Section 4 Diffusion part 2 Jaeger Chapter 4 EE143 Ali Javey Example High Concentration Arsenic diffusion profile becomes box like EE143 Ali Javey Summary of High Concentration Diffusion If doping conc ni Use constant diffusivity solutions profile is erfc or half gaussian If doping conc ni Solution requires numerical techniques EE143 Ali Javey Transient Enhanced Diffusion TED Dopant Implantation C x no annealing Si substrate 900oC several minutes After excess point defects recombine slower diffusion Implantation induced excess point defects Implantation creates large number of excess Si interstitials and vacancies 1000X than thermal process After several seconds of annealing the excess point defects recombine x 900oC several sec TED Extremely rapid diffusion due to excess point defects EE143 Ali Javey Diffusion p n Junction Formation x j Metallurgical Junction Depth P n junction occurs at the point x j where the net impurity concentration is zero i e p type doping cancels out n type doping Gaussian Profile N x j 2 Dt ln 0 NB N Error Function profile x j 2 Dt erfc 1 0 NB EE143 Ali Javey Sheet Resistance A W t L L R RS t W W RS t Sheet Resistance Ohms per Square L Number of Squares of Material W EE143 Ali Javey Resistivity vs Doping q n n p p 1 1 n type q n N D N A 1 p type q p N A N D 1 EE143 Ali Javey Irvin s Curves p type erfc n type erfc p type half gaussian n type half gaussian Explicit relationship between N surface concentration o x junction depth j N background concentration B R sheet resistance S EE143 Ali Javey Motivation to generate the Irvin s Curves Allows us to calculate doping parameters if we know 3 out of 4 of the parameters on the previous page Approach 1 The dopant profile can be uniquely determined if one knows the concentration values at two depth positions 2 We will use the concentration values No at x 0 and NB at x xj to determine the profile C x i e we can determine the Dt value 3 Once the profile C x is known the sheet resistance RS can be integrated numerically from Rs 1 xj 0 q x N x dx 4 Irvin s Curves are plots of No versus Rs xj for various NB EE143 Ali Javey Resistivity Measurement Four Point Probe V 2 s m for t s I t V m for s t ln 2 I V V RS 4 53 square t ln 2 I I Four Terminal Resistance Measurement EE143 Ali Javey Impurity Profiling Spreading Resistance Region of Interest is AngleLapped Two Point Probe Resistance Measurements vs Depth Profile Extracted EE143 Ali Javey Impurity Profiling Secondary Ion Mass Spectroscopy SIMS EE143 Ali Javey
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