Transcript Lecture9.0 Silicon Doping.ppt

Lecture 9.0
Silicon
Oxidation/Diffusion/Implantation
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

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!
– 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

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 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
1
C xi  1 hr 
C xi  2 hr 
C xi  3 hr 
time
0.5
C xi  4 hr 
0
0
0.5
xi
m
1
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

Energy Loss
dE

 T [ Sn ( E )  Se ( E )]
dx

Stopping of Ion
– Nuclear cross section, Sn(E)
– Electronic cross section, Se(E)
– ρT = atomic density of target (#/cc)
Average Range

Integration of Energy Loss equation
Rp
1
E
dE
  dx 
T 0 Sn ( E )  Se ( E )
Implantation


Create Ions in Vacuum
Accelerate in Electric
Field
High Vacuum
Ion Generator
Acceleration
Voltage
Implantation

Impinge onto
Silicon Surface
 Knock out Si ion(s)
– Charge Balance

Travel deep into
Silicon
Implantation

Effect of Ion Mass
Mi>MSi
Mi<MSi
Implant Depth
Depth Increases with Energy
Implantation Straggle
Increases with Energy
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 = straggle

Implantation Through Slit

Slit opening = a
N ( x) 
ya
ya 
N mask ( x, y ) 
erfc(
)  erfc(
)

2 
R
R 
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-xave)/2 x]
To stop 99.99% of implanted
materials, T=10-4
 Solve for x, the thickness to stop
99.99% of ions.

SiO2 Mask Thickness
Si3N4 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 = 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
1
Rp  4 DP_Sit
2 Rp
p

2
1
x 2 Rp
Rp  4 DP_Sit
1
 4 DP_Sit
yp ( x  t) 
 2R
2

 4 DP_Sit
2 Rp
2
2
 2R
x 2 Rp
1
2

p  4 DP_Si t
2

 x  Rp

C ( x  t) 
exp
2
 2  R 2  2 D t
2   Rp  2 DP_Sit
P_Si
p

1

 4 DP_Sit 2
ym( x  t) 
1
2


1
2
 1
4 xRp


   1  erf  yp ( x  t)   exp 
 1  erf  ym( x  t)   
 2
 2 Rp2  4 DP_Sit 

 



1 10
6
1 10
5

1 10
4

1 10
C( x nm  0.00001 s ) 1 103
100
C( x nm  10 s )
10
1
0.1
0.01
3
1 10
7
1
10
100 1 10 1 10 1 10
x
3
4
5