Silicon Photonics: Fundamentals and Devices

3.6 Effect of Electric Field

The effect of an external electric field in the bulk material is to change the band-to-band and exciton characteristics, which in turn change the absorption coefficient and refractive indices. An external electric field brings about interesting changes in the subband characteristics of quantum structures. These changes give rise to interesting optical phenomena of low-dimensional electron gas, which are exploited to fabricate novel optoelectronic devices. In this section, we shall study the effect of an external field on subband energies and wavefunctions in a QW. The optical processes will be discussed in Chapter 5.

We first assume that the external electric field is applied perpendicular to the QW layer plane and the field is directed along the z-direction. To understand gross features, we rely on analytical expressions obtained for an infinite barrier height [7, 8]. The origin of the coordinate system and of electrostatic potential is taken at the center of a well of width L. The Hamiltonian in the presence of an electric field F is then

(3.40)

where H₀ is the Hamiltonian without the field and the corresponding eigenvalues are already given in Section 2. If the field is weak enough so that the condition is valid, then the change in energy may be calculated ...