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## Section 4: Diffusion part 2

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**Section 4: Diffusionpart 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 900oC, several minutes (After excess point defects recombine. slower diffusion) Implantation induced excess point defects Si substrate 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**EE143 – Ali Javey**Sheet Resistance**EE143 – Ali Javey**Resistivity vs. Doping**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: 4) Irvin’s Curves are plots of No versus ( Rs xj ) for various NB. EE143 – Ali Javey**Resistivity Measurement: Four-Point Probe**EE143 – Ali Javey**Region of Interest is Angle-Lapped**Two-Point Probe Resistance Measurements vs. Depth Profile Extracted Impurity Profiling: Spreading Resistance EE143 – Ali Javey**Impurity ProfilingSecondary Ion Mass Spectroscopy (SIMS)**EE143 – Ali Javey