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IMPLANT

# IMPLANT - EE143 N Cheung Ion Implantation Profile and Range...

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EE143 N. Cheung Ion Implantation Profile and Range Data In EE143, we use a gaussian function to approximate the ion implantation concentration depth profile: C(x) = 2 R p exp [ - (x -R p ) 2 2 R p 2 ] where is the implantation dose ( in # / cm 2 ), R p is the projected range and R p is the longitudinal straggle. This gaussian approximation is reasonably good for sheet resistance calculations because the integral quantity R s ( 1 q  ) is less sensitive to details of the distribution. However, the gaussian function has too rapid a decay with distances from R p and can lead to smaller calculated junction depths x j . The rationales to choose the gaussian approximation are: (1) only two parameters ( R p and R p ) are used to describe the shape of the depth profile; (2) the gaussian function is a natural solution of the diffusion equation, which we have to deal with when further annealing steps are encountered after implantation. A better approximation for the implantation profile is the Pearson-IV distribution which requires the first four spatial moments of the distribution but such calculations will require numerical procedures [see more advanced texts such as Plummer et al]. Projected Range R p and Longitudinal Straggle R p for common dopants used in IC technology, B, P and As implanted into Si are shown in the following graphs (solid lines). The ranges (in ) are also fitted to a polynomial (dashed lines) of the form: a0+a1*E+a2*E 2 +a3*E 3 +a4*E 4 with E in keV 10 100 1000 100 1000 10000 R p =185.34201 +6.5308 E -0.01745 E 2 +2.098e-5 E 3 -8.884e-9 E 4 R p =51.051+32.60883 E -0.03837 E 2 +3.758e-5 E 3 -1.433e-8 E 4 R p R p B 11 into Si

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