Transcript Microelectronics Processing Diffusion Microelectronics Processing Course - J. Salzman - 2006 1

Microelectronics Processing
Diffusion
Microelectronics Processing Course - J. Salzman - 2006
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Doping
 Doping is the process that puts specific amounts of
dopants in the wafer surface through openings in the
surface layers.
 Thermal diffusion is a chemical process that takes place
when the wafer is heated (~1000 C) and exposed to dopant
vapor. In this process the dopants move to regions of lower
concentration.
 Doping Control is critical in MOS device scaling. (Scaling
down the gate length requires equal scaling in doping
profile)
Ion source
Thermal
diffusion
Ion implantation
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Comparison of thermal diffusion and
ion implantation
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Mathematics of diffusion:
Fick’s First diffusion law
F
F
D is thermally activated
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Mathematics of diffusion:
Fick’s Second diffusion law
What goes in and
does not go out,
stays there
C/t = (Fin-Fout)/ x
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Fick’s diffusion law
F
F
Concentration independent diffusion equation.
Often referred to as Fick’s second law.
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Analytic solutions of the diffusion equations:
Case of a spike delta function in infinite media
(x)
Boundary conditions :
C  0 as t  0 for x  0
C   as t  0 for x  0
and

 C ( x, t )  Q

The solution of Fick ' s diffusion law
describes a Gaussian profile :
 x2 
 x2 
  C (0, t ) exp  

C ( x, t ) 
exp  
2  Dt
 4 Dt 
 4 Dt 
Q
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The evolution of a Gaussian diffusion
profile
•Peak concentration decreases as 1/√t and is given by C(0,t).
•Approximate measure of how far the dopant has
diffused (the diffusion length) is given by x=2√Dt
which is the distance from origin where the
concentration has fallen by 1/e
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Carl Friedrich Gauss
(1777-1855)
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Analytic solutions of the diffusion equations:
Case of a spike delta function near the surface
The symmetry of the problem is
similar to previous case, with an
effective dose of 2Q introduced
into a (virtual) infinite medium.
The solution is thus:
 x2 
 x2 
Q
  C (0, t ) exp  

C ( x, t ) 
exp  
 Dt
 4 Dt 
 4 Dt 
Q
with C (0, t ) 
 Dt
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Constant total dopant (number) diffusion:
Impurity profile
Log scale
Linear scale
Three impurity profiles carried out under constant total dopant diffusion
conditions. Note the reduction in the surface concentration C(0,t) with
time, and the corresponding rise in the bulk density.
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Analytic solutions of the diffusion equations:
Case of an infinite source of dopant
The boundary conditions :
C  0 at t  0 for x  0
C  C at t  0 for x  0
C ( x, t ) 
C ( x, t ) 
C
2  Dt


0
2

x  
exp 
d 
4 Dt
C

C
2  Dt
n

i 1
2

x  xi 
x exp 
i
4 Dt
x / 2 Dt
2
exp
(


)d


(x  )
 
2 Dt
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The error function
A related function is
tabulated:
erf ( z ) 
2
z
exp( 


2
)d
0
The solution of the diffusion
equation from an infinite
source is finally:
C
x  C
x
C ( x, t )  1  erf (
)  erfc(
)
2
2
2 - J.Dt
2 Dt
 - 2006
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Course
Salzman
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Constant surface concentration:
diffusion depth
Log scale
Linear scale
Plots of C(x,t)/Cs vs diffusion depth x(µm) under constant surface
concentration conditions for three different values of √Dt . This
could mean either a change of temperature (i.e D(T)) or time, t.
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Total number of impurities
(predeposition dose)
As seen in the figure, the error function solution is approximately
triangular. The total dose may be estimated by an area of triangular of
height Cs and a base of 2√Dt, giving Q= Cs √Dt.
More accurately:

t
= Characteristic distance for diffusion.
CS = Surface concentration (solid solubility limit).
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Two-step junction formation:
(a) Predeposition from a constant source (erfc)
(b) Limited source diffusion (Gaussian)
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Shallow predep approximation
Q
Cs  2 ( Dt ) predep

;
C ( x, t  0)  Q   ( x)
Solution of Drive-in profile:


Q
x2

C ( x, t ) 
exp  
 ( Dt ) drivein
 4( Dt ) drivein 
In summary:
1/ 2
2Cs  D1t1 


C ( x) 
  D2t 2 

x2 

exp  
 4 D2t 2 
D1= Diffusivity at Predep temperature
t1= Predep time
D2= Diffusivity at Drive-in temperature
t2= Drive-in time
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Two-step junction formation
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Temperature dependence of D
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Diffusion coefficients (constants) for a
number of impurities in Silicon
Substitutional
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Interstitial
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Typical diffusion coefficient values
Element
D0 (cm2/sec)
EA(eV)
B
10.5
3.69
P
10.5
3.69
As
0.32
3.56
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The two principal diffusion mechanisms:
Schematic diagrams
Vacancy diffusion
in a semiconductor.
Interstitial diffusion in a
semiconductor.
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Vacancy
Intersticial
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Thermal diffusion – general
comments
Schematic diagram of a furnace for diffusing impurities (e.g.
phosphorus) into silicon.
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Rapid thermal annealing
a) Concept. b) Applied Materials 300 mm RTP system.
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Dopant diffusion sources
(a) Gas Source: AsH3, PH3, B2H6
(b) Solid Sources: BN, NH4H2PO4, AlAsO4
(c) Spin-on-glass: SiO2+dopant oxide
(d) Liquid source:
A typical bubbler arrangement
for doping a silicon wafer using
a liquid source. The gas flow is
set using mass flow controller
(MFC).
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Junction depth
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Sheet resistance
The resistance of a rectangular
block is:
R = ρL/A = (ρ/t)(L/W) ≡ Rs(L/W)
Rs is called the sheet resistance.
Its units are termed Ω/ .
L/W is the number of unit squares of material in the resistor.
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Sheet resistance
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Irving’s curves: Motivation to
generate them
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Irving’s curves
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Figure illustrating the relationship of
No, NB, xj, and Rs
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Diffusion of Gaussian implantation
profile
Q
Note: Q is the implantation dose.
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