Silicon Photonics: Fundamentals and Devices

3.2 Quantum Wells

Most of the present electronic and optoelectronic devices are based on nanostructures in which at least one dimension of the layer of interest is only a few nanometers thick. The behavior of particles in the nanostructure differs grossly from the same in bulk materials and the motion of particles is quantum mechanically confined along the concerned direction. The confinement gives rise to electron or hole gas of lower dimensions, as will be explained in this chapter. The confinement and existence of low-dimensional electron systems have also been observed in silicon and its alloys. Before we discuss the specific properties related to silicon, we first consider the conditions necessary for quantum confinement, the structures that support the low-dimensional systems, and the changes in electronic properties from the bulk materials. To start with, we first consider a quantum well (QW) that supports two-dimensional electron gases. We shall consider the well-studied GaAs–AlGaAs material system for the sake of illustration.

3.2.1 Condition for Quantum Confinement

The electrons in a bulk semiconductor have free motion in all the three dimensions, as indicated by the E–k relationship expressed by

(3.1)

Here the electron mass m_e is isotropic as in direct-gap materials like GaAs. For electrons in Si, (Eq. 2.3) applies. If the electron is confined in a one-dimensional (1D) ...