UNIVERSITY OF CALIFORNIA SANTA BARBARA
DEPARTMENT OF CHEMICAL ENGINEERING
CHE 142 and ChE 242: Microelectronics Processing
Spring 2003 Homework # 1
(Due April 16, 2003)
1)
Neatly draw the atomic configurations of the {111}, {100} and {110} planes of Si.
Show these
planes on the diamond structure and calculate their atomic densities in # of Si atoms/cm
2
.
2)
Using the lattice constants as a starting point, calculate the atomic density of Si.
Also, calculate the
density (in g/cm
3
) of Si and GaAs compare your answer to published values.
3)
Calculate the SiSi bond length and the angle between the two SiSi bonds.
4)
When a piece of Si crystal is cleaved across the (100) surface it looks like the projection you drew
in question 1.
However, this configuration is high energy and unstable. When you answer parts (a)
and (b) of this question you will find out why. The surface reconstructs by forming SiSi bonds
(dimers) to reduce the dangling bond density on the surface.
The reconstructed surface looks like
Figure 1 where you can clearly see the rows of dimers.
This surface is called the Si(100)(2x1)
surface because the unit cell required to generate the surface is a rectangle that has sides 2a x 1a
where a
×
a
×
a
are the dimensions of the Si diamond lattice unit cell.
(a) How many dangling bonds per Si atom are there on the unreconstructed surface?
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 Fall '09
 Ceweb
 Chemical Engineering, Electron, Si atom

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