Effective Mass

The physics of the effective mass tensor is explained in this tutorial

A rather important aspect is the determination of the top of the valence band (TOVB or HOMO) and the bottom of the conduction band (BOCB or LUMO). There are two ways to do this

    1. IPOL: from the interpolated bands

    1. PATH: from the calculated bands along the high symmetry path, as used by amsbands.

In case that the HOMO and LUMO are located on the high symmetry path the PATH method is more accurate. A good example are 2D systems with a triangular lattice. Often the HOMO or LUMO are at the point called “K”, which may not be present in the standard k-grid, but is always present on the high symmetry path. Also, along the path a dense k-grid is used. It remains possible that the extrema or not on the path and then the IPOL method should be used (possibly using a denser k-grid than usual). When chooising the PATH method some feedback is printed about whether IPOL and PATH produce the same HOMO and LUMO energy and k coordinates.

Input key block

EffectiveMass
   Enabled Yes/No
   KPointCoord float_list
   NumAbove integer
   NumBelow integer
   StepSize float
   UseBandStructureInfoFromPath Yes/No
End
EffectiveMass
Type:

Block

Description:

In a semi-conductor, the mobility of electrons and holes is related to the curvature of the bands at the top of the valence band and the bottom of the conduction band. With the effective mass option, this curvature is obtained by numerical differentiation. The estimation is done with the specified step size, and twice the specified step size, and both results are printed to give a hint on the accuracy. The easiest way to use this key is to enabled it without specifying any extra options.

Enabled
Type:

Bool

Default value:

No

GUI name:

Effective mass

Description:

Compute the EffectiveMass.

KPointCoord
Type:

Float List

Unit:

1/Bohr

Recurring:

True

GUI name:

At K-point

Description:

Coordinate of the k-points for which you would like to compute the effective mass.

NumAbove
Type:

Integer

Default value:

1

GUI name:

Include N bands above

Description:

Number of bands to take into account above the Fermi level.

NumBelow
Type:

Integer

Default value:

1

GUI name:

Include N bands below

Description:

Number of bands to take into account below the Fermi level.

StepSize
Type:

Float

Default value:

0.001

Description:

Size of the step taken in reciprocal space to perform the numerical differentiation

UseBandStructureInfoFromPath
Type:

Bool

Default value:

Yes

Description:

The (automatic) location of the HOMO and LUMO can be determined via band interpolation, or from the path as used by the BandStructure feature. The latter works better when they are located on the path. See also comments in the BandStructure block. To reproduce results from before ams2025 set to no.