lecture 9.0
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Lecture 9.0Lecture 9.0
Silicon Oxidation/Diffusion/Implantation
Silicon OxidationSilicon Oxidation Reactor
– Furnace at T=850C– Pure Oxygen
• Si + O2 SiO2
Kinetics– BL-Mass Transfer
• J=Kg(CA-0)
– SS-Diffusion• J=DO-SiO2 (dC/dx)
– Heat Transfer• BL, q=h(T1-T)• Solid, q=kSiO2(dT/dx)
– J=q/Hrxn
Grxn<0, Spontaneous
KineticsKinetics
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 ExperimentsThickness Experiments
Parabolic Rate– Derive it!– dx2/dt=2K
• K=Ko exp(-Ea/RgT)• x=o @ t=0• x= at t=
– Very common!!• Slow Solid State
Diffusion• Slow Heat
Conduction
Field OxideField Oxide
Thick oxide– Oxygen– Steam
High Temperature Reaction
DiffusionDiffusion
Deposition of B or P on surfaceHeat and Hold for period of time
– Solid State Diffusion– dC/dt=D d2C/dx2
• C=Co at x=0
• C=0 at x=
– C=Co(1-erf[x/(4Dt)])
Etch excess B or P from surface
Concentration ProfileConcentration Profile
0 0.5 10
0.5
1
C xi 1 hr C xi 2 hr C xi 3 hr C xi 4 hr
xi
m
time
Diffusion CoefficientDiffusion Coefficient Self Diffusion
– D*=Doexp(-Ea/RgT) Diffusion of A in B
• Depends on A and matrix B
– DAB =(D*A XB + D*B XA) (d ln [aA]/d ln [XA])– d ln [aA]/d ln [XA] = 1+ (d ln [A]/d ln [XA])– d ln [aA]/d ln [XA] ~ 1 for ideal solutions
• And • DAB =(D*A XB + D*B XA) = (D*A (1-XA) + D*B XA) • Note Concentration dependence!!• DAB ~D*A when XA ~0 , the dilute solution limit
– Good for dopants
ImplantationImplantation
Energy Loss
Stopping of Ion– Nuclear cross section, Sn(E)– Electronic cross section, Se(E)
– ρT = atomic density of target (#/cc)
)]()([ ESESdx
dEenT
Average RangeAverage Range
Integration of Energy Loss equation
E
enTp ESES
dEdxR
0 )()(
1
ImplantationImplantation
Create Ions in Vacuum
Accelerate in Electric Field High Vacuum
Ion Generator
Acceleration Voltage
ImplantationImplantation
Impinge onto Silicon Surface
Knock out Si ion(s)– Charge Balance
Travel deep into Silicon
ImplantationImplantation
Effect of Ion Mass
Mi>MSi Mi<MSi
Implant DepthImplant Depth
Depth Increases with Energy
Implantation StraggleImplantation Straggle
Increases with Energy
Implantation Concentration Implantation Concentration ProfileProfile Probability Based N(x)=Nmax exp[(x-xave)2/2x
2]
Nmax=(Ndose/[(2) x])~(0.4 Ndose/ x)
Ndose=Qdose/e
Qdose= current applied/cm2
σx = standard deviation of projected range
Implantation Through SlitImplantation Through Slit
Slit opening = a
N(x) =projected range formulaΔR = transverse straggle
)()(2
)(),(
R
ayerfc
R
ayerfc
xNyxNmask
Mask ThicknessMask 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 ThicknessMask Thickness
Transmission through mask– T=1/2 erfc[(x-xave)/2 x]
To stop 99.99% of implanted materials, T=10-4
Solve for x, the thickness to stop 99.99% of ions.
SiOSiO22 Mask Thickness Mask Thickness
SiSi33NN44 Mask Thickness Mask Thickness
Photoresist Mask ThicknessPhotoresist Mask Thickness
Implant DepthImplant Depth
Depth Increases with Energy
Diffusion of Implanted DopantsDiffusion of Implanted Dopants
Diffusion Furnace or Laser Heat Treatment
– Solid State Diffusion
– dC/dt = CT d/dz (DAB dXA /dz)• C=Co(z) = CT XA(z) at z=0• C=0 at z=
– DAB =(D*A XB + D*B XA) (d ln [aA]/d ln [XA])– Interdiffusion or mutual diffusion coefficient
Laser AnnealingLaser Annealing
yp x t( )
Rp 4 DP_Si t 1
2
2 Rp
x 2 Rp
4 DP_Si t 1
2
2 Rp2
4 DP_Si t 1
2
ym x t( )
Rp 4 DP_Si t 1
2
2 Rp
x 2 Rp
4 DP_Si t 1
2
2 Rp2
4 DP_Si t 1
2
C x t( )1
2 Rp2
2 DP_Si texp
x Rp 2
2 Rp2
2 DP_Si t
1
2 1 erf yp x t( ) exp
4 x Rp
2 Rp2
4 DP_Si t
1 erf ym x t( )
1 10 100 1 103 1 104 1 1051 10 3
0.010.1
110
1001 1031 1041 1051 1061 107
C x nm 0.00001s( )
C x nm 10 s( )
x