Biomedical Engineering Reference
In-Depth Information
a
b
1
1
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0
0
0
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0
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1
F
F
Fig. 6.3
( a ) Normalized variation of
Δφ
sp across an ellipsoid shaped QD as a function of the semi-
minor to semi-major axis ratio F
a . Solid black line : exact solution from [ 38 ]; Dashed (red)
line : cubic approximation for small F .( b ) Normalized variation of
=
b
/
pz ; solid line : exact solution
from [ 38 ]; dashed (red) line : results obtained by assuming constant strain; dashed-dotted (blue)
line accounts for the finite QD size and changes in the strain field. [From [ 16 ]]
Δφ
a
b
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
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0
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F
F
Fig. 6.4 ( a ) Normalized variation of Δφ sp across a lens-shaped QD of height h as a function of
the height to diameter ratio F = h / D ,where D is the diameter of the lens. Solid black line : exact
solution from [ 38 ]; dashed (red) line : cubic approximation for small F .( b ) Normalized variation
of
Δφ pz . Solid line : exact solution from [ 38 ]; dashed (red) line : results obtained assuming constant
strain; dashed-dotted (blue) line accounts both for the finite QD size and also for changes in the
strain field. [From [ 16 ]]
we conclude that
Δφ tot is almost the same in the first two systems, while the
calculated value of
Δφ tot is considerably larger for the cylindrical QD. Again, this
difference arises because of the vertical QD side walls in the cylindrical dot. Overall
we conclude that the combination of three effects can lead to a significant reduction
in the potential drop across a QD compared to a QW of the same composition and
height, namely (i) the reduced surface area of the QD, (ii) strain relaxation in the
QD, and (iii) the sloped side walls which are generally found in a QD structure. Such
a reduction in built-in field allows a considerably higher radiative recombination rate
in a QD compared to an equivalent QW structure, which is of significant benefit for
optoelectronic applications.
 
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