Misaligned Beam Research Articles

Experimental and computer analysis of P+-ion penetration tails in a SIO2-Si two-layer system

Penetration profiles of P+ ions with energy between 70 and 150 keV incident 7.5° off the 〈100〉 axis on silicon covered with a SiO2 layer of thicknesses ranging from 0.05 to 0.20 μm were studied both experimentally and by computer simulation. Electrical measurements were routinely performed, but occasionally CAMECA ion-probe measurements were carried out to obtain chemical profiles. For a given energy of implantation, maximum penetration occurs when the oxide thickness produces an angular spreading of the misaligned incident beam with maximum transmitted intensity along the crystallographic direction. This suggests that the tails are due to a channeling process, in agreement with the finding by Blood et al. in bare silicon. It is also shown that diffusion occurs after 1/2-h annealing at 900 °C, implying the presence of a high-diffusivity region around the penetration tail.

Ion beam optics of misaligned beam transport elements

To study the influence on misaligned ion optical beam elements on the image aberrations, a theoretical approach has been developed which is suited to higher order (≥3) beam transport matrix theory. For practical applications a set of subroutines based on this formalism has been implanted into the program IONBEAM, thus arbitrary beam element displacements and inclinations can be treated in the calculations.

Step Correction of Misaligned Beam Waveguides

This paper studies the steady-state performance of a system that stabilizes the beam position in optical waveguides. We have constrained the system to make only a single fixed amount of correction in the beam position at any given lens. We consider a symmetric corrector capable of correcting both positive and negative errors at any given lens and an unsymmetric corrector capable of correcting only positive errors at any given lens. We give the results from our studies of the performance of these systems when the lens misalignment forms a wave at the guide resonant spatial frequency, ω o , and from our simulation of 5,000 confocal guides which were subjected to uncorrelated lens misalignment. We also derive an approximate sťatistical theory relating the root mean square beam displacement to the root mean square lens misalignment. We relate systems where correction occurs at every lens to systems where correction can occur only at every nth lens.

On the Theory of Randomly Misaligned Beam Waveguides

A straightforward method for the determination of the expected attenuation in misaligned beam waveguides is presented. It applies to confocal guides and assumes that the misalignment consists of random displacements of the lenses in directions perpendicular to the beam axis. Reiterative fields, as they are present in perfectly aligned beam waveguides, do not exist in misaligned guides. However, it can be shown that there are beams whose expected field distribution is repeated from lens to lens. These "statistical modes" are determined by the eigenfunctions of a homogeneous integral equation of the second kind. The corresponding eigenvalues determine the expected attenuation per iteration. The absolute squares of the eigenvalues yield an upper bound for the expected power loss per iteration. The integral equation is solved for small mean square displacements of the lenses by a perturbation method. For infiitely extended lenses, the equation can be solved in closed form. In both cases the expected attenuation of the lower-order statistical modes has been calculated; the results are shown as function of the mean square displacement of the lenses.