Optical deformation potentials for PbSe and PbTe

The values of optical deformation potentials ($D_u$ and $D_d$) for PbSe and PbTe are analyzed using absorption, luminescence and x-ray diffraction data on high quality, deep quantum well $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{Sr}\mathrm{Se}$ and $\mathrm{Pb}\mathrm{Te}∕\mathrm{Pb}\mathrm{Eu}\mathrm{Te}$ structures. Published optical data on $\mathrm{Pb}\mathrm{Te}∕\mathrm{Ba}{\mathrm{F}}_2$ structures were also used. It is important for these evaluations to use the value of isotropic deformation potential $\left(D_{\mathrm{iso}}\right)$ which is determined from the low temperature hydrostatic pressure experiments and the intervalley splitting which was determined from differential absorption spectroscopy. The fitting procedure was done using an accurate $\mathbf{k}\bullet \mathbf{p}$ model for the band structure near the fundamental gap including anisotropy, multivalley, and band nonparabolicity effects. Photoluminescence was measured in pulsed mode at 4 and $77\mathrm{K}$, which gives the lowest energy state in the rectangular well. The strain and well parameters were measured with a high resolution x-ray diffractometer. We find the new optical deformation potential values at low temperatures: $D_u=-0.2$ and $-0.5\mathrm{eV}$, and $D_d=5.3$ and $3.5\mathrm{eV}$ for PbSe and PbTe, respectively.

Figure 1

Connection between dilatational and uniaxial optical deformation potential constants $(D_{\mathrm{iso}}=3D_d+D_u)$ for PbSe and PbTe at different temperatures. The published theoretical and experimental $D_{\mathrm{iso}}$ values are very scattered around the straight lines.

Figure 2

Crossing of $E_{11}^N$ and $E_{11}^O$ interband transitions depending on the well width and strain for deformation potential values of $D_d=6.1\mathrm{eV}$ and $D_u=-1.3\mathrm{eV}$.

Figure 3

$\omega ∕2\theta$ scan around the (222) Bragg diffraction peak for $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{Sr}\mathrm{Se}$ MQW samples with PbSe well width of $3.5\mathrm{nm}$ (upper panel) and $10.6\mathrm{nm}$ (lower panel). The solid lines are the calculated spectra that best fit the measured data represented by the open circles.

Figure 4

In-plane strain $\left({\epsilon }_{\mathrm{II}}\right)$ in the PbSe well of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{Sr}\mathrm{Se}$ MQW structures versus well width at $300\mathrm{K}$.

Figure 5

The PL spectra of $\mathrm{Pb}\mathrm{Te}∕\mathrm{Pb}\mathrm{Eu}\mathrm{Te}$ MQW structures at 4 and $77\mathrm{K}$ (a) and derivative transmission spectra of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{Sr}\mathrm{Se}$ MQW structures at $4\mathrm{K}$ for different width PbSe wells (b).

Figure 6

Calculated sub-band transition energies versus well width of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{Sr}\mathrm{Se}$ MQWs at three temperatures: $4\mathrm{K}$ (a), $77\mathrm{K}$ (b), and $295\mathrm{K}$ (c). The solid and dashed lines correspond to transitions in normal (longitudinal) and oblique valleys, respectively. The deformation potential constants used are $D_d=5.3$, 5.33, and $4.9\mathrm{eV}$, and $D_u=-0.2,-0.6$, and $-0.7\mathrm{eV}$; and the total averaged (over samples) strain is ${\epsilon }_{\mathrm{II}}=(3,2.3,\text{and}1.7)\times {10}^{-3}$ at $4\mathrm{K}$, $77\mathrm{K}$, and $295\mathrm{K}$, respectively. The PL data were obtained in pulsed mode at 4.2 and $77.4\mathrm{K}$ and in CW mode at $288\mathrm{K}$.

Figure 7

Calculated lowest transition energies for normal (longitudinal) valley versus well width of $\mathrm{Pb}\mathrm{Te}∕\mathrm{Pb}\mathrm{Eu}\mathrm{Te}$ MQWs at 4 and $77\mathrm{K}$. The deformation potential constants are $D_d=3.53\mathrm{eV}$ and $D_u=-0.5\mathrm{eV}$ and the total averaged (over samples) strain is ${\epsilon }_{\mathrm{II}}=3.9\times {10}^{-3}$ and $3.2\times {10}^{-3}$ at $4\mathrm{K}$ and $77\mathrm{K}$, respectively. The PL data were obtained in pulsed mode.