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.
(comment the line “hfo2.write(“hfo2.png”)”)
Execution of the python script
will open the ASE visualizer showing you the structure, will produce the file hfo2.xyz, (hfo2.png)
-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
usually the coordinates are provided in crystal coordinates so if a1=(a1x,a1y,a1z),a2=(a2x,a2y,a2z),a3=(a3x,a3y,a3z) are the three basis vectors of the crystal in cartesian coordinates and (x1,y1,z1) the crystal coordinates of atom 1, the cartesian coordinates of atom 1 will be: x1*a1 + x2*a2 + x3*a3
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: