To obtain the band structure of Si bulk of given lattice parameter we have to perform two steps.
First, we need to achieve SCF solution. Therefore, we run a standard bulk calculation as described in the previous chapter. Let's calculate the band structure
for the lattice parameter
alat = 5.5 Å, than we have the
fireball.in file containing:
&OPTION basisfile = Si.bas lvsfile = Si.lvs kptpreference = Si.kpts nstepf = 1 rescal = 5.5 &END
Si.kpts files are identical as those used in previous chapter.
Once we obtain the SCF solution, we can determine the Fermi level from an output file:
mac135> grep "Fermi Level" $output_file | tail -1 Fermi Level = -4.33045968490834
In next step, we run the
FIREBALL code again, but now with fixed charges (
ifixcharge = 1) and with a new set of k-points in desired high-symmetry directions in the first Brillouin zone. Remember we need having
CHARGES file in a working directory for a restart. In this particular case,we have chosen a direction
L-Γ-X-Γ stored in a
lgxg.kpts file (see also fig. 1).
In addition, we have to write out a list of eigenvalues at each k-point switching on
iwrteigen variable. Our input file
fireball.in has following form now:
&OPTION basisfile = Si.bas lvsfile = Si.lvs kptpreference = lgxg.kpts nstepf = 1 ifixcharge = 1 rescal = 5.5 &END &OUTPUT iwrteigen = 1 &END
After the run, we obtain a file
ek.dat appears in a working directory. This file contains at each line set of eigenvalues for given k-points ordered in ascending form. The Fermi level can
Now we have all information to plot the band structure of the Si bulk.
mac135> gnuplot gnuplot> set xrange [0:300] gnuplot> set yrange [-17:0] gnuplot> set xlabel "k-points" gnuplot> set ylabel "Energy [eV]" gnuplot> set nokey gnuplot> set multiplot multiplot> plot "ek.dat" using 1:2 with lines multiplot> plot "ek.dat" using 1:3 with lines multiplot> plot "ek.dat" using 1:4 with lines multiplot> plot "ek.dat" using 1:5 with lines multiplot> plot "ek.dat" using 1:6 with lines multiplot> plot "ek.dat" using 1:7 with lines
To plot Density of state, first, we have to achieve SCF solution in the same way as above (see previous section).
Next we perform calculation with fixed SCF charges (switching on
ifixcharge =1). The DOS calculation is initialized via variable
iwrtdos in the section
&OUTPUT. Hence, our
fireball.in file looks like that:
&OPTION basisfile = Si.bas lvsfile = Si.lvs kptpreference = Si.kpts nstepf = 1 ifixcharge = 1 rescal = 5.5 &END &OUTPUT iwrtdos = 1 &END
dos.optional has to be presented in a working directory having following distance:
1.0 ! scale factor (leave 1.0) 1 2 ! list of atoms to analyze DOS 360 ! number of energy steps -18.0 0.05 ! initial energy, energy step 0 ! leave untouched 0.0 0.0 ! leave untouched 0.05 ! imaginary part of Green function (controls energy level smearing)
After finishing a run, we obtain
dens_002.dat including projected DOS on two Si atoms in the unit cell (including projected DOS onto individual shells of atoms). Additionally, there is a file
dens_TOT.dat containing DOS. Here, a first column means energy and a second one DOS.
mac135> gnuplot gnuplot> set xrange [0:1] gnuplot> set yrange [-17:0] gnuplot> set xlabel "DOS [arb. units]" gnuplot> set ylabel "Energy [eV]" gnuplot> plot "dens_TOT.dat" using 2:1 title 'Total DOS' with lines, \ "dens_001.dat" using 11:1 title 'PDOS Si atom ' with lines