Electron cyclotron mass in undoped $\mathrm{Cd}\mathrm{Te}∕\mathrm{Cd}\mathrm{Mn}\mathrm{Te}$ quantum wells

Optically detected cyclotron resonance of two-dimensional electrons has been studied in nominally undoped $\mathrm{Cd}\mathrm{Te}∕(\mathrm{Cd},\mathrm{Mn})\mathrm{Te}$ quantum wells. The enhancement of carrier quantum confinement results in an increase of the electron cyclotron mass from $0.099m_0$ to $0.112m_0$ with well width decreasing from 30 down to $3.6\mathrm{nm}$. Comparison with model calculations performed for this material system highlights two contributions to the mass increase, the first one determined by band structure parameters and the second one due to the polaron effect modified by reducing the dimensionality of the electronic system.

Figure 1

Photoluminescence and ODR signal spectra measured for $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.86}{\mathrm{Mn}}_{0.14}\mathrm{Te}$ QW’s with widths equal to (a) $30\mathrm{nm}$, (b) $9\mathrm{nm}$, and (c) $3.6\mathrm{nm}$. Spectra are measured at magnetic fields for which the FIR radiation induces the maximal changes—i.e., under conditions of cyclotron resonance for electrons. $T=4.2\mathrm{K}$. The photon energies corresponding to the maximum of the ODR signal are marked with arrows. Note that the magnetic field scans of the cyclotron resonances shown in Fig. 3 were detected at these energies.

Figure 2

Exciton energy, exciton binding energy, and energy of the optical transition between the lowest levels of confined electrons and holes $\left(e1\text{−}\mathrm{hh}1\right)$ calculated for $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.86}{\mathrm{Mn}}_{0.14}\mathrm{Te}$ QW’s as a function of the QW width.

Figure 3

Magnetic field dependence of ODR signal (in % of PL signal) at $E_{\mathit{FIR}}=7.6\mathrm{meV}$ measured in $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.86}{\mathrm{Mn}}_{0.14}\mathrm{Te}$ QW’s. The shift of the resonance field is given in the inset as a function of the tilt angle $\theta$ for the $30\text{−}\mathrm{nm}$-wide QW [circles, experiment values; line, fit with $6.45∕\cos \left(\theta \right)$].

Figure 4

Electron cyclotron mass versus QW width for CdTe-based quantum wells. Experimental data of this work for $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.86}{\mathrm{Mn}}_{0.14}\mathrm{Te}$ QW’s are given by the solid circles. Experimental error bars are smaller than the symbol size. Open circles show the data for the modulation-doped $\mathrm{Cd}\mathrm{Te}∕{\mathrm{Cd}}_{0.88}{\mathrm{Mg}}_{0.12}\mathrm{Te}$ QW’s with electron density of $4\times {10}^{11}{\mathrm{cm}}^{-22}$. The bare electron mass calculated without polaron correction in a parabolic-band approximation is shown by the dashed line and that with accounting for conduction-band nonparabolicity is given by the dotted line. The solid lines show the linear muffin-tin-orbital (LMTO) calculations with account for 2D and 3D polaron corrections.