2. DOPANT
DIFFUSION
1. To form source and drain regions in MOS devices and also
to dope poly-Si gate material.
2. Used to form base regions, emitters, and resistors in
bipolar devices.
Process by which controlled amount of
chemical impurities are introduced into
semiconductor lattice.
5. Basic Concepts
• Placement of doped regions (main source/drain, S/D extensions, threshold
adjust) determine many short-channel characteristics of a MOS device.
• Resistance impacts drive current.
• As device shrinks by a factor K, junction depths should also scale by K to
maintain same e –field patterns (assuming the voltage supply also scales
down by the same factor).
• Gate doping affects poly-depletion and limits how
the gate voltage controls the channel potential.
Rcontact
Rsource
Rext Rchan
Rpoly
Silicide
VG
VS VD
Sidewall
Spacers
xJ
xW
7. Introduction
R = ρ ρS = ρ/xj
xja) b)
• The resistivity of a cube is given by
J =nqv =nqµε=
1
ρ
ε ∴ρ=
ε
J
Ωcm (1)
• The sheet resistance of a shallow junction is
R =
ρ
xj
Ω/Square ≡ρS (2)
8. Introduction
Depth
• For a non-uniformly doped layer,
ρs =
ρ
xj
=
1
q n x()−NB[ ]
0
xj
∫ µn x()[ ]dx
(3)
• Sheet resistance can be experimentally measured by a four
point probe technique.
• Doping profiles can be measured by SIMS (chemical) or
spreading R (electrical).
• Generally doping levels need to increase and xJ values need to
decrease as the devices are scaled.
9. Two Step Diffusion
• Diffusion is the redistribution of atoms from regions of high
concentration of mobile species to regions of low concentration. It
occurs at all temperatures, but the diffusivity has an exponential
dependence on T.
• Predeposition : doping often proceeds by an initial predep step to
introduce the required dose of dopant into the substrate.
• Drive-In : a subsequent drive-in anneal then redistributes the dopant
giving the required junction depth
11. Impurity Sources for Boron Diffusion
Impurity
Source
State at
Room
Temp
Source
Temp
Range
Impurity
Conc
Range
Advantages
Boron
Nitride
Solid Kept along
with wafers
High and
low
Very clean process.
Requires activation
Boric Acid Solid 600-1200o
C High and
low
Readily available and
proven source
Boron
Tribromide
Liquid 10-30o
C High and
Low
Clean system. Good
control over impurity
Methyl
Borate
Liquid 10-30o
C High Simple to prepare and
operate
Boron
Trichloride
Gas Room
Temperature
High and
Low
Accurate control of gas
concentration
Diborane Gas Room
Temperature
High and
Low
Accurate control of gas
concentration, but
highly toxic
12. Impurity Sources for Phosphorus
Diffusion
Impurity
Source
State at
Room
Temp
Source Tem.
Range
Concentra-
tion Range Advantages
Red
Phosphorus
Solid 200-300o
C < 1020
cm-3
Low surface
concentration
Phosphorus
Pentoxide
Solid 200-300o
C > 1020
cm-3
Proven source
for high
concentration
Phosphorus
Oxychloride
Liquid 2-40o
C High and
low
Clean system
Good control
over wide range
conc.
Phosphorus
Tribromide
Liquid 170o
C High and
low
Clean system
Phosphine Gas Room
Temperature
High and
low
Accurate control
by gas monito-
ring, highly toxic
14. Diffusion vs Ion Implantation
Advantages
Problems
Ion Implantation and
Annealing
Solid/Gas Phase
Diffusion
Room temperature mask No damage created by doping
Precise dose control Batch fabrication
1011
- 1016
atoms cm-2
doses
Accurate depth control
Implant damage enhances
diffusion
Usually limited to solid
solubility
Dislocations caused by damage
may cause junction leakage
Low surface concentration
hard to achieve without a
long drive-in
Implant channeling may affect
profile
Low dose predeps very
difficult
15. Dopant Solid Solubility
• Maximum conc.of a dopant that can be dissolved in Si under
equilibrium conditions without forming a separate phase is
termed as solid solubility.
.
As
P
Sb
Sn
Ga
Al
B
SolidSolubility(atomscm-3)
1022
1020
1021
1019
Temperature(ÞC)
800 900 1000 1100 1200 1300
16. • Dopants may have an “electrical” solubility that is different than
the solid solubility defined in previous slide.
• One example - As4V – electrically inactive complex.
V
Si As
As+
Dopant Solid Solubility
17. Dopant Diffusion
t1 t2
Concentration F=-DdC/dx
Distance
Concentration
• Macroscopic dopant redistribution is described by Fick’s first
law, which describes how the flux (or flow) of dopant depends
on the concentration gradient.
F =−D
∂C
∂x
(4)
18.
19. Analytical Solution of Fick’s Law
( ) ( )
( ) ( ) constQdxtxctc
dxt0,dc0,xxc
===∞
=≠=
∫
∞
,,0,
,0/00,
The solution to Fick’s Second Law for these
conditions is a Gaussian centered at x =0
Gaussian solution in infinite medium: Consider a fixed dose Q
introduced as Delta function at the origin: Drive in
(7)
20.
21. 2. Gaussian Solution : Constant Source Near A Surface:
Analytic Solutions of Fick’s Laws
• This is similar to the previous case except the diffusion only goes
in one direction.
• Dopant dose Q introduced at the surface.
• Can be treated as an effective dose of 2Q being introduced in a
virtual infinite medium.
DeltaFunction
DoseQ
(Initial Profile)
Imaginary
DeltaFunction
DoseQ
Diffused
Gaussian
Virtual
Diffusion
x
0
(8)
22. Analytic Solutions of Fick’s Laws
3.Error Function Solution : Infinite Source:
• The infinite source is made up of small slices each
diffusing as a Gaussian.
C x,t( )=
C
2 πDt
∆xi exp−
x −xi( )
2
4Dti=1
n
∑ (9)
• The solution which satisfies Fick’s second law is
C(x,t) =
C
2
1−erf
x
2 Dt
=CS erfc
x
2 Dt
(10)
C
² x
Dose C² x
Initial
Profile
Diffused
Profile
xi
x
0
Dose CΔx
Δx
Boundary conditions:
C=0 at t=0 for x> 0
C=C at t=0 for x< 0
23. Analytic Solutions of Fick’s Laws
Important consequences of error function solution:
• Symmetry about mid-point allows solution for constant surface
concentration to be derived.
• Error function solution is made up of a sum of Gaussian delta function
solutions.
• Dose beyond x = 0 continues to increase with annealing time.
.
0
0.2
0.4
0.6
0.8
1
-5 -4 -3 -2 -1 0 1 2 3 4 5
t=9*t
0
t=4*t
0
Initial
t=t
0
erf(x/2¦Dt)
X(Unitsof2¦Dt 0
)
24. Analytic Solutions of Fick’s Laws
4. Error Function Solution: Constant Surface Concentration:
• Just the right hand side of the figure on previous slide
C x,t( )=CS erfc
x
2 Dt
(11)
• Note that the dose is given by
Q = CS
0
∞
∫ 1−erf
x
2 Dt
=
2CS
π
Dt (12)
• Diffusion through Gas ambient
25. Intrinsic Dopant Diffusion Coefficients
• Intrinsic dopant diffusion coefficients are found to be of the
form:
D =D0
exp
−EA
kT
(13)
Si B In As Sb P Units
D0
560 1.0 1.2 9.17 4.58 4.70 cm2
sec-1
EA 4.76 3.5 3.5 3.99 3.88 3.68 eV
• Note that ni is very large at
process temperatures, so
"intrinsic" actually applies
under many conditions.
• Note the "slow" and "fast"
diffusers. Solubility is also an
issue in choosing a particular
dopant.
26. Effect of Successive Diffusions
• If a dopant is diffused at temperature T1 for time t1 and then is
diffused at temperature T2 for time t2, the total effective Dt is
given by the sum of all the individual Dt products.
Dteff =Dt =D1∑ t1 +D2t2 +..... (14)
• The Gaussian solution only holds if the Dt used to introduce the
dopant is small compared with the final Dt for the drive-in; i.e. if
an initial delta function approximation is reasonable.
27. Design of Diffused Layers
• Eqn. (3) has been numerically integrated for specific cases (erfc
and Gaussian).
• Example of Irvin’s curves, in this case for P type Gaussian
profiles.
1 10 100
Effective Conductivity (ohm-cm)-1
SurfaceConcentration(cm-3)
CB=1015
CB=1017
CB=1014
CB=1016
CB=1018
1020
1019
1018
1017
28. Design of Diffused Layers
• We can now consider how to design a boron diffusion process
(say for the well or tub of a CMOS process), such that:
P
P WellN Well
ρS =900 Ω/square
xj =3 µm
NBC =1x1015
cm-3
(substrate concentration)
29. Design of Diffused Layers
• The average conductivity of the layer is
σ
_
=
1
ρSxj
=
1
(900Ω/sq)(3×10−4
cm)
=3.7 Ω⋅cm( )
−1
• From Irvin’s curve we obtain
CS ≈4×1017
/cm3
• We can surmise that the profile is Gaussian after drive-in.
∴CBC =
Q
πDt
exp −
xj
2
4Dt
=CS exp −
xj
2
4Dt
so that Dt =
Xj
2
4ln
Cs
Cbc
=
3x10−4
( )
2
4ln
4x1017
1015
=3.7x10−9
cm2
30. Design of Diffused Layers
• If the drive-in is done at 1100 ˚C, then the boron diffusivity is
D =1.5×10−13
cm2
sec−1
• The drive-in time is therefore
tdrive−in =
3.7×10−9
cm2
1.5×10−13
cm2
/ sec
=6.8 hours
• Given both the surface concentration and Dt, the initial dose can
be calculated for this Gaussian profile.
Q =CS πDt =4×1017
( )π()3.7×10−9
( )=4.3×1013
cm−2
• This dose could easily be implanted in a narrow layer close to the
surface, justifying the implicit assumption in the Gaussian profile
that the initial distribution approximates a delta function.
31. Design of Diffused Layers
• If a gas/solid phase predeposition step at 950˚C were used, then
B solid solubility at 950 ˚C is
B diffusivity is
2.5×1020
cm−3
4.2×10−15
cm2
sec−1{
• The dose for an erfc profile is
Q =
2Cs
π
Dt
• So that the time required for the predeposition is
tpre−dep =
4.3×1013
2.5×1020
2
π
2
2
1
4.2×10−15
=5.5sec
Check: ( ) ( )914
107.3103.2 −
−
−
×<<× indrivepredep DtDt
