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Calculating Band Widths

As well as calculating energy gaps, it is also possible to calculate a band width via indirect excitations. In figure gif, two sets of excitations are shown for calculating the width of the valence band at the tex2html_wrap_inline6701 -point.

  
Figure: Indirect excitations to calculate the width of the valence band at the tex2html_wrap_inline6701 -point. Excitations from tex2html_wrap_inline8275 are shown in red and from tex2html_wrap_inline8277 are shown in blue. The black lines represent a pseudopotential bandstructure[94].

The band width can be calculated as the difference in energy between exciting from the bottom of the valence band at tex2html_wrap_inline6701 to the bottom of the conduction band at X or L and exciting from the top of the valence band at tex2html_wrap_inline6701 to the bottom of the conduction band at X or L,

eqnarray5028

where tex2html_wrap_inline8283 represents the energy of the state where the orbital in the Slater determinant representing the top of the valence band at the tex2html_wrap_inline6701 -point( tex2html_wrap_inline8287 ) has been replaced by one representing the bottom of the conduction band at the L-point( tex2html_wrap_inline8289 ). The results of these DMC calculations of the band width are shown in table gif. The n=2 LDA and HF band widths have been included for comparison. As with excitation energies the LDA band widths contain a very small finite size effect. The fully converged HF result for the band width is 18.5 eV[112].

The DMC results show a reasonable agreement with experiment, if not quite within error bars. As with the ordinary excitations, the DMC again overestimates the size of the band width. This overestimation could be due to the inferior quality of the nodal structure of the guiding wavefunction for the excitation from the bottom of the valence band to the bottom of the conduction band or to finite size effects.

 

1 tex2html_wrap_inline8293 Promotion 2 tex2html_wrap_inline8295 Promotion DMC (eV) Expt. (eV) LDA (eV) HF (eV)
tex2html_wrap_inline8309 tex2html_wrap_inline8299 13.3 tex2html_wrap_inline7561 0.6 12.5 12.03 16.2
tex2html_wrap_inline8303 tex2html_wrap_inline8305 14.1 tex2html_wrap_inline7561 0.6 12.5 12.03 16.2
Table: Calculations of band widths. tex2html_wrap_inline8309 refers to the promotion of an electron from the 4 tex2html_wrap_inline6553 band at the tex2html_wrap_inline6701 -point to the 5 tex2html_wrap_inline6553 band at the X-point


 


next up previous contents
Next: Excitonic Effects Up: DMC Results Previous: DMC Results

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996