Analyzing defects in bulk silicon

In the following exercise we are going to investigate the effect of defects in bulk silicon (mainly on the energy).

Use the input file as given below:

&GLOBAL
  PROJECT silicon8
  RUN_TYPE ENERGY
  PRINT_LEVEL MEDIUM
&END GLOBAL
&FORCE_EVAL
  METHOD Quickstep
  STRESS_TENSOR ANALYTICAL
  &DFT
    BASIS_SET_FILE_NAME  BASIS_SET
    POTENTIAL_FILE_NAME  POTENTIAL
    &POISSON
      PERIODIC XYZ
    &END POISSON
    &SCF
      SCF_GUESS ATOMIC
      EPS_SCF 1.0E-8
      MAX_SCF 500
    &END SCF
    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
    &END XC
  &END DFT
  &SUBSYS
    &KIND Si
      ELEMENT   Si
      BASIS_SET DZVP-GTH-PBE
      POTENTIAL GTH-PBE
    &END KIND
    &CELL
      ABC 5.430697500 5.430697500 5.430697500
      PERIODIC XYZ
    &END CELL
    &COORD
      SCALED
      Si    0    0    0
      Si    0    2/4  2/4
      Si    2/4  2/4  0
      Si    2/4  0    2/4
      Si    3/4  1/4  3/4
      Si    1/4  1/4  1/4
      Si    1/4  3/4  3/4
      Si    3/4  3/4  1/4
    &END COORD
  &END SUBSYS
&END FORCE_EVAL

Create a second input file silicon64.inp based on the above with 64 atoms in the cell (do not use MULTIPLE_UNIT_CELL but actually replicate the Si … entries by hand and make sure you don't forget to update the CELL).

Run the calculation for both geometries and compare the single atom energy for both of them to make sure you got it right.

To speed up the calculation, use

mpirun -np 4 cp2k.popt -i silicon64.inp -o silicon64.out

For both geometries create a vacancy by removing one Silicon atom, re-calculate the total energy and compare it to the total energy of the intact bulk Silicon minus the single atom energy (= vacancy formation energy). What do you observe? Why?

You may have to employ some of the techniques mentioned in Projected density of states and Band structure for WO$_3$ to make the calculations converge.

Observing changes in the density of states

Finally we are going to look at the change of the density of states due to the vacancy:

Alter the input files for the small geometry (the silicon8) with and without the vacancy to print out the projected density of states as shown in a previous exercise and plot the total density of states for both cases, comment. Can you explain why the vacancy calculation is harder to converge ?

Now do a geometry optimization on the silicon8 structure with the vacancy and plot the total density of states on that relaxed structure again. Compare again to the total density of states for the unaltered structure, what do you see?

Your last task is to compare the total energy of the geometry optimized (with the vacancy) silicon8 structure to that of the standard one minus the energy of a single atom. That is, compute the vacancy formation energy with the relaxed structure and compare it to the one obtained previously. Which of those is the best representation of reality and why ?