Doping processes in device Fabrication

Semiconductor Device
Fabrication:
Doping
Arpan Deyasi
Dept of ECE, RCCIIT, Kolkata, India
1/15/2021 Arpan Deyasi, RCCIIT

Dopant induction in semiconductor
Diffusion
Boron is the most common p-type impurity in Silicon
Arsenic and Phosphorus are used as n-type dopants
Ion implantation

Dopant atoms are introduced from the gas phase of
by using doped-oxide sources
Doping concentration decreases monotonically from
the surface
In-depth distribution of the dopant is determined
mainly by the temperature and diffusion time
Used to form a deep junction
Feature of Diffusion

solid sources (BN , As2O3 , P2O5)
liquid sources (BBr3, AsCl3, and POCl3)
gaseous sources (B2H6, AsH3, and PH3)
Nature of Sources

Diffusion Mechanism

Mathematics of Diffusion
Let ‘F’ be the flux of dopant atoms traversing through a unit
area in a unit time
C
F D
z
∂
= −
∂
D: diffusion coefficient
C: dopant concentration
z: distance in one dimension

flux is proportional to the concentration gradient
dopant atoms will diffuse from a high-concentration region
toward a low-concentration region
negative sign states that matters flow in the direction
of decreasing dopant concentration

According to the law of conservation of matter, the change of
the dopant concentration with time must be equivalent to
the local decrease of the diffusion flux, in the absence of a
source or a sink
C F
t z
∂ ∂
= −
∂ ∂
C C
D
t z z
∂ ∂ ∂ 
=− − 
∂ ∂ ∂ 

2
2
C C
D
t z
∂ ∂
=
∂ ∂
this is applicable for lower dopant concentration, so
the diffusion constant at a given temperature can be
considered as a constant

C
F D
z
∂
= −
∂
Fick’s 1st law of diffusion
2
2
C C
D
t z
∂ ∂
=
∂ ∂
Fick’s 2nd law of diffusion

Solution of Diffusion Equation
Boundary condition
at t=0, C(z,0)=0
dopant concentration in the host semiconductor is initially zero
at z=0, C(0,t)=CS
at z=∞, C(∞,t)=0
at large distances from the surface, there are no impurity atoms
at the surface level, CS is the doping concentration

( , )
2
S
z
C z t C erfc
Dt
 
=  
 
Constant-Surface-Concentration Diffusion
The total number of dopants per unit area of the semiconductor
0 0
( , )
2
S
z z
z
C z t dz C erfc dz
Dt
∝ ∝
=
 
=  
 
∫ ∫

2
( ) SQ t C Dt
π
=
( ) 1.13 SQ t C Dt=

Diffusion Profile
C(z)
z

If fixed (or constant) amount of dopant is deposited onto
the semiconductor surface in a thin layer, and the dopant is
subsequently diffused into the semiconductor
0
( , )
z
C z t dz S
∝
=
=∫
‘S’ is the total amount of dopant per unit area

Boundary condition
at t=0, C(z,0)=0
at z=∞, C(∞,t)=0
2
( , ) exp
4
S z
C z t
DtDtπ
 
= − 
 

at z=0, C(0,t)=CS
S
S
C
Dtπ
=
2
( , ) exp
4
S
z
C z t C
Dt
 
= − 
 
Constant-Total-Dopant Diffusion

1/15/2021
Arpan Deyasi, RCCIIT
Experimental set-up
of Diffusion

Experimental set-up
of Diffusion

Two-step Diffusion process
Pre-deposition is also known as constant source diffusion
pre-deposition diffused layer is first formed under the
constant surface concentration condition
Here surface concentration of dopant is always constant
I. Pre-deposition
( , )
2
S
z
C z t C erfc
Dt
 
=  
 

II. Drive-in
Drive-in process is also known as limited source diffusion
Here finite quantity of diffusing matter is first placed on the
wafer
Diffusion proceeds from this limited source & it is assumed
that all of this matter is consumed during process
As drive in progresses surface concentration decreases and
dopants move further
2
( , ) exp
4
S z
C z t
DtDtπ
 
= − 
 

C(z)
z

Ion Implantation
A low-temperature process
Ions of one element are accelerated into a solid target, thereby
changing the physical, chemical, or electrical properties of the
target

Ion Implantation
Process
[i] Dopant atoms are volatilized, ionized, accelerated,
separated by the mass-to-charge ratios, and directed at a
target
[ii] The atoms enter the crystal lattice, collide with the
host atoms, lose energy, and finally come to rest at some
depth within the solid
[iii] The average penetration depth is determined by the
dopant, substrate materials, and acceleration energy

Ion Implantation Unit

Ion Implantation

Ion Implantation: Range Distributions
Each implanted ion traverses a random path as it penetrates
the target, losing energy by nuclear and electronic stopping
The average total path length is called
the range ‘R’, which is composed of
both lateral and vertical motions
The average depth of the implanted
ions is called the projected range ‘Rp’

distribution of the implanted ions
about that depth can be
approximated as Gaussian with a
standard deviation ‘σp’
lateral motion of the ions leads to a lateral Gaussian
distribution with a standard deviation ‘σ⏊’

ion concentration at depth ‘x’
( )
2
0 2
( ) exp
2
p
p
x R
n x n
σ
 −
 = −
 
 
peak concentration

0
0.4
2 pp
n
φ φ
σπ σ
= ≅
total implanted dose

Doping processes in device Fabrication

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