1. Chapter 7: DOPANT DIFFUSION

2. DOPANT DIFFUSION Introduction Basic Concepts Manufacturing Methods
Dopant solid solubility
Macroscopic view
Analytic solutions
Successive diffusions
Design of diffused layers
Manufacturing Methods

3. 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

4. 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

6. Introduction The sheet resistance is given by
This is valid if the doping is uniform throughout the junction
If it is not, the expression becomes

8. 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.

9. NTRS Projections
Note particularly the projected junction depth

10. 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

11. In ion implantation, damaged-enhanced diffusion allows for significant diffusion of dopants
This is a major problem in very shallow junctions

12. Basic Concepts

13. 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

14. Dopant Solubility in Si

15. 1021
1020
1019
Temperature ( o C ) Sb B P As
Solubility limit
Electrical active
Impurity concentration, N (atoms/cm3 )
Solubility Limit

16. Solubility Limit Surface concentrations can be high.
At 1100oC:
B: 3.3 x 1020 cm-3
P: 1.2 x 1021 cm-3
At high temperatures, impurities cluster without precipitating and have limited electrical activity

18. III-V dopants have limited solubility in Si

19. 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

20. Fick’s Laws Diffusion is described by Fick’s Laws.
Fick’s first law is:
D = diffusion coefficient
Conservation of mass requires (This is the continuity equation)

21. Fick’s Laws
Combining the continuity equation with the first law, we obtain Fick’s second law:

22. 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

23. 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

24. Solutions To Fick’s Second Law
For a semi-infinite slab with a constant (infinite) supply of atoms at the surface
The dose is

25. Solutions To Fick’s Second Law
Complimentary error function (erfc) is defined as erfc(x) = 1 - erf(x)
The error function is defined as
This is a tabulated function. There are several approximations. It can be found as a built-in function in MatLab, MathCad, and Mathematica

26. 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 c0 cB
Distance from surface, x 1 2 3
D3t3 > D2t2 > D1t1
Impurity concentration, c(x)
c ( x, t )

27. 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
The surface concentration is given by:

28. Solutions To Fick’s Second Law
Limited source diffusion looks like
c ( x, t )
c01
c02
c03 cB 1 2 3
Distance from surface, x
D3t3 > D2t2 > D1t1
Impurity concentration, c(x)