BANDGAP: Difference between revisions

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{{TAGDEF|BANDGAP|COMPACT {{!}} WEIGHT {{!}} KPOINT|COMPACT}}
{{TAGDEF|BANDGAP|COMPACT {{!}} WEIGHT {{!}} KPOINT|COMPACT}}


Description: {{TAG|BANDGAP}} determines the verbosity of the output for reporting the bandgap to the OUTCAR file.
Description: {{TAG|BANDGAP}} determines the verbosity for reporting the bandgap to the OUTCAR file.
Only the first character is significant.
----
----


[[File:bandgap.png|thumbnail|400px|For semiconductor, the bandgap the direct and fundamental bandgap have a clear definition.
[[File:bandgap.png|thumbnail|400px|For semiconductors, the direct and fundamental bandgap have a clear definition.
For semimetals, the Fermi energy cuts through bands so the depending on the method one defines either a zero or a negative fundamental bandgap.
For semimetals, the Fermi energy cuts through bands so depending on the method one defines either a zero or a negative fundamental bandgap.
For metals, defining a bandgap is not meaningful.]]
For metals, defining a bandgap is not meaningful.]]


Describe the general function of this tag and introduce all acronyms, symbols or formulas that are required to understand multiple tag options. The details of the tag options are discussed below. In case an acronym, e.g., PAW, is used that is used in many articles, link it to the main article or category. Otherwise, the acronym should be explained in a nutshell.
The bandgap of the system separates the occupied valence bands from the unoccupied conduction bands.
Of particular interest are the fundamental bandgap between valence band maximum (VBM) and conduction band minimum (CBM) and the direct bandgap at a single '''k''' point.


==First section==
{{TAG|BANDGAP}} controls how VASP reports the bandgap information.
The following options exist:
*{{TAG|BANDGAP}}=COMPACT
: Uses Fermi weights to decide what valence and conduction bands are. Reports the VBM, CBM, and fundamental gap to the OUTCAR file.


If there are many tag options, it may pay off to make each option a heading. This way the table of content provides a good overview. However, for three options the list below suffices.
*{{TAG|BANDGAP}}=WEIGHT
: Uses Fermi weights to decide what valence and conduction bands are. Provides a comprehensive report of all band extrema.


*{{TAG|MYTAG}}=-1: Algorithm name 
*{{TAG|BANDGAP}}=KPOINT
{{NB| deprecated | This functionality is not supported in VASP version > 5.4.4.|:}}
: Considers each '''k''' point individually to decide what valence and conduction bands are. Provides a comprehensive report of all band extrema.
:A concise description of this algorithm. A long description deserves an overview article.


*{{TAG|MYTAG}}=0: Algorithm name
== Difference between WEIGHT and KPOINT ==
:A concise description of this algorithm. A long description deserves an overview article. 
{{NB| warning | Do not combine with ...|:}}


*{{TAG|MYTAG}}=1: Algorithm name
The figure illustrates different possible properties of electronic band structures.
:You do not need to use a NB template everywhere, and it can be used anywhere before, after, and in between paragraphs. 
For semiconductors, the bandgap is well defined so that the choice of {{TAG|BANDGAP}} only affects whether the output is compact or verbose.
{{NB| tip | Do not combine with ...|:}}
For metals, there is no straightforward definition of a bandgap so the default of {{TAG|BANDGAP}}=COMPACT is sufficient.
A semimetal shares properties with metals (Fermi energy crosses bands) and with semiconductors (visible bandgap in the band structure).


==Second section==
{{TAG|BANDGAP}}=WEIGHT interprets systems like a metal; valence (conduction) states are more (less) than half-filled.
In this case, the bandgap of a semimetal converges to zero with an increasing number of '''k''' points similar to a metal.
For N number of electrons, the number of valence states is not in general equal to N for all '''k''' points.
Hence, the direct bandgap is not necessarily between the N-th and the (N + 1)-th state.


Give details about an issue that can arise here and offer some advice. The paragraph started with an indent. Add your references on '''Template:Cite''' and then cite using a command like this{{cite|kresse:prb:96}}.
{{TAG|BANDGAP}}=KPOINT considers systems like a semiconductor where every '''k''' point may be treated individually.
The number of valence bands is equal to the number of electrons N for all '''k''' points and the direct bandgap is equal to the smallest difference between the N-th and (N + 1)-th state.
In a semimetal, this approach produces a negative bandgap because the Fermi energy crosses the bands.
For collinear calculations ({{TAG|ISPIN}}=2), this method will allow for a different number of up and down electrons at every '''k''' point.
{{NB|mind|Setting {{TAG|BANDGAP}}{{=}}KPOINT only impacts the output of VASP. It is not considered when evaluating the occupations of different bands. If you want to enforce certain occupations, please consider the tags {{TAG|NUPDOWN}}, {{TAG|FERWE}}, and {{TAG|FERDO}}.}}


::<math>
== Example of the verbose output ==
\tilde{P}(\xi_i)= \frac{\int  \delta\Big(\xi(q)-\xi_i\Big) \exp\left\{-\tilde{H}(q,p)/k_B\,T\right\} dq\,dp}{\int  \exp\left\{-\tilde{H}(q,p)/k_B\,T\right\}dq\,dp} = \langle\delta\Big(\xi(q)-\xi_i\Big)\rangle_{\tilde{H}},
</math>


where Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Band structure
--------------
                        spin independent            spin component 1            spin component 2
val. band max:              9.679953                    9.679953                    5.987917
cond. band min:              9.148387                    10.409707                    9.148387
fundamental gap:            -0.531566                    0.729754                    3.160470
VBM @ kpoint:      0.2949  0.4423  0.1474    0.2949  0.4423  0.1474    0.0000  -0.0000  0.0000
CBM @ kpoint:      0.5000  0.5000  0.0000    0.0000  0.0000  0.0000    0.5000  0.5000  0.0000
lower band:                  8.126216                    7.283444                    5.087674
upper band:                  9.386102                    10.916258                    9.148387
direct gap:                  1.259885                    3.632813                    4.060713
@ kpoint:          0.3846  0.3846  0.0000    0.0641  0.0962  0.0321    0.5000  0.5000  0.0000
 
The column ''spin independent'' is always present and reports the bandgap ignoring the spin of the electron.
The other two columns are only visible for {{TAG|ISPIN}}=2 and describe the bandgap for a given spin of the electron.
The first block of rows show the band edges of the fundamental bandgap and their corresponding '''k'''-point coordinates.
The second block reports analogous values for the direct gap.
In each case the energy difference of the band edges is computed and printed as fundamental and direct gap, respectively.


== Related tags and articles==
== Related tags and articles==
{{TAG|EFERMI}} {{TAG|ISMEAR}} {{TAG|SIGMA}}
{{TAG|EFERMI}}, {{TAG|ISMEAR}}, {{TAG|SIGMA}}


{{sc|BANDGAP|Examples|Examples that use this tag}}
{{sc|BANDGAP|Examples|Examples that use this tag}}


== References ==
[[Category:INCAR tag]][[Category:Electronic ground-state properties]]
<references/>
----
[[The_VASP_Manual|Contents]]
 
[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Density of States]]

Latest revision as of 10:55, 19 March 2024

BANDGAP = COMPACT | WEIGHT | KPOINT
Default: BANDGAP = COMPACT 

Description: BANDGAP determines the verbosity for reporting the bandgap to the OUTCAR file. Only the first character is significant.

For semiconductors, the direct and fundamental bandgap have a clear definition. For semimetals, the Fermi energy cuts through bands so depending on the method one defines either a zero or a negative fundamental bandgap. For metals, defining a bandgap is not meaningful.

The bandgap of the system separates the occupied valence bands from the unoccupied conduction bands. Of particular interest are the fundamental bandgap between valence band maximum (VBM) and conduction band minimum (CBM) and the direct bandgap at a single k point.

BANDGAP controls how VASP reports the bandgap information. The following options exist:

Uses Fermi weights to decide what valence and conduction bands are. Reports the VBM, CBM, and fundamental gap to the OUTCAR file.
Uses Fermi weights to decide what valence and conduction bands are. Provides a comprehensive report of all band extrema.
Considers each k point individually to decide what valence and conduction bands are. Provides a comprehensive report of all band extrema.

Difference between WEIGHT and KPOINT

The figure illustrates different possible properties of electronic band structures. For semiconductors, the bandgap is well defined so that the choice of BANDGAP only affects whether the output is compact or verbose. For metals, there is no straightforward definition of a bandgap so the default of BANDGAP=COMPACT is sufficient. A semimetal shares properties with metals (Fermi energy crosses bands) and with semiconductors (visible bandgap in the band structure).

BANDGAP=WEIGHT interprets systems like a metal; valence (conduction) states are more (less) than half-filled. In this case, the bandgap of a semimetal converges to zero with an increasing number of k points similar to a metal. For N number of electrons, the number of valence states is not in general equal to N for all k points. Hence, the direct bandgap is not necessarily between the N-th and the (N + 1)-th state.

BANDGAP=KPOINT considers systems like a semiconductor where every k point may be treated individually. The number of valence bands is equal to the number of electrons N for all k points and the direct bandgap is equal to the smallest difference between the N-th and (N + 1)-th state. In a semimetal, this approach produces a negative bandgap because the Fermi energy crosses the bands. For collinear calculations (ISPIN=2), this method will allow for a different number of up and down electrons at every k point.

Mind: Setting BANDGAP=KPOINT only impacts the output of VASP. It is not considered when evaluating the occupations of different bands. If you want to enforce certain occupations, please consider the tags NUPDOWN, FERWE, and FERDO.

Example of the verbose output

Band structure
--------------
                       spin independent             spin component 1             spin component 2
val. band max:               9.679953                     9.679953                     5.987917
cond. band min:              9.148387                    10.409707                     9.148387
fundamental gap:            -0.531566                     0.729754                     3.160470
VBM @ kpoint:       0.2949   0.4423   0.1474     0.2949   0.4423   0.1474     0.0000  -0.0000   0.0000
CBM @ kpoint:       0.5000   0.5000   0.0000     0.0000   0.0000   0.0000     0.5000   0.5000   0.0000

lower band:                  8.126216                     7.283444                     5.087674
upper band:                  9.386102                    10.916258                     9.148387
direct gap:                  1.259885                     3.632813                     4.060713
@ kpoint:           0.3846   0.3846   0.0000     0.0641   0.0962   0.0321     0.5000   0.5000   0.0000

The column spin independent is always present and reports the bandgap ignoring the spin of the electron. The other two columns are only visible for ISPIN=2 and describe the bandgap for a given spin of the electron. The first block of rows show the band edges of the fundamental bandgap and their corresponding k-point coordinates. The second block reports analogous values for the direct gap. In each case the energy difference of the band edges is computed and printed as fundamental and direct gap, respectively.

Related tags and articles

EFERMI, ISMEAR, SIGMA

Examples that use this tag

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