Transcript Intro_Diffusion

Research Paper
Chapter 7:
DOPANT DIFFUSION
DOPANT DIFFUSION
Introduction
 Basic Concepts

– Dopant solid solubility
– Macroscopic view
– Analytic solutions
– Successive diffusions
– Design of diffused layers

Manufacturing Methods
Introduction
Main challenge of front-end processing is the
accurate control of the placement of active
doping regions
 Understanding and control of diffusion and
annealing is essential to obtaining the desired
electrical performance

– If the gate length is scaled down by 1/K (K>1) ideally
the dimensions of all doped regions should also scale
by 1/K to maintain the same electric field patterns
 With the same field patterns, the device physics remains the
same except that the device is faster because of the shorter
channel
Introduction

There is a continuous drive to reduce the
junction depth with each new technology
generation
– We need high activation levels to reduce
parasitic resistances of the source, drain and
extensions
 Activation level is the ratio of the concentration of
the electrically active impurities to total
concentration of impurities
Introduction

The sheet resistance is given by
S 

xj
/square
– This is valid if the doping is uniform
throughout the junction

If it is not, the expression becomes
1
S 

 xj
1
xj
q  n( x)  N B  n( x)dx
0
Introduction

The challenge is to keep the junctions
shallow and yet keep the resistance of the
source and drain small to maximize drive
current
– These are conflicting requirements
 It is extremely difficult to obtain high concentration
of impurities in the material without the impurity
concentration extending deep into the
semiconductor.
NTRS Projections

Note particularly the projected junction depth
Planar process has dominated all methods
for creating junctions since 1960
 The fundamental change in the past 40
years has been how the “predep” has
been done.

– Predep (predeposition) controls how much
impurity is introduced into the wafer
 In the 1960s, this was done by solid state diffusion
from glass layers or by gas phase diffusion
 By the mid-1970s, ion implantation became the
method of choice
– Its only drawback is radiation damage

In ion implantation, damaged-enhanced
diffusion allows for significant diffusion of
dopants
– This is a major problem in very shallow
junctions
Basic Concepts
Basic Concepts

The desired dopants (P, As, B) have only limited
solid solubility in Si
– The solubility increases with temperature
– Some dopants exhibit retrograde solubility (where the
solubility decreases at elevated temperatures)

precipitates form when concentration is above
solid solubility limit.
– When combined in precipitates (or clusters) the
dopants do not contribute donors or acceptors
(electrons or holes)
– The dopant is not electrically active
Dopant Solubility in Si
Solubility
Limit
As
Impurity concentration, N (atoms/cm3 )
P
1021
As
P
B
1020
Sb
Solubility limit
Electrical active
1019
900
1000
1100
Temperature ( o C )
1200
Solubility Limit

Surface concentrations can be high.
– At 1100oC:
 B:
 P:

3.3 x 1020 cm-3
1.2 x 1021 cm-3
At high temperatures, impurities cluster
without precipitating and have limited

electrical
activity
3 As  As3  n
III-V dopants have limited solubility in Si
Diffusion Models

The macroscopic view describes the
overall motion of the dopant profiles
– It predicts the motion of the profile by solving
a differential equation subject to certain
boundary conditions

The atomistic approach is used to
understand some of the very complex
mechanisms by which dopants move in Si
Fick’s Laws
Diffusion is described by Fick’s Laws.
Fick’s first law is:
c
J  D
x
D = diffusion coefficient


Conservation of mass requires
(This is the continuity equation)
c
J
 
t
x
Fick’s Laws

Combining the continuity equation with the first
law, we obtain Fick’s second law:
 c
 c
  D 2
 t
x
2

Solutions to Fick’s Laws depend on the
boundary conditions.

Assumptions
– D is independent of concentration
– Semiconductor is a semi-infinite slab with either
 Continuous supply of impurities that can move into
wafer
 Fixed supply of impurities that can be depleted
Solutions To Fick’s Second Law

The simplest solution is
at steady state and there
is no variation of the
concentration with time
– Concentration of diffusing
impurities is linear over
distance

This was the solution for
the flow of oxygen from
the surface to the Si/SiO2
interface in the last
chapter
c
D 2 0
x
2
c( x)  a  bx
Solutions To Fick’s Second Law

For a semi-infinite slab with a constant
(infinite) supply of atoms at the surface
 x 
c( x, t )  co erfc

 2 Dt 

The dose is

Q   cx, t dx  2c0 Dt 
0
Solutions To Fick’s Second Law
Complimentary error function (erfc) is
defined as erfc(x) = 1 - erf(x)
 The error function is defined as

erf ( z ) 
2

 exp   d
z
2
0
– This is a tabulated function. There are
several approximations. It can be found as a
built-in function in MatLab, MathCad, and
Mathematica
Solutions To Fick’s Second Law
This solution models short diffusions from
a gas-phase or liquid phase source
 Typical solutions have the following shape
Impurity concentration, c(x)

c0
c ( x, t )
D3t3 > D2t2 > D1t1
1
2
cB
Distance from surface, x
3
Solutions To Fick’s Second Law

Constant source diffusion
has a solution of the form

Here, Q is the does or the
total number of dopant
atoms diffused into the Si
Q
c ( x, t ) 
e
Dt

Q   c( x, t )dx
0

The surface concentration
is given by:
Q
c(0, t ) 
Dt
 x2
4 Dt
Solutions To Fick’s Second Law
Limited source diffusion looks like
Impurity concentration, c(x)

c01
c ( x, t )
c02
D3t3 > D2t2 > D1t1
c03
1
2
cB
Distance from surface, x
3