Development and Demonstration of a Two-Dimensional, Accurate and Computationally-Efficient Model for Boron Implantation
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Figure 1. (a) Illustration of profile variation as a function of tilt angle. Note that the implant is incident between the two solid black boxes which are impenetrable masks. Implants are performed 3 2 at 80 keV, lxl01 cm- , 00 tilt and 0' rotation (solid lines), and 10' tilt and 0' rotation (dashed 17 16 15 , 1016, 3.12x10 , 1017, and 3.12x10 lines). The isoconcentration contours are at 3.12x10 2 cm- . (b) Illustration of 2-D DUPEX fit to one of the Monte Carlo generated curves shown in 1(a) (10' tilt, 0' rotation). The Monte Carlo simulated profiles are the dashed lines, and the solid lines are the fit to this data.
The model for the depth profiles is derived from experimentally determined profiles using SIMS analysis and the Dual-Pearson model. Details regarding the implants, analysis, and model development can be found in [4]. The key experimental points are that approximately 450 SIMS 13 profiles15were measured covering the following ranges: energies of 15 - 80 keV, doses of 1x 10 2 - 8x10 cm- , tilt angles from 0' to 100, and rotation angles from 0' to 450 (which, due to crystal symmetry will cover the full 0' to 3600 rotation angle range), and oxide thicknesses ranging from the native oxide to 40 nm oxide. Thus, the components of the model consist of a Dual-Pearson function to describe the depth profile and a depth-dependent lateral straggle for each of the Pearson functions in the Dual-Pearson function. How a 2-D profile is constructed given the model parameters is easiest to understand by first considering an ion beam incident on the wafer at a single point on the surface. In this case, the concentration at any point under the surface is determined by its depth and lateral distance from the point where the ion beam hits the surface. Concentration Distribution given a Point Source N(x,y) = P1 (y)GI(x,y) + P2(y)G2(x,Y)
P(y) - Pearson Distribution Function G(x,y) - Gaussian The ions will spread out as they enter the wafer due to nuclear collisions and scattering, so that even points not directly under the beam can have contributions from the beam. Thus, our method for determining the concentration at a given point under the surface is to integrate the contributions from such point source ion beams at each point along the surface. The methodology used by the model is as follows. First, the surface is divided up into segments whose size depends on the implant conditions and the variation of the oxide thickness along the surface. By dividing the surface into segments such that the surface variations are small within each segment, the integration of the lateral Gaussian has an analytic solution within each segment, which is the error function evaluated at the endpoints of the surface segment. Then, the contributions from all of the surf
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