Tutorials

# Density of States

### Outline

This is a simple example of using optados for calculating electronic density of states of crystalline silicon in a 2 atom cell. It shows how optados's adaptive broadening can be used to resolve fine spectral features that a fixed broadening scheme will obscure.

### Input Files:

• examples/Si2_DOS/Si2.cell - The castep cell file containing information about the simulation cell.
• examples/Si2_DOS/Si2.param - The castep param file containing information about the parameters for the SCF and spectral calculations.
• examples/Si2_DOS/Si2.odi - The optados input file, containing the parameters necessary to run optados.

## INSTRUCTIONS:

### Step 1

• Perform a castep calculation on the bulk silicon using the Si2.cell and Si2.param input files.
\$ castepsub -n 16 Si2

This should take a couple of seconds to run.

### Step 2

• Examine the optados input file - Si2.odi

This generates 3 files:

1. Si2.odo -- optados general output file.

Examine the Si2.odo file. optados has performed a Density of States calculation.

+--------------- Fermi Energy Analysis ------------------------+
| Spin Component:1 occupation between 3.99961 and 4.00003 <-Oc |
| Spin Component:2 occupation between 3.99961 and 4.00003 <-Oc |
+--------------------------------------------------------------+

It has used the integrated DOS to work out the Fermi level, and has suggested the error in the integration by indicating the number of electrons at the Fermi level. Since we had 4 up electrons and 4 down in the input file this analysis seems satisfactory.

+----------------------- Electronic Data ---------------------+
|  Number of Bands                           :       23       |
|  Grid size                                 :  10 x 10 x 10  |
|  Number of K-points                        :           110  |
|  Spin-Polarised Calculation                :           True |
|  Number of up-spin electrons               :          4.00  |
|  Number of down-spin electrons             :          4.00  |
+-------------------------------------------------------------+

Since we had efermi : optados, optados sets the internal value of the Fermi level to the one it has derived from the DOS. This is important for subsequent calculations. Other valid options are file, where optados uses the value calculated by the electronic structure code that generated the eigenvalues; insulator, where optados uses a value calculated from assuming the system is non-metallic; or a value set by the user.

optados now performs some analysis of the DOS at the Fermi level,

+-------------- DOS at Fermi Energy Analysis ----------------+
|                          Fermi energy used :   5.4109 eV   |
| Spin Component:1 DOS at Fermi Energy:0.0011 eln/cell <-DEA |
| Spin Component:2 DOS at Fermi Energy:0.0011 eln/cell<- DEA |
+------------------------------------------------------------+

From this we may assume that there is a band gap.

Importantly, then optados calculates the band energy from the DOS is has calculated.

+------------------- Band Energy Analysis -------------------+
|     Band energy (From CASTEP) :         1.3622 eV   <- BEC |
+------------------------------------------------------------+

As the quality of the optados calculation is increased these two values should converge to the same answer.

Finally optados shifts the Fermi level to 0eV, for the output files.

1. The DOS is written to Si2.adaptive.dat. This contains 5 columns as described in the header of the file:
################################################################
#
#                  O p t a D O S   o u t p u t   f i l e
#
#  Generated on 12 Feb 2012 at 16:50:37
# Column        Data
#    1        Energy (eV)
#    2        Up-spin DOS (electrons per eV)
#    3        Down-spin DOS (electrons per eV)
#    4        Up-spin Integrated DOS (electrons)
#    5        Down-spin Integrated DOS (electrons)
#
################################################################

This file can be plotted by your favourite graph-plotting software. However, optados has made things easy and generated a Si2.adaptive.agr file which is directly plottable using xmgrace.

1. We now try again with a better sampling of the DOS, by setting DOS_SPACING : 0.001 and also analyse the band gap, by setting COMPUTE_BAND_GAP : true. You can set IPRINT : 2 to see a progress report in Si2.odo.

In Si2.odo we now have a new section analysing the band gap in various ways.

+----------------------------- Bandgap Analysis ---------------+
|          Number of kpoints at       VBM       CBM            |
|                   Spin :   1  :      1         1             |
|                   Spin :   2  :      1         1             |
|               Thermal Bandgap :   0.6676272107  eV    <- TBg |
|            Between VBM kpoint :    0.05000    0.05000 0.05000|
|               and CBM kpoint:   -0.45000    -0.05000 -0.45000|
|             ==> Indirect Gap                                 |
+--------------------------------------------------------------+
|                            Optical Bandgap                   |
|                   Spin :   1  :     2.5542517447  eV  <- OBg |
|                   Spin :   2  :     2.5542463024  eV  <- OBg |
|          Number of kpoints with this gap                     |
|                   Spin :   1  :           1                  |
|                   Spin :   2  :           1                  |
+--------------------------------------------------------------+
|                            Average Bandgap                   |
|                   Spin :   1  :     3.8121372691  eV  <- ABg |
|                   Spin :   2  :     3.8121342659  eV  <- ABg |
|              Weighted Average :     3.8121357675  eV  <- wAB |
+--------------------------------------------------------------+

optados is very careful in its band gap analysis. It uses the bare eigenvalues (un-broadened) and works out the nature and size of the thermal gap, optical gap and the average gap over all of the Brillouin zone. In cases of multi-valleyed semiconductors optados will report the number of conduction band minima or valence band maxima with identical energies, but will not report the nature of the gap.

Increasing the number of integration points has improved the band energy of the adaptive smearing: