ELEC
424/6241/4-W
VLSI Process Technology
Winter
2023
Homework due on January 30th 2023
No late homework will be accepted
Homework #1
1. A process technology that has gained a great deal of interest in the last few years
is “rapid thermal annealing”. This process allows wafers that contain high
concentrations of dopant atoms to be heated to high temperatures very rapidly,
minimizing dopant redistribution (diffusion). Explain the desirability of such a
process based on the discussion of phase diagrams and solid solubility.
2. A mixture of 30% silicon and 70% germanium is heated to 1100ºC. If the material
is in thermal equilibrium, what is the concentration of silicon in the melt? At what
temperature will the entire charge melt? The sample temperature is raised to
1300ºC, then slowly cooled back down to 1100 ºC. What is the concentration of
silicon in the solid?
3. During the molecular beam epitaxial growth (MBE) of GaAs layers, there is a
strong tendency to form droplets of gallium on the surface of the wafer. These
oval defects are a serious problem for MBE growth. Avoiding them requires a
large arsenic-to-gallium flux ratio. Referring to the phase diagram (Figure 2.2 of
Campbell), explain why thermodynamics would favor the formation of these
droplets.
4. A silicon wafer that has 1016 cm-3 of boron is found to have a neutral vacancy
concentration of 2x1010 cm-3 at some processing temperature and a single ionized
vacancy concentration of 109 cm-3 at the same temperature. Determine the
temperature and the activation energy of the charged vacancy with respect to the
intrinsic level, Ei. What would happen to these values if wafer was to be doped
with 2x1019 cm-3 of boron atoms. (Hint: you might want to use the characteristics
describing the variation of ni with temperature)
5. A melt contains 0.1 atomic percent of phosphorus in silicon. Assume the wellmixed approximation and calculate the dopant concentration when 10% of the
crystal is pulled (solidified), when 50% of the crystal is pulled, and when 90% of
the crystal is pulled.
6. A Czochralski growth process is begun by inserting 1000 moles of pure silicon
and 0.01 mole of pure arsenic in a crucible. For this boule, the maximum
permissible doping concentration is 1018 cm-3. What fraction of boule is usable?
7. Discuss the role of Oxygen in intrinsic gettering. Describe typical conditions and
mechanisms of forming gettering sites.
8. Calculate temperature difference across a (100) silicon wafer necessary for the
silicon to reach its yield strength. This gradient sets an upper limit on the
temperature nonuniformity that is acceptable in a “rapid thermal annealing”
system. (Bonus problem and only for graduate students)