Microelectronics Technology discusses advanced models for dopant diffusion. Advanced models account for electric field effects, concentration-dependent diffusion, and dopant segregation. Some models are based on point defect driven diffusion at the atomic scale. Modifications to Fick's laws are also discussed, including electric field enhancement effects which become important at higher doping concentrations. Process simulations demonstrate how electric fields can dominate doping distribution near MOS device source/drain regions. Concentration dependent diffusivities and dopant segregation effects are also covered.

1. Microelectronics Technology
Dopant Diffusion III

2. Advanced Models
• Advanced diffusion process models include the modifications
to Fick’s laws to account for electric field effects,
concentration-dependent diffusion, dopant segregation etc.
• Some advanced models based on point-defect driven
diffusion processes at atomic scale have also been developed
which predict doping profile very accurately.

3. Modifications Of Fick's Laws
A. Electric field effects
• When the doping is higher
than ni, £-field effects become
important.
• ε -field induced by higher mobility of electrons and holes compared
with dopant ions.
• ε -field enhances the diffusion of dopants causing the field
2
4 i
2
nC
C
1h
Where
X
C
hDf
+
+=
∂
∂
−=
If all dopants is ionized
C: Net Doping concentration
h: Electric field enhancement factor

5. Process Simulation
• SUPREM simulation at 1000˚C. Note the boron profile after
As N+ S/D regions e -field effects added. Significant change
in the B profile in a NMOS Transistor.
• Field effects can dominate the doping distribution near the source/drain of a
MOS device (SUPREM simulation).

6. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
Modifications Of Fick's Laws
• Error function profile
• Isoconcentration exp.
B 10 & B 11

7. Si B In As Sb P
D0.0 cm2
sec-1
560 0.05 0.6 0.011 0.214 3.85
D0.E eV 4.76 3.5 3.5 3.44 3.65 3.66
D+
.0 cm2
sec-1
0.95 0.6
D+
.E eV 3.5 3.5
D.0 cm2
sec-1
31.0 15.0 4.44
D.E eV 4.15 4.08 4.0
D=
.0 cm2
sec-1
44.2
D=
.E eV 4.37
Concentration dependent diffusivities

8. Segregation
TSUPREM IV Plot of B contours after oxidation of uniformly B-doped substrate
• Dopants have different solubilities in different material: Redistribute
until chemical potential is same on both sides of the interface.
• Segregation Coefficient: Ratio of equilibrium doping conc.on
each side of interface
K0=Csi/CSiO2
K0= 0.3 (B)
K0=10
(As,Sb,P)

9. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
Segregation

10. Interfacial Dopant Pile-up
• Dopants may also pile up at the interface layer, perhaps only a
monolayer thick. Interfacial dopant dose loss or pile-up may
consume up to 50% of the dose in a shallow layer.
• In the experiment (right) 40% of the dose was lost in a 30
sec anneal.

11. Summary of Macroscopic Approach to
Diffusion
• Fick's first law correctly describes dopant diffusion
in the limit of low concentrations.
• "Fixes" to this law to account for experimental
observations (concentration dependent diffusion
and e -field effects), are useful, but at this point the
complexity of the "fixes" begins to outweigh their
usefulness.
We turn to an atomistic view of diffusion for a
deeper understanding.

13. Kick-out and Interstitial(cy) Assisted
Mechanisms.
Mathematically it is identical to the kick out process
and both are referred to as interstitial assisted
diffusion

15. Inferences About Mechanisms
• Oxidation provides an I injection source.
• Nitridation provides a V injection source.
• Stacking faults serve as "detectors" as do dopant which
diffuse.
• Roles of both I &V in assisting dopant diffusion in Si

17. Atomic Scale Interactions
• Consider the simple Dopant-Defect Interactions
A + I <----> AI
• For example OED is explained because oxidation injects I driving the
equation to the right, creating more AI pairs and enhancing the dopant D.
• Even under inert conditions, atomic-level description says that dopant
diffusion from the surface contains lot of AI,driving above Eq. to left thus
pumping interstitials (Chemical Pumping)
• In the more complex example below, phosphorus diffuses with I, and
releases them in the bulk. This enhances the tail region D.

18. Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani
Emitter Push Effect
Pumping of interstitials by diffusion of P which builds up a high
supersaturation of these point defects in the interior of sample

19. Summary of Key Ideas
• Selective doping is a key process in fabricating semiconductor
devices.
• Doping atoms generally must sit on substitutional sites to be
electrically active.
• Both doping concentration and profile shape are critical in
device electrical characteristics.
• Ion implantation is the dominant process used to introduce
dopant atoms. This creates damage and thermal annealing is
required to repair this damage.
• Powerful simulation tools exist today which model diffusion
processes and can predict complex doping profiles.