Section 7 Diffusion Jaeger Chapter 4 EE 143

Section 7: Diffusion Jaeger Chapter 4 EE 143 – Ali Javey

Dopant Diffusion Sources (a) Gas Source: As. H 3, PH 3, B 2 H 6 (b) Solid Source BN (c) Spin-on-glass (d) Liquid Source. EE 143 – Ali Javey Si BN Si Si. O 2+dopant oxide

Fick’s First Law of Diffusion EE 143 – Ali Javey

Fick’s Second Law of Diffusion EE 143 – Vivek Subramanian Slide 4 -4

Diffusion Coefficients of Impurities in Si Substitutional Diffusers Interstitial Diffusers 10 -6 Cu B, P As EE 143 – Ali Javey Au

Diffusion Coefficients EE 143 – Ali Javey

Diffusion Mechanisms in Si (a) Interstitial Diffusion Example: Cu, Fe, Li, H Fast Diffusion Cu 10 -6 cm 2/sec EE 143 – Ali Javey Au

Diffusion Mechanisms in Si (b) Substitutional Diffusion (c) Interstitialcy Diffusion Example: Dopants in Si ( e. g. B, P, As, Sb) EE 143 – Ali Javey

Constant Source Diffusion Complementary Error Function Profiles EE 143 – Vivek Subramanian Slide 4 -9

Limited Source Diffusion Gaussian Profiles EE 143 – Ali Javey

Two Step Dopant Diffusion dopant gas (1) Predeposition dose control Si. O 2 Si (2) Drive-in profile control (junction depth; concentration) Doped Si region Turn off dopant gas or seal surface with oxide Si. O 2 Si Note: Predeposition by diffusion can also be replaced by a shallow implantation step. EE 143 – Ali Javey

Normalized Concentration versus depth Predeposition EE 143 – Ali Javey Drive-in

Diffusion of Gaussian Implantation Profile EE 143 – Ali Javey

Successive Diffusions: Thermal Budget Example Temp (t) Dttotal of : Well drive-in well drive-in step S/D Anneal step and time S/D annealing For a complete process flow, only those steps with high Dt values are important EE 143 – Ali Javey

Solid Solubility Limits • There is a limit to the amount of a given impurity that can be “dissolved” in silicon (the Solid Solubility Limit) • At high concentrations, all of the impurities introduced into silicon will not be electrically active EE 143 – Ali Javey

High Concentration Diffusion Effects 1) E-Field Enhanced Diffusion 2) Charged point defects enhanced diffusion Log C(x) High conc. profile: D gets larger when C(x) is large Log C(x) J large Low conc profile: Erfc or gaussian J small x x * C(x) looks “flatter” at high conc. regions EE 143 – Ali Javey

Electric-field Enhancement Example: Acceptor Diffusion Na(x) p(x) Na(x)=Na-(x) hole gradient Hole diffusion tendency E build-in x Complete acceptor ionization at diffusion temperature EE 143 – Ali Javey At thermal equilibrium, hole current =0 Hole gradient creates build-in electric field to counteract the hole diffusion tendency

Electric Field Enhancement +[p] B- holes tends to move away due to hole concentration gradient Ebuild-in B- acceptors experience an additional drift force Enhanced Diffusion for B- acceptor atoms EE 143 – Ali Javey

Electric Field Enhancement – Substrate Perturbation As diffusion caused by As conc gradient Uniform B conc in substrate B- EE 143 – Ali Javey