Lecture 9 0
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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.

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Lecture 9.0

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Lecture 9 0

Lecture 9.0

Silicon Oxidation/Diffusion/Implantation


Silicon oxidation

Silicon 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


Kinetics

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

Thickness 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 oxide

Field Oxide

  • Thick oxide

    • Oxygen

    • Steam

  • High Temperature Reaction


Diffusion

Diffusion

  • Deposition of B or P on surface

  • Heat 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 profile

Concentration Profile

time


Diffusion coefficient

Diffusion 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


Implantation

Implantation

  • Energy Loss

  • Stopping of Ion

    • Nuclear cross section, Sn(E)

    • Electronic cross section, Se(E)

    • ρT = atomic density of target (#/cc)


Average range

Average Range

  • Integration of Energy Loss equation


Implantation1

Implantation

  • Create Ions in Vacuum

  • Accelerate in Electric Field


Implantation2

Implantation

  • Impinge onto Silicon Surface

  • Knock out Si ion(s)

    • Charge Balance

  • Travel deep into Silicon


Implantation3

Implantation

  • Effect of Ion Mass

Mi>MSi

Mi<MSi


Implant depth

Implant Depth

Depth Increases with Energy


Implantation straggle

Implantation Straggle

Increases with Energy


Implantation concentration profile

Implantation Concentration Profile

  • Probability Based

  • N(x)=Nmax exp[(x-xave)2/2x2]

  • Nmax=(Ndose/[(2) x])~(0.4 Ndose/ x)

  • Ndose=Qdose/e

  • Qdose= current applied/cm2

  • σx = standard deviation of projected range


Implantation through slit

Implantation Through Slit

  • Slit opening = a

  • N(x) =projected range formula

  • ΔR = transverse straggle


Mask thickness

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 thickness1

Mask 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.


Sio 2 mask thickness

SiO2 Mask Thickness


Si 3 n 4 mask thickness

Si3N4 Mask Thickness


Photoresist mask thickness

Photoresist Mask Thickness


Implant depth1

Implant Depth

Depth Increases with Energy


Diffusion of implanted dopants

Diffusion 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 annealing

Laser Annealing


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