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The presence of the [001] confinement combined with the off-diagonal valley coupling results in the degeneracy lifting of the unprimed subband ladder, leading to the valley splitting [72]. If the potential profile Ũ(z) is approximated by an infinite square well, the expression for the valley splitting can be approximated by [72, 151]

(3.17)

where t describes the quantum well thickness, δ is given in Equation 3.6, the parameters y and η are given by

(3.18)

(3.19)

and for the other parameters c.f. Table 3.2.

It is noted that the spin-orbit coupling △SO also impacts the valley splitting strength △E_C. △E_C oscillates with t and is drastically increased by εxy. The degeneracy between the subbands is exactly recovered, when the sinusoidal oscillating term in Equation 3.17 is zero. However, this degeneracy is not so significant, as it does not add any peculiar behavior to the spin relaxation matrix elements [151]. One has to mention that the analytical expressions for the spin relaxation matrix elements can be found in the following chapters. On the other hand, △E_C can be minimized when δ is at its minimum, owing to a very strong spin relaxation as will be described in the following sections.

Figure 3.8 shows the variation of the valley splitting with the shear strain εxy when the sample thickness t is used as a parameter. The first minimum of the valley splitting is determined by the spin-orbit interaction term alone (i.e. when δ in Equation 3.17 is minimum), and appears to be independent of the quantum well width. The other valley splitting minima (observed for t=4nm and 5nm in Figure 3.8) depend on the film thickness and are caused by vanishing values of the sin k₀t term.