For large (4.24a) has the solution
, while (4.24b) gives
, which results in the well-known quantization result
for subbands in an infinite potential square well with a single parabolic band. For the difference in energy
between the two subbands we get
in the limit of large
, which is perfectly consistent with the results shown in Fig. 4.6 and Fig. 4.7.
![]() |
Fig. 4.8 shows for several film thicknesses that the unprimed subbands split for non-zero shear strain. In ultra-thin films already at moderate stress levels the splitting energy is larger than
. In this case the higher subband becomes de-populated, indicating a mobility enhancement in
ultra-thin films strained along
direction. For small strain values the splitting is linear in strain. For large strain the quantization relations in an infinite square well potential with a single parabolic band are recovered resulting in the largest subband splitting.
Uniaxial stress is currently used to enhance performance of modern MOSFETs, where it is introduced in a controllable way. Therefore, the valley splitting can be controlled by adjusting strain and thickness
.
![]() |