4.4 Effective Mass of Primed Subbands

Applying the same numerical procedure for the derived relations for the primed as for the unprimed subbands yields the energy dispersion and the effective masses in the primed subbands. The results of these calculations are shown in Table 4.1 and exhibit excellent agreement with the results of the linear combination of bulk bands method with a potential barrier of $3\,$eV at the film interface [4]. The results are also consistent with the DFT calculations from [3].

In ultra-thin films the large separation in energy between the primed and the unprimed subbands even without stress leads to a de-population of the primed subbands. Tensile stress in $\left[110\right]$ direction generates a shear component which changes the transport effective masses of the unprimed subbands and shifts the primed subbands with unfavorable effective masses up in energy (Fig. 4.11). With decreasing film thickness the decrease of the effective mass along $\left[110\right]$ direction induced by shear strain becomes more pronounced enabling mobility enhancement even in ultra-thin films. Unfortunately, the density of states effective mass in unprimed subbands increases with shear strain and thus results in higher scattering rates which reduces the mobility gained due to the thickness-enhanced transport mass decrease at high stress values. However, the mobility enhancement remains significant [187].

Table 4.1: Comparison between the effective masses for the lowest ground subband obtained with fullband calculations [3], calculations from [4], and the two-band k.p model. Excellent agreement with the fullband calculations is achieved.

$t [$nm$]$	$\frac{m_{\text{t}}(t)}{m_{\text{t}}}$
	k.p	[3]	[4]
$1.201$	$2.404$		$1.547$
$1.496$	$2.212$		$1.418$
$1.791$	$2.065$		$1.330$
$1.965$	$1.974$	$1.871$
$2.028$	$1.950$		$1.272$
$2.323$	$1.830$		$1.228$
$2.618$	$1.718$		$1.194$
$2.978$	$1.608$	$1.578$
$3.917$	$1.406$		$1.111$
$3.972$	$1.400$	$1.399$
$4.982$	$1.283$	$1.289$
$5.276$	$1.258$		$1.075$
$6.693$	$1.169$		$1.058$
$6.984$	$1.163$	$1.174$
$7.992$	$1.126$		$1.048$
$9.350$	$1.096$		$1.040$
$9.993$	$1.082$	$1.100$