Electronic continuum states and far-infrared absorption of $\mathrm{InAs}∕\mathrm{GaAs}$ quantum dots

The electronic continuum states of $\mathrm{InAs}∕\mathrm{GaAs}$ semiconductor quantum dots embedded in a $\mathrm{GaAs}∕\mathrm{AlAs}$ superlattice are theoretically investigated and the far-infrared midinfrared absorption spectra are calculated for a variety of structures and polarizations. The effect of a strong magnetic field applied parallel to the growth direction is also investigated. We predict that the flatness of the $\mathrm{InAs}∕\mathrm{GaAs}$ dots leads to a midinfrared absorption which is almost insensitive to the magnetic field, in spite of the reorganization of the continuum into series of quasi-Landau states. We also predict that it is possible to design $\mathrm{InAs}∕\mathrm{GaAs}$ photoconductors which display very strong in-plane absorption.

Figure 1

Schematic representation of the supercell including the dot and its WL. Period $d=11\mathrm{nm}$.

Figure 2

Calculated energy levels of $S$ symmetry states versus magnetic field. The dashed lines are the results of the separable model with a Gaussian radial function. Upper panel: at the center of the first Brillouin zone, lower panel: at an edge of the first Brillouin zone. The large dots at $B=0$ are the extrapolations of the various fan.

Figure 3

Probability densities to find the electron at $z$ in the unit cell for the three lowest separable solutions with a Gaussian radial function and the three lowest states of a $\mathrm{GaAs}∕\mathrm{AlAs}∕\mathrm{InAs}$ SL at $B=0$ and $k_z=0$. From bottom to top: the ground state to the second excited state. The vertical dashed lines delimit the different regions of the structures in Fig. 1

Figure 4

Absorption coefficients versus photon energy at $B=0$ and $B=35\mathrm{T}$ calculated by two models for $\vec{\mathcal{E}}$ parallel to $\vec{z}$.

Figure 5

Absorption coefficients versus photon energy from $B=0$ to $B=35\mathrm{T}$ for $\vec{\mathcal{E}}$ parallel to $\vec{z}$.

Figure 6

Absorption coefficients versus photon energy at $B=30\mathrm{T}$ for $\vec{\mathcal{E}}$ parallel to $\vec{z}$. Usual sample and a centered sample (see text). The full line has been rigidly upshifted for clarity.

Figure 7

Oscillator strength of transitions from the ground $S$ state to the first 30 $P$ states versus energy of $P$ states at $B=0$ and $k_z=0$ for several values of base radius $R$ and $\vec{\mathcal{E}}\Vert \vec{x}$. The ordinate scale in the case $R=70\mathrm{\AA }$ is 5 times bigger than the others. The ground energies for each value of $R$ are $E_S(R=70\mathrm{\AA })=-105\mathrm{meV}$, $E_S(R=55\mathrm{\AA })=-64\mathrm{meV}$, $E_S(R=50\mathrm{\AA })=-45\mathrm{meV}$, and $E_S(R=45\mathrm{\AA })=-25\mathrm{meV}$.

Figure 8

Upper panel: Oscillator strength of transitions from the ground $S$ state to the first 30 $P$ states versus energy of $P$ states at $B=0$ and $k_z=0$ for $R=50\mathrm{\AA }$ and $\vec{\mathcal{E}}\Vert x$. Two scales of vertical axis are used below and above 150 meV. The apparent scattering of the numerical data above 150 meV is due to the contribution of two different optical channels (see text). Lower panel: Probability density to find the electron at $z$ in the unit cell of some selected states marked (from A–E) in the upper panel.