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