Section 7: Diffusion. Jaeger Chapter 4. EE143 Ali Javey

Transcription

1 Section 7: Diffusion Jaeger Chapter 4

2 Surface Diffusion: Dopant Sources (a) Gas Source: AsH 3, PH 3, B 2 H 6 (b) Solid Source BN Si BN Si (c) Spin-on-glass SiO 2 +dopant oxide (d) Liquid Source.

3 Fick s First Law of Diffusion N J D x D diffusion coefficient

4 Fick s Second Law of Diffusion Continuity Equation for Particle Flux : Rate of increase of concentration is equal to the negative of the divergence of the particle flux N J t x (in one dimension) Fick's Second Law of Combine First Law with Continuity Eqn. 2 N N D 2 t x Assumes D is concentration - independent, which isn' t true in many situations in modern devices Diffusion : EE143 Vivek Subramanian Slide 4-4

5 Diffusion Coefficients of Impurities in Si Substitutional Diffusers D D O e E A kt Interstitial Diffusers 10-6 Cu B,P Au As

6 A Diffusion Coefficients E exp A D DO kt E activation energy k Boltzmann's constant T absolute temperature Arrhenius Relationship 1.38 x10-23 J/K

7 Diffusion Mechanisms in Si (a) Interstitial Diffusion Example: Cu, Fe, Li, H Fast Diffusion Cu 10-6 cm2/sec Au

8 Diffusion Mechanisms in Si (b) Substitutional Diffusion (c) Interstitialcy Diffusion Example: Dopants in Si ( e.g. B, P,As,Sb)

9 Constant Source Diffusion Complementary Error Function Profiles Concentration : Total Dose : N 0 Q N ( x, t) 0 ( x, t) Surface Concentration erfc 2 erfc Complementary Error Function N D Diffusion Coefficient N 0 dt 2N x 0 Dt Dt π EE143 Vivek Subramanian Slide 4-9

10 Limited Source Diffusion Gaussian Profiles ( ) Gaussian Profile Diffusion Coefficient Surface Concentration 2 exp 2 exp, Concentration : D Dt Q N N Dt x Dt Q Dt x N t x N π π

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

12 Normalized Concentration versus depth Predeposition Drive-in

13 Diffusion of Gaussian Implantation Profile

14 Successive Diffusions: Thermal Budget Temp (t) Thermal Budget ( Dt) effective step i ( Dt) i Example Dt total of : Well drive-in well drive-in S/D step Anneal step time and S/D annealing For For a complete process flow, only only those steps with with high Dt Dt values are are important

15 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

16 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) Low conc profile: Erfc or gaussian x J large J small * C(x) looks flatter at high conc. regions x

17 Electric-field Enhancement Example: Acceptor Diffusion N a (x) p(x) N a (x)n a- (x) Complete acceptor ionization at at diffusion temperature x E build-in hole gradient Hole diffusion tendency At At thermal thermal equilibrium, hole hole current current 0 0 Hole Hole gradient creates creates build-in build-in electric electric field field to to counteract the the hole hole diffusion tendency

18 Electric Field Enhancement +[p] holes tend to move away due to hole concentration gradient B - E build-in B - acceptors experience an additional drift force Enhanced Diffusion for B - acceptor atoms

19 Electric Field Enhancement Substrate Perturbation As diffusion caused by As conc gradient Uniform B conc in substrate B -