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Starting from 2006 Hafnium silicates replaced SiON as gate oxide in MOSFETS. The high dielectric constant of HfO2 and the ability of HfO2 to form silicates played a key role in the industrial transition.
Construct the primitive cell of the monoclinic phase of HfO2, using ASE and teh information contained in the HfO2 manuscript
and find in this article (a pdf copy is included in dropbox)
all data necessary to construct the monoclinic phase of HfO2
modify the python script hfo2.py according to your needs.
Execution of the python script
will open the ASE visualizer showing you the structure, will produce the file hfo2.xyz, hfo2.png and hfo2.pov
to create a “nice” image of the primitive cell you can render the output file hfo2.pov with the command
povray +W320 +H320 -I./hfo2.pov -Ohfo2 +P +X +A +FJ +C
or executing the script
(that will take care of removing files hfo2.jpg and hfo2.inc)
-compute the volume of the unit cell
Have a look at the atomic coordinates, for example in the file hfo2.xyz (where you also find the cell vectors in cartesian coordinates) and
DO NOT FORGET Periodic Boundary Conditions!! but it's simple: x,y,z are given in crystal coordinates so, if for example x=0.276 for “-x” you can use -x+1 = 0.724
Check the lecture notes for the free electron model and:
Have a look at this ASE page to compute bandstructures and the symmetry points of the Brillouin zone of a crystal:
Write the CARTESIAN COORDINATES of the Gamma, X, W points of FCC