1. Lecture 9.0 Silicon Oxidation/Diffusion/Implantation

2. Silicon Oxidation Reactor –Furnace at T=850C –Pure Oxygen Si + O 2  SiO 2 Kinetics –BL-Mass Transfer J=K g (C A -0) –SS-Diffusion J=D O-SiO2 (dC/dx) –Heat Transfer BL, q=h(T 1 -T) Solid, q=k SiO2 (dT/dx) –J=q/  H rxn  G rxn <0, Spontaneous

3. Kinetics Thickness –Linear Rate Reaction Control –First Order BL-MT Control BL-HT Control –Parabolic Rate Product diffusion Control Product heat transfer Control J =(dx/dt)  SiO2 /MW SiO2

4. Thickness Experiments Parabolic Rate –Derive it! –dx 2 /dt=2K K=K o exp(-E a /R g T) x=o @ t=0 x=  at t=  –Very common!! Slow Solid State Diffusion Slow Heat Conduction

5. Field Oxide Thick oxide –Oxygen –Steam High Temperature Reaction

6. Diffusion Deposition of B or P on surface Heat and Hold for period of time –Solid State Diffusion –dC/dt=D d 2 C/dx 2 C=C o at x=0 C=0 at x=  –C=C o (1-erf[x/  (4Dt)]) Etch excess B or P from surface

7. Concentration Profile time

8. Diffusion Coefficient Self Diffusion –D*=D o exp(-E a /R g T) Diffusion of A in B Depends on A and matrix B –D AB =(D* A X B + D* B X A ) (d ln [a A ]/d ln [X A ]) –d ln [a A ]/d ln [X A ] = 1+ (d ln [  A ]/d ln [X A ]) –d ln [a A ]/d ln [X A ] ~ 1 for ideal solutions And D AB =(D* A X B + D* B X A ) = (D* A (1-X A ) + D* B X A ) Note Concentration dependence!! D AB ~D* A when X A ~0, the dilute solution limit – Good for dopants

9. Implantation Energy Loss Stopping of Ion –Nuclear cross section, S n (E) –Electronic cross section, S e (E) –ρ T = atomic density of target (#/cc)

10. Average Range Integration of Energy Loss equation

11. Implantation Create Ions in Vacuum Accelerate in Electric Field

12. Implantation Impinge onto Silicon Surface Knock out Si ion(s) –Charge Balance Travel deep into Silicon

13. Implantation Effect of Ion Mass M i >M Si M i <M Si

14. Implant Depth Depth Increases with Energy

15. Implantation Straggle Increases with Energy

16. Implantation Concentration Profile Probability Based N(x)=N max exp[(x-x ave ) 2 /2  x 2 ] N max =(N dose /[  (2  )  x ])~(0.4 N dose /  x ) N dose =Q dose /e Q dose = current applied/cm 2 σ x = standard deviation of projected range

17. Implantation Through Slit Slit opening = a N(x) =projected range formula ΔR  = transverse straggle

18. Mask Thickness To effectively prevent ions penetrating in thick zone Relatively thick Oxide Protection layer Patterned Thinning (etching) of Oxide Protection layer over implantation zone Remove oxide layer with impurities inside

19. Mask Thickness Transmission through mask –T=1/2 erfc[( x-x ave )/  2  x ] To stop 99.99% of implanted materials, T=10 -4 Solve for x, the thickness to stop 99.99% of ions.

20. SiO 2 Mask Thickness

21. Si 3 N 4 Mask Thickness

22. Photoresist Mask Thickness

23. Implant Depth Depth Increases with Energy

24. Diffusion of Implanted Dopants Diffusion Furnace or Laser Heat Treatment –Solid State Diffusion –dC/dt = C T d/dz ( D AB dX A /dz ) C=C o (z) = C T X A (z) at z=0 C=0 at z=  –D AB =(D* A X B + D* B X A ) (d ln [a A ]/d ln [X A ]) –Interdiffusion or mutual diffusion coefficient

25. Laser Annealing