Ion Implantation and Synthesis of Materials - Studium

66 6 Ion Range and Range Distribution1.0GaussianR p0.8N(x)0.60.4∆X p∆R pFWHM0.2For: R p = 2.35 ∆R p00 0.5 1.0 1.5 2.0x/R pFig. 6.3. Gaussian range distribution for implanted ions with R p = 2.35∆R p and a full widthof half-maximum (FWHM) of ∆X pall implanted ions are retained, the dose is related to the ion depth distribution by∫∞φ i= N( x)d x−∞.(6.6)The expression for peak atomic density in the ion implantation distribution isobtained by setting x = R p in (6.5)φ 0.4φiN( R ) ≡ = ≅ ,∆RipNp 1/2∆Rp(2 π )p(6.7)where N p is in units of atoms cm −3 for φ i in units of atoms cm −2 and ∆R p in centimeters.Consider a 100 keV B implantation into Si, where R p = 318 nm and∆R p = 89 nm. For an implantation dose of 1 × 10 15 atoms cm −2 , the peak atomicdensity of B will beN p = 0.4 × 10 15 (atoms cm −2 )/89 × 10 −7 (cm) = 1.82 × 10 21 (atoms cm −3 ).