1. Junction Formation
The position of the junction for a limited source diffused impurity in a constant background is given by
The position of the junction for a continuous source diffused impurity is given by x Dt N j B = 2 ln x Dt N j B = - 2 1
erfc

2. Junction Formation
Junction Depth
Lateral Diffusion

3. Design and Evaluation
There are three parameters that define a diffused region
The surface concentration
The junction depth
The sheet resistance
These parameters are not independent
Irvin developed a relationship that describes these parameters

4. Irvin’s Curves
In designing processes, we need to use all available data
We need to determine if one of the analytic solutions applies
For example,
If the surface concentration is near the solubility limit, the continuous (erf) solution may be applied
If we have a low surface concentration, the limited source (Gaussian) solution may be applied

5. Irvin’s Curves
If we describe the dopant profile by either the Gaussian or the erf model
The surface concentration becomes a parameter in this integration
By rearranging the variables, we find that the surface concentration and the product of sheet resistance and the junction depth are related by the definite integral of the profile
There are four separate curves to be evaluated
one pair using either the Gaussian or the erf function, and the other pair for n- or p-type materials because the mobility is different for electrons and holes

6. Irvin’s Curves

7. Irvin’s Curves
An alternative way of presenting the data may be found if we set eff=1/sxj

8. Example
Design a B diffusion for a CMOS tub such that s=900/sq, xj=3m, and CB=11015/cc
First, we calculate the average conductivity
We cannot calculate n or  because both are functions of depth
We assume that because the tubs are of moderate concentration and thus assume (for now) that the distribution will be Gaussian
Therefore, we can use the P-type Gaussian Irvin curve

9. Example Reading from the p-type Gaussian Irvin’s curve, CS4x1017/cc
This is well below the solid solubility limit for B in Si so we may conclude that it will be driven in from a fixed source provided either by ion implantation or possibly by solid state predeposition followed by an etch
In order for the junction to be at the required depth, we can compute the Dt value from the Gaussian junction equation

10. Example This value of Dt is the thermal budget for the process
If this is done in one step at (for example) 1100 C where D for B in Si is 1.5 x 10-13cm2/s, the drive-in time will be
Given Dt and the final surface concentration, we can estimate the dose

11. Example
Consider a predep process from the solid state source (as is done in the VT lab course)
The text uses a predep temperature of 950 oC
In this case, we will make a glass-like oxide on the surface that will introduce the B at the solid solubility limit
At 950 oC, the solubility limit is 2.5x1020cm-3 and D=4.2x10-15 cm2/s
Solving for t

12. Example
This is a very short time and hard to control in a furnace; thus, we should do the predep at a lower temperature
In the VT lab, we use 830 – 860 oC
Does the predep affect the drive in?
There is no affect on the thermal budget because it is done at such a “low” temperature

13. DIFFUSION SYSTEMS Open tube furnaces of the 3-Zone design
Wafers are loaded in quartz boat in center zone
Solid, liquid or gaseous impurities may be used
Common gases are extremely toxic (AsH3 , PH3)
Use N2 or O2 as carrier gas to move impurity downstream to crystals

14. SOLID-SOURCE DIFFUSION SYSTEMS
Valves and
flow meters
Platinum
source boat
Slices on
carrier
Quartz
diffusion
tube
diffusion boat
burn box
and/or scrubber
Exhaust

15. LIQUID-SOURCE DIFFUSION SYSTEMS
Burn box
and/or scrubber
Exhaust
Slices on
carrier
Quartz
diffusion tube
Valves and
flow meters
Liquid source
Temperature-
controlled bath N2 O2

16. GAS-SOURCE DIFFUSION SYSTEMS
Burn box
and/or scrubber
Exhaust N2
Dopant
gas O2
Valves and flow meter
To scrubber system
Trap
Slices on carrier
Quartz diffusion tube

17. DIFFUSION SYSTEMS Typical reactions for solid impurities are: - + ¾ ®2 9 6 4 30 5 3
900 CH O B CO H Si
SiO
POCl P Cl As Sb o C

18. Rapid Thermal Annealing
An alternative to the diffusion furnaces is the RTA or RTP furnace

19. Rapid Thermal Anneling
Absorption of IR light will heat the wafer quickly (but not so as to introduce fracture stresses)
It is possible to ramp the wafer at 100 oC/s
Because of the thermal conductivity of Si, a 12 in wafer can be heated to a uniform temperature in milliseconds
1 – 100 s drive or anneal times are possible
RTAs are used to diffuse shallow junctions and to anneal radiation damage

20. Rapid Thermal Annealing

21. Concentration-Dependent Diffusion
When the concentration of the doping exceeds the intrinsic carrier concentration at the diffusion temperature
We have assumed that the diffusion coefficient, D, is dependent of concentration
In this case, we see that diffusion is faster in the higher concentration regions

22. Concentration-Dependent Diffusion
The concentration profiles for P in Si look more like the solid lines than the dashed line for high concentrations (see French et al)

23. Concentration-Dependent Diffusion
We can still use Fick’s law to describe the dopant diffusion
Cannot directly integrate/solve the differential equations when D is a function of C
We thus must solve the equation numerically

24. Concentration-Dependent Diffusion
It has been observed that the diffusion coefficient usually depends on concentration by either of the following relations

25. Concentration-Dependent Diffusion
B has two isotopes: B10 and B11
Create a wafer with a high concentration of one isotope and then diffuse the second isotope into this material
SIMS is used to determine the concentration of the second isotope as a function of x
The experiment has been done using many of the dopants in Si to determine the concentration dependence of D

26. Concentration-Dependent Diffusion
Diffusion constant can usually be written in the form for n-type dopants and
for p-type dopants

27. Concentration-Dependent Diffusion
It is assumed that there is an interaction between charged vacancies and the charged diffusing species
For an n-type dopant in an intrinsic material, the diffusivity is
All of the various diffusivities are assumed to follow the Arrhenius form

28. Concentration-Dependent Diffusion
The values for all the pre-exponential factors and activation energies are known
If we substitute into the expression for the effective diffusion coefficient, we find here, =D-/D0 and =D=/D0

29. Concentration-Dependent Diffusion

30. Concentration-Dependent Diffusion
 is the linear variation with composition and  is the quadratic variation
Simulators like SUPREM include these effects and are capable of modeling very complex structures