Electron mobility
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3D mobility v carrier concentration
Using the band structure and scattering rate found earlier, the bulk drift mobility has been calculated [1] at room temperature and compared to experimental determinations. The figure below shows the mobility verses carrier concentration using a 3-band model - i.e incorporating isolated nitrogen and nitrogen pair sites. The measured data points are from R. Mouillet's PhD thesis [2].
At low carrier concentrations, the calculated values are still an over-estimate. However, in the highly degenerate case, the match is closer. The drop in mobility here is due to the Fermi energy being pushed up close to an impurity level where the fractional G character, and hence group velocity, is very small.
Figure: Mobility v carrier concentration. Data
points R. Mouillet [2].
Click on image to view larger graph
3D mobility v nitrogen composition
In the figure below, the mobility is calculated as a function of nitrogen composition for different carrier concentrations at room temperature. The dashed lines show the calculation for the 2-band model (isolated N sites only) and the solid lines are for 3-band model calculations. Again, the comparison to experiment becomes reasonable for very high carrier concentrations.
Figure: Mobility v nitrogen composition. Square data points by Fowler et al [3]: black doped
with Se (n ~ 1019 cm-3), grey doped with Si, white
with B; triangular points by Mouillet [2] (n ~ 1017
cm-3); diamond points by Strohm [4] (n not specified).
Click on image to view larger graph
Conclusions
Whilst the calculated mobilities remain an overestimate at low carrier concentrations, in the highly degenerate regime the comparison becomes good. The drop in mobility for very high carrier concentrations is due to the Fermi level being pushed close to an impurity energy level. The inclusion of more types of nitrogen environments, in particular, next nearest neighbour nitrogen pairs, at lower energies may then bring the mobility down further at lower carrier concentrations. Also, these calculations do not include scattering from defects, such as threading dislocations or (since the measured data are for quantum well structures) interface roughness. In many III-V semiconductors, the high temperature mobility is limited by polar optical scattering. However, inclusion of this scattering mechanism does not appreciably affect the calculated mobility in GaNAs [5].
References
[1] M.P. Vaughan and B.K. Ridley, Phys. Rev. B, 75, 195205 (2007) abstract; M.P. Vaughan, PhD thesis, University of Essex (2007) Download PDF version
[2] R. Mouillet, PhD thesis, l’Université Paris V1 (2004) summary and download
[3] D. Fowler, O. Makarovsky, A. Patanč, L. Eaves, L. Geelhaar, H. Reichert and K. Uesugi, AIP Conference Proceedings, 772, 497 (2005) abstract
[4] E. Strohm, MSc thesis, University of British Columbia (2002) summary and download
[5] M.P. Vaughan and B. K. Ridley, Phys. Rev. B, 72, 075211 (2005) abstract; M.P. Vaughan, PhD thesis, University of Essex (2007) Download PDF version
M.P. Vaughan (2007)