Ion-matrix sheaths related to targets with grooves

Abstract

In this work, the ion-matrix sheath near a target with a rectangular groove is studied analytically. A two-dimensional model with a single groove is adopted. The potential and electric-field profiles within the groove are analyzed to provide insight regarding the uniformity and efficiency of ion implantation on its walls. The deviation of the sheath edge from the planar geometry is also illustrated.

Controlling the ion flux on substrates of different geometry by sheath-lens focusing effect

“…One emerging technology is plasma immersion ion implantation (PIII) where objects of complex geometry are bombarded with high energy ions accelerated in a time dependent sheath created by applying a pulsed bias of the order of tens of kV [9]. Non-uniform treatment (ion dose) associated with targets of different geometry have been reported in the last two decays [10][11][12][13][14][15] and elaborate simulations and experiments have been done to estimate the ion flux impinging on the surface [16][17][18][19][20][21][22][23][24][25]. Following our interest in charge focusing by two or three-dimensional plasma-sheath systems we demonstrated that PS formation reveals useful information about D sh [26], and that the negative ion focusing can be used as a diagnostic technique for electronegative plasmas [27].…”

The free-boundary problem for space-charge regions around conductors: application of the hodograph method

“…Studies of less symmetric free-boundary problems were typically based on the numerical solution of Poisson's equation [2,3,5]. However, for particular two-dimensional configurations, some analytical treatments have been proposed, which were based on the approximate solution of Poisson's equation [7] or on alternative methods, as the application of Green's differential equation [8] or the use of a Laplacian potential in an integral identity [9]. The analyses of this author [8,9], however, required an assumption concerning the boundary shape.…”

Identification of the free boundary of a space-charge region with the aid of a Laplacian potential

“…The problem of calculating the shape and extent of the space-charge region around a conductor arises in different contexts; for instance, in plasma physics the analysis deals with ion-matrix sheaths, [1][2][3][4][5] and in semiconductor device modeling one speaks of depletion regions. 6 The analysis is made somewhat simpler by making the depletion approximation; 1,2,5 that is, by assuming uniform charge density in the sheath ͑or depletion͒ region.…”

“…1 Less symmetric free boundaries were typically identified through an iterative numerical solution of Poisson's equation with uniform charge density, 2 possibly corrected with a Boltzmann term for the density of the mobile charges of opposite sign. 5,8 The aim of the present note is to describe a method that may be of help for identifying the free boundary of a space-charge region without the necessity of solving Poisson's equation. 5,8 The aim of the present note is to describe a method that may be of help for identifying the free boundary of a space-charge region without the necessity of solving Poisson's equation.…”