Band Structures of Strained Semiconductors

Abstract

In Chap. 3, a qualitative picture of band splitting and warping under stress, e.g., as shown in Figs. 3.9–3.11, was obtained merely from symmetry considerations. But for application purpose in strain engineering, further band structure details with strain are required. Otherwise, it is not possible to determine which type of stress is advantageous for a specific application goal. That is, symmetry alone cannot provide enough information that we have to acquire before we can implement the desirable stress. For example, 〈110〉 uniaxial stress, no matter tensile or compressive, will result in the same symmetry lowering to a cubic crystal. As in Fig. 3.10, the x-y plane energy contour, which has an ellipse shape resulting from the compressive 〈110〉 uniaxial stress, could have its major axis either in the [110] direction or in the [110] direction, both complying with the uniaxial stress symmetry. Symmetry alone is not adequate to determine along which direction the ellipse major axis is oriented. However, this knowledge is critical for strain applications in n-type Si MOSFETs. Similar situations also exist in the valence bands. The band warping and splitting details, which are crucial for strain to enhance the p-type MOSFET performance, are not decisively determined by stress symmetry.