# 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:

- silicon8.inp
&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.

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?

# 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 ?