For large (4.24a) has the solution , while (4.24b) gives , which results in the wellknown 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 nonzero shear strain. In ultrathin films already at moderate stress levels the splitting energy is larger than . In this case the higher subband becomes depopulated, indicating a mobility enhancement in ultrathin 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 .
