SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

1.6. PROBLEMS 25

Material C 11 (N/m^2 ) C 12 (N/m^2 ) C 41 (N/m^2 )

Si 1.66 x 1011 0.64 x 1011 0.8 x 1011

Ge 1.29 x 1011 0.48 x 1011 0.67 x 1011

GaAs 1.2 x 1011 0.54 x 1011 0.59 x 1011

C 10.76 x 1011 1.25 x 1011 5.76 x 1011

Material C 13 (N/m^2 ) C 33 (N/m^2 )

GaN 10.9 x 1011 35.5 x 1011

AlN 12 x 1011 39.5 x 1011

Table 1.2: Elastic constant for some fcc and hcp based semiconductors. (For Si, Ge, GaAs see H.
J. McSkimin and P. Andreatch,J.Appl.Phys., 35 , 2161 (1964) and D. I. Bolef and M. Meres,J.
Appl.Phys., 31 , 1010 (1960). For nitrides see J. H. Edgar,PropertiesofIII-VNitrides, INSPEC,
London (1994) and R. B. Schwarz, K. Khachaturyan, and E. R. Weber,Appl.Phys.Lett., 74 ,
1122 (1997).)

use of a wide range of semiconductors. In table 1.3 we show an overview of some important
substrates and issues in semiconductor technology.

1.6 PROBLEMS

Problem 1.1A 10.0μm Si epitaxial layer is to be grown. The Si flux is 1014 cm−^2 s−^1.

How long will it take to grow the film if the sticking coefficient for Si atoms is 0.95?

Problem 1.2A Si wafer is nominally oriented along the (001) direction, but is found to be

cut 2 ◦off, toward the (110) axis. This off axis cut produces “steps” on the surface which

are 2 monolayers high. What is the lateral spacing between the steps of the 2 ◦off-axis

wafer?

Problem 1.3Conduct a literature search to find out what the lattice mismatch is between

GaAs and AlAs at 300 K and 800 K. Calculate the mismatch between GaAs and Si at the

same temperatures.

Problem 1.4In high purity Si crystals, defect densities can be reduced to levels of

1013 cm−^3. On an average, what is the spacing between defects in such crystals? In

heavily doped Si, the dopant density can approach 1019 cm−^3. What is the spacing

between defects for such heavily doped semiconductors?