Consider diffusion of Sb in an intrinsic silicon material De

Consider diffusion of Sb in an intrinsic silicon material. Determine the concentration of Sb at a depth of 2 m assuming the concentration of Sb at the surface to be 1x1021 cm-3, and that the system is annealed at a temperature of 1,200 C for a period of 60 minutes. Use the following method to find the answer:

Analytical solution to Fick’s equation. You will need to first calculate the diffusion coefficient D

Solution

Antimony \"Sb\" is resisting deactivation more than arsenic
“As”, since it has heavier mass with lower diffusivity when
implanted in non-strained and strained silicon \"Si\". So Sb seems
to be a potential alternative and more stable as a common
n-type spices used for ultra-shallow doping of engineering
CMOS devices. Sheet resistance of CMOS devices is critical to
the speed of integrated circuits. Therefore, heavily doped ultra-shallow junctions are required to achieve low resistance in
Source/Drain region [1-4]. The Source/Drain junction depth j
which has traditionally been controlled by ion implantation is
one of the challenged critical dimensions that need to be scaled
(nano-scaled) and engineered for modern CMOS [5]. Varying the
dopant implant energy and dopant dose with low thermal budget
processing becomes one of the important approaches to generate
ultra-shallow junctions. For low thermal budget, there are three
techniques: flash annealing, laser annealing and rapid thermal
annealing. RTA has the advantage which give rise to solid phase
epitaxial regrowth (SPER) of the radiation damaged region due
to ion implantation. RTA induced SPER has demonstrated the
highest dopant solubility for As and Sb as well as maximizing
the activation of dopants [6,7]. The electrical characterization
of the implanted junction layer is well profiled by matching
the carrier concentration profile results from Differential Hall
effect measurements (DHM) with atomic profile investigated
by Secondary Ion Mass Spectroscopy (SIMS). Alzanki et al. [8]
investigated the effect of ion implant dose (1 × 1014 cm-2 - 1 × 1015
cm-2) for low implant energies (2 keV and 5 keV) on the atomic
profiles, carrier profiles and sheet resistance. The results show
that the optimum electrical characteristics of the formed shallow
junction and its sheet resistance require much lower thermal
budget than the currently used in industry. Also Bennett [9,10]
investigated the effect of implant dose (1 × 1014cm-2 - 1 × 1015
cm-2) for 2 keV implant energy for controlled Si and strainedengineered
Si. The results indicate that the strained Si enhances
the carrier mobility by ~30% which reduces the sheet resistance
by ~30% for junction depth of ~10 nm to 15 nm. Combination
of Rutherford Back Scattering (RBS) results with Medium Energy
Ion Scattering (MEIS) results [11] could determine the lattice
site occupancy of Sb implanted in conventional Si and strained
Si for 2 keV and 40 keV. These results were compared with that
measured by DHM and prove that the Hall Scattering factor \"r\",
which appeared in the following equations, is equal to unity is
valid even the peak concentration peaks at 2 × 10 20cm-3. It is
known that this scattering factor is a correction factor due to
effects of circulating currents resulting from varying of carrier scattering degrees caused by the presence of the magnetic field
in Hall measurements.

Experimental Details

P-type (100) Si wafers of diameter 100 nm with resistivity
of 10-12 cm were implanted at room temperature with
antimony ions of implanted energies 2 keV, 5 keV, 12 keV and
40 keV for doses in the range from 1 × 1014 cm to 1 × 1015 cm.
Here we treated the energies data with doses 4 × 1014 cm-2, 5
× 1014 cm-2, 8.5 × 1014 cm-2 and 4 × 1014 cm-2, respectively. The
doses around 4 × 1014 cm-2 gave the best results for the formed
shallow junctions. The tilt and twisted angles in the implantation
were 7° and 22°, respectively. The wafer were cut into small
pieces and activated using a process product corporation RTP
system in the temperature range from 600°C to 1100°C for
times between 5 seconds and 3600 seconds in flowing nitrogen
gas. However the majority of samples were annealed for 10 s
as longer annealing times produced insignificant difference in
electrical activity or sheet resistance. Wide set of measurements
with an accent HL5500 Hall system. Several samples were
measured for each experimental point and the average is taken.
The estimated uncertainty in sheet resistance values is in the
range 2.5-4%. Details of the technique could be found in Alzanki
et al. [11] and Bennett et al. [10]. The differential Hall Technique
is a complicated method for characterizing ultra-shallow doping
in semiconductors but with careful experimental protocol and
considered data analyses it can merit reliable results, since it
has a unique advantage over other techniques as it capable
of separating the relative carrier concentration and mobility
distribution to the conduction of the doped layer under test. Also
samples were analyzed as-implanted and annealed using SIMS
technique for atomic concentration profiles by CAMECA IMS 6F
with primary beam energy of 750 eV O2
+ for 5 keV to 40 keV for
Sb whilst for 2 keV Sb a 500 eV Cs+ beam was used for analyses to
ensure reliable profile shape and dose in the near surface region.