Lecture 9.0 Silicon Oxidation/Diffusion/Implantation

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

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

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

Field Oxide Thick oxide –Oxygen –Steam High Temperature Reaction

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

Concentration Profile time

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

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)

Average Range Integration of Energy Loss equation

Implantation Create Ions in Vacuum Accelerate in Electric Field

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

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

Implant Depth Depth Increases with Energy

Implantation Straggle Increases with Energy

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

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

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

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.

SiO 2 Mask Thickness

Si 3 N 4 Mask Thickness

Photoresist Mask Thickness

Implant Depth Depth Increases with Energy

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

Laser Annealing