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The above formulae have been derived, assuming that the conduction band minima
are located at
, which is a
good approximation only for small shear strain. As can be seen from
Figure 3.12 the minimum of the conduction band is expected to move
towards the
point
as the strain-induced splitting between the conduction band becomes larger. As
a direct consequence, the conduction bands shape is deformed and the previous
assumption
is not satisfied.
Thus, a more general model for the effect of shear strain on the effective
masses needs to be developed, which takes the movement of the conduction band
minimum as a function of strain into account. The effective masses are
subsequently evaluated at the position of the conduction band minimum
.
The position of the minimum can be found from (3.73) by setting
:
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(3.91) |
The strain dependent longitudinal mass
can be obtained from
(3.73) by calculating
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(3.93) |
To derive the transverse effective masses that include the dependence
on
, first (3.73) is transformed to the
rotated coordinate system introduced in (3.85).
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(3.96) |
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(3.97) |
Finally, an analytical expression for the valley shift induced by shear strain
, which was given in Section 3.6.2, is calculated. According to
(3.92), equation (3.90) has to be evaluated at
for
. For
the energy shift at the
point
determines the overall valley shift. The shift between the valley pair along
[001] and the valley pairs along [100] or [010] is obtained from
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Previous: Energy Dispersion of the Conduction Band Minimum of Up: 3.7.2 Strain Effect on the Si Conduction Band Next: Discussion |