目录

计算指定k点的有效质量

BAND计算有效质量本身不需要计算能带,这和其他软件有所不同。其他软件的有效质量一般是从能带曲线,拟合出梯度而得到有效质量,因此是一个数值,也跟能带曲线在k空间的方向直接相关。BAND则是指定k点后,计算该k点附近各个方向的一些k点上,费米能级上下N条能带的值,因此得到的有效质量,对三维周期性体系(例如单晶硅)而言,类似椭球,存在三个轴,三个轴向各有一个值;对于二维周期性体系(例如石墨烯),则存在两个轴,BAND将会给出两个轴向的两个值。

计算设置

原本不需要计算能带、态密度,不过我们本例中,也勾选了这两项,作为对比: 一般而言,BAND的计算都需要将k点设置为Very Good甚至以上: 关于能带的设置,下图所示数值,是设置能带曲线的细腻程度,数值越小,曲线越光滑细腻,不过一般而言0.01已经非常足够了: 设定要计算有效质量的k点坐标,用空格隔开x y z值: 其中

上面设置只计算费米能级上下各一条能带(上的有效质量)

结果查看

能带

SCM - BandStructure:

有效质量

SCM - Output 接近尾部,依次给出了4个k点,在两条能带上的有效质量:

 E F F E C T I V E   M A S S

  
 Fermi energy                   -0.207568 Hartree     -5.64821 eV
 
 k-coordinates                     0.000      0.000      0.000
 fractional coords                 0.000      0.000      0.000
 
       Curvature for band index:              4
       Energy wrt fermi level:        -0.011368 Hartree     -0.30935 eV
       Energy:                        -0.218936 Hartree     -5.95756 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature   -0.40428    -0.35443    -0.35327                    -0.37782    -0.36537    -0.36507
       effective mass (m0):            -2.47351    -2.82141    -2.83069                    -2.64678    -2.73692    -2.73919
       eigenvectors:
                     eigenvector # 1   -0.557529    -0.582043    -0.591935                 -0.557005    -0.582131    -0.592342
                     eigenvector # 2   -0.119314    -0.649455     0.750981                 -0.119731    -0.649491     0.750883
                     eigenvector # 3    0.821538    -0.489320    -0.292645                  0.821833    -0.489168    -0.292070
       ------------------------------------------------------------------------------------------------------------------------
 
       Curvature for band index:              5
       Energy wrt fermi level:         0.083703 Hartree      2.27768 eV
       Energy:                        -0.123864 Hartree     -3.37052 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature    4.30233     4.30575     4.30600                     4.33204     4.33289     4.33295
       effective mass (m0):             0.23243     0.23225     0.23223                     0.23084     0.23079     0.23079
       eigenvectors:
                     eigenvector # 1    0.995717     0.076159     0.052419                  0.995464     0.078022     0.054447
                     eigenvector # 2    0.020874    -0.737512     0.675011                  0.020154    -0.732213     0.680777
                     eigenvector # 3   -0.090068     0.671026     0.735943                 -0.092982     0.676592     0.730464
       ------------------------------------------------------------------------------------------------------------------------
 
 
 k-coordinates                     0.000      1.000      0.000
 fractional coords                 0.817      0.000      0.817
 
       Curvature for band index:              4
       Energy wrt fermi level:        -0.060866 Hartree     -1.65623 eV
       Energy:                        -0.268433 Hartree     -7.30444 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature   -3.81151     1.75287     1.89730                    -3.81849     1.70969     1.95725
       effective mass (m0):            -0.26236     0.57049     0.52706                    -0.26188     0.58490     0.51092
       eigenvectors:
                     eigenvector # 1    0.000029     1.000000     0.000031                  0.000014     1.000000     0.000016
                     eigenvector # 2    0.704358    -0.000042     0.709845                  0.706707    -0.000021     0.707507
                     eigenvector # 3    0.709845     0.000002    -0.704358                  0.707507     0.000001    -0.706707
       ------------------------------------------------------------------------------------------------------------------------
 
       Curvature for band index:              5
       Energy wrt fermi level:         0.048697 Hartree      1.32511 eV
       Energy:                        -0.158871 Hartree     -4.32309 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature    0.21258     5.28351     5.28811                     0.21186     5.28021     5.28941
       effective mass (m0):             4.70421     0.18927     0.18910                     4.72017     0.18939     0.18906
       eigenvectors:
                     eigenvector # 1    0.000000    -1.000000     0.000000                  0.000000    -1.000000     0.000000
                     eigenvector # 2    0.707098     0.000000    -0.707116                  0.707111     0.000000    -0.707102
                     eigenvector # 3    0.707116     0.000000     0.707098                  0.707102     0.000000     0.707111
       ------------------------------------------------------------------------------------------------------------------------
 
 
 k-coordinates                     0.000      0.000      1.000
 fractional coords                 0.817      0.817      0.000
 
       Curvature for band index:              4
       Energy wrt fermi level:        -0.060866 Hartree     -1.65624 eV
       Energy:                        -0.268433 Hartree     -7.30444 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature   -3.81123     1.75233     1.89731                    -3.81842     1.70955     1.95725
       effective mass (m0):            -0.26238     0.57067     0.52706                    -0.26189     0.58495     0.51092
       eigenvectors:
                     eigenvector # 1    0.000028     0.000029     1.000000                  0.000014     0.000015     1.000000
                     eigenvector # 2    0.706760     0.707454    -0.000041                  0.707056     0.707158    -0.000020
                     eigenvector # 3    0.707454    -0.706760     0.000001                  0.707158    -0.707056     0.000000
       ------------------------------------------------------------------------------------------------------------------------
 
       Curvature for band index:              5
       Energy wrt fermi level:         0.048697 Hartree      1.32511 eV
       Energy:                        -0.158871 Hartree     -4.32309 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature    0.21258     5.28351     5.28811                     0.21186     5.28021     5.28941
       effective mass (m0):             4.70420     0.18927     0.18910                     4.72017     0.18939     0.18906
       eigenvectors:
                     eigenvector # 1    0.000000     0.000000     1.000000                  0.000000     0.000000     1.000000
                     eigenvector # 2   -0.707089     0.707124     0.000000                 -0.707104     0.707110     0.000000
                     eigenvector # 3   -0.707124    -0.707089     0.000000                 -0.707110    -0.707104     0.000000
       ------------------------------------------------------------------------------------------------------------------------
 
 
 k-coordinates                     1.000      0.000      0.000
 fractional coords                 0.000      0.817      0.817
 
       Curvature for band index:              4
       Energy wrt fermi level:        -0.060866 Hartree     -1.65623 eV
       Energy:                        -0.268433 Hartree     -7.30444 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature   -3.81209     1.75403     1.89730                    -3.81864     1.70997     1.95725
       effective mass (m0):            -0.26232     0.57011     0.52706                    -0.26187     0.58480     0.51092
       eigenvectors:
                     eigenvector # 1   -1.000000    -0.000029    -0.000030                 -1.000000    -0.000015    -0.000015
                     eigenvector # 2   -0.000042     0.708274     0.705937                 -0.000021     0.707276     0.706938
                     eigenvector # 3   -0.000001    -0.705937     0.708274                 -0.000001    -0.706938     0.707276
       ------------------------------------------------------------------------------------------------------------------------
 
       Curvature for band index:              5
       Energy wrt fermi level:         0.048697 Hartree      1.32511 eV
       Energy:                        -0.158871 Hartree     -4.32309 eV
       ------------------------------------------------------------------------------------------------------------------------
       Step size:                      0.001000                                            0.002000
       ------------------------------------------------------------------------------------------------------------------------
       eigenvalues of band curvature    0.21258     5.28351     5.28811                     0.21186     5.28021     5.28941
       effective mass (m0):             4.70421     0.18927     0.18910                     4.72018     0.18939     0.18906
       eigenvectors:
                     eigenvector # 1    1.000000     0.000000     0.000000                  1.000000     0.000000     0.000000
                     eigenvector # 2    0.000000     0.707087    -0.707127                  0.000000     0.707111    -0.707103
                     eigenvector # 3    0.000000     0.707127     0.707087                  0.000000     0.707103     0.707111
       ------------------------------------------------------------------------------------------------------------------------

例如最后一个k点: