by Prof. A.P. Yalin et. al., our new theory predicted N is preferentially sputtered and the surface enrichment of B; light isotope of boron , rather than heavy isotope of boron , preferentially sputtered for the steady-state in the energy region. Furthermore, based on the fact of sputtering BN, we proposed the generalized statement: Sputtering a compound target consists of condensable (shuch as Li, Be, B...) and volatile (shuch as H, N, O...) components, the volatile component should be sputtered preferentially, independent of their atomic mass ratio. For example, sputtering compound targets BN, LiF, Nacl, NaI et.al, rather than lighter atom, the heavier atom was sputtered preferentially. The statement should be also true for other particle (shuch as Laser and electron et.al.) beam bombardment.

#### Recommended Citation

Zhang, Zhu Lin, "Harmonic Sputtering Theory" (2010). *Wayne State University Dissertations*. 56.

http://digitalcommons.wayne.edu/oa_dissertations/56