Electronics Engineering Department
ECE 522 Integrated Circuit Fabrication
Practice Problems II
1. A melt contains 0.1 atomic percent phosphorus in silicon. Assume the well mixed
approximation and calculate the dopant concentration of the crystal (in dopant
atoms per unit volume) formed when 10% of the crystal is pulled, when 50% of the
crystal is pulled and when 90% of the crystal is pulled. The atomic density of silicon
in solid is 5.02x1022 silicon atoms/cm3. In doping, it is assumed that each dopant
atom replaces one silicon atom and that the dopant level is sufficiently low not to
affect the density of silicon.
2. An antimony-doped crystal is required to have a resistivity of 1.0 -cm when one
half of the crystal is grown from the melt by Czochralski method. Assuming that a
100 gm pure silicon charge is used, what is the amount of 0.01 -cm antimony-
doped silicon that must be added to the initial melt? For simplicity take electron
mobility to be 1500 cm2V-1s-1 for both the 1.0 -cm and the 0.01 -cm silicon.
3. A small silicon bar is doped with both boron and antimony. The antimony/boron
atom ratio is 10. One end of the bar is inserted into a furnace and 1 mm of the bar
is melted. The bar is now withdrawn and is allowed to regrow with a diameter ten
times that of the original bar. Sketch the dopant concentration profile that results
from the regrowth process and calculate the base width of the resulting bipolar
junction transistor.
Table of Distribution Coefficient, k, for various dopants in silicon
Dopant
P
As
Sb
B
Al
Ga
In
k
0.32
0.27
0.02
0.72
1.8x10-3
7.2x10-3
3.6x10-4
4. Calculate the junction depth formed by ion implantation of boron into an n-type
substrate with 1015 phosphorus atoms per cm3 . The implantation energy is 20 keV
and the implant dose is 5x 1013 cm-2 . Take Rp = 71.4 nm, Rp = 27.6 nm at 20 keV
for boron ions. Assume that the hole mobility is 100 cm2/V-s, estimate the sheet
resistance of the implanted p-type layer.
5. Determine the number of atoms per unit cell in a (a) face centered cubic, (b) body
centered cubic and (c) diamond lattice.
6. The lattice constant of GaAs is 5.66
0
A
. Determine the number of Ga atoms and As
atoms per cm3.
7. Consider a three dimentional cubic lattice with a lattice constant equal to a. (a)
Skech the following planes: (i) (100), (ii) (110), (iii) (310), (iv) (230). (b) Sketch
the following directions: (i) [110], (ii) [100], (iii) [310] and (iv) [230].Determine
the surface density of atoms for silicon on (a) (100) plane, (b) (110) plane, and (c)
(111) plane.
8. If 1 X 1015 boron atoms per cm3 are added to silicon as a substitutional impurity,
determine what percentage of silicon atoms are displaced in the single crystal
lattice.
