Electron-phonon interaction in quantum-dot∕quantum-well semiconductor heterostructures

Polar optical phonons are studied in the framework of the dielectric continuum approach for a prototypical quantum-dot∕quantum-well (QD∕QW) heterostructure, including the derivation of the electron-phonon interaction Hamiltonian and a discussion of the effects of this interaction on the electronic energy levels. The particular example of the $\mathrm{CdS}∕\mathrm{HgS}$ $\text{QD}∕\text{QW}$ is addressed and the system is modeled according to the spherical geometry, considering a core sphere of material “1” surrounded by a spherically concentric layer of material “2,” while the whole structure is embedded in a host matrix assumed as an infinite dielectric medium. The strength of the electron-LO phonon coupling is discussed in detail and the polaronic corrections to both ground-state and excited-state electron energy levels are calculated. Interesting results concerning the dependence of polaronic corrections with the QD∕QW structure size are analyzed.

Figure 1

Radial part of the electric potential (in units of ${\Phi }_0$) as a function of the radius (in units of $a$) for $l=0$ and $\gamma =1.8$. The potentials correspond to the first three LO phonon modes and are depicted by a dotted, dash-dotted, and solid line, respectively.

Figure 2

Same as in Fig. 1 but now displaying the potentials for the first three LO phonon modes with $l=1$.

Figure 3

Energy levels for the unperturbed $\mathrm{CdS}∕\mathrm{HgS}$ QD∕QW heterostructure (in eV) as a function of $\gamma =b∕a$. For $a=2.5\mathrm{nm}$ we show the first two levels (dotted lines). For $a=3.5\mathrm{nm}$ (solid lines) the first three energy levels are shown. For each level the corresponding value of $l$ is explicitly indicated.

Figure 4

Absolute value of the energy shifts (in meV) as a function of $\gamma =b∕a$ for the polaronic corrections to the ground state (solid line) and excited state (dotted line) energy levels considering a QD∕QW heterostructure with core radius $a=2.5\mathrm{nm}$. These energy shifts should be subtracted from the corresponding energy levels presented in Fig. 3.

Figure 5

Same as in Fig. 4 but taking $a=3.5\mathrm{nm}$. In both cases the results correspond to the $\mathrm{CdS}∕\mathrm{HgS}$ QD∕QW heterostructure.